
Class. 
Book. 



ki 



The Publishers and the Author will be grateful to 
any of the readers of this volume who will kindly call 
their attention to any errors of omission or of commis- 
sion that they may find therein. It is intended to make 
our publications standard works of study and reference, 
and, to that end, the greatest accuracy is sought. It 
rarely happens that the early editions of works of any 
size are free from errors ; but it is the endeavor of the 
Publishers to have them removed immediately upon being 
discovered, and it is therefore desired that the Author 
may be aided in his task of revision, from time to time, 
by the kindly criticism of his readers. 

JOHN WILEY & SONS. 
43 & 45 East Nineteenth Street. 



WORKS OF WILLIAM KENT 



PUBLISHED BY 



JOHN WILEY & SONS. 



The Mechanical Engineers' Pocket-Book. 

A Reference Book of Rules, Tables, Data, and 
Formula?, for the Use of Engineers, Mechanics, 
and Students, xl + 1461 pages, 16mo, morocco, 
$5.00 net. 



Steam=Boiler Economy. 

A treatise on the Theory and Practice of Fuel 
Economy in the Operation of Steam-Boilers. 
xiv + 458 pages, 136 figures, 870, cloth, $4.00. 



THE 

MECHANICAL ENGINEERS' 
POCKET-BOOK. 



A REFERENCE-BOOK OF BULES, TABLES, DATA, 
AND FORMULA K< FOR THE, ,U$E OF 
ENGINEERS, MECHAJflGS^ 
AND STUDENTS. 



WILLIAM KENT, M.E., Sc.D., 

Consulting Engineer. 
Member Amer. Soc'y Mechl. Engrs. and Amer. Inst. Mining Engrs. 



EIGHTH EDITION, REWRITTEN. 
TOTAL ISSUE EIGHTY-ONE THOUSAND. 

XTbr A fTy^ 



OF THE 



Ns5ft/FF BO 



NEW YORK: 

JOHN WILEY & SONS. 

London: CHAPMAN & HALL, Limited. 

1910. 







By tranafer from 
U.S. Tariff Board 

1 .'* 



Copyright, 1895, 1902, 1910, 

BY 

WILLIAM KENT. 



Eighth Edition entered at Stationers* Hall 



TYPOGRAPHY BY 

PRESS OF 

Stanbopc lpres^ br aun worth & co. 

K.gilson company BOOKBINDERS AND PRINTERS 

boston. U.S.A. BROOKLYN, N. Y. 



PREFACE TO THE FIRST EDITION, 1895. 

More than twenty years ago the author began to follow the advice 
given by Nystrom: " Every engineer should make his own pocket-book, 
as he proceeds in study and practice, to suit his particular business." 
The manuscript pocket-book thus begun, however,. soon gave place to 
more modern means for disposing of the accumulation of engineering 
facts and figures, viz., the index ferum, 4 tlfe' ScVap-book, the collection of 
indexed envelopes, portfolios and boxes, ^the card catalogue, etc. Four 
years ago, at the request of the publishers, the labor was begun of selecting 
from this accumulated mass such matter as pertained to mechanical 
engineering, and of condensing, digesting, and arranging it in form for 
publication. In addition to this, -a careful examination was made of the 
transactions of engineering societies, and of the most important recent 
works on mechanical engineering, in order to fill gaps that might be left 
in the original collection, and insure that no important facts had been 
overlooked. 

Some ideas have been kept in mind during the preparation of the 
Pocket-book that will, it is believed, cause it to differ from other works 
of its class. In the first place it was considered that the field of mechani- 
cal engineering was so great, and the literature of the subject so vast, that 
as little space as possible should be given to subjects which especially 
belong to civil engineering. While the mechanical engineer must con- 
tinually deal with problems which belong properly to civil engineering, 
this latter branch is so well covered by Traut wine's " Civil Engineer's 
Pocket-book " that any attempt to treat it exhaustively would not only 
fill no " long-felt want," but would occupy space which should be given 
to mechanical engineering. 

Another idea prominently kept in view by the author has been that he 
would not assume the position of an " authority " in giving rules and 
formulae for designing, but only that of compiler, giving not only the 
name of the originator of the rule, where it was known, but also the volume 
and page from which it was taken, so that its derivation may be traced 
when desired. When different formulae for the same problem have been 
found they have been given in contrast, and in many cases examples 
have been calculated by each to show the difference between them. In 
some cases these differences are quite remarkable, as will be seen under 
Safety-valves and Crank-pins. Occasionally the study of these differences 
has led to the author's devising a new formula, in which case the deriva- 
tion of the formula is given. 

Much attention has been paid to the abstracting of data of experiments 
from recent periodical literature, and numerous references to other data 
are given. In this respect the present work will be found to differ from 
other Pocket-books. 



IV PREFACE. 

The author desires to express his obligation to the many persons who 
have assisted him in the preparation of the work, to manufacturers who 
have furnished their catalogues and given permission for the use of their 
tables, and to many engineers who have contributed original data and 
tables. The names of these persons are mentioned in their proper places 
in the text, and in all cases it has been endeavored to give credit to whom 
credit is due. The thanks of the author are also due to the following 
gentlemen who have given assistance in revising manuscript or proofs 
of the sections named: Prof. De Volson "Wood, mechanics and turbines; 
Mr. Frank Richards, compressed air; Mr. Alfred R. Wolff, windmills; 
Mr. Alex. C. Humphreys, illuminating gas; Mr. Albert E. Mitchell, loco- 
motives; Prof. James E. Denton, refrigerating-machinery; Messrs. Joseph 
Wetzler and Thomas W. Varley, electrical engineering; and Mr. Walter 
S. Dix, for valuable contributions on several subjects, and suggestions 
as to their treatment. 

William Kent. 



PREFACE TO THE EIGHTH EDITION. 

SEPTEMBER, 1910. 

During the first ten years following the issue of the first edition of this 
book, in 1895, the attempt was made to keep it up to date by the method 
of cutting out pages and paragraphs, inserting new ones in their places, by 
inserting new pages lettered a, b, c, etc., and by putting some new matter 
in an appendix. In this way the book passed to its 7th edition in October, 
1904. After 50,000 copies had been printed it was found that the electro- 
typed plates were beginning to wear out, so that extensive resetting of type 
would soon be necessary. The advances in engineering practice also had 
been so great that it was evident that many chapters required to be entirely 
rewritten. It was therefore determined to make a thorough revision of the 
book, and to reset the type throughout. This has now been accomplished 
after four years of hard labor. The size of the book has increased over 300 
pages, in spite of all efforts to save space by condensation and elision of 
much of the old matter and by resetting many of the tables and formulae 
in shorter form. A new style of type for the tables has been designed for 
the book, which is believed to be much more easily read than the old. 

The thanks of the author are due to many manufacturers who have fur- 
nished new tables of materials and machines, and to many engineers who 
have made valuable contributions and helpful suggestions. He is especially 
indebted to his son, Robert Thurston Kent, M.E., who has done the work 
of revising manufacturers' tables of materials and has done practically all 
of the revising of the subjects of Compressed Air, Fans and Blowers, Hoist- 
ing and Conveying, and Machine Shop. 



CONTENTS. 

(For Alphabetical Index see page 1417.) 

MATHEMATICS. 
Arithmetic. 

PAGE 

Arithmetical and Algebraical Signs 1 

Greatest Common Divisor 2 

Least Common Multiple 2 

Fractions 2 

Decimals 3 

Table. Decimal Equivalents of Fractions of One Inch 3 

Table. Products of Fractions expressed in Decimals 4 

Compound or Denominate Numbers 5 

Reduction Descending and Ascending 5 

Decimals of a Foot Equivalent to Fractions of an Inch 5 

Ratio and Proportion 6 

Involution, or Powers of Numbers 7 

Table. First Nine Powers of the First Nine Numbers 7 

Table. First Forty Powers of 2 8 

Evolution. Square Root 8 

Cube Root 9 

Alligation 9 

Permutation 10 

Combination 10 

Arithmetical Progression 10 

Geometrical Progression 11 

Percentage, Profit and Loss, Efficiency 12 

Interest 12 

Discount 13 

Compound Interest 13 

Compound Interest Table, 3, 4, 5, and 6 per cent 14 

Equation of Payments 14 

Partial Payments 14 

Annuities 15 

Tables of Amount, Present Values, etc., of Annuities 15 

Weights and Measures. 

Long Measure 17 

Old Land Measure 17 

Nautical Measure 17 

Square Measure 18 

Solid or Cubic Measure 18 

Liquid Measure 18 

The Miners' Inch 18 

Apothecaries' Fluid Measure 18 

Dry Measure 19 

Shipping Measure 19 

Avoirdupois Weight 19 

Troy Weight 19 

Apothecaries' Weight 20 

To Weigh Correctly on an Incorrect Balance 20 

Circular Measure 20 

Measure of Time 20 

V 



VI CONTENTS. 

PAGE 

Board and Timber Measure 20 

Table. Contents in Feet of Joists, Scantlings, and Timber 21 

French or Metric Measures 22 

British and French Equivalents 22 

Metric Conversion Tables 23 

Compound Units 

of Pressure and Weight 27 

of Water, Weight, and Bulk 28 

of Air, Weight, and Volume 28 

of Work, Power, and Duty 28 

of Velocity 28 

Wire and Sheet Metal Gauges 29 

Twist-drill and Steel-wire Gauges 30 

Circular-mil Wire Gauge 31 

New U. S. Standard Wire and Sheet Gauge, 1893 31 

Decimal Gauge 33 

Algebra. 

Addition, Multiplication, etc 34 

Powers of Numbers 34 

Parentheses, Division 35 

Simple Equations and Problems 35 

Equations containing two or more Unknown Quantities 36 

Elimination 36 

Quadratic Equations 36 

Theory of Exponents 37 

Binomial Theorem 38 

Geometrical Problems of Construction 38 

of Straight Lines 38 

of Angles 39 

of Circles 40 

of Triangles 42 

of Squares and Polygons 42 

of the Ellipse 46 

of the Parabola 49 

of the Hvperbola '. 50 

of the Cycloid 51 

of the Tractrix or Schiele Anti-friction Curve 51 

of the Spiral 52 

of Rings inside a Circle 52 

of Arc of a Large Circle 52 

of the Catenary . 53 

of the Involute 53 

of plotting Angles 54 

Geometrical Propositions 54 

Mensuration, Plane Surfaces. 

Quadrilateral, Parallelogram, etc 55 

Trapezium and Trapezoid . 55 

Triangles 55 

Polygons. Table of Polygons 56 

Irregular Figures 57 

Properties of the Circle 58 

Values of n and its Multiples, etc 58 

Relations of arc, chord, etc 59 

Relations of circle to inscribed square, etc 60 

Formulas for a Circular Curve 60 

Sectors and Segments 61 

Circular Ring 61 

The Ellipse 61 

The Helix 62 

The Spiral 62 

Surfaces and Volumes of Similar Solids »* 



CONTENTS. 



Mensuration, Solid Bodies. 

PAGE 

Prism - 63 

Pyramid 63 

Wedge 63 

Rectangular Prismoid 63 

Cylinder . 63 

Cone 63 

Sphere 63 

Spherical Triangle 64 

Spherical Polygon 64 

The Prismoid 64 

The Prismoidal Formula 64 

Polyedron 64 

Spherical Zone 65 

Spherical Segment 65 

Spheroid or Ellipsoid 65 

Cylindrical Ring 65 

Solids of Revolution 65 

Spindles 65 

Frustrum of a Spheroid 65 

Parabolic Conoid 66 

Volume of a Cask 66 

Irregular Solids 66 

Plane Trigonometry. 

Solution of Plane Triangles 67 

Sine, Tangent, Secant, etc 67 

Signs of the Trigonometric Functions 68 

Trigonometrical Formulae 69 

Solution of Plane Right-angled Triangles 70 

Solution of Oblique-angled Triangles 70 

Analytical Geometry. 

Ordinates and Abscissas 71 

Equations of a Straight Line, Intersections, etc 71 

Equations of the Circle 72 

Equations of the Ellipse 72 

Equations of the Parabola r ........ . 73 

Equations of the Hyperbola , 73 

Logarithmic Curves 74 

Differential Calculus. 

Definitions 74 

Differentials of Algebraic Functions 75 

Formulae for Differentiating 75 

Partial Differentials 76 

Integrals . . . . 76 

Formulae for Integration 76 

Integration between Limits 77 

Quadrature of a Plane Surface 77 

Quadrature of Surfaces of Revolution 78 

Cubature of Volumes of Revolution 78 

Second, Third, etc., Differentials 78 

Maclaurin's and Taylor's Theorems 79 

Maxima and Minima 79 

Differential of an Exponential Function 80 

Logarithms 80 

Differential Forms which have Known Integrals . 81 

Exponential Functions 81 

Circular Functions ....;.... 82 

The Cycloid 82 

Integral Calculus 83 



V1U CONTENTS. 

The Slide Rule. 

PAGE 

Examples solved by the Slide Rule 83 

Logarithmic Ruled Paper. 

Plotting on Logarithmic Paper 85 

Mathematical Tables. 

Formula for Interpolation 87 

Reciprocals of Numbers 1 to 2000 '. 88 

Squares, Cubes, Square Roots, and Cube Roots from 0.1 to 1600. . . 94 

Squares and Cubes of Decimals a ; . 109 

Fifth Roots and Fifth Powers 110 

Circumferences and Areas of Circles Ill 

Circumferences of Circles in Feet and Inches' from 1 inch to 32 feet 

11 inches in diameter \20 

Areas of the Segments of a Circle 121 

Lengths of Circular Arcs, Degrees Given 122 

Lengths of Circular Arcs, Height of Arc Given 124 

Spheres . . . . 125 

Contents of Pipes and Cylinders, Cubic Feet and Gallons 127 

Cylindrical Vessels, Tanks, Cisterns, etc 128 

Gallons in a Number of Cubic Feet 129 

Cubic Feet in a Number of Gallons 129 

Square Feet in Plates 3 to 32 feet long and 1 inch wide 130 

Capacities of Rectangular Tanks in Gallons 132 

Number of Barrels in Cylindrical Cisterns and Tanks 133 

Logarithms 134 

Table of Logarithms 136 

Hyperbolic Logarithms 163 

Natural Trigonometrical Functions 166 

Logarithmic Trigonometrical Functions 169 

Materials. 

Chemical Elements 170 

Specific Gravity and Weight of Materials 171 

The Hydrometer 172 

Metals, Properties of 174 

Aluminum 174 

Antimony 175 

Bismuth 175 

Cadmium 175 

Copper 175 

Gold 175 

Iridium 175 

Iron 175 

Lead 175 

Magnesium 176 

Manganese 176 

Mercury 176 

Nickel 176 

Platinum 176 

Silver 176 

Tin 176 

Zinc 177 

Miscellaneous Materials. 

Order of Malleability, etc., of Metals 177 

Measures and Weights of Various Materials 177 

Formulae and Table for Calculating Weight of Rods, Plates, etc .... 178 

Commercial Sizes of Iron and Steel Bars 179 

Weights of Iron Bars 180 

of Iron and Steel Sheets 181 

of Flat Rolled Iron 182 

of Plate Iron 184 

of Steel Blooms 185 






CONTENTS. IX 

PAGE 

Sizes and Weights of Roofing Materials 186 

Terra-cotta 186 

Tiles 186 

Tin Plates 187 

Slates 189 

Pine Shingles 189 

Sky-light Glass 190 

Weights of Various Roof-coverings 190 

" Cast-iron Pipes or Columns 191 

Weights and Thickness of Cast-iron Pipes 192 

Safe Pressures on Cast-iron Pipe 194 

Cast-iron Pipe Fittings 196 

Standard Pipe Flanges 197 

Straight-way Gate Valves 199 

Forged Steel Flanges 200 

Standard Hose Couplings 207 

Standard Sizes of Welded Pipe 208 

Wrought-iron Welded Tubes 209 

Shelby Cold-drawn Tubing 210 

Riveted Iron Pipes 211 

Weight of Iron for Riveted Pipe 212 

Spiral Riveted Pipe 212 

Riveted Hydraulic Pipe ■ 212 

Coiled Pipes , 214 

Forged Steel Flanges for Riveted Pipe 214 

Seamless Brass Tubing , 215, 216 

Copper Tubing 216 

Lead and Tin-lined Lead Pipe - 217 

Wooden Stave Pipe 218 

Weight of Copper Rods 218 

Weight of Copper and Brass Wire and Plates 219 

" " Sheet and Bar Brass 220 

" " Aluminium Sheets and Bars 220 

Whitworth Screw-threads 220 

Screw-thread, U. S. Standard 221 

Automobile Screws and Nuts 222 

International Screw-thread 222 

Limit-gauges for Screw-threads 223 

Size of Iron for Standard Bolts 223 

Sizes of Screw-threads for Bolts and Taps 224 

Set Screws and Tap Screws • • • 225 

Acme Screw-thread 226 

Machine Screws, A.S.M.E. Standard 226 

Standard Taps 227 

Machine Screw Heads 228 

Weight of Bolts with Heads 229 

Round Head Rivets 229 

Track Bolts 230 

Washers 230 

Weights of Cone-head Rivets 231 

Sizes of Turnbuckles 231 

Tinners' Rivets 232 

Material Required per Mile of Railroad Track 232 

Railway Spikes 233 

Boat Spikes 233 

Wrought Spikes 233 

Cut Nails 234 

Wood Screws 234 

Lag Screws 234 

Wire Nails 235, 236 

Steel Wire, Size, Strength, etc 237 

Galvanized Iron Telegraph Wire 238 

Tests of Telegraph Wire 238 

Specifications for Galvanized Iron Wire 239 

Strength of Piano Wire 239 

Plough-steel Wire 239 

Copper Wire Table, Edison or Circular-mil Gauge 240 



X CONTENTS. 

PAGE 

Insulated Wire 241 

Copper Telegraph Wire 241 

Stranded Copper Feed Wire 242 

Rule for Resistance of Copper Wire 242 

Wires of Different Metals . . '. '. . .'.'.'.'.'.'. '.'.'.'..* \ 243 

Specirications for Copper Wire . . . , .' . . 243 

Wire Ropes . . 244 

Transmission or Haulage Rope ' . 245 

Plough-steel Ropes 246 

Lang Lay Rope . . . 246 

Galvanized Iron Wire Rope 247 

Cable Traction Ropes 247 

Flat Wire Ropes 248 

Galvanized Steel Cables 248 

Steel Hawsers 249 

Galvanized Steel-wire Strand 249 

Notes on use of Wire Rope . '. 250 

Locked Wire Rope ........ , 250 

Chains and. Chain Cables 251 

Sizes of Fire Brick 253 

Weights of Logs, Lumber,, etc 254, 255 

Fire Clay„ in Analysis 255 

Refractoriness of American Fire-brick 255 

Slag Bricks and Slag Blocks 256 

Magnesia Bricks. 257 

Asbestos , , 257 

Strength of Materials. 

Stress and Strain 258 

Elastic Limit ....." 259 

Yield Point 259 

Modulus of Elasticity 260 

Resilience 260 

Elastic Limit and Ultimate Stress 261 

Repeated Stresses 261 

Repeated Shocks 262 

Stresses due to Sudden Shocks 263 

Increasing Tensile Strength of Bars by Twisting 264 

Tensile Strength 265 

Measurement of Elongation 265 

Shapes of Test Specimens ..." 266 

Compressive Strength 267 

Columns, Pillars, or Struts 269 

Hodgkinson's Formula. Euler's Formula 269 

Gordon's Formula. Rankine's Formula. . 270 

Wrought-iron Columns 271 

Built Columns ..;'..' 271 

The Straight-line Formula 271 

Working Strains in Bridge Members . 272 

Strength of Cast-iron Columns 274 

Safe Load on Cast-iron Columns 276 

Strength of Brackets on Cast-iron Columns 277 

Eccentric Loading of Columns 278 

Moment of Inertia 279 

Radius of Gyration . 279 

Elements of Usual Sections 280 

Transverse Strength . : 282 

Formulge for Flexure of Beams 282 

Safe Loads on Steel Beams . . . / 284 

Beams of Uniform Strength :...... 286 

Properties of Rolled Structural Shapes . 287 

" Steel I Beams . . . 288 

Spacing of Steel I Beams 291 

Properties of Steel Channels 292 

" " T Shapes 294 

" '* Angles 295 

" •' Z-bars . 299 



CONTENTS. XI 

PAGE 

Dimensions of Z-bar Columns ; 300 

Dimensions and Safe Load on Channel Columns 305 

Bethlehem Special, Girder and H-beams 306 

Torsional Strength 311 

Elastic Resistance to Torsion 311 

Combined Stresses 312 

Stress due to Temperature 312 

Strength of Flat Plates 313 

Thickness of Flat Cast-iron Plates 313 

Strength of Unstayed Flat Surfaces 314 

Unbraced Heads of Boilers 314 

Strength of Stayed Surfaces 315 

Stresses in Steel Plating under Water Pressure 315 

Spherical Shells and Domed Heads 316 

Thick Hollow Cylinders under Tension 316 

Thin Cylinders under Tension 317 

Carrying Capacity of Steel Rollers and Balls 317 

Resistance of Hollow Cylinders to Collapse 318 

Collapsing Pressure of Tubes or Flues 319 

Formula for Corrugated Furnaces 193 

Hollow Copper Balls 322 

Holding Power of Nails, Spikes, Bolts, and Screws 323 

Cut versus Wire Nails 324 

Strength of Wrought-iron Bolts 325, 326 

Initial Strain on Bolts , 325 

Stand Pipes and their Design , 327 

Riveted Steel Water-pipes . ., 329 

Kirkaldy's Tests of Materials . 330 

Cast Iron. 330 

Iron Castings 330 

Iron Bars, Forgings, etc 330 

Steel Rails and Tires r 331 

; Steel Axles, Shafts, Spring Steel 332 

Riveted Joints . 333 

Welds.. . . .'. ; 333 

Copper, Brass, Bronze, etc . . . . 334 

Wire-rope 334 

Wire. 335 

Ropes, Hemp, and Cotton . 335 

Belting-Canvas ... 335 

Stones, Brick, Cement 335 

Wood 336 

Tensile Strength of Wire 336 

Watertown Testing-machine Tests 337 

Riveted Joints , 337. 

Wrought-iron Bars, Compression Tests 1 . . 337 

Steel Eye-bars 338 

Wrought-iron Columns 338 

Cold Drawn Steel 339 

Tests of Steel Angles 340 

Shearing Strength 340 

Relation of Shearing to Tensile Strength 340 

Strength of Iron and Steel Pipe 341 

Threading Tests of Pipe 341 

Old Tubes used as Columns 341 

Methods of Testing Hardness of Metals 342 

Holding Power of Boiler-tubes 342 

Strength of Glass 343 

Strength of Ice 344 

Copper at High Temperatures 344 

Strength of Timber ...;...... 344 

Expansion of Timber 345 

Tests of American Woods. 346 

Shearing Strength of Woods 347 

Strength of Brick, Stone, etc 347 

"Flagging. 350 

" " Lime and Cement Mortar 350. 



Xll CONTENTS. 

PAGE 

Moduli of Elasticity of Various Materials 351 

Tests of Portland Cement 351 

Factors of Safety 352 

Properties of Cork 355 

Vulcanized India- Rubber 356 

Nickel 357 

Aluminum, Properties and Uses 357 

Alloys. 

Alloys of Copper and Tin, Bronze 360 

Alloys of Copper and Zinc, Brass 362 

Variation in Strength of Bronze 362 

Copper-tin-zinc Alloys 363 

Liquation, or Separation of Metals 364 

Alloys used in Brass Foundries 366 

Tobin Bronze 368 

Copper-zinc-iron Alloys 369 

Alloys of Copper, Tin and Lead 369 

Phosphor Bronze 370 

Aluminum Alloys 371 

Alloys for Casting under Pressure 371 

The Thermit Process 372 

Caution as to Strength of Alloys 373 

Alloys -of Aluminum, Silicon and Iron 374 

Tungsten-aluminum Alloys 375 

Aluminum-tin Alloys 375 

Manganese Alloys 376 

Manganese Bronze 377 

German Silver 378 

Copper-nickel Alloys 378 

Alloys of Bismuth , 379 

Fusible Alloys *« 380 

Bearing Metal Alloys 380 

Bearing Metal Practice, 1907 382 

White Metal for Engine Bearings 382 

Alloys containing Antimony 383 

White-metal Alloys 383 

Type-metal 384 

Babbitt metals 384 

Solders 385 

Ropes and Cables. 

Strength of Hemp, Iron, and Steel Ropes 386 

Rope for Hoisting or Transmission 386 

Flat Ropes 387 

Cordage, Technical Terms of , . 388 

Splicing of Ropes 388 

Cargo Hoisting 390 

Working Loads for Manila Rope 390 

Knots 391 

Life of Hoisting and Transmission Rope 391 

Efficiency of Rope Tackles 391 

Splicing Wire Ropes 393 

Springs. 

Laminated Steel Springs 394 

Helical Steel Springs 395 

Carrying Capacity of Springs 396 

Elliptical Springs 399 

Springs to Resist Torsional Force 399 

Helical Springs for Cars, etc 400 

Phosphor-bronze Springs 401 

Chromium-Vanadium Spring Steel 401 

Test of a Vanadium Steel Spring — 401 



CONTENTS. 



Riveted Joints. 



PAGE 



Fairbairn's Experiments 401 

Loss of Strength by Punching 401 

Strength of Perforated Plates 402 

Hand vs. Hydraulic Riveting 402 

Formulas for Pitch of Rivets 404 

Proportions of Joints 405 

Efficiencies of Joints 405 

Diameter of Rivets 406 

Shearing Resistance of Rivet Iron and Steel 407 

Strength of Riveted Joints 408 

Riveting Pressures 412 

Iron and Steel. 

Classification of Iron and Steel 413 

Grading of Pig Iron 414 

Manufacture of Cast Iron 414 

Influence of Silicon Sulphur, Phos. and Mn on Cast Iron 415 

Microscopic Constituents 416 

Analyses of Cast Iron 416 

Specifications for Pig Iron and Castings 418 

Specifications for Cast-iron Pipe 419 

Strength of Cast Iron 421, 427 

Strength in relation to Cross-section 422 

Shrinkage of Cast Iron 423 

White Iron Converted into Gray 424 

Mobility of Molecules of Cast Iron 424 

Castings from Blast Furnace Metal . 425 

Effect of Cupola Melting 425 

Additions of Titanium, etc., to Cast Iron 426 

" Semi-steel " 428 

Permanent Expansion of Cast Iron by Heating 429 

Mixture of Cast Iron with Steel 429 

Bessemerized Cast Iron 429 

Bad Cast Iron 429 

Malleable Cast Iron 429 

Design of Malleable Castings 433 

Specifications for Malleable Iron 433 

Strength of Malleable Cast Iron 434 

Wrought Iron 435 

Chemistry of Wrought Iron 436 

Influence of Rolling on Wrought Iron 437 

Specifications for Wrought Iron 437 

Stay-bolt Iron 438 

Tenacity of Iron at High Temperatures 439 

Effect of Cold on Strength of Iron 440 

Expansion of Iron by Heat 441 

Durability of Cast Iron 441 

Corrosion of Iron and Steel 442 

Corrosion of Iron and Steel Pipes 443 

Electrolytic Theory, and Prevention of Corrosion 444 

Chrome Paints, Anti-corrosive 445 

Corrosion Caused by Stray Electric Currents 446 

Electrolytic Corrosion due to Overstrain 446 

Preservative Coatings; Paints, etc 447 

Inoxydation Processes, Bower-Barff , etc 448 

Aluminum Coatings 449 

Galvanizing 449 

Sherardizing, Galvanizing by Cementation 450 

Lead Coatings '. 450 

Manufacture of Steel 451 

Crucible, Bessemer and Open Hearth Steel 451 

Steel. 

Relation between Chemical and Physical Properties 452 

Electric Conductivity 453 

Variation in Strength 454 



XIV CONTENTS. 

PAGE 

Bending Tests of Steel 454 

Effect of Heat Treatment and of Work 454 

Hardening Soft Steel 455 

Effect of Cold Rolling 455 

Comparison of Full-sized and Small Pieces 455 

Recalescence of Steel 455 

Critical Point . 456 

Metallography 456 

Burning, Overheating, and Restoring Steel 457 

Working Steel at a Blue Heat 458 

Oil Tempering and Annealing 458 

Brittleness due to Long-continued Heating 458 

Influence of Annealing upon Magnetic Capacity 459 

Treatment of Structural Steel 459 

May Carbon be Burned out of Steel ? ., 461 

Effect of Nicking a Bar 461 

Specific Gravity 461 

Welding of Steel 461 

Occasional Failures 462 

Segregation in Ingots and Plates 462 

Endurance of Steel under Repeated Stresses 463 

The Thermit Welding Process 463 

Oxy-acetylene Welding and Cutting of Metals 464 

Hydraulic Forging. . 464 

Fluid-compressed Steel 464 

Steel Castings 464 

Crucible Steel 466 

Effect of Heat on Grain 466 

Heating and Forging 467 

Tempering Steel 468 

Kinds of Steel used for Different Purposes 469 

High-speed Tool Steel 469 

Manganese Steel 470 

Chrome Steel 470 

Nickel Steel 472 

Aluminum Steel 472 

Tungsten Steel 472 

Copper Steel 475 

Nickel- Vanadium Steel 475 

Static and Dynamic Properties of Steel 476 

Strength and Fatigue Resistance of Steels 477 

Chromium-Vanadium Steel 478 

Heat Treatment of Alloy Steels 479 

Specifications for Steel ; 480 

High-strength Steel for Shipbuilding 483 

Fire-box Steel 484 

Steel Rails 484 

MECHANICS. 

Matter, Weight, Mass 487 

Force, Unit of Force 488 

Inertia • 488 

Newton's Laws of Motion 488 

Resolution of Forces 489 

Parallelogram of Forces 489 

Moment of a Force 490 

Statical Moment, Stability 490 

Stability of a Dam 491 

Parallel Forces 491 

Couples 491 

Equilibrium of Forces 492 

Center of Gravity 492 

Moment of Inertia 493 

Centers of Oscillation and Percussion 494 

Center and Radius of Gyration .- 494 

The Pendulum 496 



CONTENTS. XV 

PAGE 

Conical Pendulum 496 

Centrifugal Force 497 

Velocity, Acceleration, Falling Bodies 497 

Value of g 498 

Angular Velocity 498 

Height due to Velocity 499 

Parallelogram of Velocities 499 

Velocity due to Falling a Given Height 500 

Mass, Force of Acceleration 501 

Formulae for Accelerated Motion 501 

Motion on Inclined Planes 502 

Momentum, Vis- Viva 502 

Work, Foot-pound 502 

Fundamental Equations in Dynamics . 502 

Power, Horse-power 503 

Energy 503 

Work of Acceleration 504 

Work of Accelerated Rotation 504 

Force of a Blow 504 

Impact of Bodies 505 

Energy of Recoil of Guns 506 

Conservation of Energy 506 

Sources of Energy 506 

Perpetual Motion 507 

Efficiency of a Machine 507 

Animal-power, Man-power 507 

Man-wheel, Tread Mills 508 

Work of a Horse 508 

Horse-gin 509 

Resistance of Vehicles 509 

Elements of Mechanics. 

The Lever 510 

The Bent Lever 511 

The Moving Strut 511 

The Toggle-joint , 511 

The Inclined Plane 512 

The Wedge 512 

The Screw 512 

The Cam 512 

The Pulley 513 

Differential Pulley 513 

Differential Windlass 514 

Differential Screw 514 

Wheel and Axle 514 

Toothed-wheel Gearing 514 

Endless Screw, Worm Gear . 514 

Stresses in Framed Structures. 

Cranes and Derricks 515 

Shear Poles and Guys 516 

King Post Truss or Bridge 517 

Queen Post Truss 517 

Burr Truss 518 

Pratt or Whipple Truss 518 

Method of Moments 519 

Howe Truss : 520 

Warren Girder 520 

Roof Truss 521 

The Economical Angle 522 

HEAT. 

Thermometers and Pyrometers 523 

Centigrade and Fahrenheit degrees compared 524 

Copper-ball Pyrometer 526 

Thermo-electric Pyrometer 526 

Temperatures in Furnaces 527 



CONTENTS. 

PAGE 

„ ir's Fire-clay Pyrometer 528 

Wiborgh Air Pyrometer 528 

Mesure and Nouel's Pyrometer 529 

Uehling and Steinbart Pyrometer 530 

Air-thermometer 530 

High Temperatures judged by Color 531 

Boiling-points of Substances 532 

Melting-points 532 

Unit of Heat 532 

Mechanical Equivalent of Heat 532 

Heat of Combustion 533 

Heat Absorbed by Decomposition 534 

Specific Heat 534 

Thermal Capacity of Gases 537 

Expansion by Heat 538 

Absolute Temperature, Absolute Zero 540 

Latent Heat of Fusion 541 

Latent Heat of Evaporation 542 

Total Heat of Evaporation 542 

Evaporation and Drying 542 

Evaporation from Reservoirs 543 

Evaporation by the Multiple System 543 

Resistance to Boiling 543 

Manufacture of Salt 543 

Solubility of Salt 544 

Salt Contents of Brines 545 

Concentration of Sugar Solutions 545 

Evaporating by Exhaust Steam 545 

Drying in Vacuum 546 

Driers and Drying 547 

Design of Drying Apparatus 550 

Humidity Table 551 

Radiation of Heat 551 

Black-body Radiation : 552 

Conduction and Convection of Heat 553 

Rate of External Conduction 554 

Heat Conduction of Insulating Materials 555, 556 

Heat Resistance, Reciprocal of Heat Conductivity 556 

Steam-pipe Coverings 558 

Transmission through Plates . . 561 

Transmission in Condenser Tubes 563 

Transmission of Heat in Feed-water Heaters 564 

Transmission through Cast-iron Plates 565 

Heating Water by Steam Coils 565 

Transmission from Air or Gases to Water 566 

Transmission from Flame to Water 567 

Cooling of Air 568 

Transmission from Steam or Hot Water to Air 569 

Thermodynamics 572 

Entropy 573 

Reversed Carnot Cycle, Refrigeration 574 

Principal Equations of a Perfect Gas 575 

Construction of the Curve PV n = C 576 

Temperature-Entropy Diagram of Water and Steam 576 

PHYSICAL PROPERTIES OF GASES. 

Expansion of Gases 577 

Boyle and Marriotte's Law 577 

Law of Charles, Avogadro's Law 578 

Saturation Point of Vapors 578 

Law of Gaseous Pressure 578 

Flow of Gases 579 

Absorption by Liquids 579 

Liquefaction of Gases, Liquid Air 579 

AIR. 

Properties of Air 580 

Afr-manorneter. 581 



CONTENTS. XV11 

PAGE 

Barometric Pressures 581 

Pressure at Different Altitudes 582 

Leveling by the Barometer and by Boiling Water 582 

To find Difference in Altitude 582 

Moisture in Atmosphere 583 

Weight of Air and Mixtures of Air and Vapor 584, 586 

Specific Heat of Air 587 

Flow of Air. 

Flow of Air through Orifices 588 

Flow of Air in Pipes 591 

Effects of Bends in Pipe 593 

Flow of Compressed Air 593 

Tables of Flow of Air 594 

Loss of Pressure in Pipes 595 

Anemometer Measurements 596 

Equalization of Pipes 597 

Wind. 

Force of the Wind 597 

Wind Pressure in Storms 598 

Windmills 599 

Capacity of Windmills 601 

Economy of Windmills 601 

Electric Power from Windmills 603 

Compressed Air. 

Heating of Air by Compression 604 

Loss of Energy in Compressed Air 604 

Volumes and Pressures 605 

Loss due to Heating 606 

Horse-power Required for Compression 606 

Work of Adiabatic Compression of Air 607 

Compressed-air Engines 608 

Compound Air-compression 609 

Table for Adiabatic Compression 610 

Mean Effective Pressures 610 

Mean and Terminal Pressures 611 

Air-compression at Altitudes 611 

Popp Compressed-air System : 612 

Small Compressed-air Motors 612 

Efficiency of Air-heating Stoves 612 

Efficiency of Compressed-air Transmission 613 

Efficiency of Compressed-air Engines 613 

Air-compressors 614 

Requirements of Rock-drills 616 

Steam Required to Compress 1 Cu. Ft. of Air 617 

Compressed air for Pumping Plants 617 

Compressed air for Hoisting Engines 618 

Practical Results with Air Transmission 619 

Effect of Intake Temperature 619 

Compressed air Motors with Return Circuit 620 

Intercoolers for Air-compressors 620 

Centrifugal Air-compressors 620 

High-pressure Centrifugal Fans 621 

Test of a Hydraulic Air-compressor 622 

Pneumatic Postal Transmission 624 

Mekarski Compressed-air Tramways 624 

Compressed Air Working Pumps in Mines 625 

Compressed Air for Street Railways , 625 

Fans and Blowers. 

Centrifugal Fans 626 

Best Proportions of Fans 626 

Pressure due to Velocity , 627 

Experiments with Blowers 629 



XV111 CONTENTS. 

PAGE 

Blast Area or Capacity Area 629 

Quantity of Air Delivered 630 

Efficiency of Fans and Positive Blowers 631 

Capacity of Fans and Blowers 632 

Table of Centrifugal Fans 632 

Steel Pressure Blowers for Cupolas 633 

Sturtevant Steel Pressure-blower 635 

Effect of Resistance on Capacity of Fans 636 

Sirocco Fans 636 

Multivane Fans 638 

Methods of Testing Fans 639 

Efficiency of Fans 641 

Diameter of Blast-pipes 643 

Centrifugal Ventilators for Mines 644 

Experiments on Mine Ventilators 645 

Disk Fans 647 

Efficiency of Disk Fans 648 

Positive Rotary Blowers 649 

Steam-jet Blowers „ 651 

Blowing Engines 652 

Steam-jet for Ventilation . 652 

HEATING AND VENTILATION. 

Ventilation 653 

Quantity of Air Discharged through a Ventilating Duct 655 

Heating and Ventilating of Large Buildings 656 

Standards for Calculating Heating Problems 658 

Heating Value of Coal 658 

Heat Transmission through Walls, etc 659 

Allowance for Exposure and Leakage 660 

Heating by Hot-air Furnaces 661 

Carrying Capacity of Air-pipes 662 

Volume of Air at Different Temperatures 663 

Sizes of Pipes Used in Furnace Heating 663 

Furnace Heating with Forced Air Supply 664 

Rated Capacity of Boilers for House Heating 664 

Capacity of Grate Surface 665 

Steam Heating, Rating of Boilers 665 

Testing Cast-iron Heating Boilers 667 

Proportioning House Heating Boilers 667 

Coefficient of Transmission in Direct Radiation 668 

Heat Transmitted in Indirect Radiation 669 

Short Rules for Computing Radiating Surface 669 

Carrying Capacity of Steam Pipes in Low Pressure Heating 669 

Proportioning Pipes to Radiating Surface 671 

Sizes of Pipes in Steam Heating Plants 672 

Resistance of Fittings 672 

Removal of Air, Vacuum Systems 673 

Overhead Steam-pipes 673 

Steam-consumption in Car-heating 673 

Heating a Greenhouse by Steam 673 

Heating a Greenhouse by Hot Water 674 

Velocity of Flow in Hot-water Heating 674 

Hot-water Heating 674 

Sizes of Pipe for Hot-water Heating 675 

Sizes of Flow and Return Pipes 678 

Heating by Hot-water, with Forced Circulation 678 

Blower Svstem of Heating and Ventilating 678 

Advantages and Disadvantages of the Plenum System 678 

Heat Radiated from Coils in the Blower System 679 

Test of Cast-iron Heaters for Hot-blast Work 680 

Factory Heating by the Fan System 681 

Artificial Cooling of Air 681 

Capacities of Fans for Hot-blast Heating 682 

Relative Efficiency of Fans and Heated Chimneys 683 

Heating a Building to 70° F .. ..,..., •. • 683 



CONTENTS. XIX 

™ . PAGE 

Heating by Electricity 684 

Mine-ventilation 685 

; Friction of Air in Underground Passages 685 

Equivalent Orifices 686 

WATER. 

Expansion of Water . . . . . 687 

Weight of Water at Different Temperatures 687, 688 

Pressure of Water due to its Weight 689, 690 

Head Corresponding to Pressures 689 

Buoyancy 690 

Boiling-point 690 

Freezing-point . 690 

Sea-water . . -...=.- 690 

Ice and Snow . .' 691 

Specific Heat of Water ... . . . 691 

Compressibility of Water ..-. . 691 

Impurities- of Water .... . . . . .-. .-. 691 

Causes of Incrustation 692 

Means for Preventing Incrustation 692 

•Analyses of Boiler-scale -..-...• 693 

Hardness of Water 694 

Purifying Feed-water 7\ 694 

Softening Hard Water , 695 

Hydraulics. Flow of Water. 

Formulae for Discharge through Orifices and Weirs 697 

Flow of Water from Orifices ' 698 

Flow in Open and Closed Channels 699 

General Formulae for Flow 699 

Chezy's Formula 699 

Values of the Coefficient c . 699, 703 

Table, Fall in Feet per mile, etc. 700 

Values of Vr for Circular Pipes 701 

Kutter's Formula 701 

D'Arcy's Formula 704 

Velocity of Water in Open Channels 704 

Mean Surface and Bottom Velocities 704 

Safe Bottom and Mean Velocities . 705 

Resistance of Soil to Erosion 705 

Abrading and Transporting Power of Water 705 

Grade of Sewers 706 

Flow of Water in a 20-inch Pipe 706 

Table of Flow of Water in Circular Pipes 707-711 

Short Formulae 710 

Flow of Water in House-service pipes 712 

Flow of Water through Nozzles 713 

Loss of Head 714 

Values of the Coefficient of Friction 715 

Resistance at the Inlet of a Pipe 715 

Flow of Water in Riveted Pipes 716 

Cox's Formula 717 

Exponential Formulae 718 

Friction Loss in Clean Cast-iron Pipe 719 

Approximate Hydraulic Formulae 720 

Compound Pipes, and Pipes with Branches 720 

Effect of Bend and Curves 721 

Hydraulic Grade-line 721 

Long Pipe Lines 721 

Rifled Pipes for Conveying Oils 721 

Loss of Pressure Caused by Valves, etc 721 

Air-bound Pipes .. , 722 

Vertical Jets 722 

Water Delivered through Meters 722 

■ Fire Streams , 722 

Water Hammer . . 722 



XX CONTENTS. 

PAGE 

Price Charged for Water in Cities 722 

Hydrant Pressures required with Different Lengths and Sizes of 

Hose 723 

Friction Losses in Hose 725 

Pump Inspection Table , 725 

Rated Capacity of Steam Fire-engines 725 

The Siphon . 726 

Measurement of Flowing Water 727 

Piezometer 727 

Pitot Tube Gauge 727 

Maximum and Mean Velocities in Pipes 727 

The Venturi Meter 728 

Measurement of Discharge by Means of Nozzles 728 

Flow through Rectangular Orifices 729 

Measurement of an Open Stream 729 

Miners' Inch Measurements 730 

Flow of Water over Weirs 731 

Francis's Formula for Weirs 731 

Weir Table , 732 

Bazin's Experiments 733 

The Cippoleti, or Trapezoidal Weir 733 

Water-power. 

Power of a Fall of Water 734 

Horse-power of a Running Stream 734 

Current Motors 734 

Bernoulli's Theorem 734 

Maximum Efficiency of a Long Conduit 735 

Mill-power 735 

Value of Water-power 735 

Water Wheels; Turbine Wheels. 

Water Wheels 737 

Proportions of Turbines 737 

Tests of Turbines 742 

Dimensions of Turbines 743 

Rating and Efficiency of Turbines 743 

Rating Table for Turbines 746 

Turbines of 13,500 H.P. each 747 

The Fall-increaser for Turbines 747 

Tangential or Impulse Water Wheel 748 

The Pelton Water Wheel 748 

Considerations in the Choice of a Tangential Wheel 749 

Control of Tangential Water Wheels 750 

Tangential Water-wheel Table 751 

Amount of Water Required to Develop a given Horse- Power 753 

Efficiency of the Doble Nozzle 753 

Water Plants Operating under High Pressure 754 

Formulae for Calculating the Power of Jet Water Wheels 754 

The Power of Ocean Waves. 

Utilization of Tidal Power 756 

Pumps. 

Theoretical Capacity of a Pump 757 

Depth of Suction 757 

The Deane Pump 758 

Amount of Water Raised by a Single-acting Lift-pump 759 

Proportioning the Steam-cylinder of a Direct-acting Pump 759 

Speed of Water through Pipes and Pump-passages 759 

Sizes of Direct-acting Pumps 759 

Efficiency of Small Pumps 759 

The Worthington Duplex Pump 760 

Speed of Piston 760 

Speed of Water through Valves 761 



CONTENTS. XXI 

PAGE 

Boiler-feed Pumps - 761 

Pump Valves 762 

The Worthington High-duty Pumping Engine 762 

The d'Auria Pumping Engine 762 

A 72,000,000-Gallon Pumping Engine 762 

The Screw Pumping Engine 763 

Finance of Pumping Engine Economy 763 

Cost of Pumping 1000 Gallons per minute 764 

Centrifugal Pumps 764 

Design of a Four-stage Turbine Pump 765 

Relation of Peripheral Speed to Head 766 

Tests of De Laval Centrifugal Pump 768 

A High-duty Centrifugal Pump 770 

Rotary Pumps 770 

Tests of Centrifugal and Rotary Pumps 770 

Duty Trials of Pumping Engines 771 

Leakage Tests of Pumps 772 

Notable High-duty Pump Records 774 

Vacuum Pumps 775 

The Pulsometer 775 

Pumping by Compressed Air 776 

The Jet Pump 776 

The Injector 776 

Air-lift Pump 776 

Air-lifts for Deep Oil-wells 777 

The Hydraulic Ram 778 

Quantity of Water Delivered by the Hydraulic Ram 778 

Hydraulic Pressure Transmission. 

Energy of Water under Pressure 779 

Efficiency of Apparatus 780 

Hydraulic Presses 781 

Hydraulic Power in London 781 

Hydraulic Riveting Machines : 782 

Hydraulic Forging 782 

Hydraulic Engine 783 

FUEL. 

Theory of Combustion 784 

Analyses of the Gases of Combustion 785 

Temperature of the Fire 785 

Classification of Solid Fuels 786 

Classification of Coals 786 

Analyses of Coals 787 

Caking and Non-caking Coals 788 

Cannel Coals 788 

Rhode Island Graphitic Anthracite 788 

Analysis and Heating Value of Coals 789 

Approximate Heating Values 791 

Tests of the U. S. Geological Survey 791 

Lord and Haas's Tests 792 

Sizes of Anthracite Coal 792 

Space occupied by Anthracite 793 

Bernice Basin, Pa., Coal 793 

Connellsville Coal and Coke 793 

Bituminous Coals of the United States 794 

Western Lignites 796 

Analysis of Foreign Coals 796 

Sampling Coal for Analyses 797 

Relative Value of Steam Coals 797 

Calorimetric Tests of Coals 797 

Purchase of Coal Under Specifications 799 

Evaporative Power of Bituminous Coals 799 

Weathering of Coal 800 

Pressed Fuel , 801 



XX11 CONTENTS. 

PAGE 

Coke . 801 

Experiments in Coking 802 

Coal Washing 802 

Recovery of By-products in Coke Manufacture 802 

Generation of Steam from the Waste Heat and Gases from Coke- 
ovens 803 

Products of the Distillation of Coal 803 

Wood as Fuel 804 

Heating Value of Wood „ 804 

Composition of Wood 805 

Charcoal 805 

Yield of Charcoal from a Cord of Wood 806 

Consumption of Charcoal in Blast Furnaces 806 

Absorption of Water and of Gases by Charcoal 806 

Composition of Charcoals 807 

Miscellaneous Solid Fuels 807 

Dust-fuel — Dust Explosions 807 

Peat or Turf 808 

Sawdust as Fuel 808 

Wet Tan-bark as Fuel 808 

Straw as Fuel 808 

Bagasse as Fuel in Sugar Manufacture 809 

Liquid Fuel. 

Products of Distillation of Petroleum 810 

Lima Petroleum 810 

Value of Petroleum as Fuel 811 

Fuel Oil Burners 812 

Oil vs. Coal as Fuel 812 

Alcohol as Fuel 813 

Specific Gravity of Ethyl Alcohol 813 

Vapor Pressures of Saturation of Alcohol and other Liquids 814 

Fuel Gas. 

Carbon Gas 814 

Anthracite Gas 815 

Bituminous -Gas 816 

Water Gas 817 

Natural Gas in Ohio and Indiana 817 

Natural Gas as a Fuel for Boilers -. 817 

Producer-gas from One Ton of Coal 818 

Proportions of Gas Producers and Scrubbers 819 

Combustion of Producer-gas 819 

Gas Producer Practice 820 

Capacity of Producers 821 

High Temperature Required for Production of C0 2 822 

The Mond Gas Producer 822 

Relative Efficiency of Different Coals in Gas-engine Tests 823 

Use of Steam in Producers and Boiler Furnaces 824 

Gas Fuel for Small Furnaces 824 

Gas Analyses by Volume and by Weight 824 

Blast-furnace Gas 825 

Acetylene and Calcium Carbide. 

Acetvlene 825 

Calcium Carbide 826 

Acetylene Generators and Burners 826 

The Acetylene Blowpipe 827 

Illuminating Gas. 

Coal-gas 828 

Water-gas 829 

Analyses of Water-gas and Coal-gas 830 

Calorific Equivalents of Constituents 830 

Efficiency of a Water-gas Plant . , 830 



CONTENTS. XX111 

PAGE 

Space Required for a Water-gas Plant — .... 832 

Fuel-value of Illuminating Gas 833 

Flow of Gas in Pipes . . 834 

Services for Lamps 834 

STEAM. 

Temperature and Pressure 836 

Total Heat 836 

Latent Heat of Steam 836 

Specific Heat of Saturated Steam 837 

The Mechanical Equivalent of Heat 837 

Pressure of Saturated Steam 837 

Volume of Saturated Steam 837 

Volume of Superheated Steam . 837 

Specific Density of Gaseous Steam 838 

Specific Heat of Superheated Steam 838 

Regnault's Experiments '..".'.'. 838 

Table of the Properties of Saturated Steam . 839 

Table of the Properties of Superheated Steam 843 

Flow of Steam. 

Napier's Approximate Rule 844 

Flow of Steam through a Nozzle 844 

Flow of Steam in Pipes 845 

Table of Flow of Steam in Pipes 846 

Carrying Capacity of Extra Heavy Steam Pipes 847 

Flow of Steam in Long Pipes, Ledoux's Formula 847 

Resistance to Flow by Bends, Valves, etc 848 

Sizes of Steam-pipes for Stationary Engines 848 

Sizes of Steam-pipes for Marine Engines 848 

Proportioning Pipes for Minimum Loss by Radiation and Friction . . .849 

Available Maximum Efficiency of Expanded Steam 850 

Steam-pipes. 

Bursting-tests of Copper Steam-pipes 851 

Failure of a Copper Steam-pipe 851 

Wire-wound Steam-pipes 851 

Materials for Pipes and Valves for Superheated Steam 851 

Riveted Steel Steam-pipes 852 

Valves in Steam-pipes 852 

The Steam Loop 852 

Loss from an Uncovered Steam-pipe 853 

Condensation in an Underground Pipe Line 853 

Steam Receivers in Pipe Lines . . . 853 

Equation of Pipes 853 

Identification of Power House Piping by Colors 854 

THE STEAM-BOILER. 

The Horse-power of a Steam-boiler 854 

Measures for Comparing the Duty of Boilers 855 

Steam-boiler Proportions 855 

Unit of Evaporation 855 

Heating-surface . . . 856 

Horse-power, Builders'. Rating . 857 

Grate-surface 857 

Areas of Flues 858 

Air-passages Through Grate-bars 858 

Performance of Boilers . . . 858 

Conditions which Secure Economy 859 

Air Leakage in Boiler Settings 859 

Efficiency of a Boiler . . 860 

Autographic C0 2 Recorders 860 

Relation of Efficiency to Rate of Driving, Air Supply, etc 862 

Tests of Steam-boilers . . 864 



XXIV CONTENTS. 

PAGE 

Boilers at the Centennial Exhibition 864 

High Rates of Evaporation 865 

Economy Effected by Heating the Air 865 

Maximum Boiler Efficiency with Cumberland Coal 865 

Boilers Using Waste Gases 865 

Rules for Conducting Boiler Tests 866 

Heat Balance in Boiler Tests 872 

Table of Factors of Evaporation 874 

Strength of Steam-boilers. 

Rules for Construction 879 

Shell-plate Formulae 880 

Rules for Flat Plates 880 

Furnace Formula?- 881 

Material for Stays 882 

Loads allowed on Stays 882 

Girders 882 

Tube Plates . < 882 

Material for Tubes 883 

Holding Power of Boiler Tubes 883 

Iron versus Steel Boiler Tubes 883 

Rules for Construction of Boilers in Merchant Vessels in U. S 884 

Safe-working Pressures 887 

Flat-stayed Surfaces 888 

Diameter of Stay-bolts 888 

Strength of Stays 888 

Boiler Attachments, Furnaces, etc. 

Fusible Plugs 889 

Steam Domes 889 

Height of Furnace 889 

Mechanical Stokers 889 

The Hawley Down-draught Furnace 890 

Under-feed Stokers 890 

Smoke Prevention 890 

Burning Illinois Coal without Smoke 892 

Conditions of Smoke Prevention 893 

Forced Combustion 894 

Fuel Economizers 894 

Thermal Storage 897 

Incrustation and Corrosion 897 

Boiler-scale Compounds 898 

Removal of Hard Scale 900 

Corrosion in Marine Boilers 900 

Use of Zinc 901 

Effect of Deposit on Flues 901 

Dangerous Boilers 901 

Safety-valves. 

Rules for Area of Safety-valves 902 

Spring-loaded Safety-valves 904 

The Injector. 

Equation of the Injector 906 

Performance of Injectors 907 

Boiler-feeding Pumps 908 

Feed-water Heaters. 

Percentage of Saving Due to Use of Heaters 909 

Strains Caused by Cold Feed-water 909 

Calculation of Surface of Heaters and Condensers 910 

Open vs. Closed Feed-water Heaters 911 

Steam Separators. 

Efficiency of Steam Separators 911 



CONTENTS. XXV 

Determination of Moisture in Steam. 

Steam Calorimeters 912 

Coil Calorimeter 913 

Throttling Calorimeters 913 

Separating Calorimeters 914 

Identification of Dry Steam 915 

Usual Amount of Moisture in Steam 915 

Chimneys. 

Chimney Draught Theory 915 

Force or Intensity of Draught 916 

Rate of Combustion Due to Height of Chimney 918 

High Chimneys not Necessary „ 919 

Height of Chimneys Required for Different Fuels 919 

Protection of Chimney from Lightning 920 

Table of Size of Chimneys 921 

Some Tall Brick Chimneys 922 

Stability of Chimneys 924 

Steel Chimneys 925 

Reinforced Concrete Chimneys 927 

Sheet-iron Chimneys 928 

THE STEAM ENGINE. 

Expansion of Steam 929 

Mean and Terminal Absolute Pressures 930 

Calculation of Mean Effective Pressure •. . 931 

Mechanical Energy of Steam Expanded Adiabatically 933 

Measures for Comparing the Duty of Engines 933 

Efficiency, Thermal Units per Minute 934 

Real Ratio of Expansion 935 

Effect of Compression 935 

Clearance in Low- and High-speed Engines 936 

Cylinder-condensation 936 

Water-consumption of Automatic Cut-off Engines 937 

Experiments on Cylinder-condensation 937 

Indicator Diagrams 938 

Errors of Indicators 939 

Pendulum Indicator Rig 939 

The Manograph 939 

The Lea Continuous Recorder , 940 

Indicated Horse-power 940 

Rules for. Estimating Horse-power 940 

Horse-power Constants 941 

Table of Engine Constants 942 

To Draw Clearance on Indicator-diagram 944 

To Draw Hyperbola Curve on Indicator-diagram 944 

Theoretical Water Consumption 945 

Leakage of Steam 946 

Compound Engines. 

Advantages of Compounding 946 

Woolf and Receiver Types of Engines 947 

Combined Diagrams 949 

Proportions of Cylinders in Compound Engines 950 

Receiver Space 950 

Formula for Calculating Work of Steam 951 

Calculation of Diameters of Cylinders 952 

Triple-expansion Engines 953 

Proportions of Cylinders 953 

Formulge for Proportioning Cylinders 953 

Types of Three-stage Expansion Engines 956 

Sequence of Cranks 956 

Velocity of Steam through Passages 956 

A Double-tandem Triple-expansion Engine 956 

Quadruple-expansion Engines 956 



XXVI CONTENTS. 

Steam-engine Economy. 

PAGE 

Economic Performance of Steam-engines 957 

Feed-water Consumption of Different Types 957 

Sizes and Calculated Performances of Vertical High-speed Engine . 959 

The Willans Law, Steam Consumption at Different Loads 962 

Relative Economy of Engines under Variable Loads 963 

Steam Consumption of Various Sizes 963 

Steam Consumption in Small Engines 964 

Steam Consumption at Various Speeds 964 

Capacity and Economy of Steam fire Engines 964 

Economy Tests of High-speed Engines 965 

Limitation of Engine Speed 966 

British High-speed Engines 966 

Advantage of High Initial and Low-back Pressure 967 

Comparison of Compound and Single-cylinder Engines 968 

Two-cylinder and Three-cylinder Engines 9"" 

The Lentz Compound Engine 9 

Steam Consumption of Different Types of Engine 9 

Steam Consumption of Engines with Superheated Steam 969 

Efficiency of Non-condensing Compound Engines 971 

Economy of Engines under Varying Loads 971 

Effect of Water in Steam on Efficiency 972 

Influence of Vacuum and Superheat on Steam Consumption 972 

Practical Application of Superheated Steam 973 

Performance of a Quadruple Engine < 974 

Influence of the Steam-jacket 975 

Best Economy of the Piston Steam Engine 977 

Highest Economy of Pumping-engines 978 

Sulphur-dioxide Addendum to Steam-engine 978 

Standard Dimensions of Direct-connected Generator Sets 979 

Dimensions of Parts of Large Engines 979 

Large Rolling-mill Engines 980 

Counterbalancing Engines 980 

Preventing Vibrations of Engines 980 

Foundations Embedded in Air 980 

Most Economical Point of Cut-off 981 

Type of Engine used when Exhaust-steam is used for Heating .... 981 

Cost of Steam-power . . 981, 982 

Cost of Coal for Steam-power 983 

Relative Commercial Economy of Compound and Triple-expansion 

Engines 984 

Power-plant Economics 984 

Economy of Combination of Gas Engines and Turbines 986 

Analysis of Operating Costs of Power-plants 987 

Storing Steam Heat in Hot Water 987 

Utilizing the Sun's Heat as a Source of Power 988 

Rules for Conducting Steam-engine Tests 988 

Dimensions of Parts of Engines. 

Cylinder 996 

Clearance of Piston 996 

Thickness of Cylinder 997 

Cylinder Heads 998 

Cylinder-head Bolts 999 

The Piston . . 999 

Piston Packing-rings 1000 

Fit of Piston-rod 1001 

Diameter of Piston-rods 1002 

Piston-rod Guides 1002 

The Connecting-rod 1003 

Connecting-rod Ends 1005 

Tapered Connecting-rods 1005 

The Crank-pin 1005 

Crosshead-pin or Wrist-pin 1009 

The Crank-arm 1009 

The Shaft, Twisting Resistance 1010 



CONTENTS. XXV11 

PAGE 

Resistance to Bending . * . . . . 1012 

Equivalent Twisting Moment 1012 

Fly-wheel Shafts 1013 

Length of Shaft-bearings 1015 

Crank-shafts with Center-crank and Double-crank Arms 1017 

Crank-shaft with two Cranks Coupled at 90° 10 IS 

Crank-shaft with three Cranks at 120° 1019 

Valve-stem or Valve-rod 1019 

Size of Slot-link 1020 

The Eccentric 1020 

The Eccentric-rod 1020 

Reversing-gear ' 1020 

Current Practice in Engine Proportions, 1897 1021 

Current Practice in Steam-engine Design, 1909 1022 

Shafts and Bearings of Engines 1023 

Calculating the Dimensions of Bearings 1024 

Engine-frames or Bed-plates 1025 

Fly-wheels. 

Weight of Fly-wheels 1026 

Weight of Fly-wheels for Alternating-current Units 1028 

Centrifugal Force in Fly-wheels 1029 

Diameters for Various Speeds 1030 

Strains in the Rims 1031 

Arms of Fly-wheels and Pulleys ' . . . . 1032 

Thickness of Rims 10^2 

A Wooden Rim Fly-wheel 1033 

Wire-wound Fly-wheels 1034 

The Slide-valve. 

Definitions, Lap, Lead, etc 1034 

Sweet's Valve-diagram 1036 

The Zeuner Valve-diagram 1036 

Port Opening, Lead, and Inside Lead 1089 

Crank Angles for Connecting-rods of Different Lengths 1040 

Ratio of Lap and of Port-opening to Valve-travel 1041 

Relative Motions of Crosshead and Crank 1042 

Periods of Admission or Cut-off for Various Laps and Travels 1042 

Piston- valves 1043 

Setting the Valves of an Engine 1043 

To put an Engine on its Center , 1043 

Link-motion 1044 

The Walschaert Valve-gear 1046 

Governors. 

Pendulum or Fly-ball Governors 1047 

To Change the Speed of an Engine 1048 

Fly-wheel or Shaft Governors 1048 

The Rites Inertia Governor 1048 

Calculation of Springs for Shaft-governors 1048 

Condensers, Air-pumps, Circulating-pumps, etc. 

The Jet Condenser 1050 

Quantity of Cooling water 1050 

Ejector Condensers 1051 

The Barometric Condensers 1051 

The Surface Condenser 1051 

Coefficient of Heat Transference in Condensers 1052 

The Power Used for Condensing Apparatus . 1053 

Vacuum, Inches of Mercury and Absolute Pressure 1053 

Temperatures, Pressures and Volumes of Saturated Air 1054 

Condenser Tubes . . 1054 

Bimetallic Condenser Tubes ...:." 1055 

Tube-plates 1055 

Spacing of Tubes ; . . 1055 



XXV111 CONTENTS. 

PAGE 

Air-pump 1055 

Area through Valve-seats 1056 

The Leblanc Condenser 1057 

Circulating-pump 1057 

Feed-pumps for Marine Engines 1057 

An Evaporative Surface Condenser 1057 

Continuous Use of Condensing Water 1058 

Increase of Power by Condensers 1058 

Advantage of High Vacuum in Reciprocating Engines 1059 

The Choice of a Condenser 1059 

Cooling Towers 1060 

Tests of a Cooling Tower and Condenser 1061 

Evaporators and Distillers 1061 

Rotary Steam Engines — Steam Turbines. 

Rotary Steam Engines 1062 

Impulse and Reaction Turbines 1062 

The DeLaval Turbine 1062 

The Zolley or Rateau Turbine 1062 

The Parsons Turbine 1062 

The Westinghouse Double-flow Turbine 1063 

Mechanical Theory of the Steam Turbine 1063 

Heat Theory of the Steam Turbine 1064 

Velocity of Steam in Nozzles 1065 

Speed of the Blades 1066 

Comparison of Impulse and Reaction Turbines 1066 

Loss due to Windage 1066 

Efficiency of the Machine 1067 

Steam Consumption of Turbines 1067 

The Largest Steam Turbine 1068 

Steam Consumption of Small Steam Turbines 1069 

Low-pressure Steam Turbines 1069 

Tests of a 15,000 K.W. Steam-engine Turbine Unit 1071 

Reduction Gear for Steam Turbines 1071 

Naphtha Engines — Hot-air Engines. 

Naphtha Engines 1071 

Hot-air or Caloric Engines 1071 

Test of a Hot-air Engine 1071 

Internal Combustion Engines. 

Four-cycle and Two-cycle Gas-engines 1072 

Temperatures and Pressures Developed 1072 

Calculation of the Power of Gas-engines 1073 

Pressures and Temperatures at End of Compression 1074 

Pressures and Temperature at Release 1075 

" " " after Combustion 1075 

Mean Effective Pressures 1076 

Sizes of Large Gas-engines 1076 

Engine Constants for Gas-engines 1077 

Rated Capacity of Automobile Engines 1077 

Estimate of the Horse-power of a Gas-engine 1077 

Oil and Gasoline Engines 1077 

The Diesel Oil Engine 1078 

The De La Vergne Oil Engine 1078 

Alcohol Engines 1078 

Ignition 1078 

Timing 1079 

Governing 1079 

Gas and Oil Engine Troubles 1079 

Conditions of Maximum Efficiency 1079 

Heat Losses in the Gas-engine 1080 

Economical Performance of Gas-engines 1080 

Utilization of Waste Heat from Gas-engines 1081 

Rules for Conducting Tests of Gas and Oil Engines 1081 



contents. xxix 

locomotives. pagb 

Resistance of Trains 1084 

Resistance of Electric Railway Cars and Trains 1086 

Efficiency of the Mechanism of a Locomotive 1087 

Adhesion 1087 

Tractive Force 1087 

Size of Locomotive Cylinders 1088 

Horse-power of a Locomotive 1089 

Size of Locomotive Boilers 1089 

Wootten's Locomotive 1090 

Grate-surface, Smokestacks, and Exhaust-nozzles 1091 

Fire-brick Arches 1091 

Economy of High Pressures 1092 

Leading American Types . 1092 

Classification of Locomotives 1092 

Steam Distribution for High Speed 1093 

Formulae for Curves 1093 

Speed of Railway Trains 1094 

Performance of a High-speed Locomotive 1094 

Fuel Efficiency of American Locomotives 1095 

Locomotive Link-motion 1095 

Dimensions of Some American Locomotives 1096 

The Mallet Compound Locomotive 1096 

Indicated Water Consumption 1098 

Indicator Tests of a Locomotive at High-speed 1098 

Locomotive Testing Apparatus 1099 

Weights and Prices 'of Locomotives 1100 

Waste of fuel in Locomotives 1101 

Advantages of Compounding 1101 

Depreciation of Locomotives 1101 

Average Train Loads 1101 

Tractive Force of Locomotives, 1893 and 1905 1101 

Superheating in Locomotives 1102 

Counterbalancing Locomotives 1102 

Narrow-gauge Railways 1103 

Petroleum-burning Locomotives 1103 

Fireless Locomotives 1 103 

Self-propelled Railway Cars 1103 

Compressed-air Locomotives 1104 

Air Locomotives with Compound Cylinders 1105 

SHAFTING. 

Diameters to Resist Torsional Strain 1106 

Deflection of Shafting 1107 

Horse-power Transmitted by Shafting 1108 

Flange Couplings 1109 

Effect of Cold Rolling 1109 

Hollow Shafts 1109 

Sizes of Collars for Shafting 1109 

Table for Laying Gut Shafting 1110 

PULLETS. 

Proportions of Pulleys 1111 

Convexity of Pulleys 1112 

Cone or Step Pulleys 1112 

Burmester's Method for Cone Pulleys 1113 

Speeds of Shafts with Cone Pulleys 1114 

Speeds in Geometrical Progression 1114 

BELTING. 

Theory of Belts and Bands 1115 

Centrifugal Tension 1115 

Belting Practice, Formulae for Belting 1116 

Horse-power of a Belt one inch wide 1117 



XXX CONTENTS. 

PAGE 

A. F. Nagle's Formula 1117 

Width of Belt for Given Horse-power 1118 

Belt Factors 1119 

Taylor's Rules for Belting 1120 

Barth's Studies on Belting 1123 

Notes on Belting 1123 

Lacing of Belts 1124 

Setting a Belt on Quarter-twist. 1124 

To Find the Length of Belt 1125 

To Find the Angle of the Arc of Contact 1125 

To Find the Length of Belt when Closely Rolled 1125 

To Find the Approximate Weight of Belts 1125 

Relations of the Size and Speeds of Driving and Driven Pulleys 1125 

Evils of Tight Belts 1126 

Sag of Belts 1126 

Arrangements of Belts and Pulleys 1126 

Care of Belts 1127 

Strength of Belting 1127 

Adhesion, Independent of Diameter 1127 

Endless Belts 1 127 

Belt Data 1127 

Belt Dressing 1128 

Cement for Cloth or Leather 1128 

Rubber Belting 1128 

Steel Belts 1129 

Roller Chain and Sprocket Drives 1129 

Belting versus Chain Drives 1132 

A 350 H.P. Silent Chain Drive 1132 

GEARING. 

Pitch, Pitch-circle, etc 1133 

Diametral and Circular Pitch 1133 

Diameter of Pitch-line of Wheels from 10 to 100 Teeth 1134 

Ohordal Pitch 1 135 

Proportions of Teeth 1 135 

Gears with Short Teeth 1135 

Formulae for Dimensions of Teeth 1136 

Width of Teeth 1136 

Proportion of Gear-wheels 1137 

Rules for Calculating the Speed of Gears and Pulleys 1 137 

Milling Cutters for Interchangeable Gears 1138 

Forms of the Teeth. 

The Cycloidal Tooth 1138 

The Involute Tooth 1140 

Approximation by Circular Arcs 1142 

Stepped Gears 1143 

Twisted Teeth 1143 

Spiral Gears 1 143 

Worm Gearing 1143 

The Hindley Worm 1144 

Teeth of Bevel-wheels 1144 

Annular and Differential Gearing 1145 

Efficiency of Gearing 1146 

Efficiency of Worm Gearing 1147 

Efficiency of Automobile Gears 1148 

Strength of Gear Teeth. 

Various Formulas for Strength 1148 

Comparison of Formulae 1150 

Raw-hide Pinions 1153 

Maximum Speed of Gearing 1153 

A Heavy Machine-cut Spur-gear 1153 

Frictional Gearing 1154 

Frictional Grooved Gearing 1154 



CONTENTS. XXXi 

PAGE 

Power Transmitted by Friction Drives 1154 

Friction Clutches 1 155 

Coil Friction Clutches 1156 

HOISTING AND CONVEYING. 

Working Strength of Blocks 1157 

Chain-blocks 1157 

Efficiency of Hoisting Tackle 1158 

Proportions of Hooks 1 159 

Iron versus Steel Hooks 1 159 

Heavy Crane Hooks 1 159 

Strength of Hooks and Shackles 1161 

Power of Hoisting Engines 1 162 

Effect of Slack Rope on Strain in Hoisting 1162 

Limit of Depth for Hoisting 1162 

Large Hoisting Records 1 163 

Pneumatic Hoisting 1163 

Counterbalancing of Winding-engines 1163 

Cranes. 

Classification of Cranes 1165 

Position of the Inclined Brace in a Jib Crane 1166 

Electric Overhead Traveling Cranes . 1166 

Power Required to Drive Cranes 1166 

Dimensions, Loads and Speeds of Electric Cranes 1167 

Notable Crane Installations 1168 

Electric versus Hydraulic Cranes 1168 

A 150-ton Pillar Crane 1168 

Compressed-air Traveling Cranes 1168 

Power Required for Traveling Cranes and Hoists 1169 

Lifting Magnets 1169 

Telpherage 1171 

Coal-handling Machinery. 

Weight of Overhead Bins 1172 

Supply-pipes from Bins 1172 

Types of Coal Elevators 1172 

Combined Elevators and Conveyors 1172 

Coal Conveyors 1173 

Horse-power of Conveyors 1173 

Weight of Chain and of Flights 1174 

Bucket, Screw, and Belt Conveyors 1175 

Capacity of Belt Conveyors 1175 

Belt Conveyor Construction 1176 

Horse-power to Drive Belt Conveyors 1176 

Relative Wearing Power of Conveyor Belts 1177 

Wire-rope Haulage. 

Self-acting Inclined Plane 1177 

Simple Engine Plane . . . 1178 

Tail-rope System 1178 

Endless Rope System 1178 

Wire-rope Tramways . 1179 

Stress in Hoisting-ropes on Inclined Planes 1179 

An Aerial Tramway 21 miles long 1180 

Formulae for Deflection of a Wire Cable 1180 

Suspension Cableways and Cable Hoists 1181 

Tension Required to Prevent Wire Slipping on Drums 1182 

Taper Ropes of Uniform Tensile Strength 1183 

WIRE-ROPE TRANSMISSION. 

Working Tension of Wire Ropes 1183 

Breaking Strength of Wire Ropes 1184 

Sheaves for Wire-rope Transmission 1184 



XXX11 CONTENTS. 

1, PAGE 

Bending Stresses of Wire Ropes 1 184 

Horse-power Transmitted 1185 

Diameters of Minimum Sheaves 1186 

Deflections of the Rope : 1187 

Limits of Span 1187 

Long-distance Transmission 1188 

Inclined Transmissions 1188 

Bending Curvature of Wire Ropes 1188 

ROPE DRIVING. 

Formulae for Rope Driving 1189 

Horse-power of Transmission at Various Speeds 1191 

Sag of the Rope between Pulleys 1191 

Tension on the Slack Part of the Rope 1192 

Data of Manila Transmission Rope 1193 

Miscellaneous Notes on Rope-driving 1193 

Cotton Ropes 1194 

FRICTION AND LUBRICATION. 

Coefficient of Friction 1194 

Rolling Friction : 1194 

Friction of Solids 1195 

Friction of Rest 1195 

Laws of Unlubricated Friction 1195 

Friction of Tires Sliding on Rails 1195 

Coefficient of Rolling Friction . 1195 

Laws of Fluid Friction 1196 

Angles of Repose of Building Materials 1196 

Coefficient of Friction of Journals 1196 

Friction of Motion 1197 

Experiments on Friction of a Journal 1197 

Coefficients of Friction of Journal with Oil Bath 1197, 1199 

Coefficients of Friction of Motion and of Rest 1198 

Value of Anti-friction Metals 1199 

Cast-iron for Bearings 1199 

Friction of Metal Under Steam-pressure 1200 

Morin's Laws of Friction 1200 

Laws of Friction of well-lubricated Journals 1201 

Allowable Pressures on Bearing-surface 1203 

Oil-pressure in a Bearing 1204 

Friction of Car-journal Brasses 1204 

Experiments on Overheating of Bearings 1205 

Moment of Friction and Work of Friction 1205 j 

Tests of Large Shaft Bearings 1206 

Clearance between Journal and Bearing 1206 

Allowable Pressures on Bearings 1206 

Bearing Pressures for Heavy Intermittent Loads 1207 

Bearings for Very High Rotative Speed 1208 

Thrust Bearings in Marine Practice 1208 

Bearings for Locomotives • 1208 

Bearings of Corliss Engines 1208 

Temperature of Engine Bearings 1209 

Pivot Bearings 1209 

The Schiele Curve 1209 

Friction of a Flat Pivot-bearing 1209 

Mercury-bath Pivot 1209 

Ball Bearings, Roller Bearings, etc • 1210 

Friction Rollers 1210 

Conical Roller Thrust Bearings 1211 

The Hyatt Roller Bearing 1211 

Notes on Ball Bearings 1212 

Saving of Power by use of Ball Bearings 1214 

Knife-edge Bearings 1214 

Friction of Steam-engines 1215 1 

Distribution of the Friction of Engines 1215: 



contents. xxxiii 

Friction Brakes and Friction Clutches. PAGE 

Friction Brakes 1216 

Friction Clutches - 1216 

Magnetic and Electric Brakes 1217 

Design of Band Brakes *. 1217 

Friction of Hydraulic Plunger Packing 1217 

Lubrication. 

Durability of Lubricants 1218 

Qualifications of Lubricants 1219 

Examination of Oils 1219 

Specifications for Petroleum Lubricants 1219 

Penna. R. R. Specifications 1220 

Grease Lubricants 1221 

Testing Oil for Steam Turbines 1221 

Quantity of Oil to run an Engine 1221 

Cylinder Lubrication 1222 

Soda Mixture for Machine Tools 1223 

Water as a Lubricant 1223 

Acheson's Deflocculated Graphite 1223 

Solid Lubricants 1223 

Graphite, Soapstone, Metaline 1223 

THE FOUNDRY. 

Cupola Practice 1224 

Melting Capacity of Different Cupolas 1225 

Charging a Cupola 1225 

Improvement of Cupola Practice 1226 

Charges in Stove Foundries 1227 

Foundry Blower Practice . . 1227 

Results of Increased Driving 1229 

Power Required for a Cupola Fan 1230 

Utilization of Cupola Gases 1230 

Loss of Iron in Melting 1230 

Use of Softeners 1230 

Weakness of Large Castings 1230 

Shrinkage of Castings 1231 

Growth of Cast Iron by Heating 1231 

Hard Iron due to Excessive Silicon 1231 

Ferro Alloys for Foundry Use 1232 

Dangerous Ferro-silicon 1232 

Quality of Foundry Coke 1232 

Castings made in Permanent Cast-iron Molds 1232 

Weight of Castings from Weight of Pattern 1233 

Molding Sand 1233 

Foundry Ladles , 1234 

THE MACHINE SHOP. 

Speed of Cutting Tools 1235 

Table of Cutting Speeds 1235 

Spindle Speeds of Lathes 1236 

Rule for Gearing Lathes 1236 

Change-gears for Lathes 1237 . 

Quick Change Gears 1237 

Metric Screw-threads . • 1238 

Cold Chisels 1238 

Setting the Taper in a Lathe 1238 

Tavlor's Experiments on Tool Steel * . 1238 

Proper Shape of Lathe Tool 1238 

Forging and Grinding Tools 1240 

Best Grinding Wheel for Tools 1240 

Chatter 1241 

Use of Water on Tool 1241 

Interval between Grindings 1241 

Effect of Feed and Depth of Cut on Speed 1241 



XXXIV CONTENTS. 

PAGE 

Best High Speed Tool Steel — Heat Treatment 1242 

Best Method of Treating Tools in Small Shops 1243 

Quality of Different Tool Steels 1243 

Parting and Thread Tools 1243 

Durability of Cutting Tools 1243 

Economical Cutting Speeds 1243- 1245 

New High Speed Steels, 1909 1246 

Use of a Magnet to Determine Hardening Temperature 1246 

Case-hardening, Cementation, Harveyizing 1246 

Change of Shape due to Hardening and Tempering 1247 

Milling Cutters 1247 

Teeth of Milling Cutters 1247 

Keyways in Milling Cutters 1248 

Power Required for Milling 1249 

Extreme Results with Milling Machines 1249 

Speed of Cutters 1250 

Typical Milling Jobs 1251 

Milling with or against Feed 1252 

Modern Milling Practice 1252 

Lubricant for Milling ^utters 1252 

Milling-machine vs. Planer 1252 

Drills, Speed of Drills • 1253 

High-speed Steel Drills 1253 

Power Required to Drive High-speed Drills 1253 

Extreme Results with Radial Drills , 1254 

Experiments on Twist Drills 1254 

Resistance Overcome in Cutting Metal 1256 

Heavy Work on a Planer 1256 

Horse-power to run Lathes 1256-1260 

Power required for Machine Tools 1256-1260 

Power used by Machine Tools 1258 

Size of Motors for Machine Tools 1260 

Horse-power Required to Drive Shafting 1261 

Power used in Maehine-shops 1261 

Power Required to Drive Machines in Groups 1262 

Abrasive Processes. 

The Cold Saw 1262 

Reese's Fusing-disk 1262 

Cutting Stone with Wire 1262 

The Sand-blast 1262 

Emery-wheels 1263-1267 

Grindstones 1264-1268 

Various Tools and Processes. 

Efficiency of a Screw 1268 

Tap Drills 1269 

Efficiency of Screw Bolts 1270 

Efficiency of a Differential Screw 1270 

Taper Bolts, Pins, Reamers, etc 1270 

Morse Tapers 1271 

The Jarno Taper 1271 

Punches, Dies, Presses 1272 

Clearance between Punch and Die 1272 

Size of Blanks for Drawing-press 1272 

Pressure of Drop-press 1273 

Flow of Metals 1273 

Forcing and Shrinking Fits 1273 

Shaft Allowances for Electrical Machinery 1274 

Running Fits 1274 

Force Required to Start Force and Shrink Fits 1275 

Proportioning Parts of Machines in Series 1276 

Keys for Gearing, etc 1276 

Holding-power of Set-screws 1278 

Holding-power of Keys 1279 



CONTENTS. XXXV 

DYNAMOMETERS. 

PAGE 

Traction Dynamometers 1280 

The Prony Brake 1280 

The Alden Dynamometer 1281 

Capacity of Friction-brakes 1281 

Transmission Dynamometers 1282 

ICE MAKING OR REFRIGERATING MACHINES. 

Operations of a Refrigerating-Machine 1283 

Pressures, etc., of Available Liquids 1284 

Properties of Ammonia and Sulphur Dioxide Gas 1285 

Solubility of Ammonia 1288 

Properties of Saturated Vapors 1288 

Heat Generated by Absorption of Ammonia 1288 

Cooling Effect, Compressor Volume and Power Required, with 

different Cooling Agents 1289 

Ratios of Condenser, Mean Effective, and Vaporizer Pressures. . . . 1289 

Properties of Brine used to absorb Refrigerating Effect 1290 

Chloride-of-calcium Solution 1290 

Ice-melting Effect 1291 

Ether-machines 1291 

Air-machines 1291 

Carbon Dioxide Machines 1292 

Methyl Chloride Machines 1292 

Sulphur-dioxide Machines s 1292 

Machines Using Vapor of Water 1292 

Ammonia Compression-machines 1292 

Dry, Wet and Flooded Systems 1292 

Ammonia Absorption-machines 1293 

Relative Performance of Compression and Absorption Machines . . 1294 

Efficiency of a Refrigerating-machine 1295 

Cylinder-heating 1296 

Volumetric Efficiency 1296 

Pounds of Ammonia per Ton of Refrigeration 1297, 1298 

Mean Effective Pressure, and Horse-power 1297 

The Voorhees Multiple Effect Compressor 1297 

Size and Capacities of Ammonia Machines 1299 

Piston Speeds and Revolutions per Minute 1300 

Condensers for Refrigerating-machines 1300 

Cooling Tower Practice in Refrigerating Plants 1301 

Test Trials of Refrigerating-machines 1302 

Comparison of Actual and Theoretical Capacity 1302 

Performance of Ammonia Compression-machines 1303 

Economy of Ammonia Compression-machines 1304 

Form of Report of Test 1306 

Temperature Range 1306 

Metering the Ammonia 1307 

Performance of Ice-making Machines 1307 

Performance of a 75-ton Refrigerating-machine 1309, 1311 

Ammonia Compression-machine.. Results of Tests 1312 

Performance of a Single-acting Ammonia Compressor 1312 

Performance of Ammonia Absorption-machine 1312 

Means for Applying the Cold 1314 

Artificial Ice-manufacture 1314 

Test of the New York Hygeia Ice-making Plant 1315 

An Absorption Evaporator Ice-making System 1315 

Ice-making with Exhaust Steam 1316 

Tons of Ice per Ton of Coal 1316 

Standard Ice Cans or Molds 1316 

MARINE ENGINEERING 

Rules for Measuring and Obtaining Tonnage of Vessels 1316 

The Displacement of a Vessel 1317 

Coefficient of Fineness 1317 

Coefficient of Water-lines 1317 



XXXVI CONTENTS. 

PAGE 

Resistance of Ships 1317 

Coefficient of Performance of Vessels 1318 

Defects of the Common Formula for Resistance 1318 

Rankine's Formula 1 319 



E. R. Mumford's Method . 
Dr. Kirk's Method. 



1319 
1320 
1320 



To find the I.H.P. from the Wetted Surface 

Relative Horse-power required for Different Speeds of Vessels i*m 

Resistance per Horse-power for Different Speeds ' ' ' io 2 i 

Estimated Displacement, Horse-power, etc., of Steam-vessels ' ' 1322 

Speed of Boats with Internal Combustion Engines '.".':'. 1322 

The Screw-propeller 

Pitch and Size of Screw 1324 

Propeller Coefficients 1325 

Efficiency of the Propeller 1326 

Pitch-ratio and Slip for Screws of Standard Form 1326 

Table for Calculating Dimensions of Screws 1327 

Marine Practice 

Dimensions and Performance of Notable Atlantic Steamers 1328 

Relative Economv of Turbines and Reciprocating Engines 1328 

Marine Practice, 1901 1329 

Comparison of Marine Engines, 1872, 1881, 1891, 1901 1329 

Turbines and Boilers of the " Lusitania " 1330 

Performance of the " Lusitania," 1908 - 1330 

Relation of Horse-power to Speed 1331 

Reciprocating Engines with a Low-pressure Turbine 1331 

The Paddle-wheel 

Paddle-wheels with Radial Floats 1331 

Feathering Paddle-wheels 1331 

Efficiency of Paddle-wheels 1332 

Jet Propulsion 

Reaction of a Jet 1332 

CONSTRUCTION OF BUILDINGS 

Foundations 

Bearing Power of Soils 1333 

Bearing Power of Piles 1334 

Safe Strength of Brick Piers 1334 

Thickness of Foundation Walls 1334 

Masonry 

Allowable Pressures on Masonry 1334 

Crushing Strength of Concrete , . 1334 

Beams and Girders 

Safe Loads on Beams 1335 

Maximum Permissible Stresses in Structural Materials 1335 

Safe Loads on Wooden Beams 1336 

Walls 

Thickness of Walls of Buildings 1336 

Walls of Warehouses, Stores, Factories, and Stables 1337 

Floors, Columns and Posts 

Strength of Floors, Roofs, and Supports 1337 

Columns and Posts 1337 

Fireproof Buildings 1338 

Iron and Steel Columns 1338 

Lintels, Bearings, and Supports 1338 



CONTENTS. XXXV11 

PAGE 

Strains on Girders and Rivets 1338 

Maximum Load on Floors 1339 

Strength of Floors 1339 

Mill Columns 1341 

Safe Distributed Loads on Southern-pine Beams 1341 

Maximum Spans for 1, 2 and 3 inch Plank 1342 

Approximate Cost of 31ill Buildings 1342 

ELECTRICAL ENGINEERING 

C. G. S. System of Physical Measurement 1344 

Practical Units used in Electrical Calculations 1345 

Relations of Various Units 1346 

Units of the Magnetic Circuit 1346 

Equivalent Electrical, and Mechanical Units 1347 

Permeability 1348 

Analogies between Flow of Water and Electricity 1348 

Electrical Resistance 

Laws of Electrical Resistance 1349 

Electrical Conductivity of Different Metals and Alloys 1349 

Conductors and Insulators 1350 

Resistance Varies with Temperature 1350 

Annealing 1351 

Standard of Resistance of Copper Wire 1351 

Direct Electric Currents 

Ohm's Law 1351 

Series and Parallel or Multiple Circuits 1352 

Resistance of Conductors in Series and Parallel 1352 

Internal Resistance 1353 

Power of the Circuit 1353 

Electrical, Indicated, and Brake Horse-power 1353 

Heat Generated by a Current 1354 

Heating of Conductors 1354 

Heating of Coils 1355 

Fusion of Wires 1355 

Allowable Carrying Capacity of Copper Wires 1355 

Underwriters' Insulation • 1355 

Drop of Voltage in Wires Carrying Allowed Currents 1356 

Wiring Table for Motor Service 1356 

Copper-wire Table 1357, 1358 

Electric Transmission, Direct-Currents 

Section of Wire Required for a Given Current 1359 

Weight of Copper for a Given Power 1359 

Short-circuiting 1360 

Economy of Electric Transmission 1360 

Wire Table for 110, 220, 500, 1000, and 2000 volt Circuits 1360 

Efficiency of Electric Systems 1361 

Resistances of Pure Aluminium Wire 1362 

Systems of Electrical Distribution 1363 

Table of Electrical Horse-powers 1364 

Cost of Copper for Long-distance Transmission 1365 

Electric Railways 

Electric Railway Cars and Motors 1366 

A 4000-H.P. Electric Locomotive 1366 

Electric Lighting. — Ilhimination 

Illumination 1367 

Terms, Units, Definitions 1367 

Relative Color Values of Illuminants 1367 

Relation of Illumination to Vision 1367 



XXXV111 CONTENTS. 

_^ PAGE 

Arc Lamps , 1368 

Illumination by Arc Lamps at Different Distances 1368 

Data of Some Arc Lamps 1369 

Watts per Square Foot Required for Arc Lighting 1369 

The Mercury Vapor Lamp 1369 

Incandescent Lamps 1370 

Rating of Incandescent Lamps 1370 

Incandescent Lamp Characteristics 1370 

Variation in Candle-power Efficiency and Life 1371 

Performance of Tantalum and Tungsten Lamps 1372 

Specifications for Lamps 1372 

Special Lamps 1372 

Nernst Lamp 1372 

Cost of Electric Lighting 1373 

Electric Welding 1374 

Electric Heaters 1375 

Electric Furnaces " 1376 

Silundum 1377 

Electric Batteries 

Description of Storage-batteries or Accumulators 1378 

Sizes and Weights of Storage-batteries 1379 

Efficiency of a Storage Cell 1380 

Rules for Care of Storage-batteries .* 1380 

Electrolysis 1381 

Electro-chemical Equivalents 1382 

The Magnetic Circuit 

Lines and Loops of Force '. 1383 

Values of B and H 1384 

Tractive or Lifting Force of a Magnet 1384 

Determining the Polarity of Electro-magnets 1385 

Determining the Direction of a Current 1385 

Dynamo-electric Machines 

Kinds of Machines as regards Manner of Winding 1385 

Moving Force of a Dynamo-electric Machine 1386 

Torque of an Armature 1386 

Torque, Horse-power and Revolutions 1386 

Electro-motive Force of the Armature Circuit 1386 

Strength of the Magnetic Field 1387 

Alternating Currents 

Maximum, Average and Effective Values 1388 

Frequency 1388 

Inductance 1389 

Capacity 1389 

Power Factor 1389 

Reactance, Impedance, Admittance 1390 

Skin Effect 1390 

Ohm's Law Applied to Alternating Current Circuits 1390 

Impedance Polygons 1390 

Self-inductance of Lines and Circuits 1393 

Capacity of Conductors 1394 

Single-phase and Polyphase Currents 1394 

Measurement of Power in Polyphase Circuits 1395 

Alternating Current Circuits 

Calculation of Alternating Current Circuits 1396 

Relative Weight of Copper Required in Different Systems 1398 

Rule for Size of Wires for Three-phase Transmission Lines 1398 

Notes on High-tension Transmission 1398 



CONTENTS. XXXIX 

Transformers, Converters, etc. 

PAGE 

Transformers 1400 

Converters 1401 

Mercury Arc Rectifiers . . 1401 

Electric Motors 

Classification of Motors 1401 

The Auxiliary-pole Type of Motors 1402 

Speed of Electric Motors 1403 

Speed Control of Motors. Rheostats 1404 

Selection of Motors for Different Kinds of Service 1405 

The Electric Drive in the Machine Shop 1407 

Choice of Motors for Machine Tools 1407 

Alternating Current Motors 

Synchronous Motors 1408 

Induction Motors 1409 

Induction Motor Applications 1409 

Alternating Current Motors for Variable Speed 1412 

Sizes of Electric Generators and Motors 

Direct-connected Engine-driven Generators 1412 

Belt-driven Generators 1412 

Belt-driven Motors 1413 

Belt-driven Alternators 1413 

Machines with Commutating Poles 1413 

Small Engine-driven Alternators 1414 

Railway Motors 1414 

Small Polyphase, Single-phase, and Direct-current Motors 1415 

Symbols Used in Electrical Diagrams 1416 



NAMES AND ABBREVIATIONS OF PERIODICALS AND 
TEXT-BOOKS FREQUENTLY REFERRED TO IN 
THIS WORK. 



Am. Mach. American Machinist. 

App. Cyl. Mech. Appleton's Cyclopaedia of Mechanics, Vols. I and II. 

Bull. I. & S. A. Bulletin of the American Iron and Steel Association. 

Burr's Elasticity and Resistance of Materials. 

Clark, R. T. D. D. K. Clark's Rules, Tables, and Data for Mechanical En- 
gineers. 

Clark, S. E. D. K. Clark's Treatise on the Steam-Engine. 

Col. Coll. Qly. Columbia College Quarterly. 

El. Rev. Electrical Review. 

El. World. Electrical World and Engineer. 

Engg. Engineering (London). 

Eng. News. Engineering News. 

Eng. Rec. Engineering Record. 

Engr. The Engineer (London). 

Fairbairn's Useful Information for Engineers. 

Flynn's Irrigation Canals and Flow of Water. 

Indust. Eng. Industrial Engineering. 

Jour. A. C. I. W. Journal of American Charcoal Iron Workers' Association. 

Jour. Ass. Eng. Soc. Journal of the Association of Engineering Societies. 

Jour. F. I. Journal of the Franklin Institute. 

Kapp's Electric Transmission of Energy. 

Lanza's Applied Mechanics. 

Machy. Machinery. 

Merriman's Strength of Materials. 

Modern Mechanism. Supplementary volume of Appleton's Cyclopaedia of 
Mechanics. 

Peabody's Thermodynamics. 

Proc. A. S. H. V. E. Proceedings Am. Soc'y of Heating and Ventilating 
Engineers. 

Proc. A. S. T. M. Proceedings Amer. Soc'y for Testing Materials. 

Proc. Inst. C. E. Proceedings Institution of Civil Engineers (London). 

Proc. Inst. M. E. Proceedings Institution of Mechanical Engineers (Lon- 
don). 

Proceedings Engineers' Club of Philadelphia. 

Rankine, S. E. Rankine's The Steam Engine and- other Prime Movers. 

Rankine's Machinery and Millwork. 

Rankine, R. T. D. Rankine's Rules, Tables, and Data. 

Reports of U. S. Iron and Steel Test Board. 

Reports of U. S. Testing Machine at Watertown, Massachusetts. 

Rontgen's Thermodynamics. 

Seaton's Manual of Marine Engineering. 

Hamilton Smith, Jr.'s Hydraulics. 

Stevens Indicator. Stevens Institute Indicator. 

Thompson's Dynamo-electric Machinery. 

Thurston's Manual of the Steam Engine. 

Thurston's Materials of Engineering. 

Trans. A. I. E. E. Transactions American Institute of Electrical Engineers. 

Trans. A. I. M. E. Transactions American Institute of Mining Engineers. 

Trans. A. S. C. E.' Transactions American Society of Civil Engineers. 

Trans. A. S. M. E. Transactions American Society of Mechanical Engineers. 

Trautwine's Civil Engineer's Pocket Book. 

The Locomotive (Hartford, Connecticut). 

Unwin's Elements of Machine Design. 

Weisbach's Mechanics of Engineering. 

Wood's Resistance of Materials. 

Wood's Thermodynamics. 



MATHEMATICS. 













Greek Letters 










A 


a 


Alpha 


H 


V 


Eta 


N v 


Nu 


T 


T 


Tau 


B 





Beta 


© 


&e 


Theta 


a i 


Xi 


Y 


V 


Upsilon 


r 


V 


Gamma 


I 


i 


Iota 


o 


Omicron 


<D 


4> 


Phi 


A 


5 


Delta 


K 


K 


Kappa 


n tt 


Pi 


X 


X 


Chi 


E 


6 


Epsilou 


A 


\ 


Lambda 


p p 


Kho 


* 


^ 


Psi 


Z 


i 


Zeta 


M 


f* 


Mu 


2 <rs 


Sigma 


o 


O) 


Omega 



Arithmetical and Algebraical Signs and Abbreviations. 



4- plus (addition). 
+ positive. 

— minus (subtraction). 

— negative. 

± plus or minus. 
T minus or plus. 
= equals. 
X multiplied by. 
ab or a.b = a X b. 
-v- divided by. 
/ divided by. 

£ = a/6 = a h- 6. 15-16 = J|- 

O 9 p lb 

2- ^0.002- — 

V square root. 

^/ cube root. 

tf 4th root. 

: is to, :: so is, : to (proportion). 

2 : 4 :: 3 : 6, 2 is to 4 as 3 is to 6. 

: ratio; divided by. 

2 : 4, ratio of 2 to 4 = 2/4. 

.". therefore. 

> greater than. 

< less than. 

□ square. 

G round. 

° degrees, arc or thermometer. 

'minutes or feet. 

* seconds or inches. 

' " '" accents to distinguish letters, 
as a', a", a'". 

fli, 0,2, a 3 , at, a c , read a sub 1, a sub 
6, etc. 

( ) [ ] \ \ parenthesis, brackets, 

braces, vinculum ; denoting 
that the numbers enclosed are 
to be taken toget her; as, 
(a + b)c = 4 + 3 X 5 = 35. 

a 2 , a 3 , a squared, a cubed. 

a n , a raised to the nth power. 



-. a- 2 = 



a 2 



10 9 = 10 to the 9th power = 

1,000,000,000. 
sin a = the sine of a. 
sin - 1 a = the arc whose sine is a. 
1 



sin a -1 



sin 



log = logarithm, 
loge or hyp log == hyperbolic loga- 
rithm. 
% per cent. 
A angle. 



L right angle. 
J. perpendicular to. 
sin, sine. 
cos, cosine, 
tan, tangent, 
sec, secant, 
versin, versed sine, 
cot, cotangent, 
cosec, cosecant, 
covers, co-versed sine. 

In Algebra, the first letters of 
the alphabet, a, b, c, d, etc., are 
generally used to denote known 
quantities, and the last letters, 
w, x, y, z, etc., unknown quantities. 

Abbreviations and Symbols com- 
monly used, 
d, differential (in calculus). 






integral (in calculus). 



integral between limits a and b. 



A, delta, difference. 

2, sigma, sign of summation. 

7r, pi, ratio of circumference of 

circle to diameter = 3.14159. 
g, acceleration due to gravity = 

32.16 ft. per second per second. 

Abbreviations frequently used in 

this Book. 
L., 1., length in feet and inches. 
B., b., breadth in feet and inches. 
D., d., depth or diameter. 
H., h., height, feet and inches. 
T., t., thickness or temperature. 
V., v., velocity. 
F., force, or factor of safety', 
f., coefficient of friction. 
E., coefficient of elasticity. 
R., r., radius. 
W., w., weight. 
P., p., pressure or load. 
H.P., horse-power. 
I.H.P., indicated horse-power. 
B.H.P., brake horse-power, 
h. p., high pressure. 
i. p., intermediate pressure. 
1. p., low pressure. 
A.W.G., American Wire Gauge 

(Brown & Sharpe). 
B.W.G., Birmingham Wire Gauge. 
r. p. m., or revs, per min., revolu- 
tions per minute. 
Q. = quantity, or volume. 



ARITHMETIC. 



ARITHMETIC. 

The user of this book is supposed to have had a training in arithmetic as 
Well as in elementary algebra. Only those rules are given here which are 
apt to be easily forgotten. 

GREATEST COMMON MEASURE, OR GREATEST 
COMMON DIVISOR OF TWO NUMBERS. 

Rule. — Divide the greater number by the less; then divide the divisor 
by the remainder, and so on, dividing always the last divisor bv the last 
remainder, until there is no remainder, and the last divisor is the greatest 
common measure required. 



LEAST COMMON 31ULTIPLE OF TWO OR MORE 
NUMBERS. 

Rule. — Divide the given numbers by any number that will divide the 
greatest number of them without a remainder, and set the quotients with 
the undivided numbers in a line beneath. 

Divide the second line as before, and so on, until there are no two num- 
bers that can be divided; then the continued product of the divisors, last 
quotients, and undivided numbers will give the multiple required. 

FRACTIONS. 

To reduce a common fraction to its lowest terms. — Divide both 

terms by their greatest common divisor: 39/ 52 = 3/ 4 . 

To change an improper fraction to a mixed number. — Divide the 
numerator by the denominator; the quotient is the whole number, and 
the remainder placed over the denominator is the fraction: 39/ 4 = 93/4. 

To change a mixed number to an improper fraction. — Multiply 
the whole number by the denominator of the fraction; to the product add 
the numerator; place the sum over the denominator: 17/g = i5/ 8 . 

To express a whole number in the form of a fraction with a given 
denominator. — Multiply the whole number by the given denominator, 
and place the product over that denominator: 13 = 39/ 3 . 

To reduce a compound to a simple fraction, also to multiply 
fractions. — Multiply the numerators together for a new numerator and 
the denominators together for a new denominator: 

2 . 4 8 . 2 . , 4 8 
3° f 3 = 9' alS ° 3 X 3 = 9- 

To reduce a complex to a simple fraction. — The numerator and 
denominator must each first be given the form of a simple fraction; then 
multiply the numerator of the upper fraction by the denominator of the 
lower for the new numerator, and the denominator of the upper by the 
numerator of the lower for the new denominator: 

_7/8_ = 7/8 = 28 = 1 
13/ 4 7/4 56 2' 

To divide fractions. — Reduce both to the form of simple fractions, 
invert the divisor, and proceed as in multiplication: 

3 = 3_ i _5 = 34 = 12 = 3 

4 /4 4 ' 4 4 X 5 20 5' 

Cancellation of fractions. — In compound or multiplied fractions, 
divide any numerator and any denominator by any number which will 
divide them both without remainder, striking out the numbers thus 
divided and setting down the quotients in their stead. 

To reduce fractions to a common denominator. — Reduce each 
fraction to the form of a simple fraction; then multiply each numerator 



DECIMALS. 



by all the denominators except its own for the new numerator, and all 
the denominators together for the common denominator: 



21 
42' 



To add fractions. — Reduce them to a common denominator, then 
add the numerators and place their sum over the common denominator: 



7 



42 



42 



= 111/42. 



To subtract fractions. — Reduce them to a common denominator, 
subtract the numerators and place the difference over the common denom- 
inator: 

1 _ 3 7-6 = 1_ 

2 7 ^ 14 14 



DECIMALS. 

To add decimals. — Set down the figures so that the decimal points 
are one above the other, then proceed as in simple addition: 18.75' -f 0.012 
= 18.762. 

To subtract decimals. — Set down the figures so that the decimal 
points are one above the other, then proceed as in simple subtraction: 
18.75 - 0.012 = 18.738. 

To multiply decimals. — Multiply as in multiplication of whole num- 
bers, then point off as many decimal places as there are in multiplier and 
multiplicand taken together: 1.5 X 0.02 = .030 = 0.03. 

To divide decimals. — Divide as in whole numbers, and point off in 
the quotient as many decimal places as those in the dividend exceed those 
in the divisor. Ciphers must be added to the dividend to make its decimal 
places at least equal those in the divisor, and as many more as it is desired 
to have in the quotient: 1.5 + 0.25 = 6. 0.1 -J- 0.3 = 0.10000 -*• 0.3 
= 0.3333 +. 





Decimal Equivalents of Fractions of One Inch. 




1-64 


.015625 


17-64 


.265625 


33-64 


.515625 


49-64 


.765625 


1-32 


.03125 


9-32 


.28125 


17-32 


.53125 


25-32 


.78125 


3-64 


.046875 


19-64 


.296875 


35-64 


.546875 


51-64 


.796875 


1-16 


.0625 


5-16 


.3125 


9-16 


.5625 


13-16 


.8125 


5-64 


.078125 


21-64 


.328125 


37-64 


.578125 


53-64 


.828125 


3-32 


.09375 


11-32 


.34375 


19-32 


.59375 


27-32 


.84375 


7-64 


.109375 


23-64 


.359375 


39-64 


.609375 


55-64 


.859375 


1-8 


.125 


3-8 


.375 


5-8 


.625 


7-8 


.875 


9-64 


.140625 


25-64 


.390625 


41-64 


.640625 


57-64 


.890625 


5-32 


.15625 


13-32 


.40625 


21-32 


.65625 


29-32 


.90625 


11-64 


.171875 


27-64 


.421875 


43-64 


.671875 


59-64 


.921875 


3-16 


.1875 


7-16 


.4375 


11-16 


.6875 


15-16 


.9375 


13-64 


.203125 


29-64 


.453125 


45-64 


.703125 


61-64 


.953125 


7-32 


.21875 


15-32 


.46875 


23-32 


.71875 


31-32 


.96875 


15-64 


.234375 


31-64 


.484375 


47-64 


.734375 


63-64 


.984375 


1-4 


.25 


1-2 


.50 


3-4 


.75 


1 


1. 



To convert a common fraction into a decimal. — Divide the nume- 
rator by the denominator, adding to the numerator as many ciphers 
prefixed by a decimal point as are necessary to give the number of decimal 
places desired in the result: 1/3 = 1.0000 + 3 = 0.3333 +. • 

To convert a decimal into a common fraction. — Set down the 
decimal as a numerator, and place as the denominator 1 with as many 
ciphers annexed as there are decimal places in the numerator; erase the 



rH 




ARITHMETIC. 

o 


Uilffl 


o m 
oo t>. 
i>. en 

00 ON 


t-lOO-* 


nO en © 
mom 
no «s r>. 
t>. 00 -co 




— o r>. in 
o o — cN 

vO — vO — 

«© t>. r> oq 


n|* 


in T en — © 
O) On nO en © 
no © in © in 
in vq n© t>. |>» 


M|50 

Hh 


fo nO no no in m 
eN in ao — T r* 
r^ — in o T co 
T m in \0 •© no 


io|oo 


vO l>» 00 00 On On O 

O On oo r>. vO m m 

On CN vO © T 00 tM 

en ■* ->r in in in no 


J® 


■^TNOrxONOCNlcriin 

no — no — r»«^t>.c^ 
— inoor^inONCNiNO 
en en en ■* ->r "T in in 


■h|(M 




oenmoooenmooo 
O — cn) en in no r-»« oo © 
inoo — •*t>.0<nNOO 




< 




too — Too — moocNin 

— oONOmoooinfNOt>. 
On — T l>« © cn in ao — en 

— tNeN«NtncnencnTT 




cc]w 




vO — inON-^-oocnrv. — voo 
© T r^ © t r>. — Too — m 
Tnooo — mmoootNint-N 
— — — tNcMcNCNentncncn 




■* 


rxfNjt^tNaOcnoo-TON-q-om 
i->t-NNONOinm-<T-q-cnenmcs| 
On — mint>.ON — mint^.ON"- 
© — — — ; — — CNj cvj cm cs cn| en 


H« 




in — t^mONOcsONin — r->^ro 
cN]oo<nONin©NO — r>. en oo T © 
vOt^ON©eNTint>.oo© — en>n 

OOO — — — — — — N N N N 




* 


© 


ONNOcnOooincNONNOcn"— oom 
NOooOfNcninh>ooOfN"^-mr>. 
T in r^ ao on © — CNjTinNor>,oo 
OOOOO — — — — — — — — 




H» 


no -«r 
m en 
— <s 

o o 


m — ONi>.incn — Onoonot«n© 
— ONNOTCNJ-Oooinm — ft N m 

rnmTmNOt->t>>a0ON©© — e» 
© © © © © © © © O — — — — 




J 50 


On 00 t-> 

o o — 

O O O 


NOinTeneneN — OOoot>.NOin 
inONtnr-'i'— inONcnNOO^aofNi 

©©©©©©©©OO©©© 




tH 


in o m 

nO fM 00 
o — — 


©in©in©in©tn©in©in 
©csln^OfNiint-NOfNinr^© 
in — i->enONoeNooin — t>.cno 
cscncnTminNONOixooaoON© 


"7 


O 


^^«pH*^e 8 »»^H B .«g-*»$«N.$H»$*H 



COMPOUND NUMBERS. 



decimal point in the numerator, and reduce the fraction thus formed to its 
lowest terms: 



«-£■ 



3333 1 
10000 = 3* neaFly - 



To reduce a recurring decimal to a common fraction. — Subtract 
the decimal figures that do not recur from the whole decimal including 
one set of recurring figures; set down the remainder as the numerator of 
the fraction, and as many nines as there are recurring figures, followed by 
as many ciphers as there are non-recurring figures, in the denominator. 
Thus: 

0.79054054, the recurring figures being 054. 
Subtract 79 

78975 , , , . .. . % 117 

■ QQQnn = (reduced to its lowest terms) — -• 



COMPOUND OR DENOMINATE NUMBERS. 

Reduction descending. — To reduce a compound number to a lower 
denomination. Multiply the number by as many units of the lower 
denomination as makes one of the higher. 

3 yards to inches: 3 X 36 = 108 inches. 

0.04 square feet to square inches: .04 X 144 = 5.76 sq. in. 

If the given number is in more than one denomination proceed in steps 
from the highest denomination to the next lower, and so on to the lowest, 
adding in the units of each denomination as the operation proceeds. 

3 yds. 1 ft. 7 in. to inches: 3X3 = 9, +1 = 10, 10 X 12 = 120, +7 = 127 in. 

Reduction ascending. — To express a number of a lower denomina- 
tion in terms of a higher, divide the number by the number of units of 
the lower denomination contained in one of the next higher; the quotient 
is in the higher denomination, and the remainder, if any, in the lower. 
127 inches to higher denomination. 
127 -s- 12 = 10 feet + 7 inches; 10 feet -=-3 = 3 yards + 1 foot. 

Ans. 3 yds. 1 ft. 7 in. 

To express the result in decimals of the higher denomination, divide the 
given number by the number of units of the given denomination contained 
in one of the required denomination, carrying the result to as many places 
of decimals as may be desired. 



127 inches to yards: 127 • 



36 



= 319/36 = 3.5277 + yards. 



Decimals of a Foot Equivalent to Inches and Fractions 
of an Inch. 



Inches 





H 


K 


% 


l A 


H 


H 


%■ 








.01042 


.02083 


.03125 


.04167 


.05208 


.06250 


.07292 


1 


.0833 


.0938 


.1042 


.1146 


.1250 


.1354 


.1458 


.1563 


2 


.1667 


.1771 


.1875 


.1979 


.2083 


.2188 


.2292 


.2396 


3 


.2500 


.2604 


.2708 


.2813 


.2917 


.3021 


.3125 


.3229 


4 


.3333 


.3438 


.3542 


.3646 


.3750 


.3854 


.3958 


.4063 


5 


.4167 


.4271 


.4375 


.4479 


.4583 


.4688 


.4792 


.4896 


6 


.5000 


.5104 


.5208 


.5313 


.5417 


.5521 


.5625 


.5729 


7 


.5833 


.5938 


.6042 


.6146 


.6250 


.6354 


.6458 


.6563 


8 


.6667 


.6771 


.6875 


.6979 


.7083 


.7188 


.7292 


.7396 


9 


.7500 


.7604 


.7708 


.7813 


.7917 


.8021 


.8125 


.8229 


10 


.8333 


.8438 


.8542 


.8646 


.8750 


.8854 


.8958 


.9063 


11 


.9167 


.9271 


.9375 


.9479 


.9583 


.9688 


.9792 


.9896 



ARITHMETIC. 



RATIO AND PROPORTION. 

Ratio is the relation of one number to another, as obtained by dividing 
the first number by the second. Synonymous with quotient. 

Ratio of 2 to 4, or 2 : 4 = 2/ 4 = l/ 2 . 
Ratio of 4 to 2, or 4 : 2 = 2. 

Proportion is the equality of two ratios. Ratio of 2 to 4 equals ratio 
of 3 to 6, 2/ 4 =3/ 6; expressed thus, 2 : 4 :: 3 : 6; read, 2 is to 4 as 3 is to 6. 

The first and fourth terms are called the extremes or outer terms, the 
second and third the means or inner terms. 

The product of the means equals the product of the extremes: 

2 : 4 : : 3 : 6; 2 X 6 = 12; 3 X 4 = 12. 

Hence, given the first three terms to find the fourth, multiply the 
second and third terms together and _di vide by the first. 

2 : 4 : : 3 : what number? Ans. — £— = 6. 

Algebraic expression of proportion. — a : b : : c : d; - = -; ad =■ be; 

, ... be , be , ad ad 

from which a =• ~? ; d= — ;&= — ; c = -r- • 
d a c b 

From the above equations may also be derived the following: 

& : a : : d : e a + b 

a : c : :b : d a + b 

a : b = c : d a — b 

a — b 



a : :c + d : c a + b : a — b : : c + d ; 
6 : : c + d : d a n : b"> : : c n : d™ 

y~a\ ^jb: :^/c y~d 



b::c - d 
a : :c — d 



Mean proportional between two given numbers, 1st and 2d, is such 
a number that the ratio which the first bears to it equals the ratio which it 
bears to the second. Thus, 2:4::4:8;4isa mean proportional between 

2 and 8. To find the mean proportional between two numbers, extract 
the square root of their product. 

Mean proportional of 2 and 8 = "^2 X 8 ■=• 4. 

Single Rule of Three; or, finding the fourth term of a proportion 
when three terms are given. — Rule, as above, when the terms are stated 
in their proper order, multiply the second by the third and divide by the 
first. The difficulty is to state the terms in their proper order. The 
term which is of the same kind as the required or fourth term is made the 
third; the first and second must be like each other in kind and denomina- 
tion. To determine which is to be made second and which first requires 
a little reasoning. If an inspection of the problem shows that the answer 
should be greater than the third term, then the greater of the other two 
given terms should be made the second term — otherwise the first. Thus, 

3 men remove 54 cubic feet of rock in a day; how many men will remove 
in the same time 10 cubic yards? The answer is to be men — make men 
third term; the answer is to be more than three men, therefore make the 
greater quantity, 10 cubic yards, the second term; but as it is not the same 
denomination as the other term it must be reduced, = 270 cubic feet. 
The proportion is then stated: 

3 X 270 
54 : 270 : : 3 : x (the required number); x = — — — = 15 men. 

The problem is more complicated if we increase the number of given 
terms. Thus, in the above question, substitute for the words "in the 
same time" the words " in 3 days." First solve it as above, as if the work 
were to be done in the same time; then make another proportion, stating 
it thus: If 15 men do it in the same time, it will take fewer men to do it in 
3 days; make 1 day the second term and 3 days the first term. 3:1:: 
15 men : 5 men. 



POWERS OF NUMBERS. 



Compound Proportion, or Double Rule of Three. — By this rule 
are solved questions like the one just given, in which two or more statings 
are required by the single rule of three. In it, as in the single rule, there 
is one third term, which is of the same kind and denomination as the 
fourth or required term, but there may be two or more first and second 
terms. Set down the third term, take each pair of terms of the same kind 
separately, and arrange them as first and second by the same reasoning as 
is adopted in the single rule of three, making the greater of the pair the 
second if this pair considered alone should require the answer to be greater. 

Set down all the first terms one under the other, and likewise all the 
second terms. Multiply all the first terms together and all the second 
terms together. Multiply the product of all the second terms by the third 
term, and divide this product by the product of all the first terms. 
Example: If 3 men remove 4 cubic yards in one day, working 12 hours a 
day, how many men working 10 hours a day will remove 20 cubic yards 
in 3 days? 



Yards 
Days 
Hours 



4: 

3 : 

10 : 



3 men. 



Products 120 : 240 : : 3 : 6 men. Ans. 

To abbreviate by cancellation, any one of the first terms may cancel 
either the third or any of the second terms; thus, 3 in first cancels 3 in 
third, making it 1, 10 cancels into 20 making the latter 2, which into 4 
makes it 2, which into 12 makes it 6, and the figures remaining are only 
1 : 6 : : 1 : 6. 



INVOLUTION, OR POWERS OF NUMBERS. 

Involution is the continued multiplication of a number by itself a given 
number of times. The number is called the root, or first power, and the 
products are called powers. The second power is called the square and 
the third power the cube. The operation may be indicated without being 
performed by writing a small figure called the index or exponent to the 
right of and a little above the root; thus, 3 3 = cube of 3, = 27. 

To multiply two or more powers of the same number, add their expo- 
nents; thus, 2 2 X 2 3 = 2 5 , or 4 X 8 = 32 = 2 5 . 

To divide two powers of the same number, subtract their exponents; 

thus, 2 3 h- 2 2 » 2 1 = 2; 2 2 -t- 2* = 2~ 2 = j 2 = | • The exponent may 

thus be negative. 2 3 -f- 2 3 = 2° = 1, whence the zero power of any 
number = 1. The first power of a number is the number itself. The 
exponent may be fractional, as 2^, 2i, which means that the root is to be 
raised to a power whose exponent is the numerator of the fraction, and 
the root whose sign is the denominator is to be extracted (see Evolution). 
The exponent may be a decimal, as 2 0#5 , 2 1-6 ; read, two to the five-tenths 
power, two to the one and five-tenths power. These powers are solved by 
means of Logarithms (which see). 

First Nine Powers of the First Nine Numbers. 



0) 


T3 % 
N O 


3^ 

C<~1 Q 


4th 


5th 


6th 


7th 


8th 


9th 


Power. 


Power. 


Power. 


Power. 


Power. 


Power. 


Ph 


P4 


Ph 














1 

2 


1 

4 


1 
8 


1 
16 


1 

32 


1 
64 


1 
128 


1 
256 


1 

512 


3 


9 


27 


81 


243 


729 


2187 


6561 


19683 


4 


16 


64 


256 


1024 


4096 


16384 


65536 


262144 


5 


25 


125 


625 


3125 


15625 


78125 


390625 


1953125 


6 


36 


216 


1296 


7776 


46656 


279936 


1679616 


10077696 


7 


49 


343 


2401 


16807 


1 1 7649 


823543 


5764801 


40353607 


8 


64 


512 


4096 


32768 


262144 


2097152 


16777216 


134217728 


9 


81 


729 


6561 


59049 


531441 


4782969 


43046721 


387420489 



ARITHMETIC, 



The First Forty Powers of 3. 







01 


i 


CD 


P4 


1 




3- 


to 

o 


i 





1 


9 


512 


18 


262144 


27 


134217728 


36 


68719476736 


1 


2 


10 


1024 


19 


52428S 


28 


268435456 


37 


137438953472 


2 


4 


11 


2048 


20 


1048576 


29 


536870912 


38 


274877906944 


3 


8 


12 


4096 


21 


2097152 


30 


1073741824 


39 


549755813888 


4 


16 


13 


8192 


22 


4194304 


31 


2147483648 


40 


1099511627776 


5 


32 


14 


16384 


23 


8388608 


32 


4294967296 






6 


64 


15 


32768 


24 


16777216 


33 


8589934592 






7 


128 


16 


65536 


25 


33554432 


34 


17179869184 






8 


256 


17 


131072 


26 


67108864 


35 


34359738368 







EVOLUTION. 

Evolution is the finding of the root (or extracting the root) of any 
number the power of which is given. 

The sign V indicates that the square root is to be extracted : ^J ty y f 
the cube root, 4th root, nth root. 

A fractional exponent with 1 for the numerator of the fraction is also 
used to indicate that the operation of extracting the root is to be per- 
formed; thus, 2*, 2* = \J2, <\/2. 

When the power of a number is indicated, the involution not being per- 
formed, the extraction of any root of that power may also be indicated by 
dividing the index of the power by the index of the root, indicating the 
division by a fraction. Thus, extract the square root of the 6th power 
of 2: _ 

V2 6 = 2§ = 2* = 2 3 = 8. 

The 6th power of 2, as in the table above, is 64; V64 = 8. 

Difficult problems in evolution are performed by logarithms, but the 
square root and the cube root may be extracted directly according to the 
rules given below. The 4th root is the square root of the square root. 
The 6th root is the cube root of the square root, or the square root of the 
cube root; the 9th root is the cube root of the cube root; etc. 

To Extract the Square Root. — Point off the given number into 
periods of two places each, beginning with units. If there are decimals, 
point these off likewise, beginning at the decimal point, and supplying 
as many ciphers as may be needed. Find the greatest number whose 
square is less than the first left-hand period, and place it as the first 
figure in the quotient. Subtract its square from the left-hand period, 
and to the remainder annex the two figures of the second period for 
a dividend. Double the first figure of the quotient for a partial divisor; 
find how many times the latter is contained in the dividend exclusive 
of the right-hand figure, and set the figure representing that number of 
times as the second figure in the quotient, and annex it to the right of 
the partial divisor, forming the complete divisor. Multiply this divisor 
by the second figure in the quotient and subtract the product from the 
dividend. To the remainder bring down the next period and proceed as 
before, in each case doubling the figures in the root already found to obtain 
the trial divisor. Should the product of the second figure in the root by 
the completed divisor be greater than the dividend, erase the second 
figure both from the quotient and from the divisor, and substitute the 
next smaller figure, or one small enough to make the product of the second 
figure by the divisor less than or equal to the dividend. 



CUBE ROOT. 



SQUARE ROOT. 

3.1415926536 LL77245 + 

1 

271214 
1189 
34712515 
|2429 
3542 8692 
7084 
160865 
141776 



35444 



35448511908936 

11772425 



CUBE ROOT. 

1,881,365.963.6251 12345 

1 

300 XI 2 = 300 881 
30 X 1 X 2 = 60 

2 2 = 4 

364J728 



300 X 122 
30 X 12 



= 43200 
X 3 = 1080 

32 = 9 

44289 



153365 



300 X 123 2 = 4538700 

30 X 123 X 4 = 14760 

42= 16 



300 X 1234 2 =456826800 

30X1234X5= 185100 

5 2 = 25 



457011925 



2285059625 



To extract the square root of a fraction, extract the root of a numerator 
and denominator separately. 



a decimal, 



VI 



sjl 



■■ V.4444 + = 0.6 



3 + . 



To Extract the Cube Root. — Point off the number into periods of 3 
figures each, beginning at the right hand, or unit's place. Point off 
decimals in periods of 3 figures from the decimal point. Find the greatest 
cube that does not exceed the left-hand period; write its root as the first 
figure in the required root. Subtract the cube from the left-hand period, 
and to the remainder bring down the next period for a dividend. 

Square the first figure of the root; multiply by 300, and divide the 
product into the dividend for a trial divisor; write the quotient after 
the first figure of the root as a trial second figure. 

Complete the divisor by adding to 300 times the square of the first 
figure, 30 times the product of the first by the second figure, and the 
square of the second figure. Multiply this divisor by the second figure; 
subtract the product from the remainder. (Should the product be greater 
than the remainder, the last figure of the root and the complete divisor 
are too large; substitute for the last figure the next smaller number, and 
correct the trial divisor accordingly.) 

To the remainder bring down the next period, and proceed as before to 
find the third figure of the root — that is, square the two figures of the 
root already found; multiply by 300 for a trial divisor, etc. 

If at any time the trial divisor is greater than the dividend, bring down 
another period of 3 figures, and place in the root and proceed. 

The cube root of a number will contain as many figures as there are 
periods of 3 in the number. 

To Extract a Higher Root than the Cube. — The fourth root is the 
square root of the square root; the sixth root is the cube root of the square 
root or the square root of the cube root. Other roots are most conve- 
niently found by the use of logarithms. 



ALLIGATION. 

shows the value of a mixture of different ingredients when the quantity 
and value of each are known. 

Let the ingredients be a, b, c, d, etc., and their respective values per 
unit w, x, y, z, etc. 



10 ARITHMETIC. 

A = the sum of the quantities = a+b+c+d, etc. 
P = mean value or price per unit of A. 
AP = aw + bx + cy + dz, etc. 
p _ aw + bx 4- cy 4- oz 

PERMUTATION 

shows in how many positions any number of things may be arranged in a 
row; thus, the letters a, b, c may be arranged in six positions, viz. abc, acb, 
cab, cba, bac, bca. 

Rule. — Multiply together all the numbers used in counting the things; 
thus, permutations of 1, 2, and 3 = 1X2X3 = 6. In how many 
positions can 9 things in a row be placed? 

1X2X3X4X5X6X7X8X9 = 362880. 

COMBINATION 

shows how many arrangements of a few things may be made out of a 
greater number. Rule: Set down that figure which indicates the greater 
number, and after it a series of figures diminishing by 1, until as many are 
set down as the number of the few things to be taken in each combination. 
Then beginning under the last one, set down said number of few things; 
then going backward set down a series diminishing by 1 until arriving 
under the first of the upper numbers. Multiply together ail the upper 
numbers to form one product, and all the lower numbers to form another; 
divide the upper product by the lower one. 

How many combinations of 9 things can be made, taking 3 in each com- 

binati0n? 9X8X7 = 504 = S4 

1X2X3 6 

ARITHMETICAL PROGRESSION, 

in a series of numbers, is a progressive increase or decrease in each succes- 
sive number by the addition or subtraction of the same amount at each 
step, as I-, 2, 3, 4, 5, etc., or 15, 12, 9, 6, etc. The numbers are called terms, 
and the equal increase or decrease the difference. Examples in arithmeti- 
cal progression may be solved by the following formulse: 

Let a = first term, I «= last term, d = common difference, n = number 
of terms, s = sum of the terms: 



I = a + (n — l)d, 

2s 
= — — a, 
n 

s = -ft [2a 4- (n - l)d], 

= (Z + a)|, 
a ^l - (n - l)d, 




-!<*±v/(' + H ! - 

, l - a 

I 2 - a* - 

2s - I - a 

I — a , , 
r - — -7— 4- 1, 

d 

=. 2s 
*~ I + a' 


■ 2ds, 



~\d± \f2ds + (c 
s (n — l)d 
n + 2 
I + a I 2 - a 2 
2 + 2d * 


\n\2l - in - l)d]. 


s 
n 
2s 
n 
2(s - 


(ft - l)d 

2 

L 

- an) , 


n (ft 
2{nl 
n(n 


-1) ' 

- s) 

- 1) 


d - 


2a ± V(2a - 



«-H* 




dy + 



21 4- d ± ^{21 4- d) 2 - 



GEOMETRICAL PROGRESSION. 



11 



GEOMETRICAL PROGRESSION. 

in a series of numbers, is a progressive increase or decrease in each suc- 
cessive number by the same multiplier or divisor at each step, as 1, 2, 4, 8, 
16, etc., or 243, 81, 27, 9, etc. The common multiplier is called the ratio. 
Let a = first term, I = last term, r = ratio or constant multiplier, n = 
number of terms, m = any term, as 1st, 2d, etc., s = sum of the terms: 



I = ar n ~ l , 

log I = log a + (n ■ 
m = arm-i 



_ a + (r — l)-s 
r 
l)logr, l(s - t)n-i - 

log m = log a + (m — 1) log r. 



. (r - l)srw 



a(s - a)n-i = 



rl — a 




~<Jl n ~ n V«" lrn-l 

log a = log I — (n — .1) log r. 



r n . 



log r ..== '- 



log r 

log Z — log a 



" log ( 



■ a) - log (s - 



log I — log a 
i - 1 

i — l ■' ' s- I 

log [a + (r — l)s] — log a 

logr 
logZ - logRr - (r - l)s] 



0. 



+ 1. 



Population of the United States. 

(A problem in geometrical progression.) 



Year. 


Population. 


1860 


31,443,321 


1870 


39,818,449* 


1880 


50,155,783 


1890 


62,622,250 


1900 


76,295,220 


1905 


Est. 83,577,000 


1910 


" 91,554,000 



Increase in 10 Annual Increase,; 
Years, per cent. per cent. 



26.63 
25.96 

24.86 
21.834 

Est. 20.0 



2.39 
2.33 
2.25 
1.994 
Est. 1.840 
" 1.840 



Estimated Population in Each Year from 1870 to 1909. 
(Based on the above rates of increase, in even thousands.) 



1870.... 


39,818 


1880 


50, 1 56 


1890 


62,622 


1900... 


76,295 


1871 


40,748 


1881 


51,281 


1891 


63,871 


1901... 


77,699 


1872 


41,699 


1882 


52,433 


1892;... 


65, 1 45 


1902... 


79,129 


1873 


42,673 


1883 


53,610 


1893 


66,444 


1903... 


80,585 


1874.... 


43,670 


1884 


54,813 


1894 


67,770 


1904... 


82,067 


1875.... 


44,690 


1885.... 


56,043 


1895 


69,122 


1905... 


83,577 


1876.... 


45,373 


1886 


57,301 


1896.... 


70,500 


1906... 


85,115 


1877.... 


46,800 


1887 


58,588 


1897 


71,906 


1907... 


86,681 


1878 


47,893 


1888 


59,903 


1898 


73,341 


1908. . . 


88,276 


1879 


49,01 1 


1889 


61,247 


1899 


74,803 


1909... 


89,900 



* Corrected by addition of 1,260,078, estimated error of the census of 
1870, Census Bulletin No. 16, Dec. 12, 1890. 



12 ARITHMETIC. 

The preceding table has been calculated by logarithms as follows: 
log r = log I — log a -5- (n — 1), log m = log a + (m — 1) log r 

Pop. 1900 . . . 76,295,220 log = 7.8824988 = log I 

" 1890. . .62,622,250 log = 7.7967285 = log a 

diff. = .0857703 
n = 11, n - 1 = 10; diff. h- 10 = .00857703 = logr, 

add log for 1890 7.7967285 = log a 

log for 1891 = 7.80530553 No. = 63,871 . . . 
add again .00857703 



log for 1892 7.81388256 No. = 65,145 . . . 
Compound interest is a form of geometrical progression; the ratio 
being 1 plus the percentage. 



PERCENTAGE: PROFIT AND LOSS: PER CENT 
OF EFFICIENCY. 

Per cent means "by the hundred." A profit of 10 per cent means a 
gain of $10 on every $100 expended. If a thing is bought for $1 and sold 
for $2 the profit is 100 per cent; but if it is bought for $2 and sold for $1 
the loss is not 100 per cent, but only 50 per cent. 

Rule for percentage: Per cent gain or loss is the gain or loss divided by 
the original cost, and the quotient multiplied by 100. 

Efficiency is defined in engineering as the quotient "output divided by 
input," that is, the energy utilized divided by the energy expended. The 
difference between the input and the output is the loss or waste of energy. 
Expressed as a fraction, efficiency is nearly always less than unity. Ex- 
pressed as a per cent, it is this fraction multiplied by 100. Thus we may 
say that a motor has an efficiency of 0.9 or of 90 per cent. 

The efficiency of a boiler is the ratio of the heat units absorbed by the 
boiler in heating water and making steam to the heating value of the coal 
burned. The saving in fuel due to increasing the efficiency of a boiler 
from 60 to 75% is not 25%, but only 20%. The rule is: Divide the gain 
in efficiency (15) by the greater figure (75). The amount of fuel used is 
inversely proportional to the efficiency; that is, 60 lbs. of fuel with 75% 
efficiency will do as much work as 75 lbs. with 60% efficiency. The 
saving of fuel is 15 lbs. which is 20% of 75 lbs. 



INTEREST AND DISCOUNT. 

Interest is money paid for the use of money for a given time; the 
factors are: 

p, the sum loaned, or the principal; 
t, the time in years; 
r, the rate of interest ; 

i, the amount of interest for the given rate and time; 
a = p + i = the amount of the principal with interest 
at the end of the time. 
Formulae: 



= interest = principal X time X rate per cent = i = 



ptr . 



a — amount = principal + interest = p + jrrr ; 

inn* 
r = rate = 

pi 
. . , lOOi ptr . 

p - pnncipal - -^ = a - — : 

lOOi 



INTEREST AND DISCOUNT. 13 

If the rate is expressed decimally as a per cent, — thus, 6 per cent 
= .06, — the formulae become 

i = prt;a = p(l + rt); r =~; *=-; p=l = — ^—. 
pV pr tr 1 + rt 

Rules for finding Interest. — Multiply the principal by the rate per 
annum divided by 100, and by the time in years and fractions of a year. 

T * 4-u i- • • -j -x principal X rate X no. of days 

If the time is given in days, interest = — l^, - ^- *±. 

obo X 100 

In banks interest is sometimes calculated on the basis of 360 days to a 
year, or 12 months of 30 days each. 

Short rules for interest at 6 per cent, when 360 days are taken as 1 year: 

Multiply the principal by number of days and divide by 6000. 

Multiply the principal by number of months and divide by 200. 

The interest of 1 dollar for one month is § cent. 



Interest of 100 Dollars for Different Times and Bates. 

Time 2% 3% 4% 5% 6% 8% 10% 

lyear $2.00 $3.00 $4.00 $5.00 $6.00 $8.00 $10.00 

1 month .16§ .25 .33| .41§ .50 .66§ .83$ 

lday= 3 ^ year .00551 .0083* .0111* .01381 .01661 .0222| .02775 
1 day= 3 &5 year .005479 .008219 .010959 .013699 .016438 .0219178.0273973 

Discount is interest deducted for payment of money before it is due. 

True discount is the difference between the amount of a debt payable 
at a future date without interest and its present worth. The present 
worth is that sum which put at interest at the legal rate will amount to 
the debt when it is due. 

To find the present worth of an amount due at a future date, divide the 
amount by the amount of $1 placed at interest for the given time. The 
discount equals the amount minus the present worth. 

What discount should be allowed on $103 paid six months before it is 
due, interest being 6 per cent per annum? 

— $100 present worth, discount = 3.00. 

1 + 1 X .06 X \ 

Bank discount is the amount deducted by a bank as interest on money 
loaned on promissory notes. It is interest calculated not on the actual 
sum loaned, but on the gross amount of the note, from which the discount 
is deducted in advance. It is also calculated on the basis of 360 days 
in the year, and for 3 (in some banks 4) days more than the time specified 
in the note. These are called days of grace, and the note is not payable 
till the last of these days. In some States days of grace have been 
abolished. 

What discount will be deducted by a bank in discounting a note for $103 
payable 6 months hence? Six months = 182 days, add 3 days grace = 185 

Compound Interest. — In compound interest the interest is added to 
the principal at the end of each year, (or shorter period if agreed upon). 

Let p = the principal, r = the rate expressed decimally, n = no. of 
years, and a the amount: 



= amount = p(l + r) n ;r = rate = 



. . , a . log a — log p 

V - principal - (1 + f)n ; no. of years- n= lQg (1 + r) • 



14 



ARITHMETIC. 



Compound Interest Table. 

(Value of one dollar at compound interest, compounded yearly, at 
3, 4, 5, and 6 per cent, from 1 to 50 years.) 



i 


Per cent 


,9 


Per cent 


& 


3 


4 


5 


6 


3 


4 


5 


6 


i 


1.03 


1.04 


1.05 


1.06 


16 


1 .6047 


1.8730 


2.1829 


2.5403 


2 


1 .0609 


1.0816 


1.1025 


1.1236 


17 


1.6528 


1 .9479 


2.2920 


2.6928 


3 


1.0927 


1.1249 


1.1576 


1.1910 


18 


1 .7024 


2.0258 


2.4066 


2.8543 


4 


1.1255 


1 . 1 699 


1.2155 


1 .2625 


19 


1.7535 


2.1068 


2.5269 


3.0256 


5 


1.1593 


1.2166 


1.2763 


1.3382 


20 


1.8061 


2.1911 


2.6533 


3.2071 


6 


1.1941 


1 .2653 


1.3401 


1.4185 


21 


1 .8603 


2.2787 


2.7859 


3.3995 


7 


1 .2299 


1.3159 


1.4071 


1.5036 


22 


1.9161 


2.3699 


2.9252 


3.6035 


8 


1 .2668 


1.3686 


1.4774 


1.5938 


23 


1.9736 


2.4647 


3.0715 


3.8197 


9 


1 .3048 


1 .4233 


1.5513 


1 .6895 


24 


2.0328 


2.5633 


3.2251 


4.0487 


10 


1.3439 


1 .4802 


1 .6289 


1.7908 


25 


2.0937 


2.6658 


3.3863 


4.2919 


11 


1 .3842 


1.5394 


1.7103 


1 .8983 


30 


2.4272 


3.2433 


4.3219 


5.7435 


12 


1.4258 


1.6010 


1.7958 


2.0122 


35 


2.8138 


3.9460 


5.5159 


7.6862 


13 


1.4685 


1.6651 


1.8856 


2.1329 


40 


3.2620 


4.8009 


7.0398 


10.2858 


14 


1.5126 


1.7317 


1 .9799 


2.2609 


45 


3.7815 


5.8410 


8.9847 


13.7648 


15 


1.5580 


1 .8009 


2.0789 


2.3965 


50 


4.3838 


7.1064 


1 1 .4670 


18.4204 



At compound interest at 3 per cent money will double itself in 23 1/2 years, 
at 4 per cent in 1 7 2/3 years, at 5 per cent in 14.2 years, and at 6 per cent in 
1 1.9 years. 

EQUATION OF PAYMENTS. 

By equation of payments we find the equivalent or average time in 
which one payment should be made to cancel a number of obligations due 
at different dates; also the number of days upon which to calculate interest 
or discount upon a gross sum which is composed of several smaller sums 
payable at different dates. 

Rule. — Multiply each item by the time of its maturity in days from a 
fixed date, taken as a standard, and divide the sum of the products by 
the sum of the items: the result is the average time in days from the stand- 
ard date. 

A owes B $100 due in 30 days, $200 due in 60 days, and $300 due in 90 
days. In how many days may the whole be paid in one sum of $600? 

100X30+200X60+300X90 = 42,000; 42,000-^-600 = 70 days, ans. 

A owes B $100, $200, and $300, which amounts are overdue respectively 
30, 60, and 90 days. If he now pays the whole amount, $600, how many 
days' interest should he pay on that sum? Ans. 70 days. 



PARTIAL PAYMENTS. 



To compute interest on notes and bonds when partial payments have 
been made. 

United States Rule. — Find the amount of the principal to the time 
of the first payment, and, subtracting the payment from it, find the 
amount of the remainder as a new principal to the time of the next pay- 
ment. 



ANNUITIES. 



15 



If the payment is less than the interest, find the amount of the principal 
to the time when the sum of the payments equals or exceeds the interest 
due, and subtract the sum of the payments from this amount. 

Proceed in this manner till the time of settlement. 

Note. — The principles upon which the preceding rule is founded are: 

1st. That payments must be applied first to discharge accrued interest, 
and then the remainder, if any, toward the discharge of the principal. 

2d. That only unpaid principal can draw interest. 

Mercantile Method. — When partial payments are made on short 
notes or interest accounts, business men commonly employ the following 
method: 

Find the amount of the whole debt to. the time of settlement; also find 
the amount of each payment from the time it was made to the time of 
settlement.. Subtract the amount of payments from the amount of the 
debt: the remainder will be the balance due. 



ANNUITIES. 

An Annuity is a fixed, sum of money paid yearly, or at other equal times 
agreed upon. The values of annuities are calculated by the principles of 
compound interest. 

1. Let i denote interest on $1 for a year, then at the end of a year the 
amount will be 1 + i. At the end of n years it will be (1 + i) n . 

2. The sum which in-n years will amount to 1 is or (1 + i) ~ n t 
or the present value of 1 due in n years. 

3. The amount of an annuity of 1 in any number of years n is 

4. The present value of an annuity of 1 for any number of years n is 
1 - (l + t)-» 



(l + i) n -l 



5. The annuity which 1 will purchase for any number of years n is 



1 - (1 + i)~ n 

6. The annuity which would amount to 1 in n years is 



(1 + i) n - 1 



Amounts, Present Values, etc., at 5% Interest. 





(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


Years 


(1 + i) n 


vW n 


(l+i)^-1 


i-a+;r n 


i 


i 




i 


X 


]-{\ + i)- n 


(\+i)n-\ 


1 . . 


1.05 


.952381 


1.00 


.952381 


1.05 


1.00 


2. . 


1.1025 


.907029 


2.05 


1.859410 


.537805 


.487805 


3. . 


1.157625 


.863838 


3.1525 


2.723248 


.367209 


.317209 


4. . 


1.215506 


.822702 


4.310125 


3.545951 


.282012 


.232012 


5. . 


1 .276282 


.783526 


5.525631 


4.329477 


.230975 


.180975 


6. . 


1.340096 


.746215 


6.801913 


5.075692 


.197017 


.147018 


7. . 


1.407100 


.710681 


8.142008 


5.786373 


.172820 


.122820 


8. . 


1.477455 


.676839 


9.549109 


6.463213 


.154722 


.104722 


9. . 


1.551328 


.644609 


1 1 .026564 


7.107822 


.140690 


.090690 


10. . 


1.628895 


.613913 


12.577893 


7.721735 


.129505 


.079505 



16 



ARITHMETIC. 





© 


485.43 
314.10 
228.60 
177.39 
143.36 


119.13 
101.03 
87.02 
75.87 
66.79 


59.28 
52.96 

47.58 
42.96 
38.95 


35.44 
32.36 
29.62 
27.18 
18.23 


12.65 
8.97 
6.46 
4.70 
3.44 




10 


486.62 
315.63 
230.29 
179.13 
145.18 


120.96 
102.86 
88.83 
77.67 
68.57 


61.03 

54.68 
49.28 
44.62 
40.58 


37.04 
33.92 
31.15 
28.68 
19.55 


13.80 
9.97 
7.32 
5.43 
4.06 




10 


487.80 
317.21 
232.01 
180.98 
147.02 


122.82 
104.72 
90.69 
79.50 
70.39 


62.83 
56.45 
51.02 
46.34 
42.27 


38.70 
35.54 
32.75 
30.24 
20.95 


15.05 
11.07 
8.28 
6.26 
4.78 




■>* 


489.00 
318.77 
233.74 
182.79 
148.88 


124.67 
106.60 
92.57 
81.38 
72.25 


64.67 
58.27 
52.82 
48.11 
44.01 


40.42 
37.24 
34.40 
31.87 
22.44 


16.39 
12.27 
9.34 
7.20 
5.60 




<* 


490.20 
320.36 
235.50 
184.63 
150.79 


126.61 
108.53 
94.49 
83.29 

74.15 


66.55 
60.14 
54.67 
49.94 
45.82 


42.20 
38.99 
36.14 
33.58 
24.01 


17.83 
13.58 
10.52 
8.26 
6.55 


CD 


CO 


490.80 
321.13 
236.38 
185.56 
151.73 


127.59 
109.50 
95.46 
84.26 
75.12 


67.51 
61.10 
55.62 
50.88 
46.75 


43.12 
39.90 
37.04 
34.47 
24.84 


18.60 
14.29 
11.17 
8.85 
7.09 


a 
1 

01 


eo 


491.40 
321.94 
237.26 
186.49 
152.67 


128.57 
110.48 
96.44 
85.24 
76.09 


68.48 
62.06 
56.57 
51.82 
47.68 


44.04 
40.82 
37.94 
35.36 
25.67 


19.37 
1.5.00 
11.83 
9.45 
7.63 


"etl 


CO 


492.00 
322.75 
238.14 
187.42 
153.64 


129.54 
111.47 
97.44 
86.24 
77.08 


69.47 
63.05 
57.55 
52.79 
48.64 


44.99 
41.76 
38.87 
36.29 
26.55 


20.19 
15.77 
12.54 
10.12 
8.25 


CO 


492.61 
323.56 
239.02 
188.35 
154.61 


130.51 
112.46 
98.44 
87.24 
78.07 


70.46 
64.03 
58.53 
53.77 
49.61 


45.95 

42.71 
39.81 
37.22 
27.43 


21.02 
16.54 
13.26 
10.78 
8.87 




(M 


493.22 
324.35 
239.93 
189.30 
155.58 


131.50 
113.46 
99.45 
88.24 
79.09 


71.47 
65.04 
59.53 

54.77 
50.60 


46.94 
43.69 
40.78 
38.18 
28.35 


.21.90 
17.37 
14.05 
11.52 
9.56 




« 


493.83 
325.14 
240.84 
190.24 
156.56 


132.49 
114.47 
100.46 
89.25 
80.11 


72.49 
66.03 
60.54 
55.77 
51.60 


47.93 
44.67 
41.76 
39.14 
29.27 


22.78 
18.20 
14.84 
12.27 
10.26 




N 


494.43 
325.94 
241.74 
191.18 
157.53 


133.51 
115.48 
101.48 
90.29 
81.14 


73.52 
67.08 
61.56 
56.79 
52.62 


48.94 
45.67 
42.76 
40.14 
30.24 


23.70 
19.09 
15.68 
13.07 
11.02 




N 


495.05 
326.72 
242.63 
192.16 
158.53 


134.52 
116.51 
102.52 
91.33 
82.18 


74.56 
68.12 
62.60 
57.83 
53.65 


49.97 
46.70 
43.78 
41.15 
31.22 


24.65 
20.00 
16.55 
13.91 
11.82 








£$ 












s- 












kH° 


eNen^mvo 


MOOO- 


eNen^-invO 


NOOOOm 
— — — (N(N 


omomo 
tfientTift 



WEIGHTS AND MEASURES. 



17 



TABLES FOB CALCULATING SINKING-FUNDS AND 
PBESENT VALUES. 

Engineers and others connected with municipal work and industrial 
enterprises often find it necessary to calculate payments to sinking-funds 
which will provide a sum of money sufficient to pay off a bond issue or 
other debt at the end of a given period, or to determine the present value 
of certain annual charges. The accompanying tables were computed by 
Mr. John W. Hill, of Cincinnati, Eng'g News, Jan. 25, 1894. 

Table I (opposite page) shows the annual sum at various rates of interest 
required to net $1000 in from 2 to 50 years, and Table II shows the present 
value at various rates of interest of an annual charge of $1000 for from 5 
to 50 years, at five-year intervals, and for 100 years. 



Table II. 



- Capitalization of Annuity of $1000 for 
from 5 to 100 Years. 



3 

V 






Rate of Interest, per cent. 








2V2 


3 


31/2 


4 


41/2 


5 


51/2 


6 


5 


5 

20 
25 

iO 
J5 
40 
*5 
>0 
)0 


4,645:88 
8,752.17 
12,381.41 
15,589.215 
18,424.67 
20,930.59 
23,145.31 
25,103.53 
26,833.15 
28,362.48 
36,614.21 


4.579.60 
8,530.13 
11,937.80 
14,877.27 
17,413.01 

19,600.21 
21,487.04 
23,114.36 
24,518.49 
25,729.58 
31,598.81 


4,514.92 
8,316.45 
11,517.23 
14,212.12 
16,481.28 

18,391.85 
20,000.43 
21,354.83 
22,495.23 
23,455.21 
27,655.36 


4,451.68 
8,110.74 
11,118.06 
13,590.21 
15,621.93 

17,291.86 
18,664.37 
19,792.65 
20,719.89 
21,482.08 
24,504.96 


4,389.91 
7,912.67 
10,739.42 
13,007.88 
14,828.12 

16,288.77 
17,460.89 
18,401.49 
19,156.24 
19,761.93 
21,949.21 


4,329.45 
7,721.73 
10,379.53 
12,462.13 
14,093.86 

15,372.36 
16,374.36 
17,159.01 
17,773.99 
18,255.86 
19,847.90 


4,268.09 
7,537.54 
10,037.48 
11,950.26 
13,413.82 
14,533.63 
15,390.48 
16,044.92 
16,547.65 
16,931.97 
18,095.83 


4,212.40 
7,360.19 
9,712.30 
11,469.96 
12,783.38 

13,764.85 
14,488.65 
15,046.31 
15,455.85 
15,761.87 
16,612.64 



WEIGHTS AND MEASURES. 

Long Measure. — Measures of Length. 

12 inches = 1 foot. 

3 feet = 1 yard. 

1760 yards, or 5280 feet = 1 mile. 

Additional measures of length in occasional use: 1000 mils = 1 inch; 
4 inches = 1 hand; 9 inches = 1 span; 2 1/2 feet = 1 military pace; 2 yards 
= 1 fathom; 51/2 yards, or 16 1/2 feet = 1 rod (formerly also called pole or 
perch). 

Old Land Measure. — 7.92 inches = 1 link; 100 links, or 66 feet, or 4 
rods = 1 chain; 10 chains, or 220 yards = 1 furlong; 8 furlongs, or 80 
chains = 1 mile; 10 square chains = 1 acre. 



Nautical Measure. 



6080.26 feet, or 1.15156 stat-1 
ute miles J 

3 nautical miles 
60 nautical miles, or 69.168 
statute miles 
360 degrees 



= 1 nautical mile, or knot.* 

= 1 league. 

= 1 degree (at the equator). 

= circumference of the earth at the equator. 



* The British Admiralty takes the round figure of 60S0 ft. which is the 
length of the " measured mile" used in trials of vessels. The value varies 
from 6080.26 to 6088.44 ft. according to different measures of the earth's 
diameter. There is a difference of opinion among writers as to the use 
of the word " knot" to mean length or a distance ■ — some holding that 
it should be used only to denote a rate of speed. The length between 
knots on the log line is 1/120 of a nautical mile, or 50.7 ft., when a half- 
minute glass is used; so that a speed of 10 knots is equal to 10 nautical 
miles per hour. 



18 ARITHMETIC. 



Square Measure. — Measures of Surface. 

144 square inches, or 183.35 circular I _ -, _„„„,.,. f ~„* 

inches ] ~ 1 S( l uare t00t - 
9 square feet = 1 square yard. 

30 1/4 square yards, or 2721/4 square feet ■— 1 square rod. 

10 sq. chains, or 160 sq. rods, or 4840 sq. ) _ , Q „ ro 

yards, or 43560 sq. feet J ~~ i acre ' 
640 acres = 1 square mile. 

An acre equals a square whose side is 208.71 feet. 

Circular Inch; Circular Mil. — A circular inch is the area of a circle 

1 inch in diameter = 0.7854 square inch. 

1 square inch = 1.2732 circular inches. 

A circular mil is the area of a circle 1 mil, or 0.001 inch in diameter. 
1000 2 or 1,000,000 circular mils = 1 circular inch. 

1 square inch = 1,273,239 circular mils. 

The mil and circular mil are used in electrical calculations involving 
the diameter and area of wires. 

Solid or Cubic Measure. — Measures of Volume. 

1728 cubic inches = 1 cubic foot. 
27 cubic feet = 1 cubic yard. 
1 cord of wood = a pile, 4X4X8 feet = 128 cubic feet. 
1 perch of masonry = I6V2 X IV2 XI foot = 243/ 4 cubic feet. 

Liquid Measure. 

4 gills = 1 pint. 
2 pints = 1 quart. 

4 miartq - 1 gallon { U - S - 231 cubic in ches. 
4 quarts - 1 gallon j Eng _ 2 ?7.274 cubic inches. 

Old Liquid Measures. — 31 1/2 gallons = 1 barrel; 42 gallons = 1 tierce; 

2 barrels, or 63 gallons = 1 hogshead; 84 gallons, or 2 tierces = 1 pun- 
cheon; 2 hogsheads, or 126 gallons = 1 pipe or butt; 2 pipes, or 3 pun- 
cheons = 1 tun. 

A gallon of water at 62° F. weighs 8.3356 lbs. 

The U. S. gallon contains 231 cubic inches; 7.4805 gallons = 1 cubic 
foot. A cylinder 7 in. diam. and 6 in. high contains 1 gallon, very nearly, 
or 230.9 cubic inches. The British Imperial gallon contains 277.274 cubic 
inches = 1.20032 U. S. gallon, or 10 lbs. of water at 62° F. 

The gallon is a very troublesome unit for engineers. Much labor might 
be saved if it were abandoned and the cubic foot used instead. The 
capacity of a tank or reservoir should be stated in cubic feet, and the 
delivery of a pump in cubic feet per second or in millions of cubic feet in 
24 hours. One cubic foot per second = 86,400 cu. ft. in 24 hours. One 
million cu. ft. per 24 hours = 11.5741 cu. ft. per sec. 

The Miner's Inch. — (Western U. S. for measuring flow of a stream 
of water.) An act of the California legislature, May 23, 1901, makes the 
standard miner's inch 1.5 cu. ft. per minute, measured through any aper- 
ture or orifice. 

The term Miner's Inch is more or less indefinite, for the reason that Cali- 
fornia water companies do not all use the same head above the centre of 
the aperture, and the inch varies from 1.36 to 1.73 cu. ft. per min., but 
the most common measurement is through an aperture 2 ins. high and 
whatever length is required, and through a plank IV4 ins. thick. The 
lower edge of the aperture should be 2 ins. above the bottom of the meas- 
uring-box , and the plank 5 ins. high above the aperture, thus making a 6-in. 
head above the centre of the stream. Each square inch of this opening 
represents a miner's inch, which is equal to a flow of IV2 cu. ft. per min. 

Apothecaries' Fluid Measure. 

60 minims = 1 fluid drachm. 8 drachms = 1 fluid ounce. 

In the U. S. a fluid ounce is the 128th part of a U. S. gallon, or 1.805 
cu. ins. It contains 456.3 grains of water at 39° F. In Great Britain 
the fluid ounce is 1.732 cu. ins. and contains 1 ounce avoirdupois, or 437.5 
grains of water at 62° F. 



WEIGHTS AND MEASUKES. 19 

Dry Measure, U. S. 
2 pints = 1 quart. 8 quarts = 1 peck. 4 pecks = 1 bushel. 

The standard U. S. bushel is the Winchester bushel, which is in cylinder 
form, I8V2 inches diameter and 8 inches deep, and contains 2150.42 cubic 
inches. 

A struck bushel contains 2150.42 cubic inches = 1.2445 cu. ft.; 1 cubic 
foot = 0.80356 struck bushel. A heaped bushel is a cylinder 18 1/2 inches 
diameter and 8 inches deep, with a heaped cone not less than 6 inches 
high. It is equal to 1V4 struck bushels. 

The British Imperial bushel is based on the Imperial gallon, and contains 
8 such gallons, or 2218.192 cubic inches = 1.2837 cubic feet. The English 
quarter = 8 Imperial bushels. 

Capacity of a cylinder in U. S. gallons = square of diameter, in inches 
X height in inches X .0034. (Accurate within 1 part in 100,000.) 

Capacity of a cylinder in U. S. bushels = square of diameter in inches 
X height in inches X 0.0003652. 



Shipping Measure. 

Register Ton. — For register tonnage or for measurement of the entire 
internal capacity of a vessel: 

100 cubic feet = 1 register ton. 

This number is arbitrarily assumed to facilitate computation. 
Shipping Ton. — For the measurement of cargo: 

1 U. S. shipping ton. 

31.16 Imp. bushels. 

32.143 C. S. 
( 1 British shipping ton. 
42 cubic feet = \ 32.719 Imp. bushels. 
(33.75 U.S. 

Carpenter's Rule. — Weight a vessel will carry = length of keel X 
breadth at main beam X depth of hold in feet -e- 95 (the cubic feet 
allowed for a ton). The result will be the tonnage. For a double-decker 
instead of the depth of the hold take half the breadth of the beam. 



Measures of Weight. — Avoirdupois, or Commercial 
Weight. 

16 drachms, or 437.5 grains = 1 ounce, oz. 
16 ounces, or 7000 grains = 1 pound, lb. 
28 pounds • = 1 quarter, qr. 

4 quarters = 1 hundredweight, cwt. = 112 lbs. 

20 hundred weight = 1 ton of 2240 lbs., gross or long ton. 

2000 pounds = 1 net, or short ton. 

2204.6 pounds = 1 metric ton. 

1 stone = 14 pounds; 1 quintal = 100 pounds. 

The drachm, quarter, hundredweight, stone, and quintal are now 
seldom used in the United States. 



Troy Weight. 

24 grains = 1 pennyweight, dwt. 

20 pennyweights = 1 ounce, oz. = 480 grains. 

12 ounces = 1 pound, lb. = 5760 grains. 



Troy weight is used for weighing gold and silver. The grain is the same 

Avoird 

weighing c 



in Avoirdupois, Troy, and Apothecaries' weights. A" carat, used in 
weighing diamonds = 3.168 grains = 0.205' i 



20 ARITHMETIC. 

Apothecaries' Weight. 

20 grains = 1 scruple, 3 
3 scruples = 1 drachm, 5 = 60 grains. 
8 drachms = 1 ounce, § = 480 grains. 

12 ounces = 1 pound, lb. = 5760 grains. 

To determine whether a balance has unequal arms. — After weigh- 
ing an article and obtaining equilibrium, transpose the article and the 
weights. If the balance is true, it will remain in equilibrium; if untrue, 
the pan suspended from the longer arm will descend. 

To weigh correctly on an incorrect balance. — First, by substitu- 
tion. Put the article to be weighed in one pan of the balance and counter- 
poise it by any convenient heavy articles placed on the other pan. 
Remove the article to be weighed and substitute for it standard weights 
until equipoise is again established. The amount of these weights is the 
weight of the article. 

Second, by transposition. Determine the apparent weight of the 
article as usual, then its apparent weight after transposing the article and 
the weights. If the difference is small, add half the difference to the 
smaller of the apparent weights to obtain the true weight. If the differ- 
ence is 2 per cent the error of this method is 1 part in 10,000. For larger 
differences, or to obtain a perfectly accurate result, multiply the two 
apparent weights together and extract the square root of the product. 

Circular Measure. 

60 seconds, " = 1 minute, '. 

60 minutes, ' = 1 degree, °. 

90 degrees = 1 quadrant. 
360 " = circumference. 

Arc of angle of 57.3°, or 360° ■*■ 6.2832 = 1 radian = the arc whose length 
is equal to the radius. 

Time. 

60 seconds = 1 minute. 
60 minutes = 1 hour. 
24 hours = 1 day. 
7 days = 1 week. 
365 days, 5 hours, 48 minutes, 48 seconds =* 1 year. 

By the Gregorian Calendar every year whose number is divisible by 4 
is a leap year, and contains 366 days, the other years containing 365 days, 
except that the centesimal years are leap years only when the number of 
the year is divisible by 400. 

The comparative values of mean solar and sidereal time are shown by 
the following relations according to Bessel: 

365.24222 mean solar days = 366.24222 sidereal days, whence 
1 mean solar day = 1.00273791 sidereal days; 
1 sidereal day = 0.99726957 mean solar day; 
24 hours mean solar time = 24* 3 56s. 555 sidereal time; 
24 hours sidereal time = 23* 5Qm 4».091 mean solar time, 

whence 1 mean solar day is 3»» 55«.91 longer than a sidereal day, reckoned 
in mean solar time. 

BOARD AND TIMBER MEASURE. 

Board Measure. 

In board measure boards are assumed to be one inch in thickness. To 
obtain the number of feet board measure (B. M.) of a board or stick of 
square timber, multiply together the length in feet, the breadth in feet, 
and the thickness in inches. 

To compute the measure or surface in square feet. — When all 
dimensions are in feet, multiply the length by the breadth, and the prod- 
uct will give the surface required. 



WEIGHTS AND MEASURES. 



21 



When either of the dimensions are in inches, multiply as above and 
divide the product by 12. 

n all dimensions are in inches, multiply as before and divide product 
by 144. 

Timber Measure. 

To compute the volume of round timber. — When all dimensions 
are in feet, multiply the length by one quarter of the product of the mean 
girth and diameter, and the product will give the measurement in cubic 
feet. When length is given in feet, and girth and diameter in inches, 
divide the product by 144; when all the dimensions are in inches, divide 
by 1728. 

To compute the volume of square timber. — When all dimensions 
are in feet, multiply together the length, breadth, and depth; the product 
will be the volume in cubic feet. When one dimension is given in inches, 
divide by 12; when two dimensions are in inches, divide by 144; when all 
three dimensions are in inches, divide by 1728. 



Contents in Feet of Joists, Scantling, and Timber. 

Length in Feet. 



12 14 16 18 20 22 24 26 28 



Feet Board Measure. 



2X4 


8 


9 


11 


12 


13 


15 


16 


17 


19 


20 


2X6 


12 


14 


16 


18 


20 


22 


24 


26 


28 


30 


2X8 


16 


19 


21 


24 


27 


29 


32 


35 


37 


40 


2 X 10 


20 


23 


27 


30 


33 


37 


40 


43 


47 


50 


2 X 12 


24 


28 


32 


36 


40 


44 


48 


52 


56 


60 


2 X 14 


28 


33 


37 


42 


47 


51 


56 


61 


65 


70 


3X8 


24 


28 


32 


36 


40 


44 


48 


52 


56 


60 


3 X 10 


30 


35 


40 


45 


50 


55 


60 


65 


70 


75 


3 X 12 


36 


42 


48 


54 


60 


66 


72 


78 


84 


90 


3 X 14 


42 


49 


56 


63 


70 


77 


84 


91 


98 


105 


4X4 


16 


19 


21 


24 


27 


29 


32 


35 


37 


40 


4X6 


24 


28 


32 


36 


40 


44 


48 


52 


56 


60 


4X8 


32 


37 


43 


48 


53 


59 


64 


69 


75 


80 


4 X 10 


40 


47 


53 


60 


67 


73 


80 


87 


93 


100 


4 X 12 


48 


56 


64 


72 


80 


88 


96 


104 


112 


120 


4 X 14 


56 


65 


75 


84 


93 


103 


112 


121 


131 


140 


6X6 


36 


42 


48 


54 


60 


66 


72 


78 


84 


90 


6X8 


48 


56 


64 


72 


80 


88 


96 


104 


112 


120 


6 X 10 


60 


70 


'80 


90 


100 


110 


120 


130 


140 


150 


6 X 12 


72 


84 


96 


108 


120 


132 


144 


156 


168 


180 


6 X 14 


84 


93 


112 


126 


140 


154 


168 


182 


196 


210 


8X8 


64 


75 


85 


96 


107 


117 


128 


139 


149 


160 


8 X 10 


80 


93 


107 


120 


133 


147 


160 


173 


187 


200 


8 X 12 


96 


112 


128 


144 


160 


176 


192 


208 


224 


240 


8 X 14 


112 


131 


149 


168 


187 


205 


224 


243 


261 


280 


10 X 10 


100 


117 


133 


150 


167 


183 


200 


217 


233 


250 


10 X 12 


120 


140 


160 


180 


200 


220 


240 


260 


280 


300 


10 X 14 


140 


163 


187 


210 


233 


257 


280 


303 


327 


350 


12 X 12 


144 


168 


192 


216 


240 


264 


288 


312 


336 


360 


12 X 14 


168 


196 


224 


252 


280 


308 


336 


364 


392 


420 


14 X 14 


196 


229 


261 


294 


327 


359 


392 


425 


457 


490 



22 



ARITHMETIC. 



FRENCH OR METRIC MEASURES. 

The metric unit of length is the metre = 39.37 inches. 

The metric unit of weight is the gram = 15. 432. grains. 

The following prefixes are used for subdivisions and multiples: Milli = 
Viooo, Centi = Vioo, Deci = i/io, Deca = 10, Hecto = 100, Kilo -= 1000, 
Myria = 10,000. 



FRENCH AND BRITISH (AND AMERICAN) 
EQUIVALENT MEASURES. 



French. • 

1 metre 
0.3048 metre 

1 centimetre 
2.54 centimetres 

1 millimetre 
25.4 millimetres 

1 kilometre 



French. 



1 square metre 

0.836 square metre 
0.0929 square metre 

1 square centimetre 
6.452 square centimetres 

1 square millimetre 
645.2 square millimetres 

1 centiare = 1 sq. metre 

1 are = 1 sq. decametre 

1 hectare =100 ares 

1 sq. kilometre 

1 sq. myriametre 



Measures of Length. 

British and U. S. 
= 39.37 inches, or 3.28083 feet, or 1.09361 yards. 
= 1 foot. 
= 0.3937 inch. 
= 1 inch. 

= 0.03937 inch, or 1/25 inch, nearly. 
= 1 inch. 
= 1093.61 yards, or 0.62137 mile. 

Of Surface. 

British and U. S. 
f 10.764 square feet, 
' \ 1.196 square yards. 
= 1 square yard. 
= 1 square foot. 
» 0.155 square inch. 
: 1 square inch. 

= 0.00155 sq. in. = 1973.5 cire. mils. 
= 1 square inch. 
= 10.764 square feet. 
= 1076.41 " 

> 107641 " " = 2.4711 acres. 
= 0.386109 sq. miles = 247.11 " 
« 38.6109 " 



French. 

1 cubic metre 

0.7645 cubic metre 
0.02832 cubic metre 

1 cubic decimetre = 



Of Volume. 

British and U. S. 
. (35.314 cubic feet, 

\ 1.308 cubic yards. 
: 1 cubic yard. 
■■ 1 cubic foot. 
( 61 .023 cubic inches; 
( 0.0353 cubic foot. 
28.32 cubic decimetres = 1 cubic foot. 

1 cubic centimetre = 0.061 cubic inch. 
16.387 cubic centimetres =»= 1 cubic inch. 
1 cubic centimetre = 1 millilitre = 0.061 cubic inch. 
1 centilitre = 0.610 

1 decilitre = 6.102 

1 litre = 1 cubic decimetre =61.023 " £ =1.05671 quarts, U.S. 

1 hectolitre or decistere =3.5314 cubic feet =2.8375 bushels, " 

1 stere, kilolitre, or cubic metre = 1.308 cubic yards = 28.37 bushels, 

Of Capacity. 

French. British and U. S. 

61.023 cubic inches, 
0.03531 cubic foot, 
0.2642 gallon (American), 
2.202 pounds of water at 62° F. 
= 1 cubic foot. 
= 1 gallon (British). 
= 1 gallon (American). 



1 litre (=1 cubic decimetre) = 



28.317 litres 
4.543 litres 
3.785 litres 



WEIGHTS AND MEASURES. 



23 



Of Weight. 

British and U. S. 
= 15.432 grains. 
= 1 grain. 

= 1 ounce avoirdupois. 
=±= 2.2046 pounds. 
• = 1 pound. 

(0.9842 ton of 2240 pounds, 

] 19.68 cwts., 

( 2204.6 pounds. 

} 1 ton of 2240 pounds. 



French. 

1 gramme 

0.0648 gramme 

28.35 gramme 

1 kilogramme 

0.4536 kilogramme 

1 tonne or metric ton = 

1000 kilogrammes 

1.016 metric tons 

1016 kilogrammes 

Mr. O. H. Titmann, in Bulletin No. 9 of the U. S. Coast and Geodetic 

urvey, discusses the work of various authorities who have compared the 

ard and the metre, and by referring all the observations to a common 

tandard has succeeded in reconciling the discrepancies within very 

iarrow limits. The following are his results for the number of inches in a 

netre according to the comparisons of the authorities named: 1817. 

iassler, 39.36994 in. 1818. Kater, 39.36990 in. 1835. Baily, 39.36973 

a. 1866. Clarke, 39.36970 in. 1885. Comstock, 39.36984 in. The mean 

if these is 39.36982 in. 

The value of the metre is now defined in the U. S. laws as 39.37 inches. 

French and British Equivalents of Compound Units. 



French. 
gramme per square millimetre 



kilogramme per square 



British. 
=" 1.422 lbs. per sq. in. 
= 1422.32 " " " " 
centimetre = 14.223 ° " " " 

..0335 kg. per sq. cm. = 1 atmosphere = 14.7 " " " 

K070308 kilogramme per square centimetre = 1 lb. per square inch. 
l kilogrammetre = 7.2330 foot-pounds. 

L gramme per litre = 0.062428 lb. per cu. ft. = 58.349 grains per U. S gal. 

of water at 62° F. 
L grain per U. S. gallon=l part in 58,349 == 1.7138 parts per 100,000 
= 0..017138 grammes per litre. 



METRIC CONVERSION TABLES. 

The following tables, with the subjoined memoranda, were published 
in 1890 by the United States Coast and Geodetic Survey, office of standard 
weights and measures, T. C. Mendenhall, Superintendent. 

Tables for Converting U. S. Weights and Measures — 
Customary to Metric. 



1 = 

2 = 

3 = 

4 = 

5 = 

6 = 

7 = 

8 = 

9 = 


Inches to Milli- 
metres. 


Feet to Metres. 


Yards to Metres. 


Miles to Kilo- 
metres. 


25.4001 
50.8001 
76.2002 
101.6002 
127.0003 

152.4003 
177.8004 
203.2004 
228.6005 


0.304801 
0.609601 
0.914402 
1.219202 
1 .524003 

1.828804 
2.133604 
2.438405 
2.743205 


0.914402 
1 .828804 
2.743205 
3.657607 
4.572009 

5.486411 
6.400813 
7.315215 
8.229616 


1.60935 
3.21869 
4.82804 
6.43739 
8.04674 

9.65608 
1 1 .26543 
12.87478 
14.48412 



24 



ARITHMETIC. 



SQUARE. 





Square Inches to 
Square Centi- 
metres. 


Square Feet to 
Square Deci- 
metres. 


Square Yards to 
Square Metres. 


Acres to 
Hectares. 


1 = 


6.452 


9.290 


0.836 


4047 


2 = 


12.903 


18.581 


1.672 


0.8094 


3 = 


19.355 


27.871 


2.508 


1.2141 


4 = 


25.807 


37.161 


3.344 


1.6187 


5 = 


32.258 


46.452 


4.181 


2.0234 


6 = 


38.710 


55.742 


5.017 


2.4281 


7 = 


45.161 


65.032 


5.853 


2.8328 


8 = 


51.613 


74.323 


6.689 


3.2375 


9 = 


58.065 


83.613 


7.525 


3.6422 





Cubic Inches to 
Cubic Centi- 
metres. 


Cubic Feet to 


Cubic Yards to 


Bushels to 




Cubic Metres. 


Cubic Metres. 


Hectolitres. 


1 = 


16.387 


0.02832 


0.765 


0.35242 


2 = 


32.774 


0.05663 


1.529 


0.70485 


3 = 


49.161 


0.08495 


2.294 


1.05727 


4 = 


65.549 


0.11327 


3.058 


1 .40969 


5 = 


81.936 


0.14158 


3.823 


1.76211 


6 = 


98.323 


0.16990 


4.587 


2.11454 


7 = 


114.710 


0.19822 


5.352 


2.46696 


8 = 


131.097 


0.22654 


6.116 


2.81938 


9 = 


147.484 


0.25485 


6.881 


3.17181 





Fluid Drachms 










to Millilitres or 
Cubic Centi- 


Fluid Ounces to 
Millilitres. 


Quarts to Litres. 


Gallons to 
Litres. 




metres. 








1 = 


3.70 


29.57 


0.94636 


3.78544 


2 = 


7.39 


59.15 


1 .89272 


7.57088 


3 = 


11.09 


88.72 


2.83908 


11.35632 


4 = 


14.79 


118.30 


3.78544 


15.14176 


5 = 


18.48 


147.87 


4.73180 


18.92720 


6 = 


22.18 


177.44 


5.67816 


22.71264 


7 = 


25.88 


207.02 


6.62452 


26.49808 


8 = 


29.57 


236.59 


7.57088 


30.28352 


9 = 


33.28 


266.16 


8.51724 


34.06896 





METRIC CONVERSION TABLES. 
WEIGHT. 


25 




Grains to Milli- 
grammes. 


Avoirdupois 
Ounces to 
Grammes. 


Avoirdupois 
Pounds to Kilo- 
grammes. 


Troy Ounces to 
Grammes. 


1 = 

2 = 

3 = 

4 = 

5 = 

6 = 

7 = 

8 = 

9 = 


64.7989 
129.5978 
194.3968 
259.1957 
323.9946 

388.7935 
453.5924 
518.3914 
583.1903 


28.3495 
56.6991 
85.0486 
113.3981 
141.7476 

170.0972 
198.4467 
226.7962 
255.1457 


0.45359 
0.90719 
1.36078 
1.81437 
2.26796 

2.72156 
3.17515 
3.62874 
4.08233 


31.10348 
62.20696 
93.31044 
124.41392 
155.51740 

186.62089 
217.72437 
248.82785 
279.93133 




1 chain = 20.1 169 metres. 
1 square mile = 259 hectares. 
1 fathom = 1 .829 metres. 
1 nautical mile = 1853.27 metres. 
1 foot = 0.304801 metre. 
1 avoir, pound = 453.5924277 gram. 
15432.35639 grains = 1 kilogramme. 


- 













Tables for Converting IT. S. Weights and Measures — 
Metric to Customary. 





Metres to 
Inches. 


Metres to 
Feet. 


Metres to 
Yards. 


Kilometres to 
Miles. 


1 = 

2 = 

3 = 

4 = 

5 = 

6 = 

7 = 

8 = 

9 = 


39.3700 
78.7400 
118.1100 
157.4800 
196.8500 

236.2200 
275.5900 
314.9600 
354.3300 


3.28083 
6.56167 
9.84250 
13.12333 
16.40417 

19.68500 
22.96583 
26.24667 
29.52750 


1.093611 
2.187222 
3.280833 
4.374444 
5.468056 

6.561667 
7.655278 
8.748889 
9.842500 


0.62137 
1 .24274 
1.86411 
2.48548 
3.10685 

3.72822 
4.34959 
4.97096 
5.59233 



SQUARE. 



Square Centi- 
metres to 
Square Inches. 

O550 
0.3100 
0.4650 
0.6200 
0.7750 

0.9300 
1 .0850 
1 .2400 
1.3950 



Square Metres 
to Square Feet. 

WJ64 
21.528 
32.292 
43.055 
53.819 

64.583 
75.347 
86.111 
96.874 



Square Metres 
to Square Yards. 

U96 
2.392 
3.588 
4.784 
5.980 

7.176 
8.372 
9.568 
10.764 



Hectares to 
Acres. 

2A7) 
4.942 
7.413 
9.884 
12.355 

14.826 
17.297 
19.768 
22.239 



26 



ARITHMETIC. 





Cubic Centi- 
metres to Cubic 
Inches. 


Cubic Deci- 
metres to Cubic 
Inches. 


Cubic Metres to 
Cubic Feet. 


Cubic Metres t 
Cubic Yards. 


1 = 


0.0610 


61.023 


35.314 


1.308 


2 = 


0.1220 


122.047 


70.629 


2.616 


3 = 


0.1831 


183.070 


105.943 


3.924 


4 = 


0.2441 


244.093 


141.258 


5.232 


5 = 


0.3051 


305.117 


176.572 


6.540 


6 = 


0.3661 


366.140 


211.887 


7.848 


7 = 


0.4272 


427.163 


247.201 


9.156 


8 = 


0.4882 


488.187 


282.516 


10.464 


9 = 


0.5492 


549.210 


317.830 


11.771 





Millilitres or 
Cubic Centi- 
metres toFluid 


Centilitres 
to Fluid 


Litres to 
Quarts. 


Dekalitres 
to 


Hektolitres 
to 




Drachms. 










1 = 


0.27 


0.338 


1.0567 


2.6417 


2.8375 


2 = 


0.54 


0.676 


2.1134 


5.2834 


5.6750 


3 = 


0.81 


1.014 


3.1700 


7.9251 


8.5125 


4 = 


1.08 


1.352 


4.2267 


10.5668 


11.3500 


5 = 


1.35 


1.691 


5.2834 


13.2085 


14.1875 


6 = 


1.62 


2.029 


6.3401 


15.8502 


17.0250 


7 = 


1.89 


2.368 


7.3968 


18.4919 


19.8625 


8 = 


2.16 


2.706 


8.4534 


21.1336 


22.7000 


9 = 


2.43 


3.043 


9.5101 


23.7753 


25.5375 





Milligrammes 
to Grains. 


Kilogrammes 
to Grains. 


Hectogrammes 
( 1 00 grammes) 
to Ounces Av. 


Kilogrammes 
to Pounds 
Avoirdupois. 


1 = 

2 = 

3 = 

4 = 

5 = 

6 = 

7 = 

8 = 

9 = 


0.01543 
0.03086 
0.04630 
0.06173 
0.07716 

0.09259 
0.10803 
0.12346 
0.13889 


15432.36 
30864.71 
46297.07 
61729.43 
77161.78 

92594.14 
108026.49 
123458.85 
138891.21 


3.5274 
7.0548 
10.5822 
14.1096 
17.6370 

21.1644 
24.6918 
28.2192 
31.7466 


2.20462 
4.40924 
6.61386 
8.81849 
11.02311 

13.22773 
15.43235 
17.63697 
19.84159 



WEIGHTS AND MEASURES. 



27 



WEIGHT — (Continued). 





Quintals to 
Pounds Av. 


Milliers or Tonnes to 
Pounds Av. 


Grammes to Ounces. 
Troy. 


1 = 

2 = 

3 = 

4 = 

5 = 

6 = 

7 = 

8 = 

9 = 


220.46 
440.92 
661.38 
881.84 
1102.30 

1322.76 
1543.22 
1763.68 
1982.14 


2204.6 
4409.2 
6613.8 
8818.4 
11023.0 

13227.6 
15432.2 
17636.8 
19841.4 


0.03215 
0.06430 
0.09645 
0.12860 
0.16075 

0.19290 
0.22505 
0.25721 
0.28936 



The British Avoirdupois pound was derived from the British standard 
Troy pound of 1758 by direct comparison, and it contains 7000 grains Troy. 

The grain Troy is therefore the same as the grain Avoirdupois, and the 
pound Avoirdupois in use in the United States is equal to the British 
pound Avoirdupois. 

By the concurrent action of the principal governments of the world an 
International Bureau of Weights and Measures has been established near 
Paris. 

The International Standard Metre is derived from the Metre des 
Archives, and its length is defined by the distance between two lines at 0° 
Centigrade, on a platinum-iridium bar deposited at the International 
Bureau. 

The International Standard Kilogramme is a mass of platinum-iridium 
deposited at the same place, and its weight in vacuo is the same as that of 
the Kilogramme des Archives. 

Copies of these international standards are deposited in the office of 
standard weights and measures of the U. S. Coast and Geodetic Survey. 

The litre is equal to a cubic decimetre of water, and it is measured by 
the quantity of distilled water which, at its maximum density, will 
counterpoise the standard kilogramme in a vacuum; the volume of such 
a quantity of water being, as nearly as has been ascertained, equal to a 
cubic decimetre. 

The metric system was legalized in the United States in 1866. Many 
attempts were made during the 40 years following to have the U. S. 
Congress pass laws to make the metric system the legal standard, but they 
have all failed. Similar attempts in Great Britain have also failed. For 
arguments for and against the metric system see the report of a committee 
of the American Society of Mechanical Engineers, 1903, Vol. 24. 



COMPOUND UNITS. 

Measures of Pressure and Weight. 



1 lb. per square inch. 



1 ounce per sq. in. 



1 atmosphere (14.7 lbs. per sq.in.) = 



144 lbs. per square foot. 

2.0355 ins. of mercury at 32° F. 
2.0416 " " " " 62° F. 

2.309 ft. of water at 62° F. 
27.71 ins. " " " 62° F. 
0.1276 in. of mercury at 62° F. 
1.732 ins. of water at 62° F. 
2116.3 lbs. per square foot. 

33.947 ft. of water at 62° F. 
30 ins. of mercury at 62° F. 

29.922 ins. of mercury at 32° F. 
760 millimetres of mercury at 32° F. 



28 ARITHMETIC. 



COMPOUND UNITS — (Continued). 

( 0.03609 lb. or .5774 oz. per sq.in. 
1 inch of water at 62° F. = < 5.196 lbs. per square foot. 

( 0.0736 in. of mercury at 62° F. 

1 inch of water at 32° F. -\ $%&£&* *Wffik. 

Hoot of water a, 62= F. -{ ^gj lb. per square inch. 

( 0.491 lb. or 7.86 oz. per sq. in. 
1 inch of mercury at 62° F. = \ 1.132 ft. of water at 62° F. 

( 13.58 ins. " " " 62° F. 

"Weight of One Cubic Foot of Pure Water. 

At 32° F. (freezing-point) 62.418 lbs. 

" 39.1° F. (maximum density) 62.425 " 

" 62° F. (standard temperature) 62.355 " 

" 212° F. (boiling-point, under 1 atmosphere) 59.76 " 

American gallon = 231 cubic ins. of water at 62° F. = 8.3356 lbs. 
British " = 277.274 " " " " " " - 10 lbs. 

Weight and Volume of Air. 

1 cubic ft. of air at 32° F. and atmospheric pressure weighs 0.080728 lb. 

(0.0005606 lb. per sq. in. 
1 ft. in height of air at 32° F„ = \ 0.008970 ounces per sq. in. 

(0.015534 inches of water at 62° F. 
For air at any other temperature T° Fahr. multiply by 460 -h (460 + T). 
1 lb. pressure per sq. ft. = 12.387 ft. of air at 32° F. 

1 " " " sq. in. = 1784. " " " " 

1 ounce " " l! " = 111.48 " " " " 

1 inch of water at 62° F. == 64.37 " " " " 

For air at any other temperature multiply by (460 + T) -*- 460. 
1 atmosphere = 14.696 lb. per sq. in. == 760 mm. or 29.921 in. of mercury. 

Measures of Work, Power, and Duty. 

Work. — The sustained exertion of pressure through space. 

Unit of work. — One foot-pound, i.e., a pressure of one pound exerted 
through a space of one foot. 

Horse-power. — The rate of work. Unit of horse-power = 33,000 
ft.-lbs. per minute, or 550 ft.-lbs. per second = 1,980,000 ft.-lbs. per hour. 

Heat unit = heat required to raise 1 lb. of water 1° F. (from 39° to 40°). 

33000 
Horse-power expressed in heat units = ' ' R = 42.416 heat units per 

minute = 0.707 heat unit per second = 2545 heat units per hour. 

1 lb. of fne! per H. P. per honr - { ^i'^a/Sinits' ^ ^ * ^ 

1,000,000 ft.-lbs. per lb. of fuel = 1.98 lbs. of fuel per H. P. per hour. 

5^80 ^2 
Velocity. — Feet per second = „~^ = ^ X miles per hour. 
3600 15 

Gross tons per mile = ooln = i"7 * bs - per yard ( sm ^ e rail.) 



WIRE AND SHEET-METAL GAUGES. 



29 



WIRE AND SHEET-METAL GAUGES COMPARED. 






sis, 




T3„»fi 


— . a5o 


British Imperial 


"S * -si 






£ * * 
.8 gc? 


rt a 5 

■ago 


£Meo 


Standard 
Wire Gauge. 

(Legal Standard 


=3 n * » 

CO ixS SS 


|| 


S-2 2 


- |sl 

03 


3|S 

v& 




in Great Britain 

since 

March 1, 1884.) 




|5 




inch. 


inch. 


inch. 


inch. 


inch. 


millim. 


inch. 




0000000 






.49 




.500 


12.7 


.5 


7/0 


000000 






.46 




.464 


11.78 


.469 


% 


00000 






.43 




.432 


10.97 


.438 


5/0 


0000 


.454 


.46 


.393 




.4 


10.16 


.406 


4/0 


000 


.425 


.40964 


.362 




.372 


9.45 


.375 


3/0 


00 


.38 


.3648 


.331 




.348 


8.84 


.344 


2/0 





.34 


.32486 


.307 




.324 


8.23 


.313 





1 


.3 


.2893 


.283 


.227 


.3 


7.62 


.281 


1 


2 


.284 


.25763 


.263 


.219 


.276 


7.01 


.266 


2 


3 


.259 


.22942 


.244 


.212 


.252 


6.4 


.25 


3 


4 


.238 


.2043 1 


.225 


.207 


.232 


5.89 


.234 


4 


5 


.22 


.18194 


.207 


.204 


.212 


5.38 


.219 


5 


6 


.203 


.16202 


.192 


.201 


.192 


4.88 


.203 


6 


—7 


.18 


.14428 


.177 


.199 


.176 


4.47 


.188 


7 


8 


.165 


.12849 


.162 


.197 


.16 


4.06 


.172 


8 


9 


.148 


.11443 


.148 


.194 


.144 


3.66 


.156 


9 


10 


.134 


.10189 


.135 


.191 


.128 


3.23 


.141 


10 


11 


.12 


.09074 


.12 


.188 


.116 


2.95 


.125 


11 


_12 


.109 


.08081 


.105 


.185 


.104 


2.64 


.109 


12 


13 


.095 


.07196 


.092 


.182 


.092 


2.34 


.094 


13 


14 


.033 


.06403 


.08 


.180 


.08 


2.03 


.078 


14 


15 


.072 


.05707 


.072 


.178 


.072 


1.83 


.07 


15 


"16 


.065 


.05032 


.063 


.175 


.064 


1.63 


.0625 


16 


17 


.058 


.04526 


.054 


.172 


.056 


1.42 


.0563 


17 


13 


.049 


.0403 


.047 


.168 


.048 


1.22 


.05 


18 


19 


.042 


.03589 


.041 


164 


.04 


1.02 


.0438 


19 


20 


.035 


.03196 


.035 


.161 


.036 


.91 


.0375 


20 


21 


.032 


.02846 


.032 


.157 


.032 


.81 


.0344 


21 


22 


.028 


.02535 


.028 


.155 


.028 


.71 


.0313 


22 


23 


.025 


.02257 


.025 


.153 


.024 


.61 


.0281 


23 


24 


.022 


.0201 


.023 


.151 


.022 


.56 


.025 


24 


25 


.02 


.0179 


.02 


.148 


.02 


.51 


.0219 


25 


26 


.018 


.01594 


.018 


.146 


.018 


.46 


.0188 


26 


- 27 


.016 


.01419 


.017 


.143 


.0164 


.42 


.0172 


27 


28 


.014 


.01264 


.016 


.139 


.0148 


.38 


.0156 


28 


29 


.013 


.01126 


.015 


.134 


.0136 


.35 


.0141 


29 


30 


.012 


.01002 


.014 


.127 


.0124 


.31 


.0125 


30 


31 


.01 


.00893 


.013 


.120 


.0116 


.29 


.0109 


31 


32 


.009 


.00795 


.013 


.115 


.0108 


.27 


.0101 


32 


33 


.008 


.00708 


.011 


.112 


.01 


.25 


.0094 


33 


34 


.007 


.0063 


.01 


.110 


.0092 


.23 


.0086 


34 


35 


.005 


.00561 


.00 


.108 


.0084 


.21 


.0078 


35 


~ 36 


.004 


.005 


.009 


.106 


.0076 


.19 


.007 


36 


37 




.00445 


.0085 


.103 


.0068 


.17 


.0066 


37 


38 




.00396 


.008 


.101 


.006 


.15 


.0063 


38 


39 




.00353 


.0075 


.099 


.0052 


.13 




39 


40 




.00314 


.007 


.097 


.0048 


.12 




40 


41 








.095 


.0044 


.11 




41 


42 








.092 


.004 


.10 




42 


43 








.088 


.0036 


.09 




43 


44 








.085 


.0032 


.08 




44 


45 








.081 


.0028 


.07 




45 


46 








.079 


.0024 


.06 




46 


47 








.077 


.002 


.05 




47 


48 








.075 


.0016 


.04 




48 


49 








.092 


.0012 


.03 




49 


50 








.069 


.001 


.025 




50 



30 



ARITHMETIC. 





EDISON, OR CIRCULAR MIL GAUGE, FOR ELEC- 
TRICAL WIRES. 




Gauge 

Num- 
ber. 


Circular 
Mils. 


Diam- 
eter in 
Mils. 


Gauge 
Num- 
ber. 


Circular 
Mils. 


Diam- 
eter in 
Mils. 


Gauge 
Num- 
ber. 


Circular 

Mils. 


Diam- 
eter in 
Mils. 


3 
5 
8 
12 
15 

20 
25 
30 
35 
40 

45 
50 
55 
60 
65 


3,000 
5,000 
8,000 
12,000 
15,000 

20,000 
25,000 
30,000 
35,000 
40,000 

45,000 
50,000 
55,000 
60,000 
65,000 


54.78 
70.72 
89.45 
109.55 
122.48 

141.43 

158.12 
173.21 
187.09 
200.00 

212.14 

223.61 
234.53 
244.95 
254.96 


70 
75 
80 
85 
90 

95 
100 
110 
120 
130 

140 
150 
160 

170 

180 


70,000 
75,000 
80,000 
85,000 
90,000 

95,000 
100,000 
110,000 
120,000 
130,000 

140,000 
150,000 
160,000 
170,000 
180,000 


264.58 
273.87 
282.85 
291.55 
300.00 

308.23 
316.23 
33 1 .67 
346.42 
360.56 

374.17 
387.30 
400.00 
412.32 
424.27 


190 
200 
220 
240 
260 

280 
300 
320 
340 
360 


190,000 
200,000 
220,000 
240,000 
260,000 

280,000 
300,000 
320,000 
340,000 
360,000 


435.89 
447.22 
469.05 
489.90 
509.91 

529.16 
547.73 
565.69 
583.10 
600.00 



TWIST DRILL AND STEEL WIRE GAUGE. 

(Morse Twist Drill and Machine Co.) 



No. 


Size. 


No. 


Size. 


No. 


Size. 


No. 


Size. 


No. 


Size. 


No. 


Size. 








inch. 




inch. 




inch. 




inch. 




inch. 


1 


.2230 


11 


.1910 


7,1 


.1590 


31 


.1200 


41 


.0960 


51 


.0670 


?. 


.2210 


12 


.1890 


22 


.1570 


32 


.1160 


42 


.0935 


52 


.0635 


3 


.2130 


13 


.1850 


23 


.1540 


33 


.1130 


43 


.0890 


53 


.0595 


4 


.2090 


14 


.1820 


7,4 


.1520 


34 


.1110 


44 


.0860 


54 


.0550 


5 


.2055 


15 


.1800 


7.5 


.1495 


35 


.1100 


45 


.0820 


55 


.0520 


6 


.2040 


16 


.1770 


26 


.1470 


36 


.1065 


46 


.0810 


56 


.0465 


7 


.2010 


17 


.1730 


27 


.1440 


37 


.1040 


47 


.0785 


57 


.0430 


8 


.1990 


18 


.1695 


28 


.1405 


38 


.1015 


48 


.0760 


58 


.0420 


9 


.1960 


19 


.1660 


29 


.1360 


39 


.0995 


49 


.0730 


59 


.0410 


10 


.1935 


20 


.1610 


30 


.1285 


40 


.0980 


50 


.0700 


60 


.0400 



STUBS' STEEL WIRE GAUGE. 

(For Nos. 1 to 50 see table on page 29.) 



No. 


Size. 


No. 


Size. 
inch. 


No. 


Size. 


No. 


Size. 


No. 


Size. 


No. 


Size. 




inch. 


inch. 


inch. 


inch. 


inch. 


Z 


.413 


P 


.323 


W 


.257 


51 


.066 


61 


.038 


71 


.026 


Y 


.404 


o 


.316 


b) 


.250 


52 


.063 


62 


.037 


72 


.024 


X 


.397 


N 


.302 


1) 


.246 


53 


.058 


63 


.036 


73 


.023 


W 


.386 


M 


.295 


C 


.242 


54 


.055 


64 


.035 


74 


.022 


V 


.377 


r, 


.290 


B 


.238 


55 


.050 


65 


.033 


75 


.020 


u 


.368 


K 


.281 


A 


.234 


56 


.045 


66 


.032 


76 


.018 


T 


.358 


.1 


.277 


1 


(See 


57 


.042 


67 


.031 


77 


.016 


s 


.348 


T 


.272 


to 


{page 


58 


.041 


68 


.030 


78 


.015 


H, 


.339 


H 


.266 


50 


(29 


59 


.040 


69 


.029 


79 


.014 


Q 


.332 


G 


.261 






60 


.039 


70 


.027 


80 


.013 



The Stubs' Steel Wire Gauge is used in measuring drawn steel wire or 
drill rods of Stubs' make, and is also used by many makers of American 
drill rods. 



WIRE AND SHEET-METAL GAUGES. 31 



THE EDISON OR CIRCULAR 3IIL WIRE GAUGE. 

(For table of copper wires by this gauge, giving weights, electrical 
resistances, etc., see Copper Wire.) 

Mr. C. J: Field (Stevens Indicator, July, 1887) thus describes the origin 
of the Edison gauge: 

The Edison company experienced inconvenience and loss by not having 
a wide enough range nor sufficient number of sizes in the existing gauges. 
This was felt more particularly in the central-station work in making 
electrical determinations for the street system. They were compelled to 
make use of two of the existing gauges at least, thereby introducing a 
complication that was liable to lead to mistakes by the contractors and 
linemen. 

In the incandescent system an even distribution throughout the entire 
system and a uniform pressure at the point of delivery are obtained by 
calculating for a given maximum percentage of loss from the potential as 
delivered from the dynamo. In carrying this out, on account of lack of 
regular sizes, it was often necessary to use larger sizes than the occasion 
demanded, and even to assume new sizes for large underground conductors. 
The engineering department of the Edison company, knowing the require- 
ments, have designed a gauge that has the widest range obtainable and 
a large number of sizes which increase in a regular and uniform manner. 
The basis of the graduation is the sectional area, and the number of the 
wire corresponds. A wire of 100,000 circular mils area is No. 100; a wire . 
of one half the size will be No. 50; twice the size No. 200. 

In the older gauges, as the number Increased the size decreased. With 
this gauge, however, the number increases with the wire, and the number 
multiplied by 1000 will give the circular mils. 

The weight per mil-foot, 0.00000302705 pounds, agrees with a specific 
gravity of 8.889, which is the latest figure given for copper. The ampere 
capacity which is given was deduced from experiments made in the com- 
pany's laboratory, and is based on a rise of temperature of 50° F. in the 
wire. 

In 1893 Mr. Field writes, concerning gauges in use by electrical engineers: 

The B. and S. gauge seems to be in general use for the smaller sizes, up 
to 100,000 cm., and in some cases a little larger. From between one and 
two hundred thousand circular mils upwards, the Edison gauge or its 
equivalent is practically in use, and there is a general tendency to desig- 
nate all sizes above this in circular mils, specifying a wire as 200,000, 
400,000, 500,000, or 1,000,000 cm, 

In the electrical business there is a large use of copper wire and rod and 
other materials of these large sizes, and in ordering them, speaking of 
them, specifying, and in every other use, the general method is to simply 
specity the circular milage. I think it is going to be the only system in 
the future for the designation of wires, and the attaining of it means 
practically the adoption of the Edison gauge or the method and basis of 
this gauge as the correct one for wire sizes. 

THE U. S. STANDARD GAUGE FOR SHEET AND 
PLATE IRON AND STEEL, 1893. 

There is in this country no uniform or standard gauge, and the same 
numbers in different gauges represent different thicknesses of sheets or 

Slates. This has given rise to much misunderstanding and friction 
etween employers and workmen and mistakes and fraud between dealers 
and consumers. 

An Act of Congress in 1893 established the Standard Gauge for sheet 
iron and steel which is given on the next page. It is based on the fact that 
a cubic foot of iron weighs 480 pounds. 

A sheet of iron 1 foot square and 1 inch thick weighs 40 pounds, or 640 
ounces, and 1 ounce in weight should be 1/640 inch thick. The scale has 
been arranged so that each descriptive number represents a certain 
number of ounces in weight and an equal number of 640ths of an inch in 
thickness. 

The law enacts that on and after July 1, 1893, the new gauge shall be 
used in determining duties and taxes levied on sheet and plate iron and 



32 






ARITHMETIC. 










U. S. STANDARD GAUGE FOR SHEET AND PLATE 




IRON AND STEEL, 


1893. 






S3 S. 

BO 




Approximate 

Thickness in 

Decimal 

Parts of an 

Inch. 


li 1 

■Ha -£ 
oo-S S 

< •* 


Weight per 

Square Foot 

in Ounces 

Avoirdupois. 


Weight per 

Square Foot 

in Pounds 

Avoirdupois. 


Hi 

>• & 


Hi 

II! 

as .3 


6^ • 
en £.22 

ill 
-.S'2 


0000000 


1-2 


0.5 


12.7 


320 


20. 


9.072 


97.65 


000000 


15-32 


0.46875 


1 1 .90625 


300 


18.75 


8.505 


91.55 


201.82 


00000 


7-16 


0.4375 


11.1125 


280 


17.50 


7.938 


85.44 


188.37 


0000 


13-32 


0.40625 


10.31875 


260 


16.25 


7.371 


79.33 


174.91 


000 


3-8 


0.375 


9.525 


240 


15. 


6.804 


73.24 


161.46 


00 


11-32 


0.34375 


8.73125 


220 


13.75 


6.237 


67.13 


148.00 





5-16 


0.3125 


7.9375 


200 


12.50 


5.67 


61.03 


134.55 


1 


9-32 


0.28125 


7.14375 


180 


11.25 


5.103 


54.93 


121.09 


2 


17-64 


0.265625 


6.746875 


170 


10.625 


4.819 


51.88 


114.37 


3 


1-4 


0.25 


6.35 


160 


10. 


4.536 


48.82 


107.64 


4 


15-64 


0.234375 


5.953125 


150 


9.375 


4.252 


45.77 


100.91 


5 


7-32 


0.21875 


5.55625 


140 


8.75 


3.969 


42.72 


94.18 


6 


13-64 


0.203125 


5.159375 


130 


8.125 


3.685 


39.67 


87.45 


7 


3-16 


0.1875 


4.7625 


120 


7.5 


3.402 


36.62 


80.72 


8 


11-64 


0.171875 


4.365625 


110 


6.875 


3.118 


33.57 


74.00 


9 


5-32 


0.15625 


3.96875 


100 


6.25 


2.835 


30.52 


67.27 


10 


9-64 


0.140625 


3.571875 


90 


5.625 


2.552 


27.46 


60.55 


11 


1-8 


0.125 


3.175 


80 


5. 


2.268 


24.41 


53.82 


12 


7-64 


0.109375 


2.778125 


70 


4.375 


1.984 


21.36 


47.09 


13 


3-32 


0.09375 


2.38125 


60 


3.75 


1.701 


18.31 


40.36 


14 


5-64 


0.078125 


1.984375 


50 


3.125 


1.417 


15.26 


33.64 


15 


9-128 


0.0703125 


1.7859375 


45 


2.8125 


1.276 


13.73 


30.27 


16 


1-16 


0.0625 


1.5875 


40 


2.5 


1.134 


12.21 


26.91 


17 


9-160 


0.05625 


1 .42875 


36 


2.25 


1.021 


10.99 


24.22 


18 


1-20 


0.05 


1.27 


32 


2. 


0.9072 


9.765 


21.53 


19 


7-160 


0.04375 


1.11125 


28 


1.75 


0.7938 


8.544 


18.84 


20 


3-80 


0.0375 


0.9525 


24 


1.50 


0.6804 


7.324 


16.15 


21 


1 1-320 


0.034375 


0.873125 


22 


1.375 


0.6237 


6.713 


14.80 


22 


1-32 


0.03125 


0.793750 


20 


1.25 


0.567 


6.103 


13.46 


23 


9-320 


0.028125 


0.714375 


18 


1.125 


0.5103 


5.49 


12.11 


24 


1-40 


0.025 


0.635 


16 


1. 


0.4536 


4.882 


10.76 


25 


7-320 


0.021875 


0.555625 


14 


0.875 


0.3969 


4.272 


9.42 


26 


3-160 


0.01875 


0.47625 


12 


0.75 


0.3402 


3.662 


8.07 


27 


1 1-640 


0.0171875 


0.4365625 


11 


0.6875 


0.3119 


3.357 


7.40 


28 


1-64 


0.015625 


0.396875 


10 


0.625 


0.2835 


3.052 


6.73 


29 


9-640 


0.0140625 


0.3571875 


9 


0.5625 


0.2551 


2 746 


6.05 


30 


1-80 


0.0125 


0.3175 


8 


0.5 


0.2268 


2.441 


5.38 


31 


7-640 


0.0109375 


0.2778125 


7 


0.4375 


0.1984 


2.136 


4.71 


32 


13-1280 


0.01015625 


0.25796875 


6V2 


0.40625 


0.1843 


1.983 


4.37 


33 


3-320 


0.009375 


0.238125 


6 


0.375 


0.1701 


1.831 


4.04 


34 


11-1280 


0.00859375 


0.21828125 


5V2 


0.34375 


0.1559 


1.678 


3.70 


35 


5-640 


0.0078125 


0.1984375 


5 


0.3125 


0.1417 


1.526 


3.36 


36 


9-1280 


0.00703125 


0.17859375 


41/2 


0.28125 


0.1276 


1.373 


3.03 


37 


1 7-2560 


0.00664062 


0.16867187 


41/4 


0.26562 


0.1205 


1.297 


2.87 


38 


1-160 


0.00625 


0.15875 


4 


0.25 


0.1134 


1.221 


2.69 





















THE DECIMAL GAUGE. 



33 



steel ; and that in its application a variation of 2 1/2 per cent either way may 
be allowed. 

The Decimal Gauge. — The legalization of the standard sheet- 
metal gauge of 1893 and its adoption by some manufacturers of 
sheet iron have only added to the existing confusion of gauges. A joint 
committee of the American Society of Mechanical Engineers and the 
American Railway Master Mechanics' Association in 1895 agreed to 
recommend the use of the decimal gauge, that is, a gauge whose number 
for each thickness is the number of thousandths of an inch in that thick- 
ness, and also to recommend " the abandonment and disuse of the various 
other gauges now in use, as tending to confusion and error." A notched 
gauge of oval form, shown in the cut below, has come into use as a standard 
form of the decimal gauge. 

In 1904 The Westinghouse Electric & Mfg- Co. abandoned the use of 
gauge numbers in referring to wire, sheet metal, etc. 

Weight of Sheet Iron and Steel. Thickness by Decimal Gauge. 







2 


Weight per 








Weight per 


• 


a 

. 


Square Foot 


• 


§ 


! 


Square Foot 


O 


in Pounds. 


3 




.2 


in Pounds. 


■£-5 
££ 
*fi 

go 
a 
a 
< 


3 


^ 


vO 


£§ 


a 


&* 


•& 


"3 • 

a 


i 


• 

00 3 




a 


*g 


i 


Sri 


§> 


01 

Q 


2 

a 
a 
< - 


a 




Oi 

Q 


aS 

a 
< 



a 
a 
< 


TO 

fife 

a 


"i Ja ri 


0.002 


1/500 


0.05 


0.08 


0.082 


0.060 


i/is- 


1.52 


2.40 


2.448 


0.004 


1/250 


0.10 


0.16 


0.163 


0.065 


13/200 


1.65 


2.60 


2.652 


0.006 


3 /500 


0.15 


0.24 


0.245 


0.070 


7 /l00 


1.78 


2.80 


2.856 


0.008 


Vl25 


0.20 


0.32 


0.326 


0.075 


3/40 


1.90 


3.00 


3.060 


0.010 


1/100 


0.25 


0.40 


0.408 


0.080 


2/25 


2.03 


3.20 


3.264 


0.012 


3 /250 


0.30 


0.48 


0.490 


0.085 


17/200 


2.16 


3.40 


3.468 


0.014 


7 /500 


0.36 


0.56 


0.571 


0.090 


9/100 


2.28 


3.60 


3.672 


0.016 


1/64 + 


0.41 


0.64 


0.653 


0.095 


19/200 


2.41 


3.80 


3.876 


0.018 


9 /500 


0.46 


0.72 


0.734 


0.100 


1/10 


2.54 


4.00 


4.080 


0.020 


1/50 


0.51 


0.80 


0.816 


0.110 


11/100 


2.79 


4.40 


4.488 


0.022 


U/500 


0.56 


0.88 


0.898 


0.125 


1/8 


3.18 


5.00 


5.100 


0.025 


1/40 


0.64 


1.00 


1.020 


0.135 


27/200 


3.43 


5.40 


5.508 


0.028 


7/250 


0.71 


1.12 


1.142 


0.150 


3/20 


3.81 


6.00 


6.120 


0.032 


1/32 + 


0.81 


1.28 


1.306 


0.165 


33/200 


4.19 


6.60 


6.732 


0.036 


9/250 


0.91 


1.44 


1.469 


0.180 


9/50 


4.57 


7.20 


7.344 


0.040 


1/25 


1.02 


1.60 


1.632 


0.200 


1/5 


5.08 


8.00 


8.160 


0.045 


9 /200 


1.14 


1.80 


1.836 


0.220 


H/50 


5.59 


8.80 


8.976 


0.050 


1/20 


1.27 


2.00 


2.040 


0.240 


6 /25 


6.10 


9.60 


9.792 


0.055 


11/200 


1.40 


2.20 


2.244 


0.250 


1/4 


6.35 10.00 


10.200 



'■9 



^OlMALGA^I^ 






STANDARD O 



34 



ALGEBRA. 

Addition. — Add a, 6, and - c. Ans. a + b - c. 

Add 2a and - 3a. Ans. - a. Add 2ab, - 3ab, — c, — 3c. Ans, 

— ab — 4c. Add a 2 and 2a. Ans. a 2 4 2a. 

Subtraction. — Subtract a from 6. Ans. b — a. Subtract - a from 

— 6. Ans. — & + a. 

Subtract b + c from a. Ans. a - 6 — c. Subtract 3a 2 & - 9c from 
4a 2 6 4 c. Ans. a 2 b + 10c. Rule: Change the signs of the subtrahend 
and proceed as in addition. 

Multiplication. — Multiply a by 6. Ans. ab. Multiply ab by a + b. 
Ans. a 2 6 + ab 1 . 

Multiply a+ b by a + b. Ans.- (a +6) (a 4 6) = a 2 4- 2a6 4 6 2 . 

Multiply — a by - b. Ans. ab. Multiply -a by 6. Ans. - ab. 
Like signs give plus, unlike signs minus. 

Powers of numbers. — The product of two or more powers of any 
number is the number with an exponent equal to the sum of the powers: 
a 2 Xa 3 = a 5 ; a 2 b 2 X ab = a 3 6 3 ; - lab X 2ac = - 14a 2 6c. 

To multiply a polynomial by a monomial, multiply each term of the 
polynomial by the monomial and add the partial products: (6a — 3b) 
X 3c = 18ac - 96c. 

To multiply two polynomials, multiply each term of one factor by each 
term of the other and add the partial products: (5a — 66) X (3a — 46) 
= 15a 2 - 38a6 + 246 2 . 

The square of the sum of two numbers = sum of their squares + twice 
their product. 

The square of the difference of two numbers = the sum of their squares 

— twice their product. 

The product of the sum and difference of two numbers = the difference 
of their squares: 

(a + 6)2 = a 2 4 2ab 4 6 2 ; (a - 6) 2 = a 2 - 2a6 + 6 2 ; 
(a + 6) X (a - 6) = a 2 - 6 2 . 

The square of half the sums of two quantities is equal to their product 
plus the square of half their difference: ( — — I = a6 4 ( — — I • 

The square of the sum of two quantities is equal to four times their 
products, plus the square of their difference: (a 4- 6) 2 = 4a6 + (a — 6) 2 . 

The sum of the squares of two quantities equals twice their product, 
plus the square of their difference: a 2 + 6 2 = 2a6 + (a - 6) 2 . 

The square of a trinomial = square of each term + twice the product 
of each term by each of the terms that follow it: (a + 6 + c) 2 = a 2 4- 6 2 
4 c 2 + 2a6 + 2ac 4- 26c; (a - 6 - c) 2 = a 2 + 6 2 + c* - 2a6- 2ac + 26c. 

The square of (any number + 1/2) = square of the number 4- the number 
+ 1/4: = the number X (the number 4- 1) + 1/4: (a + V2) 2 = a 2 + a + 1/4, 
= a(a+ 1)4- 1/4. (4V 2 ) 2 = 4 2 + 4 + l/ 4 = 4 X 5 +1/4= 20l/ 4 . 

The product of any number 4- 1/2 by any other number 4- 1/2 = product 
of the numbers 4 half their sum 4 1/4. (a 4 1/2) X (6 4- 1/2) = a6 4 l?2(& 46) 
4 1/4. 41/2 X 6V2 = 4 X 6 4- 1/2(4 4- 6) 4- 1/4 = 24 + 5 4- 1/4 = 291/4. 

Square, cube, 4th power, etc., of a binomial a+b. 

(a 4 6) 2 = a 2 4- 2a6 + 6 2 ; (a 4 6) 3 = a 3 4- 3a 2 6 4 3a6 2 + 6 3 
(a + b)* = a 4 4- 4a 3 6 4- 6a 2 6 2 4- 4a& 3 4- 6*. 

In each case the number of terms is one greater than the exponent of 
the power to which the binomial is raised. 

2. In the first term the exponent of a is the same as the exponent of the 
power to which the binomial is raised, and it decreases by 1 in each suc- 
ceeding term. 

3. 6 appears in the second term with the exponent 1, and its exponent 
increases by 1 in each succeeding term. 

4. The coefficient of the first term is 1. 

5. The coefficient of the second term is the exponent of the power to 
which the binomial is raised. 



35 



6. The coefficient of each succeeding term is found from the next pre- 
ceding term by multiplying its coefficient by the exponent of a, and 
dividing the product by "a number greater by 1 than the exponent of b. 
(See Binomial Theorem, below.) 

Parentheses. — When a parenthesis is preceded by a plus sign it may 
be removed without changing the value of the expression: a + b + (a + 
b) = 2a + 2b. When a parenthesis is preceded by a minus sign it may 
be removed if we change the signs of all the terms within the parenthesis: 
1 — (a — b — c) = l— a+b+c. When a parenthesis is within a 
parenthesis remove the inner one first: a — [& - {c — (d — e)}] = a — [ft — 
{c — d + e} ] = a — [b — c + d — e] = a — b + c — d + e. 

A multiplication sign, X, has the effect of a parenthesis, in that the 
operation indicated by it must be performed before the operations of 
addition or subtraction, a + b X a + b = a + ab + b; while (a + b) 
X (a + b) = a 2 + 2ab + b 2 , and (a + b) X a + b = a 2 + ab + b. 

The absence of any sign between two parentheses, or between a quan- 
tity and a parenthesis, indicates that the parenthesis is to be multiplied by 
the quantity or parenthesis: a(a + b + c) = a 2 + ab + ac. 

Division. — The quotient is positive when the dividend and divisor 
have like signs, and negative when they have unlike signs: abc -h b = ac; 
abc h- — b = — ac. 

To divide a monomial by a monomial, write the dividend over the 
divisor with a line between them. If the expressions have common factors, 
remove the common factors: 

9 , . a 2 bx a, 

a 2 bx -5- aby = —. — = - , 

aby y a 3 'a 5 a 2 

To divide a polynomial by a monomial, divide each term of the poly- 
nomial by the monomial: (Sab — I2ac) -j- 4a = 26 — 3c. 

To divide a polynomial by a polynomial, arrange both dividend and 
divisor in the order of the ascending or descending powers of some common 
letter, and keep this arrangement throughout the operation. 

Divide the first term of the dividend by the first term of the divisor, and 
write the result as the first term of the quotient. 

Multiply all the terms of the divisor by the first term of the quotient 
and subtract the product from the dividend. If there be a remainder, 
consider it as a new dividend and proceed as before: (a 2 — 6 2 ) -4- (a +6). 



The difference of two equal odd powers of any two numbers is divisible 
by their difference and also by their sum: 

(a* -&s) -5- (a-b) =a 2 +ab +b 2 ; (a 3 - & 3 ) -s- (a +6) =a 2 -ab +b 2 . 

The difference of two equal even powers of two numbers is divisible by 
their difference and also by their sum: (a 2 — b 2 ) -f- (a — o) = a + b. 

The sum of two equal even powers of two numbers is not divisible by 
either the difference or the sum of the numbers; but when the exponent 
of each of the two equal powers is composed of an odd and an even factor, 
the sum of the given power is divisible by the sum of the powers expressed 
by the even factor. Thus x 6 + y 6 is not divisible byx 4- y or by x — y, 
but is divisible by x 2 + y 2 . 

Simple equations. — An equation is a statement of equality between 
two expressions; as, a + b = c + d. , . ... 

A simple equation, or equation of the first degree, is one which contains 
only the first power of the unknown quantity. If equal changes be made 
(by addition, subtraction, multiplication, or division) in both sides of an 
equation, the results will be equal. 

Any term may be changed from one side of an equation to another, 
provided its sign be changed: a + b = c + d; a = c + d — b. To solve 



36 ALGEBRA. 

an equation having one unknown quantity, transpose all the terms involv- 
ing the unknown quantity to one side of the equation, and all the other 
terms to the other side; combine like terms, and divide both sides by the 
coefficient of the unknown quantity. 

Solve 8x - 29 = 26 - 3x. 8x + 3x — 29 + 26; llz = 55; x = 5, ans. 

Simple algebraic problems containing one unknown quantity are solved 
by making x = the unknown quantity, and stating the conditions of the 
problem in the form of an algebraic equation, and then solving the equa- 
tion. What two numbers are those whose sum is 48 and difference 14? 
Let x = the smaller number, x + 14 the greater, x + x + 14 = 48. 
2x = 34, x = 17; x + 14 = 31, ans. 

Find a number whose treble exceeds 50 as much as its double falls short 
of 40. Let x = the number. 3x — 50 = 40 — 2x; 5x = 90; x = 18, ans. 
Proving, 54 - 50 = 40 - 36. 

Equations containing two unknown quantities. — If one equation 
contains two unknown quantities, x and y, an indefinite number of pairs 
of values of x and y may be found that will satisfy the equation, but if a 
second equation be given only one pair of values can be found that will 
satisfy both equations. Simultaneous equations, or those that may be 
satisfied by the same values of the unknown quantities, are solved by 
combining the equations so as to obtain a single equation containing only 
one unknown quantity. This process is called elimination. 

Elimination by addition or subtraction. — Multiply the equation by 
such numbers as will make the coefficients of one of the unknown quanti- 
ties equal in the resulting equation. Add or subtract the resulting equa- 
tions according as they have unlike or like signs. 

c n1v „ | 2x + 3y = 7. Multiply by 2: 4x + 6y =14 

&olve \ 4k - 5y = 3. Subtract : 4x - by = 3 lly - 11 ; y = 1. 

Substituting value of y in first equation, 2x + 3 = 7; x = 2. 

Elimination by substitution. — From one of the equations obtain the 
value of one of the unknown quantities in terms of the other. Substi- 
tute for this unknown quantity its value in the other equation and reduce 
the resulting equations. 

Solve ! 2x + 3 V = 8 " (1 >- From (1 > we find x = 8 ~o 3V - 
bolve (3x + 7y = 7. (2). 2 

Substitute this value in (2):3( 8 ~ 3y ) +7y = 7; =24-9y + 14?/ = 14, 

whence y =— 2. Substitute this value in (1): 2x — 6 = 8; x = 7. 

Elimination by comparison. — From each equation obtain the value of 
one of the unknown quantities in terms of the other. Form an equation 
from these equal values, and reduce this equation. 

Solve 2x - 9y = 11. (1) and 3x - 4y = 7. (2). From (1) we find 

x = ik + *y. From (2) we end x = i^l. 

Equating these values of x, 1— y = "t v ; 19y = — 19; y = - 1. 

Substitute this value of y in (1): 2x + 9 = 11; x = 1. 

If three simultaneous equations are given containing three unknown 
quantities, one of the unknown quantities must be eliminated between two 
pairs of the equations; then a second between the two resulting equations. 

Quadratic equations. — A quadratic equation contains the square of 
the unknown quantity, but no higher power. A pure quadratic contains 
the square only; an affected quadratic both the square and the first power. 

To solve a pure quadratic, collect the unknown quantities on one side, 
and the known quantities on the other; divide by the coefficient of the 
unknown quantity and extract the square root of each side of the resulting 
equation; _ 

Solve 3x 2 - 15 = 0. 3z 2 = 15; x 2 = 5; x = ^5. 

A root like ^5, which is indicated, but which can be found only approxi- 
mately, is called a surd. 



ALGEBRA. 37 

Solve 3x 2 + 15 = 0. 3x = - 15; x 2 = - 5; x = V~5. 

The square root of — 5 cannot be found even approximately, for the 
square of any number positive or negative is positive; therefore a root 
which is indicated, but cannot be found even approximately, is called 
imaginary. 

To solve an affected quadratic, 1. Convert the equation into the form 
a 2 x 2 ± 2dbx = c, multiplying or dividing the equation if necessary, so as 
to make the coefficient of x 2 a square number. 

2. Complete the square of the first member of the equation, so as to 
convert it to the form of a 2 x 2 ± 2abx + b 2 , which is the square of the 
binomial ax±b, as follows: add to each side of the equation the square of 
the quotient obtained by dividing the second term by twice the square 
root of the first term. 

3. Extract the square root of each side of the resulting equation. 
Solve 3:r 2 — 4.r= 32. To make the coefficient of x 2 a square number, 

multiply by 3 : 9x 2 - 12s = 96; 12x -e- (2 X 3x) = 2; 2 2 = 4. 

Complete the square: 9a; 2 — 12x + 4 = 100. Extract the root: 
3x - 2 = ±10, whence x = 4 or — 22/ 3 . The square root of 100 is 
either + 10 or — 10, since the square of — 10 as well as + 10 2 = 100. 

Every affected quadratic may be reduced t o the form ax 2 +bx+c=0. 

— b ± *^b 2 — Aac 
The solution of this equation is x = — 

Problems involving quadratic equations have apparently two solutions, 
as a quadratic has two roots. Sometimes both will be true solutions, but 
generally one only will be a solution and the other be inconsistent with the 
conditions of the problem. 

The sum of the squares of two consecutive positive numbers is 481. 
Find the numbers. 

Let x = one number, x+1 the other, x 2 + (x + l) 2 = 481. 2z 2 + 
2x + 1 = 481. 

x 2 + x = 240. Completing the square, x 2 +x + 0.25 = 240.25. 
Extracting the root we obtain x+ 0.5 = ± 15.5; x = 15 or — 16. The 
negative root — 16 is inconsistent with the conditions of the problem. 

Quadratic equations containing two unknown quantities require 
different methods for their solution, according to the form of the equations. 
For these methods reference must be made to works on algebra. 

Theory of exponents. — ^Ja when n is a positive integer is one of n 

n /~m 
-qual factors of a. *\ja means a is to be raised to the mth power and the 

nth root extracted. 



( Vaf 



' means that the nth root of a is to be taken and the result 
raised to the mth power. 

ya m = ( Vo ) m = an. When the exponent is a" fraction, the numera- 
tor indicates a power, and the denominator a root, a 6 /2 = v / a 6 = a 3 ; 
a 3 /2 = V a s = a 1 - 5 . 

To extract the root of a quantity raised to an indicated power, divide 
the exponent by the index of the required root; as, 

m 
yaJ 1 = a » ; \/a 6 = a 6 /3 = a 2 . 

Subtracting 1 from the exponent of a is equivalent to dividing by a: 

a 2 ~i= a 1 = a; a 1 "* = a = -= 1; a - 1 = a" 1 = -; a ~ l -i = a~2= I. 
a a a 2 

A number with a negative exponent denotes the reciprocal of the num- 
ber with the corresponding positive exponent. 

A factor under the radical sign whose root can be taken may, by having 
the root taken, be removed from under the radical sign: 

VoJb = v^i x Vb = a Vb. 



38 



GEOMETRICAL PROBLEMS. 



A factor outside the radical sign may be raised to the corresponding 
power and placed under it : 



Binomial Theorem. — To obtain any power, as the nth, of an expres- 
sion of the form x + a s 
{a + x) n_ n n^„ n n-i,._ u n(n - l)a ^ n(w-l)(n-: 

etc. 



ri = a n + na a 



l x + 



- x 2 + 



1.2 1.2.3. 

The following laws hold for any term in the expansion of (a + x) n . 



x 3 -\ 



The exponent of x is less by one than the number of terms. 

The exponent of a is n minus the exponent of x. 

The last factor of the numerator is greater by one than the exponent of a. 

The last factor of the denominator is the same as the exponent of x. 

In the rth term the exponent of x will be r — 1. 

The exponent of a will be n — (r — 1), or n — r + 1. 

The last factor of the numerator will be n — r +2. 

The last factor of the denominator will be = r — 1. 

n(n - l)(n - 2) . . (n - r+ 2) „n-r + i .M. 
1.2.3....&— 1) a X 



Hence the rth term = 



GEOMETRICAL PROBLEMS. 




1. To bisect a straight line, or 
an arc of a circle (Fig. 1). — From 
the ends A, B, as centres, describe 
arcs intersecting at C and D, and 
draw a line through C and D which 
will bisect the line at E or the arc 
at F. 

2. To draw a perpendicular to 
a straight line, or a radial line to 
a circular arc. — Same as in 
Problem 1. C D is perpendicular to 
the line A 25, and also radial to the 
arc. 

3. To draw a perpendicular to 
a straight line from a given point 
in that line (Fig. 2). — With any 
radius, from the given point A in the 
line B C, cut the line at B and C. 
With a longer radius describe arcs 
from B and C, cutting each other at 
D, and draw the perpendicular D A. 

4. From the end A of a given 
line A D to erect a perpendicular 
AE (Fig. 3). — From any centre F, 
above A I), describe a circle passing 
through the given point A, and cut- 
ting the given line at D. Draw D F 
and produce it to cut the circle at E, 
and draw the perpendicular A E. 

Second Method (Fig. 4). — From 
the given point A set off a distance 
A E equal to three parts, by any 
scale; and on the centres A and E, 
with radii of four and five parts 
respectively, describe arcs intersect- 
ing at C. Draw the perpendicular 
A C. 

Note. — This method is most 
useful on very large scales, where 
straight edges are inapplicable. Any 
multiples of the numbers 3, 4, 5 may 
be taken with the same effect, as 6, 8» 
10, or 9, 12, 15. 



GEOMETRICAL PROBLEMS. 



39 



5. To draw a perpendicular to 
a straight line from any point 
without it (Fig. 5). — From the 
point A, with a sufficient radius cut 
the given line at F and G, and from 
these points describe arcs cutting at 
E. Draw the perpendicular A E. 



6. To draw a straight line 
parallel to a given line, at a given 
distance apart (Fig. 6). — From 
the centres A, B, in the given line, 
with the given distance as radius, 
describe arcs C, D, and draw the 
parallel lines C D touching the arcs. 




I I 

_<! A— 



7. To divide a straight line into 
a number of equal parts (Fig. 7). 
— To divide the line A B into, say, 
five parts, draw the line A C at an 
angle from A ; set off five equal parts; 
draw B5 and draw parallels to it 
from the other points of division in 
A C. These parallels divide A B as 
required. 

Note. — By a similar process a 
line may be divided into a number 
of unequal parts; setting off divisions 
on A C, proportional by a scale to the 
required divisions, and drawing 
parallels cutting A B. The triangles 
All, A22, A33, etc., are similar 
triangles. 



8. Upon a straight line to draw 
an angle equal to a given angle 

(Fig. 8). — Let A be the given angle 
and F G the line. From the point A 
with any radius describe the arc D E. 
From F with the same radius 
describe I H. Set off the arc / H 
equal to D E, and draw F H. The 
angle F is equal to A, as required. 



9. To draw angles of 60° and 

80° (Fig. 9). — From F, with any 
radius F I, describe an arc / H; and 
from /, with the same radius, cut 
the arc at H and draw F H to form 
the required angle I F H. Draw the 
perpendicular H K to the base line to 
form the angle of 30° F H K. 



10. To draw an angle of 45° 

(Fig. 10). — Set off the distance F I; 
draw the perpendicular / H equal to 
/ F, and join H F to form the angle at 
F, The angle at H is also 45°. 




40 



GEOMETRICAL PROBLEMS. 




11. To bisect an angle (Fig. 11). 
— Let ACB be the angle; with C as 
a centre draw an arc cutting the 
sides at A, B. From A and B as 
centres, describe arcs cutting each 
other at D. Draw C D, dividing the 
angle into two equal parts. 

12. Through two given points 
to describe an arc of a circle with 
a given radius (Fig. 12). — From 
the points A and B as centres, with 
the given radius, describe arcs cut- 
ting at C; and from C with the same 
radius describe an arc A B. 




Fig. 14. 




Fig. 15, 



13. To find the centre of a circle 
or of an arc of a circle (Fig. 13). — 
Select three points, A, B, C, in the 
circumference, well apart; with the 
same radius describe arcs from these 
three points, cutting each other, and 
draw the two lines, D E, F G, 
through their intersections. The 
point O, where they cut, is the centre 
of the circle or arc. 

To describe a circle passing 
through three given points. — 
Let A, B, C be the given points, and 
proceed as in last problem to find the 
centre O, from which the circle may- 
be described. 



14. To describe an arc of a 
circle passing through three 
given points when the centre is 
not available (Fig. 14). — From 
the extreme points A, B, as 
centres, describe arcs A H, B G. 
Through the third point C draw 
A E, BF, cutting the arcs. 
Divide A F and B E into any 
number of equal parts, and set 
off a series of equal parts of the 
same length on the upper por- 
tions of the arcs beyond the 
points E F. Draw straight 
lines, B L, B M, etc., to the 
divisions in A F, and A I, A K, 
etc., to the divisions in EG. 
The successive intersections N, 
O, etc., of these lines are points 
in the circle required between the 
given points A and C, which may 
be drawn in; similarly the remain- 
ing part of the curve B C may 
be described, (See also Problem 
54.) 



15. To draw a tangent to a 
circle from a given point in the 
circumference (Fig. 15). — Through 
the given point A, draw the radial 
line A C, and a perpendicular to it, 
FG, which is the tangent required. 



GEOMETRICAL PROBLEMS. 



41 



16. To draw tangents to a 
circle from a point without it (Fig. 
16). — From A, with the radius 
A C, describe an arc BCD, and 
from C, with a radius equal to the 
diameter of the circle, cut the arc at 
BD. Join BC, CD, cutting the 
circle at EF, and draw A E, AF, 
the tangents. 

Note. — When a tangent is 
already drawn, the exact point of 
contact may be found by drawing a 
perpendicular to it from the centre. 

17. Between two inclined lines 
to draw a series of circles touching 
these lines and touching each 
other (Fig. 17). — Bisect the inclina- 
tion of the given lines A B, CD, by 
the line N O. From a point P in this 
line draw the perpendicular PB to the 
line A B, and on P describe the circle 
BD, touching the lines and cutting 
the centre line at E. From E draw 
E F perpendicular to the centre line, 
cutting AB at F, and from F 
describe an arc E G, cutting A B at 
G. Draw GH parallel to B P, 
giving H, the centre of the next 
circle, to be described with the 
radius HE, and so on for the next 
circle IN. 

Inversely, the largest circle may 
be described first, and the smaller 
ones in succession. This problem is 
of frequent use in scroll-work. 

18. Between two inclined lines 
to draw a circular segment tan- 
gent to the lines and passing 
through a point F on the line F C 
which bisects the angle of the 
lines (Fig. 18). — Through F draw 
DA at right angles to FC\ bisect 
the angles A and D, as in Problem 
11, by lines cutting at C, and from 
C with radius C F draw the arc H FG 
required. 

19. To draw a circular arc that 
will be tangent to two given lines 
AB and C D inclined to one another, 
one tangential point E being given 

(Fig. 19). — Draw the centre line 
GF. From E draw £F at right 
angles to AB; then F is the centre 
of the circle required. 

20. To describe a circular arc 
joining two circles, and touching 
one of them at a given point (Fig. 
20). —To join the circles AB, FG, 
by an arc touching one of them at 
F, draw the radius E F, and produce 
it both ways. Set off F H equal to 
the radius A C of the other circle; 
join C H and bisect it with the per- 
pendicular L I, cutting E F at /. 
On the centre I, with radius IF, 
describe the arc FA as required. 




Fig. 20. 



42 



GEOMETRICAL PROBLEMS. 




21. To draw a circle with a 
given radius R that will be tan- 
gent to two given circles A and B 

(Fig. 21). — From centre of circle 
A with radius equal R plus radius 
of A, and from centre of B with 
radius equal to R + radius of B, 
draw two arcs cutting each other in 
C. which will be the centre of the 
circle required. 



22. To construct an equilateral 
triangle, the sides being given 

(Fig. 22). — On the ends of one side, 
A, B, with A B as radius, describe 
arcs cutting at C, and draw A C, C B. 



23. To construct a triangle of 
unequal sides (Fig. 23). — On 
either end of the base A D, with the 
side B as radius, describe an arc; 
and with the side C as radius, on the 
other end of the base as a centre, cut 
the arc at E. Join A E, D E. 



24. To construct a square on a 
given straight line A B (Fig. 24). 
— With A B as radius and A and B 
as centres, draw arcs A D and B C, 
intersecting at E. Bisect E B at 
F. With E as centre and E F as 
radius, cut the arcs A D and B C 
in D and C. Join A C, C D, and 
D B to form the square. 



25. To construct a rectangle 
with given base E F and height E H 

(Fig. 25). — On the base E F draw 
the perpendiculars E H, F G equal 
to the height, and join G H. 




26. To describe a circle about 
a triangle (Fig. 26).— Bisect two 
sides A B, A C of the triangle at 
E F, and from these points draw 
perpendiculars cutting at K. On 
the centre K, with the radius K A, 
draw the circle ABC. 



27. To inscribe a circle in a 
triangle (Fig. 27). —Bisect two of 
the angles A, C, of the triangle by 



GEOMETRICAL PROBLEMS. 



43 



lines cutting at D; from D draw a 
perpendicular D E to any side, and 
with D E as radius describe a circle. 
When the triangle is equilateral, 
draw a perpendicular from one of the 
angles to the opposite side, and from 
the side set off one third of the 
perpendicular. 

28. To describe a circle about 
a square, and to inscribe a square 
in a circle (Fig. 28). — To describe 
the circle, draw the diagonals A B, 
C D of the square, cutting at E. On 
the centre E, with the radius A E, 
describe the circle. 

To inscribe the square. — Draw 
the two diameters, A B, C D, at right 
angles, and join the points A, B, 
C D, to form the square. 

Note. — In the same way a circle 
may be described about a rectangle. 

29. To inscribe a circle in a 
square (Fig. 29). — To inscribe the 
circle, draw the diagonals A B, C D 
of the square, cutting at E; draw the 
perpendicular E F to one side, and 
with the radius E F describe the 
circle. 



30. To describe a square about 
a circle (Fig. 30). — Draw two 
diameters A B, C D at right angles. 
With the radius of the circle and 
A, B, C and D as centres, draw the 
four half circles which cross one 
another in the corners of the square. 






31. To inscribe a pentagon in 
a circle (Fig. 31). • — Draw diam- 
eters A C, B D at right angles, cut- 
ting at o. Bisect A o at E, and from 
E, with radius E B, cut A C at F; 
from B, with radius B F, cut the 
circumference at G, H, and with the 
same radius step round the circle to 
/ and K; join the points so found to 
form the pentagon. 




32. To construct a pentagon 
on a given line A B (Fig. 32). — 
From B erect a perpendicular B C 
half the length of i 5; join A C and. 
prolong it to D, making C D = B C. 
Then B D is the radius of the circle 
circumscribing the pentagon. From 
A and B as centres, with B D as 
radius, draw arcs cutting each other 
in O, which is the centre of the circle. 




44 



GEOMETRICAL PROBLEMS. 






33. To construct a hexagon 
upon a given straight line (Fig. 

33). — From A and B, the ends of 
the given line, with radius A B, 
describe arcs cutting at g; from g, 
with the radius g A, describe a circle; 
with the same radius set off the arcs 
AG, G F, and B D, D <E. Join the 
points so found to form the hexagon. 
The side of a hexagon = radius of its 
circumscribed circle. 

34. To inscribe a hexagon in a 
circle (Fig. 34). — Draw a diam- 
eter A C B. From A and B as 
centres, with the radius of the circle 
A C, cut the circumference, at D, E, 
F, G, and draw A D, D E, etc., to 
form the hexagon. The radius of 
the circle is equal to the side of the 
hexagon; therefore the points D, E, 
etc., may also be found by stepping 
the radius six times round the circle. 
The angle between the diameter and 
the sides of a hexagon and also the 
exterior angle between a side and an 
adjacent side prolonged is 60 degrees; 
therefore a hexagon may conven- 
iently be drawn by the use of a 60- 
degree triangle. 

35. To describe a hexagon 
about a circle (Fig. 35). — Draw a 
diameter A D B, and with the radius 
A D, on the centre A, cut the circum- 
ference at C; join A C, and bisect it 
with the radius D E ; through E draw 
FG, parallel to A C, cutting the diam- 
eter at F, and with the radius D F 
describe the circumscribing circle 
F H. Within this circle describe a 
hexagon by the preceding problem. 
A more convenient method is by use 
of a 60-degree triangle. Four of the 
sides make angles of 60 degrees with 
the diameter, and the other two are 
parallel to the diameter. 

36. To describe an octagon on 
a given straight line (Fig. 36). — 
Produce the given line A B both 
ways, and draw perpendiculars A E, 
B F; bisect the external angles yl and 
B by the lines A H, B C, which make 
equal to A B. Draw C D and H G 
parallel to A E, and equal to A B; 
from the centres G, D, with the 
radius A B, cut the perpendiculars at 
E, F, and draw E F to complete the 
octagon. 

37. To convert a square into 
an octagon (Fig. 37). — Draw the 
diagonals of the square cutting at e; 
from the corners A, B, C, D, with 
A e as radius, describe arcs cutting 
the sides at gn, fk, hm, and ol, and 
join the points so found to form the 
octagon. Adjacent sides of an octa- 
gon make an angle of 135 degrees. 



GEOMETRICAL PROBLEMS. 



45 



38. To inscribe an octagon in 
a circle (Fig. 38). — Draw two 
diameters, A C, B D at right angles; 
bisect the arcs A B, B C, etc., at ef, 
etc., and join A e, e B, etc., to form 
the octagon, 



39. To describe an octagon 
about a circle (Fig. 39). — Describe 
a square about the given circle A B; 
draw perpendiculars h k, etc., to the 
diagonals, touching the circle to 
form the octagon. 



40. To describe a polygon of 
any number of sides upon a given 
straight line (Fig. 40). — Produce 
the given line A B, and on A, with the 
radius A B, describe a semicircle; 
divide the semi-circumference into 
as many equal parts as there are to 
be sides in the polygon — say, in 
this example, five sides.. Draw lines 
from A through the divisional points 
D, 6, and c, omitting one point a; 
and on the centres B, D, with the 
radius A B, cut A b at E and A c at F. 
Draw D E, E F, F B to complete the 
polygon. 




41. To inscribe a circle within 
a polygon (Figs. 41, 42). — When 
the polygon has an even number of 
sides (Fig. 41), bisect two opposite 
sides at A and B; draw A B, and 
bisect it at C by a diagonal D E, and 
with the radius C A describe the 
circle. 

When the number of sides is odd 
(Fig. 42), bisect two of the sides at A 
and B, and draw lines A E, B D to the 
opposite angles, intersecting at C; 
from C, with the radius C A, describe 
the circle. 



42. To describe a circle without 
a polygon (Figs. 41, 42). — Find 
the centre C as before, and with the 
radius C D describe the circle. 

43. To inscribe a polygon of 
any number of sides within a circle 

(Fig. 43). — Draw the diameter A B 
and through the centre E draw the 




46 



GEOMETRICAL PROBLEMS. 




perpendicular E C, cutting the circle 
at F. Divide E F into four equal 
parts, and set off three parts equal 
to those from F to C. Divide the 
diameter A B into as many equal 
parts as the polygon is to have sides; 
and from C draw C D, through the 
second point of division, cutting the 
circle at D. Then A Dis equal to-one 
side of the polygon, and by stepping 
round the circumference with the 
length A D the polygon may be com- 
pleted. 



Table of Polygonal Angles. 



Number 


Angle 


Number 


Angle 


Number 


Angle 


of Sides. 


at Centre. 


of Sides. 


at Centre. 


of Sides. 


at Centre. 


No. 


Degrees. 


No. 


Degrees. 


No. 


Degrees. 


3 


120 


9 


40 


15 


24 


4 


90 


10 


36 


16 


221/2 


5 


72 


11 


328/u 


17 


21 3/ 17 


6 


60 


12 


30 


18 


20 


7 


513/7 


13 


279/ 13 


19 


19 


8 


45 


14 


25 5/ 7 


20 


18 



In this table the angle at the centre is found by dividing 360 degrees, the 
number of degrees in a circle, by the number of sides in the polygon; and 
by setting off round the centre of the circle a succession of angles by means 
of the protractor, equal to the angle in the table due to a given number of 
sides, the radii so drawn will divide the circumference into the same num- 
ber of parts, 

44. To describe an ellipse when 
the length and breadth are given 
(Fig. 44). — A B, transverse axis; 
C D, conjugate axis; F G, foci. The 
sum of the distances from C to F 
and G, also the sum of the distances 
from F and G to any other point in 
the curve, is equal to the transverse 
axis. From the centre C, with A E 
as radius, cut the axis A B at F and 
G, the foci; fix a couple of pins into 
the axis at F and G, and loop on a 
thread or cord upon them equal in 
length to the axis A B, so as when 
stretched to reach to the extremity 
C of the conjugate axis, as shown in 
dot-lining. Place a pencil inside the 
cord as at H, and guiding the pencil 
in this way, keeping the cord equally 
in tension, carry the pencil round the 
pins F, G, and so describe the 
ellipse. 

Note. — This method is employed 
in setting off elliptical garden-plots, 
walks, etc. 

2d Method (Fig. 45). — Along the 
straight edge of a slip of stiff paper 
mark off a distance a c equal to A C, 
half the transverse axis; and from 
the same point a distance a b equal 
to C D, half the conjugate axis. 




Fig. 45, 



GEOMETRICAL PROBLEMS. 



47 



Place the slip so as to bring the point 5 on the line A B of the transverse 
axis, and the point c on the line D E; and set off on the drawing the posi- 
tion of the point a> Shifting the slip so that the point b travels on the 
transverse axis, and the point c on the conjugate axis, any number of 
points in the curve may be found, through which the curve may be 

3d Method (Fig. 46). — The action 
of the preceding method may be 
embodied so as to afford the means 
of describing a large curve contin- 
uously by means of a bar m k, with 
steel points m, I, k, riveted into brass 
slides adjusted to the length of the 
semi-axis and fixed with set-screws. 
A rectangular cross E G, with guiding- 
slots is placed, coinciding with the 
two axes of the ellipse A C and B H. 
By sliding the points k, I in the slots, 
and carrying round the point m, the 
curve may be continuously described. 
A pen. or pencil may be fixed at m. 

4th Method (Fig. 47). — Bisect the 
transverse axis at C, and through C 
draw the perpendicular D E, making 
C D and C E each equal to half the 
conjugate axis. From D or E, with 
the radius AC, cut the transverse 
axis at F, F', for the foci. Divide 
A C into a number of parts at the 
points 1, 2, 3, etc. With the radius 
A I on F and F' as centres, describe 
arcs, and with the radius B I on the 
same centres cut these arcs as shown. 
Repeat the operation for the other 
divisions of the transverse axis. The 
series of intersections thus made are 
points in the curve, through which 
the curve may be traced. 

5th Method (Fig. 48). — On the 
two axes A B, D E as diameters, on 
centre C, describe circles; from a 
number of points a, b, etc., in the 
circumference A F B, draw radii cut- 
ting the inner circle at a', b', etc. 
From a, b, etc., draw perpendiculars 
to A B; and from a' , b' , etc., draw 
parallels to A B, cutting the respec- 
tive perpendiculars at n, o, etc. The 
intersections are points in the curve, 
through which the curve may be 
traced. 

6th Method (Fig. 49). — When the 
transverse and conjugate diameters 
are given, AB,C D, draw the tangent 
EF parallel to A B. Produce CD, 
and on the centre G with the radius 
of half A B, describe a semicircle 
H D K; from the centre G draw any 
number of straight lines to the points 
E, r, etc., in the line E F, cutting the 
circumference at I, m, n, etc.; from 
the centre O of the ellipse draw 
straight lines to the points E, r, etc. ; 
and from the points I, m, n, etc., 
draw parallels to GC, cutting the 
lines O E, Or, etc., at L, M, N, etc. 




4S 



GEOMETRICAL PROBLEMS. 



^-~~c 


c \ 




V \ 



77i 


/e V 



D 

Fig. 50. 




These are points in the circumference of the ellipse, and the curve may be 
traced through them. Points in the other half of the ellipse are formed 
by extending the intersecting lines as indicated in the figure. 

45. To describe an ellipse 
approximately by means of cir- 
cular arcs. — First. — With arcs 
of two radii (Fig. 50). — Find the 
difference of the semi-axes, and set 
it off from the centre O to a and c on 
O A and O C; draw ac, and set off 
half a c to d; draw d i parallel to ac; 
set off O e equal to d; join e i, and 
draw the parallels e m, d m. From 
m, with radius m C, describe an arc 
through C; and from i describe an 
arc through D; from d and e describe 
arcs through A and B. The four 
arcs form the ellipse approximately. 
Note. — This method does not 
apply satisfactorily when the con- 
jugate axis is less than two thirds of 
the transverse axis. 

2d Method (by Carl G. Barth, Fig. 
51). — In Fig. 51 a & is the major and 
c d the minor axis of the ellipse to be 
approximated. Lay off b e equal to 
the semi-minor axis c O, and use a e 
as radius for the arc at each extrem- 
ity of the minor axis. Bisect e o at f 
and lay off e g equal to e f, and use g b 
as radius for the arc at each extrem- 
Fig. 51. ity of the major axis. 

The method is not considered applicable for cases in which the minor 
axis is less than two thirds of the major 

3d Method: With arcs of three radii 
(Fig. 52). — On the transverse axis 
A B draw the rectangle B G on the 
height O C; to the diagonal A C 
draw the perpendicular G H D\ set 
off O K equal to O C, and describe a 
semicircle on A K, and produce O C 
to L; set off O M equal to C L, and 
from D describe an arc with radius 
D M; from A, with radius O L, cut 
A B at N; from H, with radius HN, 
cut arc a 6 at a. Thus the five 
centres D, a. b, H, H' are found, 
from which the arcs are described to 
form the ellipse. 

This process works well for nearly 
all proportions of ellipses. It is used 
in striking out vaults and stone 
bridges. 

Uh Method (by F. R. Honey, 
Figs. 53 and 54). — Three 
radii are employed. With 
the shortest radius describe 
the two arcs which pass 
through the vertices of the 
major axis, with the longest 
the two arcs which pass 
through the vertices of the 
minor axis, and with the third 
radius the four arcs which 
connect the former. 




GEOMETRICAL PROBLEMS. 



49 



A simple method of determining the radii of curvature is illustrated in 
Fig. 53. Draw the straight lines a f and a c, forming any angle at a. With 
a as a centre, and with radii a b and a c, respectively, equal to the semi- 
minor and semi-major axes, draw the arcs b e and c d. Join e d, and 
through b and c respectively draw b g and c f parallel to e d, intersecting 
a c at g, and a f at /; a f is the radius of curvature at the vertex of 
the minor axis; and a g the radius of curvature at the vertex of the 
major axis. 

Lay off d h (Fig. 53) equal to one eighth of b d. Join e h, and draw c k 
and b I parallel to e h. Take a k for the longest radius ( = R) t a I for the 
shortest radius (= r), and the arithmetical mean, or one half the sum of 
the semi-axes, for the third radius (= p), and employ these radii for the 
eight-centred oval as follows: 

Let a b arnd c d (Fig. 54) 
be the major and minor 
axes. Lay off a e equal 
to r, and a f equal to p; 
also lay off c g equal to R, 
and c h equal to p. With 
g as a centre and gh as a 
radius, draw the arc h k; 
with the centre e and 
radius e f draw the arc f k, a \ 
intersecting h k at k. 
Draw the line g k and 
produce it, making g I 
equal to R. Draw k e 
and produce it, making 
k m equal to p. With the 
centre g and radius g c 
(= R) draw the arc c I; 
with the centre k and 
radius kl (= p) draw the 
arc I m, and with the 
centre e and radius e m 
(= r) draw the arc m a. 

The remainder of the work is symmetrical with respect to the 
axes. 

46. The Parabola. — A parabola (D A C, Fig. 55) is a curve such 
that every point in the curve is equally distant from the directrix K L 
and the focus F. The focus lies in the axis 
A B drawn from the vertex or head of the 
curve A, so as to divide the figure into two 
equal parts. The vertex A is equidistant 
from the directrix and the focus, or A e = A F. 
Any line parallel to the axis is a diameter. 
A straight line, as E G or D C, drawn across 
the figure at right angles to the axis is a 
double ordinate, and either half of it is an 
ordinate. The ordinate to the axis E F G, 
drawn through the focus, is called the para- 
meter of the axis. A segment of the axis, 
reckoned from the vertex, is an abscissa of 
the axis, and it is an abscissa of the ordinate 
drawn from the base of the abscissa. Thus, 
A B is an abscissa of the ordinate B C. 




K 




e 


L 


E 




A 


G 


n/ 


F 


\ 




J 









J 


o 




\™ 


1 









D 


B 
b 




"«^ C 



Fig. 55. 



Abscissae of a parabola are as the squares of their ordinates. 



To describe a parabola when an abscissa and its ordinate are given 

(Fig. 55). — Bisect the given ordinate B C at a, draw A a, and then a b 
perpendicular to it, meeting the axis at b. Set off A e, A F, each equal to 
B b; and draw K eL perpendicular to the axis. Then K L is the directrix 
and F is the focus. Through F and any number of points, o, o, etc., in the 
axis, draw double ordinates, n o n, etc., and from the centre F, with the 
radii F e, o e, etc., cut the respective ordinates at E, G, n, n, etc. The 
curve may be traced through these points as shown. 

2d Method: By means of a square and a cord (Fig. 56). 



50 



GEOMETRICAL PROBLEMS. 




d cbaBabcd 
Fig. 57. 



straight-edge to the directrix E N, 
and apply to it a square LEG. 
Fasten to the end G one end of a 
thread or cord equal in length to the 
edge E G, and attach the other end 
to the focus F; slide the square along 
the straight-edge, holding the cord 
taut against the edge of the square 
by a pencil D, by which the curve is 
described. 

3d Method: When the height and 
the base are given (Fig. 57). — Let 
A B be the given axis, and C D a 
double ordinate or base; to describe 
a parabola of which the vertex is at 
A. Through A draw E F parallel to 
C D, and through C and D draw C E 
and D F parallel to the axis. Divide 
B C and B D into any number of 
equal parts, say five, at a, b, etc., and 
divide C E and D F into the same 
number of parts. Through the 
points a, b, c, d in the base CD on 
each side of the axis draw perpen- 
diculars, and through a, b, c, dinC E 
and D F draw lines to the vertex A, 
cutting the perpendiculars at e, f,g,h. 
These are points in the parabola, and 
the curve CAD may be traced as 
shown, passing through them. 
47 The Hyperbola (Fig. 58). — A hyperbola is a plane curve, such 
that the difference of the distances from any point of it to two fixed points 
is equal to a given distance. The 
fixed points are called the foci. 

To construct a hyperbola. — . 
Let F' and F be the foci, and F' F 
the distance between them. Take a 
ruler longer than the distance F' F, 
and fasten one of its extremities at 
the focus F' . At the other extrem- 
ity, II, attach a thread of such a 
length that the length of the ruler 
shall exceed the length of the thread 
by a given distance A B. Attach 
the other extremity of the thread at 
the focus F. 

Press a pencil, P, against the ruler, 
and keep the thread constantly tense, 
while the ruler is turned around F r as 
a centre. The point of the pencil 
will describe one branch of the curve. 
2d Method: By points (Fig. 59). — 
From the focus F' lay off a distance 
F' N equal to the transverse axis, or 
distance between the two branches of 
the curve, and take any other dis- 
tance, as F' II, greater than F' N. 

With F' as a centre and F' II as a 
radius describe the arc of a circle. 
Then with F as a centre and iV H as a radius describe an arc intersecting 
the arc before described at p and q. These will be points of the hyper- 
bola, for F' a — F q is equal to the transverse axis A B. 

If, with F as a centre and F' H as a radius, an arc be described, and a 

second arc be described with F' as a centre and N H as a radius, two points 

in the other branch of the curve will be determined. Hence, by changing 

the centres, each pair of radii will determine two points in each branch. 

Th,e Equilateral Hyperbola. — The transverse axis of a hyperbola is 




Fig. 58. 




GEOMETRICAL PROBLEMS. 



51 




the distance, on a line joining the foci, between the two branches of the 
curve. The conjugate axis is a line perpendicular to the transverse axis, 
drawn from its centre, and of such a length that the diagonal of the rect- 
angle of the transverse and conjugate axes is equal to the distance between 
the foci. The diagonals of this rectangle, indefinitely prolonged, are the 
asymptotes of the hyperbola, lines which the curve continually approaches, 
but touches only at an infinite distance. If these asymptotes are perpen- 
dicular to each other, the hyperbola is called a rectangular or equilateral 
hyperbola. It is a property of this hyperbola that if the asymptotes are 
taken as axes of a rectangular system of coordinates (see Analytical Geom- 
etry), the product of the abscissa and ordinate of any point in the curve is 
equal to the product of the abscissa and ordinate of any other point ; or, if 
p is the ordinate of any point and v its abscissa, and pi, and vi are the 
ordinate and abscissa of any other point, pv = pivi; or pv = a constant. 

48. The Cycloid (Fig. 
.60). — If a circle A d be 6 f 

rolled along a straight 
line A 6, any point of the 
circumference as A will 
describe a curve, which is 
called a cycloid. The 
circle is called the gene- 
rating circle, and A the 
\ generating point. 

To draw a cycloid. — 
Divide the circumference 
of the generating circle 

into an even number of equal parts, as A 1, 12, etc., and set off these dis- 
tances on the base. Through the points 1, 2, 3, etc., on the circle 
draw horizontal lines, and on them 
set off distances la = Al, 2b = A2, 3c = 
A3, etc. The points A, a, b, c, etc., 
will be points in the cycloid, through 
which draw the curve. 

49. The Epicycloid (Fig. 61) is 
generated by a point D in one circle 
D C rolling upon the circumference of 
another circle A C B, instead of on a 
flat surface or line; the former being 
the generating circle, and the latter 
the fundamental circle. The generat- 
ing circle is shown in four positions, 
in which the generating point is 
successively marked D, D', D", D'". 
A U" B is the epicycloid. 

50. The Hypocycloid (Fig. 62) 
is generated by a point in the gener- 
ating circle rolling on the inside of 
the fundamental circle. 

When the generating circle = 
radius of the other circle, the hypo- 
cycloid becomes. a straight line. 

51. The Tractrix or Schiele's 
anti-friction curve (Fig. 63).— R 
is the radius of the shaft, C, 1, 2, etc., 
the axis. From O set off on R a 
small distance, oa; with radius R and 
centre a cut the axis at 1, join a 1, 
and set off a like small distance a b\ 
from 6 with radius R cut axis at 2, 
join 6 2, and so on, thus finding 
points o, a, b, c, d, etc., through which 
the curve is to be drawn- 




Fig. 63 8 



52 



GEOMETRICAL PROBLEMS. 



52. The Spiral. — The spiral is a curve described by a point which 
moves along a straight line according to any given law, the line at the same 
time having a uniform angular motion. The line is called the radius vector. 
If the radius vector increases directly 
as the measuring angle, the spires, 
or parts described in each revolution, 
thus gradually increasing their dis- 
tance from each other, the curve is 
known as the spiral of Archimedes 
(Fig. 64). 

This curve is commonly used for 
cams. To describe it draw the 
radius vector in several different 
directions around the centre, with 
equal angles between them; set off 
corresponding to the scale upon which the 




Fig. 64. 



the distances 1, 2, 3, 4, etc . 
curve is drawn, as shown in Fig. 




In the common spiral (Fig. 64) the 
pitch is uniform; that is, the spires 
are equidistant. Such a spiral is 
made by rolling up a belt of uniform 
thickness. 

To construct a spiral with four 
centres (Fig. 65). — Given the 
pitch of the spiral, construcfa square 
about the centre, with the sum of 
the four sides equal to the pitch. 
Prolong the sides in one direction as 
shown; the corners are the centres for 
Yig. 65. eacn arc °f tne external # 

forming a quadrant of a spire. 

53. To find the diameter of a circle into which a certain number of 
rings will fit on its inside (Fig. 66). — For instance, what is the diameter 
of a circle into which twelve 1/2-inch rings will fit, as per sketch? Assume 
that we have found the diameter of the required circle, and have drawn 

the rings inside of it. Join the 
centres of the rings by straight lines, 
as shown: we then obtain a regular 
polygon with 12 sides, each side 
being equal to the diameter of a 
given ring. We have now to find 
the diameter of a circle circum- 
scribed about this polygon, and add 
the diameter of one ring to it; the 
sum will be the diameter of the circle 
into which the rings will fit. 
Through the centres A and D of two 
adjacent rings draw the radii C A 
and C D ; since the polygon has twelve 
sides the angle A C D = 30° and 
ACB = 15°. One half of the side 
A D is equal to A B. We now give 
the following proportion: The sine 
of the angle A C B is to A B as 1 is to 
the required radius. From this we 
get the following rule: Divide A B by the sine of the angle A C B; the 
quotient will be the radius of the circumscribed circle; add to the corre- 
sponding diameter the diameter of one ring; the sum will be the required 
diameter F G. 

54. To describe an arc of a circle which is too large to he drawn 
by a beam compass, by means of points in the arc, radius being given. 
— Suppose the radius is 20 feet and it is desired to obtain five points in an 
arc whose half chord is 4 feet. Draw a line equal to the half chord, full 
size, or on a smaller scale if more convenient, and erect a perpendicular at 
one end, thus making rectangular axes of coordinates. Erect perpen- 
diculars at points 1, 2, 3, and 4 feet from the first perpendicular. Find 
values of y in the formula of the circle, x 2 + y 2 — R 2 , by substituting for 




GEOMETRICAL PROBLEMS. 



53 



x the values 0, 1, 2, 3, and 4, etc and fo r R 2 the square of the radius, or 
400. The values will be y = V '#» _ x i = V 4 00, ^399, ^396, V39I, 

V384; = 20, 19.975, 19.90, 19.774, 19.596. 
Subtract the smallest, „„„„ „ * 4 

or 19.596, leaving 0.404, 0.379, 0.304, 0.178, feet. 

Lay off these distances on the five perpendiculars, as ordinates from the 
half chord, and the positions of five points on the arc will be found. 
Through these the curve may be 
drawn. (See also Problem 14.) 

55. The Catenary is the curve 
assumed by a perfectly flexible cord 
when its ends are fastened at two 
points, the weight of a unit length 
being constant. 

The equation of the catenary is 



»-l(^.~ 5 ). 



in which e is the 

base" of the Napierian system of log- 
arithms. 

To plot the catenary. — Let 
(Fig. 67) be the origin of coordinates. 
Assigning to a any value a% 3, the 
equation becomes 



,-§(.C-S). 



To find the lowest point of the 
curve. 

. Put a; - 0; .\ y=^ (e°+e- 




; (1.396 +0.717) =3.17. 



(e 3 + e 3 )= I (1.948 +0.513) =3.69. 



Then put x = l; .'. V 
Put z = 2; .'. y- 

Put x = 3 4 5 etc etc., and find the corresponding values of y. For 
each value of y we obtain two symmetrical points, as for example p and p' . 
In this way, by making a successively equal to 2, 3, 4, 5, 6, 7, and 8, the 
curves of Fig. 67 were plotted. 

In each case the distance from the origin to 
the lowest point of the curve is equal to a; for 
putting x = o, the general equation reduces to 
y = a>. 

For values of a = 6, 7, and 8 the catenary 
closely approaches the parabola. For deriva- 
tion of the equation of the catenary see Bow- 
ser's Analytic Mechanics. 

56. The Involute is a name given to the 
curve which is formed by the end of a string 
which is unwound from a cylinder and kept 
taut; consequently the string as it is unwound 
will always lie in the direction of a tangent 
to the cylinder. To describe the involute of 
any given circle, Fig. 68, take any point A on 
its circumference, draw a diameter A B, and 
from B draw B b perpendicular to A B. Make 
B b equal in length to half the circumference 
of the circle. Divide B b and the semi-circum- 
ference into the same number of equal parts, 
say six. From each point of division 1, 2, 
3, etc., on the circumference draw lines to the centre C of the circle. 
Then draw \a t perpendicular to CI; 2 a 2 perpendicular to C2; and 
so on. Make la x equal to bb x ; 2 a 2 equal to b b 2 ; 3 03 equal to 6 6 3 ; and 
so on. Join the points A, a u a 2 , az, etc., by a curve; this curve will be 
the required involute. 




Fig. 68. 



54 GEOMETRICAL PROPOSITIONS. 

57. Method of plotting angles without using a protractor. — The 

radius of a circle whose circumference is 360 is 57.3 (more accurately 
57.296). Striking a semicircle with a radius 57.3 by any scale, spacers 
set to 10 by the same scale will divide the arc into 18 spaces of 10° each, 
and intermediates can be measured indirectly at the rate of 1 by scale for 
each 1°, or interpolated by eye according to the degree of accuracy required. 
The following table shows the chords to the above-mentioned radius, for 
every 10 degrees from 0° up to 110°. By means of one of these a 10° 
point is fixed upon the paper next less than the required angle, and the 
remainder is laid off at the rate of 1 by scale for each degree. 

Angle. Chord. Angle. Chord. Angle. Chord. 

1° 0.999 40° 39.192 30° 73.658 

10° 9.98S 50° 48.429 90° 81.029 

20° 19.899 60° 57.296 100° 87.782 

30° 29.658 70°.. ........ 65.727 110° 93.869 



GEOMETRICAL PROPOSITIONS. 

In a right-angled triangle the square on the hypothenuse is equal to the 
sum of the squares on the other two sides. 

If a triangle is equilateral, it is equiangular, and vice versa. 

If a straight line from the vertex of an isosceles triangle bisects the base, 
it bisects the vertical angle and is perpendicular to the base. 

If one side of a triangle is produced, the exterior angle is equal to the 
sum of the two interior and opposite angles. 

If two triangles are mutually equiangular, they are similar and their 
corresponding sides are proportional. 

If the sides of a polygon are produced in the same order, the sum of the 
exterior angles equals four right angles. (Not true if the polygon has 
re-entering angles.) 

In a quadrilateral, the sum of the interior angles equals four right 
angles. 

In a parallelogram, the opposite sides are equal; the opposite angles are 
equal; it is bisected by its diagonal, and its diagonals bisect each other. 

If three points are not in the same straight line, a circle may be passed 
through them. 

If two arcs are intercepted on the same circle, they are proportional to 
. the corresponding angles at the centre. 

If two arcs are similar, they are proportional to their radii. 

The areas of two circles are proportional to the squares of their radii. 

If a radius is perpendicular to a chord, it bisects the chord and it bisects 
the arc subtended by the chord. 

A straight line tangent to a circle meets it in only one point, and it is 
perpendicular to the radius drawn to that point. 

If from a point without a circle tangents are drawn to touch the circle, 
there are but two; they are equal, and they make equal angles with the 
chord joining the tangent points. 

If two lines are parallel chords or a tangent and parallel chord, they 
intercept equal arcs of a circle. 

If an angle at the circumference of a circle, between two chords, is sub- 
tended by the same arc as an angle at the centre, between two radii, the 
angle at the circumference is equal to half the angle at the centre. 

If a triangle is inscribed in a semicircle, it is right-angled. 

If two chords intersect each other in a circle, the rectangle of the seg- 
ments of the one equals the rectangle of the segments of the other. 

And if one chord is a diameter and the other perpendicular to it, the 
rectangle of the segments of the diameter is equal to the square on 
half the other chord, and the half chord is a mean proportional between 
the segments of the diameter. 

If an angle is formed by a tangent and chord, it is measured by one half 
of the arc intercepted by the chord; that is, it is equal to half the angle at 
the centre subtended by the chord. 



MENSURATION — PLANE SURFACES, 55 

Degree of a Railway Curve. — This last proposition is useful in staking 
out railway curves. A curve is designated as one of so many degrees, and 
the degree" is the angle at the centre subtended by a chord of 100 ft. To 
lay out a curve of n degrees the transit is set at its beginning or " point of 
curve," pointed in the direction of the tangent, and turned through 1/2 n 
degrees; a point 100 ft. distant in the line of sight will be a point in the 
curve. The transit is then swung 1/2^ degrees further and a 100 ft. chord 
is measured from the point already found to a point in the new line of 
sight, which is a second point or " station " in the curve. 

The radius of a 1° curve is 5729.65 ft., and the radius of a curve of any 
degree is 5729.65 ft, divided by the number of degrees, 



MENSURATION. 

PLANE SURFACES. 

Quadrilateral. — A four-sided figure. 

Parallelogram. — A quadrilateral with opposite sides parallel. 

Varieties. — Square: four sides equal, all angles right angles. Rect- 
angle: opposite sides equal, all angles right angles. Rhombus: four sides 
equal, opposite angles equal, angles not right angles. Rhomboid: opposite 
sides equal, opposite angles equal, angles not right angles. 

Trapezium. — A quadrilateral with unequal sides. 

Trapezoid. — A quadrilateral with only one pair of opposite sides 
parallel. 

Diagonal of a square = * ^2 X side 2 = 1.4142 X side. 

Diag. of a rectangle = ^sum of squares of two adjacent sides. 

Area of any parallelogram = base X altitude. 

Area of rhombus or rhomboid = product of two adjacent sides X sine 
of angle included between them. 

Area of a trapezoid = product of half the sum of the two parallel sides 
by the perpendicular distance between them. 

To find the area of any quadrilateral figure. — Divide the quad- 
rilateral into two triangles; the sum of the areas of the triangles is the 
area. 

Or, multiply half the product of the two diagonals by the sine of the 
angle at their intersection. 

To find the area of a quadrilateral which may be inscribed in a 
circle. — From half the sum of the four sides subtract each side severally; 
multiply the four remainders together; the square root of the product is 
the area. 

Triangle. — A three-sided plane figure. 

Varieties. — Right-angled, having one right angle; obtuse-angled, hay- 
ing one obtuse angle; isosceles, having two equal angles and two equal 
sides; equilateral, having three equal sides and equal angles. 

The sum of the three angles of every triangle = 180°. 

The sum of the two acute angles of a right-angled triangle = 90°. 

Hypothe nuge of a right-angled triangle, the side opposite the right 
angle, = v sum of the squares of the other two si des. If a and b are the 
two sides and c the hypothenuse, c 2 =a 2 + & 2 ; a = V c 2 — & 2 = v / ( c +6)(c — 6). 

If the two sides are equal, side = hyp 4- 1.4142; or hyp X.7071. 

To find the area of a triangle; 

Rule 1. Multiply the base by half the altitude. 

Rule 2. Multiply half the product of two sides by the sine of the 
included angle. 

Rule 3. From half the sum of the three sides subtract each side 
severally; multiply together the half sum and the three remainders, and 
extract the square root of the product. 

The area of an equilateral triangle is equal to one fourth the square of 

a 2 v's 
one of its sides multiplied by the square root of 3, = — -r- , a being the 

side; or a 2 X 0.433013. 



56 



MENSURATION. 



Area of a triangle given, to find base: Base = twice area -s- perpendicular 
height. 

Area of a triangle given, to find height: Height = twice area -h base. 

Two sides and base given, to find perpendicular height (in a triangle in 
- which both of the angles at the base are acute). 

Rule. — As the base is to the sum of the sides, so is the difference of the 
sides to the difference of the divisions of the base made by drawing the 
perpendicular. Half this difference being added to or subtracted ^from 
half the base will give the two divisions thereof. As each side and its 
opposite division of the base constitutes a right-angled triangle, th e 
perpendicular is ascertained by the rule: Perpendicular = Vhyp 2 — base 2 - 

Areas of similar figures are to each other as the squares of their 
respective linear dimensions. If the area of an equilateral triangle of 
side = 1 is 0.433013 and its height 0.S6G03, what is the area of a similar 
triangle whose height = 1? 0.86603 2 : l 2 :: 0.433013 : 0.57735, Ans. 

Polygon. — A plane figure having three or more sides. Regular or 
irregular, according as the sides or angles are equal or unequal. Polygons 
are named from the number of their sides and angles. 

To find the area of an irregular polygon. — Draw diagonals dividing 
the polygon into triangles, and find the sum of the areas of these triangles. 

To find the area of a regular polygons 

Rule. — Multiply the length of a side by the perpendicular distance to 
the centre; multiply the product by the number of sides, and divide it by 
2. Or, multiply half the perimeter by the perpendicular let fall from the 
centre on one of the sides. 

The perpendicular from the centre is equal to half of one of the sides of 
the polygon multiplied by the cotangent of the angle subtended by the 
half side. 

The angle at the centre = 360° divided by the number of sides. 



Table of Regular Polygons 









Jl 


Radius of Cir- 
cun. scribed 


1> • 


03 6 








d 




i 


Circle. 


•gll 




a5 


< 








|d2 

tacj 
d"^ 


i 

m 
6 


>> 
I 
"3 

a 


II 

of 


K3 

o 
w 


2 11 

c £ 
gg 





.S'm 


3 " • 

111 


6 

"oj 
Oi 

T3> 
d 


fc 


& 


-S3 


< 


Ph 


w. 


ti 


A 


< 


< 


3 


Triangle. 


0.4330 


0.5773 


2.000 


0.5773 


0.2887 


1.732 


120° 


60° 


4 


Square 


1.0000 


1 . 0000 


1.414 


0.7071 


0.5000 


1.4142 


90 


90 


5 


Pentagon 


1 . 7205 


0.7265 


1.236 


0.8506 


0.6382 


1.1756 


72 


108 


6 


Hexagon 


2.5981 


0.8660 


1.155 


1 . 0000 


0.866 


1 . 0000 


60 


120 


7 


Heptagon 


3.6339 


0.7572 


1.11 


1 . 1 524 


1.0333 


0.8677 


51 26' 


1284-7 


8 


Octagon 


4.8284 


0.8284 


1.082 


1 . 3066 


1.2071 


0.7653 


45 


135 


9 


Nonagon 


6.1818 


0.7688 


1.064 


1.4619 


1.3737 


684 


40 


140 


10 


Decagon 


7.6942 


0.8123 


1.051 


1.613 


1.5388 


0.618 


36 


144 


11 


Undecagon 


9.3656 


0.7744 


1.042 


1.7747 


1 . 7028 


0.5634 


32 43' 


147 3-11 


12 


Dodecagon 


11.1962 


0.8038 


1.035 


1.9319 


1.666 


0.5176 


30 


150 



* -Short diameter, even number of sides, = diam. of inscribed circle; 
short diam., odd number of sides, = rad. of inscribed circle + rad. of 
circumscribed circle. ' 



AREA OF IRREGULAR FIGURES. 



57 



To find the area of a regular polygon, when the length of a side 
only is given: 

Rule. — Multiply the square of the side by the figure for " area, side = 
1," opposite to the name of the polygon in the table. 

Length of a side of a regular polygon inscribed in a circle = diam. 
X sin (180° -h no. of s" n 



of sides sin (180°/n) 


No. 


sin (180° In) 


No. 


sin (180°/n) 


3 0.86603 


9 


0.34202 


15 


0.20791 


4 .70711 


10 


.30902 


16 


.19509 


5 .58778 


11 


.28173 


17 


.18375 


6 .50000 


12 


.25882 


18 


.17365 


7 .43388 


13 


.23931 


19 


.16458 


8 .38268 


14 


.22252 


20 


.15643 



To find the area of an irregular 
figure (Fig. 69). — Draw ordinates 
across its breadth at equal distances 
apart, the first and the last ordinate 
each being one half space from the 
ends of the figure. Find the average 
breadth by adding together the 
lengths of these lines included be- 
tween the boundaries of the figure, 

and divide by the number of the lines 
added; multiply this mean breadth 
by the length. The greater the num- 
ber of lines the nearer the approxi- 
mation. 

In a figure of very irregular outline, 



1 

1 i 2 v, i. 


5 6 7 I: 9 K 



- Length 

Fig. 69. 



an indicator-diagram from a 
high-speed steam-engine, mean lines may be substituted for the actual 
lines of the figure, being so traced as to intersect the undulations, so that 
the total area of the spaces cut off may be compensated by that of the 
extra spaces inclosed. 

2d Method: The Trapezoidal, Rule. — Divide the figure into any 
sufficient number of equal parts; add half the sum of the two end ordinates 
to the sum of all the other ordinates-; divide by the number of spaces 
(that is, one less than the number of ordinates) to obtain the mean 
ordinate, and multiply this by the length to obtain the area. 

3d Method: Simpson's Rule. — DiJ'ide the length of the figure into any 
even number of equal parts, at the common distance D apart, and draw 
ordinates through the points of division to touch the boundary lines 
Add together the first and last ordinates and call the sum A ; add together 
the even ordinates and call the sum B\ add together the odd ordinates, 
except the first and last, and call the sum C. Then, 



area of the figure ■■ 



-4B+ 2C 



X D. 



4th Method: Durand's Rule. — Add together 4/io the sum of the first 
and last ordinates, 1 Vio the sum of the second and the next to the last 
(or the penultimates), and the sum of all the intermediate ordinates. 
Multiply the sum thus gained by the common distance between the ordi- 
nates to obtain the area, or divide this sum by the number of spaces to 
obtain the mean ordinate. 

Prof. Durand describes the method of obtaining his rule in Engineering 
News, Jan. 18, 1894. He claims that it is more accurate than Simpson's 
rule, and practically as simple as the trapezoidal rule. He thus describes 
its application for approximate integration of differential equations. Any 
definite integral may be represented graphically by an area. Thus, let 



Q = fu 



dx 



be an integral in which u is some function of x, either known or admitting 
of computation or measurement. Any curve plotted with x as abscissa 
and u as ordinate will then represent the variation of u with x, and the 



58 



MENSURATION. 



area between such curve and the axis X will represent the integral in 
question, no matter how simple or complex may be the real nature of the 
function u. 

Substituting in the rule as above given the word " volume" for " area" 
and the word "section" for "ordinate," it becomes applicable to the 
determination of volumes from equidistant sections as well as of areas 
from equidistant ordinates. 

Having approximately obtained an area by the trapezoidal rule, the 
area by Durand's rule may be found by adding algebraically to the sum of 
the ordinates used in the trapezoidal rule (that is, half the sum of the end 
ordinates + sum of the other ordinates) Vio of (sum of penultimates 
- sum of first and last) and multiplying by the common distance between 
the ordinates. 

5th Method. — Draw the figure on cross-section paper. Count the 
number of squares that are entirely included within the boundary; then 
estimate the fractional parts of squares that are cut by the boundary, add 
together these fractions, and add the sum to the number of whole squares. 
The result is the area in units of the dimensions of the squares. The finer 
the ruling: of the cross-section paper the more accurate the result. 

6th Method. — Use a planimeter. 

1th Method. — With a chemical balance, sensitive to one milligram, 
draw the figure on paper of uniform thickness and cut it out carefully; 
weigh the piece cut out, and compare its weight with the weight per 
square inch of the paper as tested by weighing a piece of rectangular shape. 



THE CIRCLE. 

Circumference = diameter X 3.1416, nearly; more accurately, 3.14159265359. 

Approximations, — = 3.143; ^ = 3.1415929. 

The ratio of circum. to diam. is represented by the symbol k (called Pi). 
Area = 0.7854 X square of the diameter. 



Multiples of v. 

Ik = 3.14159265359 
2k = 6.28318530718 
3k = 9.42477796077 
4rr = 12.56637061436 
5k = 15.70796326795 
6k = 18.84955592154 
In = 21.99114857513 
8k = 25.13274122872 
9k = 28.27433388231 



1/47! 



Multiples of -• 

= 0.7853982 
X 2 = 1.5707963 
X 3 = 2.3561945 
X 4 = 3.1415927 
X 5 = 3.9269908 
X 6 = 4.7123890 
X 7 = 5.4977871 
X 8 = 6.2831853 
X 9 = 7.0685835 



Ratio of diam. to circumference = 



Reciprocal of 1/4* = 1.27324. 
Multiples of 1/tt. 
1/k = 0.31831 
2/k = 0.63662 
2>/k = 0.95493 
4/tt = 1.27324 

5/tt = 1.59155 
6/k - 1.90986 



-ence 


= reciprocal of k = 0.3183099. 


1/k 
8/k 
9/k 
10/k 
12 A 


= 2.22817 
= 2.54648 
= 2.86479 
= 3.18310 
= 3.81972 


k/12 = 

tt/360 = 
360A = 

K 2 — 
1/tt* = 


0.261799 
0.0087266 
114.5915 
9.86960 
0.101321 


k/2 


=. 1.570796 


V* = 


1.772453 


k/3 


= 1.047197 


v£- 


0.564189 


k/Q 


= 0.523599 


Log k = 


0.4971498' 






Log tt/4 = 


1.895090 



Diam. in ins. = 13.5405 Varea in sq. ft. 

Area in sq. ft. = (diam. in inches) 2 X .0054542. 

D = diameter, R = radius, C = circumference, 



THE CIRCLE. 59 

C = nD; =2nR; = ~ ; = 2^71; = 3.545VJ; 

4 = Z) 2 X.7854;= ^ ; = 4# 2 X.7854; = ;r# 2 ; =^D 2 ; =^ ; = .07958C 2 ; = ~- 

£>=-; = 0.31831C; = 2 J - ; = 1.12838 V^T; 

R = £ ; = (U59155C; = 4/- ; = 0.564189 ^A. 

Areas of circles are to each other as the squares of their diameters. 
To find the length of an arc of a circle : 

Rule 1. As 360 is to the number of degrees in the arc, so is the circum- 
ference of the circle to the length of the arc. 

Rule 2. Multiply the diameter of the circle by the number of degrees 
in the arc, and this product by 0.0087266. 

Relations of Arc, Chord, Chord of Half the Arc, etc. 

Let R = radius, D = diameter, L = length of arc, 

C = chord of the arc, c = chord of half the arc, 

V = rise, or height of the arc, 

8c — C 9 f X 10F 

Length of the arc = L = (very nearly), = "' _ 27 y +2c, nearly, 

Vq* + 4F 2 X 1072 

'- 2c, nearly. 



15C 2 + 33 F 2 



Chord of the arc C, = 2 V C 2 _ y 2 . = Vd 2 - (D - 2V) 2 ; = 8c - 3L 
= 2\/R2 _ ^ R _ F)2 . = 2 V(D - V) X V. 
arc, c = 

Diameter of the circle, D = 



Chord of half the arc, c = 1/2 ^ C 2 + 4 V 2 ; = Vd x V; = (3L + C) • 

c 2 1/4 C 2 + F 2 



y 



Rise of the arc, V = ^ ; = 1/2 (D - Vd 2 - C 2 ), 



(or if V is greater than radius 1/2 (I> + V/)2 - C 2 ) ; 

= Vc 2 - i/ 4 C 2 . 

Half the chord of the arc is a mean proportional b etween the rise and 
the diameter minus the rise: 1/2 C = v'l' X ( D — V). 

Length of the Chord subtending an angle at the centre = twice the 
sine of half the angle. (See Table of Sines.) 

Ordinates to Circular Arcs. — C = chord, V = height of the arc, or 
middle ordinate, x = abscissa, or distance measured on the chord from its 
central point, y.= or dinate, or d istance fr om the arc to the chord at the 
point x, V = R - V#2 _ i/ 4C . 2; y = Vr.2 _ X 2 _ (K _ v). 

Length of a Circular Arc. — Huyghens's Approximation. 

Length of the arc, L = (8c — C) -4- 3. Professor Williamson shows 
that when the arc subtends an angle of 30°, the radius being 100,000 feet 
(nearly 19 miles), the error by this formula is about two inches, or 1/600000 
part of the radius. When the length of the arc is equal to the radius, i.e., 
when it subtends an angle of 57°. 3, the error is less than 1/7680 part of the 
radius. Therefore, if the radius is 100,000 feet, the error is less than 
100000/7680 = 13 feet. The error increases rapidly with the increase of 
the angle subtended. For an arc of 120° the error is 1 part in 400; for an 
arc of 180° the error is 1.18%. 



MENSURATION. 



In the measurement of an arc which is descrihed with a short radius the 
error is so small that it may be neglected. Describing an arc with a radius 
of 12 inches subtending an angle of 30°, the error is 1/50000 of an inch. 

To measure an arc when it subtends a large ansrle, bisect it and measure 
each half as before — in this case making 5 = length of the chord of half the 
arc, and 6 = length of the chord of one fourth the arc ; then L = (166 — 27?) ■*■ 3. 



Formulas for a Circular Curve. 

J. C. Locke, Eng. News, March 16, 1908. 
c = V272a, = vV + 6 2 , 
= \ // 2E (72 - V(72 + 6) (72 - b) 




= 2V W (272 - m), = 2R sin l/ 2 /, 
= 2Tcosy 2 I. 

= R exsec 1/2/, = R tan 1/2 ^ tan 1/4 7", 
= T tan 1/4/. 



^ x ^p.Su / 7 —* 



= R sin I, = 

= q2 + &2 
2a ' 



a cot 1/2 1- 

_c 2 __d 2 __ c 2 + An. 
"2a' 



2m ' 



8m 



m 



Fig. 70. 

/ 2 J KmT= ^R{2R - ^(272 + c) (272 - c)) f = 272 sin 1/4/. 
= 72 T 



_^1 
: 2R 
■■ R sin 1/2/ tan 1/4/, 



\/( # + !)(#- |), = £ vers 1/2/, 
1/2 c tan 1/4/. 



2S'- K - V(fi 


+ b) (72 - 6), = 272 


(sin 


V2/) 2 , 


= 72 


vers 


/, 


72 sin 7" tan 1/2/, = 


6 tan 1/2/, = I 7 sin 7 












72 tan 1/2 /. 7" 


= | X 57.295780°. 




*-r 


X 57. 


2957 


SO 


772 X 0.01745329, 


8d - c 
3 












Area of Segment 


L72 72 2 sin I 

2 2 


L72 

2 


726 

2 ' 









Relation of the Circle to its Equal, Inscribed, and Circum- 
scribed Squares. 



= side of equal square. 



Diameter of circle X 0.88623 ) = 6 

Circumference of circle X 0.28209 J 

Circumference of circle X 1.1284 = perimeter of equal square. 

Diameter of circle X 0.7071 ) 

Circumference of circle X 0.2250S \ = side of inscribed square. 

Area of circle X 0.90031 -s- diameter 3 

Area of circle X 1.2732 = area of circumscribed square. 

Area of circle X 0.63662 = area of inscribed square. 

Side of square X 1.4142 = diam. of circumscribed circle. 

X 4.4428 = circum. 

X 1.1284 = diam. of equal circle. 

X 3.5449 = circum. 

Perimeter of square X 0.88023 = 

Square inches X 1.2732 = circular inches. 



MENSURATION. 61 

Sectors and Segments. — To find the area of a sector of a circle. 

Rule 1. Multiply the arc of the sector by half its radius. 

Rule 2. As 360 is to the number of degrees in the arc, so is the area of 
the circle to the area of the sector. 

Rule 3. Multiolv the number of degrees in the arc by the square of the 
radius and by 0.00S727. 

To find the area of a segment of a circle: Find the area of the sector 
which has the same arc, and also the area of the triangle formed by the 
chord of the segment and the radii of the sector. 

Then take the sum of these areas, if the segment is greater than a semi- 
circle, but take their difference if it is less. (See Table of Segments.) 

Another Method: Area of segment = 1/2 R 2 (arc — sin A), in which A is 
the central angle, R the radius., and arc the length of arc to radius 1 . 

To find the area of a segment of a circle when its chord and height only 
are given. First find radius, as follows: 



1 fsquare of half the chord , . . , . 1 
= 2 L height ' + height J • 



2. Find the angle subtended by the arc, as follows: half chord -*■ 
radius = sine of half the angle. Take the corresponding angle from a 
table of sines, and double it to get the angle of the arc. 

3. Find area of the sector of which the segment is a part: 

area of sector = area of circle X degrees of arc -*- 360. 

4. Subtract area of triangle under the segment: 

Area of triangle = half chord X (radius — height of segment). 

The remainder is the area of the segment. 

When the chord, arc, and diameter are given, to find the area. From 
the length of the arc subtract the length of the chord. Multiply the 
remainder by the radius or one-half diameter; to the product add the 
chord multiplied by the height, and divide the sum by 2. 

Given diameter, d, and height of segment, h. 



When h is from to 1/4 <?, area = h^ l.766dh 



" " " " 1/4 <* to l/id, area = h\ / 0.0l7d 2 + \.7dh - h 2 

(approx.). Greatest error 0.23%, when h = Vid. 

To find the chord: From the diameter subtract the height; multiply 
the remainder by four times the height and extract the square root. 

When the chords of the arc and of half the arc and the rise are given: 
To the chord of the arc add four thirds of the chord of half the arc; mul- 
tiply the sum by the rise and the product by 0.40426 (approximate). 

Circular Ring. — To find the area of a ring included between the cir- 
cumferences of two concentric circles: Take the difference between the areas 
of the two circles; or, subtract the square of the less radius from the square 
of the greater, and multiply their difference by 3.14159. 

The area of the greater circle is equal to tzR 2 ; 
and the area of the smaller, itr 2 . 

Their difference, or the area of the ring, is n(R 2 — r 2 ). 
The Ellipse. — Area of an ellipse = product of its semi-axes X3. 14159 
= product of its axes X0. 785398. 

, / D 2 + d 2 
The Ellipse. — Circumference (approximate) = 3.1416 y — , D 

and d being the two axes. 

Trautwine gives the following as more accurate: When the longer axis 
D is not more than five times the length of the shorter axis, d, 



, D 2 + d 2 (D - 
Circumference = 3.1416 - 



v/ 1 



62 MENSURATION. 

When D is more than 5rf, the divisor S.8 is to be replaced by the following: 

ForZ>A? = 6 7 8 9 10 12 14 16 18 20 30 40 50 
Divisor = 9 9.2 9.3 9.35 9.4 9.5 9.6 9.68 9.75 9.8 9.92 9.98 10 

1 + T + 64 + ^6 + i^t4 + •••) , 
in which A = r^jr- — Ingenieurs Taschenbuch, 1896. (a and b, semi-axes.) 

Carl G. Barth (Machinery, Sept., 1900) gives as a very close approxi- 
mation to this formula 

, , , A $4 - 3.4 * 
C=.(a+ft) 64 _ 16A2 . 

Area of a segment, of an ellipse the base of which is parallel to one of 
the axes of the ellipse. Divide the height of the segment by the axis of 
which it is part, and find the area of a circular segment, in a table of circu- 
lar segments, of which the height is equal to the quotient; multiply the 
area thus found by the product of the two axes of the ellipse. 

Cycloid. — A curve generated by the rolling of a circle on a plane. 

Length of a cycloidal curve = 4 X diameter of the generating circle. 
Length of the base= circumference of the generating circle. 
Area of a cycloid = 3 X area of generating circle. 

Helix (Screw). — A line generated by the progressive rotation of a 
point around an axis and equidistant from its center. 

Length of a helix. — • To the square of the circumference described by the 
generating point add the square ot the distance advanced in one revolution, 
and take the square root of their sum multiplied by the number of revolu- 
tions of the generating point. Or, 

V(c 2 + h 2 )n = length, n being number of revolutions. 

Spirals. — Lines generated by the progressive rotation of a point 
around a fixed axis, with a constantly increasing distance from the axis. 

A plane spiral is made when the point rotates in one plane. . 

A conical spiral is made when the point rotates around an axis at i. 
progressing distance from its center, and advancing in the direction of the 
axis, as around a cone. 

Length of a plane spiral line. — When the distance between the coils is 
uniform. 

Rule. — Add together the greater and less diameters; divide their sum 
by 2; multiply the quotient by 3.1416, and again by the number of revo- 
lutions. Or, take the mean of the length of the greater and less circum- 
ferences and multiply it by the number of revolutions. Or, 

length = nn — - — , d and d' being the inner and outer diameters. 

Length of a conical spiral line. — Add together the greater and less 
diameters; divide their sum by 2 and multiply the quotient by 3.1416. 
To the square of the product of this circumference and the number of 
revolutions of the spiral add the square of the height of its axis and take 
the square root of the sum. 



K 



Or, length = 4/ m -^r— + h 2 . 



SOLID BODIES. 



Surfaces and Volumes of Similar Solids. — The surfaces of two 
similar solids are to each other as the squares of their linear dimensions; 
the volumes are as the cubes of their linear dimensions. If L = the side 



MENSURATION. 63 

c' a cube or other solid, and I the side of a similar body of different size, 
S, s, the surfaces and V, v. the volumes respectively, S : s :: L 2 : P; 
V : v :: U : Z 3 . 

The Prism. — To find the surface of a right prism: Multiply the perim- 
eter of the base by the altitude for the convex surface. To this add the 
areas of the two ends when the entire surface is required. 

Volume of a prism = area of its base X its altitude. 

The pyramid. — Convex surface of a regular pyramid = perimeter of 
its base X half the slant height. To this add area of the base if the whole 
surface is required. 

Volume of a pyramid = area of base X one third of the altitude. 

To find the surface of a frustum of a regular pyramid: Multiply half the 
slant height by the sum of the perimeters of the two bases for the convex 
surface. To this add the areas of the two bases when the entire surface is 
required . 

To find the volume of a frustum of a pyramid: Add together the areas of 
the two bases and a mean proportional between them, and multiply the 
sum by one third of the altitude. (Mean proportional between two 
numbers = square root of their product.) 

Wedge. — A wedge is a solid bounded by five planes, viz. : a rectangular 
base, two trapezoids, or two rectangles, meeting in an edge, and two 
triangular ends. The altitude is the perpendicular drawn from any point 
in the edge to the plane of the base. 

To find the volume of a wedge: Add the length of the edge to twice the 
length of the base, and multiply the sum by one sixth of the product of 
the height of the wedge and the breadth of the base. 

Rectangular prismoid. — A rectangular prismoid is a solid bounded 
by six planes, of which the two bases are rectangles, having their corre- 
sponding sides parallel, and the four upright sides of the solid are trape- 
zoids. 

To find the volume of a rectangular prismoid: Add together the areas of 
the two bases and four times the area of a parallel section equally distant 
from the bases, and multiply the sum by one sixth of the altitude. 

Cylinder. — Convex surface of a cylinder = perimeter of base X 
altitude. To this add the areas of the two ends when the entire surface is 
required. 

Volume of a cylinder = area of base X altitude. 

Cone. — Convex surface of a cone = circumference of base X half the 
slant height. To this add the area of the base when the entire surface is 
"required. 

Volume of a cone = area of base X one third of the altitude. 

To find the surface of a frustum of a cone: Multiply half the side by the 
sum of the circumferences of the two bases for the convex surface; to this 
add the areas of the two bases when the entire surface is required. 

To find the volume of a frustum of a cone: Add together the areas of 
the two bases and a mean proportional between them, and multiply 
the sum by one third of the altitude. Or, Vol. = 0.261Sa(b 2 + c 2 + bc)\ 
a = altitude; b and c, diams. of the two bases. 

Sphere. — To find the surface of a sphere: Multiply the diameter by the 
circumference of a great circle; or, multiply the square of the diameter by 
3.14159. 

Surface of sphere = 4 x area of its great circle. 
" " " = convex surface of its circumscribing cylinder. 

Surfaces of spheres are to each other as the squares of their diameters. 
To find the volume of a sphere: Multiply the surface by one third of the 
radius; or, multiply the cube of the diameter by */6; that is, by 0.5236.. 
Value of n/6 to 10 decimal places = 0.5235987756. 
The volume of a sphere = 2/ 3 the volume of its circumscribing cylinder. 
Volumes of spheres are to each other as the cubes of their diameters. 



64 MENSURATION. 



Spherical triangle. — To find the area of a spherical triangle: Compute 
the surface of the quadrantal triangle, or one eighth of the surface of 
the sphere. From the sum of the three angles subtract two right angles; 
divide the remainder by 90, and multiply the quotient by the area of the 
quadrantal triangle. 

Spherical polygon. — To find the area of a spherical polygon: Compute I 
the surface of the quadrantal triangle. From the sum of all the angles '•:■ 
subtract the product of two right angles by the number of sides less two; 
divide the remainder by 90 and multiply the quotient by the area of the 
quadrantal triangle. 

The prismoid. — The prismoid is a solid having parallel end areas, and 
may be composed of any combination of prisms, cylinders, wedges, pyra- 
mids, or cones or frustums of the same, whose bases and apices lie in the 
end areas. 

Inasmuch as cylinders and cones are but special forms of prisms and 
pyramids, and warped surface solids may be divided into elementary 
forms of them, and since frustums may also'be subdivided into the elemen- 
tary forms, it is sufficient to say that all prismoids may be decomposed ; 
into prisms, wedges, and pyramids. If a formula can be found which is 
equally applicable to all of these forms, then it will apply to any combi- 
nation of them. Such a formula is called 



The Prismoidal Formula. 

Let A = area of the base of a prism, wedge, or pyramid; 
Ai, Ai, A m = the two end and the middle areas of a prismoid, or of any of 
its elementary solids; h = altitude of the prismoid or elementary solid; 
V = its volume; 

V ■ 
For a prism, A\, A m and Ai are equal, 
For a wedge with parallel ends, Ai = 0, A m = -x Av,V= ~{Ai+2A:)= — • 
For a cone or pyramid, Ai = 0, A m = -j Av, V = - (Ai + Ai) = -r- • 

The prismoidal formula is a rigid formula for all prismoids. The only 
approximation involved in its use is in the assumption that the given solid 
may be generated by a right line moving over the boundaries of the end 
areas. 

The area of the middle section is never the mean of the two end areas if 
the prismoid contains any pyramids or cones among its elementary forms. 
When the three sections are similar in form the dimensions of the middle 
area are always the means of the corresponding end dimensions. This 
fact often enables the dimensions, and hence the area of the middle section, 
to be computed from the end areas. 

Polyedrons. — A polyedron is a solid bounded by plane polygons. A 
regular polyedron is one whose sides are all equal regular polygons. 

To find the surface of a regular polyedron. — Multiply the area of one of 
the faces by the number of faces; or, multiply the square of one of the 
edges by the surface of a similar solid whose edge is unity. 



A Table op theS Regular Polyedrons whose Edges are Unity. 

Names. No. of Faces. Surface. Volume. 

Tetraedron 4 1.7320508 0.1178513 

Hexaedron 6 6.0000000 1 .0000000 

Octaedron 8 3.4641016 0.4714045 

Dodecaedron 12 20.6457288 7.6631189 

Icosaedron t . , . . , , . 20 8.6602540 2.1816950 



MENSURATION. 65 

To find the volume of a regular polyedron. — Multiply the surface 
by one third of the perpendicular let fall from the centre on one of the 
faces; or, multiply the cube of one of the edges by the solidity of a similar 
polyedron whose edge is unity. 

Solid of revolution. — The volume of any solid of revolution is equal 
to the product of the area of its generating surface by the length of the 
path of the centre of gravity of that surface. 

The convex surface of any solid of revolution is equal to the product of 
the perimeter of its generating surface by the length of path of its centre 
of gravity. 

Cylindrical ring. — Let d = outer diameter; d' = inner diameter; 
1/2 (d — d') = thickness = t; Vint 2 = sectional area; 1/2 (d +d') = mean 
diameter = M ; nt = circumference of section; n M = mean circum- 
ference of ring; surface = ntXn M; = 1/4 n 2 (d 2 - d' 2 ); = 9.86965 t M; 
= 2.46741 (d 2 - d' 2 )- volume = 1/4 n t 2 M n; = 2.467241 t 2 M. 

Spherical zone. — Surface of a spherical zone or segment of a sphere 
= its altitude X the circumference of a great circle of the sphere. A 
great circle is one whose plane passes through the centre of the sphere. 

Volume of a zone of a sphere. — To the sum of the squares of the radii 
of the ends add one third of the square of the height; multiply the sum 
by the height and by 1.5708. 

Spheripal segment. — Volume of a spherical segment with one base. — 
Multiply half the height of the segment by the area of the base, and the 
cube of the height by 0.5236 and add the two products. Or, from three 
times the diameter of the sphere subtract twice the height of the segment; 
multiply the difference by the square of the height and by 0.5236. Or, to 
three times the square of the radius of the base of the segment add the 
square of its height, and multiply the sum by the height and by 0.5236. 

Spheroid or ellipsoid. — When the revolution of the generating sur- 
face of the spheroid is about the transverse diameter the spheroid is 
prolate, and when about the conjugate it is oblate. 

Convex surface of a segment of a spheroid. — Square the diameters of the 
spheroid, and take the square root of half their sum ; then, as the diameter 
from which the segment is cut is to this root so is the height of the segment 
to the proportionate height of the segment to the mean diameter. Multiply 
the product of the other diameter and 3.1416 by the proportionate height. 

Convex surface of a frustum or zone of a spheroid. — Proceed as by 
previous rule for the surface of a segment, and obtain the proportionate 
height of the frustum. Multiply the product of the diameter parallel to 
the base of the frustum and 3.1416 by the proportionate height of the 
frustum. 

Volume of a spheroid is equal to the product of the square of the revolv- 
ing axis by the fixed axis and by 0.5236. The volume of a spheroid is two 
thirds of that of the circumscribing cylinder. 

Volume of a segment of a spheroid. — 1. When the base is parallel to the 
revolving axis, multiply the difference between three times the fixed axis 
and twice the height of the segment, by the square of the height and by 
0.5236. Multiply the product by the square of the revolving axis, and 
divide by the square of the fixed axis. 

2. When the base is perpendicular to the revolving axis, multiply the 
difference between three times the revolving axis and twice the height of 
the segment by the square of the height and by 0.5236. Multiply the 
product by the length of the fixed axis, and divide by the length of the 
revolving axis. 

Volume of the middle frustum of a spheroid. — 1 . When the ends are 
circular, or parallel to the revolving axis: To twice the square of the middle 
diameter add the square of the diameter of one end; multiply the sum by 
the length of the frustum and by 0.2618. 

2. When the ends are elliptical, or perpendicular to the revolving axis: 
To twice the product of the transverse and conjugate diameters of the 
middle section add the product of the transverse and conjugate diameters 
of one end; multiply the sum by the length of the frustum and by 0.2618. 

Spindles. — Figures generated by the revolution of a plane area, 
bounded by a curve other than a circle, when the curve is revolved about 
a chord perpendicular to its axis, or about its double ordinate. They are 
designated by the name of the arc or curve from which they are generated, 
as Circular, Elliptic, Parabolic, etc., etc. 



66 MENSURATION. 



Convex surface of a circular spindle, zone, or segment of it. — Rule: Mul- 
tiply the length by the radius of the revolving arc; multiply this arc by the 
central distance, or distance between the centre of the spindle and centre 
of the revolving arc; subtract this product from the former, double the 
remainder, and multiply it by 3.1416. 

Volume of a circular spindle. — Multiply the central distance by half 
the area of the revolving segment; subtract the product from one third of 
the cube of half the length, and multiply the remainder by 12.5664. 

Volume of frustum or zone of a circular spindle. — From the square of 
half the length of the whole spindle take one third of the square of half the 
length of the frustum, and multiply the remainder by the said half length 
of the frustum; multiply the central distance by the revolving area which 
generates the frustum; subtract this product from the former, and multi- 
ply the remainder by 6.2832. 

Volume of a segment of a circular spindle. — Subtract the length of the 
segment from the half length of the spindle; double the remainder and 
ascertain the volume of a middle frustum of this. length; subtract the 
result from the volume of the whole spindle and halve the remainder. 

Volume of a cycloidal spindle = five eighths of the volume of the circum- 
scribing cylinder. — Multiply the product of the square of twice the dia- 
meter of the generating circle and 3.927 by its circumference, and divide 
this product by 8. 

Parabolic conoid. — Volume of a parabolic conoid (generated by the 
revolution of a parabola on its axis). — Multiply the area of the base by 
half the height. 

Or multiply the square of the diameter of the base by the height and by 
0.3927. 

Volume of a frustum of a parabolic conoid. ■ — Multiply half the sum of 
trie areas of the two ends by the height. 

Volume of a parabolic spindle (generated by the revolution of a parabola 
on its base). — Multiply the square of the middle diameter by the length 
and by 0.4189. The volume of a parabolic spindle is to that of a cylinder 
of the same height and diameter as 8 to 15. 

Volume of the middle frustum of a parabolic spindle. — Add together 
8 times the square of the maximum diameter, 3 times the square of the 
end diameter, and 4 times the product of the diameters. Multiply the 
sum by the length of the frustum and by 0.05236. This rule is applicable 
for calculating the content of casks of parabolic form. 

Casks. — To find the volume of a cask of any form. — Add together 39 
times the square of the bung diameter, 25 times the square of the head 
diameter, and 26 times the product of the diameters. Multiply the sum 
by the length, and divide by 31,773 for the content in Imperial gallons, or 
by 26,470 for U. S. gallons. 

This rule was framed by Dr. Hutton, on the supposition that the middle 
third of the length of the cask was a frustum of a parabolic spindle, and 
each outer third was a frustum of a cone. 

To find the ullage of a cask, the quantity of liquor in it when it is not full. 
1. For a lying cask: Divide the number of wet or dry inches by the bung 
diameter in inches. If the quotient is less than 0.5, deduct from it one 
fourth part of what it wants of 0.5. If it exceeds 0.5, add to it one fourth 
part of the excess above 0.5. Multiply the remainder or the sum by the 
whole content of the cask. The product is the quantity of liquor in the 
cask, in gallons, when the dividend is wet inches; or the empty space, if 
dry inches. 

2. For a standing cask: Divide the number of wet or dry inches by the 
length of the cask. If the quotient exceeds 0.5, add to it one tenth of its 
excess above 0.5; if less than 0.5, subtract from it one tenth of what it 
wants of 0.5. Multiply the sum or the remainder by the whole content of 
the cask. The product is the quantity of liquor in the cask, when the 
dividend is wet inches; or the empty space, if dry inches. 

Volume of cask (approximate) U. S. gallons = square of mean diam. 
X length in inches X 0.0034. Mean diameter = half the sum of the 
bung and head diameters. 

Volume of an irregular solid. — Suppose it divided into parts, resem- 
bling prisms or other bodies measurable by preceding rules. Find the con- 
tent of each part; the sum of the contents is the cubic contents of the solid. 



PLANE TRIGONOMETRY. 67 



The content of a small part is found nearly by multiplying half the sum 
of the areas of each end by the perpendicular distance between them. 

The contents of small irregular solids may sometimes be found by im- 
mersing them under water in a prismatic or cylindrical vessel, and observ- 
ing the amount by which the level of the water descends when the solid is 
withdrawn. The sectional area of the vessel being multiplied by the 
descent of the level gives the cubic contents. 

Or, weigh the solid in air and in water; the difference is the weight of 
water it displaces. Divide the weight in pounds by 62.4 to obtain volume 
in cubic feet, or multiply it by 27.7 to obtain the volume in cubic inches. 

When the solid is very large and a great degree of accuracy is not 
requisite, measure its length, breadth, and depth in several different 
places, and take the mean of the measurement for each dimension, and 
multiply the three means together. 

When the surface of the solid is very extensive it is better to divide it 
into triangles, to find the area of each triangle, and to multiply it by the 
mean depth of the triangle for the contents of each triangular portion; the 
contents of the triangular sections are to be added together. 

The mean depth of a triangular section is obtained by measuring the 
depth at each angle, adding together the three measurements, and taking 
one third of the sum. 



PLANE TRIGONOMETRY. 

Trigonometrical Functions. 

Every triangle has six parts — three angles and three sides. When any 
three of these parts are given, provided one of them is a side, the other 
parts may be determined. By the solution of a triangle is meant the 
determination of the unknown parts of a triangle when certain parts are 
given. 

The complement of an angle or arc is what remains after subtracting the 
angle or arc from 90°. 

In general, if we represent any arc by A, its complement is 90° — A. 
Hence the complement of an arc that exceeds 90° is negative. 

The supplement of an angle or arc is what remains after subtracting the 
angle or arc from 180°. If A is an arc its supplement is 180° — A. The 
supplement of an arc that exceeds 180° is negative. . 

The sum of the three angles of a triangle is equal to 180°. Either angle is 
the supplement of the other two. In a right-angled triangle, the right 
angle being equal to 90°, each of the acute angles is the complement of 
the other. 

In all right-angled triangles having the same acute angle, the sides have to 
each other the same ratio. These ratios have received special names, as 
follows : 

If A is one of the acute angles, a the opposite side, b the adjacent side, 
and c the hypothenuse. 

The sine of the angle A is the quotient of the opposite side divided by the 

hypothenuse. Sin A = — 
c 
The tangent of the angle A is the quotient of the opposite side divided by 

the adjacent side. Tan A = r~ 

The secant of the angle A is the quotient of the hypothenuse divided by the 

adjacent side. Sec A = — • 

The cosine (cos), cotangent (cot), and cosecant (cosec) of an angle 
are respectively the sine, tangent, and secant of the complement of that 
angle. The terms sine, cosine, etc., are called trigonometrical functions. 

In a circle whose radius is unity, the sine of an arc, or of the angle at the 
centre measured by that arc, is the perpendicular let fall from one extremity of 
the arc upon the diameter passing through the other extremity. 

The tangent of an arc is the line which touches the circle at one extremity 



m 



PLANE TRIGONOMETRY. 



of the arc, and is limited by the diameter (produced) passing through the other 
extremity. 

The secant of an arc is that part of the produced diameter which is inter- 
cepted between the centre and the tangent. 

The versed sine of an arc is that part of the diameter intercepted between 
the extremity of the arc and the foot of the sine. 

In a circle whose radius is not unity, the trigonometric functions of an 
arc will be equal to the lines here defined, divided by the radius of the 
circle. 

If ICA (Fig. 71) is an angle in the first quadrant, and CF = radius, 

FG „_„ CG KF 




The sine of the angle = 



Rad 



I A 
Rad " 

Cosec = 



Secant 

CL 
Rad ' 



Cos = 

= SLL 

Rad ' 

Versin = 



Rad 



Rad 



"Rad 
PL 

Rad ' 



If radius is 1, then Rad in the denominator is 
omitted, and sine = F G, etc. 

The sine of an arc = half the chord of twice the 
arc. 

The sine of the supplement of the arc is the 
same as that of the arc itself. Sine of arc B D F 
= F G = sin arc FA. 
The tangent of the supplement is equal to the tangent of the arc, but 
with a contrary sign. Tan BDF = — BM. 

The secant of the supplement is equal to the secant of the arc, but with 
a contrary sign. Sec BDF = — CM. 

Signs of the functions in the four quadrants. — If we divide a 
circle into four quadrants by a vertical and a horizontal diameter, the 
upper right-hand quadrant is called the first, the upper left the second, 
the lower left the third, and the lower right the fourth. The signs of the 
functions in the four quadrants are as follows: 

First quad. Second quad. Third quad. Fourth quad. 

Sine and cosecant, + + — — 

Cosine and secant, + — — + 

Tangent and cotangent, + — + — 

The values of the functions are as follows for the angles specified: 



Angle 

Sine 

Cosine 
Tangent . . . 
Cotangent . 

Secant ..'.'. 
Cosecant . . 
Versed sine 



o 








o 


o 


o 

















30 


45 


60 


90 


120 


135 


150 


ISO 


270 




1 


1 


V-A 




V3 


1 


1 






(1 








1 








1) 


1 




2 


v 2 


2 






V 2 








1 


V3 


1 


1 





1 


1 


Vf 


-1 







2 


v 2 


2 




2 


v 2 


2 





1 


1 


N/3 


on 


-V3 


-1 


1 





00 


00 


V 3 


1 


1 
V/3 





1 
V3 


-1 


v 3 
-V3 


00 





1 


2 


a/2 


2 


00 


-2 


-V2 


2 


-1 


CO 


00 


2 


Vi 


Vi 


1 


V3 


V£ 


2 


00 


-1 


n 


2-V3 


x/2-1 


1 


1 


3 


vT+i 


2+V3 




1 




2 


v 2 


- 




2 


V2 


2 





360 


1 




PLANE TRIGONOMETRY. 69 



TRIGONOMETRICAL FORMULAE. 

The following relations are deduced from the properties of similar 
triangles (Radius = 1): 

cos A : sin A : : 1 : tan A, whence tan A = r ; 

cos A 

• a a cos A 

sin A : cos A : : 1 : cot A, cotan A = -: — -. ; 

sin A 

cos A : 1 : : 1 : sec A, " sec A = -? ; 

cos A 

sin A : 1 : : 1 : cosec A, " cosec A = -: — — ; 

sin A 

tan A : 1 : : 1 : cot A " tan A = — - — -.■ 

cot A 

The sum of the square of the sine of an arc and the square of its cosine 
equals unity. Sin 2 A + cos 2 A = 1. 

Also, 1 + tan 2 A = sec 2 A; 1 + cot 2 A = cosec 2 A. 

Functions of the sum and difference of two angles: 

Let the two angles be denoted by A and B, their sum A + B = C, and 
their difference A — B by D. 

sin (A + B) = sin A cos B + cos A sin B; (1) 

cos (A + B) = cos A cos 5 — sin A sin 5; (2) 

sin (A — B) = sin A cos B — cos A sin B ; (3) 

cos (A — B) = cos A cos 5 + sin A sin B (4) 

From these four formulae by addition and subtraction we obtain 

sin (A + B) + sin (A - B) = 2 sin A cos 5; . . . . (5) 

sin (A + B) — sin (A - B) = 2 cos A sin B; . . . . (6) 

cos (A + B) + cos (A - B) = 2 cos A cos B; . . . . (7) 

cos (A - B) - cos (A + 5) = 2 sin A sin 5 (8) 

If we put A + 5 = C, and A - B = Z>, then A = i/ 2 (C + £>) and 5 = 
V2(C — D), and we have 

sin C + sin D = 2 sin i/ 2 (C + D) cos 1/2 (C - D) ; . . (9) 

sin C - sin Z) = 2 cos 1/2 (C + £>) sin 1/2 (C -£>);. . (10) 

cosC + cosD = 2 cos 1/2 (C + D) cos 1/2 (C - D); . . (11) 

cos D - cos C = 2 sin 1/2 (C + Z>) sin 1/2 (C - Z>). . . (12) 

Equation (9) may be enunciated thus: The sum of the sines of any two 
angles is equal to twice the sine of half the sum of the angles multiplied by 
the cosine of half their difference. These formulae enable us to transform 
a sum or difference into a product. 

The sum of the sines of two angles is to their difference as the tangent of 
half the sum of those angles is to the tangent of half their difference. 

sin A + sin B = 2 sin V 2 (A + B) cos y 2 (A-B) = tan 1/2 (A + B) 
sin A - sin B 2 cos 1/2 (A + B) sin 1/2 (A-B)~ tan 1/2 (A - B) ' ^ ' 

The sum of the cosines of two angles is to their difference as the cotan- 
gent of half the sum of those angles is to the tangent of half their difference. 

cos A + cos B 2 cos 1/2 (A + B) cos 1/2 (A - B) = cot 1/2 (A + £) 
cos B - cos A 2 sin 1/2 (A + B) sin 1/2 (A - B) tan 1/2 (A - B) ' K ' 

The sine of the sum of two angles is to the sine of their difference as the 
sum of the tangents of those angles is to the difference of the tangents. 

sin (A + B) = tan A + tan B . 
sin (A - B) tan A - tan B ' * ' 



PLANE TRIGONOMETRY. 



sin (A + B) 
cos A cos B 
sin (A - B) 
cos A cos 5 * 
cos (A + B) 
cos A cos B 
cos (A - B) 
cos A cos # 

Functions of twice an angle : 
sin 2 A — 2 sin A cos A. ; 

. _ . 2 tan A 

tan 2A = — tt—t ; 

1 - tan 2 A 

Functions of half an angle: 



= tan A + tan B; 
tan A ~ tan B; 
1 —tan A tan 5; 
1 + tan A tan B; 



tan (A + £) = 
tan (A - B) = 
cot (A + B) = 
cot (A - B) = 



tan A + tan B . 
1 -tan A tan .8 ' 
tan A — tan i? 
1 + tan A tan B ' 
cot A cot B — 1 . 
cot B + cot A ' 
cot A cot .B + 1 
cot B — cot A " 



sinV 2 A=± 



tan 1/2-4 = 






cos A 



cos 2 A 
cot 2A 


= cos 2 A — sin 2 A; 
cot 2 A — 1 
2 cot A 


cos V2-4 
cot 1/2 A 


, / 1 -f cos A , 
~* V 2 

< 4 /l + cos A 



cos A 



For tables of Trigonometric Functions, see Mathematical Tables. 



Solution of Plane Right-angled Triangles. 

Let A and B be the two acute angles and C the right angle, and a, b, and 
c the sides opposite these angles, respectively, then we have 



1. sin A = cos B = - ; 3. tan A — cot B — 



2. cos A = sin 5 < 



4. cot A = tan 5 : 



1. In any plane right-angled triangle the sine of either of the acute 
angles is equal to the quotient of the opposite leg divided by the hypothe- 
nuse. 

2. The cosine of either of the acute angles is equal to the quotient of 
the adjacent leg divided by the hypothenuse. 

3. The tangent of either of the acute angles is equal to the quotient of 
the opposite leg divided by the adjacent leg. 

4. The cotangent of either of the acute angles is equal to the quotient 
of the adjacent leg divided by the opposite leg. 

5. The square of the hypothenuse equals the sum of the squares of the 
other two sides. 



Solution of Oblique-angled Triangles. 

The following propositions are proved in works on plane trigonometry. 
In any plane triangle — 

Theorem 1. The sines of the angles are proportional to the opposite 
sides. 

Theorem 2. The sum of any two sides is to their difference as the tan- 
gent of half the sum of the opposite angles is to the tangent of half their 
difference. 

Theorem 3. If from any angle of a triangle a perpendicular be drawn to 
the opposite side or base, the whole base will be to the sum of the other 
two sides as the difference of those two sides is to the difference of the 
segments of the base. 

Case I. Given two angles and a side, to find the third angle and the 
other two sides. 1. The third angle = 180° — sum of the two angles. 
2. The sides may be found by the following proportion: 



ANALYTICAL GEOMETRY. 71 



The sine of the angle opposite the given side is to the sine of the angle 
opposite the required side as the given side is to the required side. 

Case II. Given two sides and an angle opposite one of them, to find 
the third side and the remaining angles. 

The side opposite the given angle is to the side opposite the required 
angle as the sine of the given angle is to the sine of the required angle. 

The third angle is found by subtracting the sum of the other two from 
180°, and the third side is found as in Case I. 

Case III. Given two sides and the included angle, to find the third 
side and the remaining angles. 

The sum of the required angles is found by subtracting the given angle 
from 180°. The difference of the required angles is then found by Theorem 
II. Half the difference added to half the sum gives the greater angle, and 
half the difference subtracted from half the sum gives the less angle. The 
third side is then found by Theorem I. 

Another method: 

Given the sides c, b, and the included angle A, ta find the remaining side 
a and the remaining angles B and C. 

From either of the unknown angles, as B, dra * a perpendicular Be to 
the opposite side. 

Then 

Ae = c cos A, Be = c sin A, eC = b — Ac Be -s- eC = tan C. 

Or, in other words, solve Be, Ae and BeC as right-angled triangles. 

Case IV. Given the three sides, to find the angles. 

Let fall a perpendicular upon the longest side from the opposite angle, 
dividing the given triangle into two right-angled triangles. The two seg- 
ments of the base may be found by Theorem III. There will then be 
given the hypothenuse and one side of a right-angled triangle to find the 
angles. 

For areas of triangles, see Mensuration. 



ANALYTICAL GEOMETRY. 

Analytical geometry is that branch of Mathematics which has for its 
object the determination of the forms and magnitudes of geometrical 
magnitudes by means of analysis. 

Ordinates and abscissas. — In analytical geometry two intersecting 
lines YY', XX' are used as coordinate axes, Y 

XX' being the axis of abscissas or axis of X, I 

and YY' the axis of ordinates or axis of Y . / p 

A, the intersection, is called the origin of co- -j 

ordinates. The distance of any point P / c / 

from the axis of Y measured parallel to the / / 

axis of X is called the abscissa of the point, / / 

as AD or CP, Fig. 72. Its distance from the x' — / ' x 

axis of X, measured parallel to the axis of /AD 

Y, is called the ordinate, as AC or PD. / 

The abscissa and ordinate taken together / 

are called the coordinates of the point P. / 

The angle of intersection is usually taken as Y y 

a right angle, in which case the axes of X jr IG 72 

and Y are called rectangular coordinates. 

The abscissa of a point is designated by the letter x and the ordinate 
byy. 

The equations of a point are the equations which express the distances 
of the point from the axis. Thus x = a, y = b are the equations of the 
point P. 

Equations referred to rectangular coordinates. — The equation of 
a line expresses the relation which exists between the coordinates of every 
point of the line. 

Equation of a straight line, y = ax ± 5, in which a is the tangent of the 
angle the line makes with the axis of X, and b the distance above A in 
which the line cuts the axis of Y. 

Every equation of the first degree between two variables is the equation 



72 ANALYTICAL GEOMETRY. 

of a straight line, as Ay + Bx +C^0, which can be reduced to the foria 
y = ax ± b. 

Equation of the distance between two points: 

D - vV - x') 2 + iv" - y') 2 , 

in which x'y', x"y" are the coordinates of the two points. 
Equation of a line passing through a given point: 

y - y' = a(x - x'), 

in which x'y' are the coordinates of the given point, o, the tangent of the 
angle the line makes with the axis of x, being undetermined, since any 
number of lines may be drawn through a given point. 
Equation of a line passing through two given points: 

y" — y' 

y - y = x » __ X M - x )- 

Equation of a line parallel to a given line and through a given point: 

y - y' = a(x — x'). 

Equation of an angle V included between two given lines: 

T7 a' — a 
tang V = r— — t • 
1 + a' a 

in which a and a' are the tangents of the angles the lines make with the 
axis of abscissas. 

If the lines are at right angles to each other tang V ■ = oo , and 

1 + a'a = 0. 
Equation of an intersection of two lines, whose equations are 
y = ax + b, and y — a'x + b', 
ab' — a'b 
a — a' 
Equation of a perpendicular from a given point to a given line: 

y ~ y' = - - (x - x'). 

Equation of the length of the perpendicular P: 
p _ y' - ax' - b 
Vi + a 2 

The circle. — Equation of a circle, the origin of coordinates being at 
the centre, and radius = R: 

x 2 + y z = R 2 . 

If the origin is at the left extremity of the diameter, on the axis of X: 

y 2 = 2Rx - x 2 . 

If the origin is at any point, and the coordinates of the centre are x'y' 

(x - x') 2 + (y - y') 2 = R 2 . 

Equation of a tangent to a circle, the coordinates of the point of tan- 
gency being x"y" and the origin at the centre, 

yy" + xx" = R 2 . 

The ellipse. — Equation of an ellipse, referred to rectangular coordi- 
nates with axis at the centre: 

A 2y2 + B 2 X 2 = .4252, 

in which 4 is half the transverse axis and B half the conjugate axis. 



ANALYTICAL GEOMETRY. 73 

Equation of the ellipse when the origin is at the vertex of the transverse 
axis: 

y 2 = ~(2Ax - x 2 ). 

The eccentricity of an ellipse is the distance from the centre to either 
focus, divided by the semi-transverse axis, or 



, VII 



The parameter of an ellipse is the double ordinate passing through the 
focus. It is a third proportional to the transverse axis and its conjugate, 
or 

2B 2 
2A : 2B :: 2B : parameter; or parameter = — -.— 

Any ordinate of a circle circumscribing an ellipse is to the corresponding 
ordinate of the ellipse as the semi -transverse axis to the semi-conjugate. 
Any ordinate of a circle inscribed in an ellipse is to the corresponding 
ordinate of the ellipse as the semi-conjugate axis to the semi-transverse. 

Equation of the tangent to an ellipse, origin of axes at the centre: 

A *yy" + B 2 xx" = A 2 B 2 , 

y"x" being the coordinates of the point of tangency. 

Equation of the normal, passing through the point of tangency, and 
perpendicular to the tangent: 

V ~ V = B 2 jr»(x - * )• 

The normal bisects the angle of the two lines drawn from the point of 
tangency to the foci. 

The lines drawn from the foci make equal angles with the tangent. 

The parabola. — Equation of the parabola referred to rectangular 
coordinates, the origin being at the vertex of its axis, y 2 = 2px, in which 
2p is the parameter or double ordinate through the focus. 

The parameter is a third proportional to any abscissa and its correspond- 
ing ordinate, or 

x : y :: y : 2p. 

Equation of the tangent: 

yy" = p(x + x"), 

y"x" being coordinates of the point of tangency. 
Equation of the normal: 

y - y" = - y(z - x"). 

The sub-normal, or projection of the normal on the axis, is constant, and 
equal to half the parameter. 

The tangent at any point makes equal angles with the axis and with the 
line drawn from the point of tangency to the focus. 

The hyperbola. — Equation of the hyperbola referred to rectangular 
coordinates, origin at the centre: 

A 2 y 2 - B 2 x 2 = - A 2 B 2 , 

in which A is the semi-transverse axis and B the semi-conjugate axis. 
Equation when the origin is at the right vertex of the transverse axis: 



A 2 
Conjugate and equilateral hyperbolas. — If on the conjugate axis, 



74 DIFFERENTIAL CALCULUS. 



as a transverse, and a focal distance equal to V A 2 + B 2 , we construct 
the two branches of a hyperbola, the two hyperbolas thus constructed are 
called conjugate hyperbolas. If the transverse and conjugate axes are 
equal, the hyperbolas are called equilateral, in which case y 2 — x 2 = —A' 1 
when A is the transverse axis, and x 2 — y 2 = — B 2 when B is the trans- 
verse axis. 

The parameter of the transverse axis is a third proportional to the trans- 
verse axis and its conjugate. 

2 A : 2B :: 25 : parameter. 

The tangent to a hyperbola bisects the angle of the two lines drawn from 
the point of tangency to the foci. 

The asymptotes of a hyperbola are the diagonals of the rectangle 
described on the axes, indefinitely produced in both directions. 

The asymDtotes continually approach the hyperbola, and become 
tangent to it "at an infinite distance from the centre. 

Equilateral hyperbola. — In an equilateral hyperbola the asymptotes 
make equal angles with the transverse axis, and are at right angles to each 
other. With the asymptotes as axes, and P = ordinate, V = abscissa, 
PV = a constant. This equation is that of the expansion of a perfect 
gas, in which P = absolute pressure, V = volume. 

Curve of Expansion of Gases. —PV 71 = a constant, or PiVi n = P 2 V2 n , 
in which Vi and Vi are the volumes at the pressures Pi and Pt. When 
these are given, the exponent n may be found from the formula 

= log Pi - log P 2 

log Vi — log Vi 

Conic sections, — Every equation of the second degree between two 
variables will represent either a circle, an ellipse, a parabola or a hyperbola. 
These curves are those which are obtained by intersecting the surface of a 
cone by planes, and for this reason they are called conic sections. 

Logarithmic curve- — A logarithmic curve is one in which one of the 
coordinates of any point is the logarithm of the other. 

The coordinate axis to which the lines denoting the logarithms are 
parallel is called the axis of logarithms, and the other the axis of numbers. 
If y is the axis of logarithms and x the axis of numbers, the equation of the 
curve is y = log. x. 

If the base of a system of logarithms is a, we have a y = x, in which y is 
the logarithm of x. 

Each system of logarithms will give a different logarithmic curve. If 
y ■■= 0, x = 1. Hence every logarithmic curve will intersect the axis of 
numbers at a distance from the origin equal to 1. 



DIFFERENTIAL CALCULUS. 

The differential of a variable quantity is the difference between any two 
of its consecutive values; hence it is indefinitely small. It is expressed by 
writing d before the quantity, as dx, which is read differential of x. 

The term -~ is called the differential coefficient of y regarded as a func- 
tion of x. It is also called the first derived function Or the derivative. 

The differential of a function is equal to its differential coefficient mul- 
tiplied by the differential of the independent variable; thus, -j-dx = dy. 

The limit of a variable quantity is that value to which it continually 
approaches, so as at last to differ from it by less than any assignable 
quantity. 

The differential coefficient is the limit of the ratio of the increment of 
the independent variable to the increment of the function. 

The differential of a constant quantity is equal to 0. 

The differential of a product' of a constant by a variable is equal to the 
constant multiplied by the differential of the variable. 

If u — Av, du = A dv. 



DIFFERENTIAL CALCULUS. 75 

In any curve whose equation is y = f(x), the differential coefficient 

~ = tan a; hence, the rate of increase of the function, or the ascension of 

dx 

the curve at any point, is equal to the tangent of the angle which the 

tangent line makes with the axis of abscissas. 

All the operations of the Differential Calculus comprise but two objects: 

1. To find the rate of change in a function when it passes from one state 
of value to another, consecutive with it. 

2. To find the actual change in the function: The rate of change is the 
differential coefficient, and the actual change the differential. 

Differentials of algebraic functions. — The differential of the sum 
or difference of any number of functions, dependent on the same variable, 
is equal to the sum or difference of their differentials taken separately: 

If u = y + z - w, du = dy + dz — dw. 

The differential of a product of two functions dependent on the same 
variable is equal to the sum of the products of each by the differential of 
the other: 

... j,j d(uv) du dv 

d(uv) = vdu+ udv. = 1- 

uv u v 

The differential of the product of any number of functions is equal to 
the sum of the products which arise by multiplying the differential of each 
function by the product of all the others: 

d(uts) = tsdu + us dt + ut ds. 

The differential of a fraction equals the denominator into the diffeiential 
of the numerator minus the numerator into the differential of the denom- 
inator, divided by the square of the denominator: 

_ ?u\ = vdu-udv . 

\V / V 2 

If the denominator is constant, dv = 0, and dt = -^ = — . 

If the numerator is constant, du = 0, and dt = — • 

v 2 

The differential of the square root of a quantity is equal to the differen- 
tial of the quantity divided by twice the square root of the quantity: 

If v = U V2, or v - ^u, dv = -^=; = \%r 1 l2dn. 

2^u 

The differential of any power of a function is equal to the exponent multi- 
plied by the function raised to a powerless one, multiplied by the differen- 
tial of the function, d(u n ) = nu n ~ l du. 

Formulas for differentiating algebraic functions. 

ft w ( x \ — Vdx-xdy 



1. d (a) = 0. 

2. d {ax) = a dx. 

3. d (x + y) = dx + dy. 

4. d {x — y) = dx — dy. 

5. d (xy) = xdy + y dx. 



\yf y 

7. d (x m ) = mx m ~ 

8. d (Vx) = -$* 

2 v x 



(.1. 



dx. 



To find the differential of the form u = (a + bx n ) m : 
Multiply the exponent of the parenthesis into the exponent of the vari- 
able within the parenthesis, into the coefficient of the variable, into the 



76 DIFFERENTIAL CALCULUS. 



binomial raised to a power less 1, intr- the variable within the parenthesis 
raised to a power less 1, into the differential of the variable. 

du = d(a + bx n ) m = mnb(a + bx n ) m ~ 1 x n ~ 1 dx. 

To find the rate of change for a given value of the variable: 
Find the differential coefficient, and substitute the value of the variable 
in the second member of the equation. 

Example. — If x is the side of a cube and u its volume, u = x 3 , -r- = 3x 2 . 

dx 
Hence the rate of change in the volume is three times the square of the 
edge. If the edge is denoted by 1, the rate of change is 3. 

Application. The coefficient of expansion by heat of the volume of a 
body is three times the linear coefficient of expansion. Thus if the side 
of a cube expands 0.001 inch, its volume expands 0.003 cubic inch. 1.001 3 
= 1.003003001. 

A partial differential coefficient is the differential coefficient of r 
function of two or more variables under the supposition that only ont 
of them has changed its value. 

A partial differential is the differential of a function of two or more 
variables under the supposition that only one of them has changed its 
value. 

The total differential of a function of any number of variables is equal 
to the sum of the partial differentials. 

If u = / (xy), the partial differentials are — dx, -rdy. 

, dy + -j- dz; = 2x dx + 3y 2 dy — dz. 
dx dy dz ' 

Integrals. — An integral is a functional "expression derived from a 
differential. Integration is the operation of finding the primitive func- 
tion from the differential function. It is indicated by the sign /, which is 

read "the integral of." Thus fix dx = x 2 ; read, the integral of 2x dx 
equals x 2 . 

To integrate an expression of the form mx m ~ 1 dx or x m dx, add 1 to the 
exponent of the variable, and divide by the new exponent and by the 

differential of the variable: J3x 2 dx = X s . (Applicable in all cases except 
when m = — 1. For fx dx see formula 2, page 81.) 

The integral of the product of a constant by the differential of a vari- . 
able is equal to the constant multiplied by the integral of the differential: 



The integral of the algebraic sum of any number of differentials is 
equal to the algebraic sum of their integrals: 



= 2ax 2 dx - bydy- z 2 dz; ( du= ~ 



Since the differential of a constant is 0, a constant connected with a 
variable by the sign + or — disappears in the differentiation; thus 
d{a -{■ x m ) = dx m = mx m ~ l dx. Hence in integrating a differential 
expression we must annex to the integral obtained a constant represented 
by C to compensate for the term which may have been lost in differen- 
tiation. Thus if we have dy = a dx ;/dy = aj~dx. Integrating, 

y = ax ± C. 



DIFFERENTIAL CALCULUS. 77 

The constant C, which is added to the first integral, must have such a 
value as to render the functional equation true for every possible value 
that may be attributed to the variable. Hence, after having found the 
first integral equation and added the constant C, if we then make 
the variable equal to zero, the value which the function assumes will be 
the true value of C. 

An indefinite integral is the first integral obtained before the value of 
the constant C is determined. 

A particular integral is the integral after the value of C has been found. 

A definite integral is the integral corresponding to a given value of the 
variable. 

Integration between limits. — Having found the indefinite integral 
and the particular integral, the next step is to find the definite integral, 
and then the definite integral between given limits of the variable. 

The integral of a function, taken between two limits, indicated by given 
values of x, is equal to the difference of the definite integrals correspond- 
ing to those limits. The expression 



I dy = a I d 



is read: Integral of the differential of y, taken between the limits x' and 
x": the least limit, or the limit corresponding to the subtractive integral, 
being placed below. 

Integrate du = 9x 2 dx between the limits x = 1 and x = 3, u being equal 

to 81 when x = 0. /du = /9.r 2 dx = 3.r 3 + C; C = 81 when x = 0, then 
du = 3(3)3 + 81, minus 3(1)3+ 81 = 78> 



Jx= 



Integration of particular forms. 

To integrate a differential of the form du = (a + bx n ) m x n - 1 dx. 

1. If there is a constant factor, place it without the sign of the integral, 
and omit the power of the variable without the parenthesis and the differ- 
ential ; 

2. Augment the exponent of the parenthesis by 1, and then divide 
this quantity, with the exponent so increased, by the exponent of the 
parenthesis, into the exponent of the variable within the parenthesis, 
into the coefficient of the variable. Whence 



/« 



(ra+ l)nb 

__ hypothen 
which the base is dx and the perpendicular dy. 



The differential of an arc is the hypothenuse of a right-angle triangle of 

is dx '- ' 



If z is an arc, dz = Vdx 2 + dy* z ^f^dx^ + dy 2 . 



Quadrature of a plane figure. 

The differential of the area of a plane surface is equal to the ordinate into 
the differential of the abscissa. 

ds = y dx. 

To apply the principle enunciated in the last equation, in finding the area 
of any particular plane surface: •■ 

Find the value of y in terms of x, from the equation of the bounding line; 
substitute this value in the differential equation, and then integrate 
between the required limits of x , 

Area of the parabola. — Find the area of any portion ot the com- 
mon parabola wnose equation is 

y 2 = %px; whence?/ = A ^ / 2px. 



78 DIFFERENTIAL CALCULUS. 

Substituting this value of y in the differential equation ds = y dx givea 

fds = fV^pdx = ^Tv §x h dx = ^^x B/2 + C; 
Xx = |xy + C. 

If we estimate the area from the principal vertex, x = 0, y = 0, and 
C = 0; and denoting the particular integral by s', s' = k^2/- 

That is, the area of any portion of the parabola, estimated from the 
vertex, is equal to 2/ 3 of the rectangle of the abscissa and ordinate of the 
extreme point. The curve is therefore quadrable. 

Quadrature of surfaces of revolution. — The differential of a surface 
of revolution is equal to the circumference of a circle perpendicular to the 
axis into the differential of the arc of the meridian curve. 




ds = 2ny\ / dx°~ + dy 2 ; 

in which y is the radius of a circle of the bounding surface in a plane per- 
pendicular to the axis of revolution, and r is the abscissa, or distance of 
the plane from the origin of coordinate axes. 

Therefore, to find the volume of any surface of revolution: 

Find the value of y and dy from the equation of the meridian curve in 
terms of x and dx, then substitute these values in the differential equation, 
and integrate between the proper limits of x. 

By application of this rule we may find: 

The curved surface of a cylinder equals the product of the circum- 
ference of the base into the altitude. 

The convex surface of a cone equals the product of the circumference of 
the base into half the slant height. 

The surface of a sphere is equal to the area of four great circles, or equal 
to the curved surface of the circumscribing cylinder. 

Cubature of volumes of revolution. — A volume of revolution is a 
volume generated by the revolution of a plane figure about a fixed line 
called the axis. 

If we denote the volume by V, dV = ny 2 dx. 

The area of a circle described by any ordinate y is Try 2 ; hence the differ- 
ential of a volume of revolution is equal to the area of a circle perpendicular 
to the axis into the differential of the axis. 

The differential of a volume generated by the revolution of a plane 
figure about the axis of Y is nx 2 dy. 

To find the value of V for any given volume of revolution : 

Find the value of y 2 in terms of x from the equation of the meridian 
curve, substitute this value in the differential equation, and then integrate 
between the required limits of x. 

By application of this rule we may find: 

The volume of a cylinder is equal to the area of the base multiplied 
by the altitude. 

The volume of a cone is equal to the area of the base into one third the 
altitude. 

The volume of a prolate spheroid and of an oblate spheroid (formed by 
the revolution of an ellipse around its transverse and its conjugate axis 
respectively) are each equal to two thirds of the circumscribing cylinder. 

If the axes are equal, the spheroid becomes a sphere and its volume = 
2 1 

- nR 2 X D = - tiD 3 ; R being radius and D diameter. 
o o 

The volume of a paraboloid is equal to half the cylinder having the same 
base and altitude. 

The volume of a pyramid equals the area of the base multiplied by one ■ 
third the altitude. 

Second, third, etc., differentials. — ■ The differential coefficient being 
a function of the independent variable, it may be differentiated, and we 
thus obtain the second differential coefficient: 



m 



DIFFEKENTIAL CALCULUS 79 

■ -p- Dividing by dx, we have for the second differential 

coefficient -r-g, which is read : second differential of u divided by the square 

of the differential of x (or dx squared). 
d 3 u 
The third differential coefficient -r-^ is read: third differential of u 

divided by dx cubed. 

The differentials of the different orders are obtained by multiplying 
the differential coefficient by the corresponding powers of dx; thus 

^ dx 3 = third differential of u. 
dx 3 

Sign of the first differential coefficient. — If we have a curve 
whose equation is y = fx, referred to rectangular coordinates, the curve 

will recede from the axis of X when — is positive, and approach the 

axis when it is negative, when the curve lies within the first angle of the 
coordinate axes. For all angles and every relation of y and x the curve 
will recede from the axis of X when the ordinate and first differential 
coefficient have the same sign, and approach it when they have different 
signs. If the tangent of the curve becomes parallel to the axis of X at any 

point ~- = 0. If the tangent becomes perpendicular to the axis of X at 

• j. dy 
any point -r- = <*>• 

Sign of the second differential coefficient. — The second differential 
coefficient has the same sign as the ordinate when the curve is convex 
toward the axis of abscissa and a contrary sign when it is concave. 

Maclaurin's Theorem. — For developing into a series any function 
of a single variable as u = A + Bx + Cx 2 + Dx s + Ex i , etc., in which 
A, B, C, etc., are independent of x: 

. . , (du\ , 1 (d\i\ . , 1 (d 3 u\ , , . 

U = (U) +[-r-) X +— tt X 2 + - — - -rl-r-rj X s + etc. 

In applying the formula, omit the expressions x «= 0, although the 
coefficients are always found under this hypothesis. 
Examples: 

(a + x) m = a m + ma m 

+ rn(n^(m-2 lam - ix3+e ^ 

1 = 1 _ X_ X? _ Xf X H 

a + x a a 2 a 3 a 4 ' a n + 1 

Taylor's Theorem. — For developing into a series any function of the 
sum or difference of two independent variables, as u' = f(x ± y): 



dx 2 1.2 dx 3 1 . 2 . 3 

du . , 
, — is whau -y- y 
dx dx 



in which u is what u' becomes when y = 0, — is what — ■ becomes when 



y = 0, etc. 

Maxima and minima. — To find the maximum or minimum value 
of a function of a single variable: 

1. Find the first differential coefficient of the function, place it equal 
to 0, and determine the roots of the equation. 

2. Find the second differential coefficient, and substitute each real root, 



80 DIFFERENTIAL CALCULUS. 

in succession, for the variable in the second member of the equation. 
Each root which gives a negative result will correspond to a maximum 
value of the function, and each which gives a positive result will corre- 
spond to a minimum value. 

Example. — To find the value of x which will render the function y a 
maximum or minimum in the equation of the circle, y 2 + x 2 = R 2 ; 

dv x , . x . . . 

~ == — -; making — - = gives x = 0. 



When x = 0, y = R; hence -~ = - •£> which being negative, y is a 

maximum for R positive. 

In applying the rule to practical examples we first find an expression for 
the function which is to be made a maximum or minimum. 

2. If in such expression a constant quantity is found as a factor, it may 
be omitted in the operation; for the product will be a maximum or a mini- 
mum when the variable factor is a maximum or a minimum. 

3. Any value of the independent variable which renders a function a 
maximum or a minimum will render any power or root of that function a 
maximum or minimum; hence we may square both members of an equa- 
tion to free it of radicals before differentiating. 

By these rules we may find : 

The maximum rectangle which can be inscribed in a triangle is one 
whose altitude is half the altitude of the triangle. 

The altitude of the maximum cylinder which can be inscribed in a cone 
is one third the altitude of the cone. 

The surface of a cylindrical vessel of a given volume, open at the top, 
is a minimum when the altitude equals half the diameter. 

The altitude of a cylinder inscribed in a sphere when its convex surface is 
a maximum is r *^2. r = radius. 

The altitude of a cylinder inscribed in a sphere when the volume is a 
maximum is 2r -s- V3. 

Maxima and Minima without the Calculus. — In the equation 
y = a + bx + ex 2 , in which a, b, and c are constants, either positive or 
negative, if c be positive y is a minimum when x = — b -*- 2c; if c be 
negative y is a maximum when x = — b + 2c. In the equation y = a + 
bx + c/x, y is a minimum when bx = c/x. 

Application. — The cost of electrical transmission is made up (1) of 
fixed charges, such as superintendence, repairs, cost of poles, etc., which 
may be represented by a; (2) of interest on cost of the wire, which varies 
with the sectional area, and may be represented by bx; and (3) of cost of 
the energy wasted in transmission, which varies inversely with the area 
of the wire, or c/x. The total cost, y = a + bx + c/x, is a minimum 
when item 2 = item 3, or bx = c/x. 

Differential of an exponential function. 

If u = a x (1) 

then du = da x = a x k dx (2) 

in which A; is a constant dependent on a. 

1 

The relation between a and k is a k = e; whence a = e k .... (3) 
in which e = 2.7182818 . . . the base of the Naperian system of loga- 
rithms. 

Logarithms. — The logarithms in the Naperian system are denoted by 
i, Nap. log or hyperbolic log, hyp. log, or log e ; and in the common system 
always by log. 

k = Nap. log a, log a = k log a (4) 



DIFFERENTIAL CALCULUS. 81 

The common logarithm of e, = log 2.7182818 . . . = 0.4342945 . . . , 
is called the modulus of the common system, and is denoted by M. 
Hence, if we have the Naperian logarithm of a number we can find the 
common logarithm of the same number by multiplying by the modulus. 
Reciprocally, Nap. log = com. log X 2.3025851. 

If in equation (4) we make a = 10, we have 

1 = k log e, or t = log e = M. 

That is, the modulus of the common system is equal to 1, divided by the 
Naperian logarithm of the common base. 
From equation (2) we have 

du da x 

— = — — = k dx. 

u a x 

If we make a = 10, the base of the common system, x = log u, and 

d (log u) = dx = — X ^ = — X M. 

That is, the differential of a common logarithm of a quantity is equal to 
the differential of the quantity divided by the quantity, into the modulus,. 
If we make a = e, the base of the Naperian system, x becomes the Nape- 
rian logarithm of u, and k becomes 1 (see equation (3)); hence M = 1, 
and 

, ,,, , . , du du 

d (Nap. log u) = dx = — - ; = 

a x u 

That is, the differential of a Naperian logarithm of a quantity is equal to 
the differential of the quantity divided by the quantity; and in the 
Naperian system the modulus is 1. 

Since k is the Naperian logarithm of a, du — a x I a dx. That is, the 
differential of a function of the form a x is equal to the function, into the 
Naperian logarithm of the base a, into the differential of the exponent. 

If we have a differential in a fractional form, in which the numerator is 
the differential of the denominator, the integral is the Naperian logarithm 
of the denominator. Integrals of fractional differentials of other forms 
are given below: 

Differential forms which have known integrals; exponential 
functions. (I = Nap. log.) 

1. J a x ladx = a x +C; 

2. C$2 = C 'dxx" 1 = lx + C; 

3. C (xy x ~ 1 dy + y x ly X dx) = y x +C; 

4. f . dX = Kx+^x* ± a2)4-C; 
J v x 2 ± a 2 

5. f . dX =l(x ± a+ V X 2 ± 2ax) + C; 
J VxJ ± 2ax 

J a 2 - x 2 \a - xf 



82 



DIFFERENTIAL CALCULUS. 



J x 2 — a- \x + a) 

r -ma* _ IV^- a \^ 

J x^a 2 + x 2 \v a 2 + a; 2 +a/ 

/ 2adx f a - Va 2 - xA 

x V«2 - x' 2 \ a + V a 2 - x 2 ) 

J x~ 2 dx ( 1 + Vl + a 2 x 2 \ 

x+ x - \ I 



Circular functions. — Let z denote an arc in the first quadrant, y its 
sine, x its cosine, v its versed sine, and t its tangent ; and the following nota- 
tion be employed to designate an arc by any one of its functions, viz., 

sin -1 y denotes an arc of which y is the sine, 
cos - 1 x " " " " " x is the cosine, 
tan~~M " " " " " t is the tangent, 

(read "arc whose sine is y, ,J etc.), — we have the following differential 
forms which have known integrals (r = radius): 



cos zdz = sin z + C; 
sin zdz = cos z+ C; 



/- . 

f-7 dy — = sin -i y + C; 

J VI - 2/2 

r - dx 

S 



= cos -1 x+ C; 



^2v - 
dt 



/if 

J V r 2 



/ — r dx 
\/ r 2 _ #2 



= = versin — 1 v + C ; 
v 2 

= tan -1 £ + C; 
— = sin -1 y + C; 
= cos -1 x + C\ 



J sin z dz = versin z+ C; 

C-^r =tanz+C; 
J cos 2 z 

/r dv . , , 

. = versin -1 v + C 

V2rv + v 2 

f-^5 = tan -1 *+<7; 
J r 2 + * 2 

/tfu . . u , _ 

. = sin -1 - + C; 

Va 2 -u 2 a 

. = cos- 1 - + C; 

Va 2 - z*2 a 

«/ V2 aw — u 2 

/ a du 
a 2 + x 



versin — 1 — -I 



-w 2 



The cycloid. — If a circle be rolled along a straight line, any point of 
the circumference, as P, will describe a curve which is called a cycloid. 
The circle is called the generating circle, and P the generating point. 



THE SLIDE RULE. 



83 



The transcendental equation of the cycloid is 



V2ry 



and the differential equation is dx -- 



V dx 



V2ry - 



The area of the cycloid is equal to three times the 
area of the generating circle. 

The surface described by the arc of a cycloid when 
revolved about its base is. equal to 64 thirds of the 
generating circle. 

The volume of the solid generated by revolving 
a cycloid about its base is equal to five eighths of the 
circumscribing cylinder. 

Integral calculus. — In the integral calculus we 
have to return from the differential to the function 
from which it was derived. A number of differential 
expressions are given above, each of which has a 
known integral corresponding to it. which, being 
differentiated, will produce the given differential. 

In all classes of functions any differential expression 
may be integrated when it is reduced to one of the 
known forms; and the operations of the integral cal- 
culus consist mainly in making such transformations 
of given differential expressions as shall reduce them 
to equivalent ones whose integrals are known. 

For methods of making these transformations 
reference must be made to the text-books on differen- 
tial and integral calculus. 



THE SLIDE RULE. 



The slide rule is based on the principles that the 
addition of logarithms multiplies the numbers which 
they represent, and subtracting logarithms divides 
thenumbers. By its use the operations of multiplica- 
tion, division, the finding of powers and the extraction 
of roots, may be performed rapidly and with an ap- 
proximation to accuracy which is sufficient for many 
purposes. With a good 10-inch Mannheim rule the 
results obtained are usually accurate to 1/4 of 1 per 
cent. Much greater accuracy is obtained with cylin- 
drical rules like the Thacher. 

The rule (see Fig. 73) consists of a fixed and a 
sliding part both of which are ruled with logarithmic 
scales: that is, with consecutive divisions spaced not 
equally, as in an ordinary scale, but in proportion 
to the' logarithms of a series of numbers from 1 to 
10. By moving the slide to the right or left the loga- 
rithms 'are added or subtracted, and multiplication 
or division of the numbers thereby effected. The 
scales on the fixed part of the rule are known as the 
A and D scales, and those on the slide as the B and 
C scales. A and B are the upper and C and D 
are the lower scales. The A and B scales are each 
divided into two, left hand and right hand, each 
being a reproduction, one half the size, of the C and 
D scales. A "runner," consisting of a transparent 
strip of celluloid with a vertical line on it, is used 
to facilitate some of the operations. The numbering 
on each scale begins with the figure 1, which is called 



i: **— 


U^~il 












:\ _jLa :§§ 








14-31 




1 Jit 




; M* ^ 








I *W || 




r | Jjf^ "^ 








: ' T=f- «H^- 




[\ M || 








; § i[ 








- \ 3" *j=^ 




:jl|[ % 




j 3 t§L 1 r 




■ iB 






I- I 


~ c " > ii- 




H 


Z* j [ 




3 


H"]p 


* 


r ,< -% 


F \ f 


1 








\ ' -1 


=- jr 


1 


-" =-: 


r \r~ 


s 


:: \ 


^"jr 


1 


l\ "^F" "H '- 


I 


'- N — jfl^e 1 L 


i 


■A ^|p"H^ 




■A -Mf^it 




:| A ^F 




%%i 




itME 




fit 




? 1~Th- 




i ifW\ 




ijjU it 





84 THE SLIDE RULE. 

the "index" of the scale. In using the scale the figures 1, 2, 3, etc., are 
to be taken either as representing these numbers, or as 10, 20, 30, etc., 
100, 200, 300, etc., 0.1, 0.2, 0.3, etc., that is, the numbers multiplied or 
divided by 10, 100, etc., as may be most convenient for the solution of a 
given problem. 

The following examples will give an idea of the method of using the 
slide rule. 

Proportion. — Set the first term of a proportion on the C scale opposite 
the second term on the D scale, then opposite the third term on the C 
scale read the fourth term on the D scale. 

Example. — Find the fourth term in the proportion 12 : 21 :: 30 : x. \ 
Move the slide to the right until 12 on C coincides with 21 on D, then 
opposite 30 on C read x on D = 52.5. The A and B scales may be used 
instead of C and D. 

Multiplication. — Set the index or figure 1 of the C scale to one of the 
factors on Z>„ 

Example. — 25 X 3. Move the slide to the right until the left index 
of C coincides with 25 on the D scale. Under 3 on the C scale will be 
found the product on the D scale, = 75. 

Division. — Place the divisor on C opposite the dividend on D, and the 
quotient will be found on D under the index of C. 

Example. — 750 -*■ 25. Move the slide to the left until 25 on C coin- 
cides with 750 on D. Under the left index of C is found the quotient on 
D, = 30. 

Combined Multiplication and Division. — Arrange the factors to be 
multiplied and divided in the form of a fraction with one more factor in 
the numerator than in the denominator, supplying the factor 1 if necessary. 
Then perform alternate division and multiplication, using the runner to 
indicate the several partial results. 

Example, = 8.9 nearly. Set 3 on C over 4 on D, set 

runner to 5 on C, then set 6 on C under the runner, and read under 8 on 
C the result 8.9 - on D. 

Involution and Evolution. — The numbers on scales A and B are the 
squares of their coinciding numbers on the scales C and D, and also the 
numbers on scales C and D are the square roots of their coinciding num- 
bers on scales A and B. 

Example. — 4 2 = 16. Set the runner over 4 on scale D and read 16 
on A^ 

V46 = 4. Set the runner over 16 on A and read 4 on D. 

In extracting square roots, if the number of digits is odd, take the num- 
ber on the left-hand scale of A ; if the number of digits is even, take the 
number on the right-hand scale of A. 

To cube a number, perform the operations of squaring and multiplica- 
tion. 

Example. — 2 3 = 8. Set the index of C over 2 on D, and above 2 
on B read the result 8on4„ 

Extraction of the Cube Root. — Set the runner over the number on A, 
then move the slide until there is found under the runner on B, the same- 
number which is found under the index of C on D; this number is the 
cube root desired. 

Example, — ^8 = 2. Set the runner over 8 on A, move the slide 
along until the same number appears under the runner on B and under 
the index of C on D; this will be the number 2. 

Trigonometrical Computations. — On the under side of the slide (which 
is reversible) are placed three scales, a scale of natural sines marked S, 
a scale of natural tangents marked T, and between these a scale of equal 
parts. To use these scales, reverse the slide, bringing its under side to 
the top. Coinciding with an angle on S its sine will be found on A, and 
coinciding with an angle on T will be found the tangent on D. Sines and 
tangents can be multiplied or divided like numbers. 



LOGARITHMIC RULED PAPER. 85 

LOGARITHMIC RULED PAPER. 

W. F. Durand {Eng. News, Sept. 28, 1893.) 

As plotted on ordinal cross-section paper the lines which express 
relations between two variables are usually curved, and must be plotted 
point by point from a table previously computed. It is only where the 
exponents involved in the relationship are unity that the line becomes 
straight and may be drawn immediately on the determination of two of 
its points. It is the peculiar property of logarithmic section paper that 
for ali relationships which involve multiplication, divisioH, raising to 
powers, or extraction of roots, the lines representing them are straight. 
Any such relationship may be represented by an equation of the form: 
y = Bx n . Taking logarithms we have: log y = log B + n log x. 

Logarithmic section paper is a short and ready means of plotting such 
logarithmic equations. The scales on each side are logarithmic instead 
of uniform, as in ordinary cross-section paper. The numbers and divi- 
sions marked are placed at such points that their distances from the origin 
are proportional to the logarithms of such numbers instead of to the 
numbers themselves. If we take any point, as 3, for example, on such a 
scale, the real distance we are dealing with is log 3 to some particular 
base, and not 3 itself. The number at the origin of such a scale is always 
1 and not 0, because 1 is the number whose logarithm is 0. This 1 may, 
however, represent a unit of any order, so that quantities of any size 
whatever may be dealt with. 

If we have a series of values of x and of Bx , and plot on logarithmic 
section paper x horizontally and Bx 11 vertically, the actual distances 
involved will be log x and log (Bx n ), or log B + n log x. But these dis- 
tances will give a straight line as the locus. Hence all relationships 
expressible in this form are represented on logarithmic section paper by 
straight lines. It follows that the entire locus may be determined from 
any two points; that is, from any two values of Bx n ; or, again, by any one 
point and the angle of inclination; that is, by one value of Bx n and the 
value of n, remembering that n is the tangent of the angle of inclination 
to the horizontal. 

A single square plotted on each edge with a logarithmic scale from 1 
to 10 may be made to serve for any number whatever from to oo. Thus 
to express graphically the locus of the equation: y — a* 3 /2. Let Fig. 74 
denote a square cross-sectioned with logarithmic scales, as described. 
Suppose that there were joined to it and to each other on the right and 
above, an indefinite series of such squares similarly divided. Then, con- 
sidering, in passing from one square to an adjacent one to the right or 
above, that the unit becomes of next higher order, such a series of squares 
would, with the proper variation of the unit, represent all values of either 
x or y between and oo. 

Suppose the original square divided on the horizontal edge into 3 parts, 
and on the vertical edge into 2 parts, the points of division being at A, 
B, D, F, G, I. Then lines joining these points, as shown, will be at an 
inclination to the horizontal whose tangent is 3/ 2 . Now, beginning at O, 
OF will give the value of x ,3 /2 for values of x from 1 to that denoted by HF, 
or OB, or about 4.6. For greater values of x the line would run into the 
adjacent square above, but the location of this line, if continued, would 
be exactly similar to that of BD in the square before us. Therefore the 
line BD will give values of x 3 ^ for x between B and C, or 4.6 and 10, the 
corresponding values of y being of the order of tens, and ranging from 10 
to 31.3. For larger values of x the unit of x is of the higher order, and 
we run into an adjacent square to the right without change of unit for y. 
In this square we should traverse a line similar to IG. Therefore, by a 
proper choice of units we may make use of IG for the determination of 
values of x 3 /2 where x lies between 10 and the value at (7, or about 21.5. 
We should then run into an adjacent square above, requiring the unit on 
y to be of the next higher order, and traverse a line similar to AE, which 



8 

t£ 

ir 
o 

fr 

a 
gi 

m 

H 


6 LO 

ikes us finally to the 
g this, the same ser 
-ders. 

The value of ar/2 f 
om one or another 
and 1. The locatic 
tention to the nun 
ven line may be mar 
ade. Thus, in Fig. 

Q 


GARITH1V 

opposite ( 
ies of lines 

>r any valu 
of these lii 
n of the d 
bers invol 
ked on it, t 
2 we marl 

2 G 


IIC RULE 

orner and < 
would resi 

e of x betw 
ies, and lik 
ecimal poin 
ved. The 
hus enablin 
c OF as - 

3 Q 


D PA] 

jomple 
lit for 

een 1 a 
ewise f 
t is re 
limitin 
g a pro 
- 4.6, j 

I F 


J EJ 
es 

1UI 

nd 
or 
idi 
? ^ 

3D 


R. 

th 
nb 

CO 

an 

y 

B 

ch 

as 


3 eye 

srs o 

may 
y va 
:ounr 
ies o 
oice 
4.6 

> 


le. 
E si 

thii 

ue 
1 b 
f i 
o t 


P 

cc 

s b 
be 

fc 
e r 
L0, 

8 


ollow- 
seding. 

e read 

tween 
little 
r any 
eadily 
IG as 

9 1( 




-/ ■""' ■ .1 :- 




. r • "/i ■ 
















8 t 
P_ 

V ; 


























/l.j "; o 


(i - 


'-■ / 


















!) - 




/ 






^fSP 








:■: 


— 








¥ 


4 - 








E= 


-f~A 










/.:': 






/ 




" : :'". 1 








l.____ 




|||e||e 


rrfefet 


— 




— 




^: 


/ 








1 ' 






~^~ i i < i h 


1j 


t-~~z 


tfffl 










/ 








. i.J C 








; M M / 


7 






























! 1 / 
























^A 






















I 
















/■■'■' 




! 


1 
















L. 






1 
















: H 






i 






.... 


V 
















j/| 






/ 






















/ 


























Iff 














/ 
































| 


















T 


' / 








/ 


A 




A 






_ ■ -t 


/ Mi 




= ====== 




-.j 7 : 






/ 




::..|: 




1 i | 






-^J 


/--44frTTf- 






^ — W 1 ' 






















"A"/ 


— H 




/ 




.7. ..... 




-/■ 










- 






/ / 


' 




/ 








/ 










.....j . 






/ / 






/ 






/ 








1 










/ / 






/ 


/ 




















' / 


/ . 






/ 


K 


. ... 
















/ 








/ 


w 




















it 






-J- '■ 


Twit 
















1 / 










/ 


I/Ill 


..... y 








1 




!.r.t; .|l 




1( 

d( 

VI 



ot 

se 
th 
al 
w 


— 
alt 

llH 

F i 
Tl 
her 
t 

e o 

tl 
11 1 


21.5, 

with 
is bet 
or va 
e prir 
, and 
f lines 
ther i 
ere w 
>e n li 


and AE as 
^.E will s 
ween 0.215 
ues betweei 
iciples invo 
in general if 

may be dr 
lto n parts, 
ill be (m -+- 
nes correspc 


•l 

2 
;r 

in 
l C 

V€ 
tl 

IW 

an 
n 

n< 


ft 

1.5 - 1C 
fe for vj 
d 0.1, 5 
.046 anc 
d in thi 
le expon 
n by dh 
d joining 
- 1) lin< 
ing to t 


3 ■ P 1 

Fig. 74. 

0. If valu 
dues of x I 
D for values 
I 0.001. 
3 case may 
ent be repfe 
iding one s 
I the points 
is, and oppc 
le n differei 


es c 

<"{ V 

be 

be 

sen 
de 
of c 

>sitt 
it t 


B 

f x 
r eer 
twe 

rea 
ted 
>f t 
ivi 
to 
egi 


le£ 

l 
en 

dil 

by 
he 
^io 
an 
mi 


S 1 

ar 

0.1 

y t 

m 

sq 
i a 

v I 
>gf 


ha 

(1 
a 

xt 
/re 

la 
s i 
oi 




n 
0. 

id 

en 
tl 
re 
l I 
nt 
f t 


1 a 
215 
0. 

dec 
le c 
int. 
lg. 
on 
he 


3 

re 
, / 

346 

t( 

on 
o r 

74 

X 


9 10 
C 

to be 
3 for 
, and 

) any 
plete 
i and 
. In 
there 
root 



INTERPOLATION. 87 

of the mth power, while opposite to any point on Y will be m lines corre- 
sponding to the different beginnings of the mth root of the nth power. 

> Where the complete number of lines would be quite large, it is usually- 
unnecessary to draw them all, and the number may be limited to those 

\ necessary to cover the needed range in the values of x. 

If, instead of the equation y = x n , we have a constant term as a mufti- 

Iplier, giving an equation in the more general form y =5x n , or Bx min, 
there will be the same number of lines and at the same inclination, but 
all shifted vertically through a distance equal to log B. If, therefore, 
we start on the axis of Y at the point B, we may draw in the same series 
of lines and in a similar manner. In this way PQ represents the locus 

\ giving the values of the areas of circles in term's of their diameters, being 

; the locus of the equation A = 1/4 *■ d 2 or y = 1/4 "" x 2 . 

If in any case we have x in the denominator such that the equation is 
in the form y =B/x n , this is equal to y = Bx~ n , and the same general 
rules hold. The lines in such case slant downward to the right instead of 
upward. Logarithmic ruled paper, with directions for the use, may be 
obtained from Keuffel & Esser Co., 127 Fulton St., New York. 



MATHEMATICAL TABLES. 

Formula for Interpolation. 

a.-», + (»-l)rf 1+ (B -»<"- 2 U + (n -»(»-«(» -8) A+ . . . 

at = the first term of the series; n, number of the required term; a n , the 
required' term; d u a\, d 3 , first terms of successive orders of differences 
between a t , a%, a 3 , a 4 , successive terms. 

Example. — Required the log of 40.7, logs of 40, 41, 42, 43 being given as 
below. 

Terms a u a 2 ,'az, a 4) : 1.6021 1.6128 1.6232 1.6335 

1st differences: 0.0107 0.0104 0.0103 
2d " - 0.0003 - 0.0001 

3d " + 0.0002 

For log. 40, n = 1 ; log 41 , n = 2 ; f or log 40 rr , n = 1 .7 • n - 1 = 7 • n — 2 
= - 0.3; n - 3 = - 1.3. ' ' 

a n =1.6021+0.7 (0.0107) | (°- 7 H ~0-3)( -0.0003) ( (0.7) (-0.3) (-1.3) (0.0002 ) 
2 6 

= 1.6021 4- 0.00749 + 0.000031 -h 0.000009 = 1.6096. +. 



MATHEMATICAL TABLES. 







RECIPROCALS 


OF NUMBERS. 






No. 


Recipro- 
cal. 


No. 
~~64 


Recipro- 
cal. 


No. 


Recipro- 
cal. 


No. 


Recipro- 
cal. 


No. 


Recipro- 
cal. 


1 


1 .00000000 


01562500 


127 


•00787402 


190 


.00526316 


253 


.00395257 


2 


.50000000 


5 


01538461 


8 


■00781250 


1 


.00523560 


4 


.00393701 


3 


.33333333 


6 


01515151 


9 


00775194 


2 


.00520833 


5 


.00392157 


4 


.25000000 


7 


01492537 


130 


•00769231 


3 


.00518135 


6 


.00390625 


5 


.20000000 


8 


01470588 


1 


00763359 


4 


.00515464 


7 


.00389105 


6 


.16666667 


9 


01 449275 


2 


00757576 


5 


.00512820 


8 


.00387597 


7 


.14285714 


70 


01428571 


3 


•00751880 


6 


.005-10204 


9 


.00386100 


8 


.12500C00 


1 


01408451 


4 


■00746269 


7 


.00507614 


260 


.00384615 


9 


.11111111 


2 


■01388889 


5 


■00740741 


8 


.00505051 


1 


.00383142 


10 


.10000000 


3 


■01369863 


6 


■00735294 


9 


.00502513 


2 


.00381679 


11 


.09090909 


4 


■01351351 


7 


■00729927 


200 


.00500000 


3 


.00380228 


12 


.08333333 


5 


•01333333 


8 


■00724638 


1 


.00497512 


4 


.00378788 


13 


.07692308 


6 


01315789 


9 


•00719424 


2 


.00495049 


- 5 


.00377358 


14 


.07142857 


7 


•01298701 


140 


00714286 


3 


.0049261 1 


6 


.00375940 


15 


.06666667 


8 


•01282051 


1 


■00709220 


4 


.00490196 


7 


.0037,4532 


16 


.06250000 


9 


•01265823 


2 


00704225 


5 


.00487805 


8 


.00373134 


17 


.05882353 


80 


•01250000 


3 


00699301 


6 


.00485437 


9 


.00371747 


18 


.05555556 


1 


•01234568 


4 


.00694444 


7 


.00483092 


270 


.00370370 


19 


.05263158 


2 


■01219512 


5 


■00689655 


8 


.00480769 


1 


.00369004 


20 


.05000000 


3 


■01204819 


6 


■00684931 


9 


.00478469 


2 


.00367647 


1 


.04761905 


4 


•01190476 


7 


■00680272 


210 


.00476190 


3 


.00366300 


2 


.04545455 


5 


•01176471 


6 


■00675676 


li 


.00473934 


4 


.00364963 


3 


.04347826 


6 


•01162791 


9 


■00671141 


12 


.00471698 


5 


.00363636 


4 


.04166667 


7 


•01149425 


150 


.00666667 


13 


.00469484 


6 


.00362319 


5 


.04000000 


8 


•01136364 


1 


.00662252 


14 


.00467290 


7 


.00361011 


6 


.03846154 


9 


01123595 


2 


.00657895 


15 


.00465116 


8 


.00359712 


7 


.03703704 


90 


■01111111 


3 


.00653595 


16 


.00462963 


9 


.00358423 


e 


.03571429 


1 


■01098901 


4 


.00649351 


17 


.00460829 


280 


.00357143 


? 


.03448276 


2 


■01086956 


5 


00645161 


IS 


.00458716 


1 


.00355872 


3C 


.03333333 


3 


•01075269 


6 


.00641026 


19 


.00456621 


2 


.00354610 


1 


.03225806 


4 


■01063830 


7 


.00636943 


220 


.00454545 


3 


.00353357 


2 


.03125000 


5 


•01052632 


8 


.00632911 


1 


.00452489 


4 


.00352113 


3 


.03030303 


6 


•01041667 


9 


.00628931 


2 


.00450450 


5 


.00350877 


4 


.02941176 


7 


•01030928 


160 


.00625000 


3 


.00448430 


6 


.00349650 


5 


.02857143 


8 


•01020408 


1 


.00621118 


4 


.00446429 


7 


.00348432 


£ 


.027/7778 


9 


•01010101 


2 


.00617284 


5 


.00444444 


8 


.00347222 


J 


.02702703 


100 


•01000000 


3 


.00613497 


6 


.00442478 


9 


.00346021 


£ 


.02631579 


1 


•00990099 


4 


.00609756 


7 


.00440529 


290 


.00344828 


c 


.02564103 


2 


00980392 


5 


.00606061 


8 


.00438596 


1 


.00343643 


4C 


.02500000 


3 


■00970874 


6 


.00602410 


9 


.00436681 


2 


.00342466 


1 


.02439024 


4 


■00961538 


7 


.00598802 


230 


.00434783 


3 


.00341297 


2 


.02380952 


5 


■00952381 


8 


.00595238 


1 


.00432900 


4 


.00340136 


3 


.02325581 


6 


■00943396 


9 


00591716 


2 


.00431034 


5 


.00338983 


4 


.02272727 


7 


■00934579 


170 


.00588235 


3 


.00429184 


6 


.00337838 


5 


.02222222 


8 


■00925926 


1 


.00584795 


4 


.00427350 


7 


.00336700 


e 


.02173913 


9 


■00917431 


2 


.00581395 


5 


.00425532 


8 


.00335570 


7 


.02127660 


110 


■00909091 


3 


.00578035 


6 


.00423729 


9 


.00334448 


e 


.02083333 


11 


■00900901 


4 


.00574713 


7 


.00421941 


300 


.00333333 


? 


.02040816 


12 


■00892857 


5 


.00571429 


8 


.00420168 


1 


.00332226 


5C 


.02000000 


13 


.00884956 


6 


.00568182 


9 


.00418410 


2 


.00331126 


1 


.01960784 


14 


.00877193 


7 


.00564972 


240 


.00416667 


3 


.00330033 


2 


.01923077 


15 


.00869565 


8 


.00561798 


1 


.00414938 


4 


00328947 


3 


.01886792 


16 


■00862069 


9 


.00558659 


2 


.00413223 


5 


.00327869 


4 


.01851852 


17 


.00854701 


180 


.00555556 


3 


.00411523 


6 


.00326797 


5 


.01818182 


18 


.00847458 


1 


.00552486 


4 


.00409836 


7 


.00325733 


6 


.01785714 


19 


.00840336 


2 


.00549451 


5 


.00408163 


6 


.00324675 


7 


.01754386 


120 


.00833333 


3 


.00546448 


6 


.00406504 


9 


.00323625 


fi 


.01724138 


1 


.00826446 


4 


.00543478 


7 


.00404858 


310 


.00322531 


9 


.01694915 


2 


.00819672 


5 


.00540540 


8 


.00403226 


1! 


.00321543 


6C 


.01666667 


3 


.00813008 


6 


.00537634 


9 


.00401606 


12 


.00320513 


1 


.01639344 


4 


.00806452 


7 


.00534759 


250 


.00400000 


13 


.00319489 


2 


.01612903 


5 


.00800000 


8 


.00531914 


1 


.00398406 


14 


.00318471 


3 .01587302 


6 


.00793651 


9 .00529100 


2 .00396825 


15 .00317460 



RECIPROCALS OF NUMBERS. 



No. 


Recipro- 
cal. 


No. 


Recipro- 
cal. 


No. 


Recipro- 
cal. 


No. 


Recipro- 
cal. 


No. 


Recipro- 
cal. 


316 


.00316456 


381 


.00262467 


446 


.00224215 


511 


.00195695 


576 


.00173611 


17 


.00315457 


2 


.00261780 


7 


.00223714 


12 


.00195312 


7 


.00173310 


18 


.00314465 


3 


.00261097 


8 


.00223214 


13 


.00194932 


8 


.00173010 


19 


.00313480 


4 


.00260417 


9 


.00222717 


14 


.00194552 


9 


.00172712 


320 


.00312500 


5 


.00259740 


450 


.00222222 


15 


.00194175 


580 


.00172414 


1 


.00311526 


6 


.00259067 


1 


.00221729 


16 


.00193798 


1 


.00172117 


2 


.00310559 


7 


.00258398 


2 


.00221239 


17 


.00193424 


2 


.00171821 


3 


.00309597 


8 


.00257732 


3 


.00220751 


18 


.00193050 


3 


.00171527 


4 


.00303642 


9 


.00257069 


4 


.00220264 


19 


.00192678 


4 


.00171233 


5 


.00307692 


390 


.00256410 


5 


.00219780 


520 


.00192308 


5 


.00170940 


6 


.00306748 


1 


.00255754 


6 


.00219298 


1 


.00191939 


6 


.00170648 


7 


.00305810 


2 


.00255102 


7 


.00218813 


2 


.00191571 


7 


.00170358 


8 


.00304878 


3 


.00254453 


8 


.00218341 


3 


.00191205 


8 


.00170068 


9 


.00303951 


4 


.00253807 


9 


.00217865 


4 


.00190840 


9 


.00169779 


330 


.00303030 


5 


.00253165 


460 


.00217391 


5 


.00190476 


590 


.00169491 


1 


.00302115 


6 


.00252525 


1 


.00216920 


6 


.00190114 


I 


.00169205 


2 


.00301205 


7 


.00251889 


2 


.00216450 


7 


.00189753 


2 


.00168919 


'3 


.00300300 


8 


.00251256 


3 


.00215983 


8 


.00189394 


3 


.00168634 


4 


.00299401 


9 


.00250627 


4 


.00215517 


9 


.00189036 


4 


.00168350 


5 


.00298507 


400 


.00250000 


5 


.00215054 


530 


.00188679 


5 


.00168067 


6 


.00297619 


1 


.00249377 


6 


.00214592 


1 


.00188324 


6 


.00167785 


7 


. .00296736 


2 


.00248756 


7 


.00214133 


2 


.00187970 


7 


.00167504 


8 


.00295858 


3 


.00248139 


8 


.00213675 


3 


.00187617 


8 


.00167224 


9 


.00294985 


A 


.00247525 


9 


.00213220 


4 


.00187266 


9 


.00166945 


340 


.002941 18 


5 


.00246914 


470 


.00212766 


5 


.00186916 


600 


.00166667 


1 


.00293255 


6 


.00246305 


1. 


.00212314 


6 


.00186567 


1 


.00166389 


2 


.00292398 


/ 


.00245700 


2 


.00211864 


7 


.00186220 


2 


.00166113 


3 


.00291545 


8 


.00245098 


3 


.00211416 


8 


.00185874 


3 


.00165837 


4 


.00290698 


9 


.00244499 


4 


.00210970 


9 


.00185528 


4 


.00165563 


5 


.00289855 


410 


.00243902 


5 


.00210526 


540 


.00185185 


5 


.00165289 


6 


' .00289017 


11 


.00243309 


6 


.00210084 


1 


.00184843 


6 


.00165016 


7 


.00288184 


12 


.00242718 


7 


.00209644 


2 


.00184502 


7 


.00164745 


8 


.00287356 


13 


.00242131 


8 


.00209205 


3 


.00184162 


8 


.00164474 


9 


.00236533 


14 


.00241546 


9 


.00208763 


4 


.00183823 


9 


.00164204 


350 


,00285714 


15 


.00240964 


480 


.00208333 


5 


.00183486 


610 


.00163934 


1 


.00284900 


16 


.00240385 


1 


.00207900 


6 


.C018>150 


11 


.00163666 


2 


.00284091 


17 


.00239308 


2 


.00207469 


7 


.00182815 


12 


.00163399 


3 


.00283286 


13 


.00239234 


3 


.00207039 


8 


.00182482 


13 


.00163132 


4 


.00282486 


19 


.00238663 


4 


.00206612 


9 


.00182149 


14 


.00162866 


5 


.00281690 


420 


.00238095 


5 


.00206186 


550 


.00181818 


15 


.00162602 


6 


.00280899 


1 


.00237530 


6 


.00205761 


1 


.00181488 


16 


.00162338 


7 


.00280112 


2 


.00236967 


7 


.00205339 


2 


.00181159 


17 


.00162075 


8 


.00279330 


3 


.00236407 


8 


.00204918 


3 


.00180832 


18 


.00161812 


9 


.00278551 


4 


.00235849 


9 


.00204499 


4 


.00180505 


19 


00161551 


360 


.00277778 


5 


.00235294 


490 


.00204082 


5 


.00180180 


620 


.00161290 


1 


.00277008 


6 


.00234742 


1 .00203666 


6 


.00179856 


1 


.00161031 


2 


.00276243 


7 


.00234192 


2 .00203252 


7 


.00179533 


2 


.00160772 


3 


.00275482 


8 


.00233645 


3 .00202840 


8 


.00179211 


3 


.00160514 


4 


.00274725 


9 


.00233100 


4100202429 


9 


.00178891 


4 


00160256 


5 


.00273973 


430 


.00232553 


5 .00202020 


560 


.00178571 


5 


00160000 


6 


.00273224 


1 


.00232019 


6 .00201613 


1 


.00178253 


6 


00159744 


7 


.00272480 


2 


.00231481 


7 


.00201207 


2 


.00177936 


7 


00159490 


8 


.00271739 


3 


.00230947 


8 


.00200803 


3 


.00177620 


8 


00159236 


9 


.00271003 


4 


.00230415 


Q 


.00200401 


4 


.00177305 


9 


00158982 


370 


.00270270 


5 


.00229835 


500 


.00200000 


5 


.00176991 


6301.00158730 


1 


.00269542 


6 


.00229358 


1 


.00199601 


6 


.00176678 


1 


00158479 


2 


.00268817 


7 


.00223833 


2 


.00199203 


7 


.00176367 


2 


00158228 


3 


.00268096 


8 


.00228310 


3 


.00198807 


8 


.00176056 


3 


00157978 


4 


.00267380 


9 


.00227790 


4 


.00198413 


9 


.00175747 


4 


.00157729 


5 


.00266667 


440 


.00227273 


5 


.00198020 


570 


.00175439 


5 


.00157480 


6 


.00265957 


1 


.00226757 


6 


.00197623 


1 


.00175131 


6 


.00157233 


7 


.00265252 


2 


.00226244 


7 


.00197239 


2 


.00174825 


7 


.00156986 


8 


.00264550 


3 


.00225734 


8 


.00196850 


3 


.00174520 


8 


.00156740 


9 


:00263852 


4 


.00225225 


9 


.00196464 


4 


.00174216 


9 


.00156494 


380 


.00263158 


5 .00224719 


510 .00196078 


5 .00173913 


640 .00156250 



MATHEMATICAL TABLES. 



No. 


Recipro- 
cal. 


No. 


Recipro- 
cal. 


No. 


Recipro- 
cal. 


No. 


Recipro- 
cal. 


No. 


Recipro- 
cal. 


641 


.00156006 


706 


.00141643 


771 


.00129702 


830 


.00119617 


90! 


.00110988 


2 


.00155763 


7 


.00141443 


2 


.00129534 


7 


.00119474 


2 


.00110865 


3 


.00155521 


8 


.00141243 


3 


.00129366 


8 


.001 19332 


3 


.00110742 


4 


.00155279 


9 


.00141044 


A 


.00129199 


9 


.00119189 


A 


.00110619 


5 


.00155039 


710 


.00140845 


5 


.00129032 


840 


.00119048 


5 


.00110497 


6 


.00154799 


11 


.00140647 


6 


.00128866 


1 


.001 18906 


6 


.00110375 


7 


.00154559 


12 


.00140449 


7 


.00128700 


2 


.00118765 


7 


.00110254 


8 


.00154321 


13 


.00140252 


8 


.00128535 


3 


.001 18624 


£ 


.00110132 


9 


.00154083 


14 


.00140056 


9 


.00128370 


4 


.00118483 


9 


.00110011 


650 


.00153846 


15 


.00139860 


78 J 


.00128205 


5 


.001 18343 


9iC 


.00109890 


1 


.00153610 


16 


.00139665 


1 


.00128041 


6 


.00118203 


11 


.00109769 


2 


.00153374 


17 


.00139470 


2 


.00127877 


7 


.00118064 


12 


.00109649 


3 


.00153140 


18 


.00139276 


3 


.00127714 


8 


.00117924 


13 


.00109529 


4 


.00152905 


19 


.00139032 


4 


.00127551 


9 


.00117786 


14 


.00109409 


5 


.00152672 


720 


.00138839 


5 


.0012738S 


850 


.00117647 


15 


.00109290 


6 


.00152439 


1 


.00138696 


6 


.00127226 


1 


.00117509 


16 


.00109170 


7 


.00152207 


2 


.00138504 


7 


.00127065 


2 


.00117371 


17 


.00109051 


8 


.00151975 


3 


.00138313 


3 


.00126904 


3 


.00117233 


18 


.00103932 


9 


.00151745 


4 


.00138121 


9 


.00126743 


4 


.00117096 


19 


00108814 


660 


.00151515 


5 


.00137931 


790 


.00126582 


5 


.00116959 


928 


.00108696 


1 


.00151236 


6 


.00137741 


1 


.00126422 


6 


.00116822 


1 


.00103578 


2 


.00151057 


7 


.00137552 


2 


.00126263 


7 


.00116636 


2 


.00108460 


3 


.00150330 


8 


.00137363 


3 


.00126103 


8 


.00116550 


3 


.00103342 


4 


.00150602 


9 


.00137174 


4 


.00125945 


9 


.00116414 


4 


.00108225 


5 


.00150376 


730 


.00136936 


5 


.00125786 


860 


.00116279 


5 


.00103108 


6 


.00150150 


1 


.00136799 


6 


.00125623 


1 


.00116144 


6 


.00107991 


7 


.00149925 


2 


.00136612 


7 


.00125470 


2 


.00116009 


7 


.00107375 


8 


.00149701 


3 


.00136426 


8 


.00125313 


3 


.00115875 


8 


.00107759 


9 


.00149477 


4 


.00136240 


9 


.00125156 


4 


.00115741 


9 


.00107.643 


670 


.00149254 


5 


.00136054 


008 


.00125000 


5 


.00115607 


930 


.00107527 


1 


.00149031 


6 


.00135870 


1 


.00124844 


6 


.00115473 


1 


.00107411 


2 


,00148809 


7 


.00135635 


2 


.00124688 


7 


.00115340 


2 


.00107296 


3 


.00148588 


8 


.00135501 


3 


.00124533 


8 


.00115207 


3 


.00107181 


4 


.00148368 


9 


.00135318 


4 


.00124373 


9 


.00115075 


A 


.00107066 


5 


.00148148 


740 


.00135135 


5 


.00124224 


870 


.00114942 


5 


.00106952 


6 


.00147929 


1 


.00134953 


6 


.00124069 


1 


.00114811 


6 


.00106338 


7 


.00147710 


2 


.00134771 


7 


.00123916 


2 


.00114679 


7 


.00106724 


8 


.00147493 


3 


.00134589 


8 


.00123762 


3 


.00114547 


8 


.00106610 


9 


.00147275 


A 


.00134409 


9 


00123609 


4 


.00114416 


9 


.00106496 


680 


.00147059 


5 


.00134228 


810 


.00123457 


5 


.00114286 


940 


.00106383 


1 


.00146843 


6 


.00134048 


11 


.00123305 


6 


.00114155 


1 


.00106270 


2 


.00146628 


7 


.00133869 


12 


.00123153 


7 


.00114025 


2 


.00106157 


3 


.00146413 


6 


.00133690 


13 


.00123001 


8 


.00113395 


3 


.00106044 


4 


.00146199 


9 


.00133511 


14 


.00122850 


9 


.00113766 


4 


.00105932 


5 


.00145985 


750 


.00133333 


15 


.00122699 


880 


.00113636 


5 


.00105820 


6 


.00145773 


1 


.00133156 


16 


.00122549 


1 


.00113507 


6 


00105703 


7 


.00145560 


2 


.00132979 


17 


.00122399 


2 


.00113379 


7 


.00105597 


8 


.00145349 


3 


.00132802 


18 


.00122249 


3 


.00113250 


8 


.00105485 


9 


.00145137 


4 


.00132626 


19 


.00122100 


4 


.00113122 


9 


.00105374 


690 


.00144927 


5 


.00132450 


820 


.00121951 


5 


.00112994 


930 


.00105263 


1 


.00144718 


6 


.00132275 


1 


.00121803 


6 


.00112367 


1 


.00105152 


2 


.00144509 


7 


.00132100 


2 


.00121654 


7 


.00112740 


2 


.00105042 


3 


.00144300 


8 


.00131926 


• 3 


.00121507 


8 


.00112613 


3 


.00104932 


4 


.00144092 


9 


.00131752 


4 


.00121359 


9 


.001 12486 


4 


.00104822 


5 


.00143385 


760 


.00131579 


5 


.00121212 


890 


.00112360 


5 


.00104712 


6 


.00143678 


1 


.00131406 


6 


.00121065 


1 


.00112233 


6 


00104602 


7 


.00143472 


2 


.00131234 


7 


.00120919 


2 


00112103 


1 


.00104493 


8 


.00143266 


3 


.00131062 


8 


.00120773 


3 


.00111932 


8 


.00104384 


9 


.00143061 


4 


.00130390 


9 


.00120627 


4 


.00111857 


9 


.00104275 


700 


.00142857 


5 


.00130719 


830 


.00120432 


5 


.00111732 


960 


.00104167 


1 


.00142653 


6 


.00130548 


1 


.00120337 


6 


.00111607 


1 


.00104058 


2 


.00142450 


7 


.00130378 


2 


.00120192 


/ 


.00111433 


2 


.00103950 


3 


.00142247 


8 


.00130209 


3 


00120043 


8 


.00111359 


3 


.00103842 


4 


.00142045 


9 


.00130039 


4 


.00119904 


9 


.00111235 


4 


.00103734 


5 .00141844 


770 .00129370 


5 .00119760 


900 .001 11111 


5 .00103627 



RECIPROCALS OF NUMBERS. 



91 



No. 


Recipro- 
cal. 


No. 


Recipro- 
cal. 


No. 


Recipro- 
cal. 


No. 


Recipro- 
cal. 


No. 


Recipro- 
cal. 


966 


.00103520 


1031 


.000969932 


1096 


.000912409 


1161 


.000861326 


'226 


.000815661 


7 


.00103413 


2 


.000968992 


7 


.000911577 


2 


.000860585 


7 


.000814996 


8 


.00103306 


3 


.000968054 


8 


.000910747 


3 


.000859845 


8 


.000814332 


9 


.00103199 


4 


.000967113 


9 


.000909918 


4 


.000359106 


9 


.000813670 


970 


.00103093 


5 


.000966184 


1100 


.000909091 


5 


.000858369 


1233 


.000813008 


1 


.00102937 


6 


.000965251 


1 


.000903265 


6 


.000857633 


1 


.000812348 


2 


.00102881 


7 


.000964320 


2 


.000907441 


7 


.000856898 


2 


.000811638 


3 


.00102775 


8 


.000963391 


3 


.000906618 


8 


.000856164 


3 


.000811030 


4 


.00102669 


9 


.000962464 


4 


.000905797 


9 


.000855432 


4 


.000810373 


5 


.00102564 


1040 


.000961538 


5 


.000904977 


1170 


.000354701 


5 


.000809717 


6 


.00102459 


1 


.000960615 


6 


.000904159 


1 


.00085397! 


6 


.000309061 


7 


.00102354. 


2 


.000959693 


7 


.000903342 


2 


.000853242 


7 


.000808407 


8 


.00102250 


3 


.000958774 


8 


.000902527 


3 


.000852515 


8 


.000807754 


9 


.00102145 


4 


.000957854 


9 


.000901713 


4 


.000851789 


9 


.000807102 


980 


.00102041 


5 


.000956938 


1110 


.000900901 


5 


.000851064 


1240 


.000806452 


1 


.00101937 


6 


.000956023 


11 


.000900090 


6 


.0C035034C 


1 


.000305302 


2 


.00101833 


■ 7 


.000955110 


12 


.000899231 


7 


.000849618 


2 


.000805153 


3 


.00101729 


8 


.000954198 


13 


.000898473 


8 


.000848396 


3 


.000804505 


4 


.00101626 


9 


.000953289 


14 


.000897666 


9 


.000848 176 


4 


.000303858 


5 


.00101523 


1050 


.000952331 


15 


.000396861 


1130 


.000347457 


5 


.000303213 


6 


.00101420 


1 


.000951475 


16 


.000896057 


1 


.O0OS4674C 


6 


.000802568 


7 


.00101317 


2 


.000950570 


17 


.000395255 


2 


.000346024 


7 


.000801925 


8 


.00101215 


3 


.000949668 


18 


.000894454 


3 


.000345308 


8 


.000801282 


9 


.00101112 


4 


.000948767 


19 


.000393655 


4 


.000344595 


9 


.000800640 


990 


.00101010 


5 


.000947867 


M23 


.000392857 


5 


.0333^333: 


!250 


.000800000 


1 


.00100908 


6 


.000946970 


1 


.000392061 


6 


.000343 17C 


1 


.000799360 


2 


.00100806 


7 


.000946074 


2 


.000891266 


7 


.03034246C 


2 


.000793722 


3 


.00100705 


8 


.000945180 


3 


.000890472 


8 


.00034175! 


3 


.000798085 


4 


.00100604 


9 


.000944287 


4 


.000389680 


9 


.000341043 


4 


.000797448 


5 


.00100502 


1060 


.000943396 


5 


.000SS3389 


1190 


.000340336 


5 


.000796813 


6 


.00100402 


1 


.000942507 


6 


.000888099 


1 


.000339631 


6 


.000796178 


7 


.00100301 


2 


.000941620 


7 


.000887311 


2 


.000333926 


7 


.000795545 


8 


.00100200 


3 


.000940734 


■ 8 


.000886525 


3 


.000338222 


8 


.000794913 


9 


.00100100 


4 


.000939350 


9 


.000885740 


4 


.000837521 


9 


.000794281 


1000 


.00100000 


5 


.000938967 


1130 


.000884956 


5 


.000836820 


1260 


.000793651 


1 


.000999001 


6 


.000933036 


1 


.000384173 


6 


.000836120 


1 


.000793021 


2 


.000998004 


7 


.00093720; 


2 


.000383392 


7 


.000335422 


2 


.000792393 


3 


.000997009 


8 


.000936330 


3 


.000832612 


8 


.000334724 


3 


.000791766 


4 


.000996016 


9 


.000935454 


4 


.000381834 


9 


.000834028 


4 


.000791139 


5 


.000995025 


1070 


.000934579 


5 


.000881057 


1200 


.000833333 


5 


.000790514 


6 


.000994036 


1 


.000933707 


6 


.000330232 


1 


.000832639 


■ 6 


.000789889 


7 


.000993049 


2 


000932336 


7 


.000379503 


2 


.000331947 


7 


000789266 


. 8 


.000992063 


3 


.000931966 


8 


.000378735 


3 


.000331255 


8 


.000788643 


9 


.000991080 


4 


.000931095 


9 


.000377963 


4 


.000330565 


9 


.000733022 


1010 


.000990099 


5 


.000930233 


IMG 


.000877193 


5 


.000329875 


1270 


.000787402 


11 


.000989120 


6 


.000929368 


1 


.000376424 


6 


.000829187 


1 


.000786782 


12 


.000988142 


7 


.000923505 


2 


.000375657 


7 


.000328500 


2 


.000786163 


13 


.000987167 


8 


.000927644 


3 


.000374891 


8 


.000827815 


3 


.000785546 


14 


.000986193 


9 


.000926784 


4 


.000874126 


9 


.000827130 


4 


.000784929 


15 


.000985222 


1030 


.000925926 


5 


.000873362 


1210 


.000826446 


5 


.000784314 


16 


.000984252 


1 


.000925069 


6 


.000872600 


11 


.000325764 


6 


000783699 


17 


.000983284 


2 


.000924214 


7 


.000871840 


12 


.000325082 


7 


.000783085 


18 


.000982318 


3 


.000923361 


8 


.000871080 


13 


.000324402 


8 


.000782473 


19 


.000981354 


4 


.000922509 


9 


.000870322 


14 


000323723 


9 


.000781861 


1020 


.000980392 


5 


.000921659 


1150 


.000869565 


15 


.000323045 


1230 


.000781250 


1 


.OC0979432 


6 


000920310 


1 


000868810 


16 


.000322368 


1 


.000780640 


2 


.000978474 


7 


.000919963 


2 


.000863056 


17 


.000321693 


2 


.000780031 


3 


.000977517 


8 


.000919118 


3 


.000367303 


18 


.000321018 


3 


.000779423 


4 


.000976562 


9 


.000918274 


4 


.000866551 


19 


.000320344 


4 


.000778816 


5 


.000975610 


1090 


.000917431 


5 


.000865801 


1220 


.000319672 


5 


.000778210 


6 


.000974659 


1 


.000916590 


6 


.000865052 


1 


.000319001 


6 


.000777605 


7 


.000973710 


2 


.00091575 


7 


.000864304 


2 


.000318331 


7 


.000777001 


8 


.000972763 


3 


.000914913 


8 


.000863558 


3 


.000817661 


8 


.000776397 


9 


.000971817 


4 


.00091407 


9 


.000362813 


4 


.000316993 


9 


,000775795 


1030 .000970874 


5 .000913242 


1160 


.000862069 


5 


.000816326 


1290 .000775194 



92 



MATHEMATICAL TABLES. 



No. 


Recipro- 
cal. 


No. 


Recipro- 
cal. 


No. 


Recipro- 
cal. 


No. 


Recipro- 
cal. 


No. 


Recipro- 
cal. 


1291 


.000774593 


1356 


.000737463 


1421 


.000703730 


1 4oc 


.000672948 


!5H! 


.000644745 


2 


.000773994 


7 


.000736920 


2 


.000703235 


7 


.000672495 


2 


.000644330 


3 


.000773395 


8 


.000736377 


3 


.000702741 


8 


.000672043 


3 


.000643915 


4 


.000772797 


9 


.000735835 


4 


.000702247 


9 


.000671592 


4 


.000643501 


5 


.000772201 


'>.: 


.000735294 


5 


.000701754 


1490 


.000671141 


5 


.000643067 


6 


.000771605 


1 


.000734754 


6 


.000701262 


1 


.000670691 


6 


.000642673 


7 


.000771010 


2 


.000734214 


7 


.000700771 


2 


.000670241 


7 


.000642261 


8 


.000770416 


3 


.000733676 


8 


.000700280 


3 


.000669792 


8 


;000641848 


9 


.000769823 


4 


.000733138 


9 


.000699790 


4 


.000669344 


9 


.000641437 


1300 


.000769231 


5 


.000732601 


1430 


.000699301 


5 


.000668896 


1560 


.000641026 


1 


.000768639 


6 


.000732064 


1 


.000698812 


6 


.000668449 


} 


.000640615 


2 


.000768049 


7 


.000731529 


2 


.000698324 


7 


.000668003 


2 


.000640205 


3 


.000767459 


8 


.000730994 


3 


.000697837 


8 


.000667557 


3 


.000639795 


4 


.000766871 


9 


.000730460 


4 


.000697350 


9 


.000667111 


4 


:C0G639386 


5 


.000766283 




.000729927 


5 


.000696364 


1500 


.000666667 


5 


:000638978 


6 


.00076569} 


1 


.000729395 


6 


.000696379 


1 


.000666223 


6 


;000638570 


7 


.000765111 


2 


.000728863 


7 


.000695894 


2 


.000665779 


7 


.000638162 


8 


.000764526 


3 


.000723332 


8 


.000695410 


3 


.000665336 


8 


.000637755 


9 


.000763942 


4 


.000727802 


9 


.000694927 


4 


.000664894 


9 


.000637349 


1310 


.000763359 


5 


.000727273 


1440 


.000694444 


5 


.000664452 


15/6 


.000636943 


11 


.000762776 


6 


.000726744 


1 


.000693962 


6 


.00066401 1 


1 


.000636537 


12 


.000762195 


7 


.000726216 


2 


.000693481 


7 


.000663570 


2 


.000636132 


13 


.000761615 


8 


.000725689 


3 


.000693001 


8 


.000663130 


3 


000635728 


14 


.000761035 


9 


.000725163 


4 


.00069252! 


9 


.00066269! 


4 


.000635324 


15 


.000760456 


132C 


.GG0724638 


5 


.000692041 


15 ;G 


.000662252 


5 


.000634921 


16 


.00075987C 


1 


.0007241 13 


6 


.000691563 


11 


.000661813 


6 


.000634518 


17 


.000759301 


2 


.000723589 


7 


.000691085 


12 


.000661376 


7 


.000634115 


18 


.000758725 


3 


.000723066 


8 


.000690608 


13 


.000660939 


8 


.000633714 


19 


.000758150 


4 


.000722543 


9 


.000690131 


14 


.000660502 


9 


.000633312 


1320 


.000757576 


5 


.000722022 


!450 


.000689655 


15 


.000660066 


I5EC 


.000632911 


1 


.000757002 


6 


.000721501 


1 


.000689180 


16 


.000659631 


1 


.000632511 


2 


.000756430 


7 


.000720980 


2 


.000688705 


17 


.000659196 


2 


0C0632I11 


3 


.000755856 


8 


.000720461 


3 


.00068823! 


18 


.000658761 


3 


.000631712 


4 


.000755287 


9 


.000719942 


4 


.000687758 


19 


.000658323 


4 


.000631313 


5 


.000754717 




.000719424 


5 


.000687285 


1520 


.000657895 


5 


.000630915 


6 


.000754 MS 


1 


.000718907 


6 


.000686813 


1 


.000657462 


6 


.000630517 


7 


.000753579 


2 


.000718391 


7 


.000686341 


2 


.000657030 


7 


CCC630120 


8 


.000753012 


3 


.000717875 


8 


.000635871 


3 


.000656598 


8 


.000629723 


9 


.000752445 


4 


.000717360 


9 


.000685401 


4 


.000656168 


9 


.000629327 


1330 


.00075 18SC 


5 


.000716346 


i46C 


.000634932 


5 


.000655738 


1590 


.00062893 \ 


1 


.000751315 


6 


.000716332 


1 


.000684463 


6 


.000655308 


1 


.000628536 


2 


.000750750 


7 


.000715820 


2 


.000683994 


7 


.000654879 


2 


.0CC628141 


3 


.000750187 


8 


.000715303 


3 


.000633527 


8 


.000654450 


3 


.000627746 


4 


.000749625 


9 


.000714796 


4 


.000683060 


9 


.000654022 


4 


.000627353 


5 


.000749064 


uoc 


.000714286 


5 


.000682594 


i53r 


.000653595 


5 


.000626959 


6 


.000748503 


1 


.000713776 


6 


.000682128 


1 


.000653168 


6 


.000626566 


7 


.000747943 


2 


.000713267 


7 


.000681663 


2 


.000652742 


7 


.000626174 


8 


.000747384 


3 


.000712758 


8 


.000681199 


3 


.000652316 


8 


.000625782 


9 


.000746826 


4 


.000712251 


9 


.000680735 


4 


.000651890 


9 


.000625391 


1340 


.000746269 


5 


.000711744 


!450 


.000680272 


5 


.000651466 


1600 


.000625000 


1 


.000745712 


6 


.00071 1238 


1 


.000679810 


6 


.000651042 


2 


.000624219 


2 


.000745156 


7 


.000710732 


2 


.000679348 


7 


.000650618 


4 


.000623441 


3 


.000744602 


8 


.000710227 


3 


.000678887 


8 


.000650195 


6 


.000622665 


4 


.000744048 


9 


.000709723 


4 


.000678426 


9 


.000649773 


8 


.000621890 


5 


.000743494 


1410 


.000709220 


5 


.000677966 


J54G 


.000649351 


1610 


.000621118 


6 


.000742942 


11 


.000708717 


6 


.000677507 


1 


.000648929 


12 


.000620347 


7 


.000742390 


12 


.000703215 


7 


.000677048 


2 


.000648508 


14 


.000619578 


8 


.000741840 


13 


.000707714 


8 


.000676590 


3 


.000648088 


16 


.000618812 


9 


.000741290 


14 


.000707214 


9 


.000676132 


4 


.000647668 


18 


.000618047 


1350 


.000740741 


15 


.000706714 


143C 


.000675676 


5 


.000647249 


1620 


.000617284 


1 


.000740192 


16 


.000706215 


1 


.000675219 


6 


.000646830 


2 


.000616523 


2 


.000739645 


17 


.000705716 


2 


.000674764 


7 


.000646412 


4 


.000615763 


3 


.000739098 


18 


.000705219 


3 


.000674309 


8 


.000645995 


6 .000615006 


4 


.000738552 


19 


.000704722 


4 


.000673854 


9 


.000645578 


8 .000614250 


5 


.000738007 


1420 .000704225 


5 .000673401 


1550 


.000645161 16301.000613497 



RECIPROCALS OF NUMBERS. 



93 



N Recipro- N Recipro- N Recipro- N Recipro- N Recipro- 

cal cal. ' cal. ' cal. ' cal. 

1632 
4 
6 



1640 
2 
4 



1530 
2 
4 
6 



(560 
2 



15 50 
2 
4 
6 

1690 
2 



1700 

2 
4 



.000612745 
.00061 1995 
.00061 1247 
.000610500 
.000609756 
.000609013 
.000603272 
.000607533 
.000505796 
.00050606! 
.000505327 
.000504595 
.000503365 
.000503 '36 
.000502 110 
.000301585 
.000300962 
.000300240 
;000>99520 
,000593302 
.000593086 
;on0597371 
,000596658 
.000595947 
000395238 
000594530 
.000393324 
.000593120 
.000592417 
.000591716 
:00059i0!7 
.000590319 
.000389622 
.000383923 
.000533235 
.000587544 
.000536354 



.000586166 

.000585480 

.000584795 

.0005841 12 

.000583430 

.000582750 

.000582072 

.000531395 

.000530720 

.000580046 

.000579374 

.000578704 

.000578035 

.000577367 

.000576701 

.000576037 

.000575374 

.000574713 

.000574053 

.000573394 

.000572737 

.000572082 

.000571429 

.000570776 

.000570125 

000569476 

.000563323 

.000563132 

.000567537 

.000566393 

.000566251 

.00056561 

.000564972 

.000564334 

.000563693 

.000563063 

.000562430 



.000561798 
.000561167 
.000560538 
.000559910 
.000559284 
.000558659 
.000558035 
.000557413 
.000556793 
.000556174 
.000555556 
.000554939 
.000554324 
.000553710 
.000553097 
.000552486 
.000551876 
.000551268 
.000550661 
.000550055 
.000549451 
.000548848 
.000548246 
.000547645 
.000547046 
.000546448 
.000545851 
.000545256 
.000544662 
.000544069 
.000543478 
.000542838 
.000542299 
.000541711 
.000541 125 
.000540540 
.000539957 



.000539374 

.000538793 

.000538213 

.000537634 

.000537057 

.000536480 

.000535905 

.000535332 

.000534759 

.000534188 

.000533618 

.000533049 

.00053248 

.000531915 

.000531350 

.000530785 

.000530222 

.000529661 

.000529100 

.000528541 

.000527983 

.000527426 

.000526870 

.000526316 

.000525762 

.000525210 

.000524659 

.000524109 

.000523560 

.000523012 

.000522466 

.000521920 

.000521376 

.000520833 

.000520291 

.000519750 

.000519211 



2000 



.000518672 
.000518135 
.000517599 
.000517063 
.000516528 
.000515996 
.000515464 
.000514933 
.000514403 
.000513874 
.000513347 
.000512820 
.000512295 
.000511770 
.000511247 
.000510725 
.000510204 
.000509684 
.000509165 
.000508647 
.000508130 
.000507614 
.000507099 
.000506585 
.000506073 
.000505561 
.000505051 
.000504541 
.000504032 
.000503524 
.000503018 
.000502513 
.000502008 
.000501504 
.000501002 
.000500501 
.000500000 



Use of reciprocals. — Reciprocals may be conveniently used to facili- 
tate computations in long division. Instead of dividing as usual, multiply 
the dividend by the reciprocal of the divisor. The method is especially 
useful when many different dividends are required to be divided by the 
same divisor. In this case find the reciprocal of the divisor, and make a 
small table of its multiples up to 9 times, and use this as a multiplication- 
table instead of actually performing the multiplication in each case. 

Example. — 9871 and several other numbers are to be divided by 1638. 
The reciprocal of 1638 is .000610500. 
Multiples of the 
reciprocal: 

1. .0006105 The table of multiples is made by continuous addi- 

2. .0012210 tion of 6105. The tenth line is written to check the 

3. .0018315 accuracy of the addition, but it is not afterwards used. 

4. .0024420 Operation: 

5. .0030525 Dividend 9871 

6. .0036630 Take from table 1 0006105 

7. .0042735 7 0.042735 

8. .0048840 8 00.48840. 

9. .0054945 9 005.4945 

10. .0061050 — - 

Quotient 6.0262455 

Correct quotient by direct division 6.0262515 

The result will generally be correct to as many figures as there are signi- 
ficant figures in the reciprocal, less one, and the error of the next figure will 
in general not exceed one". In the above example the reciprocal has six 
significant figures, 610500, and the result is correct to five places of figures. 



94 




MATHEMATICAL TABLES. 








SQUARES, 


CUBES 


, SQUARE ROOTS AND CUBE ROOTS OF 






NUMBERS 


FROM 0.1 TO 1600. 


No. 


Square. 


Cube. 


Sq. 
Root. 


Cube 
Root. 


No. 


Square. 


Cube. 


Sq. 
Root. 


Cube 
Root. 


0.1 


.01 


.001 


.3162 


.4642 


3.1 


9.61 


29.791 


1.761 


1.458 


.15 


.0225 


.0034 


.3873 


.5313 


.2 


10.24 


32.768 


1.789 


1.474 


.2 


.04 


.008 


.4472 


.5848 


.3 


10.89 


35.937 


1.817 


1 .489 


.25 


.0625 


.0156 


.500 


.6300 


.4 


11.56 


39.304 


1.844 


1.504 


.3 


.09 


.027 


.5477 


.6694 


.5 


12.25 


42.875 


1.871 


1.518 


.35 


.1225 


.0429 


.5916 


.7047 


.6 


12.96 


46.656 


1.897 


1.533 


.4 


16 


.064 


.6325 


.7368 


.7 


13.69 


50.653 


1.924 


1.547 


.45 


. .2025 


.0911 


.6708 


.7663 


.8 


14.44 


54.872 


1.949 


1.560 


.5 


.25 


.125 


.7071 


.7937 


.9 


15.21 


59.319 


1.975 


1.574 


.55 


.3025 


.1664 


.7416 


.8193 


4. 


16. 


64. 


2. 


1.5874 


.6 


.36 


.216 


.7746 


.8434 


.1 


16.81 


68.921 


2.025 


1.601 


.65 


.4225 


.2746 


.8062 


.8662 


.2 


17.64 


74.088 


2.049 


1.613 


.7 


.49 


.343 


.8367 


.8879 


.3 


18.49 


79.507 


2.074 


1.626 


.75 


.5625 


.4219 


.8660 


.9086 


.4 


19.36 


85.184 


2.098 


1.639 


.8 


.64 


.512 


.8944 


.9283 


.5 


20.25 


91.125 


2.121 


1.651 


.85 


.7225 


.6141 


.9219 


.9473 


.6 


21.16 


97.336 


2.145 


1.663 


.9 


.81 


.729 


.9487 


.9655 


.7 


22.09 


103.823 


2.168 


1.675 


.95 


.9025 


.8574 


.9747 


.9830 


.8 


23.04 


110.592 


2.191 


1.687 


1. 


1. 


1. 


1. 


1. 


.9 


24.01 


!'1 7.649 


2.214 


1.698 


1.05 


1.1025 


1.158 


1.025 


1.016. 


5. 


25. 


125. 


2.2361 


1.7100 


1.1 


1.21 


1.331 


1.049 


1.032 


.1 


26.01 


132.651 


2.258 


1.721 


1.15 


1.3225 


1.521 


1.072 


1.048 


.2 


27.04 


140.608 


2.280 


1.732 


1.2 


1.44 


1.728 


1.095 


1.063 


.3 


28.09 


148.877 


2.302 


1.744 


1.25 


1.5625 


1.953 


1.118 


1.077 


.4 


29.16 


157.464 


2.324 


1.754 


1.3 


1.69 


2.197 


1.140 


1.091 


.5 


30.25 


166.375 


2.345 


1 .765 


1.35 


1.8225 


2.460 


1.162 


1.105 


.6 


31.36 


175.616 


2.366 


1.776 


1.4 


1.96 


2.744 


1.183 


1.119 


.7 


32.49 


185.193 


2.387 


1.786 


1.45 


2.1025 


3.049 


1.204 


1.132 


.8 


33.64 


195.112 


2.408 


1.797 


1.5 


2.25 


3.375 


1 .2247 


1.1447 


.9 


34.81 


205.379 


2.429 


1.807 


1.55 


2.4025 


3.724 


1.245 


1.157 


3. 


36. 


216. • 


2.4495 


1.8171 


1.6 


2.56 


4.096 


1.265 


1.170 


.1 


37.21 


226.981 


2.470 


1.827 


1.65 


2.7225 


4.492 


1.285 


1.182 


.2 


38.44 


238.328 


2.490 


1 .837 


1.7 


2.89 


4.913 


1.304 


1.193 


.3 


39.69 


250.047 


2.510 


1.847 


1.75 


3.0625 


5.359 


1.323 


1.205 


.4 


40.96 


262.144 


2.530 


1.85/ 


1.8 


3.24 


5.832 


1.342 


1.216 


.5 


42.25 


274.625 


2.550 


1.866 


1.85 


3.4225 


6.332 


1.360 


1.228 


.6 


43.56 


287.496 


2.569 


1.876 


1.9 


3.61 


6.859 


1.378 


1.239 


.7 


44.89 


300.763 


2.588 


1.885 


1.95 


3.8025 


7.415 


1.396 


1.249 


.8 


46.24 


314.432 


2.608 


1.895 


2. 


4. 


8. 


1.4142 


1.2599 


.9 


47.61 


328.509 


2.627 


1.904 


.1 


4.41 


9.261 


1.449 


1.281 


7. 


49. 


343. 


2.6458 


1.9129 


.2 


4.84 


10.648 


1.483 


1.301 


J 


50.41 


357.911 


2.665 


1.922 


.3 


5.29 


12.167 


1.517 


1.320 


.2 


51.84 


373.248 


2.683 


1.931 


.4 


5.76 


13.824 


1.549 


1.339 


.3 


53.29 


389.017 


2.702 


1.940 


.5 


6.25 


15.625 


1.581 


• 1.357 


.4 


54.76 


405.224 


2.720 


1.949 


.6 


6.76 


17.576 


1.612 


1.375 


.5 


56.25 


421.875 


2.739 


1.957 


.7 


7.29 


19.683 


1.643 


1.392 


.6 


57.76 


438.976 


2.757 


1.966 


.8 


7.84 


21.952 


1.673 


1.409 


.7 


59.29 


456.533 


2.775 


1.975 


.9 


8.41 


24.389 


1.703 


1.426 


.8 


60.84 


474.552 


2.793 


1.983 


3. 


9. 


27. 


1.7321 


1 .4422 


.9 


62.41 


493.039 


2.811 


1.992 




















„ 



SQUARES, CUBES, SQUARE AND CUBE ROOTS. 



95 



No. 


Square 


Cube. 


Sq. 

Root. 


Cube 
Root. 


No 


Square Cube. 


Sq. 

Root. 


Cube 
Root. 


8. 


64. 


512. 


2.828- 


i 2. 


45 


2025 


9112: 


6.7082 


3.5569 


.1 


65.61 


531.44 


2.846 


2.008 


46 


2116 


97336 6.7823 


3.5830 


.2 


67.24 


551.36J 


2.864 


2.017 


47 


2209 


103823 


6.8557 


3.6088 


.3 


68.89 


571.78} 


2.881 


2.025 


48 


2304 


110592 


6.9282 


3.6342 


.4 


70.56 


592.70^ 


2.898 


2.033 


49 


2401 


117649 


7. 


3.6593 


.5 


72.25 


614.125 


2.915 


2.041 


50 


2500 


125000 


7.0711 


3.6840 


.6 


73.96 


636.056 


2.933 


2.049 


51 


2601 


132651 


7.1414 


3.7084 


.7 


75.69 


658.503 


2.950 


2.057 


52 


2704 


140608 


7.2111 


3.7325 


.8 


77.44 


681.472 


2.966 


2.065 


53 


2809 


148877 


7.2801 


3.7563 


;9 


79.21 


704.969 


2.983 


2.072 


54 


2916 


157464 


7.3485 


3.7798 


9. 


81. 


729. 


3. 


2.0801 


55 


3025 


166375 


7.4162 


3.8030 


.1 


82.81 


753.571 


3.017 


2.088 


56 


3136 


175616 


7.4833 


3.8259 


.2 


84.64 


778.688 


3.033 


2.095 


57 


3249 


185193 


7.5498 


3.8485 


.3 


86.49 


804.357 


3.050 


2.103 


58 


3364 


195112 


7.6158 


3.8709 


.4 


88.36 


830.584 


3.066 


2.110 


59 


3481 


205379 


7.6811 


3.8930 


.5 


90.25 


857.375 


3.082 


2.118 


60 


3600 


216000 


7.7460 


3.9149 


.6 


92.16 


884.736 


3.098 


2.125 


61 


3721 


226981 


7.8102 


3.9365 


.7 


94.09 


912.673 


3.114 


2.133 


62 


3844 


238328 


7.8740 


3.9579 


.8 


96.04 


941.192 


3.130 


2.140 


63 


3969 


250047 


7.9373 


3.9791 


.9 


98.01 


970.299 


3.146 


2.147 


64 


4096 


262 1 44 


8. 


4. 


10 


100 


1000 


3.1623 


2.1544 


65 


4225 


274625 


8.0623 


4.0207 


11 


121 


1331 


3.3166 


2.2240 


66 


4356 


287496 


8.1240 


4.0412 


12 


144 


1728 


3.4641 


2.2894 


67 


4489 


300763 


8.1854 


4.0615 


13 


169 


2197 


3.6056 


2.3513 


68 


4624 


3 1 4432 


8.2462 


4.0817 


14 


196 


2744 


3.7417 


2.4101 


69 


4761 


328509 


8.3066 


4.1016 


15 


225 


3375 


3.8730 


2.4662 


70 


4900 


343000 


8.3666 


4.1213 


16 


256 


4096 


4. 


2.5198 


71 


5041 


357911 


8.4261 


4.1408 


17 


289 


4913 


4.1231 


2.5713 


72 


5184 


373248 


8.4853 


4.1602 


18 


324 


5832 


4.2426 


2.6207 


73 


5329 


389017 


8.5440 


4. 1 793 


19 


361 


6859 


4.3589 


2.6684 


74 


5476 


405224 


8.6023 


4,1983 


20 


400 


8000 


4.4721 


2.7144 


75 


5625 


421875 


8.6603 


4.2172 


21 


441 


9261 


4.5826 


2.7589 


76 


5776 


438976 


8.7178 


4.2358 


22 


484 


10648 


4.6904 


2.8020 


77 


5929 


456533 


8.7750 


4.2543 


23 


529 


12167 


4.7958 


2.8439 


78 


6084 


474552 


8.8318 


4.2727 


24 


576 


13824 


4.8990 


2.8845 


79 


6241 


493039 


8.8882 


4.2908 


25 


625 


15625 


5. 


2.9240 


80 


6400 


512000 


8.9443 


4.3089 


26 


676 


17576 


5.0990 


2.9625 


81 


6561 


531441 


9. 


4.3267 


27 


729 


19683 


5.1962 


3. 


82 


6724 


551368 


9.0554 


4.3445 


28 


784 


21952 


5.2915 


3.0366 


83 


6889 


571787 


9.1104 


4.3621 


29 


841 


24389 


5.3852 


3.0723 


84 


7056 


592704 


9.1652 


4.3795 


30 


900 


27000 


5.4772 


3.1072 


85 


7225 


614125 


9.2195 


4.3968 


31 


961 


29791 


5.5678 


3.1414 


86 


7396 


636056 


9.2736 


4.4140 


32 


1024 


32768 


5.6569 


3.1748 


87 


7569 


658503 


9.3276 


4.4310 


33 


1089 


35937 


5.7446 


3.2075 


88 


7744 


681472 


9.3808 


4.44&v> 


34 


1156 


39304 


5.8310 


3.2396 


89 


7921 


704969 


9.4340 


4.4647 


35 


1225 


42875 


5.9161 


3.2711 


90 


8100 


729000 


9.4868 


4.4814 


36 


1296 


46656 


6. 


3.3019 


91 


8281 


753571 


9.5394 


4.4979 


37 


1369 


50653 


6.0828 


3.3322 


92 


8464 


778688 


9.5917 


4.5144 


38 


1444 


54872 


6.1644 


3.3620 


93 


8649 


804357 


9.6437 


4.5307 


39 


1521 


39319 


6.2450 


3.3912 


94 


8836 


830584 


9.6954 


4.5468 


40 


1600 


54000 


6.3246 


3.4200 


95 


9025 


857375 


9.7468 


4.5629 


41 


1681 


58921 


6 4031 


3.4482 


96 


9216 


884736 


9.7980 


4.5789 


42 


1764 


74088 


6.4807 


3.4760 


97 


9409 


912673 


9.8489 


4.5947 


43 


1849 


79507 


6.5574 


3.5034 


98 


9604 


941192 


9.8995 


4.6104 


44 


1936 


35184 


6.6332 


3.5303 


99 1 9801 


970299 


9.9499 


4.6261 



MATHEMATICAL TABLES. 



No. 


Sq. 


Cube 


Sq. 
Root. 


Cube 
Root. 


No. 


Square. 


Cube. 


Sq. 
Root. 


Cube 
Root. 


10T 


10000 


1000000 


10. 


4.6416 


155 


24025 


3723875 


12.4499 


5.3717 


101 


10201 


1030301 


10.0499 


4.6570 


156 


24336 


3796416 


12.4900 


5.3832 


102 


10404 


1061208 


10.0995 


4.6723 


157 


24649 


3869893 


12.5300 


5.3947 


103 


10609 


1092727 


1 0. 1 489 


4.6875 


158 


24964 


3944312 


12.5698 


5.4061 


104 


10816 


1 124864 


10.1980 


4.7027 


159 


2528! 


4019679 


12.6095 


5.4175 


105 


11025 


1157625 


10.2470 


4.7177 


160 


25600 


4096000 


12.6491 


5.4288 


106 


11236 


1191016 


10.2956 


4.7326 


161 


25921 


4173281 


12.6886 


5.4401 


107 


11449 


1225043 


10.3441 


4.7475 


162 


26244 


4251528 


12.7279 


5.4514 


103 


11664 


1259712 


10.3923 


4.7622 


163 


26569 


4330747 


12.7671 


5.4626 


10? 


11881 


1295029 


10.4403 


4.7769 


164 


26896 


4410944 


12.8062 


5.4737 


110 


12100 


1331000 


10.4881 


4.7914 


165 


2/225 


4492125 


12.8452 


5.4848 


II! 


12321 


1367631 


10.5357 


4.8059 


166 


27556 


4574296 


12.8841 


5.4959 


112 


12544 


1 404928 


10.5830 


4.8203 


167 


27889 


4657463 


12.9228 


5.5069 


113 


12769 


1442897 


10.6301 


4.8346 


168 


28224 


4741632 


12.9615 


5.5178 


114 


12996 


1481544 


10.6771 


4.8488 


169 


28561 


4826809 


13.0000 


5.5288 


115 


13225 


1520375 


10.7238 


4.8629 


170 


28900 


4913000 


13.0384 


5.5397 


116 


13456 


1560396 


10.7703 


4.8770 


171 


29241 


5000211 


13.0767 


5.5505 


117 


13689 


1601613 


10.8167 


4.8910 


172 


29584 


5088448 


13.1149 


5.5613 


118 


13924 


1643032 


10.8628 


4.9049 


173 


29929 


5177717 


13.1529 


5.5721 


1 19 


14161 


1685159 


10.9087 


4.9187 


174 


30276 


5268024 


13.1909 


5.5828 


120 


14400 


1 728000 


10.9545 


4.9324 


175 


30625 


5359375 


13.2288 


5.5934 


121 


14641 


1771561 


1 1 .0000 


4.9461 


176 


30976 


5451776 


13.2665 


5.6041 


122 


14884 


1815848 


11.0454 


4.9597 


177 


31329 


5545233 


13.3041 


5.6147 


123 


15129 


1860867 


1 1 .0905 


4.9732 


178 


31684 


5639752 


13.3417 


5.6252 


124 


15376 


1906624 


11.1355 


4.9866 


179 


32041 


5735339 


13.3791 


5.6357 


125 


15625 


1953125 


11.1803 


5.0000 


180 


32400 


5832000 


13.4164 


5.6462 


126 


15876 


2000376 


11.2250 


5.0133 


181 


32761 


5929741 


13.4536 


5.6567 


127 


16129 


2048383 


11.2694 


5.0265 


182 


33124 


6028568 


13.4907 


5.6671 


123 


16384 


2097152 


11.3137 


5.0397 


183 


33489 


6128487 


13.5277 


5.6774 


129 


16641 


2146639 


11.3578 


5.0528 


184 


33856 


6229504 


13.5647 


5.6877 


130 


16900 


2197000 


11.4018 


5.0658 


185 


34225 


6331625 


13.6015 


5.6980 


131 


17161 


2243091 


11.4455 


5.0788 


186 


34596 


6434856 


13.6382 


5.7083 


132 


17424 


2299963 


11.4891 


5.0916 


187 


34969 


6539203 


13.6748 


5.7185 


133 


17639 


2352637 


11.5326 


5.1045 


188 


35344 


6644672 


13.7113 


5.7287 


134 


17956 


2406104 


11.5758 


5.1172 


189 


35721 


6751269 


13.7477 


5.7388 


135 


18225 


2460375 


11.6190 


5.1299 


190 


36100 


6859000 


13.7840 


5.7489 


136 


18496 


2515456 


11.6619 


5.1426 


191 


36481 


6967871 


13.8203 


5.7590 


137 


18769 


2571353 


11.7047 


5.1551 


192 


36864 


7077888 


13.8564 


5.7690 


133 


19044 


2628072 


11.7473 


5.1676 


193 


37249 


7189057 


13.8924 


5.7790 


139 


19321 


2685619 


11.7898 


5.1801 


194 


37636 


7301384 


13.9284 


5.7890 


140 


19600 


2744000 


1 1 .8322 


5.1925 


195 


38025 


7414875 


13.9642 


5.7989 


141 


19331 


2803221 


11.8743 


5.2048 


196 


38416 


7529536 


14.0000 


5.8088 


142 


20164 


2863283 


11.9164 


5.2171 


197 


38809 


7645373 


14.0357 


5.8186 


143 


20449 


2924207 


11.9583 


5.2293 


198 


39204 


7762392 


14.0712 


5.8285 


144 


20736 


2985984 


12.0000 


5.2415 


199 


39601 


7880599 


14.1067 


5.8383 


145 


21025 


3048625 


12.0416 


5.2536 


200 


40000 


8000000 


14.1421 


5.8480 


146 


21316 


3112136 


12.0330 


5.2656 


201 


40401 


8120601 


14.1774 


5.8578 


147 


21609 


3176523 


12.1244 


5.2776 


202 


40804 


8242408 


14.2127 


5.8675 


143 


21904 


3241792 


12.1655 


5.2896 


203 


41209 


8365427 


14.2478 


5.8771 


!49 


22201 


3307949 


12.2066 


5.3015 


204 


41616 


8489664 


14.2829 


5.8868 


150 


22500 


3375000 


12.2474 


5.3133 


205 


42025 


8615125 


14.3178 


5.8964 


151 


22301 


3442951 


12.2882 


5.3251 


206 


42436 


8741816 


14.3527 


5.9059 


152 


23104 


3511803 


12.3288 


5.3368 


207 


42849 


8869743 


14.3875 


5.9155 


153 


23409 


3581577 


12.3693 


5.3485 


208 


43264 


8998912 


14.4222 


5.9250 


154 


23716 


3652264 


12.4097 


5.3601 


209 


43681 


9129329 


14.4568 


5.9345 



SQUARES, CUBES, SQUARE AND CUBE ROOTS. 97 



No. 


Sq. 


Cube. 


Sq. 
Root. 


Cube 
Root. 

5T9439 


No. 


Square. 


Cube. 


Sq. 
Root. 


Cube 
Root. 


210 


44100 


9261000 


14.4914 


265 


70225 


18609625 


16.2788 


6.4232 


211 


44521 


9393931 


14.5258 


5.9533 


266 


70756 


18821096 


16.3095 


6.4312 


212 


44944 


9528128 


14.5602 


5.9627 


267 


71289 


19034163 


16.3401 


6.4393 


213 


45369 


9663597 


14.5945 


5.9721 


268 


71824 


19248832 


16.3707 


6.4473 


214 


45796 


9800344 


14.6287 


5.9814 


269 


72361 


19465109 


16.4012 


6.4553 


215 


46225 


9938375 


14.6629 


5.9907 


270 


72900 


19683000 


16.4317 


6.4633 


216 


46656 


10077696 


14.6969 


6.0000 


271 


73441 


19902511 


16.4621 


6.4713 


217' 


47089 


10218313 


14.7309 


6.0092 


272 


73984 


20123648 


1 6.4924 


6.4792 


218 


47524 


10360232 


14.7648 


6.0185 


273 


74529 


20346417 


16.5227 


6.4872 


219 


47961 


10503459 


14.7986 


6.0277 


274 


75076 


20570824 


16.5529 


6.4951 


220 


48400 


10648000 


14.8324 


6.0368 


275 


75625 


20796875 


16.5831 


6.5030 


221 


48841 


10793861 


14.8661 


6.0459 


276 


76176 


21024576 


16.6132 


6.5108 


222 


49284 


10941048 


14.8997 


6.0550 


277 


76729 


21253933 


16.6433 


6.5187 


223 


49729 


11089567 


14.9332 


6.0641 


278 


77284 


21484952 


16.6733 


6.5265 


224 


50176 


11239424 


14.9666 


6.0732 


279 


77841 


21717639 


16.7033 


6.5343 


225 


50625 


11390625 


15.0000 


6.0822 


280 


78400 


21952000 


16.7332 


6.5421 


226 


51076 


11543176 


15.0333 


6.0912 


281 


78961 


22188041 


16.7631 


6.5499 


227 


51529 


11697083 


15.0665 


6.1002 


282 


79524 


22425768 


16.7929 


6.5577 


228 


51984 


11852352 


15.0997 


6.1091 


283 


80089 


22665187 


16.8226 


6.5654 


229 


52441 


12008989 


15.1327 


6.1180 


284 


80656 


22906304 


16.8523 


6.5731 


230 


52900 


12167000 


15.1658 


6.1269 


285 


81225 


23149125 


16.8819 


6.5808 


231 


53361 


12326391 


15.1987 


6.1358 


286 


81796 


23393656 


16.9115 


6.5885 


232 


53824 


12487168 


15.2315 


6.1446 


287 


82369 


23639903 


16.9411 


6.5962 


233 


54289 


12649337 


15.2643 


6.1534 


288 


82944 


23887872 


16.9706 


6.6039 


234 


54756 


12812904 


15.2971 


6.1622 


289 


83521 


24137569 


17.0000 


6.6115 


235 


55225 


12977875 


15.3297 


6.1710 


290 


84100 


24389000 


17.0294 


6.6191 


236 


55696 


13144256 


15.3623 


6.1797 


291 


84681 


24642171 


17.0587 


6.6267 


237 


56169 


13312053 


15.3948 


6.1885 


292 


85264 


24897088 


17.0880 


6.6343 


233 


56644 


13481272 


15.4272 


6.1972 


293 


85849 


25153757 


17.1172 


6.6419 


239 


57121 


13651919 


15.4596 


6.2058 


294 


86436 


25412184 


17.1464 


6.6494 


240 


57600 


13824000 


15.4919 


6.2145 


295 


87025 


25672375 


17.1756 


6.6569 


241 


58081 


13997521 


15.5242 


6.2231 


296 


87616 


25934336 


17.2047 


6.6644 


242 


58564 


14172488 


15.5563 


6.2317 


297 


88209 


26193073 


17.2337 


6.6719 


243 


59049 


14348907 


15.5885 


6.2403 


298 


88804 


26463592 


17.2627 


6.6794 


244 


59536 


14526784 


15.6205 


6.2488 


299 


89401 


26730899 


17.2916 


6.6869 


245 


60025 


14706125 


15.6525 


6.2573 


300 


90000 


27000000 


17.3205 


6.6943 


246 


60516 


14886936 


15.6844 


6.2658 


301 


90601 


27270901 


17.3494 


6.7018 


247 


61009 


1 5069223 


15.7162 


6.2743 


302 


91204 


27543608 


17.3781 


6.7092 


243 


61504 


15252992 


15.7480 


6.2828 


303 


91809 


27818127 


17.4069 


6.7166 


249 


62001 


1 5438249 


15.7797 


6.2912 


304 


92416 


28094464 


17.4356 


6.7240 


250 


62500 


15625000 


15.8114 


6.2996 


305 


93025 


28372625 


17.4642 


6.7313 


251 


.63001 


15813251 


15.8430 


6.3080 


306 


93636 


28652616 


17.4929 


6.7387 


252 


63504 


16003008 


15.8745 


6.3164 


307 


94249 


28934443 


17.5214 


6.7460 


253 


64009 


16194277 


15.9060 


6.3247 


308 


94864 


29218112 


17.5499 


6.7533 


254 


.64516 


16387064 


15.9374 


6.3330 


309 


95481 


29503629 


17.5784 


6.7606 


255 


65025 


16581375 


15.9687 


6.3413 


310 


96100 


29791000 


17.6068 


6.7679 


256 


65536 


16777216 


16.0000 


6.3496 


311 


. 96721 


3008023 1 


17.6352 


6.7752 


257 


66049 


16974593 


16.0312 


63579 


312 


97344 


30371328 


17.6635 


6.7824 


253 


66564 


17173512 


16.0624 


6.3661 


313 


97969 


30664297 


17.6918 


6.7897 


259 


67081 


17373979 


16.0935 


6.3743 


314 


98596 


30959144 


17.7200 


6.7969 


260 


67600 


17576000 


16.1245 


6.3825 


315 


99225 


31255875 


17.7482 


6.8041 


261 


68121 


17779581 


16.1555 


6.3907 


316 


99856 


31554496 


17.7764 


6.8113 


262 


68644 


1 7984723 


16.1864 


6.3988 


317 


100489 


31855013 


17.8045 


6.8185 


263 


69169 


18191447 


16.2173 


J6.4070 


318 


101124 


32157432 


17.8326 


6.8256 


264 


69696 


18399744 


16.2481 


"6.4151 


319 


101761 


32461759 


17.8606 


6.8328 



MATHEMATICAL TABLES. 



No. 


Square. 


Cube. 


Sq. 
Root. 


Cube 
Root. 


No. 


Square 


Cube. 


Sq. 
Root. 

19.3649 


Cube 
Rcot. 


320 


1 02400 


32768000 


17.8885 


6.8399 


375 


1 40625 


52734375 


7.2112 


321 


103041 


33076161 17.9165 


6.8470 


376 


141376 


53157376 


19.3907 


7.2177 


322 


103684 


33386248117.9444 


6.8541 


377 


142129 


53582633 


19.4165 


7.2240 


323 


104329 


33698267! 17.9722 


6.8612 


378! 142884 


54010152 


19.4422 


7.2304 


324 


104976 


34012224 18.0000 


6.8683 


379 


143641 


54439939 


19.4679 


7.2368 


325 


105625 


34328125 18.0278 


6.8753 


380 


1 44400 


54872000 


19.4936 


7.2432 


326 


106276 


34645976j18.0555j6.8824 


381 


145161 


55306341 


19.5192 


7.2495 


327 


106929 


34965783 i 18.0831 16.8894 


382 


145924 


55 742968 


19.5448 


7.2558 


328 


107584 


35287552 18.1 108 6.8964 


383 146689 


56181887 


19.5704 


7.2622 


329 


108241 


35611289 


18.1384 6.9034 


384,147456 


56623104 


19.5959 


7.2685 


330 


108900 


35937000 


18.1659 


6.9104 


3851148225 


57066625 


19.6214 


7.2748 


331 


109561 


36264691 


18.1934 


6.9174 


386H48996 


57512456 


19.6469 


7.2811 


3 32 


110224 


36594368 


18.2209 


6.9244 


387J149769 


57960603 


19.6723 


7.2874 


333 


110389 


36926037 


18.2483 


6.9313 


3831150544 


58411072 


19.6977 


7.2936 


334 


111556 


37259704 


18.2757 


6.9382 


389 151321 


58863869 


197231 


7.2999 


335 


112225 


37595375 


18.3030 


6.9451 


390 152100 


593 1 9000 


19.7484 


7.3061 


336 


112896 


37933056 


18.3303 


6.9521 


391 152381 


59776471 


19.7737 


7.3124 


337 


113569 


38272753 18.3576 


6.9589 


392 ! 153664 


60256288 


197990 


7.3186 


333 


114244 


38614472i18.3848l6.9658 


393:154449 


60598457 


19.8242 


7.3248 


339 


114921 


38958219 


18.4120 6.9727 


394 


155236 


61162984 


19.8494 


7.3310 


340 


1 1 5600 


39304000 


18.4391 6.9795 


395 


156025 


61629875 


19.8746 


7.3372 


341 


116281 


39651821 


18.46626.9864 


396 


156816 


62099136 


19.8997 


7.3434 


342 


116964 


40001683 


1 8.4932 J6. 9932 


397 


157609 


62570773 


19.9249 


7.3496 


343 


1 1 7649 


40353607 


18.52037-0000 


398 


158404 


63044792 


19.9499 


7.35^8 


344 


118336 


40707584 


18.5472 7.0068 


399 


159201 


63521199 


19.9750 


7.3619 


345 


119025 


41063625 


1 8.5742|7.0i 36 


400 160000 


64000000 


2O.CC0O 


7.3681 


346 


119716 


41421736 


18.6011 17.0203 


401 i 160801 


64481201 


20.0250 


7.3742 


347 


120409 


41731923 


',8.62797.0271 


402! 161604 


64964808 20.0499 


7.3£03 


348 


121104 


42144192 


18.65487.0338 


403 162 -'09 


65450827 20.0749 


7.3864 


349 


121801 


42503549 


18.6815 


7.0406 


404 


163216 


65939264 


20.0998 


7.3925 


359 


122500 


42375000 18.7033 


7.0473 


405 


164025 


66430125 


20.1246 


7.3986 


351 


123201 


43243551 18.7350 


7.0540 


406 


164836 


66923416 


20.1494 


7.4047 


352 


123904 


43614208118.7617 


7.0607 


407 165649 


67419143(20.1742 


7.4108 


353 


124609 


43986977 


18.7883 


7.0674 


408 


166464 


67917312 


20.1990 


7.^169 


354 


125316 


44361864 


18.8149 


7.0740 


409 


167281 


68417929 


20.2237 


7.4229 


355 


126025 


44738875 


18.8414 


7.0807 


410 


168100 


68921 COO 


20.2485 


7.4290 


356 


126736 


45118016 


18.8680 


7.0873 


411 


1 6892 1 


69426531 


20.2731 


7.4350 


357 


127449 


45499293 118.8944! 7.0940 


412| 169744 


69934528 


20.2978 


7.4410 


353 


123164 


45882712| 18.92097.1006 


413j 170569 


70444997 


20.3224 


7.4470 


359 


128881 


46268279 18.9473 1 7. 1072 


414 


171396 


70957944 


20.3470 


7.4530 


360 


129600 


46656000; 18.9737 7.1138 


415 


172225 


71473375 


20.3715 


7.4590 


361 


130321 


47045881I19.0000 7.1204 


416 


173056 


71991296 


20.3961 


7.4650 


36? 


131044 


47437928 


19.0263 


7.1269 


417 


173889 


72511713 


20.4206 


7.4710 


363 


1 3 1 769 


47832147 


19.0526 


7.1335 


418 


174724 


73034632 


20.4450 


7.4770 


364 


132496 


43228544 


19.0788 


7.1400 


419 


175561 


73560059 


20.4695 


7.4829 


365 


133225 


4S627125 


19.1050 


7.1466 


420 


1 76400 


74088000 


20.4939 


7.4889 


366 133956 


49027896 


19.1311 


7.1531 


421 


177241 


74618461 


20.5183 


7.4948 


367 


134639 


49430863 


19.1572 


7.1596 


422 


1 78084 


75151448 


20.5426 


7.5007 


363 


135424 


49836032 


19.18337.1661 


423 


1 78929 


75686967 


20.5670 


7.5067 


369 


. 136161 


50243409 19.2094 7.1 726 


424 


179776 


76225024 


20.5913 


7.5126 


370 


136900 


506530001 19.235417. 1791 


425)180625 


76765625 


20.6155 


7.5185 


371 137641 


5106431 l!l9.2614;7. 1855 


4261181476 


77308776 


20.6398 


7.5244 


372i 138384 


51478348 19.2873|7. 1920 


427; 182329 


77854^8320.6640 


7 5302 


373 139129 


51895117 19.3132(7.1984 


428,183184 


7840275270.6882 


7.5361 


374 1 139876 


5231362419.33917.2048 


429 184041 


78953589 207123 


7.5420 



SQUARES, CUBES, SQUARE AND CUBE ROOTS. 99 



No. 


Square 


Cube. 


Sq. 
Root. 


Cube 
Root. 


No. 


Square 


Cube, 


Sq. 
Root. 


Cube 
Root, 


430 


184900 


79507000 


20.7364 7.547 


485 


235225 


114084125 


22.0227 


7.8568 


431 


185761 


80062991 


20.7605 


7.5537 


486 


236196 


114791256 


22.0454 


7.8622 


432 


186624 


80621568 


20.7846 


7.5595 


487 


237169 


115501303 


22.0681 


7.8676 


433 


187489 


81182737 


20.8087 


7.5654 


488 


238144 


116214272 


22.0907 


7.8730 


434 


188356 


81746504 


20.8327 


7.5712 


489 


239121 


116930169 


22.1133 


7.8784 


435 


189225 


82312875 


20.8567 


7.5770 


490 


240100 


1 1 7649000 


22.1359 


7.8837 


436 


1 90096 


82381856 


20.8806 


7.5828 


491 


241081 


118370771 


22.1585 


7.8891 


457 


190969 


83453453 


20.9045 


7.5886 


492 


242064 


119095438 


22.1811 


7.8944 


43 J 


191844 


84027672 


20.9284 


7.5944 


493 


243049 


119823157 


22.2036 


7.8998 


439 


192721 


846045 1 9 


20.9523 


7.6001 


494 


244036 


120553784 


22.2261 


7.9051 


440 


193600 


85 1 84000 


20.9762 


7.6059 


495 


245025 


121287375 


22.2486 


7.9105 


441 


1944S1 


85766121 


21.0000 


7.6117 


496 


246016 


122023936 


22.2711 


7.9158 


442 


195364 


86350888 


21.0238 


7.6174 


497 


247009 


122763473 


22.2935 


7.9211 


443 


196249 


86938307 


21.0476 


7.6232 


498 


248004 


123505992 


22.3159 


7.9264 


444 


197136 


87528384 


21.0713 


7.6289 


499 


249001 


124251499 


22.3383 


7.9317 


445 


198025 


88121125 


21.0950 


7.6346 


500 


250000 


125000000 


22.3607 


7.9370 


44o 


198916 


88716536 


21.1187 


7.6403 


501 


251001 


125751501 


22.3830 


7.9423 


447 


199809 


893 1 4623 


21.1424 


7.6460 


502 


252004 


126506008 


22.4054 


7.9476 


443 


200704 


89915392 


21.1660 


7.6517 


503 


253009 


127263527 


22.4277 


7.9528 


449 


201601 


905 1 8849 


21.1896 


7.6574 


504 


254016 


128024064 


22.4499 


7.9581 


450 


202500 


91125000 


21.2132 


7.6631 


505 


255025 


128787625 


22.4722 


7.9634 


451 


203401 


91733851 


21.2368 


7.6688 


506 


256036 


129554216 


22.4944 


7.9686 


452 


204304 


92345408 


21.2603 


7.6744 


507 


257049 


130323843 


22.5167 


7 9739 


453 


205209 


92959677 


21.2838 


7.6800 


508 


258064 


131096512 


22.5389 


7.9791 


434 


206116 


93576664 


21.3073 


7.6857 


509 


259081 


131872229 


22.5610 


7.9843 


455 


207025 


94196375 


21.3307 


7.6914 


510 


260100 


132651000 


22.5832 


7.9896 


456 


207936 


94818816 


21.3542 


7.6970 


511 


261121 


13343283 1 


22.6053 


7.9948 


457 


208849 


95443993 


21.3776 


7.7026 


512 


262144 


134217728 


22.6274 


8.0000 


4j3 


209764 


96071912 


21.4009 


7.7082 


513 


263169 


135005697 


22.6495 


8.0052 


459 


210681 


96702579 


2 1 .4243 


7.7138 


514 


264196 


135796744 


22.6716 


8.0104 


460 


211600 


97336000 


21.4476 


7.7194 


515 


265225 


136590875 


22.6936 


8.0156 


461 


212521 


97972181 


21.4709 


7.7250 


516 


266256 


137338096 


22.7156 


8.0208 


40? 


213444 


98611128 


21.4942 


7.7306 


517 


267289 


138188413 


22.7376 


8.0260 


463 


214369 


99252847 


21.5174 


7.7362 


518 


268324 


138991832 


22.7596 


8.0311 


464 


215296 


99897344 


21.5407 


7.7418 


519 


269361 


139798359 


22.7816 


8.0363 


465 


216225 


100544625 


21.5639 


7.7473 


520 


270400 


140608000 


22.8035 


8.0415 


466 


217156 


101194696 


21.587C 


7.7529 


521 


27144! 


141420761 


22.8254 


8.0466 


467 


218089 


101847563 


21.6102 


7.7584 


522 


272484 


142236646 


22.8473 


8.0517 


468 


219024 


102503232 


21.6333 


7.7639 


523 


273529 


143055667 


22.8692 


8.0569 


469 


21996! 


103161709 


21.6564 


7.7695 


524 


274576 


143877824 


22.8910 


8.062P 


470 


220900 


103823000 


21.6795 


7.7750 


525 


275625 


144703125 


22.9129 


8.0671 


47! 


221341 


104437111 


21.7025 


7.7805 


526 


276676 


145531576 


22.9347 


8.0723 


472 


222/34 


105154048 


21.7256 


7.7860 


527 


277729 


146363183 


22.9565 


8.0774 


473 


223 729 


105823317 


21.7486 


7.7915 


528 


278784 


147197952 


22.9783 


8.0825 


474 


224676 


106496424 


21.7715 


7.7970 


529 


279841 


148035889 


23.0000 


8.0876 


475 


225625 


107171875 


21.7945 


7.8025 


530 


280900 


14887700C 


23.0217 


8.0927 


476 


226576 


107850176 


21.8174 


7.8079 


531 


281961 


149721291 


23.0434 


8.0978 


477 


227529 


103531333 


21.8403 


7.8134 


532 


283024 


150568766 


23.0651 


8.1028 


478 


228484 


109215352 


2 1 .8632 


7.8188 


533 


284089 


151419437 


23.0868 


8.1079 


479 


229441 


109902239 


21.8861 


7.8243 


534 


285156 


152273304 


23.1084 


8.1130 


4S0 


230400 


110592000 


21.9089 


7.8297 


535 


286225 


153130375 


23.1301 


8.1180 


431 


231361 


1 11284641 


21.9317 


7.8352 


536 


287296 


153990656 


23.1517 


8.1231 


432 


232324 


1 1 1980168 


21.9545 


7.8406 


537 


238369 


154854153 


23.1733 


8.1281 


433 


233239 


112678537 


21.9773 


7.8460 


538 


289444 


155720372 


23.1948 


8.1332 


484 


234256 


1 13379904 


22.0000 


7.8514 


539 


1290521 


156590819 


23.2164 


8.1382 



MATHEMATICAL TABLES. 



No. 


Square. 


Cube. 


Sq. 
Root. 


Cube 
Root. 


No. 


Square 


Cube. 


Sq. 
Root. 


Cube 
Root. 


540 


291600 


157464000 


23.2379 


8.1433 


595 


354025 


2106448/5 24. 


8.4103 


541 


292681 


158340421 


23.2594 


8.1483 


596 


355216 


211708736 


24.4131 


8.4155 


542 


293764 


1 59220088 


23.2809 


8.1533 


597 


356409 


212776173 


24.4336 


8.4202 


543 


294349 


160103007 


23.3024 


8.1583 


598 


357604 


213847192 


24.4540 


8.4249 


544 


295936 


160989184 


23.3238 


8.1633 


599 


358801 


214921799 


24.4745 


8.4296 


545 


297025 


161878625 


23.3452 


8.1683 


600 


360000 


216000000 


24.4949 


8.4343 


546 


298116 


162771336 


23.3666 


8.1733 


601 


361201 


217081801 


24.5153 


8.4390 


547 


299209 


163667323 


23.3380 


8. 1 783 


602 


362404 


218167208 


24.5357 


8.4437 


543 


300304 


164566592 


23.4094 


8.1833 


603 


363609 


219256227 


24.5561 


8.4484 


549 


301401 


165469149 


23.4307 


8.1882 


604 


364816 


220348864 


24.5764 


8.4530 


550 


302500 


166375000 


23.4521 


8.1932 


605 


366025 


221445125 


24.5967 


8.4577 


551 


303601 


167284151 


23.4734 


8.1982 


606 


367236 


222545016 


24.6171 


8.4623 


552 


304704 


163196608 


23.4947 


8.2031 


607 


36S449 


223648543 


24.6374 


8.4670 


553 


305809 


169112377 


23.5160 


8.2081 


608 


369664 


224755712 


24.6577 


8.4716 


554 


306916 


170031464 


23.5372 


8.2130 


609 


370881 


225866529 


24.6779 


8.4763 


555 


308025 


170953875 


23.5584 


8.2180 


610 


372100 


226981000 


24.6982 


8.4809 


556 


309136 


171879616 


23.5797 


8.2229 


611 


373321 


228099131 


24.7184 


8.4856 


557 


310249 


1 72808693 


23.6008 


8.2278 


612 


374544 


229220928 


24.7386 


8.4902 


553 


311364 


173741112 


23.6220 


8.2327 


613 


375769 


230346397 


24.7588 


8.4948 


559 


312481 


174676879 


23.6432 


8.2377 


614 


376996 


231475544 


24.7790 


8.4994 


560 


313600 


175616000 


23.6643 


8.2426 


635 


378225 


232608375 


24.7992 


8.5040 


561 


314721 


176558481 


23.6854 


8.2475 


616 


379456 


233744896 


24.8193 


8.5086 


562 


315844 


177504328 


23.7065 


8.2524 


617 


380689 


234885113 


24.8395 


8.5132 


563 


316969 


178453547 


23.7276 


8.2573 


618 


381924 


236029032 


24.8596 


8.5178 


564 


318096 


179406144 


23.7487 


8.2621 


619 


383161 


237176659 


24.8797 


8.5224 


565 


319225 


180362125 


23.7697 


8.2670 


620 


384400 


238328000 


24.8998 


8.5270 


566 


320356 


181321496 


23.7908 


8.2719 


621 


385641 


239483061 


24.9199 


8.5316 


567 


321489 


182284263 


23.8118 


8.2768 


622 


386884 


240641848 


24.9399 


8.5362 


568 


322624 


1*3250432 


23.8328 


8.2816 


623 


388129 


241804367 


24.9600 


8.5408 


569 


323761 


i 84220009 


23.8537 


8.2865 


624 


389376 


242970624 


24.9800 


8.5453 


570 


324900 


185193000 


23.8747 


8.2913 


625 


390625 


244140625 


25.0000 


8.5499 


571 


326041 


186169411 


23.8956 


8.2962 


626 


391876 


245314376 


25.0200 


8.5544 


572 


327184 


187149248 


23.9165 


8.3010 


627 


393129 


246491833 


25.0400 


8 5590 


573 


328329 


188132517 


23.9374 


8.3059 


628 


394384 


247673152 


25.0599 


8.5635 


574 


329476 


189119224 


23.9583 


8.3107 


629 


395641 


248858189 


25.0799 


8.5681 


575 


330625 


190109375 


23.9792 


8.3155 


630 


396900 


250047000 


25.0998 


8.5726 


576 


331776 


191102976 


24.0000 


8.3203 


631 


398161 


251239591 


25.1197 


8.5772 


577 


332929 


192100033 


24.0208 


8.3251 


632 


399424 


252435968 


25.1396 


8.5817 




334034 


193100552 


24.0416 


8.3300 


633 


400639 


253636137 


25.1595 


8.5862 


579 


335241 


194104539 


24.0624 


8.3348 


634 


401956 


254840104 


25.1794 


8.5907 


580 


336400 


195112000 


24.0832 


8.3396 


635 


403225 


256047875 


25.1992 


8.5952 


581 


337561 


196122941 


24.1039 


8.3443 


636 


404496 


257259456 


25.2190 


8.5997 


582 


338724 


197137368 


24.1247 


8.3491 


637 


405769 


258474853 


25.2389 


8.6043 


583 


339889 


198155287 


24.1454 


8.3539 


638 


407044 


259694072 


25.2587 


8.6039 


584 


341056 


199176704 


24.1661 


8.3587 


639 


408321 


260917119 


25.2784 


8.6132 


585 


342225 


200201625 


24.1868 


8.3634 


640 


409600 


262144000 


25.2982 


8.6177 


586 


343396 


201230056 


24.2074 


8.3682 


641 


410881 


263374721 


25.3180 


8.6222 


587 


344569 


202262003 


24.2281 


8.3730 


642 


412164 


264609288 


25.3377 


8.6267 


583 


345744 


203297472 


24.2487 


8.3777 


643 


413449 


265847707 


25.3574 


8.6312 


589 


34692 1 


204336469 


24.2693 


8.3825 


644 


414736 


267089934 


25.3772 


8.6357 


590 


348100 


205379000 


24.2899 


8.3872 


645 


416025 


268336125 


25.3969 


8.6401 


591 


349281 


206425071 


24.3105 


8.3919 


646 


417316 


269586136 


25.4165 


8.6446 


592 


350464 


207474688 


24.3311 


8.3967 


647 


4 1 8609 


270840n?3 


25.4362 


8 6490 


593 


351649 


208527857 24.3516 


8.4014 


648 


419904 


272097792 


25.4555 


8.6535 


594 352836 209584584 24.37218.4061 


649 421201273359449 25.4755 8.6579 



SQUARES, CUBES, SQUARE AND CUBE ROOTS. 101 



\ T o 


Square. 
422500 


Cube. 


Sq. 

Root. 


Cube 
Root. 


No. 


Square 


Cube. 


Sq. 
Root. 


Cube 
Root. 


350 


274625000 


25.4951 


8.6624 


705 


497025 


350402625 


26.5518 


8.9001 


551 


423801 


275894451 


25.5147 


8.6668 


706 


498436 


351895816 


26.5707 


8.9043 


552 


425104 


277167808 


25.5343 


8.6713 


707 


499849 


353393243 


26.5895 


8.9085 


d53 


426409 


278445077 


25.5539 


8.6757 


708 


501264 


354894912 


26.6083 


8.9127 


354 


427716 


279726264 


25.5734 


8.6801 


709 


502681 


356400829 


26.6271 


8.9169 


>55 


429025 


281011375 


25.5930 


8.6845 


710 


504100 


357911000 


26.6458 


8.9211 


)56 


430336 


282300416 


25.6125 


8.6890 


711 


505521 


359425431 


26.6646 


8.9253 


?57 


431649 


283593393 


25.6320 


8.6934 


712 


506944 


360944128 


26.6833 


8.9295 


)5S 


432964 


284890312 


25.6515 


8.6978 


713 


508369 


362467097 


26.7021 


8.9337 


)59 


434281 


286191179 


25.6710 


8.7022 


714 


509796 


363994344 


26.7208 


8.9378 


>60 


435600 


287496000 


25.6905 


8.7066 


715 


511225 


365525875 


26.7395 


8.9420 


61 


43692 1 


288804781 


25.7099 


8.7110 


716 


512656 


367061696 


26 7582 


8.9462 


62 


438244 


290117528 


25.7294 


8.7154 


717 


514089 


368601813 


26.7769 


8.9503 


33 


439569 


291434247 


25.7488 


8.7198 


718 


515524 


370146232 


26.7955 


8.9545 


64 


440896 


292754944 


25.7682 


8.7241 


719 


516961 


371694959 


26.8142 


8.9587 


65 


442225 


294079625 


25.7876 


8.7285 


720 


518400 


373248000 


26.8328 


8.9628 


66 


443556 


295408296 


25.8070 


8.7329 


721 


519841 


374805361 


26.8514 


8.9670 


67 


444889 


296740963 


25 8263 


8.7373 


722 


521284 


376367048 


26.8701 


8.9711 


6S 


446224 


298077632 


25.8457 


8.7416 


723 


522729 


377933067 


26.8887 


8.9752 


69 


447561 


299418309 


25.8650 


8.7460 


724 


524176 


379503424 


26.9072 


8.9794 


70 


448900 


300763000 


25.8844 


8.7503 


725 


525625 


381078125 


26.9258 


8.9835 


71 


450241 


302111711 


25.9037 


8.7547 


726 


527076 


382657176 


26.9444 


8.9876 


72 


451584 


303464448 


25.9230 


8.7590 


727 


528529 


384240583 


26.9629 


8.9918 


73 


452929 


304821217 


25.9422 


8.7634 


728 


529984 


385828352 


26.9815 


8.9959 


74 


454276 


306182024 


25.9615 


8.7677 


729 


531441 


387420489 


27.0000 


9.0000 


75 


455625 


307546875 


25.9808 


8.7721 


730 


532900 


389017000 


27.0185 


9.0041 


76 


456976 


308915776 


26.0000 


8.7764 


731 


534361 


390617891 


27.0370 


9.0082 


77 


458329 


310288733 


26.0192 


8.7807 


732 


535824 


392223168 


27.0555 


9.0123 


78 


459684 


311665752 


26.0384 


8.7850 


733 


537289 


393832837 


27.0740 


9.0164 


79 


461041 


313046839 


26.0576 


8.7893 


734 


538756 


395446904 


27.0924 


9.0205 


80 


462400 


314432000 


26.0768 


8.7937 


735 


540225 


397065375 


27.1109 


9.0246 


31 


463761 


315821241 


26.0960 


8.7980 


736 


541696 


398688256 


27.1293 


9.0287 


82 


465124 


317214568 


26.1151 


8.8023 


737 


543169 


400315553 


27.1477 


9.0328 


83 


466489 


318611987 


26.1343 


8.8066 


738 


544644 


401947272 


27.1662 


9.0369 


34 


467856 


320013504 


26.1534 


8.8109 


739 


546121 


403583419 


27.1846 


9.0410 


85 


469225 


321419125 


26.1725 


8.8152 


740 


547600 


405224000 


27.2029 


9.0450 


36 


470596 


322828856 


26.1916 


8.8194 


741 


54908 1 


406869021 


27.2213 


9 0491 


87 


471969 


324242703 


26.2107 


8.8237 


742 


550564 


408518488 


27.2397 


9.0532 


38 


473344 


325660672 


26.2298 


8.8280 


743 


552049 


410172407 


27.2580 


9.0572 


39 


474721 


327082769 


26.2488 


8.8323 


744 


553536 


411830784 


27.2764 


9.0613 


90 


476100 


328509000 


26.2679 


8.8366 


745 


555025 


413493625 


27.2947 


9.0654 


91 


477481 


329939371 


26.2869 


8.8408 


746 


556516 


415160936 


27.3130 


9.0694 


92 


478864 


331373888 


26.3059 


8.8451 


747 


558009 


416832723 


27.3313 


9.0735 


93 


480249 


332812557 


26.3249 


8.8493 


748 


559504 


418508992 


27.3496 


9.0775 


94 


481636 


334255384 


26.3439 


8.8536 


749 


561001 


420189749 


27.3679 


9.0816 


95 


483025 


335702375 


26.3629 


8.8578 


750 


562500 


421875000 


27.3861 


9.0856 


96 


484416 


337153536 


26.3818 


8.8621 


751 


564001 


423564751 


27.4044 


9.0896 


97 


485809 


338608873 


26.4008 


8.8663 


752 


565504 


425259008 


27.4226 


9.0937 


93 


487204 


340068392 


26.4197 


8.8706 


753 


567009 


426957777 


27.4408 


9.0977 


99 


488601 


341532099 


26.4386 


8.8748 


754 


568516 


42866106-1 


27.4591 


9.1017 


00 


490000 


343000000 


26.4575 


8.8790 


755 


570025 


430368875 


27.4773 


9.1057 


01 


491401 


344472101 


26.4764 


8.8833 


756 


571536 


432081216 


27.4955 


9.1098 


02 


492804 


345948408 


26.4953 


8.8875 


757 


573049 


433798093 


27.5136 


9.1138 


03 


494209 


347428927 


26.5141 


8.8917 


758 


574564 


435519512 


27.5318 


9.1178 


?04 


495616 


348913664 


26.5330 


8.8959 


759 


576081 


437245479 


27.5500 


9.1218 



102 



MATHEMATICAL TABLES. 



No 


. Square 


Cube. 


Sq. 
Root. 


Cube 
Root. 


No 


Square 


Cube. 


Sq. 
Root. 


Cube 
Root. 


76C 


) 57760C 


43897600C 


27.5681 


9.1258 


815 


664225 


541343375 


28.5482 


9.3408 


76 


579121 


440711081 


27.5862 


9.1298 


816 


665856 


543338496 


28.5657 


9.3447 


762 


580644 


442450725 


27.6043 


9.1338 


817 


667489 


545338513 


28.5832 


9.3485 


763 


582 1 69 


444194945 


27.6225 


9.1378 


815 


669124 


547343432 


28.6007 


9.3523 


76- 


583696 


44594374^ 


27.6405 


9.1418 


819 


670761 


549353259 


28.6182 


9.3561 


765 


585225 


447697125 


27.6586 


9.1458 


82C 


672400 


55136800C 


28.6356 


9.3599 


766 


586756 


449455096 


27.6767 


9.1498 


821 


674041 


55338766 


28.653 


9.3637 


767 


583289 


451217663 


27.6948 


9.1537 


822 


675684 


555412248 


28.6705 


9.3675 


76e 


589824 


452984832 


27.7128 


9.1577 


823 


677329 


557441767 


28.688C 


9.3713 


769 


591361 


454756609 


27.7308 


9.1617 


824 


678976 


559476224 


28.705^ 


9.3751 


770 


592900 


456533000 


27.7489 


9.1657 


825 


680625 


561515625 


28.7228 


9.3789 


771 


594441 


458314011 


27.7669 


9.1696 


826 


682276 


563559976 


28.7402 


9.3827 


772 


595984 


460099648 


27.7849 


9.1736 


827 


683929 


565609283 


28.7576 


9.3865 


773 


597529 


461889917 


27.8029 


9.1775 


828 


685584 


567663552 


28.775C 


9.3902 


774 


599076 


463684824 


27.8209 


9.1815 


829 


687241 


569722789 


28.792^ 


9.3940 


775 


600625 


465484375 


27.8388 


9.1855 


830 


688900 


571787000 


28.8097 


9.3978 


776 


602176 


46728S576 


27.8568 


9.1894 


831 


690561 


573856191 


28.8271 


9.4016 


777 


603729 


469097433 


27.8747 


9.1933 


832 


692224 


575930368 


28.8444 


9.4053 


778 


605284 


470910952 


27.8927 


9.1973 


833 


693889 


578009537 


28.8617 


9.4091 


779 


606341 


472729139 


27.9106 


9.2012 


834 


695556 


580093704 


28.8791 


9.4129 


780 


- 603400 


474552000 


27.9285 


9.2052 


835 


697225 


582182875 


28.8964 


9.4166 


781 


609961 


476379541 


27.9464 


9.2091 


836 


698896 


584277056 


28.9137 


9.4204 


782 


611524 


478211768 


27.9643 


9.2130 


837 


700569 


586376253 


28.9310 


9.4241 


783 


613039 


430048687 


27.9821 


9.2170 


838 


702244 


588480472 


28.9482 


9.4279 


784 


614656 


431890304 


28.0000 


9.2209 


839 


703921 


590589719 


28.9655 


9.4316 


785 


616225 


483736625 


28.0179 


9.2248 


840 


705600 


592704000 


28.9828 


9.4354 


786 


617796 


485587656 


28.0357 


9.2287 


841 


707281 


594823321 


29.0000 


9.4391 


787 


619369 


487443403 


28.0535 


9.2326 


842 


708964 


596947688 


29.0172 


9.4429 


783 


620944 


439303372 


28.0713 


9.2365 


843 


710649 


599077107 


29.0345 


9.4466 


789 


622521 


491169069 


28.0891 


9.2404 


844 


712336 


601211584 


29.0517 


9.4503 


793 


624100 


493039000 


28.1069 


9.2443 


845 


714025 


603351125 


29.0689 


9.4541 


791 


625631 


494913671 


28.1247 


9.2482 


846 


715716 


605495736 


29.0861 


9.4578 


792 


627264 


496793088 


28.1425 


9.2521 


847 


717409 


607645423 


29.1033 


9.4615 


793 


628349 


498677257 


28.1603 


9.2560 


848 


719104 


609800192 


29.1204 


9.4652 


794 


630436 


500566184 


28. 1 780 


9.2599 


849 


720801 


611960049 


29.1376 


9.4690 


795 


632025 


502459875 


28.1957 


9.2638 


850 


722500 


614125000 


29.1548 


9.4727 


796 


633616 


504358336 


28.2135 


9.2677 


851 


724201 


616295051 


29.1719 


9.4764 


797 


635209 


506261573 


28.2312 


9.2716 


852 


725904 


618470208 


29.1890 


9.4801 


793 


636804 


508169592 


28.2489 


9.2754 


853 


727609 


620650477 


29.2062 


9.4838 


799 


638401 


510082399 


28.2666 


9.2793 


854 


729316 


622835864 


29.2233 


9.4875 


800 


640000 


512000000 


28.2843 


9.2832 


855 


731025 


625026375 


29.2404 


9.4912 


801 


641601 


513922401 


28.3019 


9.2870 


856 


732736 


627222016 


29.2575 


9.4949 


802 


643204 


5 1 5849608 


28.3196 


9.2909 


857 


734449 


629422793 


29.2746 


9.4986 


803 


644809 


517781627 


28.3373 


9.2948 


853 


736164 


631628712 


29.2916 


9.5023 


804 


646416 


519718464 


28.3549 


9.2986 


859 


737881 


633839779 


29.3087 


9.5060 


805 


648025 


521660125 


28.3725 9.3025 


860 


739600 


636056000 


29.3258 


9.5097 


806 


649636 


523606616 


28.3901 9.3063 


861 


741321 


638277381 


29.3428 


9.5134 


807 


651249 


525557943 


28.4077 9.3102 


862 


743044 


640503928 


29.3598 


9.5171 


808 


652864 


527514112 


28.4253:9.3140 


863 


744769 


542735647 


29.3769 


9.5207 


809 


654481 


529475129 


28.4429 9.3179 


864 


746496 


544972544 


29.3939 


9.5244 


810 


656100 


531441000 


28.4605'9.3217 


865 


748225 


547214625 


29.4109 


9.5231 


811 


657721 


533411731 


28.4781 9.3255 


866 


749956 


349461896 


29.4279 


9.5317 


812 


659344 i 


535387328 


28.4956 9.3294 


867 


751689 


d5 171 4363 


29.4449 


9.5354 


813 


6609691 


537367797 


28.5132 9.3332 


868 


753424 653972032! 


29.4618 


9.5391 


814 


662596! 


5393531441 


28.5307i9.3370 


869 


755161 Io56234909|. 


29.4783 9.5427 



SQUARES, CUBES, SQUARE AND CUBE ROOTS. 103 



No. 


Square 


Cube. 


Sq. 

Root. 


Cube 
Roo : . 


No. 
^925 


Square 


Cube. 


Sq. 
Root. 


Cube 
Root. 


870 


75690C 


65850300C 


29.4958 


9.5464 


855625 


791453125 


30.4136 


9.7435 


871 


758641 


66077631 


29.5127 


9.5501 


92C 


857476 


794022776 


30.4302 


9.7470 


872 


760384 


603054845 


29.5296 


9.5537 


92/ 


859329 


796597983 


30.446/ 


9.7505 


873 


762129 


6653386H 


29.5466 


9.5574 


92£ 


861184 


799178752 


30.463 


9.7540 


874 


763876 


66762762^ 


29.5635 


9.5610 


92? 


863041 


801765089 


30.4795 


9.7575 


875 


765625 


669921875 


29.5804 


9.5647 


93C 


864900 


80435700C 


30.495? 


9.7610 


876 


767376 


67222 137<: 


29.5973 


9.5683 


931 


866761 


806954491 


30.5123 


9.7645 


877 


769129 


674526133 


29.6142 


9.5719 


932 


868624 


809557568 


30.528/ 


9.7680 


876 


770884 


676836152 


29.63 1 1 


9.5756 


933 


870489 


812166237 


30.545C 


9.7715 


879 


772641 


679151439 


29.6479 


9.5792 


934 


872356 


814780504 


30.5614 


9.7750 


880 


774400 


68147200C 


29.6648 


9.5828 


935 


874225 


817400375 


30.5778 


9.7785 


881 


776161 


683797841 


29.6816 


9.5865 


936 


876096 


820025856 


30.5941 


9.7819 


882 


777924 


686128969 


29.6985 


9.5901 


937 


877969 


822656953 


30.6105 


9.7854 


883 


779689 


688465387 


29.7153 


9.5937 


938 


879844 


825293672 


30.6268 


9.7889 


884 


781456 


690807104 


29.7321 


9.5973 


939 


881721 


827936019 


30.6431 


9.7924 


885 


783225 


693154125 


29.7489 


9.6010 


940 


883600 


830584000 


30.6594 


9.7959 


836 


784996 


695506456 


29.7658 


9.6046 


941 


885481 


833237621 


30.6757 


9.7993 


887 


786769 


697864103 


29.7825 


9.6082 


942 


887364 


835896888 


30.6920 


9.8028 


833 


788544 


700227072 


29.7993 


9.6118 


943 


889249 


838561807 


30.7083 


9.8063 


889 


790321 


702595369 


29.8161 


9.6154 


944 


891136 


841232384 


30.7246 


9.8097 


890 


792100 


704969000 


29.8329 


9.6190 


945 


393025 


843908625 


30.7409 


9.8132 


89": 


793881 


707347971 


29.8496 


9.6226 


946 


894916 


846590536 


30.7571 


9.8167 


892 


795664 


70973228S 


29.8664 


9.6262 . 


947 


896809 


849278123 


30.7734 


9.8201 


893 


797449 


712121957 


29.8831 


9.6293 


943 


898704 


851971392 


30.7896 


9.8236 


894 


799236 


714516984 


29.8998 


9.6334 


949 


900601 


854670349 


30.8058 


9.8270 


895 


801025 


716917375 


29.9166 


9.6370 


950 


902500 


857375000 


30.8221 


9.8305 


696 


802816 


719323136 


29.9333 


9.6406 


951 


904401 


860085351 


30.8383 


9.8339 


697 


804609 


721734273 


29.9500 


9.6442 


952 


906304 


862801408 


30.8545 


9.8374 


893 


806404 


724150792 


29.9666 


9.6477 


953 


908209 


865523177 


30.8707 


9.8408 


899 


808201 


726572699 


29.9833 


9.6513 


954 


910116 


868250664 


30.8869 


9.8443 


900 


810000 


729000000 


30.0000 


9.6549 


955 


912025 


870983875 


30.9031 


9.8477 


901 


811801 


731432701 


30.0167 


9.6585 


956 913936 


873722816 


30.9192 


9.8511 


002 


813604 


733870808 


30.0333 


9.6620 


957 915849 


876467493 


30.9354 


9.8546 


903 


815409 


736314327 


30.0500 


9.6656 


958 917764 


879217912 


30.9516 


9.8580 


904 


817216 


738763264 


30.0666 


9.6692 


959 919681 


881974079 


30.9677 


9.8614 


905 


819025 


741217625 


30.0832 


9.6727 


960 921600 


884736000 


30.9839 


9.8648 


906 


820836 


743677416 


30.0998 


9.6763 


961 1923521 


887503681 


3 1 .0000 


9.8683 


907 


822649 


746142643 


30.1164 


9.6799 


962 925444 


890277128 


31.0161 


9.8717 


903 


824464 


748613312 


30.1330 


9.6834 


963 


927369 


893056347 


31.0322 


9.8751 


909 


826281 


751089429 


30.1496 


9.6870 


964 


929296 


895841344 


31.0483 


9.8785 


910 


828100 


753571000 


30.1662 


9.6905 


965 


931225 


898632125 


31.0644 


9.8819 


91! 


829921 


756058031 


30.1828 


9.6941 


966 


933156 


901428696 


3 1 .0805 


9.8854 


912 


83 1 744 


758550528 


30.1993 


9.6976 


967 


935089 


90423 1 063 


31.0966 


9.8888 


913 


833569 


761048497 


30.2159 


9.7012 


963 


937024 


907039232 


31.1127 


9.8922 


914 


835396 


763551944 


30.2324 


9.7047 


969 


938961 


909853209 


31.1288 


9.8956 


915 


837225 


766060875 


30.2490 


9.7082 


970 


940900 


912673000 


31.1448 


9.8990 


916 


839056 


768575296 


30.2655 


9.7118 


971 


942841 


915498611 


31.1609 


9.9024 


917 


840889 


771095213 


30.2820 


9.7153 


972 


944784 


918330048 


31.1769 


9.9058 


918 


842724 


773620632 


30.2985 


9.7188 


973 


946729 


921167317 


3 1 . 1 929 


9.9092 


919 


844561 


776151559 


30.3150 


9.7224 


974 


948676 


924010424 


31.2090 


9.9126 


920 


846400 


778688000 


30.3315 


9.7259 


975 


950625 


926859375 


31.2250 


9.9160 


921 


843241 


781229961 


30.3430 


9.7294 


976 


952576, 


929714176 


31.2410 


99194 


922 


850084 


783777443 


30.3645 


9.7329 


977 


954529 


932574833 31.2570 


9.9227 


923 


851929 


786330467 


30.33091 


9.7364 


978 956484! 


935441352131.2730 


9.9261 


924 


853776 


788889024 


30.3974, 


9.7400 


979J 958441; 


938313739131.2890 


9.9295 



104 



MATHEMATICAL TABLES. 



No. 


Square. 


Cube. 


Sq. 
Root. 


Cube 
Root. 

9.9329 


No. 


Square. 


Cube. 


Sq. 
Root. 


Cube 
Root. 


"930 


960400 


941192000 


31.3050 


1035 


1071225 


1108717875 


32.1714 


10.1153 


931 


962361 


944076141 


31.3209 


9.9363 


1036 


1073296 


1111934656 


32.1870 


10.1186 


932 


964324 


946966168 


31.3369 


9.9396 


1037 


1075369 


1115157653 


32.2025 


10.1218 


933 


966289 


949862087 


31.3528 


9.9430 


1038 


1077444 


1118386872 


32.2180 


10.1251 


934 


968256 


952763904 


31.3688 


9.9464 


1039 


1079521 


1121622319 


32.2335 


10.1283 


735 


970225 


955671625 


31.3847 


9.9497 


1040 


1081600 


1124864000 


32.2490 


10.1316 


936 


972196 


958585256 


31.4006 


9.9531 


1041 


1083681 


1128111921 


32.2645 


10 1348 


937 


974169 


961504803 


31.4166 


9.9565 


1042 


1085764 


1131366088 


32.2800 


10.1381 


93S 


976144 


964430272 


31.4325 


9.9598 


1043 


1087849 


1134626507 


32.2955 


10.1413 


939 


978121 


967361569 


31.4484 


9.9632 


1044 


1089936 


1137893184 


32.3110 


10.1446 


990 


980100 


970299000 


31.4643 


9.9666 


1045 


1092025 


1141166125 


32.3265 


10.1478 


991 


982081 


973242271 


31.4802 


9.9699 


1046 


1094116 


1144445336 


32.3419 


10.1510 


992 


984064 


976191488 


31.4960 


9.9733 


1047 


1096209 


1 147730823 


32.3574 


10.1543 


993 


986049 


979146657 


31.5119 


9.9766 


1043 


1098304 


1151022592 


32.3728 


10.1575 


994 


988036 


982107784 


31.5278 


9.9800 


1049 


1100401 


1154320649 


32.3883 


10.1607 


995 


990025 


985074875 


31.5436 


9.9833 


1050 


1 102500 


1157625000 


32.4037 


10.1640 


996 


992016 


988047936 


31.5595 


9.9866 


1051 


1 104601 


1160935651 


32.4191 


10.1672 


997 


994009 


991026973 


31.5753 


9.9900 


1052 


1106704 


1164252608 


32.4345 


10.1704 


998 


996004 


99401 1992 


31.5911 


9.9933 


1053 


1 108809 


1167575877 


32.4500 


10.1736 


999 


998001 


997002999 


31.6070 


9.9967 


1054 


1110916 


1170905464 


32.4654 


10.1769 


1000 


1000000 


1000000000 


31.6228 


10.0000 


1055 


1113025 


1174241375 


32.4808 


10.1801 


1001 


1002001 


1003003001 


31.6386 


10.0033 


1056 


1115136 


1177583616 


32.4962 


10.1833 


1002 


1004004 


1006012008 


31.6544 


10.0067 


1057 


1117249 


1180932193 


32.5115 


10.1865 


1003 


1006009 


1009027027 


31.6702 


10.0100 


1058 


1119364 


1184287112 


32.5269 


10.1897 


1004 


1008016 


1012048064 


31.6860 


10.0133 


1059 


1121481 


1 187648379 


32.5423 


10.1929 


1005 


1010025 


1015075125 


31.7017 


10.0166 


1060 


1123600 


1 191016000 


32.5576 


10.1961 


1006 


1012036 


1018108216 


31.7175 


10.0200 


1061 


1125721 


1 194389981 


32.5730 


10.1993 


1007 


1014049 


1021147343 


31.7333 


10.0233 


1062 


1 127844 


1 197770328 


32.5883 


10.2025 


1008 


1016064 


1024192512 


31.7490 


10.0266 


1063 


1129969 


1201157047 


32.6036 


10.2057 


1009 


1018081 


1027243729 


31.7648 


10.0299 


1064 


1 132096 


1204550144 


32.6190 


10.2089 


1010 


T020100 


1030301000 


31.7805 


10.0332 


1065 


1134225 


1207949625 


32.6343 


10.2121 


1011 


1022121 


1033364331 


31.7962 


10.0365 


1066 


1136356 


1211355496 


32.6497 


10.2153 


1012 


1024144 


1036433728 


31.8119 


10.0398 


1067 


1138489 


1214767763 


32.6650 


10.2185 


1013 


1026169 


1039509197 


31.8277 


10.0431 


1068 


1140624 


1218186432 


32.6303 


10.2217 


1014 


1028196 


1042590744 


31.8434 


10.0465 


1069 


1142761 


1221611509 


32.6956 


10.2249 


1015 


1030225 


1045678375 


31.8591 


10.0498 


1070 


1144900 


1225043000 


32.7109 


10.2281 


1016 


1032256 


1048772096 


31.8748 


10.0531 


1071 


1147041 


1228480911 


32.7261 


10.2313 


1017 


1034289 


1051871913 


31.8904 


10.0563 


1072 


1149184 


1231925248 


32.7414 


10.2345 


1018 


1036324 


1054977832 


31.9061 


10.0596 


1073 


1151329 


1235376017 


32.7567 


10.2376 


1019 


1038361 


1058089859 


31.9218 


10.0629 


1074 


1153476 


1238833224 


32.7719 


10.2408 


1020 


1040400 


1061208000 


31.9374 


10.0662 


1075 


1155625 


1242296875 


32.7872 


10.2440 


1021 


1042441 


1064332261 


31.9531 


10.0695 


1076 


1157776 


1245766976 


32.8024 


10.2472 


1022 


1044484 


1067462648 


31.9687 


10.0728 


1077 


1159929 


1249243533 


32.8177 


10.2503 


1023 


1046529 


1070599167 


31.9844 


10.0761 


1078 


1162084 


1252726552 


32.8329 


10.2535 


1024 


1048576 


1073741824 


32.0000 


10.0794 


1079 


1164241 


1256216039 


32.8481 


10.2567 


1025 


1050625 


1076890625 


32.0156 


10.0826 


1030 


1166400 


1259712000 


32.8634 


10.2599 


1026 


1052676 


1030045576 


32.0312 


10.0859 


1081 


1168561 


12632 I 444 I 


32.8786 


10.2630 


1027 


1054729 


1033206683 


32.0468 


10.0892 


1032 


1170724 


1266723368 


32.8938 


10.2662 


1028 


1056784 


1036373952 


32.0624 


10.0925 


1083 


1172889 


1270238787 


32.9090 


10.2693 


1029 


1058341 


1089547389 


32.0780 


10.0957 


1034 


1175056 


1273760704 


32.9242 


10.2725 


1030 


1060900 


1092727000 


32.0936 


10.0990 


1035 


1177225 


1277289125 


32.9393 


10.2757 


1031 


1062961 


1095912791 


32.1092 


10.1023 


1086 


1179396 


1230824056 


32.9545 


10.2788 


1032 


1065024 


1099104763 


32.1243 


10.1055 


1037 


1181569 


1284365503 


32.9697 


10.2820 


1033 


10IS70S9 


1 102302937 


32.1403 


10.1088 


1038 


1183744 


1287913472 


32.9848 


10.2851 


1034 


1069156 1105507304 


32.1559'10.1121 


1089 


1185921 1291467969 33.0000 10.2883 



SQUARES, CUBES, SQUARE AND CUBE ROOTS. 105 



Square. 



Cube. 



Sq. 
Root. 



Cube 
Root. 



Square. 



Cube. 



Sq. 
Root. 



Cube 
Root. 



1188100 
1190281 
1192464 
1194649 
1196336 

1199025 
1201216 
1203409 
1205604 
1099 1207801 

1210000 
1212201 
1214404 
1216609 
1218816 

1221025 
1223236 
1225449 
1227664 
1229881 

1232100 
1234321 
1236544 
1238769 
1240996 

1243225 
1245456 
12476S9 
1249924 
1252161 

1254400 
1256641 
1258884 
1261129 
1263376 

1265625 
1267876 
1270129 
1272384 
1274641 

1276900 
1279161 
1281424 
1283689 
1285956 



1288225 
1290496 
1292769 
1295044 
1139 1297321 



1295029000 
1298596571 
1302170688 
1305751357 
1309338584 

1312932375 
1316532736 
1320139673 
1323753192 
1327373299 

1331000000 
1334633301 
1338273208 
1341919727 
1345572864 

1349232625 
1352899016 
1356572043 
1360251712 
1363938029 

1367631000 
1371330631 
1375036928 
1378749897 
1382469544 

1386195875 
1389928896 
1393668613 
1397415032 
1401168159 

1404928000 
1408694561 
1412467848 
1416247867 
1420034624 

1423828125 
1427628376 
1431435383 
1435249152 
1439069689 



33.015 
33.0303 
33.0454 
33.0606 
33.0757 

33.0 

33.1059 

33.1210 

33.1361 

33.1512 

33.1662 
33.1813 
33.1964 
33.2114 
33.2264 

33.2415 
33.2566 
33.2716 
33.2866 
33.3017 

33.3167 
33.3317 
33.3467 
33.3617 
33.3766 

33.3916 
33.4066 
33.4215 
33.4365 
33.4515 

33.4664 
33.4813 
33.4963 
33.5112 



10.2914 
10.2946 
10.297: 
10.3009 
10.3040 

10.307 
10.3103 
10.3134 
10.3165 
10.3197 

10.3228 
10.3259 
10.3290 
10.3322 
10 3353 

10.3384 
10.3415 
10.3447 
10.3478 
10.3509 

10.3540 
10.3571 
10.3602 
10.3633 
10.3664 

10.3695 
10.3726 
10.3757 
10.3788 
10.3819 

0.3850 
10.388; 
10.3912 
10.3943 



1442897000 
1446731091 
1450571968 
1454419637 
1458274104 



33.5261 10.3973 

33.5410 10.4004 
33.5559 10.4035 
33.5708 10.4066 
33.5857 10.4097 
33.6006 10.4127 



33.6155 
33.6303 
33.6452 
33.6601 
33.6749 



1462135375 33.6398 
1466003456 33.7046 
1469878353133.7174 
1473760072:33.7342 
1477648619 33.7491 



1299600 1481544000133.7639 
1301881 1485446221,33.7787 
1304164 1489355238 33.7935 
1306449 1493271207|33.8033 
13087361 1497193934:33.8231 



10.4158 
10.4189 
10.4219 
10.4250 
10.4281 

10.4311 

10.4342 
10.4373 
10.4404 
10.4434 

10.4464 
10 4495 
10 4525 
10.4556 
10.4536 



1155 
1156 
1157 
1158 
1159 

1160 
1161 
1162 
1163 



1311025 
1313316 
1315609 
1317904 
1320201 

1322500 
1324801 
1327104 
1329409 
1331716 

1334025 
1336336 
1338649 
1340964 
1343281 

1345600 
1347921 
1350244 
1352569 



1164 


1354896 


1165 


1357225 


1166 


1359556 


1167 


1361889 


1168 


1364224 


1169 


1366561 


1170 


1368900 


1171 


1371241 


1172 


1373584 


1173 


1375929 


1174 


1378276 


1175 


1380625 


1176 


1382976 


1177 


1385329 


1178 


1387684 


1179 


1390041 


1180 


1392400 


1181 


1394761 


1182 


1397124 


1183 


1399489 


1184 


1401856 


1185 


1404225 


1186 


1406596 


1187 


1408969 


1188 


1411344 


1189 


1413721 


1190 


1416100 


1191 


1418481 


1192 


1420864 


1193 


1423249 


1194 


1425636 


1195 


1428025 


1196 


1430416 


1197 


1432809 


1198 


1435204 


1199 


1437601 



1501123625 
1505060136 
1509003523 
1512953792 
1516910949 

1520875000 
152434595 
1528323808 
1532808577 
1536800264 

1540798875 
1544804416 
1548816893 
1552836312 
1556862679 

1560896000 
156493628 
1568983523 
1573037747 
1577098944 

1531167125 
1585242296 
1589324463 
1593413632 
1597509809 

1601613000 
1605723211 
1609840448 
1613964717 
1618096024 

1622234375 
1626379776 
1630532233 
1634691752 
1638858339 

1643032000 
1647212741 
1651400568 
1655595487 
1659797504 



33.8378 
33.8526 
33.8674 
33.8321 
33.8969 

33.9116 

33.9264 

33.941 

33.9559 

33.9706 



10.4617 
10.4647 
10.4678 
10.4708 
10.4739 

10.4769 
10.4799 
10.4830 
10.4860 
10.4890 



1664006625 
1668222856 
1672446203 
1676676672 
1680914269 

1685159000 
1689410871 
1693669838 
1697936057 
702209384 

1706489875 
710777536 
1715072373 
1719374392 
723683599 



33.9853 10.492! 



34.0147 
34.0294 
34.0441 

34.0588 
34.0735 
34.0881 
34.1028 
34.1174 

34.132 
34.1467 
34.1614 
34.1760 
34.1906 

34.2053 
34.2199 
34.2345 
34.2491 
34.2637 

34.2783 
34.2929 
34.3074 
34.3220 
34.3366 

34.3511 

34.3657 
34.3802 
34.3948 
34.4093 



34.4233 
34.4384 
34.4529 
34.4674 
34.4819 

34.4964 
34.5109 

34.5254 
34.5393 



34.5543 10.6088 



34.5688 
34.5832 
34.5977 
34.6121 
34.6266 



10.4981 
10.5011 
10.5042 

10.5072 
10.5102 
10.5132 
10.5162 
10.5192 

10.5223 
10.5253 
10.5283 
10.5313 
10.5343 

10.5373 
10.5403 
10.5433 
10.5463 
10.5493 

10.5523 
10.5553 
10.5583 
10.5612 
10.5642 

10.5672 
10.5702 
10.5732 
10.5762 
10.5791 

10.5821 
10.5851 
10.5881 
10.5910 
10.5940 

10.5970 
10.6000 
10.6029 
10.6059 



10.6118 
10.6148 
10.6177 
10.6207 
10.6235 



106 



MATHEMATICAL TABLES. 



. Square. 



Cube. 



Sq. 
Root. 



Cube 
Root. 


No. 


Square. 


10.6266 


1255 


1575025 


10.6295 


1256 


1577536 


10.6325 


1257 


1580049 


10.6354 


1258 


1582564 


10.6384 


1259 


1585081 


10.6413 


1260 


1587600 


10.6443 


1261 


1590121 


10.5472 


1262 


1592644 


10.6501 


1263 


1595169 


10.6530 


1264 


1597696 


10.6560 


1265 


1600225 


10.6590 


1266 


1602756 


10.6619 


1267 


1605289 


10.6648 


1268 


1607824 


10.6678 


1269 


1610361 


10.6707 


1270 


1612900 


10.6736 


1271 


1615441 


10.6765 


1272 


1617984 


10.6795 


1273 


1620529 


10.6324 


1274 


1623076 


10.6353 


1275 


1625625 


10.6382 


1276 


1628176 


10.6911 


1277 


1630729 


10.6940 


1278 


1633284 


10.6970 


1279 


1635841 


10.6999 


1280 


1638400 


10.7028 


1281 


1640961 


10.7057 


1232 


1643524 


30.7086 


1283 


1646089 


10.7115 


1284 


1648656 


10.7144 


1285 


1651225 


10.7173 


1286 


1653796 


10.7202 


1287 


1656369 


10.7231 


1288 


1658944 


10.7260 


1289 


1661521 


10.7289 


1290 


1664100 


10.7318 


1291 


1666681 


10.7347 


1292 


1669264 


10.7376 


1293 


1671849 


10.7405 


1294 


1674436 


10.7434 


1295 


1677025 


10.7463 


1296 


1679616 


10.7491 


1297 


1632209 


10.7520 


1298 


1684804 


10.7549 


1299 


1687401 


10.7578 


1300 


1690000 


10.7607 


1301 


169260! 


10.7635 


1302 


1695204 


10.7664 


1303 


1697809 


10.7693 


1304 


1700416 


10.7722 


1305 


1703025 


10.7750 


1306 


1705636 


10.7779 


1307 


1703249 


10.7803 


1308 


1710364 


10.7837 


1309 


1713481 



Cube. 



Sq. 
Root 



Cube 
Root. 



1440000 
1442401 
1444304 
1447209 
1449616 

1452025 
1454436 
1455349 
1459264 
1461 5! 

1451100 

14555 21 
1 46394 < 
1471369 
1473796 

1476225 
1478656 
1431039 
1433524 
1485961 

1438400 
1490341 
1493234 
1495729 
1493176 

1500625 
1503076 
1505529 
1507984 
1510441 

1512900 
1515361 
1517824 
1520289 
1522756 

1525225 
1527696 
1530169 
1532644 
153512 

1537690 
1540031 
1542564 
1545049 
1547536 

1550025 
1552516 
155500? 
1557504 
1560301 

1562503 

155503 

1557504 

1570009 

1572516 



1 728000000 
1732323601 
1736654403 
1740992427 
1745337664 

1749690125 
1754049316 
1758416743 
1762790912 
1767172329 

1771561000 
177595693! 
1780360128 
1734770597 
1789133344 

1793613375 
1793045696 
1802435313 
806932232 



34.6410 
34.6554 
34.6699 
34.6343 
34.6987 

34.7131 

34.7275 
34.7419 
34.7563 
34.7707 

34.7851 
34.7994 
34.8138 
34.8281 

34.8425 

34.8569 
34.8712 

34.8355 
34.8999 



1811336459 34.9142 



1815343000 
1820316361 
1824793043 
1829276567 
1833767424 

1838265625 
1342771176 
1847234033 
1851S04352 
1856331939 

1860867000 
1865409391 
1869959163 
1874516337 
1879030904 

1883652875 
1838232256 
1892819053 
1897413272 
1902014919 

1906624000 
1911240521 
1915864488 
1920495907 
1925134784 

1929781125 
1934434936 
1939096223 
1943764992 
1948441249 

1953125000 
1957016251 
1962515008 
1967221277 
1971935064 



34.9235 
34.9423 
34.9571 
34.9714 
34.9857 

35.0000 
35.0143 
35.0236 
35.0428 
35.0571 

35.0714 
35.0856 
35.0999 
35.1141 
35.1233 

35.1426 
35.1568 
35.1710 
35.1852 
35.1994 

35.2136 
35.2278 
35.2420 
35.2562 
35.2704 

35.2846 
35.2987 
35.3129 
35.3270 
35.3412 

35.3553 
35.3695 
35.3836 
35.3977 
35.4119 



1976656375 
1981385216 
1986121593 
1990865512 
1995616979 

2000376000 
2005142581 
2009916728 
2014698447 
2019487744 

2024284625 
2029089096 
2033901163 
2038720832 
2043548109 

2048383000 
205322551 1 
2058075648 
2062933417 
2067798824 

2072671875 
2077552576 
2082440933 
2087336952 
2092240639 

2097152000 
210207104 
2106997768 
2111932187 
2116874304 

2121824125 
2126781656 
2131746903 
2136719872 
2141700569 



35.4260 
35.4401 
35.4542 
35.4683 
35.4824 

35.4965 
35.5106 
35.5246 
35.5387 
35.5528 

35.5668 
35.5809 
35.5949 
35.6090 
35.6230 

35.6371 
35.6511 
35.6651 
35.6791 
35.6931 

35.7071 

35.7211 
35.7351 
35.7491 
35.7631 

35.7771 
35.7911 
35.8050 
35.8190 
35.8329 

35.8469 
35.8608 
35.8748 
35.8887 
35.9026 



2146689000 35.9166 
2151685171 35.9305 
2156639038 35.9444 
2161700757 35.9583 
2166720184 35.9722 



2171747375 
2176782336 
2181825073 
2186875592 
2191933399 

2197000000 
2-02073901 
2207155603 
2212245127 
2217342464 

2222447625 
2227560616 
2232681443 
2237810112 
2242946629 



35.9861 
36.0000 
36.0139 
36.0278 
36.0416 

36.0555 
36.0694 
36.0332 
36.0971 
36.1109 

36.1243 
36.1386 
36.1525 
36.1663 
36.1801 



10.7865 
10.7894 
10.7922 
10.7951 
10.7980 

10.8008 
10.8037 
10.8065 
10.8094 
10.8122 

10.8151 

10.8179 
10.8208 
10.8236 
10.8265 

10.8293 
10.8322 
10.8350 
10.8378 
10.8407 

10.8435 
10.8463 
10.8492 
10.8520 
10.8548 

10.8577 
10.8605 
10.3633 
10.8661 
10.8690 

10.8718 
10.8746 
10.8774 
10.8802 
10.8831 

10.8859 
10.8887 
10.8915 
10.8943 
10.8971 

10.8999 
10.9027 
10.9055 
10.9083 
10.9111 

10.9139 
10.9167 
10.9195 
10.9223 
10.9251 

10.9279 
10.9307 
10.9335 
10.9363 
10.9391 



SQUARES, CUBES, SQUARE AND CUBE ROOTS. 107 



Square, 



1716100 
1718721 
1721344 
1723969 
1726596 

1729225 
1731856 
1734489 
1737124 
1739761 

1742400 
174504! 
1747684 
1750329 
1752976 

1755625 
1753276 
1760929 
1763584 
1766241 

1768900 
1771561 
1774224 
1776889 
1779556 

1782225 
1784396 
1787569 
1790244 
1792921 

1795600 
1798281 
1800964 
1803649 
1806336 

1809025 
1811716 
1814409 
1817104 
1819801 

1322500 
1825201 
1327904 
1330609 
1833316 

1836025 
1338736 
1841449 
1844164 
184688 

1849600 
1852321 
1855044 
1857769 
1860496 



Cube. 



2248091000 
2253243231 
2258403328 
2263571297 
2268747144 

2273930875 
2279122496 
2284322013 
2289529432 
2294744759 

2299968000 
2305199161 
2310438248 
2315685267 
2320940224 

2326203125 
2331473976 
2336752783 
2342039552 
2347334289 

2352637000 
2357947691 
2363266368 
2368593037 
2373927704 

2379270375 
2384621056 
2389979753 
2395346472 
2400721219 

2406104000 
2411494821 
2416893688 
2422300607 
2427715584 



2433138625 36.6742 
2438569736 36.6879 
2444003923 36.7015 
2449456192 36.7151 
2454911549 36.7287 



Sq. 
Root. 



36.1939 
36.2077 
36.2215 
36.2353 
36.2491 

36.2629 
36.2767 
36.2905 
36.3043 
36.31 

36.3318 
36.3456 
36.3593 
36.3731 
36.3868 

36.4005 
36.4143 
36.4280 
36.4417 
36.4555 

36.4692 
36.4829 
36.4966 
36.5103 
36.5240 

36.5377 

36.5513 
36.5650 
36.5787 
36.5923 

36.6060 
36.6197 
36.6333 
36.6469 

36.6606 



Cube 
Root. 



1460375000 
2465846551 
2471326208 
2476313977 
24323G9864 

2487813875 
2493326016 
2498846293 
2504374712 
2509911279 

2515456000 
2521008881 
2.526569928 
2532139147 
2537716544 



36.7423 
36.7560 
36.7696 
36.7831 
36.7967 

36.8103 
36.8239 
36.8375 
36.8511 
36.8646 

36.8782 
36.8917 
36.905: 
36.9188 
36.9324 



10.9418 
10.9446 
10.9474 
10.9502 
10.9530 

10.9557 
10.9585 
10.9613 
10.9640 
10.9668 

10.9696 
10.9724 
10.9752 
10.9779 
10. 

10.9834 
10.9862 
10.9890 
10.9917 
0.9945 

0.9972 
1 1 .0000 
1 1 .0028 
1 1 .0055 
1 1 .0083 

11.0110 

1.0138 
11.0165 
11.0193 
1 1 .0220 

1 .0247 
11.0275 
1 1 .0302 
1 1 .0330 
1 1 .0357 

1 1 .0384 
11.0412 
1 1 .0439 
1 1 .0466 
11.0494 

11.0521 
1 1 .0548 
1 1 .0575 
1 1 .0603 
1 1 .0630 

11.0657 
11.0684 
11.0712 
1 1 .0739 
1 1 .0766 

1 1 .0793 
1 1 .0820 
1 1 .0847 
1 1 .0875 
i 1 .0902 



Square. 



1365 
1366 
1367 
1368 
1369 

1370 
137 
1372 
1373 
1374 

1375 
1376 
1377 
1378 
1379 

1380 
1381 

1382 
1383 
1384 

1385 
1386 
1387 
1388 
1389 

1390 
139 

1392 
1393 
1394 

1395 

1396 
1397 
1398 
1399 

1400 
1401 

1402 
1403 
1404 

1405 
1406 

!407 


1409 

1410 
1411 
1412 

1413 
1414 

1415 
1416 
1417 

1413 
1419 



1863225 
1865956 
1868689 
1871424 
1874161 

1876900 
1879641 

1882384 
1885129 
1887876 



Cube. 



Sq. 
Root 



2543302125 
2548895896 
2554497863 
2560108032 
2565726409 

2571353000 
257698781 1 
2582630848 
2588282117 
2593941624 



1890625 2599609375 
1893376 2605285376 
1896129 2610969633 
1898884 2616662152 
1901641 2622362939 



1904400 
1907161 
1909924 
1912689 
1915456 

1918225 
1920996 
1923769 
1926544 
192932 

1932100 
1934881 
1937664 
1940449 
1943236 

1946025 
1948816 
1951609 
1954404 
1957201 

1960000 
1962801 
1965604 
1968409 
1971216 

1974025 
1976836 
1979649 
1982464 
1985281 

1988100 
1990921 
1993744 
1996569 
1999396 

2002225 
2005056 
2007889 
2010724 
2013561 



2628072000 
2633789341 
2639514968 
2645248887 
2650991104 

2656741625 
2662500456 
2668267603 
2674043072 
2679326869 

2685619000 
269141947 
2697228288 
2703045457 
2708870984 

2714704875 
2720547136 
2726397773 
2732256792 
2738124199 

2744000000 
274988420 
2755776808 
2761677827 
2767587264 

2773505125 
2779431416 
2785366143 
2791309312 
2797260929 

2803221000 
2809189531 
2815166528 
2821151997 
2827145944 

2833148375 
2839159296 
2845178713 
2851206632 
2857243059 



36.9459 
36.9594 
36.9730 
36.9865 
37.0000 

37.0135 
37.0270 
37.0405 
37.0540 
37.0675 

37.0810 
37.0945 
37.1080 
37.1214 
37.1349 

37.1484 
37.1618 
37.1753 
37.1887 
37.202 

37.2156 
37.2290 
37.2424 
37.2559 
37.2693 

37.2827 
37.2961 
37.3095 
37.3229 
37.3363 

37.3497 
37.3631 
37.3765 
37.3898 
37.4032 

37.4166 
37.4299 
37.4433 
37.4566 
37.4700 

37.4833 
37.4967 
37.5100 
37.5233 
37.5366 

37.5500 
37.5633 
37.5766 
37.5899 
37.6032 

37.6165 
37.6298 
37.6431 
37.6563 
37.6696 



Cube 
Root. 

1T0929 
1 1 .0956 
1 1 .0983 
11.1010 
11.1037 

11.1064 
11.1091 
11.1118 
11.1145 
11.1172 

11.1199 
11.1226 
11.1253 
11.1280 
11.1307 

H.1334 
11.1361 
11.1387 
11.1414 
11.1441 

11.1468 
11.1495 
11.1522 
11.1548 
11.1575 

11.1602 
11.1629 
11.1655 
11.1682 
11.1709 

11.1736 

11.1762 
11.1789 
11.1816 
11.1842 

11.1869 
11.1896 
11.1922 
11.1949 
11.1975 

1 1 .2002 
1 1 .2028 
1 1 .2055 
1 1 .2082 
11.2108 

11.2135 
11.2161 
11.2188 
11.2214 
11.2240 

11.2267 
11.2293 
11.2320 
1 1 2346 
1 1 2373 



108 



MATHEMATICAL TABLES. 



. Square. 

2016400 
2019241 
2022034 
2024929 
2027776 

2030625 
2033476 
2036329 
2039184 
2042041 

2044900 
2047761 
2050624 
2053439 
2056356 

2059225 
2062096 
2064969 
2067844 
2070721 

2073600 
2076431 
2079364 
2082249 
2085136 

2033025 
2090916 
2093309 
2096704 
2099601 

2102500 
2105401 
2103304 
2111209 
2114116 

2117025 
2119936 
2122349 
2125764 
212868 

2131600 
2134521 
2137444 
2140369 
2143296 

2146225 
2149156 
2152089 
2155024 
2157961 

2160900 
2163841 
2166784 
2169779 
2172676 



Cube. 



2363288000 
2869341461 
2875403448 
2881473967 
2887553024 

2893640625 
2899736776 
2905841483 
2911954752 
2918076589 

2924207000 
2930345991 
2936493568 
2942649737 
2948814504 

2954987875 
2961169856 
2967360453 
2973559672 
2979767519 

2985984000 
2992209121 
2993442888 
3004685307 
3010936384 

3017196125 
3023464536 
3029741623 
3036027392 
3042321849 

3048625000 
3054936851 
3061257403 
3067586677 
3073924664 

3030271375 
3086626816 
3092990993 
3099363912 
3105745579 

3112136000 
31 18535 "" 

3124943128 
3131359847 
3137785344 

3144219625 
3150662696 
3157114563 
3163575232 
3170044709 

3176523000 
3183010111 
3189506048 
3196010817 
3202524424 



Sq. 
Root. 



37.6829 
37.6962 
37.7094 
37.7227 
37.7359 

37.7492 
37.7624 
37.7757 
37.7889 
37.8021 

37.8153 
37.8286 
37.8418 
37.8550 
37.8682 

37.8814 
37.8946 
37.9078 
37.9210 
37.9342 

37.9473 
37.9605 
37.9737 
37.9368 
38.0000 

38.0132 
38.0263 
38.0395 
38.0526 
38.0657 

38.0789 
38.0920 
38.1051 
38.1182 
38.1314 

38.1445 
38.1576 
38.1707 
38.1838 
38.1969 

38.2099 
38.2230 
38.236 
38.2492 
33.2623 

38.2753 
38.2884 
38.3014 
38.3145 
33.3275 

383406 
383536 
383667 
38.3797 
38.3927 



Cube 
Root. 



1 1 .2399 
1 1 .2425 
1 1 .2452 
1 1 .2478 
11.2505 

11.2531 
1 1 .2557 
11.2583 
11.2610 
11.2636 

11.2662 
11.2639 
11.2715 
1 1 .2741 
11.2767 

11.2793 
11.2820 
11.2846 
1 1 .2872 

ii.r" 

1 1 .2924 
11.2950 
1 1 .2977 
11.3003 
11.3029 

11.3055 
11.3081 
11.3107 
11.3133 
11.3159 

11.3185 
11.3211 
1 1 .3237 
1 1 .3263 
1 1 .3289 

11.3315 
1 1 .3341 
1 1 .3367 
1 1 .3393 
11.3419 

11.3445 
11.3471 
1 1 .3496 
1 1 .3522 
11.3548 

1 1 .3574 
1 1 .3600 
1 1 .3626 
1 1 .3652 
11.3677 

1 1 .3703 
1 1 .3729 
11.3755 
1 1 .3780 
1 1 .3806 



1475 
1476 
1477 
1478 
1479 

1480 
148 
1432 
1483 
1484 

1485 
1486 
1487 
1488 
1489 

1490 
1491 

1492 
1493 
1494 

1495 
1496 
1497 
1498 

1499 

1500 
150 
1502 
1503 
1504 

1505 
1506 
1507 

1503 
1509 

1510 
1511 
1512 
1513 
1514 

1515 
1516 
1517 
1518 

1519 

1520 
1521 
1522 
1523 
1524 

1525 
1526 
1527 
1528 
1529 



Square. 



2175625 
2178576 
2181529 
2184484 
2187441 

2190400 
2193361 
2196324 
2199289 
2202256 

2205225 
2208196 
2211169 
2214144 
221712 

2220100 
2223081 
2226064 
2229049 
2232036 

2235025 
2238016 
2241009 
2244004 
2247001 

2250000 
2253001 
2256004 
2259009 
2262016 

2265025 
2268036 
2271049 
2274064 
2277081 

2280100 
2283121 
2286144 
2239169 
2292196 

2295225 
2298256 
2301289 
2304324 
2307361 

2310400 
2313441 
2316434 
2319529 
2322576 

2325625 
2328676 
2331729 
2334784 
2337841 



Cube. 



3209046875 
3215578176 
3222118333 
3228667352 
3235225239 

3241792000 
3248367641 
3254952168 
3261545587 
3268147904 

3274759125 
3281379256 
3288008303 
3294646272 
3301293169 

3307949000 
3314613771 
3321287488 
3327970157 
3334661784 

3341362375 
3348071936 
3354790473 
3361517992 
3368254499 

3375000000 
3381754501 
3388518008 
3395290527 
3402072064 

3408862625 
3415662216 
3422470843 
3429288512 
3436115229 

3442951000 
3449795831 
3456649728 
3463512697 
3470384744 

3477265875 
3484156096 
3491055413 
3497963832 
3504881359 

3511808000 
3518743761 
3525688648 
3532642667 
3539605824 

3546578125 
3553559576 
3560550183 
3567549952 
3574558889 



Sq. 
Root. 



38.4057 
38.4187 
38.4318 
38.4448 
38.4578 

38.4708 
38.4838 
38.4968 
38.5097 
38.5227 

38.5357 
38.5487 
38.5616 
38.5746 
38.5876 

38.6005 
38.6135 
38.6264 
38.6394 
38.6523 

38.6652 
38.6782 
38.691 1 
38.7040 
38.7169 

38.7298 
38.7427 
38.7556 
38.7685 
38.7814 

38.7943 
38.8072 
38.8201 
38.8330 
38.8458 

38.8587 
38.8716 
38.8844 
38.8973 
38.9102 

38.9230 
38.9358 
38.9487 
38.9615 
38.9744 

38.9872 
39.0000 
39.0128 
39.0256 
39.0384 

39.0512 
39.0640 
39.0768 
39.0896 
39.1024 



Cube 
Root. 



1 1 .3832 
1 1 .3858 
1 1 3883 
11.3909 
11.3935 

11.3960 
11.3986 
11.4012 
11.4037 
11.4063 

11.4089 
11.4114 
11.4140 
11.4165 
11.4191 

11.4216 
1 1 .4242 
1 1 .4268 
1 1 .4293 
11.4319 

11.4344 
11.4370 
11.4395 
11.4421 
lt.4446 

11.4471 
11.4497 
11.4522 
1 1 .4548 
1 1,4573 

11.4598 
11.4624 
11.4649 
11.4675 
11.4700 

11.4725 
11.4751 
11.4776 
11.4801 
1.4826 

11.4852 
11.4877 
1 1 .4902 
11.4927 
11.4953 

1 1 .4978 
11.5003 
11.5028 
11.5054 
11.5079 

11.5104 
11.5129 
11.5154 
11.5179 
11.5204 



SQUARES, CUBES, SQUARE AND CUBE ROOTS. 109 



Square. 



2340900 
2343961 
2347024 
2350089 
2353156 

2356225 
2359296 
2362369 
2365444 
2368521 

2371600 
2374681 
2377764 
2380849 
2383936 

2387025 
23901 16 
2393209 
2396304 
2399401 

2402500 
2405601 
2408704 
2411809 
2414916 

2418025 
2421136 
2424249 
2427364 
2430481 

2433600 
2436721 
2439844 
2442969 
2446096 



Cube. 



3581577000 
3588604291 
3595640768 
3602686437 
3609741304 

3616805375 
3623878656 
3630%! 153 
3638052872 
3645153819 

3652264000 
365938342 
3666512088 
3673650007 
3680797184 

3687953625 
3695119336 
3702294323 
3709478592 
3716672149 

3723875000 
3731087151 
3738308608 
3745539377 
3752779464 

3760028875 
3767287616 
3774555693 
3781833112 
3789119879 

3796416000 
3803721481 
381 1036328 
3818360547 
3825694144 



Sq. 
Root. 



39.1152 
39.1280 
39.1408 
39.1535 
39.1663 

39.1791 
39.1918 
39.2046 
39.2173 
39.2301 

39.2428 
39.2556 
39.2683 
39.2810 
39.2938 

39.3065 
39.3192 
39.3319 
39.3446 
39.3573 

39.3700 

39.3827 
39.3954 
39.4081 
39.4208 

39.4335 
39.4462 
39.4583 
39.4715 
39.4842 

39.4968 
39.5095 
39.5221 
39.5348 
39.5474 



Cube 
Root. 



1 1 .5230 
11.5255 
11.5280 
1 1 .5305 
1 1 .5330 

11.5355 
1 1 .5380 
1 1 .5405 
1 1 .5430 
1 1 .5455 

11.5480 
1 1 .5505 
11.5530 
11.5555 
11.5580 

1 1 .5605 
11.5630 
11.5655 
1 1 .5680 
11.5705 

1 1 .5729 
11.5754 
1 1 .5779 
1 1 .5804 
1 1 .5829 

1 1 .5854 
1 1 .5879 
1 1 .5903 
1 1 .5928 
11.5953 

11.5978 
1 1 .6003 
1 1 .6027 
1 1 .6052 
11.6077 



1565 
1566 
1567 

1568 
1569 

1570 
1571 
1572 
1573 
1574 

1575 
1576 
1577 
1578 
1579 

1580 
1581 
1582 
1583 
1584 

1585 
1586 
1587 
1583 
1539 

1590 
159! 
1592 
1593 
1594 

1595 
1596 
1597 
1593 
1599 



Square. 



2449225 
2452356 
2455489 
2458624 
2461761 

2464900 
246804 
2471184 
2474329 
2477476 

2480625 
24837-76 
2486929 
2490084 
2493241 

2496400 
2499561 
2502724 
2505889 
2509056 

2512225 
2515396 
2518569 
2521744 
2524921 

2528100 
2531281 
2534464 
2537649 
2540836 

2544025 
2547216 
2550409 
2553604 
2556801 



Cube. 



3833037125 
3840389496 
3847751263 
3855123432 
3862503009 

3869893000 
38772924! 1 
3884701248 
3892119517 
3899547224 

3906984375 
3914430976 
3921887033 
3929352552 
3936827539 

3944312000 
1951805941 

3959309368 
3966822287 
3974344704 

3981876625 
3989418056 
3996969003 
4004529472 
4012099469 

4019679000 
4027268071 
4034S66683 
4042474857 
4050092584 

4057719875 
4065356736 
4073003173 
4080659192 
4088324799 



2560000 4096000000 40.0000 1 1 .6961 



Sq. 
Root. 



39.5601 
39.5727 
39.5854 
39.5980 
39.6106 

39.6232 
39.6358 
39.6485 
39.661 1 
39.6737 

39.6863 
39.6989 
39.7115 
39.7240 
39.7366 

39.7492 
39.7618 
39.7744 
39.7869 
39.7995 

39.8121 
39.8246 
39.8372 
39.8497 
39.8623 

39.8748 
39.8873 
39.8999 
39.9124 
39.9249 

39.9375 
39.9500 
39.9625 
39.9750 
39.9875 



Cube 
Root. 



11.6102 
11.6126 
11.6151 
11.6176 
1 1 .6200 

1 1 .6225 
1 1 .6250 
1 1 .6274 
1 1 .6299 
11.6324 

1 1 .6348 
1 1 .6373 
1 1 .6398 
1 1 .6422 
1 1 .6447 

11.6471 
1 1 .6496 
1 1 .6520 
1 1 .6545 
1 1 .6570 

11.6594 
11.6619 
1 1 .6643 
11.6668 
1 1 .6692 

11.6717 

1 1 .6741 
1 1 .6765 
1 1 .6790 
11.6814 

1 1 .6839 
1 1 .6863 
1 1 .6888 
11.6912 
1 1 .6936 



SQUARES AND CUBES OF DECIMALS. 



No. 


Square 


Cube. 


No. 


Square 


Cube. 


No. 


Square. 


Cube. 


1 


.01 


.001 


01 


.0001 


.000 001 


.001 


.00 00 01 


.000 000 001 


7 


.04 


.008 


02 


.0004 


.000 008 


.002 


.00 00 04 


.000 000 008 


3 


.09 


.027 


03 


.0009 


.000 027 


.003 


.00 00 09 


.000 000 027 


4 


.16 


.064 


04 


.0016 


.000 064 


.004 


.00 00 16 


.000 000 064 


5 


.25 


.125 


05 


.0025 


.000 125 


.005 


.00 00 25 


.000 000 125 


6 


.36 


.216 


06 


.0036 


.000 216 


.006 


.00 00 36 


.000 000 216 


7 


.49 


.343 


07 


.0049 


.000 343 


.007 


.00 00 49 


.000 000 343 


8 


.64 


.512 


08 


.0064 


.000 512 


.008 


.00 00 64 


.000 000 512 


9 


.81 


.729 


09 


.0081 


.000 729 


.009 


.00 00 81 


.000 000 729 


1 


1.00 


1.000 


10 


.0100 


.001 000 


.010 


.00 01 00 


.000 001 000 


1.2 


1.44 


1.728 


.12 


.0144 


.001 728 


.012 


.00 01 44 


.000 001 728 



Note that the square has twice as many decimal places, and the cube 
three times as many decimal places, as the root. 



110 



MATHEMATICAL TABLES. 



FIFTH ROOTS AND FIFTH POWERS. 

(Abridged from Trautwine.) 



u 




u 




u 


u 




u 




0+» 




Z ■:' 




O-ti 




z - 




°-s 






Power. 


- ■■* 


Power. 


. O 

o o 


Power. 


. 
z z 


Power. 


. o 
o o 


Power. 


£f§ 




£& 




£Ph 




■',- 




z* 




.10 


.000010 


3.7 


693.440 


9.8 


90392 


2!. 8 


4923597 


40 


102400000 


.15 


.000075 


3.8 


792.352 


9.9 


95099 


22.0 


5153632 


41 


115856201 


.20 


.000320 


3.9 


902.242 


10.0 


100000 


2.2.2 


5392186 


42 


130691232 


.25 


.000977 


4.0 


1024.00 


10.2 


110408 


12, i 


5639493 


43 


. 147003443 


.30 


.002430 


4.1 


1158.56 


10.4 


121665 


12.6 


5895793 


44 


164916224 


.35 


.005252 


4.2 


1306.91 


10.6 


133823 


11.?. 


6161327 


45 


184523125 


.40 


.010240 


4.3 


1470.08 


10.8 


146933 


2; i 


6436343 


46 


205962976 


.45 


.018453 


4.4 


1649.16 


11.0 


161051 


-' 


6721093 


47 


229345007 


.50 


.031250 


4.5 


1845.28 


11.2 


176234 


l-.A 


7015834 


48 


254803963 


.55 


.050328 


4.6 


2059.63 


11.4 


192541 


-. 


7320825 


49 


282475249 


.60 


.077760 


4.7 


2293.45 


11.6 


210034 


:3 


7636332 


50 


312500000 


.65 


.116029 


4.8 


2548.04 


11.8 


228776 


2-: C 


7962624 


51 


345025251 


.70 


.168070 


4.9 


2824.75 


12.0 


248832 


24.2 


8299976 


52 


380204032 


.75 


.237305 


5.0 


3125.00 


12.2 


27027 1 


24.-: 


8648666 


53 


418195493 


.80 


.327680 


5.1 


3450.25 


12.4 


293163 


24.6 


9008978 


54 


459165024 


.85 


.443705 


5.2 


3802.04 


12.6 


317580 


24 


9381200 


55 


503234375 


.90 


.590490 


5.3 


4181.95 


12.8 


343597 


25.0 


9765625 


56 


550731776 


.95 


.773781 


5.4 


4591.65 


13.0 


371293 


2 5.2 


10162550 


57 


601692057 


1.00 


1 .00000 


5.5 


5032.84 


13.2 


400746 


5. 


10572278 


58 


656356768 


1.05 


1.27628 


5.6 


5507.32 


13.4 


432040 


: 


10995116 


-59 


714924299 


1.10 


1.61051 


5.7 


6016.92 


13.6 


465259 


■: P 


11431377 


60 


777600000 


1.15 


2.01135 


5.3 


6563.57 


13.8 


500490 




11881376 


61 


844596301 


1.20 


2.48832 


5.9 


7149.24 


14.0 


537824 


:1.2 


12345437 


62 


916132332 


1.25 


3.05176 


6.0 


7776.00 


14.2 


577353 


:•'.■.-: 


12823886 


63 


992436543 


1.30 


3.71293 


6.1 


8445.96 


14.4 


619174 


22,2 


13317055 


64 


1073741824 


1.35 


4.48403 


6.2 


9161.33 


14.6 


663383 


26.8 


13825281 


65 


1160290625 


1.40 


5.37824 


6.3 


9924.37 


14.8 


710032 


a c. 


14348907 


66 


1252332576 


1.45 


6.4097 3 


6.4 


10737 


15.0 


759375 


'7.2 


14888280 


67 


1350125107 


1.50 


7.59375 


6.5 


11603 


15.2 


811368 


. - 


15443752 


68 


1453933568 


1.55 


8.94661 


6.6 


12523 


15.4 


866171 


27.6 


16015681 


69 


1564031349 


1.60 


10.4858 


o.7 


13501 


15.6 


923896 


2 7.8 


16604430 


70 


1680700000 


1.65 


12.2298 


6.8 


14539 


15.8 


934658 


28.0 


17210368 


71 


1804229351 


1.70 


14.1986 




15640 


16.0 


1048576 


_J _ 


17833868 


72 


1934917632 


1.75 


16.4131 


2 


16807 


16.2 


1115771 




18475309 


73 


2073071593 


1.80 


18.8957 


7.1 


18042 


16.4 


1186367 


L 3/; 


19135075 


74 


2219006624 


1.85 


21.6700 


7.2 


19349 


16.6 


1260493 




19813557 


75 


2373046875 


1.90 


24.7610 


7.3 


20731 


16.8 


1338278 


29.0 


20511149 


76 


2535525376 


1.95 


28.1951 


7 4 


22190 


17.0 


1419357 


29 2 


21228253 


77 


2706784157 


2.00 


32.0000 


7.5 


23730 


17.2 


1505366 


1~:, 


21965275 


78 


2887174368 


2.05 


36.2051 


7.6 


25355 


17.4 


1 594947 


2 


22722628 


79 


3077056399 


2.10 


40.8410 


7.7 


27068 


17.6 


1688742 


29; 


23500728 


80 


3276800000 


2.15 


45.9401 


7.8 


28872 


17.8 


1 786899 




24300000 


81 


3486784401 


2.20 


51.5363 


7.9 


30771 


18.0 


1889568 


30.5 


26393634 


82 


3707398432 


2.25 


57.6650 


8.0 


32768 


18.2 


1996903 


31.0 


28629151 


83 


3939040643 


2.30 


64.3634 


8.1 


34868 


18.4 


2109061 


31.5 


31013642 


84 


4182119424 


2.35 


71.6703 


8.2 


37074 


18.6 


2226203 


32.0 


33554432 


85 


4437053125 


2.40 


79.6262 


8.3 


39390 


18.8 


2348493 


32.5 


36259082 


86 


4704270176 


2.45 


88.2735 


8.4 


41821 


19.0 


2476099 


33.0 


39135393 


87 


4984209207 


2.50 


97.6562 


8.5 


44371 


19.2 


2609193 


33.5 


42191410 


88 


5277319168 


2.55 


107.820 


8.6 


47043 


19.4 


2747949 


34.0 


45435424 


89 


5584059449 


2.60 


118.814 


8.7 


49842 


19.6 


2892547 


34.5 


48875930 


90 


5904900000 


2.70 


143.489 


8.3 


52773 


19.8 


3043 1 68 


35.0 


52521875 


91 


6240321451 


2.80 


172.104 


8.9 


55841 


20.0 


3200000 


35.5 


56382167 


92 


6590815232 


2.90 


205.111 


9.0 


59049 


20.2 


3363232 


26.0 


60466176 


93 


6956883693 


3.00 


243.000 


9.1 


62403 


20.4 


3533059 


26 5 


64783487 


94 


7339040224 


3.10 


286.292 


9.2 


65908 


20.6 


3709677 


37.0 


69343957 


95 


7737809375 


3.20 


335.544 


9.3 


69569 


20.8 


3893289 


37. 5 


74157715 


96 


8153726976 


3.30 


391.354 


9.4 


73390 


21.0 


4034101 


38.0 


79235168 


97 


8587340257 


3.40 


454.354 


9.5 


77378 


21.2 


4282322 


38.5 


84587005 


98 


9039207968 


3.50 


525.219 


9.6|81537 


21.4 


4433166 


39.0 


90224199 


99 


9509900499 


3.60 


604.662 


9.7'85873 21.6 4701850 


39.5 96158012 







CIRCUMFERENCES AND AREAS OP CIRCLES. 
CIRCUMFERENCES AND AREAS OF CIRCLES. 



Ill 



Diam. 


Circum. 


Area. 


Diam. 


Circum. 


Area. 


Diam. 


Circum. 


Area. 


V64 


. 04909 


.00019 


3 3 /8 


7.4613 


4.4301 


6V8 


19.242 


29 465 


V32 


.09818 


.00077 


7/16 


7.6576 


4.6664 


1/4 


19.635 


30 680 


3/64 


.14726 


.00173 


1/2 


7.8540 


4.9087 


3/8 


20.028 


31 919 


1/16 


.19635 


.00307 


9/16 


8.0503 


5.1572 


1/2 


20.420 


33. 183 


3 /32 


.29452 


. 00690 


5/8 


8.2467 


5.4119 


5/8 


20.813 


34.472 


1/8 


.39270 


.01227 


. U/16 


8.4430 


5.6727 


3/ 4 


21.206 


35.785 


5 /32 


.49087 


.01917 


3/4 


8.6394 


5.9396 


7/8 


21.598 


37.122 


3/16 


.58905 


.02761 


13/16 


8.8357 


6.2126 


7. 


21.991 


38.485 


7/32 


.68722 


.03758 


7/8 


9.0321 


6.4918 


1/8 


22.384 


39.871 








15/16 


9.2284 


6.7771 


1/4 


22.776 


41.282 


V4 


. 78540 


. 04909 








3 /s 


23.169 


42.718 


9 /32 


.88357 


. 062 1 3 


3. 


9.4248 


7.0686 


1/2 


23.562 


44. 179 


5/16 


.98175 


.07670 


Vl6 


9.6211 


7.3662 


5/8 


23.955 


45.664 


H/32 


1.0799 


.09281 


1/8 


9.8175 


7 . 6699 


3/ 4 


24.347 


47.173 


3/8 


1.1781 


.11045 


3/16 


10.014 


7.9798 


7/8 


24.740 


48.707 


13/32 


1.2763 


.12962 


V4 


10.210 


8.2958 


8. 


25.133 


50.265 


7/16 


1.3744 


.15033 


5/16 


10.407 


8.6179 


1/8 


25.525 


51.849 


15/32 


1.4726 


.17257 


3/8 


10.603 


8 . 9462 


1/4 


25.918 


53.456 








7/16 


10.799 


9.2806 


3/8 


26.311 


55.088 


1/2 


1.5708 


.19635 


1/2 


10.996 


9.6211 


1/2 


26.704 


56.745 


17/32 


1 . 6690 


.22166 


9/16 


11.192 


9.9678 


5 /8 


27.096 


58.426 


9/16 


1.7671 


.24850 


5/8 


11.388 


10.321 


3/4 


27.489 


60.132 


19/32 


1.8653 


.27688 


U/16 


11.585 


10.680 


7/8 


27.882 


61.862 


5/8 


1.9635 


.30680 


3/ 4 


11.781 


11.045 


9. 


28.274 


63.617 


21/32 


2.0617 


.33824 


13/16 


11.977 


11.416 


1/8 


28.667 


65.397 


H/16 


2.1598 


.37122 


7/8 


12.174 


11.793 


1/4 


29.060 


67.201 


23 /32 


2.2580 


.40574 


15/16 


12.370 


12.177 


3/8 


29.452 


69.029 








4. 


12.566 


12.566 


1/2 


29.845 


70.882 


3/4 


2.3562 


.44179 


Vl6 


12.763 


12.962 


5/8 


30.238 


72.760 


23/32 


2.4544 


.47937 


1/8 


12.959 


13.364 


3/4 


30.631 


74.662 


13/16 


2.5525 


.51849 


3 /l6 


13.155 


13.772 


7 /8 


31.023 


76.589 


27/32 


2.6507 


.55914 


1/4 


13.352 


14. 186 


10. 


31.416 


78.540 


7/8 


2.7489 


.60132 


5/16 


13.548 


14.607 


1/8 


31.809 


80.516 


29/32 


2.8471 


.64504 


3/8 


13.744 


15.033 


1/4 


32.201 


82 . 5 1 6 


15/16 


2.9452 


. 69029 


7/16 


13.941 


15.466 


3/8 


32.594 


84.541 


31,32 


3 . 0434 


.73708 


1/2 


14.137 


1 5 . 904 


1/2 


32.987 


86.590 








9/16 


14.334 


16.349 


5/8 


33.379 


88.664 


1. 


3.1416 


.7854 


5/8 


14.530 


16.800 


3/4 


33.772 


90.763 


Vl6 


3.3379 


.8866 


U/16 


14.726 


17.257 


' 7/g 


34.165 


92 . 886 


1/8 


3.5343 


.9940 


3/ 4 


14.923 


17.721 


11. 


34.558 


95.033 


3/16 


3.7306 


1.1075 


13/16 


15.119 


18.190 


1/8 


34.950 


97.205 


1/4 


3.9270 


1.2272 


7/8 


15.315 


18.665 


1/4 


35.343 


99.402 


5/16 


4.1233 


1.3530 


15/16 


15.512 


19.147 


3/8 


35.736 


101.62 


3/8 


4.3197 


1.4849 


5. 


1 5 . 708 


19.635 


1/2 


36. 128 


103.87 


7/16 


4.5160 


1.6230 


Vl6 


1 5 . 904 


20.129 


5/8 


36.521 


106.14 


1/2 


4.7124 


1.7671 


1/8 


16.101 


20.629 


3/4 


36.914 


1C8.43 


9/16 


4.9087 


1.9175 


3 /l6 


16.297 


21.135 


7/8 


37.306 


110.75 


% 


5.1051 


2.0739 


1/4 


16.493 


21.648 


12. 


37.699 


113.10 


U/16 


5.3014 


2.2365 


5/16 


16.690 


22 . 1 66 


1/8 


38.092 


115.47 


3/4 


5 . 4978 


2.4053 


3 /8 


16.886 


22.691 


1/4 


38.485 


117.86 


13/16 


5.6941 


2.5802 


7/16 


17.082 


23.221 


3/8 


38.877 


120.28 


7/8 


5 . 8905 


2.7612 


1/2 


17.279 


23.758 


1/2 


39.270 


122.72 


15/16 


6.0868 


2.9483 


9/16 


17.475 


24.301 


5/8 


39.663 


125.19 








5/8 


17.671 


24.850 


3/4 


40.055 


127.68 


2. 


6.2832 


3.1416 


U/16 


1 7 . 868 


25.406 


7/8 


40.448 


130.19 


Vl6 


6.4795 


3.3410 


3/4 


18.064 


25.967 


13. 


40.841 


132.73 


1/8 


6.6759 


3.5466 


13/16 


18.261 


26.535 


1/8 


41.233 


135 30 


3/16 


6.8722 


3.7583 


7/8 


18.457 


27.109 


1/4 


41.626 


137.89 


1/4 


7 . 0686 


3.9761 


15/16 


18.653 


27.688 


3/8 


42.019 


140.50 


5/16 


7 . 2649 


4.2000 


6. 


18.850 


28.274 


1/2 


42.412 


143.14 



MATHEMATICAL TABLES. 



Diam. 


Circura. 


Area. 


Diam. 


Circum. 


Area. 


Diam. 


Circum. 


Area. 


13-3/s 


42.804 


145.80 


217/s 


68.722 


375.83 


30 V8 


94.640 


712.76 


3/ 4 


43.197 


148.49 


22. 


69.115 


380.13 


1/4 


95.033 


718.69 


7/8 


43.590 


1 5 1 . 20 


1/8 


69.503 


384.46 


3/8 


95.426 


724.64 


14. 


43.982 


153.94 


1/4 


69 . 900 


388.82 


1/2 


95.819 


730.62 


Vs 


44.375 


156.70 


3/8 


70.293 


393.20 


5/8 


96.211 


736.62 


1/4 


44.768 


159.48 


1/2 


70.686 


397.61 


3/ 4 


96.604 


742.64 


3/8 


45.160 


162.30 


5/8 


71.079 


402 . 04 


7/8 


96.997 


748.69 


1/2 


45.553 


165.13 


3/ 4 


71.471 


406.49 


31. 


97.389 


754.77 


5/8 


45.946 


167.99 


7/8 


71.864 


410.97 


1/8 


97.782 


760.87 


3/ 4 


46.338 


170.87 


23. 


72.257 


4 1 5 . 48 


1/4 


98.175 


766.99 


7 /8 


46.731 


173.78 


1/8 


72.649 


420.00 


3/8 


98.567 


773.14 


15. 


47.124 


176.7! 


1/4 


73.042 


424.56 


1/2 


98.960 


779.31 


1/8 


47.517 


179.67 


3/8 


73.435 


429.13 


5/8 


99.353 


785.51 


V4 


47.909 


1 82 . 65 


1/2 


73.827 


433.74 


3/4 


99.746 


791 73 


3/8 


48.302 


185.66 


5/8 


74.220 


438.36 


7/8 


100.138 


797.98 


1/2 


48.695 


188.69 


3/ 4 


74.613 


443.01 


32. 


100.531 


804.25 


5/8 


49.0*7 


191.75 


7/8 


75.006 


447.69 


1/8 


100.924 


810.54 


3/4 


49.480 


194.83 


24. 


75.398 


452.39 


1/4 


101.316 


816.86 


' 7/ 8 


49.873 


197.93 


1/8 


75.791 


457.11 


3/8 


101.709 


823.21 


16. 


50.265 


201.06 


1/4 


76.184 


461.86 


1/2 


102.102 


829.58 


1/8 


50.658 


204.22 


3/8 


76.576 


466.64 


5/8 


1 02 . 494 


835.97 


1/4 


51.051 


207.39 


1/2 


76.969 


471.44 


3/4 


102.887 


842.39 


3/8 


51.444 


210.60 


5/8 


77.362 


476.26 


7/8 


103.280 


848.83 


1/2 


51.836 


213.82 


3/4 


77.754 


481.11 


33. 


103.673 


855.30 


5/8 


52.229 


2 1 7 . 08 


7/8 


78.147 


485.98 


1/8 


104.065 


861.79 


3/4 


52.622 


220.35 


25. 


78.540 


490.87 


1/4 


104.458 


868.31 


7/8 


53.014 


223.65 


1/8 


78.933 


495.79 


3/8 


104.851 


874.85 


17. 


53.407 


226.98 


1/4 


79.325 


500.74 


1/2 


105.243 


881.41 


1/8 


53.800 


230.33 


3/8 


79.718 


505.71 


5/8 


105.636 


888.00 


1/4 


54.192 


233.71 


1/2 


80.111 


510.71 


3/4 


106.029 


894.62 


3/8 


54.585 


237.10 


5/8 


80.503 


515.72 


7/8 


106.421 


901.26 


1/2 


54.978 


240.53 


3/ 4 


80.896 


520.77 


34. 


106.814 


907.92 


5/8 


55.371 


243.98 


7/8 


81.289 


525.84 


1/8 


107.207 


914.61 


3/4 


55.763 


247.45 


26. 


81.681 


530.93 


1/4 


107.600 


921.32 


7/8 


56.156 


250.95 


1/8 


82.074 


536.05 


3/8 


107.992 


928.06 


18. 


56.549 


254.47 


1/4 


82.467 


541.19 


l/ 2 


103.385 


934.82 


1/8 


56.941 


258.02 


3/8 


82.860 


546.35 


5/8 


108.778 


941.61 


1/4 


57.334 


261.59 


1/2 


83.252 


551.55 


3/4 


109.170 


948.42 


3/8 


57.727 


265.18 


5/8 


83.645 


556.76 


7/8 


109.563 


955.25 


1/2 


58.119 


268.80 


3/4 


84.038 


562.00 


35. 


109.956 


962 . 1 1 


5/8 


58.512 


272.45 


7/8 


84.430 


567.27 


1/8 


110.348 


969.00 


3/4 


58.905 


276.12 


27. 


84.823 


572.56 


1/4 


110.741 


975.91 


7/8 


59.298 


279.81 


1/8 


85.216 


577.87 


3/8 


111.134 


982.84 


19. 


59.690 


283.53 


1/4 


85.608 


583.21 


1/2 


111.527 


989.80 


1/8 


60.083 


287.27 


3/8 


86.001 


588.57 


5/8 


111.919 


996.78 


1/4 


60.476 


291.04 


1/2 


86.394 


593.96 


3/4 


112.312 


1003.8 


3/8 


60.868 


294.83 


5/8 


86.786 


599.37 


7/8 


112.705 


1010.8 


1/2 


61.261 


298.65 


3/4 


87.179 


604.81 


36. 


113.097 


1017.9 


5/8 


61.654 


302.49 


7/8 


87.572 


610.27 


1/8 


1 1 3 . 490 


1025.0 


3/ 4 


62.046 


306.35 


28. 


87.965 


615.75 


1/4 


113.883 


1032.1 


7/8 


62.439 


310.24 


1/8 


88,357 


621.26 


3/8 


114.275 


1039.2 


20. 


62.832 


314.16 


1/4 


88.750 


626.80 


1/2 


114.668 


1046.3 


1/8 


63.225 


318.10 


3/8 


89.143 


632.36 


5/8 


115.061 


1053.5 


1/4 


63.617 


322.06 


1/2 


89.535 


637.94 


3/4 


115.454 


1060.7 


3/8 


64.010 


326.05 


5/8 


89.928 


643.55 


7/8 


115.846 


1068.0 


1/2 


64.403 


330.06 


3/4 


90.321 


649.18 


37. 


116.239 


1075.2 


5/8 


64.795 


334.10 


7/8 


90.713 


654.84 


1/8 


116.632 


1082.5 


3/4 


65. 188 


338.16 


29. 


91.106 


660.52 


1/4 


117.024 


1089.8 


7/8 


65.581 


342.25 


1/8 


91 .499 


666.23 


3/8 


117.417 


1097.1 


21. 


65.973 


346.36 


1/4 


91.892 


671.96 


1/2 


117.810 


1104.5 


'-'a 


66.366 


350.50 


3/8 


92.284 


677.71 


5 /8 


118.202 


1111.8 


V4 


66.759 


354.66 


1/2 


92.677 


683.49 


3/4 


118.596 


1119.2 


3/8 


67.152 


358.84 


5/8 


93.070 


689.30 


7/8 


118.988 


1126.7 


1/2 


67.544 


363.05 


3/4 


93.462 


695.13 


38. 


119.381 


1134.1 


5/8 


67.937 


367.28 


7/8 


93.855 


700.98 


1/8 


119.773 


1141.6 


3/4 


63.330 


371 .54 


30. 


94.248 


706 . 86 


1/4 


120.166 


1149.1 



CIRCUMFERENCES AND AREAS OF CIRCLES. 



113 



Diana. 


Circuin. 


Area. 


Diana. 


Circum. 


Area. 


Diam 


I Circum. 


I Area. 


383/s 


120.559 


1156.6 


465/s 


146.477 


1707.4 


547/ 8 


172.395 


1 2365.0 


V2 


120.951 


1164.2 


3/4 


146.869 


1716.5 


55. 


172.788 


2375.8 


5 /8 


121.344 


1171.7 


7/8 


147.262 


1725.7 


Vs 


173. 180 


2386.6 


3/ 4 


121.737 


1179.3 


47. 


147.655 


1734.9 


V4 


173.573 


2397.5 


7 /8 


122.129 


1186.9 


Vs 


148.048 


1744.2 


3/8 


1 73 . 966 


2408.3 


39. 


122.522 


1194.6 


V4 


1 48 . 440 


1753.5 


1/2 


174.358 


2419.2 


V8 


122.915 


1202.3 


3/8 


148.833 


1762.7 


5/8 


174.751 


2430. 1 


V4 


123.308 


1210.0 


V2 


149.226 


1772.1 


3/4 


175. 144 


2441. 1 


3/8 


123.700 


1217.7 


5/8 


149.618 


1 78 1 . 4 


7/8 


175.536 


2452.0 


V2 


124.093 


1225.4 


3/4 


150.011 


1790.8 


56. 


175.929 


2463.0 


5/8 


124.486 


1233.2 


7/8 


150.404 


1800.1 


Vs 


176.322 


2474.0 


3/4 


124.878 


1241.0 


48. 


150.796 


1809.6 


V4 


176.715 


2485.0 


7/8 


125.271 


1248.8 


Vs 


151.189 


1819.0 


3 /8 


177. 107 


2496. 1 


40. 


125.664 


1256.6 


1/4 


151.582 


1828.5 


V2 


177.500 


2507.2 


Vs 


126.056 


1264.5 


3/8 


151.975 


1837.9 


5 /8 


177.893 


2518.3 


V4 


126.449 


1272.4 


V2 


152.367 


1847.5 


3/4 


178.285 


2529.4 


3/8 


126.842 


1280.3 


5/8 


152.760 


1857.0 


7/8 


178.678 


2540.6 


V2 


127.235 


1288.2 


3/4 


153.153 


1866.5 


57. 


179.071 


2551.8 


5 /8 


127.627 


1296.2 


7/8 


153.545 


1876.1 


Vs 


179.463 


2563.0 


3/4 


128.020 


1304.2 


49. 


153.938 


1885.7 


V4 


179.856 


2574.2 


7/8 


128.413 


1312.2 


Vs 


154.331 


1895.4 


3/8 


180.249 


2585.4 


41. 


128.805 


1320.3 


1/4 


154.723 


1905.0 


V2 


180.642 


2596.7 


Vs 


129.198 


1328.3 


3/8 


155.116 


1914.7 


5/8 


181.034 


2608.0 


Va 


129.591 


1336.4 


1/2 


155.509 


1924.4 


3/4 


181.427 


2619.4 


3 /8 


129.983 


1344.5 


5/8 


155.902 


1934.2 


7/8 


181.820 


2630.7 


V2 


130.376 


1352.7 


3/4 


156.294 


1943.9 


58. 


182.212 


2642. 1 


5/8 


130.769 


1360.8 


7/8 


156.687 


1953.7 


• Vs 


182.605 


2653.5 


3/ 4 


131.161 


1369.0 


50. 


157.080 


1963.5 


V4 


182.998 


2664.9 


7/8 


131.554 


1377.2 


Vs 


157.472 


1973.3 


3/8 


183.390 


2676.4 


42. 


131.947 


1385.4 


V4 


157.865 


1983.2 


V2 


183.783 


2687.8 


Vs 


132.340 


1393.7 


3/8 


158.258 


1993. 1 


5 /8 


184.176 


2699.3 


1/4 


132.732 


1402.0 


V2 


158.650 


2003.0 


3/4 


184.569 


2710.9 


3/8 


133.125 


1410.3 


5/8 


159.043 


2012.9 


7/8 


184.961 


2722.4 


V2 


133.518 


1418.6 


3/4 


159.436 


2022.8 


59. 


185.354 


2734.0 


5 /8 


133.910 


1427.0 


7/8 


159.829 


2032.8 


1/8 


185.747 


2745.6 


3/4 


134.303 


1435.4 


51. 


160.22! 


2042.8 


V4 


186.139 


2757.2 


7/8 


134.696 


1443.8 


Vs 


160.614 


2052.8 


3/8 


186.532 


2768.8 


43. 


135.088 


1452.2 


V4 


161.007 


2062.9 


v 2 


186.925 


2780.5 


Vs 


135.481 


1460.7 


3/8 


161.399 


2073.0 


5/8 


187.317 


2792.2 


1/4 


135.874 


1469.1 


• V2 


161.792 


2083.1 


3/4 


187.710 


2803.9 


3/8 


136.267 


1477.6 


5/8 


162.185 


2093.2 


7/8 


188. 103 


2815.7 


V 2 


136.659 


1486.2 


3/4 


162.577 


2103.3 


60. 


188.496 


2827.4 


5 /8 


137.052 


1494.7 


7/8 


162.970 


2113.5 


Vs 


188.888 


2839.2 


3/4 


137.445 


1503.3 


52. 


163.363 


2123.7 


V4 


189.281 


2851.0 


7/8 


137.837 


1511.9 


Vs 


163.756 


2133.9 


3/8 


189.674 


2862.9 


44. 


138.230 


1520.5 


V4 


164.148 


2144.2 


V2 


190.066 


2874.8 


Vs 


138.623 


1529.2 


3/8 


164.541 


2154.5 


5/8 


190.459 


2886.6 


V4 


139.015 


1537.9 


V2 


164.934 


2164.8 


3/4 


190.852 


2898.6 


3/8 


139.408 


1546.6 


5/8 


165.326 


2175.1 


7/8 


191.244 


2910.5 


V2 


139.801 


1555.3 


3/4 


165.719 


2185.4 


61. 


191.637 


2922.5 


5 /8 


140.194 


1564.0 


7/8 


166.112 


2195.8 


Vs 


192.030 


2934.5 


3/4 


140.586 


1572.8 


53. 


166.504 


2206.2 


1/4 


192.423 


2946.5 


7/8 


140.979 


1581.6 


Vs 


166.897 


2216.6 


3/8 


192.815 


2958.5 


45. 


141.372 


1590.4 


V4 


167.290 


2227.0 


V2 


193.208 


2970.6 


V8 


141.764 


1599.3 


3/8 


167.683 


2237.5 


5/8 


193.601 


2982.7 


V4 


142.157 


1608.2 


V2 


168.075 


2248.0 


3/4 


193.993 


2994.8 


3/8 


142.550 


1617.0 


5/8 


168.468 


2258.5 


7/8 


194.386 


3006.9 


V2 


142.942 


1626.0 


3/4 


168.861 


2269. 1 


62. 


194.779 


3019.1 


5/8 


143.335 


1634.9 


7/8 


169.253 


2279.6 


Vs 


195.171 


3031.3 


3/4 


143.728 


1643.9 


54. 


1 69 . 646 


2290.2 


1/4 


195.564 


3043.5 


7/8 


144.121 


1652.9 


Vs 


170.039 


2300.8 


3/8 


195.957 


3055.7 


46. 


144.513 


1661.9 


V4 


170.431 


2311.5 


1/2 


196.350 


3068.0 


Vs 


144.906 


1670.9 


3/8 


170.824 


2322.1 


5/8 


196.742 


3080.3 


1/4 


145.299 


1680.0 


V2 


171.217 


2332.8 


3/4 


197.135 


3092.6 


3/8 


145.691 


1689. 1 


5/8 


171.609 


2343.5 


7/8 


197.528 


3 1 04 9 


V2 


146.084 


1698.2 


3/ 4 


1 72 . 002 


2354.3 


63. 


197.920 


3117.2 



114 



MATHEMATICAL TABLES. 



Diam. 


Circum. 


Area. 


Diam. 


Circum. 


Area. 


Diam.l Circum. 


Area. 


63 V8 


198.313 


3129.6 


713/8 


224.23 1 


4001. 1 


795/ 8 


250.149 


49/9.5 


V4 


198.706 


3 1 42 . 


1/2 


224.624 


4015.2 


3/4 


250.542 


4995.1 


3 /8 


199.098 


3154.5 


5/8 


225.017 


4029.2 


7/8 


250.935 


5010.9 


V2 


199.491 


3166.9 


3/ 4 


225.409 


4043.3 


80. 


251.327 


5026.5 


5 /8 


199.884 


3179.4 


7/8 


225.802 


4057.4 


1/8 


251.720 


5042.3 


3/ 4 


200.277 


3191.9 


72. 


226.195 


4071.5 


1/4 


252.113 


5053.0 


7 /8 


200.669 


3204.4 


1/8 


226.587 


4085.7 


3 /8 


252.506 


5073.8 


64. 


201.062 


3217.0 


1/4 


226.980 


4099.8 


1/2 


252.393 


50S9.6 


V8 


201.455 


3229.6 


3/8 


227.373 


4114.0 


5/8 


253.291 


5105.4 


V4 


201.847 


3242 . 2 


1/2 


227.765 


4128.2 


3/ 4 


253.634 


5121.2 


3/8 


202.240 


3254.8 


5 /8 


228.158 


4142.5 


7/8 


254.076 


5137. 1 


V2 


202.633 


3267.5 


3/4 


228.551 


4156.8 


81. 


254.469 


5153.0 


5 /8 


203.025 


3280.1 


7/8 


228.944 


4171.1 


Vs 


254.862 


5168.9 


3/ 4 


203.418 


3292.8 


73. 


229.336 


4185.4 


V4 


255.254 


5184.9 


7/8 


203.811 


3305.6 


1/8 


229.729 


4199.7 


3/8 


255.647 


5200. 8 


65. 


204.204 


3318.3 


1/4 


230.122 


4214.1 


1/2 


256.040 


5216.8 


Vs 


204.596 


3331.1 


3/8 


230.514 


4228.5 


5/8 


256.433 


5232.8 


Vt 


204.989 


3343.9 


1/2 


230.907 


4242.9 


3/4 


256.825 


5248.9 


3/8 


205.382 


3356.7 


5/8 


231.300 


4257.4 


7/8 


257.218 


5264.9 


V2 


205.774 


3369.6 


3/4 


23 1 . 692 


4271.8 


82. 


257.611 


5281.0 


5 /8 


206.167 


3382.4 


7/8 


232.085 


4286.3 


Vs 


258.003 


5297. 1 


3/ 4 


206.560 


3395.3 


74. 


232.478 


4300.8 


1/4 


258.396 


5313.3 


7/8 


206.952 


3408.2 


1/8 


232.871 


4315.4 


3/8 


258.789 


5329.4 


66. 


207.345 


3421.2 


1/4 


233.263 


4329.9 


1/2 


259.181 


5345.6 


Vs 


207.738 


3434.2 


3/8 


233.656 


4344.5 


5/8 


259.574 


5361.8 


V4 


208.131 


3447.2 


1/2 


234.049 


4359.2 


3/4 


259.967 


5378.1 


3/8 


208.523 


3460.2 


5/8 


234.441 


4373.8 


7/8 


260.359 


5394.3 


V2 


208.916 


3473.2 


3/4 


234.834 


4388.5 


83. 


260.752 


5410.6 


5 /8 


209.309 


3486.3 


7/8 


235.227 


4403 . 1 


1/8 


261.145 


5426.9 


3/4 


209.701 


3499.4 


75. 


235.619 


4417.9 


V4 


261.538 


5443.3 


7/8 


210.094 


3512.5 


1/8 


236.012 


4432.6 


3/8 


261.930 


5459.6 


67. 


210.487 


3525.7 


1/4 


236.405 


4447.4 


1/2 


262.323 


5476.0 


V8 


210.879 


3538.8 


3/8 


236.798 


4462.2 


5/8 


262.716 


5492.4 


V4 


211.272 


3552.0 


1/2 


237.190 


4477.0 


3/4 


263 . 1 08 


5503.8 


3/8 


211.665 


3565.2 


5/8 


237.583 


4491.8 


7/8 


263.501 


5525.3 


1/2 


212.058 


3578.5 


3/4 


237.976 


4506.7 


84. 


263.894 


5541.8 


5/8 


212.450 


3591.7 


7/8 


233.368 


4521.5 


Vs 


264.236 


5558.3 


3/4 


212.843 


3605.0 


76c 


238.761 


4536.5 


1/4 


264.679 


5574.8 


7/8 


213.236 


3618.3 


1/8 


239.154 


4551.4 


3/8 


265.072 


5591.4 


68. 


213.628 


3631.7 


1/4 


239.546 


4566.4 


1/2 


265.465 


5607.9 


1/8 


214.021 


3645.0 


3/8 


239.939 


4581.3 


5 /8 


265.857 


5624.5 


1/4 


214.414 


3658.4 


1/2 


240.332 


4596.3 


3/4 


266.250 


5641.2 


3/8 


214.806 


3671.8 


5/8 


240.725 


4611.4 


7/8 


266.643 


5657.8 


1/2 


215.199 


3685.3 


3/4 


241.117 


4626.4 


85. 


267.035 


5674.5 


5 /8 


215.592 


3698.7 


7/8 


241 .510 


4641.5 


1/8 


267.428 


5691.2 


3/ 4 


2 1 5 . 984 


3712.2 


77. 


241.903 


4656.6 


1/4 


267.821 


5707.9 


7/8 


216.377 


3725.7 


1/8 


242.295 


4671.8 


3/8 


268.213 


5724.7 


69. 


216.770 


3739,3 


1/4 


242.633 


4686.9 


1/2 


263.606 


5741.5 


1/8 


217.163 


3752.8 


3/8 


243.081 


4702.1 


5/8 


263.999 


5758.3 


1/4 


217.555 


3766.4 


1/2 


243.473 


4717.3 


3/4 


269.392 


5775.1 


3/8 


217.948 


3780.0 


5/8 


243.866 


4732.5 


7/8 


269.784 


5791.9 


1/2 


218.341 


3793.7 


3/4 


244.259 


4747.8 


86. 


270.177 


5808.8 


5/8 


218.733 


3807.3 


7/8 


244.652 


4763.1 


Vs 


270.570 


5825.7 


3/4 


219. 126 


3821.0 


78. 


245.044 


4778.4 


1/4 


270.962 


5842.6 


7/8 


219.519 


3834.7 


1/8 


245.437 


4793.7 


3/8 


271.355 


5859.6 


70. 


219.911 


3848.5 


1/4 


245.830 


4809.0 


1/2 


271.748 


5876.5 


1/8 


220.304 


3862.2 


3/8 


246.222 


4824.4 


5/8 


272.140 


5893.5 


1/4 


220.697 


3876.0 


l/ 2 


246.615 


4839.8 


3/ 4 


272.533 


5910.6 


3/8 


221.090 


3889.8 


5/8 


247.003 


4855.2 


7/8 


272.926 


5927.6 


1/2 


221.482 


3903.6 


3/4 


247.400 


4870.7 


87. 


273.319 


5944.7 


5/8 


221.875 


3917.5 


7/8 


247.793 


4886.2 


1/8 


273.711 


5961.8 


3/4 


222.268 


3931.4 


7 a 


248. 186 


4901.7 


1/4 


274.104 


5978.9 


7/8 


222.660 


3945.3 


1/8 


243.579 


4917.2 


3/8 


274.497 


5996.0 


71. 


223.053 


3959 2 


1/4 


248.971 


4932.7 


1/2 


274.889 


60 1 3 . 2 


1/8 


223.446 


3973 1 


3/8 


249.364 


4948 . 3 


5/8 


275.282 


6030.4 


1/4 


223.838 


3987.1 


1/2 249.75 7 


4963.9 


3/4 


275.675 


6047.6 



CIRCUMFERENCES AND AREAS OF CIRCLES. 115 



Area. Diam. Circum. Area. Diani. Circum. Area 



276.067 

276.460 

276.853 

277.246, 

277.633! 

278.031 

278.424 

278.816 

279.209 

279.602 

279.994 

280.387 

280.780 

281. 173 

281.565 

281.958 

282.351 

282.743 

283. 136 

283.529 

283.921 

284.314 

284.707 

285.100 

285.492 

285.835 

286.278 

286.670 

237.063 

287.456 

2S7.848 

288.241 

288.634 

239.027 

289.419 

239.812 

290.205 

290.597 

290.990 

291.333 

291.775 

292.168 

292.561 

292.954 

293.346 

293.739 

294.132 

294.524 

294. 91 7 

295.310 

295.702 

296.095 

296.488 

296.881 

297.273 

297.666 

293.059 

298.451 

298.844 

299.237 

299.629 

300.022 

300.415 

300.807 



6064.9 

6082.1 

6099.4 

6116.7 

6134. 1 

6151.4 

6168.8 

6186.2 

6203 . 7 

6221.1 

6238.6 

6256.1 

6273.7 

6291.2 

6308.8 

6326.4 

6344.1 

6361.7 

6379.4 

6397.1 

6414.9 

6432.6 

6450.4 

6468.2 

6436.0 

6503.9 

6521.8 

6539.7 

6557.6 

6575.5 

6593.5 

66H.5 

6629.6 

6647.6 

6665 . 7 

6683.8 

6701.9 

6720.1 

6738.2 

6756.4 

6774.7 

6792.9 

6811.2 

6829.5 

6847.8 

6366.1 

6834.5 

6902 . 9 

6921.3 

6939.8 

6958.2 

6976.7 

6995 . 3 

7013.8 

7032.4 

7051.0 

7069.6 

7088 . 2 

7106.9 

7125.6 

7144.3 

7163.0 

7181.8 

7200.6 



95 7/ 8 
96. 

V8 

V4 



Vs 

1/4 
3/8 
1/2 
5/8 
3/4 
7/8 
100 
101 
102 
103 
104 
105 
106 
107 
108 
109 
110 
111 
112 
113 
114 
115 
116 
117 
118 
119 
120 
121 
122 
123 
124 
125 
126 
127 
128 
129 



301.200 

301.593 

301.986 

302.378 

302.771 

303. 164 

303.556 

303.949 

304.342 

304.734 

305.127 

305.520 

305.913 

306.305 

306.698 

307.091 

307.483 

307.876 

308.269 

308.661 

309.054 

309.447 

309.840 

310.232 

310.625 

311.018 

311.410 

311.803 

312. 196 

312.538 

312.981 

313.374 

313.767 

314.159 

317.30 

320.44 

323.58 

326.73 

329.87 

333.01 

336.15 

339.29 

342.43 

345.58 

343.72 

351.86 

355.00 

353.14 

361.28 

364.42 

367.57 

370:71 

373.85 

376.99 

380.13 

383.27 

386.42 

389.56 

392.70 

395.84 

398.98 

402. 12 

405.27 



7219.4 
7238.2 
7257.1 
7276.0 
7294.9 
7313.8 
7332.8 
7351.8 
7370.8 
7389.8 
7408 . 9 
7428.0 
7447.1 
7466.2 
7435.3 
7504.5 
7523.7 
7543.0 
7562.2 
7581.5 
7600.8 

7620. 1 
7639.5 
7658.9 
7678.3 
7697.7 
7717.1 
7736.6 
7756.1 
7775.6 
7795.2 
7814.8 
7834.4 
7854.0 
8011.85 
8171.28 
8332.29 
8494.87 
8659.01 
8324.73 

8992 . 02 
9160. ._ 
9331.32 
9503.32 
9676.89 
9852.03 

10028.75 
10207.03 
10386.89 
10568.32 
10751.32 
10935.88 
11122.02 
11309.73 
I 1499.01 
11689.87 
11882.29 
12076.28 
12271.85 
12468.98 
12667.69 
12867.96 
13069.81 



130 

131 
132 
133 
134 
135 
136 
137 
138 
139 
140 
141 
142 
143 
144 
145 
146 
147 
148 
149 
150 
151 
152 
153 
154 
155 
156 
157 
158 
159 
160 
161 
162 
163 
164 
165 
166 
167 
168 
169 
170 
171 
172 
173 
174 
175 
176 
177 
178 
179 
180 
181 
182 
183 
184 
185 
186 
187 
188 
189 
190 
191 
192 



408.41 

411.55 

414.69 

417.83 

420.97 

424. 12 

427.26 

430.40 

433.54 

436.68 

439.82 

442 . 96 

446. 11 

449.25 

452.39 

455.53 

458.67 

461.81 

464.96 

468.10 

471.24 

474.38 

477.52 

480.66 

483.81 

486.95 

490.09 

493.23 

496.37 

499.51 

502.65 

505.80 

508.94 

512.08 

5 1 5 . 22 

518.36 

521.50 

524.65 

527.79 

530.93 

534.07 

537.21 

540.35 

543.50 

546.64 

549.78 

552.92 

556.06 

559.20 

562.35 

565.49 

568.63 

571.77 

574.91 

578.05 

581.19 

584.34 

587.48 

590.62 

593.76 

596.90 

600.04 

603.19 



13273.23 

13478.22 

13684.78 

13892.91 

14102.61 

14313.88 

14526.72 

14741. 14 

14957. 12 

15174.68 

15393.80 

15614.50 

15836.77 

16060.61 

16286.02 

16513.00 

16741.55 

16971.67 

17203.36 

17436.62 

17671.46 

17907.86 

18145.84 

18385.39 

18626.50 

18869.19 

19113.45 

19359.28 

19606.68 

19855.65 

20106.19 

20358.31 

20611.99 

20867.24 

21124.07 

21382.46 

21642.43 

21903.97 

22167.08 

22431.76 

22698.01 

22965.83 

23235.22 

23506. 18 

23778.71 

24052.82 

24328.49 

24605.74 

24884.56 

25164.94 

25446.90 

25730.43 

26015.53 

26302.20 

26590.44 

26880.25 

27171.63 

27464.59 

27759.11 

28055.21 

28352.87 

28652. 11 

28952 . 92 



116 



MATHEMATICAL TABLES. 



Diam. Circum. Area. Diam. Circum. Area. Diam. Circum. 



606.33 
609.47 
612.61 
615.75 
618.89 
622.04 
625. 18 
628.32 
63 1 . 46 
634.60 
637.74 
640.88 
644.03 
647. 17 
650.31 
653.45 
656.59 
659.73 
662.88 
666.02 
669. 16 
672.30 
675.44 
678.58 
681.73 
684.87 
688.01 
691.15 
694.29 
697.43 
700.58 
703.72 
706.86 
710.00 
713.14 
716.28 
719.42 
722.57 
725.71 
728.85 
731.99 
735.13 
738.27 
741.42 
744.56 
747.70 
750.84 
753.98 
757. 12 
760.27 
763.41 
766.55 
769 . 69 
772.83 
775.97 
779.11 
782.26 
785.40 
783.54 
791.68 
794.82 
797.96 
801. 11 
804.25 
807.39 
810.53 
813.67 



29255.30 

29559.25 

29864.77 

30171.86 

30480.52 

30790.75 

31102.55 

31415.93 

31730.87 

32047.39 

32365.47 

32685. 13 

33006.36 

33329. 16 

33653.53 

33979.47 

34306 

34636.06 

34966.71 

35298.94 

35632,73 

35963.09 

36305.03 

36643.54 

36983.61 

37325.26 

37668. 

38013.27 

38359.63 

38707.56 

39057.07 

39408. 14 

39760.78 

401 15.00 

40470.78 

40828. 14 

41187.07 

41547.56 

4190^.63 

42273.27 

42638.48 

43005.26 

43373.61 

43743.54 

44115.03 

44488 . 09 

44862.73 

45238.93 

45616.71 

45996.06 

46376 

46759.47 

47143.52 

47529. 16 

47916.36 

48305. 13 

48695.47 

49087.39 

49480.87 

49875.92 

50272.55 

50670.75 

51070.52 

51471.85 

51874.76 

52279.24 

52685 29 



260 

261 

262 

263 

264 

265 

266 

267 

268 

269 

270 

271 

272 

273 

274 

275 

276 

277 

278 

279 

280 

281 

282 

283 

284 

285 

286 

287 

288 

289 

290 

291 

292 

293 

294 

295 

296 

297 

298 

299 

300 

301 

302 

303 

304 

305 

306 

307 

303 

309 

310 

311 

312 

313 

314 

315 

316 

317 

318 

319 

320 

321 

322 

323 

324 

325 

326 



816.81 
819.96 
823. 10 
826.24 
829.33 
832.52 
835.66 
838.81 
841.95 
845.09 
848.23 
851.37 
854.5! 
857.65 
860.80 
863.94 
867.08 
870.22 
873.36 
876.50 
879.65 
882.79 
885.93 
889.07 
892.2 
895.35 
893.50 
901.64 
904.78 
907.92 
911.06 
914.20 
917.35 
920.49 
923.6: 
926.77 
929.91 
933.05 
936. 19 
939.34 
942.48 
945.62 
948.76 
951.90 
955.04 
958. 19 
961.33 
964.47 
967.61 
970.75 
973.89 
977.04 
930. 18 
983.32 
986.46 
989.60 
992.74 
995.88 
999.03 
1002.17 
1005.31 
1008.45 
1011.59 
1014.73 
1017.8^ 
1021.02 
1024. 16 



53092 
53502 
53912 
54325 
54739 
55154 
55571 
55990 
56410 
56832 
57255 
57680 
58106 
58534 
58964 
59395 
59823 
60262 
60698 
61 136 
61575 
62015 
62458 
62901 
63347 
63793 
64242 
64692 
65144 
65597 
66051 
66508 
66966 
67425 
67886 
68349 
68813 
69279 
69746 
70215 
70685 
71157 
71631 
72106 
72583 
73061 
73541 
74022 
74506 
74990 
75476. 
75964, 
76453. 
76944. 
77437. 
77931. 
78426 
78923 
79422 
79922 
80424 
80928 
81433 
81939 
82447 
82957 
83468 



327 

328 

329 

330 

331 

332 

333 

334 

335 

336 

337 

338 

339 

340 

341 

342 

343 

344 

345 

346 

347 

348 

349 

350 

351 

352 

353 

354 

355 

356 

357 

358 

359 

3fiO 

361 

362 

363 

364 

365 

366 

367 

368 

369 

370 

371 

372 

373 

374 

375 

376 

377 

378 

379 

380 

381 

382 

383 

384 

385 

386 

387 

388 

389 

390 

391 

392 

393 



1027.30 

1030.44 

1033.58 

1036.73 

1039.87 

1043.0 

1046. 15 

1049.29 

1052.43 

1055.58 

1058.72 

1061.86 

1065.00 

1068. 14 

1071.28 

1074.42 

1077.57 

1080.71 

1083.85 

1086.99 

1090.13 

1093.27 

1096.42 

1099.56 

1102.70 

1105.84 

1108.98 

1112. 12 

1115.27 

1118.41 

1121.55 

1124.69 

1127.83 

1130.97 

1134.11 

1137-26 

1140.40 

1143.54 

1146.68 

1149.82 

1152.96 

1156.11 

1159.25 

1162.39 

1165.53 

1168.67 

1171.8 

1174.96 

1178. 10 

1181.24 

1184.38 

1187.52 

1190.66 

1193.81 

1196.95 

1200.09 

1203.23 

1206.37 

1209.51 

1212.65 

1215.80 

1218.94 

1222.08 

1225.22 

1228.36 

1231.50 

1234.65 



Area. 

83981.84 

84496.28 

85012.28 

85529.86 

86049.01 

86569.73 

87092.02 

87615.88 

88141.31 

88668.31' 

89196.88 

89727.03 

90258.74 

90792.03 

91326.88 

91863.31 

92401.31 

92940.88 

93482.02 

94024.73 

94569.01 

95114.86 

95662.28 

96211.28 

96761.84 

97313.97 

97867.68 

98422.96 

98979.80 | 

99538.22 

1 00098. 2| 

100659.77 ;; 

101222.90 I 

101787.60 

102353. 8J I 

102921.72 ji 

103491. 13 I 

104062. 12 ji 

104634.67 

105208.80 J 

105784.49 

106361.76 ! 

106940.60 

107521.01 II 

108102.9) 

108686.51 ! 

109271.66 | 

09853.35 

10446.62 

11 1036.45 

111627.86 

1220.83 

112815.38 

13411.49 

114009. 13 

1 14603.44 

115209.27 

115811.67 

116415.64 

117021.18 

117628.30 

118236.98 

118847.24 

119459.06 

120072.46 

120687.46 

121303.96 



CIRCUMFERENCES AND AREAS OP CIRCLES. 



117 



Diam. Circum Area. Diam. Circum. Area. Diam. Circum. Area 



1237 

1240 

1244 

1247 

1250 

1253 

1256 

1259 

1262 

1266 

1269 

1272 

1275 

1278 

1281 

1284 

1288 

1291 

1294 

1297 

1300 

1303 

1306 

1310 

1313 

1316 

1319 

1322 

1325 

1328 

1332 

1335 

1338 

1341. 

1344 

1347 

1350 

1354 

1357 

1360 

1363. 

1366 

1369 

1372 

1376 

1379. 

1382 

1385 

1388 

1391 

1394 

1398 

1401 

1404 

1407 

1410 

1413 

1416 

1420 

1423 

1426 

1429 

1432 

1435 

1438 

1441 

1445 



121922.07 

122541.75 
123163.00 
123785.82 
124410.21 
125036.17 
125663.71 
126292.81 
1 26923 . 48 
127555.73 
128189.55 
128824.93 
129461 
130100.42 
130740.52 
131382. 19 
132025.43 
132670.24 
133316.63 
133964.58 
134614. 10 
135265.20 
135917.86 
136572.10 
137227.91 
137885.29 
138544.24 
139204.76 
139866.85 
140530.51 
141195.74 
141862.54 
142530.92 
143200.86 
143872.38 
144545.46 
145220.12 
145896.35 
146574.15 
147253.52 
147934.46 
148616.97 
149301.05 
149986.70 
150673.93 
151362.72 
152053.08 
44 1 152745. 02 
5S 153438.53 
154133.60 
154830.25 
155528.47 
156228.26 
156929.62 
157632.55 
158337.06 
159043.13 
159750.77 
160459.99 
161170.77 
161883.13 
162597.05 
163312.55 
164029.62 
164748.26 
165468.47 
166190.25 



461 
462 
463 
464 
465 
466 
467 
468 
469 
470 
471 
472 
473 
474 
475 
476 
477 
478 
479 
480 
481 
482 
483 
484 
485 
486 
487 
488 
489 
490 
491 
492 
493 
494 
495 
496 
497 
498 
499 
500 
501 
502 
503 
504 
505 
506 
507 
508 
500 
510 
511 
512 
513 
514 
515 
516 
517 
518 
519 
520 
521 
522 
523 
524 
525 
526 
527 



1448.27 

1451.42 

1454.56 

1457.70 

1460.84 

1463.98 

1467. 12 

1470.27 

1473.41 

1476.55 

1479.69 

1482.83 

1485.97 

1489.11 

1492.26 

1495.40 

1498.54 

1501.68 

1504.82 

1507.96 

1511.11 

1514.25 

1517.39 

1520.53 

1523.67 

1526.81 

1529.96 

1533 

1536.24 

1539.38 

1542.52 

1545.66 

1548.81 

1551.95 

1555.09 

1558.23 

1561.37 

1564.51 

1567.65 

1570.80 

1573.94 

1577. 05 
1580.22 
1583.36 
1586.50 
1589.65 
1592.79 
1595.93 
1599.07 
1602.21 
1605.35 
1608.50 
1611 .64 
1614.78 
1617.92 

1 62 1 . 06 
1624.20 
1627.34 
1630.49 
1633.63 
1636.77 
1639.91 
1643.05 
1646. 19 
1649.34 
1652.48 
1655.62 



166913.60 

167638.53 

168365.02 

169093.08 

169822.72 

170553.92 

171286.70 

172021.05 

172756.9! 

173494.45 

174233.51 

174974. 14 

175716.35 

176460.12 

177205.46 

177952.3: 

178700.86 

179450.91 

180202.54 

180955.74 

181710.50 

182466.84 

183224.75 

183984.23 

184745.28 

185507.90 

186272.10 

187037.86 

187805.19 

188574.10 

189344.5: 

190116.62 

190890.2 

191665.43 

192442.18 

193220.51 

194000.41 

194781.85 

195564.93 

196349.54 

197135.72 

197923.48 

198712.80 

199503.70 

200296.1 

201090.20 

201885.81 

202682.99 

203481.74 

204282.06 

205083.95 

205887.42 

206692.45 

207499.05 

208307.23 

209116.97 

209928.29 

210741.18 

211555.63 

212371.66 

213189.26 

214008.43 

214829. 17 

215651 .49 

216475.37 

217300.82 

218127.85 



528 

529 

530 

531 

532 

533 

534 

535 

536 

537 

538 

539 

540 

541 

542 

543 

544 

545 

546 

547 

548 

549 

550 

551 

552 

553 

554 

555 

556 

557 

558 

559 

560 

561 

562 

563 

564 

565 

566 

567 

568 

569 

570 

571 

572 

573 

574 

575 

576 

577 

578 

579 

580 

581 

582 

583 

584 

585 

586 

587 

588 

589 

590 

591 

592 

593 

594 



1658.76 

1661.90 

1665.04 

1 668 . 1 . 

1671.33 

1674.47 

1677.61 

1680.75 

1 683 . 89 

1687.04 

1690.18 

1693.32 

1696.46 

1699.60 

1702.74 

1705.88 

1709.03 

1712.17 

1715.31 

1718.45 

1721.59 

1724.73 

1727.88 

1 73 1 . 02 

1734.16 

1737.30 

1740.44 

1743.58 

1746.73 

1749.87 

1753.0 

1756.15 

1759.29 

1762.43 

1765.58 

1768.72 

1771.86 

1775.00 

1778.14 

1781.28 

1784.42 

1787.57 

1790.71 

1793.85 

1796.99 

1800.13 

1803.27 

1806.42 

1809.56 

1812.70 

1815.84 

1818.98 

1822.12 

1825.27 

1828.41 

1831.55 

1834.69 

.837.83 

1840.97 

1844.11 

1847.26 

1850.40 

1853.54 

1856.68 

1859.82 

1862.96 

1866.11 



218956.44 
219786.61 
220618.34 
221451.65 
222286.53 
223122.98 
223961. CO 
224800.59 
225641.75 
226484.48 
227328.79 
228174.66 
229022. 10 
229871.12 
230721.71 
231573.86 
232427.59 
233282.89 
234139.76 
234998.20 
235858.21 
236719.79 
237582.94 
238447.67 
239313.96 
240181.83 
241051.26 
241922.27 
242794.85 
243668.99 
244544.71 
245422.00 
246300.86 
247181.30 
248063.30 
248946.87 
249832.01 
250718.73 
251607.01 
252496.87 
253388.30 
254281.29 
255175.86 
256072.00 
256969.71 
257868.99 
258769.85 
259672.27 
260576.26 
261481.83 
262388.96 
263297.67 
264207.94 
265119.79 
266033.21 
266948.20 
267864.76 
268782.89 
269702.59 
270623.86 
271546.70 
272471.12 
273397.10 
274324.66 
275253.78 
276184.48 
277116.75 



118 



MATHEMATICAL TABLES. 



Diam 


Circum. 


Area. 


Dkm 


Circum 


Area. 


Diam. 


Circum. 


Area. 


595 


1869.25 


278050.58 


663 


2082 . 88 


345236.69 


731 


2296.50 


419686. 15 


596 


1872.39 


278985.99 


664 


2086.02 


346278.91 


732 


2299.65 


420835. 19 


597 


1875.53 


279922.97 


665 


2089.16 


347322.70 


733 


2302.79 


421985.79 


598 


1878.67 


280861.52 


666 


2092.30 


348368.07 


734 


2305.93 


423137.97 


599 


1881.81 


281801.65 


667 


2095.44 


349415.00 


735 


2309.07 


424291.72 


600 


1884.96 


282743.34 


668 


2098.58 


350463.51 


736 


2312.21 


425447.04 


601 


1888. 10 


283686.60 


669 


2101.73 


351513.59 


737 


2315.35 


426603.94 


602 


1891.24 


284631.44 


670 


2104.87 


352565.24 


738 


2318.50 


427762.40 


603 


1894.38 


285577.84 


671 


2108.01 


353618.45 


739 


2321.64 


428922 . 43 


604 


1897.52 


286525.82 


672 


2111.15 


354673.24 


740 


2324.78 


430084.03 


605 


1900.66 


237475.36 


673 


2114.29 


355729.60 


741 


2327.92 


431247.21 


606 


1903.81 


283426.48 


674 


2117.43 


356787.54 


742 


233 1 . 06 


432411.95 


607 


1906.95 


239379. 17 


675 


2120.58 


357847.04 


743 


2334.20 


433578.27 


608 


1910.09 


290333.43 


676 


2123.72 


358908.11 


744 


2337.34 


434746.16 


609 


1913.23 


291289.26 


677 


2126.86 


359970.75 


745 


2340.49 


435915.62 


610 


1916.37 


292246.66 


678 


2130.00 


361034.97 


746 


2343.63 


437086.64 


611 


1919.51 


293205.63 


679 


2133.14 


362100.75 


747 


2346.77 


438259.24 


612 


1922.65 


294166.17 


630 


2136.28 


3631:8.11 


748 


2349.91 


439433.41 


613 


1925.80 


295128.28 


631 


2139.42 


364237.04 


749 


2353.05 


440609.16 


614 


1928.94 


296091.97 


632 


2142.57 


365307.54 


750 


2356.19 


441786.47 


615 


1932.08 


297057.22 


683 


2145.71 


366379.60 


751 


2359.34 


442965.35 


616 


1935.22 


298024.05 


634 


2148.85 


367453.24 


752 


2362.48 


444145.80 


617 


1938.36 


298992.44 


635 


2151.99 


368528.45 


753 


2365.62 


445327.83 


618 


1941.50 


299962.41 


686 


2155.13 


369605.23 


754 


2368.76 


445511.42 


619 


1944.65 


300933.95 


637 


2158.27 


370683.59 


755 


2371.90 


447696.59 


620 


1947.79 


301907.05 


633 


2161.42 


371763.51 


756 


2375.04 


448883.32 


621 


1950.93 


302881.73 


639 


2164.56 


372845.00 


757 


2378.19 


450071.63 


622 


1954.07 


303857.98 


090 


2167.70 


373928.07 


758 


2381.33 


451261.51 


623 


1957.21 


304835. 8G 


691 


2170.84 


375012.70 


759 


2384.47 


452452.96 


624 


1960.35 


305815.20 


692 


2173.98 


376098.91 


760 


2387.61 


453645.98 


625 


1963.50 


306796.16 


693 


2177.12 


377186.68 


761 


2390.75 


454840.57 


626 


1966.64 


307778.69 


694 


2180.27 


378276.03 


762 


2393.89 


456036.73 


627 


1969.73 


308762.75 


695 


2183.41 


379366.95 


763. 


2397.04 


457234.46 


628 


1972.92 


309748. 4/ 


696 


2186.55 


380459.44 


764 


2400.18 


458433.77 


629 


1976.06 


310735.71 


697 


2189.69 


381553.50 


765 


2403.32 


459634.64 


630 


1979.20 


311724.53 


698 


2192.83 


382649.13 


766 


2406.46 


460837.08 


631 


1982.35 


312714.92 


699 


2195.97 


383746.33 


767 


2409.60 


462041.10 


632 


1985.49 


313706.88 


700 


2199.11 


384845.10 


768 


2412.74 


463246.69 


633 


1988.63 


314700.40 


701 


2202.26 


385945.44 


769 


2415.88 


464453.84 


634 


1991.77 


315695.50 


702 


2205.40 


387047.36 


770 


2419.03 


465662.57 


635 


1994.91 


3 1 6692 . 1 7 


703 


2208.54 


388150.84 


771 


2422. 1, 


466872.87 


636 


1998.05 


317690.42 


704 


2211.68 


389255.90 


772 


2425.31 


468084.74 


637 


2001. 19 


318690.23 


705 


2214.82 


390362.52 


773 


2423.45 


469298.18 


638 


2004.34 


319691.61 


706 


2217.96 


391470.72 


774 


2431.59 


470513.19 


639 


2007.48 


320694.56 


707 


2221.11 


392580.49 


775 


2434.73 


471729.77 


640 


2010.62 


321699.09 


708 


2224.25 


393691.82 


776 


2437.88 


472947.92 


641 


2013.76 


322705.18 


709 


2227.39 


394804.73 


777 


2441.02 


474167.65 


642 


2016.90 


323712.85 


710 


2230.53 


395919.21 


778 


2444.16 


475388.94 


643 


2020.04 


324722.09 


711 


2233.67 


397035.26 


779 


2447.30 


476611.81 


644 


2023. 19 


325732.89 


712 


2236.81 


398152.89 


780 


2450.44 


477836.24 


645 


2026.33 


326745.27 


713 


2239.96 


399272.03 


781 


2453.58 


479062.25 


646 


2029.47 


327759.22 


714 


2243.10 


00392.84 


782 


2456.73 


480289.83 


647 


2032.61 


328774.74 


715 


2246.24 


401515.18 


703 


2459.87 


481518.97 


648 


2035.75 


329791.83 


716 


2249.38 


402639.08 


784 


2463.01 


482749.69 


649 


2038.89 


330810.49 


717 


2252.52 


403764.56 


785 


2466.15 


483981.98 


650 


2042.04 


331830.72 


718 


2255.66 


40489 1 . 60 


786 


2469.29 


485215.84 


651 


2045. 18 


332852.53 


719 


2258.81 


406020.22 


787 


2472.43 


486451.28 


652 


2048.32 


333875.90 


720 


2261.95 


407150.41 


788 


2475.58 


487688.28 


653 


2051.46 


334900.85 


721 


2265.09 


408282.17 


789 


2478.72 


488926.85 


654 


2054.60 


335927.36 


722 


2268.23 


409415.50 


790 


2481.86 


490166.99 


655 


2057.74 


336955.45 


723 


2271.37 


410550.40 


791 


2485.00 


491408.71 


655 


2060.88 


337985.10 


724 


2274.51 


411686.87 


792 


2488.14 


492651.99 


657 


2064.03 


339016.33 


725 


2277.65 


412824.91 


793 


2491.28 


493896.85 


653 


2067. 17 


340049.13 


726 


2280.80 


413964.52 


794 


2494.42 


495143.28 


659 


2070.3 1 


341083.50 


727 


2283.94 


415105.71 


795 


2497.57 


496391.27 


660 


2073.45 


342119.44 


728 


2287.08 


416248.46 


796 


2500.71 


497640.84 


661 


2076 59 


343156.95 


729 


2290.22 


417392.79 


797 


2503.85^ 


498891.98 


662 2079. 731344196.03 


730 


2293.36 


418538.68 


798 2506.99 500144.69 



CIRCUMFERENCES AND AREAS OF CIRCLES. 



110 



Area. 



Circum.l Area. 



Diam. Cireum. 



2937.39 
2940.53 
2943.67 
2946.81 
2949.96 
2953.10 
2956.24 
2959.38 
2^62.52 
2965.66 
2968.81 
2971.95 
2975.09 
2978.23 
2981.37 
2984.51 
2987.65 
2990.80 
2993.94 
2997 . 08 
3000.22 
3003.36 
3006.50 
3009.65 
3012.79 
3015.93 
3019.07 
3022.21 
3025.35 
3028.50 
3031.64 
3034.78 
3037.92 
3041.06 
3044.20 
3047.34 
3050.49 
3053.63 
3056.77 
3059.91 
3063.05 
3066.19 
3069.34 
3072.48 
3075.62 
3078.76 
3081.90 
3085.04 
3088.19 
3091.33 
3094.47 
3097.61 
3100.75 
3103.89 
3107.04 
3110.18 
3113.32 
3116.46 
3119.60 
3122.74 
3125.88 
3129.03 
3132.17 
3135.31 
3138.45 
3141.59 



Area. 



799 
800 

801 
802 
803 
804 
805 
806 
807 
808 
809 
810 
811 
812 
813 
814 
815 
816 
817 
818 
819 
820 
821 
822 
823 
824 
825 
826 
827 
828 
829 
830 
831 
832 
833 
834 
835 
836 
837 
838 
839 
840 
841 
842 
843 
844 
845 
846 
847 
848 
849 
850 
851 
852 
853 
854 
855 
856 
857 
858 
859 
860 
861 
862 
863 
864 
865 
866 



2510 

2513 

2516 

2519 

2522 

2525 

2528 

2532 

2535 

2538. 

2541. 

2544. 

2547. 

2550. 

2554. 

2557. 

2560. 

2563 

2566 

2569 

2572. 

2576 

2579 

2582 

2585 

2588. 

2591 

2594. 

2598 

2601. 

2604 

2607. 

2610. 

2613. 

2616. 

2620. 

2623. 

2626. 

2629. 

2632. 

2635. 

2638. 

2642 

2645. 

2648 

2651. 

2654 

2657. 

2660 

2664. 

2667. 

2670 

2673 

2676 

2679 

2682. 

2686. 

2689. 

2692, 

2695, 

2698. 

2701. 

2704 

2708 

2711 

2714 

2717 

2720 



13 501398 
27 502654 
42 503912 
56J505171 



506431 

507693 

508957 

5 1 0222 

511489 

512758 

514028 

515299 

516572 

517847 

519123 

520401 

521681 

522962 

524244 

525528 

5268 1 4 

528101. 

529390 

530680. 

531972 

533266. 

534561 

535858. 

537156 

538456. 

539757 

541060. 

542365 

543671. 

544979. 

546288. 

547599. 

548911. 

550225. 

551541. 

552858. 

554176. 

555497 

556819 

558142 

559467. 

560793 

562122. 

563451 

564782. 

566115. 

567450. 

568786. 

570123. 

571462. 

572803. 

574145. 

575489, 

576834, 

578181, 

579530, 

580880. 

582232, 

5G3585, 

584940 

586296 

587654 

589014 



867 
868 
869 
870 
871 
872 
873 
874 
875 
876 
877 
878 
879 
880 
881 
882 
883 
884 
885 
886 
887 



890 
891 
892 
893 
894 
895 
896 
897 
898 
899 
900 
901 
902 
903 
904 
905 
906 
907 
908 
909 
910 
911 
912 
913 
914 
915 
916 
917 
918 
919 
920 
921 
922 
923 
924 
925 
926 
927 
928 
929 
930 
931 
932 
933 
934 



2723.761590375 
2726.90J591737, 
2730.041593102. 
2733.19,594467. 
2736.331595835, 
2739.47!597204. 
2742.611598574. 
2745.75 599946. 
2748.89 601320. 
2752.04 602695. 
2755.181604072. 
2758.32 605450. 



935 
936 
937 
938 
939 
940 
941 



2761.46 
2764.60 
2767.74 
2770.88 
2774.03 
2777,17 
2780.31 
2703.45 
2786.59 
2789.73 
2792.88 
2796.02 
2799.16 
2802.30 
2805.44 
2808.58 
2811.73 
2814.87 
2818.01 
2821.15 
2824.29 
2827.43 
2830.58 
2833.72 
2836.86 
2840.00 
2843.14 
2846.28 
2849.42 
2852.57 
2855.71 
2858.85 
2861.99 
2865.13 
2868.27 
2871.42 
2874.56 
2877.70 
2880.84 
2883.98 
2887.12 
2890.27 
2893.41 
2896.55 
2899.69 
2902.83 
2905.97 
2909.11 
2912.26 
2915.40 



606830. J 

6082 12.: 

609595. 

610980J 

612366. 

613754. 

615143. 

616534.. 

617926.' 

619321. 

620716j 

622113. 

623512. 

624913J 

6:6314.' 

627718 

629123.. 

630530.; 

631938.4 

633348.; 

634759. 

636172.5 

637587J 

639003.0 

640420.; 

641839.9 

643260.: 

644683J 

646107J 

647532. 

648959. 

650388.2 

6518 ' 

653250.2 

654683. f 

656118 

657554.' 

658993.' 

660432. 

661873., 

66331 6. ( 

664761 . 

t 66206.' 

667654. 

669103 

670554. 

672006.: 

673460.1 

674915. 

676372.: 



2918.54J677830.J 
2921.68|679290.i 
2924.82 680752. 
2927.96 ! 682215.i 
2931 . 11 683680. 
2934.25 6851 46. i 



81 


942 


47 


943 


70 


944 


50 


945 


88 


946 


rV 


947 


4 


948 




949 




950 


31 


951 


11 


952 


4;-', 


953 


: 


954 


9^ 


955 


01 


956 


66 


957 


89 


958 


68 


959 


04 


960 


9f 


961 


-:■<; 


962 


5( 


963 


?.} 


964 




965 




966 


58 


967 


51 


968 


01 


969 


09 


970 


73 


971 


95 


972 


73 


973 


09 


974 


01 


975 


51 


976 


58 


977 


17. 


978 


-n 


979 


21 


980 


56 


981 


48 


982 


98 


983 


04 


984 


68 


985 


88 


986 


66 


987 


01 


988 


92 


989 


41 


990 


47 


991 


1(1 


992 


30 


993 


08 


994 


■■:; 


995 


3; 


996 


r-l 


997 


87 


998 


50 


999 


69 


1000 



686614.71 
688084. 19 
689555.24 
691027.86 
692502.05 
693977.82 
695455. 15 
696934.06 
698414.53 
699896.58 
701380.19 
702865.38 
704352.14 
705840.47 
707330.37 
708821.84 
710314.88 
711809.50 
713305.68 
714803.43 
716302.76 
717803.66 
719306.12 
720810.16 
722315.77 
723822*. 95 
725331.70 
726842.02 
728353.91 
729867.37 
731382.40 
732899.01 
734417.18 
735936.93 
737458.24 
738981.13 
740505.59 
742031.62 
743559.22 
745088.39 
746619. 13 
748151.44 
749685 -.32 
751220.78 
752757.80 
754296.40 
755836.56 
757378.30 
758921.61 
760466.48 
762012.93 
763560.95 
765110.54 
766661 .70 
768214.44 
769768.74 
771324.61 
772882.06 
774441.07 
776001.66 
777563.82 
779127.54 
780692 . 84 
782259.71 
783828.15 
785398.16 



120 CIRCUMFERENCE OP CIRCLES, FEET AND INCHES. 



OONlAiAMOOO- 



■XOCOO CAT 



T\Q t>>0 — © CN -3- m r^ O — ON'fifilMJOONf mrsOvOOf 



-NtvOMJ- 



^ "$• vO r» O © - 



^Tr^N^-ON'TmtN^-ON'rmN 



u — TOO — Tt^OcAvOOcA^OC- 



l-miniri\OvOvOf>.r«.r^coooooooo^OO^O 



vOoOO — — mmvOooO- — cat \O0O© — — CA T ^O CO 0\ — — tr\T \OQ0& — 



- — — cseNCNCMcncAcATTTir 



nvO^OOtstNlNOOOOoOtoaaO^O 



^oooo-cc,ifii>,cooo-^ift^cooo-t(MnvOooO' tnm>oooo 



ocntu-u^oo©^ 



ni\0»OONc<MnN00OO- CAint^OO©© — C 



+J — ■'^-r^OcA^OC^cAvOO^C- 



+a tf\NO(A^O>Nin!>NiACCI- T rv — ^■tsOff\vOO>(A'00>Nin!0.- moo- 



-; — CN fN CN <* 



rivO»OvO*OtsNNOOOOooaoao 



H >o go o ■ NTj-vOr^o — — fNTvOr*o*-- ©<NT>oi>»t>— ■©NT»ni>.0'>--© 

-Tj-hN,— 

-ivOvOvcot^r^r^ooooooo^o^o^o 



^ cA T nO GO C - * ■ 

+-j ca vo o n »**> o* n «■* * 



- (NT vO GO C> — — CNT vO r>0^ - 



-oiT \Dr-> o 



'.-cAin-oioo- 
; ca vo o^ cs in go — 



nvOoOO ^^-OCOO- 



at\0 ooo* — — cat o 



fl-s 



o — N«i-iriiOMOO>o- 



AREAS OF THE SEGMENTS OF A CIRCLE. 



121 



AREAS OF THE SEGMENTS OF A CIRCLE. 
(Diameter=l; Rise or Height in parts of Diameter being given.) 

Rule for Use of the Table. — Divide the rise or height of the segment 
by the diameter. Multiply the area in the table corresponding to the 
quotient thus found by the square of the diameter. 

// the segment exceeds a semicircle its area is area of circle — area of seg- 
ment whose rise is (diam. of circle ~- rise of given segment). 

Given chord and rise, to find diameter. Diam. = (square of half chord -s- 
rise) + rise. The half chord is a mean proportional between the two parts 
into which the chord divides the diameter which is perpendicular to it. 



Rise 




Rise 




Rise 




Rise 




Rise 




-*- 


Area. 


-j- 


Area. 


-L- 


Area. 


-i- 


Area, 


-^ 


Area. 


Diam. 




Diam: 




Diam. 


.04514 


Diam. 




Diam. 




.001 


.00004 


.054 


•01646 


.107 


.16 


.08111 


.213 


.12235 


.002 


.00012 


.055 


.01691 


.108 


.04576 


.161 


.08185 


.214 


.12317 


.003 


.00022 


.056 


.01737 


.109 


.04638 


.162 


.03258 


.215 


.12399 


.004 


.00034 


.057 


.01783 


.11 


.04701 


.163 


.08332 


.216 


.12481 


.005 


.00047 


.058 


.01830 


.111 


.04763 


.164 


.08406 


.217 


.12563 


.006 


.00062 


.059 


.01877 


.112 


.04826 


.165 


.08480 


.218 


.12646 


.007 


.00078 


.06 


.01924 


.113 


.04889 


.166 


.08554 


.219 


.12729 


.003 


.00095 


.061 


.01972 


.114 


.04953 


.167 


.08629 


.22 


.12811 


.009 


.00113 


.062 


.02020 


.115 


.05016 


.168 


.08704 


.221 


.12894 


.01 


.00133 


.063 


.02068 


.116 


.05080 


.169 


.08779 


.222 


.12977 


.011 


.00153 


.064 


.02117 


.117 


.05145 


.17 


.08854 


.223 


.13060 


.012 


.00175 


.065 


.02166 


.118 


.05209 


.171 


.08929 


.224 


.13144 


.013 


.00197 


.066 


.02215 


.119 


.05274 


.172 


.09004 


.225 


.13227 


.014 


.0022 


.067 


.02265 


.12 


.05338 


.173 


.09080 


.226 


.13311 


.015 


.00244 


.068 


.02315 


.121 


.05404 


.174 


.09155 


.227 


.13395 


.016 


.00268 


.069 


.02366 


.122 


.05469 


.175 


.09231. 


.228 


.13478 


.017 


.00294 


.07 


.02417 


.123 


.05535 


.176 


.09307 


.229 


.13562 


.018 


.0032 


.071 


.02468 


.124 


.05600 


.177 


.09384 


.23 


.13646 


.019 


.00347 


.072 


.02520 


.125 


.05666 


.178 


.09460 


.231 


.13731 


.02 


.00375 


.073 


.02571 


.126 


.05733 


.179 


.09j37 


.232 


.13815 


.021 


.00403 


.074 


.02624 


.127 


.05799 


.18 


.09613 


.233 


.13900 


.022 


00432 


.075 


.02676 


.128 


.05866 


.181 


.09690 


.234 


.13984 


.023 


.00462 


.076 


.02729 


.129 


.05933 


.182 


.09767 


.235 


.14069 


.024 


.00492 


.077 


.02782 


.13 


.06000 


.183 


.09845 


.236 


.14154 


.025 


.00523 


.078 


.02836 


.131 


.06067 


.184 


.09922 


.237 


.14239 


.026 


.00555 


.079 


.02889 


.132 


.06135 


.185 


.10000 


.238 


.14324 


.027 


.00587 


.08 


.02943 


.133 


.06203 


.186 


.10077 


.239 


.14409 


.028 


.00619 


.081 


.02998 


.134 


.06271 


.187 


.10155 


.24 


.14494 


.029 


.00653 


.082 


.03053 


.135 


.06339 


.188 


.10233 


.241 


.14580 


.03 


.00687 


.033 


.03108 


.136 


.06407 


.189 


.10312 


.242 


. 1 4666 


.031 


.00721 


.084 


.03163 


.137 


.06476 


.19 


.10390 


.243 


.14751 


.032 


.00756 


.085 


.03219 


.138 


.06545 


.191 


.10469 


.244 


.14837 


.033 


.00791 


.086 


.03275 


.139 


.06614 


.192 


.10547 


.245 


.14923 


.034 


.00327 


.087 


.03331 


.14 


.06683 


.193 


.10626 


.246 


.15009 


.035 


.00864 


.088 


.03387 


.141 


.06753 


.194 


.10705 


.247 


.15095 


.036 


.00901 


.089 


.03444 


.142 


.06822 


.195 


.10784 


.248 


.15182 


.037 


.00938 


.09 


.03501 


.143 


.06892 


.196 


.10864 


.249 


.15263 


.038 


.00976 


091 


.03559 


.144 


.06963 


.197 


.10943 


.25 


.15355 


.039 


.01015 


.092 


.03616 


.145 


.07033 


.198 


.11023 


.251 


.15441 


.04 


.01054 


.093 


.03674 


.146 


.07103 


.199 


.11102 


.252 


.15528 


.041 


.01093 


.094 


.03732 


.147 


.07174 


.2 


.11182 


.253 


.15615 


.042 


.01133 


.095 


.03791 


.148 


.07245 


.201 


J 1262 


.254 


.15702 


.043 


.01173 


.096 


.03850 


.149 


.07316 


.202 


.11343 


.255 


.15789 


.044 


.01214 


.097 


.03909 


.15 


.07387 


.203 


.11423 


.256 


.15876 


.045 


.01255 


.098 


.03968 


.151 


.07459 


.204 


.11504 


.257 


.15964 


.046 


.01297 


.099 


.04028 


.152 


.07531 


.205 


.11584 


.258 


.16051 


.047 


.01339 


.1 


.04087 


.153 


.07603 


.206 


.11665 


.259 


.16139 


.048 


.01382 


.101 


.04148 


.154 


.07675 


.207 


.11746 


.26 


J 6226 


.049 


.01425 


.102 


.04208 


.155 


.07747 


.203 


.11827 


.261 


.16314 


.05 


.01468 


.103 


.04269 


.156 


.07819 


.209 


.11908 


.262 


.16402 


051 


.01512 


.104 


.04330 


.157 


.07892 


.21 


.11990 


.263 


.16490 


.052 


01556 


.105 


.04391 


.158 


.07965 


.211 


.12071 


.264 


.16578 


.053 


.01601 


.106 


.04452 


.159 


.08038 


.212 


.12153 


.265 


.16666 



MATHEMATICAL TABLES. 



Rise 




Rise 




Rise 




Rise 




Rise 






Area. 


-H 


Area. 


■*■ 


Area. 


•*" 


Area. 


-i- 


Area. 


Diam. 




Diam. 




Diam. 




Diam. 




Diam. 




.266 


.16755 


.313 


.21015 


.36 


.25455 


.407 


.30024 


.454 


.34676 


.267 


.16843 


.314 


.21108 


.361 


.25551 


.408 


.30122 


.455 


.34776 


.268 


.16932 


.315 


.21201 


.362 


.25647 


.409 


.30220 


.456 


.34876 


.269 


17020 


316 


.21294 


.363 


.25743 


.41 


.30319 


.457 


.34975 


.27 


.17109 


.317 


.21387 


.364 


.25839 


.411 


.30417 


.458 


.35075 


.271 


.17198 


.318 


.21480 


.365 


.25936 


.412 


.30516 


.459 


.35175 


.272 


.17287 


.319 


.21573 


.366 


.26032 


.413 


.30614 


.46 


.35274 


.273 


.17376 


.32 


.21667 


.367 


.26128 


.414 


.30712 


.461 


.35374 


.274 


.17465 


.321 


.21760 


.368 


.26225 


.415 


.30811 


.462 


.35474 


.275 


.17554 


.322 


.21853 


.369 


.26321 


.416 


.30910 


.463 


.35573 


.276 


.17644 


.323 


.21947 


.37 


.26418 


.417 


.31008 


.464 


.35673 


.277 


.17733 


.324 


.22040 


.371 


.26514 


.418 


.31107 


.465 


.35773 


.278 


.17823 


.325 


.22134 


.372 


.26611 


.419 


.31205 


.466 


.35873 


.279 


.17912 


.326 


.22228 


.373 


.26708 


.42 


.31304 


.467 


.35972 


.23 


.18002 


.327 


.22322 


.374 


.26805 


.421 


.31403 


.468 


.36072 


.281 


.18092 


.328 


.22415 


.375 


.26901 


.422 


.31502 


.469 


.36172 


.282 


.18182 


.329 


.22509 


.376 


.26998 


.423 


.31600 


.47 


.36272 


.283 


.18272 


.33 


.22603 


.377 


.27095 


.424 


.3 1 699 


.471 


.36372 


.284 


.18362 


.331 


.22697 


.378 


.27192 


.425 


.31798 


.472 


.36471 


.285 


.18452 


.332 


.22792 


.379 


.27289 


.426 


.31897 


.473 


.36571 


.286 


.18542 


.333 


.22886 


.38 


.27386 


.427 


.31996 


.474 


.36671 


.287 


.18633 


.334 


.22980 


.381 


.27483 


.428 


.32095 


.475 


.36771 


.283 


.18723 


.335 


.23074 


.382 


.27580 


.429 


.32194 


.476 


.36871 


.289 


.18814 


.336 


.23169 


.383 


.27678 


.43 


.32293 


.477 


.36971 


.29 


.18905 


.337 


.23263 


.384 


.27775 


.431 


.32392 


.478 


.37071 


.291 


.18996 


.338 


.23358 


.385 


.27872 


.432 


.32491 


.479 


.37171 


.292 


.19086 


.339 


.23453 


.386 


.27969 


.433 


.32590 


.48 


.37270 


.293 


.19177 


.34 


.23547 


.387 


.28067 


.434 


.32689 


.481 


.37370 


.294 


.19268 


.341 


.23642 


.388 


.28164 


.435 


.32788 


.482 


.37470 


.295 


.19360 


.342 


.23737 


.389 


.28262 


.436 


.32887 


.483 


.37570 


.296 


.19451 


.343 


.23332 


.39 


.28359 


.437 


.32987 


.484 


.37670 


.297 


.19542 


.344 


.23927 


.391 


.28457 


.438 


.33086 


.485 


.37770 


.293 


.19634 


.345 


.24022 


.392 


.28554 


.439 


.33185 


.486 


.37870 


.299 


.19725 


.346 


.24117 


.393 


.28652 


.44 


.33284 


.487 


.37970 


.3 


.19817 


.347 


.24212 


.394 


.28750 


.441 


.33334 


.488 


.38070 


.301 


.19908 


.348 


.24307 


.395 


.28848 


.442 


.33483 


.489 


.38170 


.302 


.20000 


.349 


.24403 


.396 


.28945 


.443 


.33582 


.49 


.38270 


.303 


.20092 


.35 


.24493 


.397 


.29043 


.444 


.33682 


.491 


.38370 


.304 


.20184 


.351 


.24593 


.398 


.29141 


.445 


.33781 


.492 


.38470 


.305 


.20276 


.352 


.24689 


.399 


.29239 


.446 


.33880 


.493 


.38570 


.306 


.20368 


.353 


.24784 


.4 


.29337 


.447 


.33980 


.494 


.38670 


307 


.20460 


.354 


.24880 


.401 


.29435 


.448 


.34079 


.495 


.38770 


.303 


.20553 


.355 


.24976 


.402 


.29533 


.449 


.34179 


.496 


.38870 


.309 


.20645 


.356 


.25071 


.403 


.29631 


.45 


.34278 


.497 


.38970 


.31 


.20738 


.357 


.25167 


.404 


.29729 


.451 


.34378 


.498 


.39070 


.311 


.20830 


.358 


.25263 


.405 


.29827 


.452 


.34477 


.499 


.39170 


.312 


.20923 


.359 


.25359 


.406 


.29926 


.453 


.34577 


.5 


.39270 



For rules for finding the area of a segment see Mensuration, page 61. 

LENGTHS OF CIRCULAR ARCS. 

(Degrees being given. Radius of Circle =■ 1.) 

Formula. — Length of arc — ~ X radius X number of degrees. 

Rule. — Multiply the factor in the table (see next page) for any given 
number of degrees by the radius. 

Example. — Given a curve of a radius of 55 feet and an angle of 78° 20'. 

Factor from table for 78° 1 .3613568 

Factor from table for 20' .0058178 

Factor. 1.3671746 

1.3671746X55 = 75.19 feet. 



LENGTHS OF CIRCULAR ARCS. 



123 



Factors for Lengths of Circular Arcs. 



Degrees. 


Minutes. 


1 


.0174533 


61 


1.0646508 


121. 


2.1118484 


1 


.0002909 


2 


.0349066 


62 


1.0821041 


122 


2.1293017 


2 


.0005818 


3 


.0523599 


63 


1.0995574 


123 


2.1467550 


3 


.0008727 


4 


.0698 1 32 


64 


1.1170107 


124 


2. 1 642083 


4 


.001 1636 


5 


.0872665 


65 


1.1344640 


125 


2.1816616 


5 


.0014544 


6 


.1047198 


66 


1.1519173 


126 


2.1991149 


6 


.0017453 


7 


.1221730 


67 


1.1693706 


127 


2.2165682 


7 


.0020362 


8 


.1396263 


68 


1.1868239 


128 


2.2340214 


8 


.0023271 


9 


.1570796 


69 


1.2042772 


129 


2.2514747 


9 


.0026180 


10 


.1745329 


70 


1.2217305 


130 


2.2689280 


10 


.0029089 


11 


.1919862 


71 


1.2391838 


131 


2.2863813 


11 


.003 1 998 


12 


.2094395 


72 


1.2566371 


132 


2.3038346 


12 


.0034907 


13 


.2268928 


73 


1 .2740904 


133 


2.3212879 


13 


.0037815 


14 


.2443461 


74 


1.2915436 


134 


2.3387412 


14 


.0040724 


15 


.2617994 


75 


1.3089969 


135 


2.3561945 


15 


.0043633 


16 


.2792527 


76 


1.3264502 


136 


2.3736478 


16 


.0046542 


17 


• .2967060 


77 


1.3439035 


137 


2.3911011 


17 


.0049451 


18 


.3141593 


78 


1.3613568 


138 


2.4085544 


18 


.0052360 


19 


.3316126 


79 


1.3788101 


139 


2.4260077 


19 


.0055269 


20 


.3490659 


80 


1.3962634 


140 


2.4434610 


20 


.0058178 


21 


.3665191 


81 


1.4137167 


141 


2.4609142 


21 


.0061087 


22 


.3839724 


82 


1.4311700 


142 


2.4783675 


22 


.0063995 


23 


.4014257 


83 


1.4486233 


143 


2.4958208 


23 


.0066904 


24 


.4188790 


84 


1 .4660766 


144 


2.5132741 


24 


.0069813 


25 


.4363323 


85 


1.4835299 


145 


2.5307274 


25 


.0072722 


26 


.4537856 


86 


1.5009832 


146 


2.5481807 


26 


.0075631 


27 


.4712389 


87 


1.5184364 


147 


2.5656340 


27 


.0078540 


28 


.4886922 


88 


1.5358897 


148 


2.5830873 


28 


.0081449 


29 


.5061455 


89 


1.5533430 


149 


2.6005406 


29 


.0084358 


30 


.5235988 


90 


1.5707963 


150 


2.6179939 


30 


.0087266 


31 


.5410521 


91 


1.5882496 


151 


2.6354472 


31 


.0090175 


32 


.5585054 


92 


1.6057029 


152 


2.6529005 


32 


.0093084 


33 


.5759587 


93 


1.6231562 


153 


2.6703538 


33 


.0095993 


34 


.5934119 


94 


1 .6406095 


154 


2.6878070 


34 


.0098902 


35 


.6108652 


95 


1.6580628 


155 


2.7052603 


35 


.0101811 


36 


.6283185 


96 


1.6755161 


156 


2.7227136 


36 


.0104720 


37 


.6457718 


97 


1 .6929694 


157 


2.7401669 


37 


.0107629 


38 


.6632251 


98 


1.7104227 


158 


2.7576202 


38 


.0110538 


39 


.6806784 


99 


1.7278760 


159 


2.7750735 


39 


.0113446 


40 


.6981317 


100 


1.7453293 


160 


2.7925268 


40 


.0116355 


41 


.7155850 


101 


1.7627825 


161 


2.8099801 


41 


.0119264 


42 


.7330383 


102 


1.7802358 


162 


2.8274334 


42 


.0122173 


43 


.7504916 


103 


1.7976891 


163 


2.8448867 


43 


.0125082 


44 


.7679449 


104 


1.8151424 


164 


2.8623400 


44 


.0127991 


45 


.7853982 


105 


1.8325957 


165 


2.8797933 


45 


.0130900 


46 


.8028515 


106 


1 .8500490 


166 


2.8972466 


46 


.0133809 


47 


.8203047 


107 


1.8675023 


167 


2.9146999 


47 


.0136717 


48 


.8377580 


108 


1.8849556 


168 


2.9321531 


48 


.0139626 


49 


.8552113 


109 


1 .9024089 


169 


2.9496064 


49 


.0142535 


50 


.8726646 


-110 


1.9198622 


170 


2.9670597 


50 


.0145444 


51 


.8901179 


111 


1.9373155 


171 


2.9845130 


51 


.0148353 


52 


.9075712 


112 


1.9547688 


172 


3.0019663 


52 


.0151262 


53 


.9250245 


113 


1.9722221 


173 


3.0194196 


53 


.0154171 


54 


.9424778 


114 


1 .9896753 


174 


3.0368729 


54 


.0157080 


55 


.95993 1 1 


115 


2.0071286 


175 


3.0543262 


55 


.0159989 


56 


.9773844 


116 


2.0245819 


176 


3.0717795 


56 


.0162897 


57 


.9948377 


117 


2.0420352 


177 


3.0892328 


57 


.0165806 


58 


1.0122910 


118 


2.0594885 


178 


3.1066861 


58 


.0168715 


59 


1.0297443 


119 


2.0769418 


179 


3.1241394 


59 


.0171624 


60 


1.0471976 


120 


2.0943951 


180 


3.1415927 


60 


.0174533 



124 






MATHEMATICAL TABLES. 






LENGTHS OF CIRCULAR ARCS. 


(Diameter = 1 


. Given the Chord and Height of the Arc.) 


Rule for Use of the Table. — Divide the height by the chord. Find! 


in. the column of heights the number equal to this quotient. Take out the' 


corresponding number from the column of lengths. Multiply this last 
number by the length of the given chord; the product will be length of the! 


If the arc is greater than a semicircle, first find the diameter from the. 


formula, Diam. = (square of half chord -*- rise) + rise; the formula is true 


whether the arc exceeds a semicircle or not. Then find the circumference. 


From the diameter 


subtract the given height of arc, the remainder will be 


height of the smaller arc of the circle; find its length according to the rule, 


and subtract it from the circumference. 


Hgts. 


Lgths. 


Hgts. 


Lgths. 


Hgts. 


Lgths. 


Hgts. 


Lgths. 


Hgts. 


Lgths. 1 


.001 


1 .00002 


.15 


1 .05896 


.238 


1.14480 


.326 


1 .26288 


.414 


1.407811 


.005 


1 .00007 


.152 


1.06051 


.24 


1.14714 


.328 


1 .26588 


.416 


1.41141 


.01 


1 .00027 


.154 


1 .06209 


.242 


1.14951 


.33 


1 .26892 


.418 


1.4150 


.015 


1.00061 


.156 


1 .06368 


.244 


1.15189 


.332 


1.27196 


.42 


1.4186 


.02 


1.00107 


.158 


1.06530 


.246 


1.15428 


.334 


1.27502 


.422 


1 .4222 


.025 


1.00167 


.16 


1 .06693 


.248 


1.15670 


.336 


1.27810 


.424 


1.4258: 


.03 


1 .00240 


.162 


1.06353 


.25 


1.15912 


.338 


1.28118 


.426 


1.4294. 


.035 


1.00327 


.164 


1.07025 


.252 


1.16156 


.34 


1 .28428 


.428 


I.4330 1 


.04 


1.00426 


.166 


1.07194 


.254 


1.16402 


.342 


1 .28739 


.43 


1.4367.1 


.045 


1.00539 


.163 


1 .07365 


.256 


1.16650 


.344 


1 .29052 


.432 


1 .4-403'! 


.05 


1.00665 


.17 


1.07537 


.258 


1.16899 


.346 


1.29366 


.434 


1.4440 


055 


1.00305 


.172 


1.07711 


.26 


1.17150 


.348 


1.29681 


.436 


1.4477; 


.05 


1.O0957 


.174 


1.07833 


.262 


1.17403 


.35 


1 .29997 


.438 


1.4514:1 


.055 


1.01123 


.176 


1.03066 


.264 


1.17657 


.352 


1.30315 


.44 


1.4551:1 


.0/ 


1.01302 


.178 


1.03246 


.266 


1.17912 


.354 


1 .30634 


.442 


1.4588:1 


.075 


1.01493 


.18 


1.03423 


.268 


1.18169 


.356 


1.30954 


.444 


1.4625:i 


.03 


1.01693 


.182 


1.03611 


.27 


1.18429 


.358 


1.31276 


.446 


1.46621! 


.035 


1.01916 


.184 


1.08797 


.272 


1.18689 


.36 


1.31599 


.448 


1 .4700; 


.09 


1.02146 


.186 


1.08934 


.274 


1.18951 


.362 


1.31923 


.45 


1.4737; 


.095 


1.02339 


.188 


1.09174 


.276 


1.19214 


.364 


1 .32249 


.452 


1.4775; 


.10 


1.02646 


.19 


1 .09365 


.278 


1.19479 


.366 


1.32577 


.454 


1.4813 j 


.102 


1.02752 


.192 


1.09557 


.28 


1.19746 


.368 


1 .32905 


.456 


1.4850' 1 


.104 


1 .02860 


.194 


1.09752 


.282 


1.20014 


.37 


1.33234 


.458 


1.4888<l 


.106 


1 .02970 


.196 


1 .09949 


.284 


1 .20284 


.372 


1.33564 


.46 


1.4926' I 


.108 


1.03032 


.198 


1.10147 


.286 


1.20555 


.374 


1 .33896 


.462 


1 .4965;] 


.11 


1.03196 


.20 


1.10347 


.288 


1 .20827 


.376 


1 .34229 


.464 


1.5003; 


.112 


1.03312 


.202 


1.10548 


.29 


1.21102 


.378 


1 .34563 


.466 


1.504 If 


.114 


1.03430 


.204 


1.10752 


.292 


1.21377 


.38 


1 .34899 


.468 


1.5080( 


.116 


1.03551 


.206 


1.10958 


.294 


1.21654 


.382 


135237 


.47 


1.5118; 


.118 


1.03672 


.203 


1.11165 


.296 


1.21933 


.384 


1.35575 


.472 


1.51571 


.12 


1.03797 


.21 


1.21374 


.293 


1.22213 


.386 


1.35914 


.474 


1.5195^ 


.122 


1.03923 


.212 


1.11584 


.30 


1 .22495 


.388 


1.36254 


.476 


1.5234( 


.124 


1.04051 


.214 


1.11796 


.302 


1 .22778 


.39 


1.36596 


.478 


1.52736 


.126 


1.04181 


.216 


1.12011 


.304 


1 .23063 


.392 


1 .36939 


.48 


1.53126 


.128 


1.04313 


.218 


1.12225 


.306 


1.23349 


.394 


1 .37283 


.482 


1.53516] 


.13 


1.04447 


.22 


1.12444 


303 


1.23636 


.396 


1.37628 


.484 


1.5391C! 


.132 


1.04534 


.222 


1.12664 


.31 


1 .23926 


.398 


1 .37974 


.486 


1 54302! 


.134 


1.04722 


.224 


1.12885 


.312 


1.24216 


.40 


1 .38322 


.488 


1.54696] 


.136 


1.04362 


.226 


1.13108 


.314 


1 .24507 


.402 


1.38671 


.49 


1.550911 


.138 


1.05003 


.228 


1.13331 


.316 


1.24801 


.404 


1.39021 


.492 


1.55487' 


.14 


1.05147 


.23 


1.13557 


.318 


1 .25095 


.406 


1.39372 


.494 


1.55854 


.142 


1.05293 


.232 


1.13785 


.32 


1.25391 


.408 


1.39724 


.496 


1.56282 


144 


1.05441 


.234 


1.1^015 


.322 


1 .25689 


.41 


1.40077 


.498 


1.56681 


145 


1.05591 


.236 


1.14247 


.324 


1 .25988 


.412 


1 .40432 


.50 


1.57080 


.143 


1.05743 







































SPHEKES. 






125 






SPHERES. 




(Some errors of 1 


n the last figure only. From Trautwine.) 


Diam. 


Sur- 
face. 


Vol- 
ume. 


Diam. 


Sur- 
face. 


Vol- 
ume. 


Diam. 


Sur- 
face. 


Vol- 
ume. 


V32 


.00307 


.00002 


31/4 


33.183 


17.974 


9 7/ 8 


306.36 


"504.21 


Vi6 


.01227 


.00013 


5/16 


34.472 


19.031 


10. 


314.16 


523.60 


3/32 


.02761 


.00043 


3/8 


35.784 


20.129 


1/8 


322.06 


543.48 


1/8 


.04909 


.00102 


7/16 


37.122 


21.268 


1/4 


330.06 


563.86 


5 /32 


.07670 


.00200 


1/2 


38.484 


22.449 


3/8 


338.16 


584.74 


3/16 


.11045 


.00345 


9/16 


39.872 


23.674 


1/3 


346.36 


606.13 


7/32 


.15033 


.00548 


5/8 


41.283 


24.942 


5/8 


354.66 


628.04 


1/4 


.19635 


.00818 


H/16 


42.719 


26.254 


3/4 


363.05 


650.46 


9/32 


.2485 1 


.01165 


3/4 


44.179 


27.611 


7/8 


371.54 


673.42 


5/16 


.30680 


.01598 


13/16 


45.664 


29.016 


11. 


380.13 


696.91 


U/32 


.37123 


.02127 


7/8 


47.173 


30.466 


1/8 


388.83 


720.95 


3/8 


.44179 


.02761 


15/16 


48.708 


31.965 


1/4 


397.61 


745.51 


13/32 


.51848 


.03511 


4. 


50.265 


33.510 


3/8 


406.49 


770.64- 


7/16 


.60132 


.04385 


1/8 


53.456 


36.751 


1/2 


415.48 


796.33 


15/32 


.69028 


.05393 


1/4 


56.745 


40.195 


5 /8 


424.50 


822.58 


1/2 


.78540 


.06545 


3/8 


60.133 


43.847 


3/4 


433.73 


849.40 


9/16 


.99403 


.09319 


1/2 


63.617 


47.713 


7/8 


443.01 


876.79 


5/8 


1 .2272 


.12783 


5/8 


67.201 


51.801 


12. 


452.39 


904.78 


H/16 


1 .4849 


.17014 


3/4 


70.883 


56.116 


1/4 


471.44 


962.52 


3/4 


1.7671 


.22089 


7/8 


74.663 


60.663 


1/2 


490.87 


1 022.7 


13/16 


2.0739 


.28084 


5. 


78.540 


65.450 


3/4 


510.71 


1085.3 


7/8 


2.4053 


.35077 


1/8 


82.516 


70.482 


13. 


530.93 


1150.3 


15/16 


2.7611 


.43143 


1/4 


86.591 


75.767 


1/4 


551.55 


1218.0 




3.1416 


.52360 


3/8 


90.763 


81 .308 


1/2 


572.55 


1288.3 


Vl6 


3.5466 


.62804 


1/2 


95.033 


87.113 


3/4 


593.95 


1361.2 


1/8 


3.9761 


.74551 


5/8 


99.401 


93.189 


14. 


615.75 


1436.8 


3/16 


4.4301 


.87681 


3/4 


103.87 


99.541 


1/4 


637.95 


1515.1 


1/4 


4.9088 


1 .0227 


7/8 


108.44 


106.18 


1/2 


660.52 


1596.3 


5/16 


5.4119 


1.1839 


6. 


113.10 


113.10 


3/4 


683.49 


1680.3 


3/8 


5.9396 


1.3611 


1/8 


117.87 


120.31 


15. 


706.85 


1767.2 


7/16 


6.4919 


1.5553 


1/4 


122.72 


127.83 


1/4 


730.63 


1857.0 


1/2 


7.0686 


1.7671 


3/8 


127.68 


135.66 


1/2 


754.77 


1949.8 


9/16 


7.6699 


1 .9974 


1/2 


132.73 


143.79 


3/4 


779.32 


2045.7 


5/8 


8.2957 


2.2468 


5/8 


137.89 


152.25 


16. 


804.25 


2144.7 


11/16 


8.9461 


2.5161 


3/4 


143.14 


161.03 


1/4 


829.57 


2246.8 


3/4 


9.6211 


2.8062 


7/8 


148.49 


170.14 


1/2 


855.29 


2352.1 


13/16 


10.321 


3.1177 


7. 


153.94 


179.59 


3/ 4 


881.42 


2460.6 


7/8 


1 1 .044 


3.4514 


1/8 


159.49 


189.39 


17. 


907.93 


2572.4 


15/16 


11.793 


3.8083 


1/4 


165.13 


199.53 


1/4 


934.83 


2687.6 




12.566 


4.1888 


3/8 


170.87 


210.03 


1/2 


962.12 


2806.2 


Vl6 


13.364 


4.5939 


1/2 


176.71 


220.89 


3/4 


989.80 


2928.2 


1/8 


14.186 


5.0243 


5/8 


182.66 


232.13 


18. 


1017.9 


3053.6 


3/16 


15.033 


5.4809 


3/4 


188.69 


243.73 


1/4 


1046.4 


3182.6 


1/4 


15.904 


5.9641 


7/8 


194.83 


255.72 


1/2 


1075.2 


3315.3 


5/16 


16.800 


6.4751 


8. 


201.06 


268.08 


3/4 


1104.5 


3451.5 


3/8 


17.721 


7.0144 


1/8 


207.39 


280.85 


19. 


1134.1 


3591.4 


7/18 


18.666 


7.5829 


1/4 


213.82 


294.01 


1/4 


1164.2 


3735.0 


1/2 


19.635 


8.1813 


3/8 


220.36 


307.58 


1/2 


1194.6 


3882.5 


9/16 


20.629 


8.8103 


1/2 


226.98 


321.56 


3/4 


1225.4 


4033.7 


5/8 


21.648 


9.4708 


5/8 


233.71 


335.95 


20. 


1256.7 


4188.8 


H/16 


22.691 


10.164 


3/4 


240.53 


350.77 


1/4 


1288.3 


4347.8 


3/4 


23.758 


10.889 


7/8 


247.45 


366.02 


1/?. 


1320.3 


4510.9 


13/16 


24.850 


1 1 .649 


9. 


254.47 


381.70 


3/4 


1352.7 


4677.9 


7/8 


25.967 


12.443 


1/8 


261.59 


397.83 


21. 


1385.5 


4849.1 


15/16 


27.109 


13.272 


1/4 


268.81 


414.41 


1/4 


1418.6 


5024.3 




28.274 


14.137 


3/8 


270.12 


43 1 .44 


1/2 


1452.2 


5203.7 


1/16 


29.465 


15.039 


1/2 


283.53 


448.92 


3/4 


1486.2 


5387.4 


1/8 


30.680 


15.979 


5/8 


291.04 


466.87 


22. 


1520.5 


55753 


3/16 


31.919 


16.957 


3/ 4 


289.65 


435.31 


1/4 '1555.3 


5767.6 



126 




MATHEMATICAL TABLES. 










SPHERES — Continued. 




Diam. 


Sur- 
face. 


Vol- 
ume. 


Diam. 


Sur- 
face. 


Vol- 
ume. 


Diam. 


Sur- 
face. 


Vol- 
ume. 


22 1/2 


1590.4 


5964.1 


40 1/2 


5153.1 


34783 


70 1/2 


15615 


183471 


3/4 


1626.0 


6165.2 


41. 


5281.1 


36087 


71. 


15837 


18740? 


23. 


1661.9 


6370.6 


1/2 


5410.7 


37423 


1/2 


16061 


19138? 


V4 


1698.2 


6580.6 


43. 


5541.9 


38792 




16286 


195433 


V2 


1735.0 


6795.2 


1/2 


5674.5 


40194 


' 1/2 


16513 


199532 


3/ 4 


1772.1 


7014.3 


43. 


5808.8 


41630 


73. 


16742 


203689 


24. 


1809.6 


7238.2 


V2 


5944.7 


43099 


1/2 


16972 


207903 


1/4 


1847.5 


7466.7 


44. 


6082.1 


44602 


74. 


17204 


212175 


1/2 


1885.8 


7700.1 


V2 


6221.2 


46141 


1/2 


17437 


216505 


3/4 


1924.4 


7938.3 


45. 


6361.7 


47713 


75. 


17672 


220894 


25. 


1963.5 


8181.3 


1/2 


6503.9 


49321 


1/2 


17908 


225341 


1/4 


2002.9 


8429.2 


46. 


6647.6 


50965 


78. 


18146 


229848 


V2 


2042.8 


8682.0 


1/2 


6792.9 


52645 


1/2 


18386 


234414 


3/4 


2083.0 


8939.9 


47. 


6939.9 


54362 


77. 


18626 


239041 


26. 


2123.7 


9202.8 


v 2 


7088.3 


56115 


1/2 


18869 


243728 


• 1/4 


2164.7 


9470.8 


48. 


7238.3 


57906 


78. 


19114 


248475 


V2 


2206.2 


9744.0 


V2 


7389.9 


59734 


1/2 


19360 


253284 


3 /4 


2248.0 


10022 


49. 


7543.1 


61601 


79. 


19607 


258155 


27. 


2290.2 


10306 


V2 


7697.7 


63506 


1/2 


19856 


26308S 


V4 


2332.8 


10595 


50. 


7854.0 


65450 


80. 


20106 


268083 


V2 


2375.8 


10889 


1/2 


8011.8 


67433 


1/2 


20358 


273141 


3/4 


2419.2 


11189 


51. 


8171.2 


69456 


81. 


20612 


278263 


28. 


2463.0 


11494 


V2 


8332.3 


71519 


1/2 


20867 


283447 


Vi 


2507.2 


11805 


52. 


8494.8 


73622 


82. 


21124 


288696 


V2 


2551.8 


12121 


V2 


8658.9 


75767 


1/2 


21382 


294010 


3/4 


2596.7 


12443 


53. 


8824.8 


77952 


83. 


21642 


299388 


29. 


2642.1 


12770 


V2 


8992.0 


80178 


1/2 


21904 


304831- 


V4 


2687.8 


13103 


54. 


9160.8 


82448 


84. 


22167 


310340 


V2 


2734.0 


13442 


1/2 


9331.2 


84760 


1/2 


22432 


315915 


3/4 


2780.5 


13787 


55. 


9503.2 


87114 


85. 


22698 


321556 


30. 


2827.4 


14137 


V2 


9676.8 


89511 


1/2 


22966 


327264 


V4 


2874.8 


14494 


58. 


9852.0 


91953 


86. 


23235 


333039 


. V2 


2922.5 


14856 


V2 


10029 


94438 


1/2 


23506 


338882 


3/4 


2970.6 


15224 


57. 


10207 


96967 


87. 


23779 


344792 


31c 


3019.1 


15599 


1/2 


10387 


99541 


1/2 


24053 


350771 


V4 


3068.0 


15979 


58. 


10568 


102161 


88. 


24328 


356819 


V2 


3117.3 


16366 


1/2 


10751. 


104826 


1/2 


24606 


362935 


3/4 


3166.9 


16758 


59. 


10936 


107536 


89. 


24885 


369122 


32. 


3217.0 


17157 


1/2 


11122 


110294 


1/2 


25165 


375378 


V4 


3267.4 


17563 


60. 


11310 


113098 


90. 


25447 


381704 


V2 


3318.3 


17974 


1/2 


11499 


115949 


1/2 


25730 


388102 


3/4 


3369.6 


18392 


61. 


11690 


118847 


91. 


26016 


394570 


33. 


3421.2 


18817 


V2 


11882 


121794 


1/2 


26302 


401109 


V4 


3473.3 


19248 


63. 


12076 


124789 


92. 


26590 


407721 


V2 


3525.7 


19685 


1/2 


12272 


127832 


1/2 


26880 


414405 


3/4 


3578.5 


20129 


63. 


12469 


130925 


93. 


27172 


421161 


34. 


3631.7 


20580 


1/2 


12668 


134067 


1/2 


27464 


427991 


1/4 


3685.3 


21037 


64. 


12868 


137259 


94. 


27759 


434894 


V2 


3739.3 


21501 


1/2 


13070 


140501 


1/2 


28055 


441871 


35. 


3848.5 


22449 


65. 


13273 


143794 


95. 


28353 


448920 


V2 


3959.2 


23425 


1/2 


13478 


147138 


1/2 


28652 


456047 


36. 


4071.5 


24429 


66. 


13685 


150533 


98. 


28953 


463248 J 


V2 


4185.5 


25461 


1/2 


13893 


1 53980 


1/2 


29255 


470524 


37. 


4300.9 


26522 


67. 


14103 


157480 


97. 


29559 


477874 


V2 


4417.9 


27612 


1/2 


.14314 


161032 


1/2 


29865 


485302 


38. 


4536.5 


28731 


68. 


14527 


164637 


98. 


30172 


492803 J 


1/2 


4656.7 


29880 


1/2 


14741 


168295 


1/2 


30481 


500388 


39. 


4778.4 


31059 


69. 


14957 


172007 


99. 


30791 


508047 


V2 


4901.7 


32270 


1/2 


15175 


175774 


V? 


31103 


515785 


40. 


5026.5 


33510 


70. 


15394 


179595 100. 


31416 


523 593 





















CAPACITY OF CYLINDRICAL VESSELS. 



127 



CONTENTS IN CUBIC FEET AND U. S. GALLONS OF PIPES 

AND CYLINDERS OF VARIOUS DIAMETERS AND ONE 

FOOT IN LENGTH. 





1 gallon 


= 231 cubic inches. 1 cubic foot 


= 7.4805 gallons 






For 1 Foot in 


.5 

1 


For 1 Foot in 




For 1 Foot in 


83 i 

i-s 

, | a 


Length . 


Len 


gth. 


.5 


Length. 


Cu.Ft. 


U.S. 


Cu.Ft. 


U.S. 


Cu.Ft. 


U.S. 


also 


Gals., 


also 


Gals., 


also 


Gals.. 


5 


Area in 


231 


5 


Area in 


231 


fl M 


Area in 


231 


Sq.Ft. 


Cu.In. 




Sq.Ft. 


Cu.In. 


Sq.Ft. 


Cu. In. 


V4 


.0003 


.0025 


63/4 


.2485 


1.859 


19 


1.969 


14.73 


5/16 


.0005 


.004 


7 


.2673 


1.999 


191/2 


2 074 


15.51 


3/8 


.0008 


.0057 


71/4 


.2867 


2.145 


20 


2.182 


16.32 


7/16 


.001 


.0078 


71/2 


.3068 


2.295 


201/2 


2.292 


17.15 


1/2 


.0014 


.0102 


73/4 


.3276 


2.45 


21 


2.405 


17.99 


9/16 


.0017 


.0129 


8 


.3491 


2.611 


211/2 


2.521 


18.86 


5/8 


.0021 


.0159 


81/4 


.3712 


2.777 


22 


2.640 


19.75 


H/16 


.0026 


.0193 


81/2 


.3941 


2.948 


221/2 


2.761 


20.66 


3/ 4 


.0031 


.0230 


83/4 


.4176 


3.125 


23 


2.885 


21.58 


13/16 


.0036 


.0269 


9 


.4418 


3.305 


231/2 


3.012 


22.53 


7/8 


.0042 


.0312 


91/4 


.4667 


3.491 


24 


3.142 


23.50 


15/16 


.0048 


.0359 


91/2 


.4922 


3.682 


25 


3.409 


25.50 


1 


.0055 


.0408 


93/4 


.5185 


3.879 


26 


3.687 


27.58 


U/4 


.0085 


.0638 


10 


.5454 


4.08 


27 


3.976 


29.74 


U/2 


.0123 


.0918 


101/4 


.5730 


4.286 


28 


4.276 


31.99 


13/4 


.0167 


.1249 


10l/ 2 


.6013 


4.498 


29 


4.587 


34.31 


2 


.0218 


.1632 


103/4 


.6303 


4.715 


30 


4.909 


36.72 


|2l/ 4 


.0276 


.2066 


11 


.66 


4.937 


31 


5.241 


39.21 


21/2 


.0341 


.2550 


111/4 


.6903 


5.164 


32 


5.585 


41.78 


23/4 


.0412 


.3085 


IH/2 


.7213 


5.396 


33 


5.940 


44.43 


3 


.0491 


.3672 


1 1 3/4 


.7530 


5.633 


34 


6.305 


47.16 


31/4 


.0576 


.4309 


12 


.7854 


5.875 


35 


6.681 


49.98 


31/2 


.0668 


.4998 


121/2 


.8522 


6.375 


36 


7.069 


52.88 


33/4 


.0767 


.5738 


13 ' 


.9218 


6.895 


37 


7.467 


55.86 


4 


.0873 


.6528 


131/2 


.994 


7.436 


38 


7.876 


58.92 


41/4 


.0985 


.7369 


14 


1.069 


7.997 


39 


8.296 


62.06 


41/2 


.1104 


.8263 


141/2 


1.147 


8.578 


40 


8.727 


65.28 


43/4 


.1231 


.9206 


15 


1.227 


9.180 


41 


9.168 


68.58 


5 


.1364 


1.020 


151/2 


1.310 


9.801 


42 


9.621 


71.97 


51/4 


.1503 


1.125 


16 


1.396 


10.44 


43 


10.085 


75.44 


51/2 


.1650 


1.234 


161/2 


1.485 


11.11 


44 


10.559 


78.99 


53/4 


.1803 


1.349 


17 


1.576 


11.79 


45 


11.045 


82.62 


6 


.1963 


1.469 


171/2 


1.670 


12.49 


46 


11.541 


86.33 


61/ 4 


.2131 


1.594 


18 


1.768 


13.22 


47 


12.048 


90.10 


61/2 


.2304 


1.724 


181/2 


1.867 


13.96 


48 


12.566 


94.00 



To find the capacity of pipes greater than the largest given in the table, 
look in the table for a pipe of one-half the given size, and multiply its capa- 
city by 4; or one of one-third its size, and multiply its capacity by 9, etc. 

To find the weight of water in any of the given sizes, multiply the capacity 
in cubic feet by 621/4 or the gallons by 8 1/3, or, if a closer approximation is 
required, by the weight of a cubic foot of water at the actual temperature 
in the pipe. 

Given the dimensions of a cylinder in inches, to find its capacity in U. S. 
gallons: Square the diameter, multiply by the length and by 0.0034. If d = 

rf2vn 78^4. V / 

diameter, I = length, gallons = OQ , = 0.0034 &1. If D and L are 



in feet, gallons = 5.875 D 2 L. 



231 



128 




MATHEMATICAL 


TABLES. 






CYLINDRICAL VESSELS, TANKS, CISTERNS, ETC. 


Diameter in 


Feet and Inches, Area in Square Feet, and V. S. 




Gallons Capacity 


for One Foot in Depth. 




1 gallon = 231 cubic inches 


1 cubic foot 
7.4805 


D. 13368 cubic feet. 


Diam. 


Area. 


Gals. 


Diam. 


Area. 


Gals. 


Diam. 


Area. 


Gals. 


Ft. In. 


Sq.ft. 


1 foot 
depth. 


Ft. In. 


Sq. ft. 


1 foot 
depth. 


Ft. In. 


Sq.ft. 


1 foot 
depth. 


1 


.785 


5.87 


5 8 


25.22 


188 .66 


19 


283 .53 


2120.9 


1 1 


.922 


6.89 


5 9 


25.97 


194.25 


19 3 


291.04 


2177.1 


1 2 


1.069 


8.00 


5 10 


26.73 


199.92 


19 6 


298.65 


2234.0 


1 3 


1.227 


9.18 


5 11 


27.49 


205.67 


19 9 


306.35 


2291.7 


1 4 


1.396 


10.44 


G 


28.27 


211.51 


20 


314.16 


2350.1 


1 5 


1.576 


11.79 


6 3 


30.68 


229.50 


20 3 


322.06 


2409.2 


1 6 


1.767 


13.22 


6 6 


33.18 


248.23 


20 6 


330.C6 


2469.1 


I 7 


1.969 


14.73 


6 9 


35.78 


267.69 


20 9 


338.16 


2529.6 


1 8 


2.182 


16.32 


7 


38.48 


287.88 


21 


346.36 


2591.0 


1 9 


2.405 


17.99 


7 3 


41.28 


308.81 


21 3 


354.66 


2653.0 


1 10 


2.640 


19.75 


7 6 


44.18 


330.48 


21 6 


363.05 


2715.8 


1 11 


2.885 


21.58 


7 9 


47.17 


352.88 


21 9 


371.54 


2779.3 


2 


3.142 


23.50 


8 


50.27 


376.01 


22 


380.13 


2843.6 


2 1 


3.409 


25.50 


8 3 


53.46 


399.88 


22 3 


388.82 


2908.6 


2 2 


3.687 


27.58 


8 6 


56.75 


424.48 


22 6 


397.61 


2974.3 


2 3 


3.976 


29.74 


8 9 


60.13 


449.82 


22 9 


406.49 


3040.8 


2 4 


4.276 


31.99 


9 


63.62 


475.89 


23 


415.48 


3108.0 


2 5 


4.587 


34.31 


9 3 


67.20 


502.70 


23 3 


424.56 


3175.9 


2 6 


4.909 


36.72 


9 6 


70.88 


530.24 


23 6 


433.74 


3244.6 


2 7 


5.241 


39.21 


9 9 


74.66 


558.51 


23 9 


443.01 


3314.0 


2 8 


5.585 


41.78 


10 


78.54 


587.52 


24 


452.39 


3384.1 


2 9 


5.940 


44.43 


10 3 


82.52 


617.26 


24 3 


461.86 


3455.0 


2 10 


6.305 


47.16 


10 6 


86.59 


647.74 


24 6 


471.44 


3526.6 


2 11 


6.681 


49.98 


10 9 


90.76 


678.95 


24 9 


481.11 


3598.9 


3 


7.069 


52.88 


11 


95.03 


710.90 


25 


490.87 


3672.0 


3 1 


7.467 


55.86 


11 3 


99.40 


743.58 


25 3 


500.74 


3745.8 


3 2 


7.876 


58.92 


11 6 


103.87 


776.99 


25 6 


510.71 


3820.3 


3 3 


8.296 


62.06 


11 9 


108.43 


811.14 


25 9 


520.77 


3895.6 


3 4 


8.727 


65.28 


12 


113.10 


846.03 


26 


530.93 


3971.6 


3 5 


9.168 


68.58 


12 3 


117.86 


881.65 


26 3 


541.19 


4048.4 


3 6 


9.621 


71.97 


12 6 


122.72 


918.00 


26 6 


551.55 


4125.9 


3 7 


10.085 


75.44 


12 9 


127.68 


955.09 


. 26 9 


562.00 


4204.1 


3 8 


10.559 


78.99 


13 


132.73 


992.91 


27 


572.56 


4283.0 


3 9 


1 1 .045 


82.62 


13 3 


137.89 


1031.5 


27 3 


583.21 


4362.7 


3 10 


11.541 


86.33 


13 6 


143.14 


1070.8 


27 6 


593.96 


4443.1 


3 11 


12.048 


90.13 


13 9 


148.49 


1110.8 


27 9 


604.81 


4524.3 


4 


12.566 


94.00 


14 


153.94 


1151.5 


28 


615.75 


4606.2 


4 1 


13.095 


97.96 


14 3 


159.48 


1193.0 


28 3 


626.80 


4688.8 


4 2 


13.635 


102.00 


14 6 


165.13 


1235.3 


28 6 


637.94 


4772.1 


4 3 


14.186 


106.12 


14 9 


170.87 


1278.2 


28 9 


649.18 


4856.2 


4 4 


14.748 


110.32 


15 


176.71 


1321.9 


29 


660.52 


4941.0 


4 5 


15.321 


114.61 


15 3 


182.65 


1366.4 


29 3 


671.96 


5026.6 


4 6 


15.90 


118.97 


15 6 


188.69 


1411.5 


29 6 


683.49 


5112.9 


4 7 


16.50 


123.42 


15 9 


194.83 


1457.4 


29 9 


695.13 


5199.9 


4 8 


17.10 


127.95 


16 


201.06 


1504.1 


30 


706.86 


5287.7 


4 9 


17.72 


132.56 


16 3 


207.39 


1551.4 


30 3 


718.69 


5376.2 


4 10 


18.35 


137.25 


16 6 


213.82 


1599.5 


30 6 


730.62 


5465.4 


4 11 


18.99 


142.02 


16 9 


220.35 


1648.4 


30 9 


742.64 


5555.4 


5 


19.63 


146.88 


17 


226.98 


1697.9 


31 


754.77 


5646.1 


5 1 


20.29 


151.82 


17 3 


233.71 


1748.2 


31 3 


766.99 


5737.5 


5 2 


20.97 


156.83 


17 6 


240.53 


1 799.3 


31 6 


779.31 


5829.7 


5 3 


21.65 


161.93 


17 9 


247.45 


1851.1 


31 9 


791.73 


5922.6 


5 4 


22.34 


167.12 


18 


254.47 


1903.6 


32 


804.25 


6016.2 


5 5 


23.04 


172.38 


18 3 


261.59 


1956.8 


32 3 


816.86 


6110.6 


5 6 


23.76 


177.72 


18 6 


268.80 


2010.8 


32 6 


829.58 


6205.7 


5 7 


24.48 


183.15 


18 9 


276.12 


2065.5 


32 9 


842.39 


6301.5 





















GALLONS AND CUBIC FEET. 



129 



GALLONS AND CUBIC FEET. 

United States Gallons in a given Number of Cubic Feet. 

cubic foot = 7.480519 U.S. gallons; 1 gallon = 231 cu.in. = 0.13368056cu.ft. 



Cubic Ft. 


Gallons. 


Cubic Ft. 


Gallons. 


Cubic Ft. 


Gallons. 


0.1 
0.2 
0.3 
0.4 
0.5 


0.75 
1.50 

2.24 
2.99 
3.74 


50 
60 
70 
80 
90 


374.0 
448.8 
523.6 
598.4 
673.2 


8,000 
9,000 
10,000 
20,000 
30,000 


59,844.2 

67,324.7 

74,805.2 

149,610.4 

224.415.6 


0.6 
0.7 
0.8 
0.9 

1 


4.49 
5.24 
5.98 
6.73 

7.48 


100 
200 
300 
400 
500 


748.0 
1,496.1 
2,244.2 
2,992.2 
3,740.3 


40,000 
50,000 
60,000 
70,000 
80,000 


299,220.8 
374,025.9 
448,831.1 
523,636.3 
598,441.5 


2 
3 

4 

5 
6 


14.96 

22.44 
29.92 
37.40 
44.88 


600 
700 
800 
900 
1,000 


4,488.3 
5,236.4 
5,984.4 
6,732.5 
7,480.5 


90,000 
100,000 
200,000 
300,000 
400,000 


673,246. 

748,051.9 
1,496,103.8 
2,244,155.7 
2,992,207.6 


7 
8 
9 
10 
20 


52.36 

59.84 
67.32 
74.80 
149.6 


2,000 
3,000 
4,000 
5,000 
6,000 


14,961.0 
22,441.6 
29,922.1 
37,402.6 
44,883.1 


500,000 
600,000 
700,000 
800,000 
900,000 


3,740,259.5 
4,488,3.11.4 
5,236,363.3 
5,984,415.2 
6,732,467.1 


30 
40 


224.4 
299.2 


7,000 


52,363.6 


1,000,000 


7,480,519.0 



Cubic Feet in a given Number of Gallons. 



Gallons. 


Cubic Ft. 


Gallons. 


Cubic Ft. 


Gallons. 


Cubic Ft. 


1 


.134 


1,000 


133.681 


1,000,000 


133,680.6 


2 


.267 


2,000 


267.361 


2,000,000 


267,361.1 


3 


.401 


3,000 


401.042 


3,000,000 


401,041.7 


4 


.535 


4,000 


534.722 


4,000,000 


534,722.2 


5 


.668 


5,000 


668.403 


5,000,000 


668,402.8 


6 


.802 


6,000 


802.083 


6,000,000 


802,083.3 


7 


.936 


7,000 


935.764 


7,000,000 


935,763.9 


8 


1.069 


8,000 


1,069.444 


8,000,000 


1,069,444.4 


9 


1.203 


9,000 


1,203.125 


9,000,000 


1,203,125.0 


10 


1.337 


10,000 


1,336.806 


10,000,000 


1,336,805.6 



Cubic Feet per Second, Gallons in 24 hours, etc 

1/60 1 



Cu. ft. per sec. 
Cu. ft. per min. 
U. S. Gals, per min. 
" 24hrs. 
Pounds of water ) 
(at 62° F.) per min. J 
The gallon is a troublesome and unnecessary measure, 
engineers and pump manufacturers would stop using it, and use cubic 
feet instead, many tedious calculations would be saved, 



7.480519 
10,771.95 

62.355 



448.31 
646,317 
3741.3 



1.5472 
92.834 
694.444 
1,000,000 

5788.66 



2.2801 
133.681 
1,000. 
1,440,000 

8335.65 
If hydraulic 



130 



MATHEMATICAL TABLES. 



NUMBER 


OF SQUARE FEET IN PLATES 3 TO 32 FEET 






LONG, AND 1 INCH WIDE. 






For other widths, multiply by the 


width in inches. lsq.in.= 


0.00694/9 sq.ft. 


Ft. and 


Ins. 


Square 


Ft. and 

Ins. 
Long. 


Ins. 


Square 


Ft. and 

Ins. 
Long. 


Ins. 


Square 
Feet. : 


Ins. 
Long. 


Long. 


Feet. 


Long. 


Feet. 


Long. 


3. 


36 


.25 


7. 10 


94 


.6528 


12. 8 


152 


1.056 


1 


37 


.2569 


11 


95 


.6597 


9 


153 


1.063 


2 


38 


.2639 


8. 


96 


.6667 


10 


154 


1.069 


3 


39 


.2708 


1 


97 


.6736 


11 


155 


1.076 


4 


40 


.2778 


2 


98 


.6806 


13. 


156 


1.083 


5 


41 


.2847 


3 


99 


.6875 


1 


157 


1.09 


6 


42 


.2917 


4 


100 


.6944 


2 


158 


1.097 


7 


43 


.2986 


5 


101 


.7014 


3 


159 


1.104 


8 


44 


.3056 


6 


102 


.7083 


4 


160 


1.114 


9 


45 


. .3125 


7 


103 


.7153 


5 


161 


1.118 


10 


46 


.3194 


8 


104 


.7222 


6 


162 


1.125 


11 


47 


.3264 


9 


105 


.7292 


7 


163 


1.132 


4. 


48 


.3333 


10 


106 


.7361 


8 


164 


1.139 


1 


49 


.3403 


11 


107 


.7431 


9 


165 


1.146 


2 


50 


.3472 


9. 


108 


.75 


10 


166 


1.153 


3 


51 


.3542 


1 


109 


.7569 


11 


167 


1.159 


4 


52 


.36.1 1 


2 


110 


.7639 


14. 


168 


1.167 


5 


53 


.3681 


3 


111 


.7708 


1 


169 


1.174 


6 


54 


.375 


4 


112 


.7778 


2 


170 


1.181 


7 


55 


.3819 


5 


113 


.7847 


3 


171 


1.188 


8 


56 


.3889 


6 


114 


.7917 


4 


172 


1.194 


9 


57 


.3958 


7 


115 


.7986 


5 


173 


1.201 


10 


58 


.4028 


8 


116 


.8056 


6 


174 


1.208 


11 


59 


.4097 


9 


117 


.8125 


7 


175 


1.215 


5. 


60 


.4167 


10 


118 


.8194 


8 


176 


1.222 


1 


61 


.4236 


11 


119 


.8264 


9 


177 


1.229 


2 


62 


.4306 


10. o 


120 


.8333 


10 


178 


1.236 


3 


63 


.4375 


1 


121 


.8403 


11 


179 


1.243 


4 


64 


.4444 


2 


122 


.8472 


15. 


180 


1.25 


5 


65 


.4514 


3 


123 


.8542 


1 


181 


1.257 


6 


66 


.4583 


4 


124 


.8611 


2 


182 


1.264 


7 


67 


.4653 


5 


125 


.8681 


3 


183 


1.271 


8 


68 


.4722 


6 


126 


.875 


4 


184 


1.278 


9 


69 


.4792 


7 


127 


.8819 


5 


185 


1.285 


10 


70 


.4861 


8 


128 


.8889 


6 


186 


1.292 


11 


71 


.4931 


9 


129 


.8958 


7 


187 


1.299 


6. 


72 


.5 


10 


130 


.9028 


8 


188 


1.306 


1 


73 


.5069 


11 


131 


.9097 


9 


189 


. 1.313 


2 


74 


.5139 


11. o 


132 


.9167 


10 


190 


1.319 


3 


75 


.5208 


1 


133 


.9236 


11 


191 


1.326 


4 


76 


.5278 


2 


134 


.9306 


16. 


192 


1.333 


5 


77 


.5347 


3 


135 


.9375 


1 


193 


1.34 


6 


78 


.5417 


4 


136 


.9444 


2 


194 


1.347 


7 


79 


.5486 


5 


137 


.9514 


3 


195 


1.354 


8 


80 


.5556 


6 


138 


.9583 


4 


196 


1.361 


9 


81 


.5625 


7 


139 


.9653 


5 


197 


1.368 


10 


82 


.5694 


8 


140 


.9722 


6 


198 


1.375 


11 


83 


.5764 


9 


141 


.9792 


7 


199 


1.382 


7. 


84 


.5834 


10 


142 


.9861 


8 


200 


1.389 


1 


85 


.5903 


11 


143 


.9931 


9 


201 


1.396 


2 


86 


.5972 


12. 


144 


1.000 


10 


202 


1.403 i 


3 


87 


.6042 


t 


145 


1.007 


11 


203 


1.41 


4 


88 


.6111 


2 


146 


1.014 


17. 


204 


1.417 


5 


89 


.6181 


3 


147 


1.021 


1 


205 


1.424 


6 


90 


.625 


4 


148 


1.028 


2 


206 


1.431 


7 


91 


.6319 


5 


149 


1.035 


3 


207 


1.438 


8 


92 


.6389 


6 


150 


1.042 


4 


208 


1.444 


9 


93 


.6458 


7 


151 


1.049 


5 


209 


1.451 





















NUMBER OF SQUARE FEET IN PLATES. 



131 





SQUARE FEET 


IN PLATES.— 


Continued. 




Ft .and 

Ins. 

Long. 


Ins. 


Square 


Ft. and 

Ins. 
Long. 


Ins. 


Square 


Ft. and 
Ins. 
Long. 


Ins. 


Square 


Long. 


Feet. 


Long. 


Feet. 


Long 


Feet. 


17. 6 


210 


1.458 


22. 5 


269 


1.868 


27o 4 


328 


2.278 


7 


211 


1.465 


6 


270 


1.875 


5 


329 


2.285 


8 


212 


1.472 


7 


271 


1.882 


6 


330 


2.292 


9 


213 


1.479 


8 


272 


1.889 


7 


331 


2.299 


10 


214 


1.486 


9 


273 


1.896 


8 


332 


2.306 


11 


215 


1.493 


10 


274 


1.903 


9 


333 


2.313 


18. 


216 


1.5 


II 


275 


1.91 


10 


334 


2.319 


1 


217 


1.507 


23. 


276 


1.917 


11 


335 


2.326 


2 


218 


1.514 


1 


211 


1.924 


28. 


336 


2.333 


3 


219 


1.521 


2 


278 


1.931 


1 


337 


2.34 


4 


220 


1.528 


3 


279 


1.938 


2 


338 


2.347 


5 


221 


1.535 


4 


280 


1.944 


3 


339 


2.354 


6 


222 


1.542 


5 


281 


1.951 


4 


340 


2.361 


7 


223 


1.549 


6 


282 


1.958 


5 


341 


2.368 


8 


224 


1.556 


7 


283 


1.965 


6 


342 


2.375 


9 


225 


1.563 


8 


284 


i 972 


7 


343 


2.382 


10 


226 


1.569 


9 


285 


1 .979 


8 


344 


2.389 


11 


227 


1.576 


10 


286 


1.986 


9 


345 


2.396 


19. 


228 


1.583 


11 


287 


1.993 


10 


346 


2.403 


1 


229 


1.59 


24. 


288 


2. 


11 


347 


2.41 


2 


230 


1.597 


1 


289 


2.007 


29. 


348 


2.417 


3 


231 


1.604 


2 


290 


2.014 


1 


349 


2.424 


4 


232 


1.611 


3 


291 


2.021 


2 


350 


2.431 


5 


233 


1.618 


4 


292 


2.028 


3 


351 


2.438 


6 


234 


1.625 


5 


293 


2.035 


4 


352 


2.444 


7 


235 


1.632 


6 


294 


2.042 


5 


353 


2.451 


8 


236 


1.639 


7 


295 


2.049 


6 


354 


2.458 


9 


237 


1.645 


8 


296 


2.056 


7 


355 


2.465 


10 


238 


1.653 


9 


297 


2.063 


8 


356 


2.472 


11 


239 


1.659 


10 


298 


2.069 


9 


357 


2.479 


20. 


240 


1.667 


11 


299 


2.076 


10 


358 


2.486 


1 


241 


1.674 


25. 


300 


2.083 


11 


359 


2.493 


2 


242 


1.681 


1 


301 


2.09 


30. 


360 


2.5 


3 


243 


1.688 


2 


302 


2.097 


1 


361 


2.507 


4 


244 


1.694 


3 


303 


2.104 


2 


362 


2.514 


5 


245 


1.701 


4 


304 


2.111 


3 


363 


2.521 


6 


246 


1.708 


5 


305 


2.118 


4 


364 


2.528 


7 


247 


1.715 


6 


306 


2.125 


5 


365 


-2.535 


8 


248 


1.722 


7 


307 


2.132 


6 


366 


2.542 


9 


249 


1.729 


8 


308 


2.139 


7 


367 


2.549 


10 


250 


1.736 


9 


309 


2.146 


8 


368 


2.556 


11 


251 


1.743 


10 


310 


2.153 


9 


369 


2.563 


21. 


252 


1.75 


11 


311 


2.16 


10 


370 


2.569 


1 


253 


1.757 


26. 


312 


2.167 


11 


371 


2.576 


2 


254 


1.764 


1 


313 


2.174 


31. 


372 


2.583 


3 


255 


1.771 


2 


314 


2.181 


1 


373 


2.59 


4 


256 


1.778 


3 


315 


2.188 


2 


374 


2.597 


5 


257 


1.785 


4 


316 


2.194 


3 


375 


2.604 


6 


258 


1.792 


5 


317 


2.201 


4 


376 


2.61 1 


7 


259 


1.799 


6 


318 


2.208 


5 


377 


2.618 


8 


260 


1.806 


7 


319 


2.215 


6 


378 


2.625 


9 


261 


1.813 


8 


320 


2.222 


7 


379 


2.632 


10 


262 


1.819 


9 


321. 


2.229 


8 


380 


2.639 


11 


263 


1.826 


10 


322 


2.236 


9 


381 


2.646 


23. 


264 


1.833 


11 


323 


2.243 


10 


382 


2.653 


1 


265 


1.84 


27. 


324 


2.25 


11 


333 


2.66 


2 


266 


1.847 


1 


325 


2.257 


32. 


384 


2.667 


3 


267 


1.854 


2 


326 


2.264 


1 


385 


2.674 


4 


268 


1.861 


3 


327 


2.271 


2 


386 


2.(81 



132 



MATHEMATICAL TABLES, 



CAPACITIES OP RECTANGULAR TANKS IN TJ. S. 
GALLONS, FOR EACH FOOT IN DEPTH. 



1 cubic foot = 7.4805 U. S. gallons. 



Width 

of 
Tank. 



Length of Tank. 



feet. ft. in. feet. ft. in 
2 2 6 3 3 6 



feet. ft. in 
4 4 6 



feet. ft. in. feet. ft. in. 
5 5 6 6 6 6 



feet. 

7 



ft. 
2 
2 
3 
3 
4 

4 
5 
5 
6 
6 



37.40 
46.75 



52.36 
65.45 
78.54 
91.64 



59.84 
74.80 
89.77 
104.73 
1 19.69 



67.32 
84.16 
100.99 
117.82 
134.65 

151.48 



74.81 
93.51 
112.21 
130.91 
149.61 

168.31 
187.01 



82.29 
102.86 
123.43 
144.00 
164.57 

185.14 
205.71 
226.28 



89.77 
112.21 
134.65 
157.09 
179.53 

201.97 

224.41 
246.86 
269.30 



97.25 
121.56 
145.87 
170.1 
194.49 

218.80 
243.11 
267.43 
291.74 
316.05 



104.73 
130.91 
157.09 
183.27 
209.45 

235.62 
261.82 
288.00 
314.18 
340.36 

366.54 





Length of Tank. 


Width 




of 




















Tank. 


ft. in 


feet. 


ft. in 


feet. 


ft. in 


feet. 


ft. in 


feet. 


ft. in 


feet. 




7 6 


8 


8 6 


9 


9 6 


10 


10 6 


11 


11 6 


12 


ft. in. 
2 


112.21 


119.69 


127.17 


134.65 


142.13 


149.61 


157.09 


164.57 


172.05 


179.53 


2 6 


140.26 


149.61 


158.96 


168.31 


177.66 


187.01 


196.36 


205.71 


215.06 


224.41 


3 


168.31 


179.53 


190.75 


202.97 


213.19 


224.41 


235.63 


246.86 


258.07 


269.30 


3 6 


196.36 


209.45 


222.54 


235.63 


248.73 


261.82 


274.9C 


288.00 


301.09 


314.18 


4 


224.41 


239.37 


254.34 


269.30 


284.26 


299.22 


314.18 


329.14 


344.10 


359.06 


4 6 


252.47 


269.30 


286.13 


302.96 


319.79 


336.62 


353.45 


370.28 


387.11 


403.94 


5 


280.52 


299.22 


317.92 


336.62 


355.32 


374.03 


392.72 


411.43 


430.13 


448.83 


5 6 


308.57 


329.14 


349.71 


370.28 


390.85 


411.43 


432.00 


452.57 


473.1' 


493.71 


6 


336.62 


359.06 


381.50 


403.94 


426.39 


448.83 


471.27 


493.71 


516.15 


538.59 


6 6 


364.67 


388.98 


413.30 


437.60 


461.92 


486.23 


510.54 


534.85 


559.16 


583.47 


7 


392.72 


418.91 


445.09 


471 .27 


497.45 


523.64 


549.81 


575.99 


602.18 


628.36 


7 6 


420.78 


448.83 


476.88 


504.93 


532.98 


561.04 


589.08 


617.14 


645.19 


673.24 


8 




478.75 


508.67 


538.59 


568.51 


598.44 


628.36 


658.28 


688.20 


718.12 


8 6 






540.46 


572.25 


604.05 


635.84 


667.63 


699.42 


731.21 


763.00 


9 








605.92 


639.58 


673.25 


706.90 


740.56 


774.23 


807.89 


9 6 










675.11 


710.65 


746. 1 7 


781.71 


817.24 


852.77 


10 












748.05 


785.45 


822.86 


860.26 


897.66 


10 6 














824.73 


864.00 


903.26 


942.56 


11 
















905.14 


946.27 


987.43 


11 6 

















989.29 


1032.3 


12 













... j ... 




1077.2 



CAPACITY OF CYLINDRICAL CISTERNS AND TANKS. 133 



NUMBER OF BARRELS (31 1-2 GALLONS) IN 
CISTERNS AND TANKS. 



I barrel = 3 1 J^ j 



31.5X 231 
1728 



= 4.21094 cu. ft. Reciprocal = 0.2 37 477 



Depth 

in 
Feet. 








Diameter 


in Feet 










5 


6 


7 


8 


9 


10 


11 


13 


13 


14 


1 


4.663 


6.714 


9.139 


11.937 


15.108 


18.652 


22.569 


26.859 


31.522 


36.557 


5 


23.3 


33.6 


45.7 


59.7 


75.5 


93.3 


112.8 


134.3 


157.6 


182.8 


6 


28.0 


40.3 


54.8 


71.6 


90.6 


111.9 


135.4 


161.2 


189.1 


219.3 


7 


32.6 


47.0 


64.0 


83.6 


105.8 


130.6 


158.0 


188.0 


220.7 


255.9 


8 


37.3 


53.7 


73.1 


95.5 


120.9 


149.2 


180.6 


214.9 


252.2 


292.5 


9 


42.0 


60.4 


62.3 


107.4 


136.0 


167.9 


203.1 


241.7 


283.7 


329.0 


10 


46.6 


67.1 


91.4 


119.4 


151.1 


186.5 


225.7 


268.6 


315.2 


365.6 


11 


51.3 


73.9 


100.5 


131.3 


166.2 


205.2 


248.3 


295.4 


346.7 


402.1 


12 


56.0 


80.6 


109.7 


143.2 


181.3 


223.8 


270.8 


322.3 


378.3 


438.7 


13 


60.6 


87.3 


118.8 


155.2 


196.4 


242.5 


293.4 


349.2 


409.8 


475.2 


14 


65.3 


94.0 


127.9 


167.1 


211.5 


261.1 


316.0 


376.0 


441.3 


511.8 


15 


69.9 


100.7 


137.1 


179.1 


226.6 


279.8 


338.5 


402.9 


472.8 


548.4 


16 


74.6 


107.4 


146.2 


191.0 


241.7 


298.4 


361.1 


429.7 


504.4 


584.9 


17 


79.3 


114.1 


155.4 


202.9 


256.8 


317.1 


383.7 


456.6 


535.9 


621.5 


18 


83.9 


120.9 


164.5 


214.9 


271.9 


335.7 


406.2 


483.5 


567.4 


658.0 


19 


88.6 


127.6 


173.6 


226.8 


287.1 


354.4 


428.8 


510.3 


598.9 


694.6 


20 


93.3 


134.3 


182.8 


238.7 


302.2 


373.0 


451.4 


537.2 


630.4 


731.1 



Depth 








Diameter 


in Feet. 








Feet. 


15 


1G 


17 


18 


19 


20 


21 


22 


1 
5 
6 
7 
8 


41.966 
209.8 
251.8 
293.8 
335.7 


47.748 
238.7 
286.5 
334.2 
382.0 


53.903 
269.5 
323.4 
377.3 
431.2 


60.431 
302.2 
362.6 
423.0 

483.4 


67.332 
336.7 
404.0 
471.3 
538.7 


74.606 
373.0 
447.6 
522.2 
596.8 


82.253 
411.3 
493.5 
575.8 
658.0 


90.273 
451.4 
541.6 
631.9 
722.2 


9 
10 
11 
12 
13 


377.7 
419.7 
461.6 
503.6 
545.6 


429.7 
477.5 
525.2 
573.0 
620.7 


485.1 
539.0 
592.9 
646.8 
700.7 


543.9 
604.3 
664.7 
725.2 
785.6 


606.0 
673.3 
740.7 
808.0 
875.3 


671.5 
746.1 
820.7 
895.3 
969.9 


740.3 

822.5 
904.8 
987.0 
1069.3 


812.5 
902.7 
993.0 
1083.3 
1173.5 


14 
15 
16 
17 
18 


587.5 
629.5 
671.5 
713.4 
755.4 


668.5 
716.2 
764.0 
811.7 
859.5 


754.6 

808.5 
862.4 
916.4 
970.3 


846.0 
906.5 
966.9 
1027.3 
1087.8 


942.6 
1010.0 
1077.3 
1144.6 
1212.0 


1044.5 
1119.1 
1193.7 
1268.3 
1342.9 


1151.5 
1233.8 
1316.0 
1398.3 
1480.6 


1263.8 
1354.1 
1444.4 
1534.5 
1624.9 


19 
20 


797.4 
839.3 


907.2 
955.0 


1024.2 
1078.1 


1148.2 
1208.6 


1279.3 
1346.6 


1417.5 
1492.1 


1562.8 
1645.1 


1715.2 
1805.5 



134 



MATHEMATICAL TABLES. 



NUMBER OF BARRELS (31 1-3 GALLONS) IN CISTERNS 
AND TANKS. — Continued. 



Depth 








Diametei 


in Feet 








Feet. 


23 


24 


25 


26 


27 


28 


29 


30 


1 
5 
6 
7 
8 


98.666 

493.3 

592.0 

690.7 

789.3 


107.432 
537.2 
644.6 
752.0 
859.5 


116.571 
582.9 
699.4 
816.0 
932.6 


126.083 
630.4 
756.5 
882.6 

1008.7 


135.968 
679.8 
815.8 
951.8 

1087.7 


146.226 
731.1 

877.4 
1023.6 
1169.8 


157.858 
784.3 
941.1 
1098.0 
1254.9 


167.863 
839.3 
1007.2 
1175.0 
1342.9 


9 
10 
11 
12 
13 


888.0 
986.7 
1085.3 
1184.0 
1282.7 


966.9 

1074.3 
1181.8 
1289.2 
1396.6 


1049.1 

1165.7 
1282.3 
1398.8 
1515.4 


1134.7 
1260.8 
1386.9 
1513.0 
1639.1 


1223.7 
1359.7 
1495.6 
1631.6 
1767.6 


1316.0 
1462.2 
1608.5 
1754.7 
1900.9 


1411.7 
1568.6 
1725.4 
1882.3 
2039.2 


1510.8 
1678.6 
1846.5 
2014.4 
2182.2 


14 
15 
16 
17 
18 


1381.3 
1480.0 
1578.7 
1677.3 
1776.0 


1504.0 
1611.5 
1718.9 
1826.3 
1933.8 


1632.0 
1748.6 
1865.1 
1981.7 
2098.3 


1765.2 
1891.2 
2017.3 
2143.4 
2269.5 


1903.6 
2039.5 
2175.5 
2311.5 
2447.4 


2047.2 
2193.4 
2339.6 
2485.8 
2632.0 


2196.0 
2352.9 
2509.7 
2666.6 
2823.4 


2350.1 
2517.9 
2685.8 
2853.7 
3021.5 


19 
20 


1874.7 
1973.3 


2041.2 
2148.6 


2214.8 
2321.4 


2395.6 
2521.7 


2583.4 
2719.4 


2778.3 
2924.5 


2980.3 
3137.2 


3189.4 
3357.3 



LOGARITHMS. 

Logarithms (abbreviation log). — The log of a number is the exponent 
of the power to which it is necessary to raise a fixed number to produce 
the given number. The fixed number is called the base. Thus if the 
base is 10, the log of 1000 is 3, for 10 3 = 1000. There are two systems 
of logs in general use, the common, in which the base is 10, and the Naperian, 
or hyperbolic, in which the base is 2.718281828 .... The Naperian base 
is commonly denoted by e, as in the equation e y = x, in which y is the 
Nap. log of x. The abbreviation log e is commonly used to denote the 
Nap log. 

In any system of logs, the log of 1 is 0; the log of the base, taken in that 
system, is 1 . In any system the base of which is greater than 1 , the logs of 
all numbers greater than 1 are positive .and the logs of all numbers less 
than 1 are negative. 

The modulus of any system is equal to the reciprocal of the Naperian log 
of the base of that system. The modulus of the Naperian system is 1, that 
of the common system is 0.4342945. 

The log of a number in any system equals the modulus of that system X 
the Naperian log of the number. 

The hyperbolic or Naperian log of any number equals the common 
logX 2.3025851. 

Every log consists of two parts, an entire part called the characteristic, 
or index, and the decimal part, or mantissa. The mantissa only is given 
in the usual tables of common logs, with the decimal point omitted. The 
characteristic is found by a simple rule, viz., it is one less than the number 
of figures to the left of the decimal point in the number whose log is to be 
found. Thus the characteristic of numbers from 1 to 9.99 4- is 0, from 
10 to 99.99 + is 1, from 100 to 999 + is 2, from 0.1 to 0.99 + is - 1, from 
0.01 to 0.099 + is - 2, etc. Thus 



log of 2000 is 3.30103 

" " 200 " 2.30103 

" " 20 " 1.30103 

" " 2 " 0.30103 



log of 0.2 is - 1.30103, or 9.30103 - 10 
" " 0.02 " - 2.30103, " 8.30103 - 10 
" " 0.002 " - 3.30103, " 7.30103 - 10 
" " 0.0002 " - 4.30103, " 6.30103 - 10 



LOGARITHMS OF NUMBERS- 135 

The minus sign is frequently written above the characteristic thus: 
log 0.002 = 3.30103. The characteristic only is negative, the decimal part, 
or mantissa, being always positive. 

When a log consists of a negative index and a positive mantissa, it is 
usual to write the negative sign over the index, or else to add 10 to the 
index, and to indicate the subtraction of 10 from the resulting logarithm. 

Thus log 0.2 = 1.30103, and this may be written 9.30103 - 10. 

In tables of logarithmic sines, etc., the — 10 is generally omitted, as 
being understood. 

Rules for use of the table of logarithms. — To find the log of any 
whole number. — For 1 to 100 inclusive the log is given complete in the 
jmall table on page 136. 

For 100 to 999 inclusive the decimal part of the log is given opposite the 
given number in the column headed in the table (including the two 
figures to the left, making six figures). Prefix the characteristic, or 
index, 2. 

For 1000 to 9999 inclusive: The last four figures of the log are found 
opposite the first three figures of the given number and in the vertical 
column headed with the fourth figure of the given number ; prefix the two 
figures under column 0, and the index, which is 3. 

For numbers over 10,000 having five or more digits: Find the decimal 
part of the log for the first four digits as above, multiply the difference 
figure in the last column by the remaining digit or digits, and divide by 10 
if there be only one digit more, by 100 if there be two more, and so on; 
add the quotient to the log of the first four digits and prefix the index, 
vhich is 4 if there are five digits, 5 if there are six digits, and so on. The 
table of proportional parts may be used, as shown below. 

To find the log of a decimal fraction or of a whole number and a 
-decimal. — First find the log of the quantity as if there were no decimal 
point, then prefix the index according to rule; the index is one less than 
the number of figures to the left of the decimal point. 

Required log of 3.141593. 

log of 3.141 =0.497068. Diff. = 138 

From proportional parts 5 = 690 

09 = 1242 

003 = 041 



log 3.141593 0.4971498 

To find the number corresponding to a given log. — Find in the 

table the log nearest to the decimal part of the given log and take the 
first four digits of the required number from the column N and the top or 
foot of the column containing the log which is the next less than the given 
log. To find the 5th and 6th digits subtract the log in the table from the 
given log, multiply the difference by 100, and divide by the figure in the 
Diff. column opposite the log; annex the quotient to the four digits 
already found, and place the decimal point according to the rule; the 
number of figures to the left of the decimal point is one greater than the 
index. The number corresponding U a log is called the anti-logarithm. 

Find the anti-log of 0.497150 

Next lowest log in table corresponds to 3141 0.497068 Diff. = 82 

Tabular diff. = 138; 82 h- 138 = 0.59 + 
The index being 0, the number is therefore 3.14159 +. 

To multiply two numbers by the use of logarithms. — Add together 
the logs of the two numbers, and find the number whose log is the sum. 

To divide two numbers. — ■ Subtract the log of the divisor from the 
log of the dividend, and find the number whose log is the difference. 
Log of a fraction. Log of a/6 = log a — log b. 

To raise a number to any given power. — Multiply the log of the 
number by the exponent of the power, and find the number whose log 
is the product. 

To find any root of a given number. — Divide the log of the number 
by the index of the root. The quotient is the log of the root. 



136 



LOGARITHMS OF NUMBERS. 



To find the reciprocal of a number. — Subtract the decimal part 
of the log of the number from 0, add 1 to the index and change the sign of 
the index. The result is the log of the reciprocal. 

Required the reciprocal of 3.141593. 

Log of 3.141593, as iound above 0.4971498 

Subtract decimal part from gives __. 0.5028502 

Add 1 to the index, and changing sign of the index gives. . 1.5028502 
which is the log of 0.31831. 

To find the fourth term of a proportion by logarithms. — Add 
the logarithms of the second and third terms, and from their sum subtract 
the logarithm of the first term. 

When one loga:ithm is to "be subtracted from another, it may be more 
convenient to convert the subtraction into an addition, which may be 
done by first subtracting the given logarithm from 10, adding the difference 
to the other logarithm, and afterwards rejecting the 10. 

The difference between a given logarithm and 10 is called its arithmetical 
complement, or cologarithm. 

To subtract one logarithm from another is the same as to add its com- 
plement and then reject 10 from the result. For a — b = 10 — 6+ a — 10. 

To work a proportion, then, by logarithms, add the complement of the 
logarithm of the first term to the logarithms of the second and third terms. 
The characteristic must afterwards be diminished by 10. 

Example in logarithms with a negative index. — Solve by 

(596 \ 2 - 4 5 
j , which means divide 526 by 1011 and raise the 

quotient to the 2.45 power. 

log 526 == 2.720986 
log 1011 = 3.004751 
log of quotient = 
Multiply by 



10 



= 9.716235- 
2.45 
.48581175 
3.8864940 
19.432470 
23.80477575 - (10 X 2.45) = 1.30477575 = 0.20173, Ans. 



Logarithms of Numbers from 1 to 100. 












LOGARITHMS OF NUMBERS. 








137 


No. 100 L. 000.] 




[No. 109 L. 040. 


N. 





1 


2 


3 


4 


5 


6 


7 


8 
346! 


9 

"389 


Diff. 


100 


000000 


0434 


0868 


1301 


1734 


2166 


2598 


3029 


'l 432 


1 


4321 


4751 


5181 


5609 


6038 


6466 


6894 


7321 


7748 


8174 428 


2 


86^ ft 


9026 


9451 


9876 




















0300 

4521 


0724 


1147 
5360 


1570 
5779 


1993 
6197 


2415 424 
6616 420 


3 


012837 


3259 


3680 


4100 


4940 


i 4 


70^ 


7451 


7868 


8284 


8700 


9116 


9532 


9947 












0361 


0775 416 




















5 


021189 


1603 


2016 


2428 


2841 


3252 


3664 


4075 


4486 


4896 412 


6 


5306 


5715 


6125 


6533 


6942 


7350 


7757 


8164 


8571 


8978 408 


7 




9789 
























0195 

4227 


0600 

4628 


1004 
5029 


1408 
5430 


1812 
5830 


2216 
6230 


2619 
6629 


3021 404 
7028 400 


8 


033424 


3826 


9 


74 9A 


7825 


8223 


8620 


9017 


9414 


9811 










04 




0207 


0602 


0998 397 


Proportional Parts. 


Diff. 


1 


2 


3 


4 


5 


6 


7 
303.8 


8 


9 


434 


43.4 


86.8 


130.2 


173.6 


217.0 


260.4 


347.2 


390.6 


433 


43.3 


86.6 


129.9 


173.2 


216.5 


259.8 


303.1 


346.4 


389.7 


432 


43.2 


86.4 


129.6 


172.8 


216.0 


259.2 


302.4 


345.6 


338.8 


431 


43.1 


86.2 


129.3 


172.4 


215.5 


258.6 


301.7 


344.8 


337.9 


430 


43.0 


86.0 


129.0 


172.0 


215.0 


258.0 


301.0 


344.0 


387.0 


429 


42.9 


85.8 


128.7 


171.6 


214.5 


257.4 


300.3 


343.2 


386.1 


428 


42.8 


85.6 


128.4 


171.2 


214.0 


256.8 


299.6 


342.4 


385.2 


427 


42.7 


85.4 


128.1 


170.8 


213.5 


256.2 


298.9 


341.6 


384.3 


426 


42.6 


85.2 


127.8 


170.4 


213.0 


255.6 


293.2 


340.8 


383.4 


425 


42.5 


85.0 


127.5 


170.0 


212.5 


255.0 


297.5 


340.0 


382.5 


424 


42.4 


84.8 


127.2 


169.6 


212.0 


254.4 


296.8 


339.2 


381.6 


423 


42.3 


84.6 


126.9 


169.2 


211.5 


253.8 


296.1 


338.4 


380.7 


422 


42.2 


84.4 


126.6 


168.8 


211.0 


253.2 


295.4 


337.6 


379.8 


421 


42.1 


84.2 


126.3 


168.4 


210.5 


252.6 


294.7 


336.8 


378.9 


420 


42.0 


84.0 


126.0 


168.0 


210.0 


252.0 


294.0 


336.0 


378.0 


419 


41.9 


83.8 


125.7 


167.6 


209.5 


251.4 


293.3 


335.2 


377.1 


413 


41.8 


83.6 


125.4 


167.2 


209.0 


250.8 


292.6 


334.4 


376.2 


417 


41.7 


83.4 


125.1 


166.8 


208.5 


250.2 


291.9 


333.6 


375.3 


416 


41.6 


83.2 


124.8 


166.4 


208.0 


249.6 


291.2 


332.8 


374.4 


415 


41.5 


83.0 


124.5 


166.0 


207.5 


249.0 


290.5 


332.0 


373.5 


414 


41.4 


82.8 


124.2 


165.6 


207.0 


248.4 


289.8 


331.2 


372.6 


413 


41.3 


82.6 


123.9 


165.2 


206.5 


247.8 


289.1 


330.4 


371.7 


412 


41.2 


82.4 


123.6 


164.8 


206.0 


247.2 


288.4 


329.6 


370.8 


411 


41.1 


82.2 


123.3 


164.4 


205.5 


246.6 


287.7 


328.8 


369.9 


410 


41.0 


82.0 


123.0 


164.0 


205.0 


246.0 


287.0 


328.0 


369.0 


409 


40.9 


81.8 


122.7 


163.6 


204.5 


245.4 


286.3 


327.2 


368.1 


403 


40.8 


81.6 


122.4 


163.2 


204.0 


244.8 


285.6 


326.4 


367.2 


407 


40.7 


81.4 


122.1 


162.8 


203.5 


244.2 


284.9 


325.6 


366.3 


406 


40.6 


81.2 


121.8 


162.4 


203.0 


243.6 


284.2 


324.8 


365.4 


405 


40.5 


81.0 


121.5 


162.0 


202.5 


243.0 


283.5 


324.0 


364.5 


404 


40.4 


80.8 


121.2 


161.6 


202.0 


242.4 


282.8 


323.2 


363.6 


403 


40.3 


80.6 


120.9 


161.2 


201.5 


241.8 


282.1 


322.4 


362.7 


402 


40.2 


80.4 


120.6 


160.8 


201.0 


241.2 


281.4 


321.6 


361.8 


401 


40.1 


80.2 


120.3 


160.4 


200.5 


240.6 


280.7 


320.8 


360.9 


400 


40.0 


80.0 


120.0 


160.0 


200.0 


240.0 


280.0 


320.0 


360.0 


399 


39.9 


79.8 


119.7 


159.6 


199.5 


239.4 


279.3 


319.2 


359.1 


393 


39.8 


79.6 


119.4 


159.2 


199.0 


238.8 


278.6 


318.4 


358.2 


397 


39.7 


79.4 


119.1 


158.8 


198.5 


238.2 


277.9 


317.6 


357.3 


396 


39.6 


79.2 


118.8 


158.4 


198.0 


237.6 


277.2 


316.8 356.4 


395 


39.5 


7< 


).0 




18.5 


158.( 


) 


197.5 




237.0 


276.5 1 


316.0 ' 


355.5 



138 



LOGARITHMS OF NUMBERS. 



No. 110 L. 041.] 



[No. 119 L. 078. 



N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


110 

1 
2 


04)393 
5323 

9218 


1787 
5714 
9606 


2182 
6105 
9993 


2576 
6495 


2969 
6885 


3362 
7275 


3755 
7664 


4148 
8053 


4540 
8442 


4932 
8830 


393 

390 


0380 
4230 
8046 


0766 
4613 
8426 


1153 
4996 
8805 


1538 
5378 
9185 


1924 
5760 
9563 


2309 
6142 
9942 


2694 
6524 


386 
383 


3 
4 


053078 
6905 


3463 
7286 


3846 
7666 


0320 
4083 
7815 


379 
376 
373 


5 

6 
7 


060693 
4458 
8186 


1075 

4832 
8557 


1452 
5206 
8928 


1829 
5580 
9298 


2206 
5953 
9668 


2582 
6326 


2958 
6699 


3333 
7071 


3709 

7443 


0038 
3718 
7368 


0407 
4085 
7731 


0776 
4451 
8094 


1145 
4816 
8457 


1514 
5182 
8819 


370 
366 
363 


8 
9 


071882 

5547 


2250 
5912 


2617 
6276 


2985 
6640 


3352 
7004 



Proportional Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


395 


39.5 


79.0 


118.5 


158.0 


197.5 


237.0 


276.5 


316.0 


355.5 


394 


39.4 


78.8 


118.2 


157.6 


197.0 


236.4 


275.8 


315.2 


354.6 


393 


39.3 


78.6 


117.9 


157.2 


196.5 


235.8 


275.1 


314.4 


353.7 


392 


39.2 


78.4 


117.6 


156.8 


196.0 


235.2 


274.4 


313.6 


352.8 


391 


39.1 


78.2 


117.3 


156.4 


195.5 


234.6 


273.7 


312.8 


351.9 


390 


39.0 


78.0 


117.0 


156.0 


195.0 


234.0 


273.0 


312.0 


351.0 


389 


38.9 


77.8 


116.7 


155.6 


194.5 


233.4 


272.3 


311.2 


350.1 


388 


38.8 


77.6 


116.4 


155.2 


194.0 


232.8 


271.6 


310.4 


349.2 


387 


38.7 


77.4 


116.1 


154.8 


193.5 


232.2 


270.9 


309.6 


348.3 


386 


38.6 


77.2 


115.8 


154.4 


193.0 


231.6 


270.2 


308.8 


347.4 


385 


38.5 


77.0 


115.5 


154.0 


192.5 


231.0 


269.5 


308.0 


346.5 


384 


38.4 


76.8 


115.2 


153.6 


192.0 


230.4 


268.8 


307.2 


345.6 


383 


38.3 


76.6 


114.9 


153.2 


191.5 


229.8 


268.1 


306.4 


344.7 


382 


38.2 


76.4 


114.6 


152.8 


191.0 


229.2 


267.4 


305.6 


343.8 


381 


38.1 


76.2 


114.3 


152.4 


190.5 


228.6 


266.7 


304.8 


342.9 


380 


38.0 


76.0 


114.0 


152.0 


190.0 


228.0 


266.0 


304.0 


342.0 


379 


37.9 


75.8 


113.7 


151.6 


189.5 


227.4 


265.3 


303.2 


341.1 


378 


37.8 


75.6 


113.4 


151.2 


189.0 


226.8 


264.6 


302.4 


340.2 


377 


37.7 


75.4 


113.1 


150.8 


188.5 


226.2 


263.9 


301.6 


339.3 


376 


37.6 


75.2 


112.8 


150.4 


188.0 


225.6 


263.2 


300.8 


338.4 


375 


37.5 


75.0 


112.5 


150.0 


187.5 


225.0 


262.5 


300.0 


337.5 


374 


37.4 


74.8 


112.2 


149.6 


187.0 


224.4 


261.8 


299.2 


336.6 


373 


37.3 


74.6 


1.11.9 


149.2 


186.5 


223.8 


261.1 


298.4 


335.7 


372 


37.2 


74.4 


111.6 


148.8 


186.0 


223.2 


260.4 


297.6 


334.8 


371 


37.1 


74.2 


111.3 


148.4 


185.5 


222.6 


259.7 


296.8 


333.9 


370 


37.0 


74.0 


111.0 


148.0 


185.0 


222.0 


259.0 


296.0 


333.0 


369 


36.9 


73.8 


110.7 


147.6 


184.5 


221.4 


258.3 


295.2 


332.1 


368 


36.8 


73.6 


110.4 


147.2 


184.0 


220.8 


257.6 


294.4 


331.2 


367 


36.7 


73.4 


110.1 


146.8 


183.5 


220.2 


256.9 


293.6 


330.3 


366 


36.6 


73.2 


109.8 


146.4 


183.0 


219.6 


256.2 


292.8 


329.4 


365 


36.5 


73.0 


109.5 


146.0 


182.5 


219.0 


255.5 


292.0 


328.5 


364 


36.4 


72.8 


109.2 


145.6 


182.0 


218.4 


254.8 


291.2 


327.6 


363 


36.3 


72.6 


108.9 


145.2 


181.5 


217.8 


254.1 


290.4 


326.7 


362 


36.2 


72.4 


108.6 


144.8 


181.0 


217.2 


253.4 


289.6 


325.8 


361 


36.1 


72.2 


108.3 


144.4 


180.5 


216.6 


252.7 


288.8 


324.9 


360 


36.0 


72.0 


108.0 


144.0 


180.0 


216.0 


252.0 


288.0 


324.0 


359 


35.9 


71.8 


107.7 


143.6 


179.5 


215.4 


251.3 


287.2 


323.1 


358 


35.8 


71.6 


107.4 


143.2 


179.0 


214.8 


250.6 


286.4 


322.2 


357 


35.7 


71.4 


107.1 


142.8 


178.5 


214.2 


249.9 


285.6 


321.3 


356 


35.6 


71.2 


106.8 


142.4 


178.0 


213.6 


249.2 


284.8 


320.4 



LOGARITHMS OF NUMBERS. 



139 



No. 120 L. 079.] 














[No 


134 L 


. 130. 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


120 


079181 


9543 






















0266 
3861 
7426 


0626 
4219 
7781 


0987 
4576 
8136 


1347 
4934 
8490 


1707 
5291 
8845 


2067 
5647 
9198 


2426 
6004 
9552 


360 
357 

355 


1 

2 
3 


082785 
6360 
9905 


3144 
6716 


3503 
7071 


0258 
3772 
7257 


0611 
4122 
7604 


0963 
4471 
7951 


1315 
4320 
8298 


1667 
5169 
8644 


2018 
5518 
8990 


2370 
5866 
9335 


2721 
6215 
9681 


3071 
6562 


352 
349 


4 
5 


093422 
6910 


0026 
3462 
6871 


346 
343 
341 


6 
7 
8 


100371 
3804 
7210 


0715 
4146 
7549 


1059 

4487 
7888 


1403 
4828 
8227 


1747 
5169 
8565 


2091 
5510 
8903 


2434 
5851 
9241 


2777 

6191 
9579 


3119 
6531 
9916 


0253 
3609 

6940 


338 
335 

333 


9 

130 


110590 

3943 
7271 


0926 

4277 
7603 


1263 

4611 
7934 


1599 

4944 
8265 


1934 

5278 
8595 


2270 

5611 
8926 


2605 

5943 
9256 


2940 

6276 
9586 


3275 

6608 
9915 




0245 
3525 
6781 


330 
328 
325 


2 
3 
4 


120574 
3852 
7105 

13 


0903 

4178 
7429 


1231 
4504 
7753 


1560 
4830 
8076 


1888 
5156 
8399 


2216 
5481 
8722 


2544 
5806 
9045 


2871 
6131 
9368 


3198 
6456 
9690 


0012 


323 



Proportional Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


355 


35.5 


71.0 


106.5 


142.0 


177.5 


213.0 


248.5 


284.0 


319.5 


354 


35.4 


70.8 


106.2 


141.6 


177.0 


212.4 


247.8 


283.2 


318.6 


353 


35.3 


70.6 


105.9 


141.2 


176.5 


211.8 


247.1 


282.4 


317.7 


352 


35.2 


70.4 


105.6 


140.8 


176.0 


211.2 


246.4 


281.6 


316.8 


351 


35.1 


70.2 


105.3 


140.4 


175.5 


210.6 


245.7 


280.8 


315.9 


350 


35.0 


70.0 


105.0 


140.0 


175.0 


210.0 


245.0 


280.0 


315.0 


349 


34.9 


69.8 


104.7 


139.6 


174.5 


209.4 


244.3 


279.2 


314.1 


348 


34.8 


69.6 


104.4 


139.2 


174.0 


208.8 


243.6 


278.4 


313.2 


347 


34.7 


69.4 


104.1 


138.8 


173.5 


208.2 


242.9 


277.6 


312.3 


346 


34.6 


69.2 


103.8 


138.4 


173.0 


207.6 


242.2 


276.8 


311.4 


345 


34.5 


69.0 


103.5 


138.0 


172.5 


207.0 


241.5 


276.0 


310.5 


344 


34.4 


68.8 


103.2 


137.6 


172.0 


206.4 


240.8 


275.2 


309.6 


343 


34.3 


68.6 


102.9 


137.2 


171.5 


205.8 


240.1 


274.4 


308.7 


342 


34.2 


68.4 


102.6 


136.8 


171.0 


205.2 


239.4 


273.6 


307.3 


341 


34.1 


68.2 


102.3 


136.4 


170.5 


204.6 


238.7 


272.8 


306.9 


340 


34.0 


68.0 


102.0 


136.0 


170.0 


204.0 


238.0 


272.0 


306.0 


33y 


33.9 


67.8 


101.7 


135.6 


169.5 


203.4 


237.3 


271.2 


305.1 


338 


33.8 


67.6 


101.4 


135.2 


169.0 


202.8 


236.6 


270.4 


304.2 


337 


33.7 


67.4 


101.1 


134.8 


168.5 


202.2 


235.9 


269.6 


303.3 


336 


33.6 


67.2 


100.8 


134.4 


168.0 


201.6 


235.2 


268.8 


302.4 


335 


33.5 


67.0 


100.5 


134.0 


167.5 


201.0 


234.5 


268.0 


301.5 


334 


33.4 


66.8 


100.2 


133.6 


167.0 


200.4 


233.8 


267.2 


300.6 


333 


33.3 


66.6 


99.9 


133.2 


166.5 


199.8 


233.1 


266.4 


299.7 


332 


33.2 


66.4 


99.6 


132.8 


166.0 


199.2 


232.4 


265.6 


298.8 


331 


33.1 


66.2 


99.3 


132.4 


165.5 


198.6 


231.7 


264.8 


297.9 


330 


33.0 


66.0 


99.0 


132.0 


165.0 


198.0 


231.0 


264.0 


297.0 


329 


32.9 


65.8 


98.7 


131.6 


164.5 


197.4 


230.3 


263.2 


296.1 


328 


32.8 


65.6 


98.4 


131.2 


164.0 


196.8 


229.6 


262.4 


295.2 


327 


32.7 


65.4 


98.1 


130.8 


163.5 


196.2 


228.9 


261.6 


294.3 


326 


32.6 


65.2 


97.8 


130.4 


163.0 


195.6 


228.2 


260.8 


293.4 


325 


32.5 


65.0 


97.5 


130.0 


162.5 


195.0 


227.5 


260.0 


292.5 


324 


32.4 


64.8 


97.2 


129.6 


162.0 


194.4 


226.8 


259.2 


291.6 


323 


32.3 


64.6 


96.9 


129.2 


161.5 


193.8 


226.1 


258.4 


290.7 


322 


32.2 


64.4 


96.6 


128.8 


161.0 


193.2 


225.4 


257.6 


239.8 



140 



LOGARITHMS OF NUMBERS. 



No. 135 L. 130.] 














[No 


. 149 L. 175. 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


135 

6 
7 
8 


130334 
3539 
6721 
9879 


0o55 
3858 
7037 


0977 
4177 
7354 


1298 
4496 
7671 


1619 

4814 
7987 


1939 
5133 
8303 


2260 
5451 
8618 


2580 
5769 
8934 


2900 
6086 
9249 


3219 
6403 
9564 


321 
318 
316 


0194 
3327 

6438 
9527 


0508 
3639 

6748 
9835 


0822 
3951 

7058 


1136 
4263 

7367 


1450 

4574 

7676 


1763 
4885 

7985 


2076 
5196 

8294 


2389 
5507 

8603 


2702 
5818 

8911 


314 
311 

309 


9 
140 


143015 

6128 
9219 


' 


0142 
3205 
6246 
9266 


0449 
3510 
6549 
9567 


0756 
3815 
6852 
9868 


1063 
4120 
7154 


1370 

4424 
7457 


1676 
4728 
7759 


1982 
5032 
8061 


307 
305 
30? 


2 
3 
4 


152288 
5336 
8362 


2594 
5640 
8664 


2900 
5943 
8965 


0168 
3161 
6134 
9086 


0469 
3460 
6430 
9380 


0769 
3758 
6726 
9674 


1068 
4055 
7022 
9968 


301 
299 
297 
295 


5 
6 

7 


161368 
4353 

7317 


1667 
4650 
7613 


1967 
4947 
7908 


2266 
5244 
8203 


2564 
5541 
8497 


2863 
5838 
8792 


8 
9 


1 70262 
3186 


0555 

3478 


0848 
3769 


1141 
4060 


1434 
4351 


1726 
4641 


2019 
4932 


2311 
5222 


2603 
5512 


2895 
5802 


293 
291 



Proportional Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


321 


32.1 


64.2 


96.3 


128.4 


160.5 


192.6 


224.7 


256.8 


288.9 


320 


32.0 


64.0 


96.0 


128.0 


160.0 


192.0 


224.0 


256.0 


288.0 


319 


31.9 


63.8 


95.7 


127.6 


159.5 


191.4 


223.3 


255.2 


28>.1 


318 


31.8 


63.6 


95.4 


127.2 


159.0 


190.8 


222.6 


254.4 


286.2 


317 


31.7 


63.4 


95.1 


126.8 


158.5 


190.2 


221.9 


253.6 


285.3 


316 


31.6 


63.2 


94.8 


126.4 


158.0 


189.6 


221.2 


252.8 


284.4 


315 


31.5 


63.0 


94.5 


126.0 


157.5 


189.0 


220.5 


252.0 


283.5 


314 


31.4 


62.8 


94.2 


125.6 


157.0 


188.4 


219.8 


251.2 


282.6 


313 


31.3 


62.6 


93.9 


125.2 


156.5 


187.8 


219.1 


250.4 


281.7 


312 


31.2 


62.4 


93.6 


124.8 


156.0 


187.2 


218.4 


249.6 


280.8 


311 


31.1 


62.2 


93.3 


124.4 


155.5 


186.6 


217.7 


248.8 


279.9 


310 


31.0 


62.0 


93.0 


124.0 


155.0 


186.0 


217.0 


248.0 


279.0 


309 


30.9 


61.8 


92.7 


123.6 


154.5 


185.4 


216.3 


247.2 


278.1 


308 


30.8 


61.6 


92.4 


123.2 


154.0 


184.8 


215.6 


246.4 


277.2 


307 


30.7 


61.4 


92.1 


122.8 


153.5 


184.2 


214.9 


245.6 


276.3 


306 


30.6 


61.2 


91.8 


122.4 


153.0 


183.6 


214.2 


244.8 


275.4 


305 


30.5 


61.0 


91.5 


122.0 


152.5 


183.0 


213.5 


244.0 


274.5 


304 


30.4 


60.8 


91.2 


121.6 


152.0 


182.4 


212.8 


243.2 


273.6 


303 


30.3 


60.6 


90.9 


121.2 


151.5 


181.8 


212.1 


242.4 


272.7 


302 


30.2 


60.4 


90.6 


120.8 


151.0 


181.2 


211.4 


241.6 


271.8 


301 


30.1 


60.2 


90.3 


120.4 


150.5 


180 6 


210.7 


240.8 


270.9 


300 


30.0 


60.0 


90.0 


120.0 


150.0 


180.0 


210.0 


240.0 


270.G 


299 


29.9 


59.8 


89.7 


119.6 


149.5 


179.4 


209.3 


239.2 


269.1 


298 


29.8 


59.6 


89.4 


119.2 


149.0 


178.8 


208.6 


238.4 


268.2 


297 


29.7 


59.4 


89.1 


118.8 


148.5 


178.2 


207.9 


237.6 


267.3 


296 


29.6 


59.2 


88.8 


118.4 


143.0 


177.6 


207.2 


236.8 


266.4 


295 


29.5 


59.0 


8S.5 


118.0 


147.5 


177.0 


206.5 


236.0 


265.5 


294 


29.4 


58.8 


88.2 


117.6 


147.0 


176.4 


205.8 


235.2 


264.6 


293 


29.3 


58.6 


87.9 


117.2 


146.5 


175.8 


205.1 


234.4 


263.7 


292 


29.2 


58.4 


87.6 


116.8 


146.0 


175.2 


204.4 


233.6 


262.8 


291 


29.1 


58.2 


87.3 


116.4 


145.5 


174.6 


203.7 


232.8 


261.9 


290 


29.0 


58.0 


87.0 


116.0 


145.0 


174.0 


203.0 


232.0 


261.0 


289 


28.9 


57.8 


86.7 


115.6 


144.5 i 


173.4 


202.3 


231.2 


260.1 


288 


28.8 


57.6 


86.4 


115.2 


144.0 


172.8 


20'. 6 


230.4 


259.2 


287 


28.7 


57.4 


86.1 


114.8 


143.5 


172.2 


200.9 


229.6 


258.3 


286 


28.6 


57.2 


85.8 


114.4 


143.0 


171.6 


200.2 


228.8 


257.4 



LOGARITHMS OF NUMBERS. 



141 



No. 150 L. 176.] 














[No. 


169 L. 230 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


DiflF. 


150 


176091 
8977 


6381 
9264- 


6670 
9552 


6959 


7248 


7536 


7825 


8113 


8401 


8689 


289 


' 




0126 
2985 
5825 
8647 


0413 
3270 
6108 
8928 


0699 
3555 
6391 
9209 


0986 
3839 
6674 
9490 


1272 
4123 
6956 
9771 


1558 
4407 
7239 


287 
285 
283 


2 
3 
4 


181844 
4691 
7521 


2129 
4975 
7803 


2415 
5259 
8084 


2700 
5542 
8366 


0051 
2846 
5623 
6382 


281 
279 
278 
276 


5 
6 
7 
8 


190332 
3125 
5900 
8657 


0612 
3403 
6176 
8932 


0892 
3681 
6453 
9206 


1171 
3959 
6729 
9481 


1451 
4237 
7005 
9755 


1730 
4514 
7281 


2010 
4792 
7556 


2289 
5069 
7832 


2567 
5346 
8107 


0029 
2761 

5475 
8173 


0303 
3033 

5746 
8441 


0577 
3305 

6016 
8710 


0850 
3577 

6286 
8979 


1124 
3848 

6556 

9247 


274 
272 

271 
269 


9 

160 

1 
2 


201397 

4120 
6826 
9515 


1670 

4391 
7096 
9783 


1943 

4663 
7365 


2216 

4934 
7634 


2488 

5204 
7904 


0051 
2720 
5373 
8010 


0319 
2986 
5638 
8273 


0586 
3252 
5902 
8536 


0853 
3518 
6166 
8798 


1121 
3783 
6430 
9060 


1388 
4049 
6694 
9323 


1654 
4314 
6957 
9585 


1921 
4579 
7221 
9846 


267 
266 
264 
262 


3 

4 
5 


212188 
4844 
7484 


2454 
5109 
7747 


6 
7 
8 
9 


220108 
2716 
5309 
7887 

23 


0370 
2976 
5568 
8144 


0631 
3236 
5826 
8400 


0892 
3496 
6084 
8657 


1153 
3755 
6342 
8913 


1414 
4015 
6600 
9170 


1675 
4274 
6858 
9426 


1936 
4533 
7115 
9682 


2196 
4792 
7372 
9938 


2456 
5051 
7630 


261 
259 
258 


0193 


256 



Proportional Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


285 


28.5 


57.0 


85.5 


114.0 


142.5 


171.0 


199.5 


228.0 


256.5 


284 


28.4 


56.8 


85.2 


113.6 


142.0 


170.4 


198.8 


227.2 


255.6 


283 


28.3 


56.6 


84.9 


113.2 


141.5 


169.8 


198.1 


226.4 


254.7 


282 


28.2 


56.4 


84.6 


112.8 


141.0 


169.2 


197.4 


225.6 


253.8 


281 


28.1 


56.2 


84.3 


112.4 


140.5 


168.6 


196.7 


224.8 


252.9 


280 


28.0 


56.0 


84.0 


112.0 


140.0 


168.0 


196.0 


224.0 


252.0 


279 


27.9 


55.8 


83.7 


111.6 


139.5 


167.4 


195.3 


223.2 


251.1 


278 


27.8 


55.6 


83.4 


111.2 


139.0 


166.8 


194.6 


222.4 


250.2 


277 


27.7 


55.4 


83.1 


110.8 


138.5 


166.2 


193.9 


221.6 


249.3 


276 


27.6 


55.2 


82.8 


110.4 


138.0 


165.6 


193.2 


220.8 


248.4 


275 


27.5 


55.0 


82.5 


110.0 


137.5 


165.0 


192.5 


220.0 


247.3 


274 


27.4 


54.8 


82.2 


109.6 


137.0 


164.4 


191.8 


219.2 


246.6 


273 


27.3 


54.6 


81.9 


109.2 


136.5 


163.8 


191.1 


218.4 


245.7 


272 


27.2 


54.4 


81.6 


108.8 


136.0 


163.2 


190.4 


217.6 


244.8 


271 


27.1 


54.2 


81.3 


108.4 


135.5 


162.6 


189.7 


216.8 


243.9 


270 


27.0 


54.0 


81.0 


108.0 


135.0 


162.0 


189.0 


216.0 


243.0 


269 


26.9 


53.8 


80.7 


107.6 


134.5 


161.4 


188.3 


215.2 


242.1 


268' 


26.8 


53.6 


80.4 


107.2 


134.0 


160.8 


187.6 


214.4 


241.2 


267 


26.7 


53.4 


80.1 


106.8 


133.5 


160.2 


186.9 


213.6 


240.3 


266 


26.6 


53.2 


79.8 


106.4 


133.0 


159.6 


186.2 


212.8 


239.4 


265 


26.5 


53.0 


79.5 


106.0 


132.5 


159.0 


185.5 


212.0 


238.5 


264 


26.4 


52.8 


79.2 


105.6 


132.0 


158.4 


184.8 


211.2 


237.6 


263 


26.3 


52.6 


78.9 


105.2 


131.5 


157.8 


184.1 


210.4 


236.7 


262 


26.2 


52.4 


78.6 


104.8 


131.0 


157.2 


183.4 


209.6 


235.8 


261 


26.1 


52.2 


78.3 


104.4 


130.5 


156.6 


182.7 


208.8 


234.9 


260 


26.0 


52.0 


78.0. 


104.0 


130.0 


156.0 


182.0 


208.0 


234.0 


259 


25.9 


51.8 


77.7 


103.6 


129.5 


155.4 


181.3 


207.2 


233.1 


253 


25.8 


51.6 


77.4 


103.2 


129.0 


154.8 


180.6 


206.4 


232.2 


257 


25.7 


51.4 


77.1 


102.8 


128.5 


154.2 


179.9 


205.6 


231.3 


256 


25.6 


51.2 


76.8 


102.4 


128.0 


153.6 


179.2 


204.8 


230.4 


255 


25.5 


51.0 


76.5 


102.0 


127.5 


1530 


178.5 


204.0 


229.5 



142 



LOGARITHMS OF NUMBERS. 



No. 170 L. 230. 
















[No 


. 189 L. 278. 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


170 
1 

2 
3 


230449 
2996 
5528 
8046 


0704 
3250 
5781 
8297 


0960 
3504 
6033 
8548 


1215 
3757 
6285 
8799 


1470 
4011 
6537 
9049 


1724 
4264 
6789 
9299 


1979 
4517 
7041 
9550 


2234 
4770 
7292 
9800 


2488 
5023 
7544 


2742 
5276 
7795 


255 
253 
252 


0050 

254-1 
5019 
7482 
9932 


0300 
2790 
5266 
7728 


250 

249 
248 
246 


4 
5 
6 
7 


240549 
3038 
5513 
7973 


0799 
3286 
5759 
8219 


1048 
3534 
6006 
8464 


1297 
3782 
6252 
8709 


1546 
4030 
6499 
8954 


1795 
4277 
6745 
9198 


2044 
4525 
6991 
9443 


2293 
4772 
7237 
9687 


0176 
2610 
5031 

7439 
9833 


245 
243 
242 

241 
239 


8 
9 

180 

1 


250420 
2853 

5273 
7679 


0664 
3096 

5514 
7918 


0908 
3338 

5755 

8158 


1151 
3580 

5996 

8398 


1395 
3822 

6237 
8637 


1638 
4064 

6477 

8877 


1881 
4306 

6718 
9116 


2125 
4548 

6958 
9355 


2368 
4790 

7198 
9594 


2 
3 
4 
5 
6 


260071 
2451 
4818 
7172 
9513 


0310 
2688 
5054 
7406 
9746 


0548 
2925 
5290 
7641 
9980 


0787 
3162 
5525 
7875 


1025 
3399 
5761 
81 10 


1263 
3636 
5996 
8344 


1501 
3873 
6232 
8578 


1739 
4109 
6467 
8812 


1976 
4346 
6702 
9046 


2214 
4582 
6937 
9279 


238 
237 
235 
234 


0213 

2538 
4850 
7151 


0446 
2770 
5081 
7380 


0679 
3001 
5311 
7609 


0912 
3233 
5542 
7838 


1144 
3464 
5772 
8067 


1377 
3696 
6002 
8296 


1609 
3927 
6232 
8525 


233 
232 
230 
229 


7 
8 
9 


271842 
4158 
6462 


2074 
4389 
6692 


2306 
4620 
6921 



Proportional, Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


1 


8 


9 


255 


25.5 


51.0 


76.5 


102.0 


127.5 


153.0 


178.5 


204.0 


229.5 


254 


25.4 


50.8 


76.2 


101.6 


127.0 


152.4 


177.8 


203.2 


228.6 


253 


25.3 


50.6 


75.9 


101.2 


126.5 


151.8 


177.1 


202.4 


227.7 


252 


25.2 


50.4 


75.6 


100.8 


126.0 


151.2 


176.4 


201.6 


226.8 


251 


25.1 


50.2 


75.3 


100.4 


125.5 


150.6 


175.7 


200.8 


225.9 


250 


25.0 


50.0 


75.0 


100.0 


125.0 


150.0 


175.0 


200.0 


225.0 


249 


24.9 


49.8 


74.7 


99.6 


124.5 


149.4 


174.3 


199.2 


224.1 


248 


24.8 


49.6 


74.4 


99.2 


124.0 


148.8 


173.6 


198.4 


223.2 


247 


24.7 


49.4 


74.1 


98.8 


123.5 


148.2 


172.9 


197.6 


222.3 


246 


24.6 


49.2 


73.8 


98.4 


123.0 


147.6 


172.2 


196.8 


221.4 


245 


24.5 


49.0 


73.5 


98.0 


122.5 


147.0 


171.5 


196.0 


220.5 


244 


24.4 


48.8 


73.2 


97.6 


122.0 


146.4 


170.8 


195.2 


219.6 


243 


24.3 


48.6 


72.9 


97.2 


121.5 


145.8 


170.1 


194.4 


218.7 


242 


24.2 


48.4 


72.6 


96.8 


121.0 


145.2 


169.4 


193.6 


217.8 


241 


24.1 


48.2 


72.3 


96.4 


120.5 


144.6 


168.7 


192.8 


216.9 


240 


24.0 


48.0 


72.0 


96.0 


120.0 


144.0 


168.0 


192.0 


216.0 


239 


23.9 


47.8 


71.7 


95.6 


119.5 


143.4 


167.3 


191.2 


215.1 


238 


23.8 


47.6 


71.4 


95.2 


119.0 


142.8 


166.6 


190.4 


214.2 


237 


23.7 


47.4 


71.1 


94.8 


118.5 


142.2 


165.9 


189.6 


213.3 


236 


23.6 


47.2 


70.8 


94.4 


118.0 


141.6 


165.2 


188.8 


212.4 


235 


23.5 


47.0 


70.5 


94.0 


117.5 


141.0 


164.5 


188.0 


211.5 


234 


23.4 


46.8 


70.2 


93.6 


117.0 


140.4 


163.8 


187.2 


210.6 


233 


23.3 


46.6 


69.9 


93.2 


116.5 


139.8 


163.1 


186.4 


209.7 


232 


23.2 


46.4 


69.6 


92.8 


116.0 


139.2 


162.4 


185.6 


208.8 


231 


23.1 


46.2 


69.3 


92.4 


115.5 


138.6 


161.7 


184.8 


207.9 


230 


23.0 


46.0 


69.0 


92.0 


115.0 


138.0 


161.0 


184.0 


207.0 


229 


22.9 


45.8 


68.7 


91.6 


114.5 


137.4 


160.3 


183.2 


206.1 


228 


22.8 


45.6 


68.4 


91.2 


114.0 


136.8 


159.6 


182.4 


205.2 


227 


22.7 


45.4 


68.1 


90.8 


113.5 


136.2 


158.9 


181.6 


204.3 


226 


22.6 


45.2 


67.8 


90.4 


113.0 


135.6 


158.2 


180.8 


203.4 



LOGARITHMS OP NUMBERS. 



143 



No. 190 L. 278.] 














[No 


214 L 


.332. 


N. 





1 


2 1 3 1 4 


5 


6 


7 


8 


9 


Diflf. 


190 


278754 


8982 


9211 


943S 


9667 


9895 












0123 
2396 
4656 
6905 
9143 


0351 
2622 
4882 
7130 
9366 


0576 

2845 
5107 
7354 
9589 


0806 
3075 

5332 
7578 
9812 


228 
.227 
226 
225 
223 


1 
2 
3 
4 


281033 
3301 
5557 
7802 


1261 
3527 
5782 
8026 


1488 
3753 
6007 
8249 


1715 
3979 
6232 
8473 


1942 
4205 
6456 
8696 


2169 
4431 
6681 
8920 


5 
6 
7 
8 
9 


290035 
2256 
4466 
6665 
8853 


0257 

2478 
4687 
6884 
9071 


0480 
2699 
4907 
7104 
9289 


0702 
2920 
5 127 
7323 
9507 


0925 
3141 
5347 
7542 
9725 


1147 
3363 
5567 
7761 
9943 


1369 

3584 
5787 
7979 


1591 
3804 
6007 
8198 


1813 
4025 
6226 
8416 


2034 
4246 
6446 
8635 


222 
221 
220 
219 


0161 

2331 

4491 
6639 
8778 


0378 

2547 
4706 
6854 
8991 


0595 

2764 
4921 
7068 
9204 


0813 

2980 
5136 
7282 
9417 


218 

217 
216 
215 
213 


200 
1 

2 
3 

4 


301030 
3196 
5351 
7496 
9630 


1247 
3412 
5566 
7710 
9843 


1464 
3628 
5781 
7924 


1681 
3844 
5996 
8137 


1898 
4059 
6211 
8351 


2114 
4275 
6425 
8564 


0056 
2177 
4289 
6390 
8481 


0268 
2389 
4499 
6599 
8689 


0481 
2600 
4710 
6809 
8898 


0693 
2812 
4920 
7018 
9106 


0906 
3023 
5130 
7227 
9314 


1118 
3234 
5340 
7436 
9522 


1330 
3445 
5551 
7646 
9730 


1542 
3656 
5760 
7854 
9938 


212 
21J 
210 
209 
208 


5 
6 
7 
8 


311754 
3867 
5970 
8063 


1966 
4078 
6180 
8272 


9 

210 

1 

2 
3 


320146 

2219 
4282 
6336 
8380 


0354 

2426 
4488 
6541 
8583 


0562 

2633 
4694 
6745 
8787 


0769 

2839 
4899 
6950 
8991 


0977 

3046 
5105 
7155 
9194 


1184 

3252 
5310 
7359 
9398 


1391 

3458 
5516 
7563 
9601 


1598 

3665 
5721 
7767 
9805 


1805 

3871 
5926 
7972 

0008 
2034 


2012 

4077 
6131 
8176 


207 

206 
205 
204 


0211 
2236 


203 
202 


4 


330414 1 0617 


0819 


1022 


1225 


14271 1630 


1832 









Proportional 


Parts. 








Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


225 


22.5 


45.0 


67.5 


90.0 


112.5 


135.0 


157.5 


180.0 


202.5 


224 


22.4 


44.8 


67.2 


89.6 


112.0 


134.4 


156.8 


179.2 


201.6 


223 


22.3 


44.6 


66.9 


89.2 


111.5 


133.8 


156.1 


178.4 


200.7 


222 


22.2 


44.4 


66.6 


88.8 


111.0 


133.2 


155.4 


177.6 


199.8 


221 


22.1 


44.2 


66.3 


88.4 


110.5 


132.6 


154.7 


. 176.8 


198.9 


220 


22.0 


44.0 


66.0 


88.0 


110.0 


132.0 


154.0 


176.0 


198.0 


219 


21.9 


43.8 


65.7 


87.6 


109.5 


131.4 


153.3 


175.2 


197.1 


218 


21.8 


43.6 


65.4 


87.2 


109.0 


130.8 


152.6 


174.4 


196.2 


217 


21.7 


43.4 


65.1 


86.8 


108.5 


130.2 


151.9 


173.6 


195.3 


216 


21.6 


43.2 


64.8 


86.4 


108.0 


129.6 


151.2 


172.8 


194.4 


215 


21.5 


43.0 


64.5 


86.0 


107.5 


129.0 


150.5 


172.0 


193.5 


214 


21.4 


42.8 


64.2 


85.6 


107.0 


128.4 


149.8 


171.2 


192.6 


213 


21.3 


42.6 


63.9 


85.2 


106.5 


127.8 


149.1 


170.4 


191.7 


212 


21.2 


42.4 


63.6 


84.8 


106.0 


127.2 


148.4 


169.6 


190.8 


211 


21.1 


42.2 


63.3 


84.4 


105.5 


126.6 


147.7 


168.8 


189.9 


210 


21.0 


42.0 


63.0 


84.0 


105.0 


126.0 


147.0 


168.0 


189.0 


209 


20.9 


41.8 


62.7 


83.6 


104.5 


125.4 


146.3 


167.2 


188.1 


208 


20.8 


41.6 


62.4 


83.2 


104.0 


124.8 


145.6 


166.4 


187.2 


20/ 


20.7 


41.4 


62.1 


82.8 


103.5 


124.2 


144.9 


165.6 


186.3 


206 


20.6 


41.2 


61.8 


82.4 


103.0 


123.6 


144.2 


164.8 


185.4 


205 


20.5 


41.0 


61.5 


82.0 


102.5 


123.0 


143.5 


164.0 


184.5 


204 


20.4 


40.8 


61.2 


81.6 


102.0 


122.4 


142.8 


163.2 


183.6 


203 


20.3 ! 


40.6 


60.9 


81.2 


101.5 


121.8 


142.1 


162.4 


182.7 


202 


20.2 1 


40.4 1 


60.6 


80.8 1 


101.0 1 


121.2 


141.4 1 


161.6 


181.8 



144 



LOGARITHMS OF NUMBERS. 



No. 215 L. 332.] 



[No. 239 L. 380. 



N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 

"4253 
6260 
8257 


Diff. 


215 
6 

7 
8 


332438 
4454 
6460 
8456 


2640 
4655 
6660 
8656 


2842 
4856 
6860 
8855 


3044 
5057 
7060 
9054 


3246 
5257 
7260 
9253 


3447 
5458 
7459 
9451 


3649 
5658 
7659 
9650 


3850 
5859 
7858 
9849 


4051 
6059 
8058 


202 
201 
200 


0047 
2028 

3999 
5962 
7915 
9860 


0246 
2225 

4196 
6157 
8110 


199 
198 

197 
196 
195 


9 

220 

1 

2 
3 


340444 

2423 
4392 
6353 
8305 


0642 

2620 
4589 
6549 
8500 


0841 

2817 

4785 
6744 
8694 


1039 

3014 

4981 
6939 
8889 


1237 

3212 

5178 
7135 
9083 


1435 

3409 

5374 
7330 
9278 


1632 

3606 
5570 
7525 
9472 


1830 

3802 
5766 
7720 
9666 

1603 
3532 
5452 
7363 
9266 


0054 
1989 
3916 
5834 
7744 
9646 


194 
193 
193 
192 
191 
190 


4 
5 
6 
7 
8 
9 


350248 
2183 
4108 
6026 
7935 
9835 


0442 
2375 
4301 
6217 
8125 


0636 
2568 
4493 
6408 
8316 

0215 

2105 

3988 
5862 
7729 
9587 


0829 
2761 
4685 
6599 
8506 


1023 
2954 
4876 
6790 
8696 


1216 
3147 
5068 
6981 
8886 


1410 
3339 
5260 
7172 
9076 


1796 

3724 
5643 
7554 
9456 


0025 

1917 
3800 
5675 
7542 
9401 


0404 

2294 
4176 
6049 
7915 
9772 


0593 

2482 
4363 
6236 
8101 
9958 


0783 

2671 
4551 
6423 
8287 


0972 

2859 
4739 
6610 
8473 


1161 

3048 
4926 
6796 
8659 


1350 

3236 
5113 
6983 
8845 


1539 

3424 
5301 
7169 
9030 


189 

188 
188 
187 
186 


230 

1 

2 
3 
4 


361728 
3612 
5433 
7356 
9216 


0143 
1991 
3831 
5664 
7488 
9306 


0328 
2175 
4015 
5846 
7670 
9487 


0513 
2360 
4198 
6029 
7852 
9668 


0698 

2544 
4382 
6212 
8034 
9849 


0883 
2728 
4565 
6394 
8216 


185 
184 
184 
183 
182 


5 
6 
7 
8 
9 


371063 
2912 
4743 
6577 
8398 

38 


1253 
3096 
4932 
6759 
8580 


1437 
3280 
5115 
6942 
8761 


1622 
3464 
5298 
7124 
8943 


1806 
3647 
5481 
7306 
9124 


0030 


181 











Proportional 


Parts. 








Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


202 


20.2 


40.4 


60.6 


80.8 


101.0 


121.2 


141.4 


161.6 


181.8 


?,01 


20.1 


40.2 


60.3 


80.4 


100.5 


120.6 


140.7 


160.8 


180.9 


7.00 


20.0 


40.0 


60.0 


80.0 


100.0 


120.0 


140.0 


160.0 


180.0 


199 


19.9 


39.8 


59.7 


79.6 


99.5 


119.4 


139.3 


159.2 


179.1 


193 


19.8 


39.6 


59.4 


79.2 


99.0 


118.8 


138.6 


158.4 


178.2 


197 


19.7 


39.4 


59.1 


78.8 


98.5 


118.2 


137.9 


157.6 


177.3 


196 


19.6 


39.2 


58.8 


78.4 


98.0 


117.6 


137.2 


156.8 


176.4 


195 


19.5 


39.0 


58.5 


78.0 


97.5 


117.0 


136.5 


156.0 


175. S 


194 


19.4 


38.8 


58.2 


77.6 


97.0 


116.4 


,135.8 


155.2 


174.6 


193 


19.3 


38.6 


57.9 


77.2 


96.5 


115.8 


135.1 


154.4 


173.7 


192 


19.2 


38.4 


57.6 


76.8 


96.0 


115.2 


134.4 


153.6 


172.8 


191 


19.1 


38.2 


57.3 


76.4 


95.5 


114.6 


133.7 


152.8 


171.9 


190 


19.0 


38.0 


57.0 


76.0 


95.0 


114.0 


133.0 


152.0 


171.0 


189 


18.9 


37.8 


56.7 


75.6 


94.5 


113.4 


132.3 


151.2 


170.1 


183 


18.8 


37.6 


56.4 


75.2 


94.0 


112.8 


131.6 


150.4 


169.2 


187 


18.7 


37.4 


56.1 


74.8 


93.5 


112.2 


130.9 


149.6 


168.3 


186 


18.6 


37.2 


55.3 


74.4 


93.0 


111.6 


130.2 


148.8 


167.4 


185 


18.5 


37.0 


55.5 


74.0 


92.5 


111.0 


129.5 


148.0 


166.5 


184 


18.4 


36.8 


55.2 


73.6 


92.0 


110.4 


128.8 


147.2 


165.6 


183 


18.3 


36.6 


54.9 


73.2 


91.5 


109.8 


128.1 


146.4 


164.7 


182 


18.2 


36.4 


54.6 


72.8 


91.0 


109.2 


127.4 


145.6 


163.8 


181 


18.1 


36.2 


54.3 


72.4 


90.5 


108.6 


126.7 


144.8 


162.9 


180 


18.0 


36.0 


54.0 


72.0 


90.0 


108.0 


126.0 


144.0 


162.0 


179 


17.9 


35.8 


53.7 


71.6 


89.5 


107.4 


125.3 


143.2 


161.1 



LOGARITHMS OF NUMBERS. 



145 



No. 240 L. 380.] 














[No 


269 L. 431. 


N. 





1 


2 


3 


4 


5 


6 


7 


8 

T656 
3456 
5249 
7034 
8811 


9 


Diff. 


240 
1 

2 
3 
4 
5 


3802 1 1 
2017 
3815 
5606 
7390 
9166 


0392 
2197 
3995 
5785 
7568 
9343 


0573 
2377 
4174 
5964 
7746 
9520 


0754 
2557 
4353 
6142 
7924 
9698 


0934 
2737 
4533 
6321 
8101 
9875 


1115 
2917 
4712 
6499 

8279 


1296 
3097 
4891 
6677 

8456 


1476 
3277 
5070 
6856 
8634 


1837 
3636 
5428 
7212 
8989 


181 
180 
179 
178 

178 


0051 
1817 
3575 
5326 
7071 

8808 


0228 
1993 
3751 
5501 

7245 

8981 


0405 
2169 
3926 
5676 
7419 

9154 


0582 
2345 
4101 
5850 
7592 

9328 


0759 
2521 
4277 
6025 
7766 

9501 


177 
176 
176 
175 
174 

173 


6 

7 
8 
9 

250 


390935 
2697 
4452 
6199 

7940 
9674 


1112 
2873 
4627 
6374 

8114 

9847 


1288 
3048 
4802 
6548 

8287 


1464 
3224 
4977 
6722 

8461 


1641 
3400 
5152 
6896 

8634 




0020 
1745 
3464 
5176 
6881 
8579 


0192 
1917 
3635 

5346 
7051 
8749 


0365 
2039 
3807 
5517 
7221 
8918 


0538 
2261 
3978 
5688 
7391 
9087 


0711 
2433 
4149 
5858 
7561 
9257 


0883 
2605 
4320 
6029 
7731 
9426 


1056 
2777 
4492 
6199 
7901 
9595 


1228 
2949 
4663 
6370 
8070 
9764 


173 

172 
171 
171 

170 
169 


2 
3 
4 
5 
6 
7 


401401 
3121 
4834 
6540 
8240 
9933 


1573 
3292 
5005 
6710 
8410 


0102 
1788 
3467 

5140 
6807 
8467 


0271 
1956 
3635 

5307 
6973 
8633 


0440 
2124 
3803 

5474 
7139 
8798 


0609 
2293 
3970 

5641 
7306 
8964 


0777 
2461 
4137 

5808 
7472 
9129 


0946 
2629 
4305 

5974 
7638 
9295 


1114 
2796 
4472 

6141 

7804 
9460 


1283 
2964 
4639 

6308 
7970 
9625 


1451 
3132 
4806 

6474 
8135 
9791 


169 
168 
167 

167 
166 
165 


8 
9 

260 
1 

2 
3 


411620 
3300 

4973 
6641 
8301 




0121 
1768 
3410 
5045 
6674 
8297 
9914 


0286 
1933 
3574 
5208 
6836 
8459 


0451 
2097 
3737 
5371 
6999 
8621 


0616 
2261 
3901 
5534 
7161 
8783 


0781 
2426 
4065 
5697 
7324 
8944 


0945 
2590 
4228 
5860 
74S6 
9106 


1110 

2754 
4392 
6023 
7648 
9268 


1275 
2918 
4555 
6186 
7811 
9429 


1439 
3082 
4718 
6349 
7973 
9591 


165 
164 
164 
163 
162 
162 


4 
5 
6 
7 
8 
9 


421604 
3246 
4882 
6511 
8135 
9752 

43 


0075 


0236 


0398 


0559 


0720 


0881 


1042 


1203 


161 



Proportional Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


178 


17.8 


35.6 


53.4 


71.2 


89.0 


106.8 


124.6 


142.4 


160.2 


177 


17.7 


35.4 


53.1 


70.8 


88.5 


106.2 


123.9 


141.6 


159.3 


176 


17.6 


35.2 


52.8 


70.4 


88.0 


105.6 


123.2 


140.8 


158.4 


175 


17.5 


35.0 


52.5 


70.0 


87.5 


105.0 


122.5 


140.0 


157.5 


174 


17.4 


34.8 


52.2 


69.6 


87.0 


104.4 


121.8 


139.2 


156.6 


173 


173 


34.6 


51.9 


69.2 


86.5 


103.8 


121.1 


138.4 


155.7 


172 


17.2 


34.4 


51.6 


68.8 


86.0 


103.2 


120.4 


137.6 


154.8 


171 


17.1 


34.2 


51.3 


68.4 


85.5 


102.6 


119.7 


i36.8 


153.9 


170 


17.0 


34.0 


51.0 


68.0 


85.0 


102.0 


119.0 


136.0 


153.0 


169 


16.9 


33.8 


50.7 


67.6 


84.5 


101.4 


118.3 


135.2 


152.1 


168 


16.8 


33.6 


50.4 


67.2 


84.0 


100.8 


117.6 


134.4 


151.2 


167 


16.7 


33.4 


50.1 


66.8 


83.5 


100.2 


116.9 


133.6 


150.3 


166 


16.6 


33.2 


49.8 


66.4 


83.0 


99.6 


116.2 


132.8 


149.4 


165 


16.5 


33.0 


49.5 


66.0 


82.5 


99.0 


115.5 


132.0 


148.5 


164 


16.4 


32.8 


49.2 


65.6 


82.0 


98.4 


114.8 


131.2 


147.6 


163 


16.3 


32.6 


48.9 


65.2 


81.5 


97.8 


114.1 


130.4 


146.7 


162 


16.2 


32.4 


48.5 


64.8 


81.0 


97.2 


113.4 


129.6 


145.8 


161 


16.1 


32.2 


48.3 


64.4 


80.5 


96.6 


112.7 


128.8 


144.9 



146 



LOGARITHMS OF NUMBERS. 



No. 270 L. 431.] 



[No. 299 L. 476. 



N. 





1 


2 ■ 


3 


4 


5 


6 


7 


8 


9 


Diff. 


270 
1 

2 
3 
4 
5 


431364 
2969 
4569 
6163 
7751 
9333 


1525 
3130 
4729 
6322 
7909 
9491 


1685 
3290 
4888 
6481 
8067 
9648 


1846 
3450 
5048 
6640 
8226 
9806 


2007 
3610 
5207 
6799 

8384 


2167 
3770 
5367 
6957 
8542 


2328 
3930 
5526 
7116 
8701 


2433 
40?0 
5685 
7275 
8359 


2649 
4249 
5844 
7433 
9017 


2809 
4409 
6004 
7592 
9175 


161 
160 
159 
159 

153 




0122 
1695 
3263 
4825 
6382 

7933 

9478 


0279 
1852 
3419 
4981 
6537 

8088 
9633 


0437 
2009 
3576 
5137 
6692 

8242 
9787 


0594 
2166 
3732 
5293 
6848 

8397 
9941 


0752 
2323 
3889 
5449 
7003 

8552 


158 
157 
157 
156 

155 

155 


6 

7 
8 
9 

280 


440909 
2480 
4045 
5604 

7158 
8706 


1066 
2637 
4201 
5760 

7313 
8361 


1224 
2793 
4357 
5915 

7468 
9015 


1381 
2950 
4513 
6071 

7623 
9170 


1536 
3106 
4669 
6226 

7778 
9324 




0095 
1633 
3165 
4692 
6214 
7731 
9242 

0748 
2248 

3744 
5234 
6719 
8200 
9675 


154 
154 
153 
153 
152 
152 
151 


2 
3 
4 
5 
6 
7 
8 


450249 
1786 
3318 
4845 
6366 
7882 
9392 


0403 
1940 
3471 
4997 
6518 
8033 
9543 


0557 
2093 
3624 
5150 
6670 
8184 
9694 


0711 

2247 
3777 
5302 
682! 
8336 
9845 


0865 
2400 
3930 
5454 
6973 
8487 
9995 


1018 
2553 
4082 
5606 
7125 
8638 


1172 
2706 
4235 
5758 
7276 
8789 


1326 
2859 
4387 
5910 
7428 
8940 


1479 
3012 
4540 
6062 
7579 
9091 

0597 
2098 

3594 
5085 
6571 
8052 
9527 


0146 
1649 

3146 
4639 
6126 
7608 
9035 


0296 
1799 

3296 

4788 
6274 
7756 
9233 


0447 
1948 

3445 
4936 
6423 
7904 
9380 


151 
150 

150 
149 
149 

148 
148 


9 

290 
1 

2 
3 
4 
5 


460898 

2398 
3893 
5383 
6868 
8347 
9322 


1048 

2548 
4042 
5532 
7016 
8495 
9969 


1198 

2697 
4191 
5680 
7164 
8643 


1348 

2847 
4340 
5829 
7312 
8790 


1499 

2997 
4490 
5977 
7460 
8938 


0116 
1585 
3049 
4503 
5962 


0263 
1732 
3195 
4653 
6107 


0410 
1878 
3341 
4799 
6252 


0557 
2025 
3487 
4944 
6397 


0704 
2171 
3633 
5090 

6542 


0851 
2318 
3779 
5235 
6687 


0998 
2464 
3925 
5381 
6832 


1145 
2610 
4071 
5526 
6976 


147 
146 
146 
146 
145 


f 

8 
9 


471292 
2756 
4216 
5671 


1438 
2903 
4362 
5816 



Proportional Parts. 



1 


2 


3 


4 


5 


6 


7 


16.1 


32.2 


48.3 


64.4 


80.5 


96.6 


112.7 


16.0 


32.0 


48.0 


64.0 


80.0 


96.0 


112.0 


15.9 


31.8 


47.7 


63.6 


79.5 


95.4 


111.3 


15.8 


31.6 


47.4 


63.2 


79.0 


94.8 


110.6 


15.7 


31.4 


47.1 


62.8 


78.5 


94.2 


109.9 


15.6 


31.2 


46.8 


62.4 


78.0 


93.6 


109.2 


15.5 


31.0 


46.5 


62.0 


77.5 


93.0 


108.5 


15.4 


30.8 


46.2 


61.6 


77.0 


92.4 


107.8 


15.3 


30.6 


45.9 


61.2 


76.5 


91.8 


107.1 


15.2 


30.4 


45.6 


60.8 


76.0 


91.2 


106.4 


15.1 


30.2 


45.3 


60.4 


75.5 


90.6 


105.7 


15.0 


30.0 


45.0 


60.0 


75.0 


90.0 


105.0 


14.9 


29.8 


44.7 


59.6 


74.5 


89.4 


104.3 


14.8 


29.6 


44.4 


59.2 


74.0 


88.8 


103.6 


14.7 


29.4 


44.1 


58.8 


73.5 


88.2 


102.9 


14.6 


29.2 


43.8 


58.4 


73.0 


87.6 


102.2 


14.5 


29.0 


43.5 


58.0 


72.5 


87.0 


101.5 


14.4 


28.8 


43.2 


57.6 


72.0 


86.4 


100.8 


14.3 


28.6 


42.9 


57.2 


71.5 


85.8 


100.1 


14.2 


28.4 


42.6 


56.8 


71.0 


85.2 


99.4 


14.1 


28.2 


42.3 


56.4 


70.5 


84.6 


98.7 


14.0 


28.0 


42.0 


56.0 


70.0 


84.0 


98.0 



128.8 
128.0 
127.2 
126.4 
125.6 
124.8 
124.0 
123.2 
122.4 
121.6 
120.8 

120.0 
119.2 
118.4 
117.6 
116.8 
116.0 
115.2 
114.4 
113.6 
112.8 
112.0 



144.9 
144.0 
143. 1 
142.2 
141.3 
140.4 
139.5 
138.6 
137.7 
136.8 
135.9 

135.0 
134.1 
133.2 
132.3 
131.4 
130.5 
129.6 
128.7 
127.8 
126.9 
126.0 









LOGARITHMS OF NUMBERS. 






147 


No. 300 L. 477 


] 








[No. 339 L. 531. 


•N. 





1 


2 


3 1 4 


5 


G 


7 


8 


9 


Diff. 


300 


477121 


726f 


7411 


7555 


770C 


7844 


7989 


8133 


8278 


8422 


145 


1 


8566 


8711 


8855 


8999 


9143 


9287 


9431 


9575 


9719 


9863 


144 


?. 


480007 


0151 


0294 


0438 


0582 


0725 


0369 


1012 


1156 


1299 


144 


3 


1443 


1586 


1729 


1872 


2016 


2159 


2302 


2445 


2538 


2731 


143 


4 


2874 


3016 


3159 


3302 


3445 


3587 


373C 


3872 


4015 


4157 


143 


5 


4300 


444? 


4585 


4727 


4869 


5011 


5153 


5295 


5437 


5579 


142 


6 


5721 


5863 


6005 


6147 


6289 


6430 


6572 


6714 


6855 


6997 


142 


7 


7138 


728( 


7421 


7563 


7704 


7845 


7986 


8127 


8269 


8410 


141 


8 


8551 


8692 


8833 


8974 


9114 


9255 


9396 


9537 


9677 


9818 


141 


9 


9958 


0099 
1502 


0239 
1642 


0380 
1782 


0520 
1922 


0661 
2062 


0801 
2201 


0941 
2341 


1081 
2481 


1222 
2621 


140 


310 


491362 


140 


1 


2760 


29<)( 


3040 


3179 


3319 


3458 


3597 


3737 


3876 


4015 


139 


2 


4155 


429^ 


4433 


4572 


4711 


4850 


4989 


5128 


5267 


5406 


139 


3 


5544 


5683 


5822 


5960 


6099 


623S 


6376 


6515 


6653 


6791 


139 


4 


6930 


7068 


7206 


7344 


7483 


7621 


7759 


7897 


8035 


8173 


138 


5 


8311 


8448 


8586 


8724 


8862 


8999 


9137 


9275 


9412 


9550 


138 


6 


9687 
501059" 


9824 


9962 


0099 
1470 


0236 
1607 


0374 
1744 


0511 
1880 


0648 
2017 


0785 
2154 


0922 
2291 


137 


7 


1196 


1333 


137 


8 


2427 


2564 


2700 


2837 


2973 


3109 


3246 


3382 


3518 


3655 


136 


9 


3791 


3927 


4063 


4199 


4335 


4471 


4607 


4743 


4878 


5014 


136 


320 


5150 


5286 


5421 


5557 


5693 


5828 


5964 


6099 


6234 


6370 


136 


1 


6505 


6640 


6776 


6911 


7046 


7181 


7316 


7451 


7586 


7721 


135 


2 


7856 


7991 


8126 


8260 


8395 


8530 


8664 


8799 


8934 


9068 


135 


3 


9203 


9337 


9471 


9606 


9740 


9374 


0009 
1349 


0143 
1482 


0277 
1616 


0411 
1750 


134 


4 


510545 


0679 


0813 


0947 


1031 


1215 


134 


5 


1883 


2017 


2151 


2284 


2418 


2551 


2684 


2818 


2951 


3084 


133 


6 


3218 


3351 


3484 


3617 


3750 


3383 


4016 


4149 


4282 


4415 


133 


7 


4548 


4681 


4813 


4946 


5079 


5211 


5344 


5476 


5609 


5741 


133 


8 


5874 


6006 


6139 


6271 


6403 


6535 


6668 


6800 


693?, 


7064 


132 


9 


7196 


7328 


7460 


7592 


7724 


7355 


7987 


8119 


8251 


8382 


132 


330 


8514 


8646 


8777 


8909 


9040 


9171 


9303 


9434 


9566 


9697 


131 


1 


9823 


9959 


0090 
1400 


0221 
1530 


0353 
1661 


0484 
1792 


0615 
1922 


0745 
2053 


0876 
2183 


1007 
2314 


131 


2 


521138 


1269 


131 


3 


2444 


2575 


2705 


2835 


2966 


3096 


3226 


3356 


3486 


3616 


130 


4 


3746 


3876 


4006 


4136 


4266 


4396 


4526 


4656 


4785 


4915 


130 


5 


5045 


5174 


5304 


5434 


5563 


5693 


58?.?, 


5951 


6081 


6210 


129 


6 


6339 


6469 


6598 


6727 


6856 


6985 


7114 


7243 


7372 


7501 


129 


7 


7630 


7759 


7888 


8016 8145 


8274 


8402 


8531 


8660 


8788 


129 


8 


8917 


9045 


9174 


9302 


9430 
0712 


9559 


9687 
0968 


9815 
1096 


9943 


0072 


128 


9 


530200 ' 


0328 


0456 


05841 


0840 


1223^ 


1351 


128 









Proportional Parts. 








Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


139 


13.9 


27.8 


41.7 


55.6 


69.5 


83.4 


97.3 


111.2 


125.1 


138 


13.8 


27.6 


41.4 


55.2 


69.0 


82.8 


96.6 


110.4 


124.2 


137 


13.7 


27.4 


41.1 


54.8 


68.5 


82.2 


95.9 


109.6 


123.3 


136 


13.6 


27.2 


40.8 


54.4 


68.0 


81.6 


95.2 


108.8 


122.4 


135 


13.5 


27.0 


40.5 


54.0 


67.5 


81.0 


94.5 


108.0 


121.5 


134 


13.4 


26.8 


40.2 


53.6 


67.0 


80.4 


93.8 


107.2 


120.6 


133 


13.3 


26.6 


39.9 


53.2 


66.5 


79.8 


93.1 


106.4 


119.7 


13? 


13.2 


26.4 


39.6 


52.8 


66.0 


79.2 


92.4 


105.6 


118.8 


131 


13.1 


26.2 


39.3 


52.4 


65.5 


78.6 


91.7 


104.8 


117.9 


130 


13.0 


26.0 


39.0 


52.0 


65.0 


78.0 


91.0 


104.0 


117.0 


129 


12.9 


25.8 


38.7 


51.6 


64.5 


77.4 


90.3 


103.2 


116.1 


178 


12.8 


• 25.6 


38.4 


51.2 


64.0 


76.8 


89.6 


102.4 


115.2 


127 


12.7 


25.4 


38.1 


50.8 


63.5 


76.2 


88.9 


101.6 


114.3 



148 



LOGARITHMS OF NUMBERS. 



No. 340 L. 531.] 














[No. 


379 L 


579. 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


340 
1 

2 
3 
4 
5 
6 


531479 
2754 
4026 
5294 
6558 
7819 
9076 


1607 
2882 
4153 
5421 
6685 
7945 
9202 


1734 
3009 
4280 
5547 
6811 
8071 
9327 


1862 
3136 
4407 
5674 
6937 
8197 
9452 


1990 

3264 
4534 
5800 
7063 
8322 
9578 


2117 
3391 
4661 
5927 
7189 
8443 
9703 


2245 
3518 
4787 
6053 
7315 
8574 
9829 

1080 
2327 
3571 

4812 
6049 

7282 
8512 
9739 


2372 
3645 
4914 
6180 
7441 
8699 
9954 


2500 

3772 
5041 
6306 
7567 
8825 


2627 
3899 
5167 
6432 
7693 
8951 


128 
127 
127 
126 

126 
126 

125 
125 
125 
124 

124 
124 
123 
123 


0079 
1330 
2576 
3820 

5060 
6296 
7529 
8758 
9984 


0204 
1454 
2701 
3944 

5183 
6419 
7652 
8881 


7 
8 
9 

350 
1 

2 
3 

4 


540329 
1579 

2825 

4068 
5307 
6543 
7775 
9003 


0455 
1704 
2950 

4192 
5431 
6666 
7898 
9126 


0580 
1829 
3074 

4316 
5555 
6} 89 
8021 
9249 


0705 
1953 
3199 

4440 
5678 
6913 
8144 
9371 


0830 
2078 
3323 

4564 
5802 
7036 
8267 
9494 


0955 

2203 
3447 

4688 
5925 
7159 
8389 
9616 


1205 
2452 
3696 

4936 
6172 
7405 
8635 
9861 


0106 
1328 
2547 
3762 
4973 
6182 

7387 
8589 
9787 


123 
122 
122 
121 
121 
121 

120 
120 
120 


5 
6 
7 
8 
9 

360 
1 

2 
3 


550228 
1450 
2668 
3883 
5094 

6303 
7507 
8709 
9907 


0351 
1572 
2790 
4004 
5215 

6423 
7627 
8829 


0473 
1694 
2911 
4126 
5336 

6544 

7748 
8948 


0595 
1816 
3033 
4247 
5457 

6664 
7868 
9068 

0265 
1459 
2650 
3837 
5021 
6202 
7379 

8554 
9725 


0717 
1938 
3155 
4368 
5578 

6785 

7988 
9188 


0840 
2060 
3276 
4- 59 
5699 

6905 
8108 
9308 


0962 
2181 
3398 
4610 
5820 

7026 
8228 
9428 


1034 
2303 
3519 
4731 
5940 

7146 
8349 
9548 


1206 

2425 
3640 
4852 
6061 

7267 
8469 
9667 


0026 
1221 
2412 
3600 
4784 
5966 
7144 

8319 
9491 


0146 
1340 
2531 
3718 
4903 
6084 
7262 

8436 
9608 


0385 
1578 
2769 
3955 
5139 
6320 
7497 

8671 
9842 


0504 
1698 

2887 
4074 
5257 
6437 
7614 

8788 
9959 


0624 
1817 
3006 
4192 
5376 
6555 
7732 

8905 


0743 
1936 
3125 
4311 
5494 
6673 
7849 

9023 


0863 
2055 
3244 
4429 
5612 
6791 
7967 

9140 


0982 
2174 
3362 
4548 
5730 
6909 
8084 

9257 


119 
119 
119 
119 
118 
118 
118 

117 


4 
5 
6 
7 
8 
9 

370 


561101 
2293 
3481 
4666 
5848 
7026 

8202 
9374 




0076 
1243 
2407 
3568 
4726 
5880 
7032 
8181 
9326 


0193 
1359 
2523 
3684 
4841 
5996 
7147 
8295 
9441 


0309 
1476 
2639 
3800 
4957 
6111 
7262 
8410 
9555 


0426 
1592 
2755 
3915 
5072 
6226 
7377 
8525 
9669 


117 
117 
116 
116 
116 
115 
115 
115 
114 


2 
3 
4 
5 
6 
7 
8 
9 


570543 
1709 
2872 
4031 
5188 
6341 
7492 
8639 


0660 

1825 
2988 
4147 
5303 
6457 
7607 
8754 


0776 

1942 
3104 
4263 
5419 
6572 
7722 
8868 


0893 
2058 
3220 
4379 
5534 
6687 
7836 
8983 


1010 
2174 
3336 
4494 
5650 
6802 
7951 
9097 


1126 
2291 
3452 
4610 
5765 
6917 
8066 
9212 



Proportional Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


128 


12.8 


25.6 


38.4 


51.2 


64.0 


76.8 


89.6 


102.4 


115.2 


127 


12.7 


25.4 


38.1 


50.8 


63.5 


76.2 


88.9 


101.6 


114.3 


126 


12.6 


25.2 


37.8 


50.4 


63.0 


75.6 


88.2 


100.8 


113.4 


125 


12.5 


25.0 


37.5 


50.0 


62.5 


75.0 


87.5 


100.0 


112.5 


124 


12.4 


24.8 


37.2 


49.6 


62.0 


74.4 


86.8 


99.2 


111.6 


123 


12.3 


24.6 


36.9 


49.2 


61.5 


73.8 


86.1 


98.4 


110.7 


122 


12.2 


24.4 


36.6 


48.8 


61.0 


73.2 


85.4 


97.6 


109.8 


121 


12.1 


24.2 


36.3 


48.4 


60.5 


72.6 


84.7 


96.8 


108.9 


120 


12.0 


24.0 


36.0 


48.0 


60.0 


72.0 


84.0 


96.0 


108.0 


119 


11.9 


23.8 


35.7 


47.6 


59.5 


71.4 


83.3 


95.2 


107.1 



LOGARITHMS OF NUMBERS. 



149 



tfo. 3S0 L. 579.] 
















[No. 


414 L 


617. 


N. 





1 


2 


3 


4 


5 6 


7 


8 


9 


Diff. 


380 

1 

2 
3 
4 
5 
6 
7 
8 
9 

390 
1 

2 
3 
4 
5 
6 
7 
8 

9 

400 
1 

2 
3 
4 
5 
6 
7 

8 
9 

410 

1 

2 
3 
4 


5/9784 


9698 






0241 
1381 
2518 
3652 
4783 
5912 
7037 
8160 
9279 














0012 
1153 
2291 
3426 
4557 
5636 
6812 
7935 
9056 


0126 
1267 
2404 
3539 
4670 
5799 
6925 
8047 
9167 


0355 
1495 
2631 
3765 
4896 
'6024 
7149 
8272 
9391 


0469 
1608 

2745 
3879 
5009 
6137 
7262 
8384 
9503 


0583 
1722 
2858 
3992 
5122 
6250 
7374 
8496 
9615 


0697 
1836 
2972 
4105 
5235 
6362 
7486 
8608 
9726 


0811 
1950 
3085 
4218 
5348 
6475 
7599 
8720 
9838 


114 

113 
112 


580925 
2063 
3199 
4331 
5461 
6587 
7711 
8832 
9950 


1039 
2177 
3312 
4444 
5574 
6700 
7823 
8944 


• 0061 

1176 
2288 
3397 
4503 
5606 
6707 
7805 
8900 
9992 


0173 

1287 
2399 
3508 
4614 
5717 
6817 
7914 
9009 


0284 

1399 
2510 
3618 
4724 
5827 
6927 
8024 
9119 


0396 

1510 
2621 
3729 
4834 
5937 
7037 
8134 
9226 


0507 

1621 

2732 
3840 
4945 
6047 
7146 
8243 
9337 


0619 

1732 
2843 
3950 
5055 
6157 
7256 
8353 
9446 


0730 

1843 
2954 
4061 
5165 
6267 
7366 
8462 
9556 

0646 
1734 

2819 
3902 
4982 
6059 
7133 
8205 
9274 


0842 

1955 
3064 
4171 
5276 
6377 
7476 
8572 
9665 

0755 
1843 

2928 
4010 
5089 
6166 
7241 
8312 
9381 

0447 
1511 
2572 

3630 
4686 
5740 
6790 
7839 


0953 

2066 
3175 
4282 
5386 
6487 
7586 
8681 
9774 




591065 
2177 
3286 
4393 
5496 
6597 
7695 
8791 
9883 


111 

110 
109 


0101 
1191 

2277 
3361 
4442 
5521 
6596 
7669 
8740 
9808 


0210 
1299 

2386 
3469 
4550 
5628 
6704 
7777 
8847 
9914 


0319 
1406 

2494 
3577 
4658 
5736 
6811 
7884 
8954 


0428 
1517 

2603 
3686 
4766 
5844 
6919 
7991 
9061 


0537 
1625 

2711 

3794 
4874 
5951 
7026 
8098 
9167 


0864 
1951 

3036 
4118 
5197 
6274 
7348 
8419 
9488 


600973 

2060 

3144 
4226 
5305 
6381 
7455 
8526 
9594 


1082 

2169 

3253 
4334 
5413 
6439 
7562 
8633 
9701 


108 
107 


0021 
1086 
2148 

3207 
4264 
5319 
6370 
7420 


0128 
1192 
2254 

3313 
4370 
5424 
6476 
7525 


0234 
1298 
2360 

3419 
4475 
5529 
6581 
7629 


0341 
1405 
2466 

3525 
4581 
5634 
6686 

7734 


0554 
1617 
2678 

3736 
4792 
5845 
6895 
7943 




610660 
1723 

2784 
3842 
4897 
5950 
7000 


0767 
1829 

2890 
3947 
5003 
6055 
7105 


0873 
1936 

2996 
4053 
5108 
6160 
7210 


0979 
2042 

3102 
4159 
5213 
6265 
7315 


106 
105 



Proportional Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


118 


1.1.8 


23.6 


35.4 


47.2 


5-9.0 


70.8 


82.6 


94.4 


106.2 


117 


11.7 


23.4 


35.1 


46.8 


58.5 


70.2 


81.9 


93.6 


105.3 


116 


11.6 


23.2 


34.8 


46.4 


58.0 


69.6 


81.2 


92.8 


104.4 


115 


11.5 


23.0 


34.5 


46.0 


57.5 


69.0 


80.5 


92.0 


103.5 


114 


11.4 


22.8 


34.2 


45.6 


57.0 


68.4 


79.8 


91.2 


102.6 


113 


11.3 


22.6 


33.9 


45.2 


56.5 


67.8 


79.1 


90.4 


101.7 


112 


11.2 


22.4 


33.6 


44.8 


56.0 


67.2 


78.4 


89.6 


100.8 


111 


11.1 


22.2 


33.3 


44.4 


55.5 


66.6 


77.7 


88.8 


99.9 


110 


11.0 


22.0 


33.0 


44.0 


55.0 


66.0 


77.0 


88.0 


99.0 


109 


10.9 


21.8 


32.7 


43.6 


54.5 


65.4 


76.3 


87.2 


98.1 


108 


10.8 


21.6 


32.4 


43,2 


54.0 


64.8 


75.6 


86.4 


97.2 


107 


10.7 


21.4 


32.1 


42.8 


53.5 


64.2 


74.9 


85.6 


96.3 


106 


10.6 


21.2 


31.8 


42.4 


53.0 


63.6 


74.2 


84.8 


95.4 


105 


10.5 


21.0 


31.5 


42.0 


52.5 


63.0 


73.5 


84.0 


94.5 


104 


10.4 


20.8 


31.2 


41.6 


52.0 


62.4 


72.8 


83.2 


93.6 



150 



LOGARITHMS OF NUMBERS. 



No. 415 L. 618.] 














[No. 


459 L 


.662 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


415 


618048 


8153 


8257 


8362 


8466 


8571 


8676 


8780 


8884 


8989 


105 


6 


9093 


9198 


9302 


9406 


9511 


9615 


9719 


9824 


9928 


0032 
1072 




7 


620136 


0240 


0344 


0448 


0552 


0656 


0760 


0864 


0968 


104 


8 


1176 


1280 


1384 


1488 


1592 


1695 


1799 


1903 


2007 


2110 




9 


2214 


2318 


2421 


2525 


2628 


2732 


2835 


2939 


3042 


3146 




420 


3249 


3353 


3456 


3559 


3663 


3766 


3869 


3973 


4076 


4179 




1 


4232 


4335 


4488 


4591 


4695 


4793 


4901 


5004 


5107 


5210 


103 


2 


5312 


5415 


5518 


5621 


5724 


5827 


5929 


6032 


6135 


6238 




3 


6340 


6443 


6546 


6648 


6751 


6853 


6956 


7058 


7161 


7263 




4 


7356 


7463 


7571 


7673 


7775 


7878 


7930 


8082 


8185 


8287 




5 


8389 


8491 


8593 


8695 


8797 


8900 


9002 


9104 


9206 


9308 


102 


6 


9410 


9512 


9613 


9715 


9317 


9919 


0021 
1038 


0123 
1139 


0224 
1241 


0326 
1342 




7 


630423 


0530 


0631 


0733 


0335 


0936 




8 


1444 


1545 


1647 


1748 


1849 


1951 


2052 


2153 


2255 


2356 




9 


2457 


2559 


2660 


2761 


2862 


2963 


3064 


3165 


3266 


3367 




430 


3463 


3569 


3670 


3771 


3872 


3973 


4074 


4175 


4276 


4376 


101 


1 


4477 


4578 


4679 


4779 


4880 


4981 


5081 


5132 


5283 


5383 




2 


5434 


5584 


5635 


5785 


5886 


5986 


6087 


6187 


6287 


6388 




3 


6433 


6588 


6638 


6789 


6389 


6939 


70S9 


7189 


7290 


7390 




4 


7490 


7590 


7690 


7790 


7890 


7990 


8090 


8190 


8290 


8389 


1(»U 


5 


8439 


8589 


8639 


8789 


8838 


8988 


9088 


9188 


9287 


9387 




6 


9486 


9586 


9636 


9785 


9885 


9984 


0084 
1077 


0183 
1177 


0283 
1276 


0382 
1375 




7 


640431 


0581 


0680 


0779 


0879 


0978 




8 


1474 


1573 


1672 


1771 


1871 


1970 


2069 


2168 


2267 


2366 




9 


2465 


2563 


2662 


2761 


2860 


2959 


3058 


3156 


3255 


3354 


99 


440 


3453 


3551 


3650 


3749 


3847 


3946 


4044 


4143 


4242 


4340 




1 


4439 


4537 


4636 


4734 


4832 


4931 


5029 


5127 


5226 


5324 




2 


5422 


5521 


5619 


5717 


5815 


5913 


6011 


6110 


6208 


6306 




3 


6404 


6502 


6600 


6698 


6796 


6894 


6992 


7089 


7187 


7285 


98 


4 


7333 


7481 


7579 


7676 


7774 


7872 


7969 


8067 


8165 


8262 




5 


8360 


8458 


8555 


8653 


8750 


8848 


8945 


9043 


9140 


9237 




6 


9335 
650303 


9432 


9530 


9627 


9724 


9821 


9919 


0016 
0987 


0113 
1084 


0210 
1181 




7 


0405 


0502 


0599 


0696 


0793 


0890 




8 


1278 


1375 


1472 


1569 


1666 


1762 


1859 


1956 


2053 


2150 


97 


9 


2246 


2343 


2440 


2536 


2633 


2730 


2826 


2923 


3019 


3116 




450 


3213 


3309 


3405 


350?, 


3598 


3695 


3791 


3888 


3984 


4080 




1 


4177 


4273 


4369 


4465 


4562 


4658 


4754 


4850 


4946 


5042 




2 


5138 


5235 


5331 


5427 


5523 


5619 


5715 


5310 


5906 


6002 


96 


3 


6093 


6194 


6290 


6386 


6482 


6577 


6673 


6769 


6864 


6960 




4 


7056 


7152 


7247 


7343 


7438 


7534 


7629 


7725 


7820 


7916 




5 


8011 


8107 


8202 


8298 


8393 


8488 


8584 


8679 


8774 


8870 




6 


8965 
9916 


9060 


9155 
0106 
1055 


9250 


9346 


9441 


9536 


9631 


9726 
0676 
1623 


9821 
0771 
1718 




7 


0011 
0960 


0201 
1150 


0296 
1245 


0391 
1339 


0486 
1434 


0581 
1529 


95 


8 


660365 




9 


1813 


1907 


2002 


2096 


2191 


2286 


2380 


2475 


2569 


2663 





Proportional, Parts. 



1 


2 


3 


4 


5 


6 


7 


8 


10.5 


21.0 


31.5 


42.0 


52.5 


63.0 


73.5 


84.0 


10.4 


20.8 


31.2 


41.6 


52.0 


62.4 


72.8 


83.2 


10.3 


20.6 


30.9 


41.2 


51.5 


61.8 


72.1 


82.4 


10.2 


20.4 


30.6 


40.8 


51.0 


61.2 


71.4 


81.6 


10.1 


20.2 


30.3 


40.4 


50.5 


60.6 


70.7 


80.8 


10.0 


20.0 


30.0 


40.0 


50.0 


60.0 


70.0 


80.0 


9.9 


19.8 


29.7 


39.6 


49.5 


59.4 


69.3 


79.2 



LOGARITHMS OP NUMBERS. 



151 



No. 460 L. 632.] 














[No 


499 L. 698 


N. 





1 


2 


3 


4 

Tl35 
4078 
5018 
5956 
6892 
7826 
8759 
9689 


5 


6 

3324 
4266 
5206 
6143 
7079 
8013 
8945 
9875 


7 


8 


9 


Diff. 


460 
1 

2 
3 
4 
5 
6 
7 


662758 
3701 
4642 
5581 
6518 
7453 
8336 
9317 


2852 
3795 
4736 
5675 
6612 
7546 
8479 
9410 


2947 
3889 
4830 
5769 
6705 
7640 
8572 
9503 


3041 
3983 
4924 
5862 
6799 
7733 
8665 
9596 


3230 
4172 
5112 
6050 
6986 
7920 
8852 
9782 


3418 
4360 
5299 
6237 
7173 
8106 
9038 
9967 


3512 
4454 
5393 
6331 
7266 
8199 
9131 


3607 
4548 
5487 
6424 
7360 
8293 
9224 


94 


0060 
0988 
1913 

2836 
3758 
4677 
5595 
6511 
7424 
8336 
9246 


0153 
1080 
2005 

2929 
3850 
4769 
5687 
6602 
7516 
8427 
9337 

0245 
1151 

2055 
2957 
3857 
4756 
5652 
6547 
7440 
8331 
9220 


93 

92 
91 


8 
9 

470 

1 

2 
3 
4 
5 
6 
7 
8 


670246 
1173 

2098 
3021 
3942 
4861 
5778 
6694 
7607 
8518 
9423 


0339 
1265 

2190 
3113 

4034 
4953 
5870 
6785 
7698 
8609 
9519 


0431 
1358 

2283 
3205 
4126 
5045 
5962 
6876 
7789 
8700 
9610 


0524 
1451 

2375 
3297 
4218 
5137 
6053 
6968 
7881 
8791 
9700 


C617 
1543 

2467 
3390 
4310 
5228 
6145 
7059 
7972 
8882 
9791 


0710 
1636 

2560 
3482 
4402 
5320 
6236 
7151 
8063 
8973 
9882 


0802 
1728 

2652 
3574 
4494 
5412 
6328 
7242 
8154 
9064 
9973 


0895 
1821 

2744 
3666 
4586 
5503 
6419 
7333 
8245 
9155 

0063 
0970 

1874 
2777 
3677 
4576 
5473 
6368 
7261 
8153 
9042 
9930 


0154 
1060 

1964 
2867 
3767 
4666 
5563 
6458 
7351 
8242 
9131 




9 

480 
1 

2 
3 
4 
5 
6 
7 
8 
9 


680336 

1241 
2145 
3047 
3947 
4845 
5742 
6636 
7529 
8420 
9309 


0426 

1332 
2235 
3137 
4037 
4935 
5831 
6726 
7618 
8509 
9398 


0517 

1422 
2326 
3227 
4127 
5025 
5921 
6815 
7707 
8598 
9486 


0607 

1513 

2416 
3317 
4217 
5114 
6010 
6904 
7796 
8687 
9575 


0698 

1603 
2506 
3407 
4307 
5204 
6100 
6994 
7886 
8776 
9664 


0789 

1693 
2596 
3497 
4396 
5294 
6189 
7083 
7975 
8865 
9753 


0879 

1784 
2686 
3587 
4486 
5383 
6279 
7172 
8064 
8953 
9841 


90 
89 


0019 

0905 
1789 
2671 
3551 
4430 
5307 
6182 
7055 
7926 
8796 


0107 

0993 
1877 
2759 
3639 
4517 
5394 
6269 
7142 
8014 
8883 




490 
1 

2 
3 
4 
5 
6 
7 
8 
9 


690196 
1081 
1965 
2847 
3727 
4605 
5482 
6356 
7229 
8100 


0285 
1170 
2053 
2935 
3815 
4693 
5569 
6444 
7317 
8188 


0373 
1258 
2142 
3023 
3903 
4781 
5657 
6531 
7404 
8275 


0462 
1347 
2230 
3111 
3991 
4868 
5744 
6618 
7491 
8362 


0550 
1435 
2318 
3199 
4078 
4956 
5832 
6706 
7578 
8449 


0639 
1524 
2406 
3287 
4166 
5044 
5919 
6793 
7665 
8535 


0728 
1612 
2494 
3375 
4254 
5131 
6007 
6880 
7752 
8622 


0816 
1700 
2583 
3463 
4342 
5219 
6094 
6968 
7839 
8709 


88 
87 



Proportional Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


98 


9.8 


19.6 


29.4 


39.2 


49.0 


58.8 


68.6 


78.4 


88.2 


97 


9.7 


19.4 


29.1 


38.8 


48.5 


58.2 


67.9 


77.6 


87.3 


96 


9.6 


19.2 


28.8 


38.4 


48.0 


57.6 


67.2 


76.8 


86.4 


95 


9.5 


19.0 


28.5 


38.0 


47.5 


57.0 


66.5 


76.0 


85.5 


94 


9.4 


18.8 


28.2 


37.6 


47.0 


56.4 


65.8 


75.2 


84.6 


93 


9.3 


18.6 


27.9 


37.2 


46.5 


55.8 


65.1 


74.4 


83.7 


92 


9.2 


18.4 


27.6 


36.8 


46.0 


55.2 


64.4 


73.6 


82.8 


91 


9.1 


18.2 


27.3 


36.4 


45.5 


54.6 


63.7 


72.8 


81.9 


90 


9.0 


18.0 


27.0 


36.0 


45.0 


54.0 


63.0 


72.0 


81.0 


89 


8.9 


17.8 


26.7 


35.6 


44.5 


53.4 


62.3 


71.2 


80.1 


88 


8.8 


17.6 


26.4 


35.2 


44.0 


52.8 


61.6 


70.4 


79.2 


87 


8.7 


17.4 


26.1 


34.8 


43.5 


52.2 


60.9 


69.6 


78.3 


86 


8.6 


17.2 


25.8 


34.4 


43.0 


51.6 


60.2 


68.8 


77.4 



152 



LOGARITHMS OF NUMBERS. 



No. 500 L. 698.1 



[No. 544 L. 736. 






1 


2 


3 


4 


5 


6 


7 


8 


9 


698970 


9057 


9144 


9231 


9317 


9404 


9491 


9578 


9664 


9751 


9838 


9924 


















0011 
0877 


0098 
0963 


0184 
1050 


0271 
1136 


0358 
1222 


0444 
1309 


0531 
1395 


0617 
1482 


700704 


0790 


1568 


1654 


1741 


1827 


1913 


1999 


2086 


2172 


2258 


2344 


2431 


2517 


2603 


2689 


2775 


2861 


2947 


3033 


3119 


3205 


3291 


3377 


3463 


3549 


3635 


3721 


3807 


3893 


3979 


4065 


4151 


4236 


4322 


4408 


4494 


4579 


4665 


4751 


4837 


4922 


5008 


5094 


5179 


5265 


5350 


5436 


5522 


5607 


5693 


5778 


5864 


5949 


6035 


6120 


6206 


6291 


6376 


6462 


6547 


6632 


• 6718 


6803 


6888 


6974 


7059 


7144 


7229 


7315 


7400 


7485 


7570 


7655 


7740 


7826 


7911 


7996 


8081 


8166 


8251 


8336 


8421 


8506 


8591 


8676 


8761 


8846 


8931 


9015 


9100 


9185 


9270 


9355 


9440 


9524 


9609 


9694 


9779 


9863 


9948 




0033 
0879 


710117 


0202 


0287 


0371 


0456 


0540 


0625 


•0710 


0794 


0963 


1048 


1132 


1217 


1301 


1385 


1470 


1554 


1639 


1723 


1807 


1892 


1976 


2060 


2144 


2229 


2313 


2397 


2481 


2566 


2650 


2734 


2818 


2902 


2986 


3070 


3154 


3238 


3323 


3407 


3491 


3575 


3659 


3742 


3826 


3910 


3994 


4078 


4162 


4246 


4330 


4414 


4497 


4581 


4665 


4749 


4833 


4916 


5000 


5084 


5167 


5251 


5335 


5418 


5502 


5586 


5669 


5753 


5836 


5920 


6003 


6087 


6170 


6254 


6337 


6421 


6504 


6588 


6671 


6754 


6838 


6921 


7004 


7088 


7171 


7254 


7338 


7421 


7504 


7587 


7671 


7754 


7837 


7920 


8003 


8086 


8169 


8253 


8336 


8419 


8502 


8585 


8668 


8751 


8834 


8917 


9000 


9083 


9165 


9248 


9331 


9414 


9497 


9580 


9663 


9745 


9828 


9911 


9994 






0077 
0903 


720159 


0242 


0325 


0407 


0490 


0573 


0655 


0738 


0821 


0986 


1068 


1151 


1233 


1316 


1398 


1481 


1563 


1646 


1728 


1811 


1893 


1975 


2058 


2140 


2222 


2305 


2387 


2469 


2552 


2634 


2716 


2798 


2881 


2963 


3045 


3127 


3209 


3291 


3374 


3456 


3538 


3620 


3702 


3784 


3866 


3948 


4030 


4112 


4194 


4276 


4358 


4440 


4522 


4604 


4685 


4767 


4849 


4931 


5013 


5095 


5176 


5258 


5340 


5422 


5503 


5585 


5667 


5748 


5830 


5912 


5993 


6075 


6156 


6238 


6320 


6401 


6483 


6564 


6646 


6727 


6809 


6890 


6972 


7053 


7134 


7216 


7297 


7379 


7460 


7541 


7623 


7704 


7785 


7866 


7948 


8029 


8110 


8191 


8273 


8354 


8435 


8516 


8597 


8678 


8759 


8841 


8922 


9003 


9084 


9165 


9246 


9327 


9408 


9489 


9570 


9651 


9732 


9813 


9893 


9974 






















0055 
0863 


0136 
0944 


0217 
1024 


0298 
1105 


0378 
1186 


0459 
1266 


0540 
1347 


0621 
1428 


0702 
1508 


730782 


1589 


1669 


1750 


1830 


1911 


1991 


2072 


2152 


2233 


2313 


2394 


2474 


2555 


2635 


2715 


2796 


2876 


2956 


3037 


3117 


3197 


3278 


3358 


3438 


3518 


3598 


3679 


3759 


3839 


3919 


3999 


4079 


4160 


4240 


4320 


4400 


4480 


4560 


4640 


4720 


4800 


4880 


4960 


5040 


5120 


5200 


5279 


5359 


5439 


5519 


5599 


5679 


5759 


5838 


5918 


5998 


6078 


6157 


6237 


6317 



Proportional, Parts. 


Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


87 
86 

85 
84 


8.7 
8.6 
8.5 
8.4 


17.4 
17.2 
17.0 
16.8 


26.1 
25.8 
25.5 
25.2 


34.8 
34.4 
34.0 
33.6 


43.5 
43.0 
42.5 
42.0 


52.2 
51.6 
51.0 
50.4 


60.9 
60.2 
59.5 
58.8 


69.6 
68.8 
68.0 
67.2 


78.3 
77.4 
76.5 
75.6 



LOGARITHMS OF NUMBERS. 



153 



No. 545 L. 736.] 














[No 


. 584 L. 767. 


N. 





1 

~6476 
7272 
8067 
8860 
9651 


2 

~6556 
7352 
8146 
8939 
9731 


3 

~6635 
7431 
8225 
9018 
9810 


4 


5 


6 


7 


8 


9 


Diff. 


545 
6 
7 
8 
9 


736397 
7193 
7987 
8781 
9572 


6715 
7511 
8305 
9097 
9889 


6795 
7590 
8384 
9177 
9968 


6874 
7670 
8463 
9256 


6954 
7749 
8543 
9335 


7034 
7829 
8622 
9414 


7113 
7908 
8701 
9493 

0284 

1073 
1860 
2647 
3431 
4215 
4997 
5777 
6556 
7334 
8110 

8885 
9659 




0047 

0836 
1624 
2411 
3196 
3980 
4762 
5543 
6323 
7101 
7878 

8653 
9427 


0126 

0915 
1703 
2489 
3275 
4058 
4840 
5621 
6401 
7179 
7955 

8731 
9504 


0205 

0994 
1782 
2568 
3353 
4136 
4919 
5699 
6479 
7256 
8033 

8808 
9582 


79 
78 


550 
1 

2 
3 
4 
5 
6 
7 
8 
9 

560 

2 


740363 
1152 
1939 
2725 
3510 
4293 
5075 
5855 
6634 
7412 

8188 
8963 
9736 


0442 
1230 
2018 
2804 
3588 
4371 
5153 
5933 
6712 
7489 

8266 
9040 
9814 


0521 
1309 
2096 
2882 
3667 
4449 
5231 
6011 
6790 
7567 

8343 
9118 
9891 


0600 

1388 
2175 
2961 
3745 
4528 
5309 
6089 
6868 
7645 

8421 
9i95 
9968 


0678 
1467 
2254 
3039 
3823 
4606 
5387 
6167 
6945 
7722 

8498 
9272 


0757 
1546 
2332 
3118 
3902 
4684 
5465 
6245 
7023 
7800 

8576 
9350 


0045 
0817 
1587 
2356 
3123 
3889 
4654 
5417 

6180 
6940 
7700 
8458 
9214 
9970 


0123 
0894 
1664 
2433 
3200 
3966 
4730 
5494 

6256 
7016 
7775 
8533 
9290 


0200 
0971 
1741 
2509 
3277 
4042 
4807 
5570 

6332 
7092 
7851 
8609 
9366 


0277 
1048 
1818 
2586 
3353 
4119 
4883 
5646 

6408 
7168 
7927 
8685 
9441 


0354 
1125 
1895 
2663 
3430 
4195 
4960 
5722 

6484 
7244 
8003 
8761 
9517 


0431 
1202 
1972 
2740 
3506 
4272 
5036 
5799 

6560 
7320 
8079 
8836 
9592 




3 
4 
5 
6 
7 
8 
9 

570 
1 

2 
3 
4 
5 


750508 
1279 
2048 
2816 
3583 
4348 
5112 

5875 
6636 
7396 
8155 
8912 
9668 


0586 
1356 
2125 
2893 
3660 
4425 
5189 

5951 
6712 
7472 
8230 
8988 
9743 


0663 
1433 
2202 
2970 
3736 
4501 
5265 

6027 
6788 
7548 
8306 
9063 
9819 


0740 
1510 
2279 
3047 
3813 
4578 
5341 

6103 
6864 
7624 
8382 
9139 
9894 


77 
76 


0045 
0799 
1552 
2303 
3053 

3802 
4550 
5296 
6041 
6785 


0121 
0875 
1627 
2378 
3128 

3877 
4624 
5370 
6115 
6859 


0196 
0950 
1702 
2453 
3203 

3952 
4699 
5445 
6190 
6933 


0272 
1025 
1778 
2529 
3278 

4027 
4774 
5520 
6264 
7007 


0347 
1101 
1853 
2604 
3353 

4101 
4848 
5594 
6338 
7082 




6 
7 

8 
9 

580 
1 

2 
3 
4 


760422 
1176 
1928 
2679 

3428 
4176 
4923 
5669 
6413 


0498 
1251 
2003 
2754 

3503 
4251 
4998 
5743 
6487 


0573 
1326 
2078 
2829 

3578 
4326 
5072 
5818 
6562 


0649 
1402 
2153 
2904 

3653 
4400 
5147 
5892 
6636 


0724 
1477 
2228 
2978 

3727 
4475 
5221 
5966 
6710 


75 



Proportional. Parts. 



Diff. 


1 


3 


3 


4 


5 


6 


7 


8 


9 


83 


8.3 


16.6 


24.9 


33.2 


41.5 


49.8 


58.1 


66.4 


74.7 


82 


8.2 


16.4 


24.6 


32.8 


41.0 


49.2 


57.4 


65.6 


73.8 


81 


8.1 


16.2 


24.3 


32.4 


40.5 


48.6 


56.7 


64.8 


72.9 


80 


8.0 


16.0 


24.0 


32.0 


40.0 


48.0 


56.0 


64.0 


72.0 


79 


7.9 


15.8 


23.7 


31.6 


39.5 


47.4 


55.3 


63.2 


71.1 


78 


7.8 


15.6 


23.4 


31.2 


39.0 


46.8 


54.6 


62.4 


70.2 


77 


7.7 


15.4 


23.1 


30.8 


38.5 


46.2 


53.9 


61.6 


69.3 


76 


7.6 


15.2 


22.8 


30.4 


38.0 


45.6 


53.2 


60.8 


68.4 


75 


7.5 


15.0 


22.5 


30.0 


37.5 


45.0 


52.5 


60.0 


67.5 


74 


7.4 


14.8 


22.2 


29.6 


37.0 


44.4 


51.8 


59.2 


66.6 



154 



LOGARITHMS OF NUMBERS. 



No. 585 L.767J 














[No 


629 1 


.799. 


N. 





1 


2 


3 


4 


5 


6 

7601 
8342 
9082 
9820 


7 


8 


9 


Difif. 


585 
6 
7 
8 


767156 
7898 
8638 
9377 


7230 
7972 
8712 
9451 


7304 
8046 
8786 
9525 


7379 
8120 
8860 
9599 


7453 
8194 
8934 
9673 


7527 
8268 
9008 
9746 


7675 
8416 
9156 
9894 


7749 
8490 
9230 
9968 


7823 
8564 
9303 


74 


0042 
0778 

1514 
2248 
2981 
3713 
4444 
5173 
5902 
6629 
7354 
8079 

8802 
9524 




9 

590 
1 

2 
3 
4 
5 
6 
7 
8 
9 

600 

1 
2 


770115 

0852 
1587 
2322 
3055 
3786 
4517 
5246 
5974 
6701 
7427 

8151 
8874 
9596 


0189 

0926 
1661 
2395 
3128 
3860 
4590 
5319 
6047 
6774 
7499 

8224 
8947 
9669 


0263 

0999 
1734 
2468 
3201 
3933 
4663 
5392 
6120 
6846 
7572 

8296 
9019 
9741 


0336 

1073 
1808 
2542 
3274 
4006 
4736 
5465 
6193 
6919 
7644 

8368 
9091 
9813 


0410 

1146 
1881 
2615 
3348 
4079 
4809 
5538 
6265 
6992 
7717 

8441 
9163 
9885 


0484 

1220 
1955 
2688 
3421 
4152 
4882 
5610 
6338 
7064 
7789 

8513 
9236 
9957 


0557 

1293 
2028 
2762 
3494 
4225 
4955 
5683 
6411 
7137 
7862 

8585 
9308 


0631 

1367 
2102 
2835 
3567 
4298 
5028 
5756 
6483 
7209 
7934 

8658 
9380 


0705 

1440 
2175 
2908 
3640 
4371 
5100 
5829 
6556 
7282 
8006 

8730 
9452 


73 


0029 
0749 
1468 
2186 
2902 
3618 
.4332 
5045 

5757 
6467 
7177 
7885 
8593 
9299 


0101 
0821 
1540 
2258 
2974 
3689 
4403 
5116 

5828 
6538 
7248 
7956 
8663 
9369 


0173 
0893 
1612 
2329 
3046 
3761 
4475 
5187 

5899 
6609 
7319 
8027 
8734 
9440 


0245 
0965 
1684 
2401 
3117 
3832 
4546 
5259 

5970 
6680 
7390 
8098 
8804 
9510 




3 
4 
5 
6 
7 
8 
9 

610 

1 

2 
3 
4 
5 
6 


780317 
1037 
1755 
2473 
3189 
3904 
4617 

5330 
6041 
6751 
7460 
8168 
8875 
9581 


0389 
1109 
1827 
2544 
3260 
3975 
4689 

5401 
6112 
6822 
7531 
8239 
8946 
9651 


0461 
1181 
1899 
2616 
3332 
4046 
4760 

5472 
6183 
6893 
7602 
8310 
9016 
9722 


0533 
1253 
1971 
2683 
3403 
4118 
4831 

5543 
6254 
6964 
7673 
8381 
9087 
9792 


0605 

1324 
2042 
2759 
3475 
4189 
4902 

5615 
6325 
7035 
7744 
8451 
9157 
9863 


0677 
1396 
2114 
2831 
3546 
4261 
4974 

5686 
6396 
7106 
7815 
8522 
9228 
9933 


72 
71 


0004 
0707 
1410 
2111 

2812 
3511 
4209 
4906 
5602 
6297 
6990 
7683 
8374 
9065 


0074 
0778 
1480 
2181 

2882 
3581 
4279 
4976 
5672 
6366 
7060 
7752 
8443 
9134 


0144 
0848 
1550 
2252 

2952 
3651 
4349 
5045 
5741 
6436 
7129 
7821 
8513 
9203 


0215 
0918 
1620 
2322 

3022 
3721 
4418 
5115 
5811 
6505 
7198 
7890 
8582 
9272 




7 

8 
9 

620 
1 

2 
3 
4 
5 
6 
7 
8 
9 


790285 
0988 
1691 

2392 
3092 
3790 
4488 
5185 
5880 
6574 
7268 
7960 
8651 


0356 
1059 
1761 

2462 
3162 
3860 
4558 
5254 
5949 
6644 
7337 
8029 
8720 


0426 
1129 
1831 

2532 
3231 
3930 
4627 
5324 
6019 
6713 
7406 
8098 
8789 


0496 
1199 
1901 

2602 
3301 
4000 
4697 
5393 
6088 
6782 
7475 
8167 
8858 


0567 
1269 
1971 

2672 
3371 
4070 
4767 
5463 
6158 
6852 
7545 
8236 
8927 


0637 
1340 
2041 

2742 
3441 
4139 
4836 
5532 
6227 
6921 
7614 
8305 
8996 


70 
69 



Proportional Parts. 



Diff. 


1 


3 


3 


4 


5 


6 


7 


8 


9 


75 


7.5 


15.0 


22.5 


30.0 


37.5 


45.0 


52.5 


60.0 


67.5 


74 


7.4 


14.8 


22.2 


29.6 


37.0 


44.4 


51.8 


59.2 


66.6 


73 


7.3 


14.6 


21.9 


29.2 


36.5 


43.8 


51.1 


58.4 


65.7 


72 


7.2 


14.4 


21.6 


28.8 


36.0 


43.2 


50.4 


57.6 


64.8 


71 


7.1 


14.2 


21.3 


28.4 


35.5 


42.6 


49.7 


56.8 


63.9 


70 


7.0 


14.0 


21.0 


28.0 


35.0 


42.0 


49.0 


56.0 


63.0 


69 


6.9 


13.8 


20.7 


27.6 


34.5 


41.4 


48.3 


55.2 


62.1 



LOGARITHMS OF NUMBERS. 



155 



No. 630 L. 799.] 














[No 


. 674 L. 829. 


N. 





1 


3 


3 


4 


5 


6 


7 


8 


9 


Diff. 


630 


799341 


9409 


9478 


9547 


9616 


9685 


9754 


9823 


9892 


9961 




1 


800029 


0098 


0167 


0236 


0305 


0373 


0442 


0511 


0580 


0648 




2 


0717 


0786 


0854 


0923 


0992 


1061 


1129 


1198 


1266 


1335 




3 


1404 


1472 


1541 


1609 


1678 


1747 


1815 


1884 


1952 


2021 




4 


2089 


2158 


2226 


2295 


2363 


2432 


2500 


2568 


2637 


2705 




5 


2774 


2842 


2910 


2979 


3047 


3116 


31S4 


3252 


3321 


3389 




6 


3457 


3525 


3594 


3662 


3730 


3798 


3867 


3935 


4003 


4071 




7 


4139 


4208 


4276 


4344 


4412 


4480 


4548 


4616 


4685 


4753 




8 


4821 


4889 


4957 


5025 


5093 


5161 


5229 


5297 


5365 


5433 


68 


9 


5501 


5569 


5637 


5705 


5773 


5841 


5908 


5976 


6044 


6112 




640 


806180 


6248 


6316 


6384 


6451 


6519 


6587 


6655 


6723 


6790 




1 


6858 


6926 


6994 


7061 


7129 


7197 


7264 


7332 


7400 


7467 




2 


7535 


7603 


7670 


7738 


7806 


7873 


7941 


8008 


8076 


8143 




3 


8211 


8279 


8346 


8414 


8481 


8549 


8616 


8684 


8751 


8818 




4 


8886 


8953 


9021 


9088 


9156 


9223 


9290 


9358 


9425 


9492 




5 


9560 


9627 


9694 


9762 


9829 


9896 


9964 




















0031 
0703 


0098 
0770 


0165 

0837 




6 


810233 


0300 


0367 


0434 


0501 


0569 


0636 




7 


0904 


0971 


1039 


1106 


1173 


1240 


1307 


1374 


1441 


1508 


67 


8 


1575 


1642 


1709 


1776 


1843 


1910 


1977 


2044 


2111 


2178 




9 


2245 


2312 


2379 


2445 


2512 


2579 


2646 


2713 


2780 


2847 




650 


2913 


2980 


3047 


3114 


3181 


3247 


3314 


3381 


3448 


3514 




1 


3581 


3648 


3714 


3781 


3848 


3914 


3981 


4048 


4114 


4181 




2 


4248 


4314 


4381 


4447 


4514 


4581 


4647 


4714 


4780 


4847 




3 


4913 


4980 


5046 


5113 


5179 


5246 


5312 


5378 


5445 


5511 




4 


5578 


5644 


5711 


5777 


5843 


5910 


5976 


6042 


6109 


6175 




5 


6241 


6308 


6374 


6440 


6506 


6573 


6639 


6705 


6771 


6838 




6 


6904 


6970 


7036 


7102 


7169 


7235 


7301 


7367 


7433 


7499 




7 


7565 


7631 


7698 


7764 


7830 


7896 


7962 


8028 


8094 


8160 




8 


8226 


8292 


8358 


8424 


8490 


8556 


8622 


8688 


8754 


8820 


66 


9 


8885 


8951 


9017 


9083 


9149 


9215 


9281 


9346 


9412 


9478 




660 


9544 


9610 


9676 


9741 


9807 


9873 


9939 










0004 


0070 


0136 




1 


820201 


0267 


0333 


0399 


0464 


0530 


0595 


0661 


0727 


0792 




2 


0858 


0924 


0989 


1055 


1120 


1186 


1251 


1317 


1382 


1448 




3 


1514 


1579 


1645 


1710 


1775 


1841 


1906 


1972 


2037 


2103 




4 


2168 


2233 


2299 


2364 


2430 


2495 


2560 


2626 


2691 


2756 




5 


2822 


2887 


2952 


3018 


3083 


3148 


3213 


3279 


3344 


3409 




6 


3474 


3539 


3605 


3670 


3735 


3800 


3865 


3930 


3996 


4061 




7 


4126 


4191 


4256 


4321 


4386 


4451 


4516 


4581 


4646 


4711 




8 


4776 


4841 


4906 


4971 


5036 


5101 


5166 


5231 


5296 


5361 


65 


9 


5426 


5491 


5556 


5621 


5686 


5751 


5815 


5880 


5945 


6010 




670 


6075 


6140 


6204 


6269 


6334 


6399 


6464 


6528 


6593 


6658 




1 


6723 


6787 


6852 


6917 


6981 


7046 


7111 


7175 


7240 


7305 




2 


7369 


7434 


7499 


7563 


7628 


7692 


7757 


7821 


7886 


7951 




3 


8015 


8080 


8144 


8209 


8273 


8338 


8402 


8467 


8531 


8595 




4 


8660 


8724 


8789 


8853 


8918 


8982 


9046 


9111 


9175 9239 



Proportional, Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


68 


6.8 


13.6 


20.4 


27.2 


34.0 


40.8 


47.6 


54.4 


61.2 


67 


6.7 


13.4 


20.1 


26.8 


33.5 


40.2 


46.9 


53.6 


60.3 


66 


6.6 


13.2 


19.8 


26.4 


33.0 


39.6 


46.2 


52.8 


59.4 


65 


6.5 


13.0 


19.5 


26.0 


32.5 


39.0 


45.5 


52.0 


58.5 


64 


6.4 


12.8 


19.2 


25.6 


32.0 


38.4 


44.8 


51.2 


57.6 



156 



LOGARITHMS OF NUMBERS. 



No. 675 L. 829.] 














[No 


. 719 L. 857. 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


675 


829304 
9947 


9368 


9432 


9497 


9561 


9625 


9690 


9754 


9818 


9882 




6 


0011 


0075 


0139 


0204 


0268 


0332 


0396 


0460 


0525 




7 


830589 


0653 


0717 


0781 


0845 


0909 


0973 


1037 


1102 


1166 




8 


1230 


1294 


1358 


1422 


1486 


1550 


1614 


1678 


1742 


1806 


64 


9 


1870 


1934 


1998 


2062 


2126 


2189 


2253 


2317 


2381 


2445 




680 


2509 


2573 


2637 


2700 


2764 


2828 


2892 


2956 


•3020 


3083 




1 


3147 


3211 


3275 


3338 


3402 


3466 


3530 


3593 


3657 


3721 




2 


3784 


3848 


3912 


3975 


4039 


4103 


4166 


4230 


4294 


4357 




3 


4421 


4484 


4548 


4611 


4675 


4739 


4802 


4866 


4929 


4993 




4 


5056 


5120 


5183 


5247 


5310 


5373 


5437 


5500 


5564 


5627 




5 


5691 


5754 


5817 


5881 


5944 


6007 


6071 


6134 


6197 


6261 




6 


6324 


6387 


6451 


6514 


6577 


6641 


6704 


6767 


6830 


6894 




7 


6957 


7020 


7083 


7146 


7210 


7273 


7336 


7399 


7462 


7525 




8 


7588 


7652 


7715 


7778 


7841 


7904 


7967 


8030 


8093 


8156 


63 


9 


8219 


8282 


8345 


8408 


8471 


8534 


8597 


8660 


8723 


8786 




690 


8849 


8912 


8975 


9038 


9101 


9164 


9227 


9289 


9352 


9415 






9478 


9541 


9604 


9657 


9729 


9792 


9855 


9918 


9981 






' 










0043 
0671 




2 


840106 


0169 


0232 


0294 


0357 


0420 


0482 


0545 


0608 




3 


0733 


0796 


0859 


0921 


0934 


1046 


1109 


1172 


1234 


1297 




4 


1359 


1422 


1485 


1547 


1610 


1672 


1735 


1797 


1860 


1922 




5 


1985 


2047 


2110 


2172 


2235 


2297 


2360 


2422 


2484 


2547 




6 


2609 


2672 


2734 


2796 


2859 


2921 


2983 


3046 


3108 


3170 




7 


3233 


3295 


3357 


3420 


3432 


3544 


3606 


3669 


3731 


3793 




8 


3855 


3918 


3980 


4042 


4104 


4166 


4229 


4291 


4353 


4415 




9 


4477 


4539 


4601 


4664 


4726 


4788 


4850 


4912 


4974 


5036 




700 


5098 


5160 


5222 


5284 


5346 


5408 


5470 


5532 


5594 


5656 


62 


1 


5718 


5780 


5842 


5904 


5966 


6028 


6090 


6151 


6213 


6275 




2 


6337 


6399 


6461 


6523 


6585 


6646 


6708 


6770 


6832 


6894 




3 


6955 


7017 


7079 


7141 


7202 


7264 


7326 


7388 


7449 


7511 




4 


7573 


7634 


7696 


7758 


7819 


7881 


7943 


8004 


8066 


8128 




5 


8189 


8251 


8312 


8374 


8435 


8497 


8559 


8620 


8682 


8743 




6 


8805 


8S66 


8928 


8989 


905! 


9112 


9174 


9235 


9297 


9358 




7 


9419 


9431 


9542 


9604 


9665 


9726 


9788 


9849 


9911 


9972 




6 


850033 


0095 


0156 


0217 


0279 


0340 


0401 


0462 


0524 


0585 




9 


0646 


0707 


0769 


0830 


0891 


0952 


1014 


1075 


1136 


1197 




710 


1258 


1320 


1381 


1442 


1503 


1564 


1625 


1686 


1747 


1809 




1 


1870 


1931 


1992 


2053 


2114 


2175 


2236 


2297 


2358 


2419 


61 


2 


2480 


2541 


2602 


2663 


2724 


2785 


2846 


2907 


2963 


3029 




3 


3090 


3150 


3211 


3272 


3333 


3394 


3455 


3516 


3577 


3637 




4 


3698 


3759 


3820 


3881 


3941 


4002 


4063 


4124 


4185 


4245 




5 


4306 


4367 


4428 


4488 


4549 


4610 


4670 


473! 


4792 


4852 




6 


4913 


4974 


5034 


5095 


5156 


5216 


5277 


5337 


5398 


5459 




7 


5519 


5580 


5640 


570! 


5761 


5822 


5882 


5943 


6003 


6064 




8 


6124 


6185 


6245 


6306 


6366 


6427 


6487 


6548 


6608 


6668 




9 


6729 


6789 


6850 


6910 


6970 


7031 


7091 


7152 


7212 


7272 



Proportional Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


65 


6.5 


13.0 


19.5 


26.0 


32.5 


39.0 


45.5 


52.0 


58.5 


64 


6.4 


12.8 


19.2 


25.6 


32.0 


38.4 


44.8 


51.2 


57.6 


63 


6.3 


12.6 


18.9 


25.2 


31.5 


37.8 


44.1 


50.4 


56.7 


67 


6.2 


12.4 


18.6 


24.8 


31.0 


37.2 


43.4 


49.6 


55.8 


61 


6.1 


12.2 


18.3 


24.4 


30.5 


36.6 


42.7 


48.8 


54.9 


60 


6.0 


12.0 


18.0 


24.0 


30.0 


36.0 


42.0 


48.0 


54.0 



LOGARITHMS OF NUMBERS. 



157 



No. 720 L. 857 


] 














[No 


. 764 L. 883. 


N. 





1 


3 


3 


4 


5 


6 


7 


8 


9 


Diff. 


720 
1 

2 
3 
4 


857332 
7935 
8537 
9138 
9739 


7393 
7995 
8597 
9198 
9799 


7453 
8056 
8657 
9258 
9859 


7513 
8116 
8718 
9318 
9918 


7574 
3176 
8778 
9379 
9978 


7634 
8236 
8838 
9439 

0038 
0637 
1236 
1833 
2430 
3025 

3620 
4214 
4808 
5400 
5992 
6583 
7173 
7762 
8350 
8938 

9525 


7694 
8297 
8898 
9499 


7755 
8357 
8958 
9559 


7815 
8417 
9018 
9619 


7875 
8477 
9078 
9679 


60 


0098 
0697 
1295 
1893 
2489 
3085 

3680 
4274 
4867 
5459 
6051 
6642 
7232 
7821 
8409 
8997 

9584 


0158 
0757 
1355 
1952 
2549 
3144 

3739 

4333 
4926 
5519 
6110 
6701 
7291 
7880 
8468 
9056 

9642 


0218 
0817 
1415 
2012 
2608 
3204 

3799 

4392 
4985 
5578 
6169 
6760 
7350 
7939 
8527 
9114 

9701 


0278 
0877 
1475 
2072 
2668 
3263 

3858 
4452 
5045 
5637 
6228 
6819 
7409 
7998 
8586 
9173 

9760 




5 
6 

7 
8 
9 

730 
1 

2 
3 
4 
5 
6 
7 
8 
9 

740 


860338 
0937 
1534 
2131 
2728 

3323 
3917 
4511 
5104 
5696 
6287 
6878 
7467 
8056 
8644 

9232 
9318 


0398 
0996 
1594 
2191 
2787 

3382 
3977 
4570 
5163 
5755 
6346 
6937 
7526 
8115 
8703 

9290 
9877 


0453 
1056 
1654 
2251 
2847 

3442 
4036 
4630 
5222 
5814 
6405 
6996 
7535 
8174 
8762 

9349 
9935 


0518 
1116 
1714 
2310 
2906 

3501 
4096 
4689 
5282 
5874 
6465 
7055 
7644 
8233 
8821 

9408 


0578 
1176 
1773 
2370 
2966 

3561 

4155 
4748 
5341 
5933 
6524 
7114 
7703 
8292 
8879 

9466 


59 






0053 
063-S 

1223 
1806 
2389 
2972 
3553 
4134 
4714 

5293 
5871 
6449 
7026 
7602 
8177 
8752 
9325 
9898 


0111 
0696 
128! 
1865 
2448 
3030 
3611 
4192 
4772 

5351 
5929 
6507 
7083 
7659 
8234 
8809 
9383 
9956 


0170 
0755 
1339 
1923 
2506 
3088 
3669 
4250 
4830 

5409 
5987 
6564 
7141 
7717 
8292 
8866 
9440 


0228 
0313 
1398 
1931 
2564 
3146 
3727 
4308 
4888 

5466 
6045 
6622 
7199 
7774 
8349 
8924 
9497 


0287 
0372 
1456 
2040 
2622 
3204 
3785 
4366 
4945 

5524 
61-02 
6680 
7256 
7832 
8407 
8981 
9555 


0345 
0930 
1515 
2098 
2681 
3262 
3844 
4424 
5003 

'5582 
6160 
6737 
7314 
7889 
8464 
9039 
9612 




2 
3 
4 
5 
6 
7 
8 
.9 

750 
1 

2 
3 
4 
5 
6 
7 
8 


870404 
0989 
1573 
2156 
2739 
3321 
3902 
4482 

5061 
5640 
6218 
6795 
7371 
7947 
8522 
9096 
9669 


0462 
1047 
1631 
2215 
2797 
3379 
3960 
4540 

5119 
5698 
6276 
6853 
7429 
8004 
8579 
9153 
9726 


0521 
1106 
1690 
2273 
2855 
3437 
4018 
4598 

5177 

5756 
6333 
6910 
7487 
8062 
8637 
9211 
9784 


0579 
1164 
1748 
2331 
2913 
3495 
4076 
4656 

5235 
5813 
6391 
6968 
7544 
8119 
8694 
9268 
9841 


58 


0013 
0585 

1156 

1727 
2297 
2866 
3434 


0070 
0642 

1213 
1784 
2354 
2923 
3491 


0127 
0699 

1271 
1841 
2411 
2980 
3548 


0185 
0756 

1328 
1898 
2468 
3037 
3605 




9 

760 
1 

2 
3 
4 


880242 

0814 
1385 
1955 
2525 
3093 


0299 

0871 

1442 
2012 
2581 
3150 


0356 

0928 
1499 
2069 
2638 
3207 


0413 

0985 
1556 
2126 
2695 
3264 


0471 

1042 
1613 
2183 
2752 
3321 


0528 

1099 
1670 
2240 
2809 
3377 


57 



Proportional Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


59 


5.9 


11.8 


17.7 


23.6 


29.5 


35.4 


41.3 


47.2 


53.1 


58 


5.8 


11.6 


17.4 


23.2 


29.0 


34.8 


40.6 


46.4 


52.2 


57 


5.7 


11.4 


17.1 


22.8 


28.5 


34.2 


39.9 


45.6 


51.3 


56 


5.6 


11.2 


16.8 


22.4 


28.0 


33.6 


39.2 


44.8 


50.4 



158 



LOGARITHMS OF NUMBERS. 



No. 765 L. 883.] 



[No. 5 






1 


2 


3 


4 


5 


6 


7 


8 


9 

4172 


883661 


3718 


3775 


3832 


3888 


3945 


4002 


4059 


4115 


4229 


4285 


4342 


4399 


4455 


4512 


4569 


4625 


4682 


4739 


4795 


4852 


4909 


4965 


5022 


5078 


5135 


5192 


5248 


5305 


5361 


5418 


5474 


5531 


5587 


5644 


5700 


5757 


5813 


5870 


5926 


5983 


6039 


6096 


6152 


6209 


6265 


6321 


6378 


6434 


6491 


6547 


6604 


6660 


6716 


6773 


6829 


6885 


6942 


6998 


7054 


7111 


7167 


7223 


7280 


7336 


7392 


7449 


7505 


7561 


7617 


7674 


7730 


7786 


7842 


7898 


7955 


8011 


8067 


8123 


8179 


8236 


8292 


8348 


8404 


8460 


8516 


8573 


8629 


8685 


8741 


8797 


8853 


8909 


8965 


9021 


9077 


9134 


9190 


9246 


9302 


9358 


9414 


9470 


9526 


9582 


9638 


9694 


9750 


9806 


9862 


9918 


9974 
















0030 
0589 


0086 
0645 


0141 
0700 


0197 
0756 


0253 
0812 


0309 
0868 


0365 
0924 


890421 


0477 


0533 


0980 


1035 


1091 


1147 


1203 


1259 


1314 


1370 


1426 


1482 


1537 


1593 


1649 


1705 


1760 


1816 


1872 


1928 


1983 


2039 


2095 


2150 


2206 


2262 


2317 


2373 


2429 


2484 


2540 


2595 


2651 


2707 


2762 


2818 


2873 


2929 


2985 


3040 


3096 


3151 


3207 


3262 


3318 


3373 


3429 


3484 


3540 


3595 


3651 


3706 


3762 


3817 


3873 


3928 


3984 


4039 


4094 


4150 


4205 


4261 


4316 


4371 


4427 


4482 


4538 


4593 


4648 


4704 


4759 


4814 


4870 


4925 


4980 


5036 


5091 


5146 


5201 


5257 


5312 


5367 


5423 


5478 


5533 


5588 


5644 


5699 


5754 


5809 


5864 


5920 


5975 


6030 


6085 


6140 


6195 


6251 


6306 


6361 


6416 


6471 


6526 


6581 


6636 


6692 


6747 


6802 


6857 


6912 


6967 


7022 


7077 


7132 


7187 


7242 


7297 


7352 


7407 


7462 


7517 


7572 


7627 


7682 


7737 


7792 


7847 


7902 


7957 


8012 


8067 


8122 


8176 


8231 


8286 


8341 


8396 


8451 


8506 


8561 


8615 


8670 


8725 


8780 


8835 


8890 


8944 


8999 


9054 


9109 


9164 


9218 


9273 


9328 


9383 


9437 


9492 


9547 


9602 


9656 


9711 


9766 


9821 


9875 


9930 


9985 














0039 
0586 


0094 
0640 


0149 
0695 


0203 
0749 


0258 
0804 


0312 
0859 


900367 


0422 


0476 


0531 


0913 


0968 


1022 


1077 


1131 


1186 


1240 


1295 


1349 


1404 


1458 


1513 


1567 


1622 


1676 


1731 


1785 


1840 


1894 


1948 


2003 


2057 


2112 


2166 


2221 


2275 


2329 


2384 


2438 


2492 


2547 


2601 


2655 


2710 


2764 


2818 


2873 


2927 


2981 


3036 


3090 


3144 


3199 


3253 


3307 


3361 


3416 


3470 


3524 


3578 


3633 


3687 


3741 


3795 


3849 


3904 


3958 


4012 


4066 


4120 


4174 


4229 


4283 


4337 


4391 


4445 


4499 


4553 


4607 


4661 


4716 


4770 


4824 


4878 


4932 


4986 


5040 


5094 


5148 


5202 


5256 


5310 


5364 


5418 


5472 


5526 


5580 


5634 


5688 


5742 


5796 


5850 


5904 


5958 


6012 


6066 


6119 


6173 


6227 


6281 


6335 


6389 


6443 


6497 


6551 


6604 


6658 


6712 


6766 


6820 


6874 


6927 


6981 


7035 


7089 


7143 


7196 


7250 


7304 


7358 


7411 


7465 


7519 


7573 


7626 


7680 


7734 


7787 


7841 


7895 


7949 


8002 


8056 


8110 


8163 


8217 


8270 


8324 


8378 


8431 



Proportional Parts. 


Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


57 
56 
55 
54 


5.7 
5.6 
5.5 
5.4 


11.4 
11.2 
11.0 
10.8 


17.1 

16.8 
16.5 
16.2 


22.8 
22.4 
22.0 
21.6 


28.5 
28.0 
27.5 
27.0 


34.2 
33.6 
33.0 

32.4 


39.9 
39.2 
38.5 
37.8 


45.6 
44.8 
44.0 
43.2 


51.3 
50.4 
49.5 
48.6 







LOGARITHMS OF NUMBERS. 






159 


No. 810 L. 908.] 










[No. 854 L. 931. 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


810 


908485 


8539 


8592 


8646 


8699 


8753 


8807 


8860 


8914 


8967 




1 


9021 


9074 


9128 


9181 


9235 


9289 


9342 


9396 


9449 


9503 




2 


9556 


9610 


9663 


9716 


9770 


9823 


9877 


9930 


9984 














0037 
0571 




3 


910091 


0144 


0197 


0251 


0304 


0358 


0411 


0464 


0518 




4 


0624 


0678 


0731 


0784 


0838 


0891 


0944 


0998 


1051 


1104 




5 


1158 


1211 


1264 


1317 


1371 


1424 


1477 


1530 


1584 


1637 




6 


1690 


1743 


1797 


1850 


1903 


1956 


2009 


2063 


2116 


2169 




7 


2222 


2275 


2328 


2381 


2435 


2488 


2541 


2594 


2647 


2700 




8 


2753 


2806 


2859 


2913 


2966 


3019 


3072 


3125 


3178 


3231 




9 


3284 


3337 


3390 


3443 


3496 


3549 


3602 


3655 


3708 


3761 


53 


820 


3814 


3867 


3920 


3973 


4026 


4079 


4132 


4184 


4237 


4290 




I 


4343 


4396 


4449 


4502 


4555 


4608 


4660 


4713 


4766 


4819 




2 


4872 


4925 


4977 


5030 


5083 


5136 


5189 


5241 


5294 


5347 




3 


5400 


5453 


5505 


5558 


5611 


5664 


5716 


5769 


5822 


5875 




4 


5927 


5980 


6033 


6085 


6138 


6191 


6243 


6296 


6349 


6401 




5 


6454 


6507 


6559 


6612 


6664 


6717 


6770 


6822 


6875 


6927 




6 


6980 


7033 


7085 


7138 


7190 


7243 


7295 


7348 


7400 


7453 




7 


7506 


7558 


7611 


7663 


7716 


7768 


7820 


7873 


7925 


7978 




8 


8030 


8083 


8135 


8188 


8240 


8293 


8345 


8397 


8450 


8502 




9 


8555 


8607 


8659 


8712 


8764 


8816 


8869 


8921 


8973 


9026 




830 


9078 


9130 


9183 


9235 


9287 


9340 


9392 


9444 


9496 


9549 




I 


9601 


9653 


9706 


9758 


9810 


9862 


9914 


9967 










0019 
0541 


0071 
0593 




2 


920123 


0176 


0228 


0280 


0332 


0384 


0436 


0489 




3 


0645 


0697 


0749 


0801 


0853 


0906 


0958 


1010 


1062 


1114 


52 


4 


1166 


1218 


1270 


1322 


1374 


1426 


1478 


1530 


1582 


1634 




5 


1686 


1738 


1790 


1842 


1894 


1946 


1998 


2050 


2102 


2154 




6 


2206 


2258 


2310 


2362 


2414 


2466 


2518 


2570 


2622 


2674 




7 


2725 


2777 


2829 


2881 


2933 


2985 


3037 


3089 


3140 


3192 




8 


3244 


3296 


3348 


3399 


3451 


3503 


3555 


3607 


3658 


3710 




9 


3762 


3814 


3865 


3917 


3969 


4021 


4072 


4124 


4176 


4228 




840 


4279 


4331 


4383 


4434 


4486 


4538 


4589 


4641 


4693 


4744 




1 


4796 


4848 


4899 


4951 


5003 


5054 


5106 


5157 


5209 


5261 




2 


5312 


5364 


5415 


5467 


5518 


5570 


5621 


5673 


5725 


5776 




3 


5828 


5879 


5931 


5982 


6034 


6085 


6137 


6188 


6240 


6291 




4 


6342 


6394 


6445 


6497 


6548 


6600 


6651 


6702 


6754 


6805 




5 


6857 


6908 


6959 


7011 


7062 


7114 


7165 


7216 


7268 


7319 




6 


7370 


7422 


7473 


7524 


7576 


7627 


7678 


7730 


7781 


7832 




7 


7883 


7935 


7986 


8037 


8088 


8140 


8191 


8242 


8293 


8345 




8 


8396 


8447 


8498 


8549 


8601 


8652 


8703 


8754 


8805 


8857 




9 


8908 


8959 


9010 


9061 


9112 


9163 


9215 


9266 


9317 


9368 




850 
1 


9419 
9930 


9470 
9981 


9521 


9572 


9623 


9674 


9725 


9776 


9827 


9879 


51 




0032 
0542 


0083 
0592 


0134 
0643 


0185 
0694 


0236 
0745 


0287 
0796 


0338 
0847 


0389 
0898 


2 


930440 


0491 




3 


0949 


1000 


1051 


1102 


1153 


1204 


1254 


1305 


1356 


1407 




4 


1458 


1509 


1560 


1610 


1661 


1712 


1763 


1814 


1865 


1915 





Proportional Parts. 



5.3 
5.2 
5.1 
5.0 



10.6 
10.4 
10.2 
10.0 



15.9 
15.6 
15.3 
15.0 



21.2 
20.8 
20.4 
20.0 



26.5 
26.0 
25.5 
25.0 



6 

31.8 
31.2 
30.6 
30.0 



37.1 
36.4 
35.7 
35.0 



8 

42.4 
41.6 
40.8 
40.0 



160 



LOGARITHMS OF NUMBERS. 



No. 855 L. 931.] 














[No 


. 899 L. 954. 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


855 


931966 


2017 


2068 


2118 


2169 


2220 


2271 


2322 


2372 


2423 




6 


2474 


2524 


2575 


2626 


2677 


2727 


2778 


2829 


2879 


2930 




7 


2981 


3031 


3082 


3133 


3183 


3234 


3285 


3335 


3386 


3437 




8 


3487 


3538 


3589 


3639 


3690 


3740 


3791 


3841 


3892 


3943 




9 


3993 


4044 


4094 


4145 


4195 


4246 


4296 


4347 


4397 


4448 




860 


4498 


4549 


4599 


4650 


4700 


4751 


4801 


4852 


4902 


4953 




1 


5003 


5054 


5104 


5154 


5205 


5255 


5306 


5356 


5406 


5457 




2 


5507 


5558 


5608 


5658 


5709 


5759 


5809 


5860 


5910 


5960 




3 


6011 


6061 


6111 


6162 


6212 


6262 


6313 


6363 


6413 


6463 




4 


6514 


6564 


6614 


6665 


6715 


6765 


6815 


6865 


6916 


6966 




5 


7016 


7066 


7116 


7167 


7217 


7267 


7317 


7367 


7418 


7468 




6 


7518 


7568 


7618 


7668 


7718 


7769 


7819 


7869 


7919 


7969 




7 


8019 


8069 


8119 


8169 


8219 


8269 


8320 


8370 


8420 


8470 


50 


8 


8520 


8570 


8620 


8670 


8720 


8770 


8820 


8870 


8920 


8970 




9 


9020 


9070 


9120 


9170 


9220 


9270 


9320 


9369 


9419 


9469 




870 


9519 


9569 


9619 


9669 


9719 


9769 


9819 


9869 


9918 


9968 
0467 




1 


940018 


0068 


0118 


0168 


0218 


0267 


0317 


0367 


0417 




2 


0516 


0566 


0616 


0666 


0716 


0765 


0815 


0865 


0915 


0964 




3 


1014 


1064 


1114 


1163 


1213 


1263 


1313 


1362 


1412 


1462 




4 


1511 


1561 


1611 


1660 


1710 


1760 


1809 


1859 


1909 


1958 




5 


2008 


2058 


2107 


2157 


2207 


2256 


2306 


2355 


2405 


2455 




6 


2504 


2554 


2603 


2653 


2702 


2752 


2801 


2851 


2901 


2950 




7 


3000 


3049 


3099 


3148 


3198 


3247 


3297 


3346 


3396 


3445 




8 


3495 


3544 


3593 


3643 


3692 


3742 


3791 


3841 


3890 


3939 




9 


3989 


4038 


4088 


4137 


4186 


4236 


4285 


4335 


4384 


4433 




880 


4483 


4532 


4581 


4631 


4680 


4729 


4779 


4828 


4877 


4927 




1 


4976 


5025 


5074 


5124 


5173 


5222 


5272 


5321 


5370 


5419 




2 


5469 


5518 


5567 


5616 


5665 


5715 


5764 


5813 


5862 


5912 




3 


5961 


6010 


6059 


6108 


6157 


6207 


6256 


6305 


6354 


6403 




4 


6452 


6501 


6551 


6600 


6649 


6698 


6747 


6796 


6845 


6894 




5 


6943 


6992 


7041 


7090 


7139 


7189 


7238 


7287 


7336 


7385 




6 


7434 


7483 


7532 


7581 


7630 


7679 


7728 


7777 


7826 


7875 


49 


7 


7924 


7973 


8022 


8070 


8119 


8168 


8217 


8266 


8315 


8364 




8 


8413 


8462 


8511 


8560 


8608 


8657 


8706 


8755 


8804 


8853 




9 


8902 


8951 


8999 


9048 


9097 


9146 


9195 


9244 


9292 


9341 




890 
I 


9390 

9878 


9439 
9926 


9488 
9975 


9536 


9585 


9634 


9683 


9731 


97.80 


9829 






0024 
0511 


0073 
0560 


0121 
0608 


0170 
0657 


0219 
0706 


0267 
0754 


0316 
0303 




2 


950365 


0414 


0462 




3 


0851 


0900 


0949 


0997 


1046 


1095 


1143 


1192 


1240 


1289 




4 


1338 


1386 


1435 


1483 


1532 


1580 


1629 


1677 


1726 


1775 




5 


1823 


1872 


1920 


1969 


2017 


2066 


2114 


2163 


2211 


2260 




6 


2308 


2356 


2405 


2453 


2502 


2550 


2599 


2647 


2696 


2744 




7 


2792 


2841 


2889 


2938 


2986 


3034 


3033 


3131 


3180 


3228 




8 


3276 


3325 


3373 


3421 


3470 


3518 


3566 


3615 


3663 


3711 




9 


3760 


3808 


3856 


3905 


3953 


4001 


4049 


4098 


4146 


4194 





Proportional Parts. 



5.1 
5.0 
4.9 

4.8 



10.2 
10.0 
9.8 
9.6 



15.3 
15.0 
14.7 
14.4 



20.4 
20.0 
19.6 
19.2 



25.5 
25.0 
24.5 
24.0 



30.6 
30.0 
29.4 
28.8 



35.7 
35.0 
34.3 
33.6 



8 

40.8 
40.0 
39.2 
38.4 



LOGARITHMS OF NUMBERS. 



161 



No. 900 L. 954.] 














[No 


944 L 


.975. 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


900 
1 

2 
3 
4 
5 
6 
7 
8 
9 

910 

1 
2 


954243 
4725 
5207 
5683 
6168 
6649 
7128 
7607 
8086 
8564 

9041 
9518 
9995 


4291 
4773 
5255 
5736 
6216 
6697 
7176 
7655 
8134 
8612 

9089 
9566 


4339 
4821 
5303 
5784 
6265 
6745 
7224 
7703 
8181 
8659 

9137 

9614 


4387 
4869 
5351 
5832 
6313 
6793 
7272 
7751 
8229 
8707 

9185 
9661 


4435 
4918 
5399 
5880 
6361 
6840 
7320 
7799 
8277 
8755 

9232 
9709 


4484 
4966 
5447 
5928 
6409 
6888 
7368 
7847 
8325 
8803 

9280 
9757 


4532 
5014 
5495 
5976 
6457 
6936 
7416 
7894 
8373 
8850 

9328 
9804 


4580 
5062 
5543 
6024 
6505 
6984 
7464 
7942 
8421 
8898 

9375 
9852 


4628 
5110 
5592 
6072 
6553 
7032 
7512 
7990 
8468 
8946 

9423 
9900 


4677 
5158 
5640 
6120 
6601 
7080 
7559 
8038 
8516 
8994 

9471 
9947 


48 


0042 
0518 
0994 
1469 
1943 
2417 
2890 
3363 

3835 
4307 
4778 
5249 
5719 
6189 
6658 
7127 
7595 
8062 

8530 
8996 
9463 

9928 


0090 
0566 
1041 
1516 
1990 
2464 
2937 
3410 

3882 
4354 
4825 
5296 
5766 
6236 
6705 
7173 
7642 
8109 

8576 
9043 
9509 
9975 


0138 
0613 
1089 
1563 
2038 
2511 
2985 
3457 

3929 
4401 
4872 
5343 
5813 
6283 
6752 
7220 
7688 
8156 

8623 
9090 
9556 


0185 
0661 
1136 
1611 
2085 
2559 
3032 
3504 

3977 
4448 
4919 
5390 
5860 
6329 
6799 
7267 
7735 
8203 

8670 
9136 
9602 


0233 
0709 
1184 
1658 
2132 
2606 
3079 
3552 

4024 
4495 
4966 
5437 
5907 
6376 
6845 
7314 
7782 
8249 

8716 

9183 
9649 


0280 
0756 
1231 
1706 
2180 
2653 
3126 
3599 

4071 

4542 
5013 
5484 
5954 
6423 
6892 
7361 
7829 
8296 

8763 
9229 
9695 


0328 
0804 
1279 
1753 
2227 
2701 
3174 
3646 

4118 
4590 
5061 
5531 
6001 
6470 
6939 
7408 
7875 
8343 

8810 
9276 
9742 


0376 
0851 
1326 
1801 
2275 
2748 
3221 
3693 

4165 
4637 
5108 
5578 
6048 
6517 
6986 
7454 
7922 
8390 

8856 
9323 
9789 


0423 
0899 
1374 
1848 
2322 
2795 
3268 
3741 

4212 
4684 
5155 
5625 
6095 
6564 
7033 
7501 
7969 
8436 

8903 
9369 
9835 




3 
4 
5 
6 
7 
8 
9 

920 
1 

2 
3 
4 
5 
6 
7 
8 
9 

930 

1 

2 
3 


960471 
0946 
1421 
1895 
2369 
2843 
3316 

3788 
4260 
4731 
5202 
5672 
6142 
6611 
7080 
7548 
8016 

8483 
8950 
9416 

9882 


47 


0021 
0486 

0951 
1-415 
1879 
2342 
2804 

3266 
3728 
4189 
4650 
5110 


0068 
0533 
0997 
1461 
1925 
2388 
2851 

3313 

3774 
4235 
4696 
5156 


0114 
0579 
1044 
1508 
1971 
2434 
2897 

3359 
3820 
4281 
4742 
5202 


0161 
0626 
1090 
1554 
2018 
2481 
2943 

3405 
3866 

4327 
4788 

5248 


0207 
0672 
1137 
1601 
2064 
2527 
2989 

3451 
3913 

4374 
4834 
5294 


0254 
0719 
1183 
1647 
2110 
2573 
3035 

3497 
3959 
4420 
4880 
5340 


0300 
0765 
1229 
1693 
2157 
2619 
3082 

3543 
4005 
4466 
4926 
5386 




4 
5 
6 
7 
8 
9 

940 
1 

2 
3 

4 


970347 
0812 
1276 
1740 
2203 
2666 

3128 
3590 
4051 
4512 
4972 


0393 

0858 
1322 
1786 
2249 
2712 

3174 
3636 
4097 

4558 
5018 


0440 
0904 
1369 

1832 
2295 
2758 

3220 
3682 
4143 
4604 
5064 


46 



Proportional Parts. 



Diff. 


1 


2 


3 


4 


5 ■ 


6 


7 


8 


9 


47 
46 


4.7 
4.6 


9.4 
9.2 


14.1 
13.8 


18.8 
18.4 


23.5 
23.0 


28.2 
27.6 


32.9 

32.2 


37.6 
36.8 


42.3 

41.4 



162 



LOGARITHMS OF NUMBERS. 



No. 945 L. 975.] 



[No. 



N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


945 
6 
7 
8 
9 

950 

1 
2 
3 

4 


975432 
5891 
6350 
6808 
7266 

7724 

8181 
8637 
9093 
9548 


5478 
5937 
6396 
6854 
7312 

7769 

8226 
8683 
9138 
9594 


5524 
5983 
6442 
6900 
7358 

7815 

8272 
8728 
9184 
9639 


5570 
6029 
6488 
6946 
7403 

7861 

8317 
8774 
9230 
9685 


5616 
6075 
6533 
6992 
7449 

7906 
8363 
8819 
9275 
9730 


5662 
6121 
6579 
7037 
7495 

7952 
8409 
8865 
9321 
9776 


5707 
6167 
6625 
7083 
7541 

7998 
8454 
8911 
9366 
9821 


5753 
6212 
6671 
7129 
7586 

8043 
8500 
8956 
9412 
9867 


5799 
6258 
6717 
7175 
7632 

8089 
8546 
9002 
9457 
9912 


5845 
6304 
6763 
7220 
7678 

8135 
8591 
9047 
9503 
9958 




5 
6 

7 
8 
9 

960 

1 

2 
3 
4 
5 
6 
7 
8 
9 

970 

1 
2 

A 

5 
6 

7 


980003 
0458 
0912 
1366 
1819 

2271 
2723 
3175 
3626 
4077 
4527 
4977 
5426 
5875 
6324 

6772 
7219 
7666 
8113 
8559 
9005 
9450 
9895 


0049 
0503 
0957 
1411 
1864 

2316 
2769 
3220 
3671 
4122 
4572 
5022 
5471 
5920 
6369 

6817 
7264 
7711 
8157 
8604 
9049 
9494 
9939 


0094 
0549 
1003 
1456 
1909 

2362 
2814 
3265 
3716 
4167 
4617 
5067 
5516 
5965 
6413 

6861 
7309 
7756 
8202 
8648 
9094 
9539 
9983 


0140 
0594 
1048 
1501 
1954 

2407 
2859 
3310 
3762 
4212 
4662 
5112 
5561 
6010 
6458 

6906 
7353 
7800 
8247 
8693 
9138 
9583 


0185 
0640 
1093 
1547 
2000 

2452 
2904 
3356 
3807 
4257 
4707 
5157 
5606 
6055 
6503 

6951 

7398 
7845 
8291 
8737 
9183 
9628 


0231 
0685 
1139 
1592 
2045 

2497 
2949 
3401 
3852 
4302 
4752 
5202 
5651 
6100 
6548 

6996 
7443 
7890 
8336 
8782 
9227 
9672 


0276 
0730 
1184 
1637 
2090 

2543 
2994 
3446 
3897 
4347 
4797 
5247 
5696 
6144 
6593 

7040 
7488 
7934 
8381 
8826 
9272 
9717 


0322 
0776 
1229 
1683 
2135 

2588 
3040 
3491 
3942 
4392 
4842 
5292 
5741 
6189 
6637 

7085 
7532 
7979 
8425 
8871 
9316 
9761 


0367 
0821 
1275 
1728 
2181 

2633 
3085 
3536 
3987 
4437 
4887 
5337 
5786 
6234 
6682 

7130 
7577 
8024 
8470 
8916 
9361 
9806 


0412 
0867 
1320 
1773 
2226 

2678 
3130 
3581 
4032 
4482 
4932 
5382 
5830 
6279 
6727 

7175 
7622 
8068 
8514 
8960 
9405 
9850 


45 


0028 
0472 
0916 

1359 
1802 
2244 
2686 
3127 
3568 
4009 
4449 
4889 
5328 


0072 
0516 
0960 

1403 
1846 
2288 
2730 
3172 
3613 
4053 
4493 
4933 
5372 


0117 
0561 
1004 

1448 
1890 
2333 
2774 
3216 
3657 
4097 
4537 
4977 
5416 


0161 
0605 
1049 

1492 
1935 
2377 
2819 
3260 
3701 
4141 
4581 
5021 
5460 


0206 
0650 
1093 

1536 
1979 
2421 
2863 
3304 
3745 
4185 
4625 
5065 
5504 


0250 
0694 
1137 

1580 
2023 
2465 
2907 
3348 
3789 
4229 
4669 
5108 
5547 


0294 
0738 
1182 

1625 
2067 
2509 
2951 
3392 
3833 
4273 
4713 
5152 
5591 




8 
9 

980 
1 

2 
3 
4 
5 
6 
7 
8 
9 


990339 
0783 

1226 
1669 
2111 
2554 
2995 
3436 
3877 
4317 
4757 
5196 


0383 
0827 

1270 
1713 
2156 

2598 
3039 
3480 
3921 
4361 
4801 
5240 


0428 
0871 

1315 

1758 
2200 
2642 
3083 
3524 
3965 
4405 
4845 
5284 


44 



Proportional Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


46 


4.6 


9.2 


13.8 


18.4 


23.0 


27.6 


32.2 


36.8 


41.4 


45 


4.5 


9.0 


13.5 


18.0 


22.5 


27.0 


31.5 


36.0 


40.5 


44 


4.4 


8.8 


13.2 


17.6 


22.0 


26.4 


30.8 


35.2 


39.6 


43 


4.3 


8.6 


12.9 


17.2 


21.5 


25.8 


30.1 


34.4 


38.7 



HYPERBOLIC LOGARITHMS. 



163 



No. 990 L. 995.] 



[No. 999 L. 999. 



N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


990 


995635 


5679 


5723 


5767 


5811 


5854 


5898 


5942 


5986 


6030 




1 


6074 


6117 


6161 


6205 


6249 


6293 


6337 


6380 


6424 


6468 


44 


2 


6512 


6555 


6599 


6643 


6687 


6731 


6774 


6818 


6862 


6906 




3 


6949 


6993 


7037 


7080 


7124 


7168 


7212 


7255 


7299 


7343 




4 


7386 


7430 


7474 


7517 


7561 


7605 


7648 


7692 


7736 


7779 




3 


7823 


7867 


7910 


7954 


7998 


8041 


8085 


8129 


8172 


8216 




6 


8259 


8303 


8347 


8390 


8434 


8477 


8521 


8564 


8608 


8652 




7 


8695 


8739 


8782 


8826 


8869 


8913 


8956 


9000 


9043 


9087 




8 


9131 


9174 


9218 


9261 


9305 


9348 


9392 


9435 


9479 


9522 




9 


9565 


9609 


9652 


9696 


9739 


9783 


9826 


9870 


9913 


9957 


43 



HYPERBOLIC LOGARITHMS. 



No. 


Log. 


No. 


Log. 


No. 


Log. 


No. 


Log. 


No. 


Log. 


1.01 


.0099 


1.45 


.3716 


1.89 


.6366 


2.33 


.8458 


2.77 


1.0188 


1.02 


.0198 


1.46 


.3784 


1.90 


.6419 


2.34 


.8502 


2.78 


1 .0225 


1.03 


.0296 


1.47 


.3853 


1.91 


.6471 


2.35 


.8544 


2.79 


1 .0260 


1.04 


.0392 


1.48 


.3920 


1.92 


.6523 


2.36 


.8587 


2.80 


1 .0296 


1.05 


.0488 


1.49 


.3988 


1.93 


.6575 


2.37 


.8629 


2.81 


1 .0332 


1.06 


.0583 


1.50 


.4055 


1.94 


.6627 


2.38 


.8671 


2.82 


1 .0367 


1.07 


.0677 


1.51 


.4121 


1.95 


.6678 


2.39 


.8713 


2.83 


1 .0403 


1.08 


.0770 


1.52 


.4187 


1.96 


.6729 


2.40 


.8755 


2.84 


1 .0438 


1.09 


.0862 


1.53 


.4253 


1.97 


.6780 


2.41 


.8796 


2.85 


1.0473 


1.10 


.0953 


1.54 


.4318 


1.98 


.6831 


2.42 


.8838 


2.86 


1 .0508 


1.11 


.1044 


1.55 


.4383 


1.99 


.6881 


2.43 


.8879 


2.87 


1.0543 


1.12 


.1133 


1.56 


.4447 


2.00 


.6931 


2.44 


.8920 


2.88 


1.0578 


1.13 


.1222 


1.57 


.4511 


2.01 


.6981 


2.45 


.8961 


2.89 


1.0613 


1.14 


.1310 


1.58 


.4574 


2.02 


.7031 


2.46 


.9002 


2.90 


1 .0647 


1.15 


.1398 


1.59 


.4637 


2.03 


.7080 


2.47 


.9042 


2.91 


1 .0682 


1.16 


.1484 


1.60 


.4700 


2.04 


.7129 


2.48 


.9083 


2.92 


1.0716 


1.17 


.1570 


1.61 


.4762 


2.05 


.7178 


2.49 


.9123 


2.93 


1.0750 


1.18 


.1655 


1.62 


.4824 


2.06 


.7227 


2.50 


.9163 


2.94 


1 .0784 


1.19 


.1740 


1.63 


.4886 


2.07 


.7275 


2.51 


.9203 


2.95 


1.0818 


1.20 


.1823 


1.64 


.4947 


2.08 


.7324 


2.52 


.9243 


2.96 


1 .0852 


1.21 


.1906 


1.65 


.5008 


2.09 


.7372 


2.53 


.9282 


2.97 


1 .0886 


1.22 


.1988 


1.66 


.5068 


2.10 


.7419 


2.54 


.9322 


2.98 


1.0919 


1.23 


.2070 


1.67 


.5128 


2.11 


.7467 


2.55 


.9361 


2.99 


1 .0953 


1.24 


.2151 


1.68 


.5188 


2.12 


.7514 


2.56 


.9400 


3.00 


1 .0986 


1.25 


.2231 


1.69 


.5247 


2.13 


.7561 


2.57 


.9439 


3.01 


1.1019 


1.26 


.2311 


1.70 


.5306 


2.14 


.7608 


2.58 


.9478 


3.02 


1.1056 


1.27 


.2390 


1.71 


.5365 


2.15 


.7655 


2.59 


.9517 


3.03 


1.1081 


1.28 


.2469 


1.72 


.5423 


2.16 


.7701 


2.60 


.9555 


3.04 


1.1113 


1.29 


.2546 


1.73 


.5481 


2.17 


.7747 


2.61 


.9594 


3.05 


1.1154 


1.30 


.2624 


1.74 


.5539 


2.18 


.7793 


2.62 


.9632 


3.06 


1.1187 


1.31 


.2700 


1.75 


.5596 


2.19 


.7839 


2.63 


.9670 


3.07 


1.1219 


1.32 


.2776 


1.76 


.5653 


2.20 


.7885 


2.64 


.9708 


3.08 


1.1246 


1.33 


.2852 


1.77 


.5710 


2.21 


.7930 


2.65 


.9746 


3.09 


1.1284 


1.34 


.2927 


1.78 


.5766 


2.22 


.7975 


2.66 


.9783 


3.10 


1.1312 


1.35 


.3001 


1.79 


.5822 


2.23 


.8020 


2.67 


.9821 


3.11 


1.1349 


1.36 


.3075 


1.80 


.5878 


2.24 


.8065 


2.68 


.9858 


3.12 


1.1378 


1.37 


.3148 


1.81 


.5933 


2.25 


.8109 


2.69 


.9895 


3.13 


1.1410 


1.38 


.3221 


1.82 


.5988 


2.26 


.8154 


2.70 


.9933 


3.14 


1.1442 


1.39 


.3293 


1.83 


.6043 


2.27 


.8198 


2.71 


.9969 


3.15 


1.1474 


1.40 


.3365 


1.84 


.6098 


2.28 


.8242 


2.72 


1 .0006 


3.16 


1.1506 


1.41 


.3436 


1.85 


.6152 


2.29 


.8286 


2.73 


1 .0043 


3.17 


1.1537 


1.42 


.3507 


1.86 


.6206 


2.30 


.8329 


2.74 


1 .0080 


3.18 


1.1569 


1.43 


.3577 


1.87 


.6259 


2.31 


.8372 


2.75 


1.0116 


3.19 


1.1600 


1.44 


.3646 


1.88 


.6313 


2.32 


.8416 


2.76 


1.0152 


3.20 


1.1632 



164 



MATHEMATICAL TABLES. 



No. 


Log. 


No. 


Log. 


No. 


Log. 


No. 


Log. 


No. 


Log. 


3.21 


1.1663 


3.87 


1.3533 


4.53 


1.5107 


5.19 


1 .6467 


5.85 


1.7664 


3.22 


1.1694 


3.88 


1.3558 


4.54 


1.5129 


5.20 


1.6487 


5.86 


1.7681 


3.23 


1.1725 


3.89 


1.3584 


4.55 


1.5151 


5.21 


1.6506 


5.87 


1 .7699 


3.24 


1.1756 


3.90 


1.3610 


4.56 


1.5173 


5.22 


1.6525 


5.88 


1.7716 


3.25 


1.1787 


3.91 


1.3635 


4.57 


1.5195 


5.23 


1.6544 


5.89 


1.7733 


3.26 


1.1817 


3.92 


1.3661 


4.58 


1.5217 


5.24 


1 .6563 


5.90 


1.7750 


3.27 


1.1848 


3.93 


1.3686 


4.59 


1.5239 


5.25 


1.6582 


5.91 


1.7766 


3.28 


1.1878 


3.94 


1.3712 


4.60 


1.5261 


5.26 


1.6601 


5.92 


1.7783 


3.29 


1.1909 


3.95 


1.3737 


4.61 


1.5282 


5.27 


1 .6620 


5.93 


1.7800 


3.30 


1.1939 


3.96' 


1.3762 


4.62 


1.5304 


5.28 


1 .6639 


5.94 


1.7817 


3.31 


1.1969 


3.97 


1.3788 


4.63 


1.5326 


5.29 


1 .6658 


5.95 


1.7834 


3.32 


1.1999 


3.98 


1.3813 


4.64 


1.5347 


5.30 


1 .6677 


5.96 


1.7851 


3.33 


1 .2030 


3.99 


1.3838 


4.65 


1.5369 


5.31 


1 .6696 


5.97 


1.7867 


3.34 


1 .2060 


4.00 


1.3863 


4.66 


1.5390 


5.32 


1.6715 


5.98 


1 .7884 


3.35 


1 .2090 


4.01 


1.3888 


4.67 


1.5412 


5.33 


1.6734 


5.99 


1.7901 


3.36 


1.2119 


4.02 


1.3913 


4.68 


1.5433 


5.34 


1.6752 


6.00 


1.7918 


3.37 


1.2149 


4.03 


1.3938 


4.69 


1.5454 


5.35 


1.6771 


6.01 


1.7934 


3.38 


1.2179 


4.04 


1 .3962 


4.70 


1.5476 


5.36 


1 .6790 


6.02 


1.7951 


3.39 


1 .2208 


4.05 


1.3987 


4.71 


1.5497 


5.37 


1 .6808 


6.03 


1.7967 


3.40 


1.2238 


4.06 


1.4012 


4.72 


1.5518 


5.38 


1 .6827 


6.04 


1.7984 


3.41 


1 .2267 


4.07 


1.4036 


4.73 


1.5539 


5.39 


1 .6845 


6.05 


1.8001 


3.42 


1 .2296 


4.08 


1.4061 


4.74 


1.5560 


5.40 


1 .6864 


606 


1.8017 


3.43 


1.2326 


4.09 


1 .4085 


4.75 


1.5581 


5.41 


1 .6882 


6.07 


1.8034 


3.44 


1.2355 


4.10 


1.4110 


4.76 


1.5602 


5.42 


1.6901 


6.08 


1 .8050 


3.45 


1.2384 


4.11 


1.4134 


4.77 


1.5623 


5.43 


1.6919 


6.09 


1 .8066 


3.46 


1.2413 


4.12 


1.4159 


4.78 


1.5644 


5.44 


1 .6938 


6.10 


1 .8083 


3.47 


1 .2442 


4.13 


1.4183 


4.79 


1.5665 


5.45 


1.6956 


6.11 


1 .8099 


3.48 


1 .2470 


4.14 


1 .4207 


4.80 


1.5686 


5.46 


1 .6974 


6.12 


1.8116 


3.49 


1.2499 


4.15 


1 .423 1 


4.81 


1.5707 


5.47 


1 .6993 


6.13 


1.8132 


3.50 


1.2528 


4.16 


1.4255 


4.82 


1.5728 


5.48 


1.7011 


6.14 


1.8148 


3.51 


1.2556 


4.17 


1 .4279 


4.83 


1.5748 


5.49 


1 .7029 


6.15 


1.8165 


3.52 


1.2585 


4.18 


1 .4303 


4.84 


1.5769 


5.50 


1.7047 


6.16 


1.8181 


3.53 


1.2613 


4.19 


1.4327 


4.85 


1.5790 


5.51 


1 .7066 


6.17 


1.8197 


3.54 


1.2641 


4.20 


1.4351 


4.86 


1.5810 


5.52 


1.7084 


6.18 


1.8213 


3.55 


1 .2669 


4.21 


1.4375 


4.87 


1.5831 


5.53 


1.7102 


6.19 


1 .8229 


3.56 


1 .2698 


4.22 


1.4398 


4.88 


1.5851 


5.54 


1.7120 


6.20 


1.8245 


3.57 


1.2726 


4.23 


1 .4422 


4.89 


1.5872 


5.55 


1.7138 


6.21 


1.8262 


3.58 


1.2754 


4.24 


1 .4446 


4.90 


1.5892 


5.56 


1.7156 


6.22 


1.8278 


3.59 


1.2782 


4.25 


1 .4469 


4.91 


1.5913 


5.57 


1.7174 


6.23 


1.8294 


3.60 


1 .2809 


4.26 


1 .4493 


4.92 


1.5933 


5.58 


1.7192 


6.24 


1.8310 


3.61 


1.2837 


4.27 


1.4516 


4.93 


1.5953 


5.59 


1.7210 


6.25 


1.8326 


3.62 


1.2865 


4.28 


1 .4540 


4.94 


1.5974 


5.60 


1.7228 


6.26 


1.8342 


3.63 


1 .2892 


4.29 


1.4563 


4.95 


1.5994 


5.61 


1.7246 


6.27 


1.8358 


3.64 


1 .2920 


4.30 


1 .4586 


4.96 


1.6014 


5.62 


1.7263 


6.28 


1.8374 


3 65 


1.2947 


4.31 


1 .4609 


4.97 


1.6034 


5.63 


1.7281 


6.29 


1.8390 


3.66 


1.2975 


4.32 


1.4633 


4.98 


1.6054 


5.64 


1 .7299 


6.30 


1 .8405 


3.67 


1.3002 


4.33 


1.4656 


4.99 


1.6074 


5.65 


1.7317 


6.31 


1.8421 


3.68 


1 .3029 


4.34 


1 .4679 


5.00 


1 .6094 


5.66 


1.7334 


6.32 


1.8437 


3.69 


1.3056 


4.35 


1 .4702 


5.01 


1.6114 


5.67 


1.7352 


6.33 


1.8453 


3.70 


1.3083 


4.36 


1 .4725 


5.02 


1.6134 


5.68 


1.7370 


6.34 


1 .8469 


3.71 


1.3110 


4.37 


1 .4748 


5.03 


1.6154 


5.69 


1.7387 


6.35 


1 .8485 


3.72 


1.3137 


4.38 


1.4770 


5.04 


1.6174 


5.70 


1 .7405 


6.36 


1.8500 


3.73 


1.3164 


4.39 


1.4793 


5.05 


1.6194 


5.71 


1.7422 


6.37 


1.8516 


3.74 


1.3191 


4.40 


1.4816 


5.06 


1.6214 


5.72 


1.7440 


6.38 


1.8532 


3.75 


1.3218 


4.41 


1.4839 


5.07 


1.6233 


5.73 


1.7457 


6.39 


1.8547 


3.76 


1.3244 


4.42 


1.4861 


5.08 


1.6253 


5.74 


1.7475 


6.40 


1.8563 


3.77 


1.3271 


4.43 


1 .4884 


5.09 


1.6273 


5.75 


1 .7492 


6.41 


1.8579 


3.78 


1.3297 


4.44 


1 .4907 


5.10 


1 .6292 


5.76 


1.7509 


6.42 


1.8594 


3.79 


1.3324 


4.45 


1 .4929 


5.11 


1.6312 


5.77 


1.7527 


6.43 


1.8610 


3.80 


1.3350 


4.46 


1.4951 


5.12 


1.6332 


5.78 


1.7544 


6.44 


1.8625 


3.81 


1.3376 


4.47 


1.4974 


5.13 


1.6351 


5.79 


1.7561 


6.45 


1.8641 


3.82 


1.3403 


4.48 


1 .4996 


5.14 


1.6371 


5.80 


1.7579 


6.46 


1 .8656 


3.83 


1.3429 


4.49 


1.5019 


5.15 


1.6390 


5.81 


1.7596 


6.47 


1.8672 


3.84 


1.3455 


4.50 


1.5041 


5.16 


1 .6409 


5.82 


1.7613 


6.43 


1.8687 


3.85 


1.3481 


4.51 


1.5063 


5.17 


1 .6429 


5.83 


1.7630 


6.49 


1.8703 


3.86 


1.3507 


4.52 


1.5085 


5.18 


1 .6448 


5.84 


1.7647 


6.50 


1.8713 



HYPERBOLIC LOGARITHMS. 



165 



No. 


Log. 


No. 


Log. 


No. 


Log. 


No. 


Log. 


No 


Log. 


6.51 


1.8733 


7.15 


1.9671 


7.79 


2.0528 


8.66 


2.1587 


9.94 


2.2966 


6.52 


1.8749 


7.16 


1.9685 


7.80 


2.0541 


8.68 


2.1610 


9.96 


2.2986 


6.53 


1.8764 


7.17 


1 .9699 


7.81 


2.0554 


8.70 


2.1633 


9.98 


2.3006 


6.54 


1.8779 


7.18 


1.9713 


7.82 


2.0567 


8.72 


2.1656 


10.00 


2.3026 


6.55 


1.8795 


7.19 


1.9727 


7.83 


2.0580 


8.74 


2.1679 


10.25 


2.3279 


6.56 


1.8810 


7.20 


1.9741 


7.84 


2.0592 


8.76 


2.1702 


10.50 


2.3513 


6.57 


1.8825 


7.21 


1.9754 


7.85 


2.0605 


8.78 


2.1725 


10.75 


2.3749 


6.58 


1 .8840 


7.22 


1 .9769 


7.86 


2.0618 


8.80 


2.1743 


11.00 


2.3979 


6.59 


1.8856 


7.23 


1.9782 


7.87 


2.0631 


8.82 


2.1770 


11.25 


2.4201 


6.60 


1.8871 


7.24 


1.9796 


7.88 


2.0643 


8.84 


2.1793 


11.50 


2.4430 


6.61 


1 .8886 


7.25 


1.9810 


7.89 


2.0656 


8.86 


2.1815 


11.75 


2.4636 


6.62 


1.8901 


7.26 


1.9824 


7.90 


2.0669 


8.88 


2.1838 


12.00 


2.4849 


6.63 


1.8916 


7.27 


1 .9838 


7.91 


2.0681 


8.90 


2.1861 


12.25 


2.5052 


6.64 


1.8931 


7.28 


1.9851 


7.92 


2.0694 


8.92 


2.1883 


12.50 


2.5262 


6.65 


1 .8946 


7.29 


1 .9865 


7.93 


2.0707 


8.94 


2.1905 


12.75 


2.5455 


6.66 


1.8961 


7.30 


1.9879 


7.94 


2.0719 


8.96 


2.1928 


13.00 


2.5649 


6.67 


1.8976 


7.31 


1 .9892 


7.95 


2.0732 


8.98 


2.1950 


13.25 


2.5840 


6.68 


1.8991 


7.32 


1 .9906 


7.96 


2.0744 


9.00 


2.1972 


13.50 


2.6027 


6.69 


1 .9006 


7.33 


1 .9920 


7.97 


2.0757 


9.02 


2.1994 


13.75 


2.6211 


6.70 


1.9021 


7.34 


1 .9933 


7.98 


2.0769 


9.04 


2.2017 


14.00 


2.6391 


6.71 


1 .9036 


7.35 


1 .9947 


7.99 


2.0782 


9.06 


2.2039 


14.25 


2.6567 


6.72 


1.9051 


7.36 


1.9961 


8.00 


2.0794 


9.08 


2.2061 


14.50 


2.6740 


6.73 


1 .9066 


7.37 


1 .9974 


8.01 


2.0807 


9.10 


2.2083 


14.75 


2.6913 


6.74 


1.9081 


7.38 


1 .9988 


8.02 


2.0819 


9.12 


2.2105 


15.00 


2.7081 


6.75 


1 .9095 


7.39 


2.0001 


8.03 


2.0832 


9.14 


2.2127 


15.50 


2.7408 


6.76 


1.9110 


7.40 


2.0015 


8.04 


2.0844 


9.16 


2.2148 


16.00 


2.7726 


6.77 


1.9125 


7.41 


2.0028 


8.05 


2.0857 


9.18 


2.2170 


16.50 


2.8034 


6.78 


1.9140 


7.42 


2.0041 


8.06 


2.0869 


9.20 


2.2192 


17.00 


2.8332 


6.79 


1.9155 


7.43 


2.0055 


8.07 


2.0882 


9.22 


2.2214 


17.50 


2.8621 


6.80 


1.9169 


7.44 


2.0069 


8.08 


2.0894 


9.24 


2.2235 


18.00 


2.8904 


6.81 


1.9184 


7.45 


2.0082 


8.09 


2.0906 


9.26 


2.2257 


18.50 


2.9178 


6.82 


1.9199 


7.46 


2.0096 


8.10 


2.0919 


9.28 


2.2279 


19.00 


2.9444 


6.83 


1.9213 


7.47 


2.0108 


8.11 


2.0931 


9.30 


2.2300 


19.50 


2.9703 


6.84 


1 .9228 


7.48 


2.0122 


8.12 


2.0943 


9.32 


2.2322 


20.00 


2.9957 


6.85 


1 .9242 


7.49 


2.0136 


8.13 


2.0956 


9.34 


2.2343 


21 


3.0445 


6.86 


1.9257 


7.50 


2.0149 


8.14 


2.0968 


9.36 


2.2364 


22 


3.0910 


6.87 


1.9272 


7.51 


2.0162 


8.15 


2.0980 


9.38 


2.2386 


23 


3.1355 


6.88 


1 .9286 


7.52 


2.0176 


8.16 


2.0992 


9.40 


2.2407 


24 


3.1781 


6.89 


1.9301 


7.53 


2.0189 


8.17 


2.1005 


9.42 


2.2428 


25 


3.2189 


6.90 


1.9315 


7.54 


2.0202 


8.18 


2.1017 


9.44 


2.2450 


26 


3.2581 


6.91 


1 .9330 


7.55 


2.0215 


8.19 


2.1029 


9.46 


2.2471 


27 


3.2958 


6.92 


1 .9344 


7.56 


2.0229 


8.20 


2.1041 


9.48 


2.2492 


28 


3.3322 


6.93 


1.9359 


7.57 


2.0242 


8.22 


2.1066 


9.50 


2.2513 


29 


3.3673 


6.94 


1.9373 


7.58 


2.0255 


8.24 


2.1090 


9.52 


2.2534 


30 


3.4012 


6.95 


1.9387 


7.59 


2.0268 


8.26 


2.1114 


9.54 


2.2555 


31 


3.4340 


6.96 


1 .9402 


7.60 


2.0281 


8.28 


2.1138 


9.56 


2.2576 


32 


3.4657 


6.97 


1.9416 


7.61 


2.0295 


8.30 


2.1163 


9.58 


2.2597 


33 


3.4965 


6.98 


1 .9430 


7.62 


2.0308 


8.32 


2.1187 


9.60 


2.2618 


34 


3.5263 


6.99 


1 .9445 


7.63 


2.0321 


8.34 


2.1211 


9.62 


2.2638 


35 


3.5553 


7.00 


1 .9459 


7.64 


2.0334 


8.36 


2.1235 


9.64 


2.2659 


36 


3.5835 


7.01 


1 .9473 


7.65 


2.0347 


8.38 


2.1258 


9.66 


2.2680 


37 


3.6109 


7.02 


1 .9488 


7.66 


2.0360 


8.40 


2.1282 


9.68 


2.2701 


38 


3.6376 


7.03 


1.9502 


7.67 


2.0373 


8.42 


2.1306 


9.70 


2.2721 


39 


3.6636 


7.04 


1.9516 


7.68 


2.0386 


8.44 


2.1330 


9.72 


2.2742 


40 


3.6889 


7.05 


1.9530 


7.69 


2.0399 


8.46 


2.1353 


9.74 


2.2762 


41 


3.7136 


7.06 


1 .9544 


7.70 


2.0412 


8.48 


2.1377 


9.76 


2.2783 


42 


3.7377 


7.07 


1.9559 


7.71 


2.0425 


8.50 


2.1401 


9.78 


2.2803 


43 


3.7612 


7.08 


1.9573 


7.72 


2.0438 


8.52 


2.1424 


9.80 


2.2824 


44 


3.7842 


7.09 


1.9587 


7.73 


2.0451 


8.54 


2.1448 


9.82 


2.2844 


45 


3.8067 


7.10 


1.9601 


7.74 


2.0464 


8.56 


2.1471 


9.84 


2.2865 


46 


3.8286 


7.11 


1.9615 


7.75 


2.0477 


8.58 


2.1494 


9.86 


2.2885 


47 


5.8501 


7.12 


1 .9629 


7.76 


2.0490 


8.60 


2.1518 


9.88 


2.2905 


48 


3.8712 


7.13 


1 .9643 


7.77 


2.0503 


8.62 


2.1541 


9.90 


2.2925 


49 


3.8918 


7.14 


1.9657 


7.78 


2.0516 


8.64 


2.1564 


9.92 


2.2946 


50 


3.9120 



166 



MATHEMATICAL TABLES. 







NATURAL TRIGONOMETRICAL FUNCTIONS. 






• 


M. 


Sine. 


Co- 
vers. 


Cosec. 


Tang. 


Cotan. 


Se- 
cant. 


Ver. 
Sin. 


Cosine. 






~0~ 


~0 


.00000 


1 .0000 


Infinite 


.00000 


Infinite 


1 .0000 


.00000 


1 .0000 


90 







15 


.00436 


.99564 


229.18 


.00436 


229.18 


1 .0000 


.00001 


.99999 




45 




30 


.00873 


.99127 


114.59 


.00873 


114.59 


1 .0000 


.00004 


.99996 




30 




45 


.01309 


.98691 


76.397 


.01309 


76.390 


1.0001 


.00009 


.99991 




15 


1 





.01745 


.98255 


57.299 


.01745 


57.290 


1.0001 


.00015 


.99985 


89 







15 


.02181 


.97819 


45.840 


.02182 


45.829 


1 .0002 


.00024 


.99976 




45 




30 


.02618 


.97382 


38.202 


.02618 


38.188 


1 .0003 


.00034 


.99966 




30 




45 


.03054 


.96946 


32.746 


.03055 


32.730 


1 .0005 


.00047 


.99953 




15 


3 





.03490 


.96510 


28.654 


.03492 


28.636 


1 .0006 


.00061 


.99939 


88 







15 


.03926 


.96074 


25.471 


.03929 


25.452 


1 .0008 


.00077 


.99923 




45 




30 


.04362 


.95638 


22.926 


.04366 


22.904 


1 .0009 


.00095 


.99905 




30 




45 


.04798 


.95202 


20.843 


.04803 


20.819 


1.0011 


.00115 


.99885 




15 


3 





.05234 


.94766 


19.107 


.05241 


19.081 


1.0014 


.00137 


.99863 


87 







15 


.05669 


.94331 


17.639 


.05678 


17.611 


1.0016 


.00161 


.99839 




45 




30 


.06105 


.93895 


16.380 


.06116 


16.350 


1.0019 


.00187 


.99813 




30 




45 


.06540 


.93460 


15.290 


.06554 


15.257 


1.0021 


.00214 


.99786 




15 


4 





.06976 


.93024 


14.336 


.06993 


14.301 


1.0024 


.00244 


.99756 


86 







15 


.07411 


.92589 


13.494 


.07431 


13.457 


1 .0028 


.00275 


.99725 




45 




30 


.07846 


.92154 


12.745 


.07870 


12.706 


1.0031 


.00308 


.99692 




30 




45 


.08281 


.91719 


12.076 


.08309 


12.035 


1 .0034 


.00343 


.99656 




15 


5 





.08716 


.91284 


11.474 


.08749 


11.430 


1.0038 


.00381 


.99619 


85 







15 


.09150 


.90850 


10.929 


.09189 


10.883 


1 .0042 


.00420 


.99580 




45 




30 


.09585 


.90415 


10.433 


.09629 


10.385 


1 .0046 


.00460 


.99540 




30 




45 


.10019 


.89981 


9.9812 


.10069 


9.9310 


1.0051 


.00503 


.99497 




15 


6 





.10453 


.89547 


9.5668 


.10510 


9.5144 


1.0055 


.00548 


.99452 


84 







15 


.10887 


.89113 


9.1855 


.10952 


9.1309 


1 .0060 


.00594 


.99406 




45 




30 


.11320 


.88680 


8.8337 


.11393 


8.7769 


1 .0065 


.00643 


.99357 




30 




45 


.11754 


.88246 


8.5079 


.11836 


8.4490 


1 .0070 


.00693 


.99307 




15 


7 





.12187 


.87813 


8.2055 


.12278 


8.1443 


1.0075 


.00745 


.99255 


83 







15 


.12620 


.87380 


7.9240 


.12722 


7.8606 


1.0081 


.00800 


.99200 




45 




30 


.13053 


.86947 


7.6613 


.13165 


7.5958 


1 .0086 


.00856 


.99144 




30 




45 


.13485 


.86515 


7.4156 


.13609 


7.3479 


1 .0092 


.00913 


.99086 




15 


8 





.13917 


.86083 


7.1853 


.14054 


7.1154 


1 .0098 


.00973 


.99027 


82 







15 


.14349 


.85651 


6.9690 


.14499 


6.8969 


1.0105 


.01035 


.98965 




45 




30 


.14781 


.85219 


6.7655 


.14945 


6.6912 


1.0111 


.01098 


.98902 




30 




45 


.15212 


.84788 


6.5736 


.15391 


6.4971 


1.0118 


.01164 


.98836 




15 


9 





.15643 


.84357 


6.3924 


.15838 


6.3138 


1.0125 


.01231 


.98769 


81 







15 


.16074 


.83926 


6.2211 


.16286 


6.1402 


1.0132 


.01300 


.98700 




45 




30 


.16505 


.83495 


6.0589 


.16734 


5.9758 


1.0139 


.01371 


.98629 




30 




45 


.16935 


.83065 


5.9049 


.17183 


5.8197 


1.0147 


.01444 


.98556 




15 


10 





.17365 


.82635 


5.7588 


.17633 


5.6713 


1.0154 


.01519 


.98481 


80 







15 


.17794 


.82206 


5.6198 


.18083 


5.5301 


1.0162 


.01596 


.98404 




45 




30 


.18224 


.81776 


5.4874 


.18534 


5.3955 


1.0170 


.01675 


.98325 




30 




45 


.18652 


.81348 


5.3612 


.18986 


5.2672 


1.0179 


.01755 


.98245 




15 


11 





.19081 


.80919 


5.2408 


.19438 


5.1446 


1.0187 


.01837 


.98163 


79 







15 


.19509 


.80491 


5.1258 


.19891 


5.0273 


1.0196 


.01921 


.98079 




45 




30 


.19937 


.80063 


5.0158 


.20345 


4.9152 


1.0205 


.02008 


.97992 




30 




45 


.20364 


.79636 


4.9106 


.20800 


4.8077 


1.0214 


.02095 


.97905 




15 


13 





.20791 


.79209 


4.8097 


.21256 


4.7046 


1 .0223 


.02185 


.97815 


78 







15 


.21218 


.78782 


4.7130 


.21712 


4.6057 


1.0233 


.02277 


.97723 




45 




30 


.21644 


.78356 


4.6202 


.22169 


4.5107 


1 .0243 


.02370 


.97630 




30 




45 


.22070 


.77930 


4.5311 


.22628 


4.4194 


1.0253 


.02466 


.97534 




15 


13 





.22495 


.77505 


4.4454 


.23087 


4.3315 


1 .0263 


.02563 


.97437 


77 







15 


.22920 


.77080 


4.3630 


.23547 


4.2468 


1.0273 


.02662 


.97338 




45 




30 


.23345 


.76655 


4.2837 


.24008 


4.1653 


1 .0284 


.02763 


.97237 




30 




45 


.23769 


.76231 


4.2072 


.24470 


4.0867 


1 .0295 


.02866 


.97134 




15 


14 





24192 


.75808 


4.1336 


.24933 


4.0108 


1.0306 


.02970 


.97030 


76 







15 


.24615 


.75385 


4.0625 


.25397 


3.9375 


1.0317 


.03077 


.96923 




45 




30 


.25038 


.74962 


3.9939 


.25862 


3.8667 


1 .0329 


.03185 


.96815 




30 




45 


.25460 


.74540 


3.9277 


.26328 


3.7983 


1.0341 


.03295 


.96705 




15 


15 





.25882 


.74118 


3.8637 


.26795 


3.7320 


1.0353 


03407 


.96593 


75 







Co- 
sine. 


Ver. 
Sin. 


Secant. 


Cotan 


Tang. 


Cosec. 


Co- 
vers. 


Sine. 


:\i. 



From 75° to 90° read from bottom of table upwards. 



NATURAL TRIGONOMETRICAL FUNCTIONS. 



167 



" 


M. 


Sine. 


Co- 
vers. 


Cosec. 


Tang. Cotan. 


Secant. 


Ver. 

Sin. 


Cosine. 






15 





.25882 


.74118 


3.8637 


.26795 


3.7320 


1.0353 


.03407 


.96593 


75 







15 


.26303 


.73697 


3.8018 


.27263 


3.6680 


1.0365 


.03521 


.96479 




45 




30 


.26724 


.73276 


3.7420 


.27732 


3.6059 


1.0377 


.03637 


.96363 




30 




45 


.27144 


.72856 


3.6840 


.28203 


3.5457 


1.0390 


.03754 


.96246 


74 


15 


16 





.27564 


.72436 


3.6280 


.28674 


3.4874 


1 .0403 


.03874 


.96126 









15 


.27983 


.72017 


3.5736 


.29147 


3.4308 


1.0416 


.03995 


.96005 




45 




30 


.28402 


.71598 


3.5209 


.29621 


3.3759 


1.0429 


.04118 


.95882 




30 




45 


.28820 


.71180 


3.4699 


.30096 


3.3226 


1 .0443 


.04243 


.95757 




15 


17 





.29237 


.70763 


3.4203 


.30573 


3.2709 


1.0457 


.04370 


.95630 


73 







15 


.29654 


.70346 


3.3722 


.31051 


3.2205 


1.0471 


.04498 


.95502 




45 




30 


.30070 


.69929 


3.3255 


.31530 


3.1716 


1 .0485 


.04628 


.95372 




30 




45 


.30486 


.69514 


3.2801 


.32010 


3.1240 


1.0500 


.04760 


.95240 




15 


18 





.30902 


.69098 


3.2361 


.32492 


3.0777 


1.0515 


.04894 


.95106 


73 







15 


.31316 


.68684 


3.1932 


.32975 


3.0326 


1.0530 


.05030 


.94970 




45 




30 


.31730 


.68270 


3.1515 


.33459 


2.9887 


1.0545 


.05168 


.94832 




30 




45 


.32144 


.67856 


3.1110 


.33945 


2.9459 


1.0560 


.05307 


.94693 




15 


19 





.32557 


.67443 


3.0715 


.34433 


2.9042 


1.0576 


.05448 


.94552 


71 







15 


.32969 


.6703 1 


3.0331 


.34921 


2.8636 


1.0592 


.05591 


.94409 




45 




30 


.33381 


.66619 


2.9957 


.35412 


2.8239 


1 .0608 


.05736 


.94264 




30 




45 


.33792 


.66208 


2.9593 


.35904 


2.7852 


1 .0625 


.05882 


.94118 




15 


20 





.34202 


.65798 


2.9238 


.36397 


2.7475 


1 .0642 


.0603 1 


.93969 


70 







15 


.34612 


.65388 


2.8892 


.36892 


2.7106 


1.0659 


.06181 


.93819 




45 




30 


.35021 


.64979 


2.8554 


.37388 


2.6746 


1.0676 


.06333 


.93667 




30 




45 


.35429 


.64571 


2.8225 


.37887 


2.6395 


1 .0694 


.06486 


.93514 




15 


21 





.35837 


.64163 


2.7904 


.38386 


2.6051 


1.0711 


.06642 


.93358 


69 







15 


.36244 


.63756 


2.7591 


.38888 


2.5715 


1.0729 


.06799 


.93201 




45 




30 


.36650 


.63350 


2.7285 


.39391 


2.5386 


1 .0743 


.06958 


.93042 




30 




45 


.37056 


.62944 


2.6986 


.39896 


2.5065 


1 .0766 


.07119 


.92881 




15 


22 





.37461 


.62539 


2.6695 


.40403 


2.4751 


1.0785 


.07282 


.92718 


68 







15 


.37865 


.62135 


2.6410 


.40911 


2.4443 


1 .0804 


.07446 


.92554 




45 




30 


.38268 


.61732 


2.6131 


.41421 


2.4142 


1 .0824 


.07612 


.92388 




30 




45 


.38671 


.61329 


2.5859 


.41933 


2.3847 


1 .0844 


.07780 


.92220 




15 


23 





.39073 


.60927 


2.5593 


.42447 


2.3559 


1 .0864 


.07950 


.92050 


67 







15 


.39474 


.60526 


2.5333 


.42963 


2.3276 


1 .0884 


.08121 


.91879 




45 




30 


.39875 


.60125 


2.5078 


.43481 


2.2998 


1 .0904 


.08294 


.91706 




30 




45 


.40275 


.59725 


2.4829 


.44001 


2.2727 


1 .0925 


.08469 


.91531 




15 


24 





.40674 


.59326 


2.4586 


.44523 


2.2460 


1 .0946 


.08645 


.91355 


66 







15 


.41072 


.58928 


2.4348 


.45047 


2.2199 


1 .0968 


.08824 


.91176 




45 




30 


.41469 


.58531 


2.4114 


.45573 


2.1943 


1.0989 


.09004 


.90996 




30 




45 


.41866 


.58134 


2.3886 


.46101 


2.1692 


1.1011 


.09186 


.90814 




15 


25 





.42262 


.57738 


2.3662 


.46631 


2.1445 


1.1034 


.09369 


.90631 


65 







15 


.42657 


.57343 


2.3443 


.47163 


2.1203 


1.1056 


.09554 


.90446 




45 




30 


.43051 


.56949 


2.3228 


.47697 


2.0965 


5.1079 


.09741 


.90259 




30 




45 


.43445 


.56555 


2.3018 


.48234 


2.0732 


1.1102 


.09930 


.90070 




15 


26 





.43837 


.56163 


2.2812 


.48773 


2.0503 


1.1126 


.10121 


.89879 


64 







15 


.44229 


.55771 


2.2610 


.49314 


2.0278 


1.1150 


.10313 


.89687 




45 




30 


.44620 


.55380 


2.2412 


.49858 


2.0057 


1.1174 


.10507 


.89493 




30 




45 


.45010 


.54990 


2.2217 


.50404 


1 .9840 


1.1198 


.10702 


.89298 




15 


27 





.45399 


.54601 


2.2027 


.50952 


1 .9626 


1.1223 


.10899 


.89101 


63 







15 


.45787 


.54213 


2.1840 


.51503 


1.9416 


1.1248 


.11098 


88902 




45 




30 


.46175 


.53825 


2.1657 


.52057 


1.9210 


1.1274 


.11299 


.88701 




30 




45 


.46561 


.53439 


2.1477 


.52612 


1 .9007 


1.1300 


.11501 


.88499 




15 


28 





.46947 


.53053 


2.1300 


.53171 


1 .8807 


1.1326 


.11705 


.88295 


62 







15 


.47332 


.52668 


2.1127 


.53732 


1.8611 


1.1352 


.11911 


.88089 




45 




30 


.47716 


.52284 


2.0957 


.54295 


1.8418 


1.1379 


.12118 


.87882 




30 




45 


.48099 


.51901 


2.0790 


.54862 


1 .8228 


1.1406 


.12327 


.87673 




15 


29 





.48481 


.51519 


2.0627 


.55431 


1 .8040 


1.1433 


.12538 


.87462 


61 







15 


.48862 


.51138 


2.0466 


.56003 


1.7856 


1.1461 


.12750 


.87250 




45 




30 


.49242 


.50758 


2.0308 


.56577 


1.7675 


1.1490 


.12964 


.87036 




30 




45 


.49622 


.50378 


2.0152 


.57155 


1.7496 


1.1518 


.13180 


.86820 




15 


30 





.50000 


.50000 


2.0000 


.57735 


1.7320 


1.1547 


.13397 


.86603 


60 


_0 






Co- 
sine. 


Ver. 

Sin. 


Se- 
cant. 


Cotan. 


Tang. 


Cosec. 


Co- 
vers. 


Sine. 


• 


M. 



From 60° to 75° read from bottom of table upwards. 



168 



MATHEMATICAL TABLES. 



° 


M. 

~~ 0" 


Sine. 


Co- 
vers. 


Cosec. 


Tang. 


Co tan. 


Secant. 


Ver. 
Sin. 


Cosine 






3tT 


.50000 


.50000 


2.0000 


.57735 


1.7320 


1.1547 


.13397 


.86603 


60 







15 


.50377 


.49623 


1 .9850 


.58318 


1.7147 


1.1576 


.13616 


.86384 




45 




30 


.50754 


.49246 


1.9703 


.58904 


1 .6977 


1.1606 


.13837 


.86163 




30 




45 


.51129 


.48871 


1.9558 


.59494 


1 .6808 


1.1636 


.14059 


.85941 




15 


31 





.51504 


.48496 


1.9416 


.60086 


1 .6643 


1.1666 


.14283 


.85717 


59 







15 


.51877 


.48123 


1.9276 


.60681 


1 .6479 


1.1697 


.14509 


.85491 




45 




30 


.52250 


.47750 


1.9139 


.61280 


1.6319 


1.1728 


.14736 


.85264 




30 




45 


.52621 


.47379 


1 .9004 


.61882 


1.6160 


1.1760 


.14965 


.85035 




15 


33 





.52992 


.47008 


1.8871 


.62487 


1 .6003 


1.1792 


.15195 


.84805 


58 







15 


.53361 


.46639 


1.8740 


.63095 


1 .5849 


1.1824 


.15427 


.84573 




45 




30 


.53730 


.46270 


1.8612 


.63707 


1.5697 


1.1857 


.15661 


.84339 




30 




45 


.54097 


.45903 


1 .8485 


.64322 


1.5547 


1.1890 


.15896 


.84104 




15 


33 





.54464 


.45536 


1.8361 


.64941 


1.5399 


1.1924 


.16133 


.83867 


57 







15 


.54829 


.45171 


1.8238 


.65563 


1.5253 


1.1958 


.16371 


.83629 




45 




30 


.55194 


.44806 


1.8118 


.66188 


1.5108 


1.1992 


.16611 


.83389 




30 




45 


.55557 


.44443 


1 .7999 


.66818 


1 .4966 


1.2027 


.16853 


.83147 




15 


34 





.55919 


.44081 


1.7883 


.67451 


1 .4826 


1 .2062 


.17096 


.82904 


56 







15 


.56280 


.43720 


1.7768 


.68087 


1 .4687 


1 .2098 


.17341 


.82659 




45 




30 


.56641 


.43359 


1.7655 


.68728 


1.4550 


1.2134 


.17587 


.82413 




30 




45 


.57000 


.43000 


1.7544 


.69372 


1.4415 


1.2171 


.17835 


.82165 




15 


35 





.57358 


.42642 


1.7434 


.70021 


1.4281 


1 .2208 


.18085 


.81915 


55 







15 


.57715 


.42285 


1.7327 


.70673 


1.4150 


1.2245 


.18336 


.81664 




45 




30 


.58070 


.41930 


1.7220 


.71329 


1.4019 


1 .2283 


.18588 


.81412 




30 




45 


.58425 


.41575 


1.7116 


.71990 


1.3891 


1.2322 


.18843 


.81157 




15 


36 





.58779 


.41221 


1.7013 


.72654 


1.3764 


1.2361 


.19098 


.80902 


54 







15 


.59131 


.40869 


1.6912 


.73323 


1.3638 


1 .2400 


.19356 


.80644 




45 




30 


.59482 


.40518 


1.6812 


.73996 


1.3514 


1 .2440 


.19614 


.80386 




30 




45 


.59832 


.40168 


1.6713 


.74673 


1.3392 


1 .2480 


.19875 


.80125 




15 


37 





.60181 


.39819 


1.6616 


.75355 


1.3270 


1.2521 


.20136 


.79864 


53 







15 


.60529 


.39471 


1.6521 


.76042 


1.3151 


1.2563 


.20400 


.79600 




45 




30 


.60876 


.39124 


1.6427 


.76733 


1.3032 


1 .2605 


.20665 


.79335 




30 




45 


.61222 


.38778 


1.6334 


.77428 


1.2915 


1 .2647 


.20931 


.79069 




15 


38 





.61566 


.38434 


1.6243 


.78129 


1 .2799 


1 .2690 


.21199 


.78801 


52 







15 


.61909 


.38091 


1.6153 


.78834 


1 .2685 


1.2734 


.21468 


.78532 




45 




30 


.62251 


.37749 


1 .6064 


.79543 


1.2572 


1.2778 


.21739 


.78261 




30 




45 


.62592 


.37403 


1.5976 


.80258 


1 .2460 


1 2822 


.22012 


.77988 




15 


39 





.62932 


.37068 


1.5890 


.80978 


1.2349 


1 .2868 


.22285 


.77715 


51 







15 


.63271 


.36729 


1.5805 


.81703 


1.2239 


1.2913 


.22561 


.77439 




45 




30 


.63608 


.36392 


1.5721 


.82434 


1.2131 


1 .2960 


.22838 


.77162 




30 




45 


.63944 


.36056 


1.5639 


.83169 


1 .2024 


1.3007 


.23116 


.76884 




15 


40 





.64279 


.35721 


1.5557 


.83910 


1.1918 


1.3054 


.23396 


.76604 


50 







15 


.64612 


.35388 


1.5477 


.84656 


1.1812 


1.3102 


.23677 


.76323 




45 




30 


.64945 


.35055 


1.5398 


.85408 


1.1708 


1.3151 


.23959 


.76041 




30 




45 


.65276 


.34724 


1.5320 


.86165 


1 . 1 606 


1 .3200 


.24244 


.75756 




15 


41 





.65606 


.34394 


1.5242 


.86929 


1.1504 


1.3250 


.24529 


.75471 


49 







15 


.65935 


.34065 


1.5166 


.87698 


1.1403 


1.3301 


.24816 


.75184 




45 




30 


.66262 


.33738 


1.5092 


.88472 


1.1303 


1.3352 


.25104 


.74896 




30 




45 


.66588 


.33412 


1.5018 


.89253 


1.1204 


1.3404 


.25394 


.74606 




15 


42 





.66913 


.33087 


1.4945 


.90040 


1.1106 


1.3456 


.25686 


.74314 


48 







15 


.67237 


.32763 


1.4873 


.90834 


1.1009 


1.3509 


.25978 


.74022 




45 




30 


.67559 


.32441 


1 .4802 


.91633 


1.0913 


1.3563 


.26272 


.73728 




30 




45 


.67880 


.32120 


1.4732 


.92439 


1.0818 


1.3618 


.26568 


.73432 




15 


43 





.68200 


.31800 


1 .4663 


.93251 


1 .0724 


1.3673 


.26865 


.73135 


47 







15 


.68518 


.31482 


1.4595 


.94071 


1 .0630 


1.3729 


.27163 


.72837 




45 




30 


.68835 


.31165 


1.4527 


.94896 


1.0538 


1.3786 


.27463 


.72537 




30 




45 


.69151 


.30849 


1.4461 


.95729 


1 .0446 


1.3843 


.27764 


.72236 




15 


44 





.69466 


.30534 


1 .4396 


.96569 


1.0355 


1.3902 


.28066 


.71934 


46 







15 


.69779 


.30221 


1.4331 


.97416 


1 .0265 


1.3961 


.28370 


.71630 




45 




30 


.70091 


.29909 


1 .4267 


.98270 


1.0176 


1 .4020 


.28675 


.71325 




30 




45 


.70401 


.29599 


1 .4204 


.99131 


1 .0088 


1.4081 


.28981 


.71019 




15 


45 





.70711 


.29289 


1.4142 


1 .0000 


1 .0000 


1.4142 


.29289 


.70711 


45 









Cosine 


Ver. 
Sin. 


Se- 
cant. 


Cotan. 


Tang. 


Cosec. 


Co- 
Verc. 


Sine. 





M. 



From 45° to 60° read from bottom of table upwards. 



LOGARITHMIC TRIGONOMETRICAL FUNCTIONS. 169 



LOGARITHMIC SINES, ETC. 





Sine. 


Cosec. 


Versin. 


Tangent 


Co tan. 


Covers. 


Secant. 


Cosine. 







In.Neg. 


Infinite. 


In.Neg. 


In.Neg. 


Infinite. 


1 0.00000 


1 0.00000 


10.00000 


90 


1 


8.24186 


11.75814 


6.18271 


8.24192 


11.75808 


9.99235 


10.00007 


9.99993 


89 


2 


8.54282 


11.45718 


6.78474 


8.54308 


11.45692 


9.98457 


10.00026 


9.99974 


88 


3 


8.71880 


11.28120 


7.13687 


8.71940 


1 1 .28060 


9.97665 


10.00060 


9.99940 


87 


4 


8.84358 


11.15642 


7.38667 


8.84464 


11.15536 


9.96860 


10.00106 


9.99894 


86 


5 


8.94030 


11.05970 


7.58039 


8.94195 


1 1 .05805 


9.96040 


10.00166 


9.99834 


85 


6 


9.01923 


10.98077 


7.73863 


9.02162 


10.97838 


9.95205 


10.00239 


9 99761 


84 


7 


9.08589 


10.91411 


7.87238 


9.08914 


10.91086 


9.94356 


10.00325 


9.99675 


83 


8 


9.14356 


10.85644 


7.98820 


9.14780 


10.85220 


9.93492 


10.00425 


9.99575 


82 


9 


9.19433 


10.80567 


8.09032 


9.19971 


10.80029 


9.92612 


50.00538 


9.99462 


81 


10 


9.23967 


10.76033 


8.18162 


9.24632 


10.75368 


9.91717 


10.00665 


9.99335 


80 


11 


9.28060 


10.71940 


8.26418 


9.28865 


10.71135 


9.90805 


10.00805 


9.99195 


79 


12 


9.31788 


10.68212 


8.33950 


9.32747 


10.67253 


9.89877 


10.00960 


9.99040 


78 


13 


9.35209 


10.64791 


8.40875 


9.36336 


10.63664 


9.88933 


10.01128 


9.98872 


77 


14 


9.38368 


10.61632 


8.47282 


9.39677 


10.60323 


9.87971 


10.01310 


9.98690 


76 


15 


9.41300 


10.58700 


8.53243 


9.42805 


10.57195 


9.86992 


10.01506 


9.98494 


75 


16 


9.44034 


10.55966 


8.58814 


9.45750 


10.54250 


9.85996 


10.01716 


9.98284 


74 


17 


9.46594 


10.53406 


8.64043 


9.48534 


10.51466 


9.84981 


10.01940 


9.98060 


73 


18 


9.48998 


10.51002 


8.68969 


9.51178 


10.48822 


9.83947 


10.02179 


9.97821 


72 


19 


9.51264 


10.48736 


8.73625 


9.53697 


10.46303 


9.82894 


10.02433 


9.97567 


71 


20 


9.53405 


10.46595 


8.78037 


9.56107 


10.43893 


9.81821 


10.02701 


9.97299 


70 


21 


9.55433 


10.44567 


8.82230 


9.58418 


10.41582 


9.80729 


10.02985 


9.97015 


69 


22 


9.57358 


10.42642 


8.86223 


9.60641 


10.39359 


9.79615 


10.03283 


9.96717 


68 


23 


9.59188 


10.40812 


8.90034 


9.62785 


10.37215 


9.78481 


10.03597 


9.96403 


67 


24 


9.60931 


10.39069 


8.93679 


9.64858 


10.35142 


9.77325 


10.03927 


9.96073 


66 


25 


9.62595 


10.37405 


8.97170 


9.66867 


10.33133 


9.76146 


10.04272 


9.95728 


65 


26 


9.64184 


10.35816 


9.00521 


9.68818 


10.31182 


9.74945 


10.04634 


9.95366 


64 


27 


9.65705 


10.34295 


9.03740 


9.70717 


10.29283 


9.73720 


10.05012 


9.94988 


63 


28 


9.67161 


10.32839 


9.06838 


9.72567 


10.27433 


9.72471 


10.05407 


9.94593 


62 


29 


9.68557 


10.31443 


9.09823 


9.74375 


10.25625 


9.71197 


10.05818 


9.94182 


61 


30 


9.69897 


10.30103 


9.12702 


9.76144 


10.23856 


9.69897 


10.06247 


9.93753 


60 


31 


9.71184 


10.28816 


9.15483 


9.77877 


10.22123 


9.68571 


10.06693 


9.93307 


59 


32 


9.72421 


10:27579 


9.18171 


9.79579 


10.20421 


9.67217 


10.07158 


9.92842 


58 


33 


9.73611 


10.26389 


9.20771 


9.81252 


10.18748 


9.65836 


10.07641 


9.92359 


57 


34 


9.74756 


10.25244 


9.23290 


9.82899 


10.17101 


9.64425 


10.08143 


9.91857 


56 


35 


9.75859 


10.24141 


9.25731 


9.84523 


10.15477 


9.62984 


10.08664 


9.91336 


55 


36 


9.76922 


10.23078 


9.28099 


9.86126 


10.13874 


9.61512 


10.09204 


9.90796 


54 


37 


9.77946 


10.22054 


9.30398 


9.87711 


10.12289 


9.60008 


10.09765 


9.90235 


53 


38 


9.78934 


10.21066 


9.32631 


9.89281 


10.10719 


9.58471 


10.10347 


9.89653 


52 


39 


9.79887 


10.20113 


9.34802 


9.90837 


10.09163 


9.56900 


10.10950 


9.89050 


51 


40 


9.80807 


10.19193 


9.36913 


9.92381 


10.07619 


9.55293 


10.11575 


9.88425 


50 


41 


9.81694 


10.18306 


9.38968 


9.93916 


10.06084 


9.53648 


10.12222 


9.87778 


49 


42 


9.82551 


10.17449 


9.40969 


9.95444 


10.04556 


9.51966 


10J2893 


9.87107 


48 


43 


9.83378 


10.16622 


9.42918 


9.96966 


10.03034 


9.50243 


10.13587 


9.86413 


47 


44 


9.84177 


10.15823 


9.44S18 


9.98484 


10.01516 


9.48479 


10.14307 


9.85693 


46 


45 


9.84949 


10.15052 


9.46671 


10.00000 


10.00000 


9.46671 


10.15052 


9.84949 


45 




Cosine. 


Secant. 


Covers. 


Cotan. 


Tangent 


Versin. 


Cosec. 


Sine. 





From 45° to 90° read from bottom of table upwards. 



170 



MATERIALS. 



MATERIALS. 

THE CHEMICAL ELEMENTS. 

Common Elements (42). 



s a 




«;£ 


o"° 




2-? 


g"o 




oi 


Name. 


!•» 


al 


Name. 


a-| c 


al 


Name. 


■% bfl 


P 




& 








6" 




^ 


Al 


Aluminum 


27.1 


F 


Fluorine 


19. 


Pd 


Palladium 


106.5 


Sb 


Antimony 


120.2 


Au 


Gold 


197.2 


P 


Phosphorus 


31. 


As 


Arsenic 


75.0 


H 


Hydrogen 


1.01 


Pt 


Platinum 


194.8 


Ba 


Barium 


137.4 


I 


Iodine 


127.0 


K 


Potassium 


39.1 


Bi 


Bismuth 


209.5 


Ir 


Iridium 


193.0 


Si 


Silicon 


28.4 


B 


Boron 


11.0 


Fe 


Iron 


55.9 


Ag 


Silver 


107.9 


Br 


Bromine 


80.0 


Pb 


Lead 


206.9 


Na 


Sodium 


23. 


Cd 


Cadmium 


112.4 


Li 


Lithium 


7.03 


Sr 


Strontium 


87.6 


Ca 


Calcium 


40.1 


Mg 


Magnesium 


24.36 


S 


Sulphur 


32.1 


C 


Carbon 


12. 


Mn 


Manganese 


55. 


Sn 


Tin 


119. 


CI 


Chlorine 


35.4 


Hg 


Mercury 


200. 


Ti 


Titanium 


48.1 


Cr 


Chromium 


52.1 


Ni 


Nickel 


58.7 


W 


Tungsten 


184.0 


Co 


Cobalt 


59. 


N 


Nitrogen 


14.04 


Va 


Vanadium 


51.2 


Cu 


Copper 


63.6 


O 


Oxygen 


16. 


Zn 


Zinc 


65.4 



The atomic weights of many of the elements vary in the decimal place 
as given by different authorities. The above are the most recent values 
referred to O = 16 and H = 1.008. When H is taken as 1, O = 15.879, 
and the other figures are diminished proportionately. (See Jour. Am. 
Chem. Soc, March, 1896.) 



Rare Elements (27). 



Beryllium, Be. 
Csesium, Cs. 
Cerium, Ce. 
Erbium, Er. 
Gallium, Ga. 
Germanium, Ge. 
Glucinum, G. 



Indium, In. 
Lanthanum, La. 
Molybdenum, Mo. 
Niobium, Nb. 
Osmium, Os. 
Rhodium, R. 
Rubidium, Rb. 



Ruthenium, Ru. 
Samarium, Sm. 
Scandium, Sc. 
Selenium, Se. 
Tantalum, Ta. 
Tellurium, Te. 
Terbium, Tb. 



Thallium, Tl. 
Thorium, Th. 
Uranium, U. 
Ytterbium, Yr. 
Yttrium, Y. 
Zirconium, Zr. 



Elements recently discovered (1900-1905): Argon, A, 39.9; Krypton, 
Kr, 81.8; Neon, Ne, 20.0; Xenon, X, 128.0; constituents of the atmos- 
phere, which contains about 1 per cent by volume of Argon, and very 
small quantities of the others. Helium, He, 4.0; Radium, Ra, 225.0; 
Gadolinium, Gd, 156.0; Neodymium, Nd, 143.6; PraBsodymium, Pr, 140.5; 
Thulium, Tm, 171.0. 



SPECIFIC GRAVITY. 

The specific gravity of a substance is its weight as compared with the 
weight of an equal bulk of pure water. 

To find the specific gravity of a substance. 

W = weight of body in air; w = weight of body submerged in water. 



Specific gravity = 



W 



SPECIFIC GRAVITY. 



171 



If the substance be lighter than the water, sink it by means of a heavier 
substance, and deduct the weight of the heavier substance. 

Specific gravity determinations are usually referred to the standard of 
the weight of water at 62° F., 62.355 lbs. per cubic foot. Some experi- 
menters have used 60° F. as the standard, and others 32° and 39.1° F. 
There is no general agreement. 

Given sp. gr. referred to water at 39.1° F., to reduce it to the standard 
of 62° F. multiply it by 1.00112. 

Given sp. gr. referred to water at 62° F., to find weight per cubic foot 
multiply by 62.355. Given weight per cubic foot, to find sp. gr. multiply 
by 0.016037. Given sp. gr., to find weight per cubic inch multiply by 
0.036085. 



Weight and Specific Gravity of Metals. 





Specific Gravity. 
Range accord- 
ing to 
several 
Authorities. 


Specific Grav- 
ity. Approx. 
Mean Value, 

used in 
Calculation 
of Weight. 


Weight 
per 

Cubic 
Foot, 
lbs. 


Weight 
per 
Cubic 
Inch, 

lbs. 




2.56 to 2.71 
6.66 to 6.86 
9.74 to 9.90 

7.8 to 8.6 

8.52 to 8.96 

8.6 to 8.7 
1.58 
5.0 
8.5 to 8.6 
19.245 to 19.361 
8.69 to 8.92 
22.38 to 23. 

6.85 to 7.48 
7.4 to 7.9 

11.07 to 11.44 
7. to 8. 
1 .69 to 1 .75 
13.60 to 13.62 

13.58 
13.37 to 13.38 
8.279 to 8.93 
20.33 to 22.07 

0.865 
10.474 to 10.511 

0.97 
7.69* to 7.932f 
7.291 to 7.409 

5.3 
17. to 17.6 

6.86 to 7.20 


2.67 
6.76 
9.82 

(8.60 
J8.40 
18.36 
1.8.20 

8.853 

8.65 

1.58 

5.0 

8.55 

19.258 
8.853 

22.38 
7.218 
7.70 

11.38 
8. 
1.75 

13.62 

13.58 

13.38 
8.8 

21.5 
0.865 

10.505 
0.97 
7.854 
7.350 
5.3 

17.3 
7.00 


166.5 
421.6 
612.4 

536.3 

523.8 
521.3 
511.4 

552. 
539. 
98.5 
311.8 
533.1 

1200.9 
552. 

1396. 
450. 
480. 
709.7 
499. 
109. 
849.3 
846.8 
834.4 
548.7 

1347.0 
53.9 
655.1 
60.5 
489.6 
458.3 
330.5 

1078.7 
436.5 


0.0963 




0.2439 




0.3544 


Brass: Copper + Zinc^ 
80 20 
70 30l. . 
60 40 
50 50* 

Rrm^p/CoP-' 95 to 80 1 
Bronze \Tin, 5 to 20/ 


0.3103 
0.3031 
0.3017 
0.2959 

0.3195 
0.3121 




0.0570 




0.1804 


Cobalt. 


0.3085 


Gold, pure 


0.6949 
0.3195 




0.8076 




0.2604 


Iron, Wrought 


0.2779 
0.4106 




0.2887 




0.0641 


( 32° 
Mercury < 60° 

1212° 


0.4915 
0.4900 
0.4828 
0.3175 




0.7758 




0.0312 




0.3791 




0.0350 


Steel 


0.2834 


Tin 


0.2652 




0.1913 




0.6243 




0.2526 







* Hard and burned. 

t Very pure and soft. The sp. gr. decreases as the carbon is increased. 

In the first column of figures the lowest are usually those of cast metals, 
which are more or less porous; the highest are of metals finely rolled or 
drawn into wire. 



172 



MATERIALS. 



Specific Gravity of Liquids at 60° F. 



Acid, Muriatic 1 .200 

" Nitric 1.217 

" Sulphuric. 1.849 

Alcohol, pure 0.794 

95 percent 0.816 

50 per cent 0.934 

Ammonia, 27.9 per cent .. . 0.891 

Bromine 2.97 

Carbon disulphide. .1 1 .26 

Ether, Sulphuric 0.72 

Oil, Linseed, 0.94 



Oil, Olive 0.92 

" Palm 0.97 

" Petroleum 0.78 to 0.88 

" Rape 0.92 

" Turpentine 0.87 

" Whale 0.92 

Tar I. 

Vinegar 1 .08 

Water 1 . 

Water, Sea ............ . 1.026 to 1.03 



Compression of the following Fluids under a Pressure of 15 lbs. 
per Square Inch. 



Water 0.00004663 

Alcohol... 0.0000216 



Ether.... 0.00006158 

Mercury 0.00000265 



The Hydrometer. 

The hydrometer is an instrument for determining the density of liquids. 
It is usually made of glass, and consists of three parts: (1) the upper 
part, a graduated stem or fine tube of uniform diameter; (2) a bulb, or 
enlargement of the tube, containing air; and (3) a small bulb at the 
bottom, containing shot or mercury which causes the instrument to float 
in a vertical position. The graduations are figures representing either 
specific gravities, or the numbers of an arbitrary scale, as in Baume^s 
Twaddell's, Beck's, and other hydrometers. 

There is a tendency to discard all hydrometers with arbitrary scales and 
to use only those which read in terms of the specific gravity directly. 



Baume's Hydrometer and Specific Gravities Compared. 



r„ rni11 u /Heavy liquids, Sp. gr. 
* ormulse \Light liquids, Sp. gr. 



145 ■«- (145 - deg. Be.) 
140 -r- (130 + deg. Be.) 



Degrees 
Baume - 


Liquids 
Heavier 
than 
Water, 
Sp. Gr. 


Liquids 
Lighter 
than 
Water, 
Sp. Gr. 


Degrees 
Baume 


Liquids 
Heavier 

than 
Water, 
Sp. Gr 


Liquids 
Lighter 

than 
Water, 
Sp. Gr. 


Degrees 
Baume" 


Liquids 
Heavier 

than 
Water, 
Sp. Gr. 


Liquids 
Lighter 

than 
Water, 
Sp. Gr. 


0.0 
1.0 
2.0 
3.0 
4.0 
5.0 
6.0 
7.0 
8.0 
9.0 
10.0 
11.0 
12.0 
13.0 
14.0 
15.0 
16.0 
17.0 


1.000 
1.007 
1.014 
1 021 
1.028 
1.036 
1.043 
1.051 
1.058 
1.066 
1.074 
1.082 
1.090 
1.099 
1.107 
1.115 
1.124 
1.133 
1.142 


' Y.666' 
0.993 
0.986 
0.979 
0.972 
0.966 
0.959 
0.952 
0.946 


19.0 
20.0 
21.0 
22.0 
23.0 
24.0 
25.0 
26.0 
27.0 
28.0 
29.0 
30.0 
31.0 
32.0 
33 
34.0 
35.0 
36.0 
37.0 


1.151 
1.160 
1.169 
1.179 
1.189 
1.198 
1.208 
1.219 
1.229 
1.239 
1.250 
1.261 
1.272 
1.283 
1.295 
1.306 
1.318 
1.330 
1.343 


0.940 
0.933 
0.927 
0.921 
0.915 
0.909 
0.903 
0.897 
0.892 
0.886 
0.881 
0.875 
0.870 
0.864 
0,859 
0.854 
0.849 
0.843 
0.838 


38.0 
39.0 
40.0 
41.0 
42.0 
44.0 
46.0 
48.0 
50.0 
52.0 
54.0 
56.0 
58.0 
60.0 
65.0 
70.0 
75.0 


1.355 
1.368 
1.381 
1 394 
1.408 
1.436 
1.465 
1.495 
1.526 
1.559 
1.593 
1.629 
1 .667 
1.706 
1.813 
1.933 
2.071 


0.833 

0.828 
0.824 
0.819 
0.814 
0.805 
0.796 
0.787 
0.778 
0.769 
761 
0.753 
0.745 
0.737 
0.718 
0.700 
0.683 


18.0 

















SPECIFIC GRAVITY. 



173 



Specific Gravity and Weight of Gases at Atmospheric Pressure 
and 32° F. 



(For other temperatures and pressures see Physical Properties of Gases.) 





Density, 
Air = 1 . 


Density, 
H = 1. 


Grammes 
per Litre. 


Lbs. per 
Cu. Ft. 


Cubic Ft. 
per Lb. 


Air 

Oxygen, O 

Hydrogen, H 

Nitrogen, N 

Carbon monoxide, CO . 
Carbon dioxide, CO2 . . 
Methane,marsh-gas, CPU 

Ethylene, C2H4 

Acetylene, C2H2 

Ammonia, NH3 

Water vapor, H2O .... 


1 .0000 
1.1052 
0.0692 
0.9701 
0.9671 
1.5197 
0.5530 
0.9674 
■ 0.8982 
0.5889 
0.6218 


14.444 
15.963 

1.000 
14.012 
13.968 
21.950 

7.987 
13.973 
12.973 

8.506 

8.981 


1 .293 1 
1.4291 
0.0895 
1 .2544 
1.2505 
1 .9650 
0.7150 
1.2510 
1.1614 
0.7615 
0.8041 


0.080728 

0.08921 

0.00559 

0.0783 1 

0.07807 

0.12267 

0.04464 

0.07809 

0.07251 

0.04754 

0.05020 


12.388 
1 1 .209 
178.931 
12.770 
12.810 
8.152 
22.429 
12.805 
13.792 
21.036 
19.922 



Specific Gravity and Weight of Wood. 

















„- 




Specific 









Specific 




^ 




Gravity 




M~ O 

'S0P-1 




Gravity 




lT3o 




. Avge- 






Avge. 




Alder 


0.56 to 0.80 


0,68 


42 


Hornbeam. . 


0.76 


76 


47 


Apple 


0.73 to 0.79 


0.76 


47 


Juniper .... 


0.56 


0.56 


35 


Ash 


0.60 to 0.84 


0.72 


45 


Larch 


0.56 


56 


35 


Bamboo .... 


0.31 to 0.40 


0.35 


22 


Lignum vita 1 


0.65 to 1 .33 


1.00 


62 


Beech 


0.62 to 0.85 


73 


46 


Linden . . . 


0.604 




37 


Birch ...... 


0.56 to 0.74 


65 


41 


Locust 


0.728 




46 


Box 


0.91 to 1.33 


1.12 


70 


Mahogany. . 


0.56 to 1.06 


081 


51 


Cedar. ....... 


0.49 to 0.75 


0,62 


39 


Maple 


0.57 to 0.79 


68 


42 


Cherry. ..... 


0.61 to 0.72 


0.66 


41 


Mulberry. . . 


0.56 to 0.90 


0,73 


46 


Chestnut. . . . 


0.46 to 0.66 


56 


35 


Oak, Live . . 


0.96 to 1 .26 


1 11 


69 


Cork: 


0.24 


24 


15 


Oak, White. 


0.69 to 0.86 


77 


48 


Cvpress ..... 


0.41 to 0.66 


0.53 


33 


Oak, Red . . 


0.73 to 0.75 


74 


46 


Dogwood . . . 


0.76 


0.76 


47 


Pine, White 


0.35 to 0.55 


45 


28 


Ebony 


1.13 to 1.33 


1.23 


76 


" Yellow 


0.46 to 0.76 


61 


38 


Elm........ 


0.55 to 0.78 


0.61 


38 


Poplar 


0.38 to 0.58 


48 


30 


Fir 


0.48 to 0.70 
0.84 to 1 .00 


0.59 
0.92 


37 
57 


Spruce 

Sycamore . . 


0.40 to 0.50 
0.59 to 0.62 


0.45 
60 


28 


Gum 


37 


Hackmatack 


0.59 


59 


37 


Teak 


0.66 to 0.98 


82 


51 


Hemlock. . . . 


0.36 to 0.41 


38 


24 


Walnut 


0.50 to 0.67 


58 


36 


Hickory 


0.69 to 0.94 


0.77 


48 


Willow .... 


0.49 to 0.59 


0,54 


34 


Holly 


0.76 


0.76 


47 











174 



MATERIALS. 



Weight and Specific Gravity of Stones, Brick, Cement, etc. 
Water = 1.00.) 





Lb. per Cu. Ft. 


Sp. Gr. 




87 
100 
112 
125 
135 

140 to 150 
136 
100 
112 

92 
115 

120 to 150 
120 to 155 
72 to 80 
90 to 110 
250 

156 to 172 
180 to 196 

160 to 170 
100 to 120 
130 to 150 
200 to 220 

55 to 57 

50 to 60 
140 to 185 
150 

160 to 180 
140 to 160 
140 to 180 
175 

90 to 100 
104 to 120 

72 

93 to 113 
165 

90 to 110 
118 to 129 
140 to 150 
170 to 180 
166 to 175 
135 to 200 
170 to 200 
110 to 120 


1 39 


Brick, Soft 


1.6 




1.79 


" Hard 


2 




2 16 


Fire 


2 24 to 2 4 




2 18 




1 6 




1.79 




2.8 to 3.2 




3.05 to 3.15 






" " in barrel 




Clay 


1 .92 to 2.4 




1 .92 to 2.48 




1.15 to 1.28 




1 .44 to 1 .76 




4. 


Glass 


2.5 to 2.75 


" flint 


2.88 to 3.14 




2.56 to 2.72 


Granite/ 


1 6 to 1.92 




2.08 to 2.4 




3.2 to 3.52 




0.88 to 0.92 




0.8 to 0.96 




2.30 to 2.90 




2.4 




2.56 to 2.88 




2.24 to 2.56 




2.24 to 2.88 




2.80 




1 .44 to 1 .6 




1 .67 to 1 .92 


Pitch 


1.15 




1.50 to 1.81 




2.64 




1 .44 to 1 .76 




1.89 to 2.07 




2.24 to 2.4 


Slate 


2.72 to 2.88 




2.65 to 2.8 




2.16 to 3.4 


Trap 


2.72 to 3.4 


Tile 


1 .76 to 1 .92 







PROPERTIES OF THE USEFUL METALS. 

Aluminum, Al. — Atomic weight 27.1. Specific gravity 2.6 to 2.7. 
The lightest of all the useful metals except magnesium. A soft, ductile, 
malleable metal, of a white color, approaching silver, but with a bluish 
cast. Very non-corrosive. Tenacity about one third that of wrought 
iron. Formerly a rare metal, but since 1890 its production and use have 
greatly increased on account of the discovery of cheap processes for 
reducing it from the ore. Melts at 1215° F. For further description see 
Aluminum, under Strength of Materials , page 357. 



PROPERTIES OF THE USEFUL METALS. 175 

Antimony (Stibium), Sb. — At. wt. 120.2. Sp. gr. 6.7 to 6.8. A 
brittle metal of a bluish-white color and highly crystalline or laminated 
structure. Melts at 842° F. Heated in the open air it burns with a 
bluish-white flame. Its chief use is for the manufacture of certain alloys, 
as type-metal (antimony 1, lead 4), britannia (antimony 1, tin 9), and 
various anti-friction metals (see Alloys). Cubical expansion by heat 
from 32° to 212° F., 0.0070. Specific heat 0.050. 

Bismuth, Bi. — At. wt. 208.5. Bismuth is of a peculiar light reddish 
color, highly crystalline, and so brittle that it can readily be pulverized. 
It melts at 510° F., and boils at about 2300° F. Sp. gr. 9.823 at 54° F., 
and 10.055 just above the melting-point. Specific heat about 0.0301 at 
ordinary temperatures. Coefficient of cubical expansion from 32° to 
21 2°, 0*.0040. Conductivity for heat about 1/56 and for electricity only 
about V80 of that of silver. Its tensile strength is about 6400 lbs. per 
square inch. Bismuth expands in cooling, and Tribe has shown that 
this expansion does not take place until after solidification. Bismuth is 
the most diamagnetic element known, a sphere of it being repelled by a 
magnet. 

Cadmium, Cd. — At. wt. 112.4. Sp. gr. 8.6 to 8.7. A bluish-white 
metal, lustrous, with a fibrous fracture. Melts below 500° F. and vola- 
tilizes at about 680° F. It is used as an ingredient in some fusible alloys 
with lead, tin, and bismuth. Cubical expansion from 32° to 212° F., 
0.0094. 

Copper, Cu. — At. wt. 63.6. Sp. gr. 8.81 to 8.95. Fuses at about 
1930° F. Distinguished from all other metals by its reddish color. Very 
ductile and malleable, and its tenacity is next to iron. Tensile strength 
20,000 to 30,000 lbs. per square inch. Heat conductivity 73.6% of that 
of silver, and superior to that of other metals. Electric conductivity 
equal to that of gold and silver. Expansion by heat from 32° to 212° F., 
0.0051 of its volume. Specific heat 0.093. (See Copper under Strength 
of Materials; also Alloys.) 

Gold (Aurum), Au. — At. wt. 197.2. Sp. gr., when pure and pressed 
in a die, 19.34. Melts at about 1915° F. The most malleable and duc- 
tile of all metals. One ounce Troy may be beaten so as to cover 160 sq. 
ft. of surface. The average thickness of gold-leaf is 1/282000 of an inch, 
or 100 sq. ft. per ounce. One grain may be drawn into a wire 500 ft. in 
length. The ductility is destroyed by the presence of 1/2000 part of lead, 
bismuth, or antimony. Gold is hardened by the addition of silver or of 
copper. U. S. gold coin is 90 parts gold and 10 parts alloy, which is 
chiefly copper with a little silver. By jewelers the fineness of gold is 
expressed in carats, pure gold being 24 carats, three-fourths fine 18 
carats, etc. 

Iridium, Ir. — Iridium is one of the rarer metals. It has a white 
lustre, resembling that of steel; its hardness is about equal to that of the 
ruby; in the cold it is quite brittle, but at white heat it is somewhat 
malleable. It is one of the heaviest of metals, having a specific gravity 
of 22.38. It is extremely infusible and almost absolutely inoxidizable. 

For uses of iridium, methods of manufacturing it, etc., see paper by 
W. L, Dudley on the "Iridium Industry," Trans. A. I. M. E., 1884. 

Iron (Ferrum),Fe. — At. wt.55.9. Sp.gr.: Cast, 6.85 to 7.48; Wrought, 
7.4 to 7.9. Pure iron is extremely infusible, its melting point being above 
3000° F., but its fusibility increases with the addition of carbon, cast 
iron fusing about 2500° F. Conductivity for heat 11.9, and for electricity 
12 to 14.8, silver being 100. Expansion in bulk bv heat: cast iron 
0.0033, and wrought iron 0.0035, from 32° to 212° F. Specific heat: 
cast iron 0.1298, wrought iron 0.1138, steel 0.1165. Cast iron exposed 
to continued heat becomes permanently expanded 1 1/2 to 3 per cent of its 
length. Grate-bars should therefore be allowed about 4 per cent play. 
(For other properties see Iron and Steel under Strength of Materials.) 

Lead (Plumbum), Pb. — At. wt. 206.9. Sp. gr. 11.07 to 11.44 by dif- 
ferent authorities. Melts at about 625° F., softens and becomes pasty 
at about 617° F. If broken by a sudden blow when just below the 
melting-point it is quite brittle and the fracture appears crystalline. 
Lead is very malleable and ductile, but its tenacity is such that it can 
be drawn into wire with great difficulty. Tensile strength, 1600 to 
2400 lbs. per square inch. Its elasticity is very low, and the metal 



176 MATERIALS. 

flows under very slight strain. Lead dissolves to some extent in pure 
water, but water containing carbonates or sulphates forms over it a 
film of insoluble salt which prevents further action. 

Magnesium, Mg. — At. wt. 24.36. Sp. gr. 1.69 to 1.75. Silver-white, 
brilliant, malleable, and ductile. It is one of the lightest of metals, 
weighing only about two thirds as much as aluminum. In the form of 
filings, wire, or thin ribbons it is highly combustible, burning with a 
light of dazzling brilliancy, useful for signal-lights and for flash-lights 
for photographers. It is nearly non-corrosive, a thin film of carbonate 
of magnesia forming on exposure to damp air, winch protects it from 
further corrosion. It may be alloyed with aluminum, 5 per cent Mg 
added to Al giving about as much increase of strength and hardness as 
10 per cent of copper. Cubical expansion by heat 0.0083, from 32° to 
212° F. Melts at 1200° F. Specific heat 0.25. 

Manganese, In. — At. wt. 55. Sp. gr. 7 to 8. The pure metal is not 
used in the arts, but alloys of manganese and iron, called spiegeleisen 
when containing below 25 per cent of manganese, and ferro-manganese 
when containing from 25 to 90 per cent, are used in the manufacture of 
steel. Metallic manganese, when alloyed with iron, oxidizes rapidly in 
the air, and its function in steel manufacture is to remove the oxygen 
from the bath of steel whether it exists as oxide of iron or as occluded 
gas. 

Mercury (Hydrargyrum), Hg. — At. wt. 199.8. A silver-white metal, 
liquid at temperatures above — 39° F., and boils at 680° F. Unchange- 
able as gold, silver, and platinum in the atmosphere at ordinary tem- 
peratures, but oxidizes to the red oxide when near its boiling-point. 
Sp. gr.: when liquid 13.58 to 13.59, when frozen 14.4 to 14.5. Easily 
tarnished by sulphur fumes, also by dust, from which it may be freed 
by straining through a cloth. No metal except iron or platinum should 
be allowed to touch mercury. The smallest portions of tin, lead, zinc, 
and even copper to a less extent, cause it to tarnish and lose its perfect 
liquidity. Coefficient of cubical expansion from 32° to 212° F. 0.0182; 
per deg. 0.000101. 

Nickel, Ni. — At. wt. 58.7. Sp. gr. 8.27 to 8.93. A silvery-white 
metal with a strong lustre, not tarnishing on exposure to the air. Duc- 
tile, hard, and as tenacious as iron. It is attracted to the magnet and 
may be made magnetic like iron. Nickel is very difficult of fusion, melt- 
ing at about 3000° F. Chiefly used in alloys with copper, as german- 
silver, nickel-silver, etc., and also in the manufacture of steel to increase 
its hardness and strength, also for nickel-plating. Cubical expansion 
from 32° to 212° F., 0.0038. Specific heat 0.109. 

Platinum, Pt. — At. wt. 194.8. A whitish steel-gray metal, malleable, 
very ductile, and as unalterable by ordinary agencies as gold. When 
fused and refined it is as soft as copper. Sp. gr. 21.15. It is fusible only 
by the oxyhydrogen blowpipe or in strong electric currents. When com- 
bined with iridium it forms an alloy of great hardness, which has been 
used for gun-vents and for standard weights and measures. The most 
important uses of platinum in the arts are for vessels for chemical labo- 
ratories and manufactories, and for the connecting wires in incandescent 
electric lamps and for electrical contact points. Cubical expansion from 
32° to 212° F., 0.0027, less than that of any other metal except the rare 
metals, and almost the same as glass. 

Silver (Argentum), Ag. — At. wt. 107.9. Sp. gr. 10.1 to 11.1, accord- 
ing to condition and purity. It is the whitest of the metals, very malle- 
able and ductile, and in hardness intermediate between gold and copper. 
Melts at about 1750° F. Specific heat 0.056. Cubical expansion from 
32° to 212° F., 0.0058. As a conductor of electricity it is equal to copper. 
As a conductor of heat it is superior to all other metals. 

Tin (Stannum), Sn. — At. wt. 119. Sp. gr. 7.293. White, lustrous, 
soft, malleable, of little strength, tenacity about 3500 lbs. per square 
inch. Fuses at 442° F. Not sensiblv volatile when melted at ordinary 
heats. Heat conductivity 14.5, electric conductivity 12.4: silver being 
100 in each case. Expansion of volume bv heat 0.0069 from 32° to 212° F. 
Specific heat 0.055. Its chief uses are for coating of sheet-iron (called 
tin plate) and for making alloys with copper and other metals. 



MEASURES AND WEIGHTS OF VARIOUS MATERIALS. 177 



Zinc, Zn. — At. wt. 65.4. Sp. gr. 7.14. Melts at 780° F. Volatilizes 
land burns in the air when melted, with bluish-white fumes of zinc oxide, 
ilt is ductile and malleable, but to a much less extent than copper, and 
jits tenacity, about 5000 to 6000 lbs. per square inch, is about one tenth 
that of wrought iron. It is practically non-corrosive in the atmosphere, 
a thin film of carbonate of zinc forming upon it. Cubical expansion 
between 32° and 212° F., 0.0088. Specific heat 0.096. Electric conduc- 
tivity 29, heat conductivity 36, silver being 100. Its principal uses are 
for coating iron surfaces, called "galvanizing," and for making brass and 
other alloys. 



Table Showing the Order of 



Gold 

Silver 

Aluminum 

Copper 

Tin 

Lead 

Zinc 

Platinum 

Iron 



Ductility. 


Tenacity. 


Infusibility 


Platinum 


Iron 


Platinum 


Silver 


Copper 


Iron 


Iron 


Aluminum 


Copper 
Gold 


Copper 
Gold 


Platinum 


Silver 


Silver 


Aluminum 


Zinc 


Aluminum 


Zinc 


Gold 


Zinc 


Tin 


Tin 


Lead 


Lead 


Lead 


Tin 



MEASURES AND WEIGHTS OF VARIOUS MATERIALS 
(APPROXIMATE). 

Brickwork. — Brickwork is estimated by the thousand, and for 
various thicknesses of wall runs as follows: 

8i/4-in. wall, or 1 brick in thickness, 14 bricks per superficial foot. 
123/4 " " " 11/2" " " 21 " 

17 " " " 2 " " " 28 " 

211/2 " " " 21/2 " " " 35 " 



An ordinary brick measures about 81/4X4 X 2 inches, which is equal 
to 66 cubic inches, or 26.2 bricks to a cubic foot. The average weight is 
41/2 lbs. 

Fuel. — A bushel of bituminous coal weighs 76 pounds and contains 
26S8 cubic inches = 1.554 cubic feet. 29.47 bushels = 1 gross ton. 

One acre of bituminous coal contains 1600 tons of 2240 pounds per 
foot of thickness of coal worked. 15 to 25 per cent must be deducted for 
waste in mining. 

41 to 45 eubic feet bituminous coal when broken down = 1 ton, 2240 lbs. 

34 to 41 " " anthracite prepared for market. . . =1 ton, 2240 lbs. 

123 " " of charcoal =1 ton, 2240 dbs. 

70.9 " " "coke = 1 ton, 2240 ibs. 

1 cubic foot of anthracite coal = 55 to 66 lbs. 

1 " " " bituminous coal = 50 to 55 lbs. 

1 " " Cumberland (semi-bituminous) coal =53 lbs. 

1 " " Cannel coal = 50.3 lbs. 

1 " " Charcoal (hardwood) = 18.5 lbs. 

1 " " " (pine) =18 lbs. 

A bushel of coke weighs 40 pounds (35 to 42 pounds). 

A bushel of charcoal. — In 1881 the American Charcoal-Iron Work- 
ers' Association adopted for use in its official publications for the stand- 
ard bushel of charcoal 2748 cubic inches, or 20 pounds. A ton of char- 
coal is to be taken at 2000 pounds. This figure of 20 pounds to the 
bushel was taken as a fair average of different bushels used throughout 
the country, and it has since been established by law in some States. 



178 MATERIALS. 



Ores, Earths, etc. 

13 cubic feet of ordinary gold or silver ore, in mine 

20 " " " broken quartz 

18 feet of gravel in bank 

27 cubic feet of gravel when dry 

25 " " " sand . 
18 " 
27 " 
17 " 






1 ton = 2000 lbs. 
■■ 1 ton = 2000 lbs. 

. . . =1 ton. 

=1 ton. 

= 1 ton.; 



1 earth in bank =1 ton. 

earth when dry =1 ton.; 

clay = 1 ton. 



Cement. — Portland, per bbl. net, 376 lbs., per bag, net 94 lbs. 

Nat ural, per bbl. net, 282 lbs., per bag net 94 lbs. 

Lime. — A struck bushel 72 to 75 lbs. 

Grain. — A struck bushel of wheat = 60 lbs.; of corn = 56 lbs.; of i 
oats = 30 lbs. 

Salt. — A struck bushel of salt, coarse, Syracuse, N. Y. = 56 lbs.; 
Turk's Island = 76 to 80 lbs. 



WEIGHT OF RODS, BARS, PLATES, TUBES, AND SPHERES 
OF DIFFERENT MATERIALS. 

Notation: b = breadth, t = thickness, s = side of square, D = ex- 
ternal diameter, d = internal diameter, all in inches. 

Sectional areas: of square bars = s 2 ; of flat bars = bt; of round rods 
= 0.7854 D 2 ; of tubes = 0.7854 (Z> 2 - d 2 ) = 3.1416 (Dt - t 2 ). 

Volume of 1 foot in length: of square bars = 12s 2 ; of flat bars = 12bt; 
of round bars = 9.4248D 2 ; of tubes = 9.4248 (£ 2 - d 2 ) = 37.699 (Dt - P), 
in cu. in. 

Weight per foot length = volume X weight per cubic inch of mate- 
rial. Weight of a sphere = diam. 3 X 0.5236 X weight per cubic inch. 

















































® a 


tH O 




























§ ° m 

°a^ 
5^ M 
Wo § 




Material. 


> 

6 


3 
O ^ 

if 




g^3 

m u^ 

«w ® -- 

o a-g 
.S>5 § 


O <D - 
g oa'M 


3 

a^ 
bo" 




a- 

02 ^ 

JdCQ 




a 
m 


(D&h 


4>-C£ 


^Wf-1 


«P£W 




13 J- 


Stfi^ 






£ 


& 


£ 


& 


£ 


tf£ 


£ 


£ 










s 2 X 


MY 






7) 2 X 


£> 3 X 




7.218 
7.7 


450. 
480. 


37.5 
40. 


31/8 
31/3 


31/8 
31/3 


.2604 
.2779 


15^16 
1. 


2.454 
2.618 


.1363 


Wrought iron 


.1455 


Steel 


7.854 


489.6 


40.8 


3.4 


3.4 


.2833 


1.02 


2.670 


.1484 


Copper & Bronze ) 
(copper and tin) 1 


8.855 


552. 


46. 


3.833 


3.833 


.3195 


1.15 


3.011 


.1673 


Brass | 35 zinc J 


8.393 


523.2 


43.6 


3.633 


3.633 


.3029 


1.09 


2.854 


.1586 


11.38 
2.67 
2.62 
0.481 


709.6 
166.5 
163.4 
30.0 


59.1 
13.9 
13.6 

2.5 


4.93 
1.16 
1.13 
0.21 


4.93 
1.16 
1.13 
0.21 


.4106 
.0963 
.0945 
.0174 


1.48 
0.347 
0.34 
1-16 


3.870 
0.908 
0.891 
0.164 


.2150 




.0504 




.0495 


Pine wood, dry. . . . 


.0091 



Weight per cylindrical in., 
last col.-*- 12. 



1 in. long, — coefficient of D 2 in next to 



SIZES OF IRON AND STEEL BARS. 



179 



For tubes use the coefficient of D 2 in next to last column, as for rods, 
and multiply it into (D 2 - d 2 ); or multiply it by 4 (Dt - t 2 ). 

For hollow spheres use the coefficient of D s in the last column and 
multiply it into (D 3 - d 3 ). 

For hexagons multiply the weight of square bars by 0.866 (short 
diam. of hexagon = side of square). For octagons multiply by 0.8284. 



COMMERCIAL SIZES OF IRON AND STEEL BARS. 

Flats. 



Width. 


Thickness. 


Width. 


Thickness . 


Width. 


Thickness. 


3/4 


1/8 to 5/ 8 


17/8 


1/2 to 1 1/2 


4 


1/4 to 2 


7/8 


1/8 to 3/ 4 


2 


1/8 to 1 3/ 4 


41/2 


1/4 to 2 


1 


1/8 to 15/16 


21/4 


1/4 to 1 3/ 4 


5 


1/4 to 2 


U/8 


1/8 to 1 


23/ 8 


1/4 to 1 1/8 


51/2 


1/4 to 2 


U/4 


1/8 to 1 1/8 


21/2 


3/16 to 1 3/4 


6 


1/4 to 2 


13/8 


1/8 to 1 1/8 


25/ 8 


1/4 to 1 1/8 


61/2 


1/4 to 2 


U/2 


1/8 to 1 l/ 4 


23/ 4 


1/4 to 1 1/8 


7 


1/4 to 2 


15/8 


1/4 to 1 1/4 


3 


1/4 to 2 


71/2 


1/4 to 2 


13/ 4 


3/16 to 1 1/2 


31/2 


1/4 to 2 







Commercial Sizes of Iron and Steel Bars. 



Rounds: Iron. 1/4 to 13/s in., advancing by 1/16 in.; 13/ 8 in. to 5 in., 
advancing by l/s in. Steel. 1/4 in. to li/s in., advancing by 1/32 in.; 
11/8 in. to 2 in., advancing by Vie in.; 2 in. to 4 in., advancing by i/ 8 in.; 
4 to 63/ 4 in., advancing by 1/4 in. Also the following intermediate sizes: 

23/64, 2 5/64, 29/ 64 , 31/64, 33/ 64 , 35/ 64 , 39/ 64 , 47/ 64 , 53/^, 55/ 64 , 63/ 64 , \7/ m and 115/ 32 

in. 

Squares: Iron. 5/i 6 to 11/4 in., advancing by Vie in.; 11/4 to 3 in., 
advancing by Vs in. Steel. 1/4 to 2 in., advancing by Vi6in.; 2 l/s in.; 
21/4 to 4 in., advancing by 1/4 in.; 41/2 in.; 5 in. 

Half rounds: Iron. 7/ m , i/ 2 , 5/ 8 , u/ 16 , 3/ 4i i, n/ 8 , ii/ 4j n/ 2 , 13/4, and 

2 in. Steel. 3/ 8 , 25/ 64 , 13/ 32t 7/ 16 , 29/ 64 , 15/ 32 , l/ 2 , 33/04, 17/ 32 , 9/i6, l 9 /32, 5 / 8 , 2 V 32 , 
11/16, 23 /32, 3/4, 25/ 32 , 13/ 16 , 27/ 32 , 7/ 8 , 29/ 32 , 15/i 6 , 1, 1 1/ 32 , 1 1/ 8? 1 1/ 4? 1 3/ 8 , 1 l/ 2 , 

13/4, 2, 21/2, and 3 in. Weights of half rounds, one half of corresponding 
rounds. See table, page 180. 

Ovals: Iron. 1/2 X 1/4, VsXS/ie, 3 / 4 x 3/ 8 , and 7/ 8 x7/i 6 in. Steel. 

5/8 X 5/i 6 , I/2 X 3/ 8 , 17/32 X 9/ 32 , 9/i 6 X 3/ 8l 19/ 32 X 9/ 32 , 3/ 4 X 5/i 6 , 3/ 4 X 3/ 8 , 7/ 8 X 5/i 6l 

7/8 X 7/i6, 1 X 1/2, and 1 l/s X 9/i6 in. 

Half Ovals: Iron. 1/2 X Vs, 5 / 8 X5/ 32 , 3/ 4 x3/ie, 7/ 8 X7/ 32) 1 1/2 X 1/2. 

13/4X5/8, 17/ 8 X 5/ 8 in. 

Round Edge Flats: Iron. 1 1/2 X 1/2, l 3 / 4 X5/ 8 , 17/ 8 X5/ 8 in. Steel. 

1 X 3/i6, 1 X 1/4, 1 X 5/16, 1 X 3/ 8 , 1 X 7/i6, 1 Vi X 3/ 16 , 1 1/ 4 X l/ 4 , U/4 X 5/ le> 

H/4X 3/ 8 , H/4X 7/i 6 in.; H/2X 1/4 to H/2X 1 in., advancing by i/i 6 in.; 
13/4X1/4 to 13/ 4 x 1 in., advancing by i/i 6 in.; 2X 1/4 to 2 X 1 in., 
advancing by Vi6 in.; 21/4X 1/4 to 21/4X 1 in., advancing by 1/16 in.; 
21/2 X 1/4 to 21/2X 1 in., advancing by i/i 6 in.; 23/ 4 x 1/4 to 23/ 4 x 1 in., 
advancing by i/iein.; 3 X 1/4 to 3 X 1 in., advancing by Vie in. 

Bands: Iron. 1/2 toll/s in., advancing by l/s in., 7 to 16 B. W. G.; 
11/4 to 5 in.; advancing by 1/4 in., 7 to 16 gauge up to 3 in., 4 to 14 gauge, 
31/4 to 5 in. 



180 



MATERIALS. 



WEIGHTS OF SQUARE AND ROUND BARS OF WROUGHT 
IRON IN POUNDS PER LINEAL FOOT. 



Iron weighing 480 lb. per cubic foot. For steel add 2 per cent. 



°K A 


*S«8 ^ 


«*tfM 


o 


•j-SjM 


^PQ o 


O j_ • 


•s £ 5P 


«** w 


m% % 


^ffl O 


°«§ 


X$ 4> 


°W O 


M V CD 


°«§ 


°PQ S 








gQ.S 




SPe ■ 


2Q.S 


j3 gi-} 
'53 3,*^ 


bJ3 c 

M5 









H/16 


24.03 


18.91 


3/8 


96.30 


75.64 


1/16 


0.013 


0.010 


3/4 


25.21 


19.80 


7/16 


98.55 


77.40 


1/8 


.052 


.041 


13/16 


26.37 


20.71 


1/2 


100.8 


79.19 


3/16 


.117 


.092 


7/8 


27.55 


21.64 


•/16 


103.1 


81.00 


1/4 


.208 


.164 


15/16 


28.76 


22.59 


5/8 


105.5 


82.83 


5 /l6 


.326 


.256 


3 


30.00 


23.56 


H/16 


107.8 


84.69 


3/8 


.469 


.368 


1/16 


31.26 


24.55 


3/4 


110.2 


86.56 


7/16 


.638 


.501 


1/8 


32.55 


25.57 


13/16 


112.6 


88.45 


-/2 


.833 


.654 


3/16 


33.87 


26.60 


7/8 


115.1 


90.36 


9/16 


1.055 


.828 


1/4 


35.21 


27.65 


15/16 


117.5 


92.29 


5/8 


1.302 


1.023 


5/16 


36.58 


28.73 


6 


120.0 


94.25 


H/16 


1.576 


1.237 


3/8 


37.97 


29.82 


1/8 


125.1 


98.22 


3/4 


1.875 


1.473 


7/16 


39.39 


30.94 


1/4 


130.2 


102.3 


13/16 


2.201 


1.728 


1/2 


40.83 


32.07 


3 /8 


135.5 


106.4 


7/8 


2.552 


2.004 


9/16 


42.30 


33.23 


1/2 


140.8 


110.6 


15/16 


2.930 


2.301 


5/8 


43.80 


34.40 


5/8 


146.3 


114.9 


1 


3.333 


2.618 


H/16 


45.33 


35.60 


3/4 


151.9 


119.3 


1/16 


3.763 


2.955 


3/4 


46.88 


36.82 


7/8 


157.6 


123.7 


1/8 


4.219 


3.313 


13/16 


48.45 


38.05 


7 


163.3 


128.3 


3/16 


4.70! 


3.692 


7/8 


50.05 


39.31 


1/8 


169.2 


132.9 


1/4 


5.208 


4.091 


15/16 


51.68 


40.59 


1/4 


175.2 


137.6 


5/16 


5.742 


4.510 


4 


53.33 


41.89 


3/8 


181.3 


142.4 


3/8 


6.302 


4.950 


Vl6 


55.01 


43.21 


1/2 


187.5 


147.3 


7/16 


6.888 


5.410 


1/8 


56.72 


44.55 


5/8 


193.8 


152.2 


1/2 


7.500 


5.890 


3/16 


58.45 


45.91 


3/4 


200.2 


157.2 


9/16 


8.138 


6.392 


1/4 


60.21 


47.29 


7/8 


206.7 


162.4 


5/8 


8.802 


6.913 


5/16 


61.99 


48.69 


8 


213.3 


167.6 


H/16 


9.492 


7.455 


3/8 


63.80 


50.11 


1/4 


226.9 


178.2 


3/4 


10.21 


8.018 


7/16 


65.64 


51.55 


1/2 


240.8 


189.2 


13/16 


10.95 


8.601 


1/2 


67.50 


53.01 


3/4 


255.2 


200.4 


7/8 


11.72 


9.204 


9/16 


69.39 


54.50 


9 


270.0 


212.1 


15/16 


12.51 


9.828 


5/8 


71.30 


56.00 


1/4 


285.2 


224.0 


2 


13.33 


10.47 


11/16 


73.24 


57.52 


1/2 


300.8 


236.3 


1/16 


14.18 


11.14 


3/4 


75.21 


59.07 


3/4 


316.9 


248.9 


1/8 


15.05 


11.82 


13/16 


77.20 


60.63 


10 


333.3 


261.8 


3 /l6 


15.95 


12.53 


7/8 


79.22 


62.22 


1/4 


350.2 


275.1 


1/4 


16.88 


13.25 


15/16 


81.26 


63.82 


1/2 


367.5 


288.6 


5/16 


17.83 


14.00 


5 


83.33 


65.45 


3/4 


385.2 


302.5 


3/8 


18.80 


14.77 


Vl6 


85.43 


67.10 


11 


403.3 


3168 


7/16 


19.80 


15.55 


1/8 


87.55 


68.76 


1/4 


421.9 


331.3 


1/2 


20.83 


16.36 


3/16 


89.70 


70.45 


1/2 


440.8 


346.2 


9/16 


21.89 


17.19 


1/4 


91.88 


72.16 


3/4 


460.2 


361.4 


5/8 


22.97 


18.04 


5/16 


94.08 


73.89 


12 


480. 


377. 



WEIGHT OF IRON AND STEEL SHEETS. 



181 



WEIGHT OF IRON AND STEEL SHEETS. 

Weights in Pounds per Square Foot. 

(For weights by the Decimal Gauge, see page 33.) 



Thickness by Birmingham 


Gauge. 


U.S. Standard Gauge, 1893. 
p. 32.) 


(See 


' No", of 
Gauge. 


Thick- 
ness in 
Inches. 


Iron. 


Steel. 


No. of 
Gauge. 


Thick- 
ness, In. 
(Approx.) 


Iron. 


Steel. 


0000 


0.454 


18.16 


18.52 


0000000 


0.5 


20. 


20.40 


000 


.425 


17.00 


17.34 


000000 


0.4688 


18.75 


19.125 


00 


.38 


15.20 


15.50 


00000 


0.4375 


17.50 


17.85 





.34 


13.60 


13.87 


0000 


0.4063 


16.25 


16.575 


1 


.3 


12.00 


12.24 


000 


0.375 


15. 


15.30 


2 


.284 


11.36 


11.59 


00 


0.3438 


13.75 


14.025 


3 


.259 


10.36 


10.57 





0.3125 


12.50 


12.75 


4 


.238 


* 9.52 


9.71 


1 


0.2813 


11.25 


11.475 


5 


.22 


8.80 


8.98 


2 


0.2655 


10.625 


10.837 


6 


.203 


8.12 


8.28 


3 


0.25 


10. 


10.20 


7 


.18 


7.20 


7.34 


4 


0.2344 


9.375 


9.562 


8 


.165 


6.60 


6.73 


5 


0.2188 


8.75 


8.925 


9 


.148 


5.92 


6.04 


6 


0.2031 


8.125 


8.287 


10 


.134 


5.36 


5.47 


7 


0.1875 


7.5 


7.65 


11 


.12 


4.80 


4.90 


8 


0.1719 


6.875 


7.012 


12 


.109 


4.36 


4.45 


9 


0.1563 


6.25 


6.375 


13 


.095 


3.80 


3.88 


10 


0.1405 


5.625 


5.737 


14 


.083 


3.32 


3.39 


11 


0.125 


5. 


5.10 


15 


.072 


2.88 


2.94 


12 


0.1094 


4.375 


4.462 


16 


.065 


2.60 


2.65 


13 


0.0938 


3.75 


3.825 


17 


.058 


2.32 


2.37 


14 


0.0781 


3.125 


3.187 


18 


.049 


1.96 


2.00 


15 


0.0703 


2.8125 


2.869 


19 


.042 


1.68 


1.71 


16 


0.0625 


2.5 


2.55 


20 


.035 


1.40 


1.43 


17 


0.0563 


2.25 


2.295 


21 


.032 


1.28 


1.31 


18 


0.05 


2. 


2.04 


22 


.028 


1.12 


1.14 


19 


0.0438 


1.75 


1.785 


23 


.025 


1.00 


1.02 


20 


0.0375 


1.50 


1.53 


24 


.022 


.88 


.898 


21 


0.0344 


1.375 


1.402 


25 


.02 


.80 


.816 


22 


0.0312 


1.25 


1.275 


26 


.018 


.72 


.734 


23 


0.0281 


1.125 


1.147 


27 


.016 


.64 


.653 


24 


0.025 


1. 


1.02 


28 


.014 


.56 


.571 


25 


0.0219 


0.875 


0.892 


29 


.013 


.52 


.530 


26 


0.0188 


0.75 


0.765 


30 


.012 


.48 


.490 


27 


0.0172 


0.6875 


0.701 


31 


.01 


.40 


.408 


28 


0.0156 


0.625 


0.637 


32 


.009 


.36 


.367 


29 


0.0141 


0.5625 


0.574 


33 


.008 


.32 


.326 


30 


0.0125 


0.5 


0.51 


34 


.007 


.28 


.286 


31 


0.0109 


0.4375 


0.446 


35 


.005 


.20 


.204 


32 


0.0102 


0.40625 


0.414 


36 


.004 


.16 


.163 


33 


0.0094 


0.375 


0.382 










34 


0.0086 


0.34375 


0.351 










35 


0.0078 


0.3125 


0.319 










36 


0.0070 


0.28125 


0.287 










37 


0.0066 


0.26562 


0.271 










38 


0.0063 


0.25 


0.255 



Specific gravity 

Weight per cubic foot . 



Iron. Steel. 

7.7 7.854 

480. 489.6 

0.2778 0.2833 



As there are many gauges in use differing from each other, and even the 
thicknesses of a certain specified gauge, as the Birmingham , are not assumed 
the same by all manufacturers, orders for sheets and wires should always 
state the weight per square foot, or the thickness in thousandths of an inch. 



182 



MATERIALS. 



-oooeooc 
> oo ao oo at 



-©OooOrNiOm^frc^cN — OOoOIn 



niOlNOOOi© — CNcON"U" 



<*i vO © "* oo — mo 
q m_ in tj- co co cn — 
n id in oo' d o — co 



PnO in in oo oo © — 



Nodofo.ts 



oj CN CN CN CN CN CN CN <o 



fiNOmNOf 



nvOtNOOO^OO- 



nco — ooooomco — © 



into — c 
in code 



oo iO If to — c 
©'— "cn'co'co'-< 



cojvooocNma 
in -<r — oo vq c 
© — cn cn to n 



in in to — O oo oc 
^(Nooqinto — 
'm' id in in code 



on- — oor> 



n cn cn cn cn to 



n oo — N- in o c* 



toto^r 
n d id In 



OOOvO 
aq-<t_ 

odd© 



CO — a^O^NONiA 
© — <N CN c 



\OiOIn0O00Oi©©- 



CNm oo O tou - 
vqcojoqin — t^ 

© — — CN to' C> 



ootomooOt<- 
to. o iq cn aq in — 
r'm'm'vdvdi<oc 



0©cO- . 
O O -O (N 



oqin- 



om oo © com oo © 
OtNoom — incoO 
n' id id r-s," oo' od d ©' 



O — — CN CN CO T T if 



niOiOINOOOOOiOiOO- 



© — — CNCNcOcON-N-ininvOoOINtNOOOOOiOi©© — — CNtOCOTN-inm' 
O00 

iOto — con- — oomcNOnOcoooiOcoorNTj' — oo^ - — comcNOOoOcooooOco© 
•"* Oi "T oo to oo tN in cn vO — oO © in O in Oi T Oi to oo to in cn in — iO — in © «n i © 
O* "— — 'cNCN'co'co'VN-'inin'ddtNiN'tNao'co'dd©'©' — ■— ' cn cn co' co V ' 



toONiOOmat^N- 



vOCNOOiOCNOnntNOOm — oCtOtNCOOoOcOOOoOCNOnn — OON - - tNN - © I-- 
to IN O T 00 — in Oi CN iO O to In — N - 00 tN in Oi tN oO i O to , IN — . IT 00 CN | in i OO .to oO 
d '—" — — cn'cn'cn'cWco't't V in m' m' id id od IN In OO CO 00 Oioooooo© — — 



— cNtomiOooooo — to-^imoooooo — to-^-moOooOiO — toN-miOcoooo 
to_ iq o> cn in oo — in oo — n- in o to ■■o © to iO oo cn m aq — in oo_ — "T in o to -© © 
<-> — ' — cn cn cn co' to' to' T ' ^f " N" m i m" m" m" od iO iO in in r> oo oo oo oo oo oo o 

©' 

lOcoiooN-OootNoo-^-OoOrooim — in to Oi m — iNtoOoin — in co oo in — r, .. , 
cn in in o to in oo o to iO oo — to iO c> — N- iO oo cn N - in oo coi^ in in o cn in oq o co 
' — ' — *-' — ' cm' cn cn cn ico' to' co' co' -* ' N - 't' N" in'min'moo lOooiNtNiNrNoooo 

coin m co 

o — cNto^rmioiNooooooo — cNtoco^J-mooiNtNooooo — NcQjjjjin^.^ 

CNN-iOOOOCNN-iOOOOtNinrNOi — CO in rN Oi — co m IN O -CN ^ oO oq O CN ■* oO 

' — — ' — ' — ' — ' cn cn cn cn cn co to to co co ^' ^' ^' ^' in in in in' in od od id oo' 






WEIGHTS OF FLAT WROUGHT IRON. 



183 





« 


oooooooooooooooooooooooo 

in © «n © in O In © m O m o <n , © in o ; © ; © © O O O ; q ; O 
pj in r%'o <N m' r>.' o' cn m' r>." o eN m' r--.' ©' in o m' ©' m o in o 
^^X — — — eNvNvNCNencnenen^r^-mmvovOt^t^oo 


3 


2.29 

4.58 
6.88 
9.17 
11.46 
13.75 
16.04 
18.33 
20.63 
22.92 
25.21 
27.50 
29.79 
32.08 
34.38 
36.67 
41.25 
45.83 
50.42 
55.00 
59.58 
64.17 
68.75 
73.33 


b 


2.08 
4.17 
6.25 

8.33 
10.42 
12.50 
14.58 
16.67 
18.75 
20.83 
22.92 
25.00 
27.08 
29.17 
31.25 
33.33 
37.50 
41.67 
45.83 
50.00 
54.17 
58.33 
62.50 
66.67 


05 


1.88 
3.75 
5.63 
7.50 
9.38 
11.25 
13.13 
15.00 
16.88 
18.75 
20.63 
22.50 
24.38 
26.25 
28.13 
30.00 
33.75 
37.50 
41.25 
45.00 
48.75 
52.50 
56.25 
60.00 


So 


1.77 
3.54 
5.31 
7.08 
8.85 
10.63 
12.40 
14.17 
15.94 
17.71 
19.48 
21.25 
23.02 
24.79 
26.56 
28.33 
31.88 
35.42 
33.96 
42.50 
46.04 
49.58 
53.13 
56.67 


00 


1.67 
3.33 
5.00 
6.67 
8.33 
10.00 
11.67 
13.33 
15.00 
16.67 
18.33 
20.00 
21.67 
23.33 
25.00 
26.67 
30.00 
33.33 
36.67 
40.00 
43.33 
46.67 
50.00 
53.33 


r« 


1.56 
3.13 
4.69 
6.25 
7.81 
9.38 
10.94 
12.50 
14.06 
15.63 
17.19 
18.75 
20.31 
21.88 
23.44 
25.00 
28.13 
31.25 
34.38 
37.50 
40.63 
43.75 
46.88 
50.00 


r» 


1.46 
2.92 
4.38 
5.83 
7.29 
8.75 
10.21 
11.67 
13.13 
14.58 
16.04 
17.50 
18.96 
20.42 
21.88 
23.33 
26.25 
29.17 
32.08 
35.00 
37.92 
40.83 
43.75 
46.67 


CO 


1.41 

2.81 

4.22 

5.63 

7.03 

8.44 

9.84 

11.25 

12.66 

14.06 

15.47 

16.88 

18.28 

19.69 

21.09 

22.50 

25.31 

28.13 

30.94 

33.75 

36.56 

39.38 

42.19 

45.00 


CO 


1.35 
2.71 
4.06 

5.42 
6.77 
8.13 
9.48 
10.83 
12.19 
13.54 
14.90 
16.25 
17.60 
18.96 
20.31 
21.67 
24.38 
27.08 
29.79 
32.50 
35.21 
37.92 
40.63 
43.33 


CO 


1.30 
2.60 
3.91 
5.21 
6.51 
7.81 
9.11 
10.42 
11.72 
13.02 
14.32 
15.63 
16.93 
18.23 
19.53 
20.83 
23.44 
26.04 
28.65 
31.25 
33.85 
36.46 
39.06 
41.67 


b 


1.25 
2.50 
3.75 
5.00 
6.25 
7.50 
8.75 
10.00 
11.25 
12.50 
13.75 
15.00 
16.25 
17.50 
18.75 
20.00 
22.50 
25.00 
27.50 
30.00 
32.50 
35.00 
37.50 
40.00 


w 


1.20 

2.40 

3.59 

4.79 

5.99 

7.19 

8.39 

9.58 

10.78 

11.98 

13.18 

14.38 

15.57 

16.77 

17.97 

19.17 

21.56 

23.96 

26.35 

28.75 

31.15 

33.54 

35.94 

38.33 


»0 


1.15 

2.29 

3.44 

4.58 

5.73 

6.88 

8.02 

9.17 

10.31 

11.46 

12.60 

13.75 

14.90 

16.04 

17.19 

18.33 

20.63 

22.92 

25.21 

27.50 

29.79 

32.08 

34.38 

36.67 


10 


1.09 
2.19 

3.28 

4.38 

5.47 

6.56 

7.66 

8.75 

9.84 

10.94 

12.03 

13.13 

14.22 

15.31 

16.41 

17.50 

19.69 

21.88 

24.06 

26.25 

28.44 

30.63 

32.81 

35.00 


W5 


1.04 

2.08 

3.13 

4.17 

5.21 

6.25 

7.29 

8.33 

9.38 

10.42 

11.46 

12.50 

13.54 

14.58 

15.63 

16.67 

18.75 

20.83 

22.92 

25.00 

27.08 

29.17 

31.25 

33.33 




i! 


cocD«oir>c©222 



T 


~ 


rs-a 


> 


o 




O 


-£ 


x£ 


- 


M 




a; 




c< 


— 


£^£S 



R 








s 




"3 


Z%$'* 


■§ 


A 1.13 £ u 


>> 




o> 


1*11 


a 


C^ g-Q 






V 




S 




■jj-j 


x-S-x 




t>r 5 Xt 


O 


_h £vO<N 








^5 --C 




tr.+- b£ M 


3 


'loll 


* 







184 





40.00 

43.33 

46.67 

50.00 

53.33 

56.67 

60.00 

63.33 

66.67 

70.00 g 

73.33 > 

76.67 t-3 

80.00 H 

83.33 ft 

86.67 £ 

90.00 £ 

93.33 5 

96.67 

00.0 

06.7 

13.3 

20.0 

26.7 

33.3 

40 

46.7 

53.3 

60.0 

66.7 

73.3 

80.0 

86.7 






s 


OmfMDOCMA^Ot^inooOtfMntoomm 

m q rx ao q — ; cn tn^/O^aqo — Ntnin^OrsOtniftcoot'iinoootniAcootf 
tx' o en <i ©' en ' >0 O cn m co — m oo — -T rx ©' cn ©' voVi cd m' — ' rx cn ©' vd cn oc i m' — 
r r V T)-'<r-<TmmmmvO^OvOr>t-«.t>.flOoocoo^O^OO — — cNcncn^-mmvO-Orxoc 






£ 


O O so rx q q q t q N^OO.C^i»t>\qiriiritfi--qa3iNintfvNOcONiAcfit 
iTih,Oc^^O^NinoD— 'tt > >ONinoO'- , tINtf\0 1 ifiO\0(SOO' , to'iri — rstfio 
rAcA^^^^^ in ^^^^ t ^ r ^ I ^ t>,0 O a OO s O N 0-— ■— tS<NcriTr->rininvO< 






1 


0-NtAcAinminiMOiOOOONmT>nintstoo 

n cn 0\ q en p rx "<r — ; cq q q © rx "T — oo q CN q O q q q rx cn O O "f oo en tx - 1 
r^ in rx o en cc — ^' o o^' cn in ix ©' en in cd ^ \d cn tx cn cd en o^ t' ©' m' ©' vd — ' r 
^cncn^r-<3-N-^-ininininvOO>orxrxrxrxoococ>c>©©. cn en en n- t m u 




. 


£ 


OOOOOOOOOOOOOOOOOOOOOOO 

q in q q q q q m q m q q q m q q q m q q q q q q q q q q q q o o c 
©CN'n rx ONin^o'Niri^'o'Nift'NO'Nifio'in'o'inbirio'ifiOino'ino'u 
ciMnf r it f lT1"t'tminininvO>0\OvOrNr>t>.oOoOO>i>00- — <N CN en en -T •» 


3 


©ONcoaoixNOm-^-cneneN — O (Mo on in \0 m en — o O rx m 

m_ ix q en q q cn m oq — ; ■* rx q cm m co — ->t tx en q q q q cn co T q q cn oq en c 

rx' o' cn V -o co' — ' en m' co' ©' cn m' ix o' — ' ■*' -6 od en ix' cn rx — ' ^d © m' ©' -*r o' en oo f 

eNjeNSenenenen'<rTj--q--q-ininininin\OvO^O'Ot^t^OOOOO^O > -00 — — — eSeNe 


£ 


O(0rsmte,(SO00r>UMeiNOC0MTitfiNOt>^OrMnOr>Cl 

© q — cn en •>* in m O rx oo O O O — CN en N - in vO co O <— en in q oq © cn en in ix 1 1 

m rx O- -- en in rx' o' — ' en" m' rx' ©' cn tj-' vd co' o' eN >© ©' m' o' en ix — in ©' ■*' oo cn \0 < ■ 

NfNjNtf|ce\cnrrirA , t"1"^"fininifMnm\O^0>Ot>r>r>oD00ai^OOO--M 


2 


©coqcnOGOmrx©comenOoomenOGOm©m©in©m©mOinO 

in i en CN ! — O q ix , q in en cn — © co ix -O in en cn © ix in i cn © . rx in eN iq rx m ; cn , © ■ ; 

<M -3- --O no © — en in rx' a- — ' en m' \d od ©' eN '■S - <> ©' en" rx -- m' od eN \D o' cn rx — m' 1 1 

eNeNeNeNenenenenenen^r-^--^--^--^-ininininvOvO^Or->t^r^oOoOO^O N O v -0©'' 


5 


©rxcn©rxcn©rxcnorxcn©rxcnorxen©cnrx©cnrx©cnrx©enrx©cnr 
©qen©\Oen©vOen©NOen©^Oen©vOen©envOOenvO©envO©e<*iqOeni 

q — m 'n vO - rd ©" — ' en' in ^6 od ©' — ' en m' \d od O en \d C i en \0 ' O en <©' O en vO © en : 
(s leNf>leNeNeNenenenenenen-<3--^-'T'^-^r'1 - mininvOsOvOt^r>.t~«GOGOGOO^O^ 1 


cs 


OvONcOtnOMn- i^cnco^-OvOeNoOeno^int^aOOeNeninr>GOO-- eninvOJ 
in iO» -T q en r> eN r^. — o © in o -<r O^ en go eN r^ vO m in tj- en eN — ; q q & q r% q < 
^.° TO d — ' en V sd I-n' o' ©' CN en in' vd P^.' cK O CN en vO o' CN in GO — -<r t-> p CN m CO -; ; 
CN>4CNeN(N(NCNenenenenenenen-^ T TTrN-N m ininin\0^O'O^ rs-l^ t^ GO . 


.00 


©'nOm©mO'n©m©m©momOmO©©©©©0©0©00©0$ 
©r^in r> © cn in t^ ocn m t^ ©csm t-> ©CN in ©m ©m qm qm© inqmq J 
in so v»' -O ©' — ' cn' f\ in vo' r>.' od ©' — ' cn en m' ■■6 rx' ©' cn in i< ©' cn m' t--' ©' cn in tx p ; 
— ' — cn cn tN (N eNeNeNeNcncncnmenencnT'<J-TTmmmmvO'0^0*©f> 


ec 


3i-(0tAN-in»cf\(0N'OO^c0enN-iriff 1 NOC^rNiA^NO5tNir;rA : 

■ n in in q q i-n [^ t>s, co co c> c> o © o •— •— cn cn en ■*_ in in q t>. q o_ q q — ; cn en 
CN en ■* in \D r-> od o' O — ' CN en in vO tx cd o' C i — " en i in r^ C> — ' en iflrs © CN N" vO CO : 
— — — — ■ ■— — cNeNeNeNeNCNCNCNeNcncncncncncn-'l-TT r rmmmmm» 


5 


Ornt5 0enrx©enr^©enrx©entx©entx©rxen©rxenor>;en©t>»cnor>.| 
© ao q >n en — © co o m en — O co O m en — © O en © q en q q en q q en q q • 

d ©' — cn en t' m' in vo' r>i cd o' ©' ©' — ' CN cn ^r m! *6 od ©' — '■ en m' \6 cd O •- en in -O ; 
— _ — — . , (scNCNCNCNCNCNCNCNenenenenenen-^rT'^ -, T T r 


2 


DcnmcOOenm!x©enmoO©CNinooOensnOmOmOm©mpin©inO. 
n — ix en © q cn co in — rx en O vO cn co in — tx © CN in ix q cn q t->. q cN q tx q 
x, GO GO O O © — — cN en en ^ in in O O tx cd 00 O ^ CN en in vO tx co © — CN en in J 






-9° 


OCNcn intxooonienintxoo©cNeninixco©entx©enix©fntxOcntx©en. , 
© ^ q cn q © q o en ix — m © n- oo cn q q q q — _ q q q q q — ; q q q q q « 
m' m" in vd O ix rx rx cd GO o' O © O O — ' — " CN CN cn ^ '^ in O tx cd O^ O O •- nj en J 


s 


O — CNenenirmorxaocooo — cNenen^inixnoocNeninrxcoocNeninixl 
in tx q — q q rx q — q q rx © cN ->r q q O CN q O q q q rx — q © tj- q cN q r 
cn cn N en en en en en ■^-' ■*' T -<r in in m m' m' vd ^d vd rx tx rx' oo co o s O O O -^ ^ g 



^ A 



WEIGHTS OF STEEL BLOOMS. 



185 



WEIGHTS OF STEEL BLOOMS. 

Soft steel. 1 cubic inch = 0.284 lb. 1 cubic foot = 490.75 lbs. 











Lengths. 




Size, 
Inches 














1" 


6" 


12" 


18" 


24" 


30" 


36" 


42" 


48" 


54" 


60" 


66" 


12 X6 


20.45 


123 


245 


368 


491 


613 


736 


859 


982 


1 104 


1227 


1350 


X5 


17.04 


102 


204 


307 


409 


511 


613 


716 


818 


920 


1022 


1125 


X4 


13.63 


82 


164 


245 


327 


409 


491 


573 


654 


736 


818 


900 


11 X6 


18.75 


113 


225 


338 


450 


563 


675 


788 


900 


1013 


1 125 


1238 


X5 


15.62 


94 


188 


281 


375 


469 


562 


656 


750 


843 


937 


1031 


X4 


12.50 


75 


150 


225 


300 


375 


450 


525 


600 


675 


750 


825 


10 X8 


22.72 


136 


273 


409 


545 


682 


818 


954 


1091 


1227 


1363 


1500 


X7 


19.88 


120 


239 


358 


477 


596 


715 


835 


955 


1074 


1193 


1312 


X6 


17.04 


102 


204 


307 


409 


511 


613 


716 


818 


920 


1022 


1125 


X5 


14.20 


85 


170 


256 


341 


426 


511 


596 


682 


767 


852 


937 


X4 


11.36 


68 


136 


205 


273 


341 


409 


477 


546 


614 


682 


750 


X3 


8.52 


51 


102 


153 


204 


255 


306 


358 


409 


460 


511 


562 


9 X8 


20.45 


123 


245 


368 


491 


613 


736 


859 


982 


1104 


1227 


1350 


X7 


17.89 


107 


215 


322 


430 


537 


644 


751 


859 


966 


1073 


118! 


X6 


15.34 


92 


184 


276 


368 


460 


552 


644 


736 


828 


920 


1012 


X5 


12.78 


77 


153 


230 


307 


383 


460 


537 


614 


690 


767 


844 


X4 


10.22 


61 


123 


184 


245 


307 


368 


429 


490 


552 


613 


674 


X3 


7.66 


46 


92 


138 


184 


230 


276 


322 


368 


414 


460 


506 


8 X8 


18.18 


109 


218 


327 


436 


545 


655 


764 


873 


982 


1091 


1200 


X7 


15.9 


95 


191 


286 


382 


477 


572 


668 


763 


859 


954 


1049 


X6 


13.63 


82 


164 


245 


327 


409 


491 


573 


654 


736 


818 


900 


X5 


11.36 


68 


136 


205 


273 


341 


409 


477 


546 


614 


682 


750 


X4 


9.09 


55 


109 


164 


218 


273 


327 


382 


436 


491 


545 


600 


X3 


6.82 


41 


82 


123 


164 


204 


245 


286 


327 


368 


409 


450 


7 X7 


13.92 


83 


167 


251 


334 


418 


501 


585 


668 


752 


835 


919 


X6 


11.93 


72 


143 


215 


286 


358 


430 


501 


573 


644 


716 


788 


X5 


9.94 


60 


119 


179 


238 


298 


358 


417 


477 


536 


596 


656 


X4 


7.95 


48 


96 


143 


191 


239 


286 


334 


382 


429 


477 


525 


X3 


5.96 


36 


72 


107 


143 


179 


214 


250 


286 


322 


358 


393 


,61/2X61/2 


12. 


72 


144 


216 


288 


360 


432 


504 


576 


648 


720 


792 


X4 


7.38 


44 


89 


133 


177 


221 


266 


310 


354 


399 


443 


487 


6 X6 


10.22 


61 


123 


184 


245 


307 


368 


429 


490 


551 


613 


674 


X5 


8.52 


51 


102 


153 


204 


255 


307 


358 


409 


460 


511 


562 


; X4 


6.82 


41 


82 


123 


164 


204 


245 


286 


327 


368 


409 


450 


X3 


5.11 


31 


61 


92 


123 


153 


184 


214 


245 


276 


307 


337 


51/2X51/2 


8.59 


52 


103 


155 


206 


258 


309 


361 


412 


464 


515 


567 


X4 


6.25 


37 


75 


112 


150 


188 


225 


262 


300 


337 


375 


412 


5 X5 


7.1C 


43 


85 


128 


170 


213 


256 


298 


341 


383 


426 


469 


X4 


5.68 


34 


68 


102 


136 


170 


205 


239 


273 


307 


341 


375 


! 41/2X41/2 


5.75 


35 


69 


104 


138 


173 


207 


242 


276 


311 


345 


380 


j X4 


5.11 


31 


61 


92 


123 


153 


184 


215 


246 


276 


307 


338 


4 X4 


4.54 


27 


55 


82 


109 


136 


164 


191 


218 


246 


272 


300 


X31/2 


3.97 


24 


48 


72 


96 


119 


143 


167 


181 


215 


238 


262 


X3 


3.4C 


20 


41 


61 


82 


102 


122 


143 


163 


184 


204 


224 


131/2X31/2 


3.4S 


21 


42 


63 


84 


104 


125 


146 


167 


188 


209 


230 


X3 


2.9e 


18 


36 


54 


72 


89 


107 


125 


143 


161 


179 


197 


3 X3 


2.56 


15 


31 


46 


61 


77 


92 


108 123 


138 154 


169 



186 



MATERIALS. 



SIZES AND WEIGHTS OF ROOFING MATERIALS. 

Corrugated Iron or Steel Plates. —Weight per 100 Sq. Ft., Lb. 

(American Sheet and Tin Plate Co., 1905.) 

SCHEDULE OF WEIGHTS. 



Corruga- 
tions. 


5/8 


in. 


U/4 


<3/ 8 in. 


2x1/ 


2 in. 


21/ 2 X 


1/2 in. 


3x3/ 4 in. 


5x7/ 8 in. 


U. S.Std. 


T3 


a 


i. 


h 


T3 


h 


'i 


a 


^3 


c 


T3 




Sheet 
Metal 
Gauge. 




- 




<* — 

d tsj 


.3 
"3 


-3-~ 






g 






g ■ 
— <o 

-« 


28 


72 


87 


72 


87 


68 


85 


68 


85 


68 


85 


68 


85 


27 


79 


94 


79 


94 


76 


91 


76 


91 


76 


91 


76 


91 


26 


86 


101 


86 


101 


83 


98 


83 


98 


83 


98 


83 


98 


25 


100 


115 


100 


115 


96 


11! 


96 


111 


96 


111 


96 


111 


24 


114 


129 


114 


129 


110 


124 


110 


124 


110 


124 


110 


124 


23 






128 
!42 
156 
170 


143 
157 
171 
185 


123 
136 

150 
163 
217 

271 


138 
151 
165 

178 
232 
286 


123 
136 
150 
163 
217 
271 


138 
151 
165 
178 
232 
286 


123 
136 
150 
163 
217 
271 


138 
151 
165 
178 
232 
286 


123 
136 
150 
163 

217 
271 


138 


22 






151 


21 






165 


20 






178 


18 






232 


16 










286 















Covering width of plates, lapped one corrugation, 24 in. Standard 
lengths, 5, 6, 7, 8, 9, and 10 ft.; maximum length, 12 ft. 

Ordinary corrugated sheets should have a lap of 1 1/2 or 2 corrugations 
side-lap for roofing in order to secure water-tight side seams; if the roof 
is rather steep 11/2 corrugations will answer. Some manufacturers make 
a special high-edge corrugation on sides of sheets, and thereby are enabled 
to secure a water-proof side-lap with one corrugation only, thus saving 
. from 6% to 12% of material to cover a given area. 

No. 28 gauge corrugated iron is generally used for applying to wooden 
buildings; but for applying to iron framework No. 24 gauge or heavier 
should be adopted. 

Galvanizing sheet iron adds about 21/2 oz. to its weight per square foot. 

Corrugated Arches. 

For corrugated curved sheets for floor and ceiling construction in fire- . 
proof buildings, No. 16, 18, or 20 gauge iron is commonly used, and sheets 
may be curved from 4 to 10 in. rise — the higher the rise the stronger the 
arch. By a series of tests it has been demonstrated that corrugated ' 
arches give the most satisfactory results with a base length not exceeding: 
6 ft., and 5 ft. or even less is preferable where great strength is required.! 
These corrugated arches are made with 11/4X3/8, 21/2 X 1/2, 3X 3/4 and 
5 X 7/8 in. corrugations, and in the same width of sheet as above men- 
tioned. 

Terra-Cotta. 

Porous terra-cotta roofing 3 in. thick weighs 16 lb. per square foot and 
2 in. thick, 12 lb. per square foot. 

Ceiling made of the same material 2 in. thick weighs 11 lb. per square 
foot. 

Tiles. 

Flat tiles 6V4 X 101/2 X 5/ 8 in. weigh from 1480 to 1850 lb. per square of 
roof (100 square feet), the lap being one-half the length of the tile. 

Tiles with grooves and fillets weigh from 740 to 925 lb. per square of roof.] 

Pan-tiles 141/2X 10 1/2 laid 10 in. to the weather weigh 850 lb. per,; 
square. 



SIZE AND WEIGHT OF ROOFING MATERIALS. 



187 



Standard Weights and Gauges of Tin Plates. 

American Sheet and Tin Plate Co., Pittsburg, Pa. 



rrade term. 


56 1b. 


60 1b. 


65 1b. 


70 1b. 


75 1b. 


80 1b. 


85 1b. 


90 1b. 


95 1b. 


Nearest wire 




















gauge No. 

height per 

sq.ft., lb.. 


38 


37 


35 


35 


34 


33 


32 


31 


31 


0.257 


0.275 


0.298 


0.322 


0.345 


0.367 


0.390 


0.413 


0.436 


height, box, 




















14x20 in., 




















lb 


56 


60 


65 


70 


75 


80 


85 


90 


95 



1001b. 
301/2 
0.459 

100 



Trade term 

Nearest wire gauge 

No 

iVeight per sq. ft., 

lb 

height, box, 14x20, 

lb 



IC 


IXL 


IX 


IXX 


IXXX 


IXXXX 


30 


28 


28 


27 


26 


25 


0.491 


0.588 


0.619 


0.712 


0.803 


0.895 


107 


128 


135 


155 


175 


195 



IXXXXX 

24 

0.987 

215 



Trade term 

height, per sq. ft., lb 

Nearest equivalent in I 

plates 

21/2x17 in. 100 sheets, per 

box. lbs 

7x25 in. 50 sheets, per 

box, lbs 

5x21 in. 100 sheets, per 

box, lbs 



DC 

0.637 


DX 

0.826 


IX 


IXXX 


94 


122 


94 


122 


140 


181 



DXX 
0.962 


DXXX 

1.10 


xxxx 


1-6 X 


142 


162 


142 


162 


211 


241 



DXXXX 
1.23 

1-7 X 

182 

182 

271 



Sizes and Net Weight per Box of 100-lb. (0.459 lb. per sq. ft.) 
Tin Plates. 





Sheets 


Weight 




Sheets 


Weight 


Sheets. 


per 
Box. 


per 
Box. 


Sheets. 


per 
Box. 


per 
Box. 


xl4 


225 


100 


15x15 


225 


161 


4 x20 


112 


100 


16x16 


225 


183 


) x28 


112 


200 


17x17 


225 


206 


3 x20 


225 


143 


18x18 


112 


116 


1 x22 


225 


172 


19x19 


112 


129 


11/2x23 


225 


189 


20x20 


112 


143 


2 Xl2 


225 


103 


21x21 


112 


158 


2 X24 


112 


103 


22x22 


112 


172 


3 X13 


225 


121 


23x23 


112 


189 


J X26 


112 


121 


24x24 


112 


204 


4 xl4 


225 


140 


26x26 


112 


241 


4 x28 


112 


140 


16x20 


112 


114 



Size of 


Sheets. 


14 x3I 


111/ 4 x223/ 4 


13l/ 4 x 173/4 


131/ 4 x191/ 4 


131/oXl91/-> 


13l/ 2 x193/4 


14 X 183/4 


14 X 191/4 


14 X21 


14 X22 


14 X221/4 



151/ 2 x23 



Sheets 


Weight 


per 


per 


Box. 


Box. 


112 


155 


112 


91 


112 


84 


112 


91 


112 


94 


112 


95 


124 


103 


120 


103 


112 


105 


112 


110 


112 


in 


112 


127 



For weight per box of other than 100-lb. plates, multiply by the 
Igures in the fourth line of the two upper tables, and divide by 100. 
Ihus for IX plates 20 X 28 in., 200 X 135 -*- 100 = 270. 
I Tin Plates are made of soft sheet steel coated with tin. The words 
[charcoal" and "coke" plates are trade terms retained from the time 



188 



MATERIALS. 



when high-grade tin plates were made from charcoal iron and lower 
grade from coke iron (sheet iron made with coke as fuel). The terms 
are now used to distinguisli the percentage of tin coating, and the finish. 
Coke plates, with light coating, are used for cans. Charcoal plates are 
designated by letters A to AAAAA, the latter having the heaviest 
coating and the highest polish. Plates lighter than 65-lb. per base box 
(14 X 20 in., 112 plates) are called taggers tin. 

Terne Plates, or Roofing Tin, are coated with an alloy of tin and lead. 
In the "U. S. Eagle, N.M." brand the alloy is 32% tin, 68% lead. 
The weight per 112 sheets of this brand before and after coating is as 
follows: 

IC 14 X 20 IC 20 X 28 IX 14 X 20 IX 20 X 28 . 
Black plates 95 to 100 lb. 190 to 200 lb. 125 to 130 lb. 250 to 260 lb.. 
After coating 115 to 120 230 to 240 145 to 150 290 to 300 

Long terne sheets are made in gauges, Nos. 20 to 30, from 20 to 40 in 
wide and up to 120 in. long. Continuous roofing tin, 10, 14, 20 and 28 in 
wide, is made from terne coated sheets 72, 84 and 96 in. long, single lock 
seam and soldered. 

A box of 112 sheets 14 X 20 in. will cover approximately 192 sq. ft. 
of roof, flat seam, or 583 sheets 1000 sq. ft. For standing seam roofing 
a sheet 20 X 28 in. will cover 475 sq. in., or 303 sheets 1000 sq. ft. A 
box of 112 sheets 20 X 28 in. will cover approximately 370 sq. ft. 

The common sizes of tin plates are 10 X 14 in. and multiples of that 
measure. The sizes most generally used are 14 X 20 and 20 X 28 in. 

Specifications for Tin and Terne Plate. (Penna. R.R. Co., 1903.) 





Material Desired. 




Tin Plate. 


No. I Terne. 


No. 2 Terne, 




Pure tin 
0.023 lb. 

0.496 " 
0.625 " 
0.716 " 
0.808 " 
0.900 " 


26 tin, 74 lead 
0.46 1b. 

0.519 " 

0.648 " 
0.739 " 
0.831 " 
0.923 " 


16tin,841eat 
0.023 lb. 

0.496 " 
0.625 " 
0.716 " 
0.808 " 
0.900 " 


Amount of coating per sq. ft 

Weight per sq. ft. of — 

Grade IC 


Grade IX 


Grade IXX 


Grade IXX 


Grade IXXX 






Will be r 


ejected if less than 


Amount of coating per sq. ft 

Weight per sq. ft. of — 

Grade IC 


0.0183 1b. 

0.468 " 
0.590 " 
0.676 " 
0.763 " 
0.850 " 


0.0413 1b. 

0.490 ** 
0.612 " 
0.699 " 
0.787 " 
0.874 " 


0.0183 1b. 

0.468 " 
0.590 " 

0.676 " 
0.763 " 
0.850 " j 


Grade IX 


Grade IXX 


Grade IXXX 


Grade IXXXX 





Each sheet in a shipment of tin or terne plate must (1) be cut as near! 
exact to size ordered as possible; (2) must be rectangular and flat and frel 
from flaws; (3) must double seam successfully under reasonable treatmen a 
(4) must show a smooth edge with no sign of fracture when bent through 
an angle of 180 degrees and flattened down with a wooden mallet; («'! 
must be so nearly like every other sheet in the shipment, both in thickne 
and in uniformity and amount of coating, that no difficulty will arise il 
the shops, due to varying thickness of sheets. • 



SIZE AND WEIGHT OF ROOFING MATERIALS. 189 



Number and superficial area of slate required for one square of roof. 
(1 square = 100 square feet.) 



Size, 
Inches. 


Num- 
ber per 
Square. 


Area in 
Sq. Ft. 


Size, 
Inches. 


Num- 
ber per 
Square. 


Area in 

Sq.Ft. 


Size, 
Inches. 


Num- 
ber per 
Square. 


Area in 
Sq. Ft. 


6x12 
7x12 
8x12 
9x12 
7x14 
8x14 
9x14 
10x14 
8x16 


533 
457 
400 
355 
374 
327 
291 
261 
277 


267 
"254" 
"246" 


9x16 
10x16 

9x18 
10x18 
12x18 
10x20 
11x20 
12x20 
14x20 


246 
221 
213 
192 
160 
169 
154 
141 
121 


"240" 

"240" 
235 


16x20 
12x22 
14x22 
12x24 
14x24 
16x24 
14x26 
16x26 


137 
126 
108 
114 
98 
86 
89 
78 


23 T ' " 

"228" 

"225" 











As slate is usually laid, the number of square feet of roof covered by one 
slate can be obtained from the following formula: 

width X (length - 3 inches) ,, , . . , . ■ . , 

■ ^r = the number of square feet of roof covered. 

Weight of slate of various lengths and thicknesses required for one 
square of roof: based on the number of slate required for one square of 
roof, taking the weight of a cubic foot of slate at 175 pounds. 



Length 




Weight 


in Pounds per Square for the Thickness. 




Inches. 


1/8 In. 


3/ieIn. 


1/4 In. 


3/8 In. 


1/2 In. 


5/8 In. 


3/ 4 In. 


lln. 


12 


483 


724 


967 


1450 


1936 


2419 


2902 


3872 


14 


460 


688 


920 


1379 


1842 


2301 


2760 


3683 


16 


445 


667 


890 


1336 


1784 


2229 


2670 


3567 


18 


434 


650 


869 


1303 


1740 


2174 


2607 


3480 


20 


425 


637 


851 


1276 


1704 


2129 


2553 


3408 


22 


418 


626 


836 


1254 


1675 


2093 


2508 


3350 


24 


412 


617 


825 


1238 


1653 


2066 


2478 


3306 


26 


407 


610 


815 


1222 


1631 


2039 


2445 


3263 



Pine Shingles. 

Number and weight of shingles required to cover one square of roof: 



[nches exposed to weather 

Number of shingles per square of roof 

Weight of shingles on one square, pound. . . . 



41/2 



51/2 
655 
157 



600 
144 



The number of shingles per square is for common gable-roofs, 
nip-roofs add five per cent to these figures. 



190 



MATERIALS. 



Skylight Glass. 



The weights of various sizes and thicknesses of fluted or rough plate- 
glass required for one square of roof. 



Dimensions in 
Inches. 


Thickness in 
Inches. 


Area in Square 
Feet. 


Weight in Lbs. per 
Square of Roof. 


I2x 48 
15 x 60 
20x100 
94x156 


3/16 
V4 
3/8 

1/2 


3.997 

6.246 

13.880 

101.768 


250 
350 
500 
700 



In the above table no allowance is made for lap. 



If ordinary window-glass is used, single thick glass (about Vie inch) 
will weigh about 82 lb. per square, and double thick glass (about Vs inch) 
will weigh about 164 lb. per square, no allowance being made for lap. A 
box of ordinary window-glass contains as nearly 50 square feet as the 
size of the panes will admit of. Panes of any size are made to order by 
the manufacturers, but a great variety of sizes are usually kept in stock, 
ranging from 6X8 inches to 36 X 60 inches. 



APPROXIMATE WEIGHT OF MATERIALS FOR ROOFS. 

American Sheet and Tin Plate Co. 



Corrugated galvanized iron, No. 20, unboarded 

Copper, 16 oz. standing seam. 

Felt and asphalt, without sheathing. ..... 

Glass, 1/8 in. thick 

Hemlock sheathing, 1 in. thick. 

Lead, about 1/8 in. thick 

Lath and plaster ceiling (ordinary) 

Mackite, 1 in. thick, with plaster 

Neponset roofing, felt, 2 layers 

Spruce sheathing, 1 in. thick 

Slate, 3/ig in. thick, 3 in. double lap 

Slate, 1/8 in. thick, 3 in. double lap 

Shingles, 6 in. X 18 in., 1/3 to weather 

Skylight of glass, 3/jg to 1/2 in., inc. frame 

Slag roof, 4-ply 

Terne plate, IC, without sheathing 

Terne plate, IX, without sheathing 

Tiles (plain), 10 l/ 2 in. X 6 1/4 in. X 5/ 8 - 51/4U1. to weather . 

Tiles (Spanish) Hl/2 in. X 1 1/ 2 in. - 71/4 in. to weather 

White pine sheathing, 1 in. thick 

Yellow pine sheathing, I in. thick 



Average 
Weight, 
Lb. per 
Sq. Ft. 



21/4 

U/4 

2 

13/4 

2 

6 to 8 

6 to 8 

10 

1/2 

21/2 

63/ 4 

41/2 
2 
4 to 10 
4 
1/2 

18 5/8 
8 1/2 
21/2 



WEIGHT OF CAST-IRON PIPES OR COLUMNS. 



191 



WEIGHT OF CAST-IRON PIPES OR COLUMNS. 

In Pounds per Lineal Foot. 

Cast iron = 450 lbs. per cubic foot. 



Jo.re. 


Thick. 

of 
Metal. 


Weight 
per Foot. 


Bore. 


Thick. 

of 
Metal. 


Weight 
per Foot. 


Bore. 


Thick. 

of 
Metal. 


Weight 
per Foot. 


Ins. 


Ins. 


Lbs. 


Ins. 


Ins. 


Lbs. 


Ins. 


Ins. 


Lbs. 


3 


3 /8 


12.4 


10 


3/4 


79.2 


22 


3/4 


167.5 




1/2 


17.2 


10 1/ 2 


1/2 


54.0 




7/8 


196.5 




5/8 


22.2 




5/8 


68.2 


23 


3/4 


174.9 


3 1/2 


3/8 


14.3 




3/4 


82.8 




7/8 


205.1 




1/2 


19.6 


11 


1/2 


56.5 






235.6 




5/8 


25.3 




5/8 


71.3 


24 


3/4 


182.2 


4 


3/8 


16.1 




3/4 


86.5 




7/8 


213.7 




1/2 


22.1 


111/2 


1/2 


58.9 






245.4 




5/8 


28.4 




5/S 


74.4 


25 


3/4 


189.6 


41/2 


3/8 


18.0 




3/4 


90.2 




7/8 


222.3 




1/2 


24.5 


12 


1/2 


61.4 






255.3 




5/8 


31.5 




5/8 


77.5 


26 


3/4 


197.0 




3/8 


19.8 




3/4 


93.9 




7/8 


230.9 


1 


• 1/2 


27.0 


121/2 


1/2 


63.8 






265.1 




5/8 


34.4 




5/8 


80.5 


27 


3/4 


204.3 


51/2 


3/8 


21.6 




3/4 


97.6 




7/8 


239.4 




1/2 


29.4 


13 


1/2 


66.3 






274.9 




5/8 


37.6 




5/8 


83.6 


28 


3/4 


211.7 


6 


3/8 


23.5 




3/4 


101.2 




7/8 


248.1 




1/2 


31.9 


14 


1/2 


71.2 






284.7 




5/8 


40.7 




5/8 


89.7 


29 


3/4 


219.1 


61/2 


3/8 


25.3 




3/4 


108.6 




7/8 


256.6 




1/2 


34.4 


15 


5/8 


95.9 






294.5 




5/8 


43.7 




3/4 


116.0 


30 


7/8 


265.2 


7 


3/8 


27.2 




7/8 


136.4 






304.3 




1/2 


36.8 


16 


5/8 


102.0 




U/8 


343.7 




5/8 


46.8 




3/4 


123.3 


31 


7/8 


273.8 


71/2 


3/8 


29.0 




7/8 


145.0 






314.2 




1/2 


39.3 


17 


5/8 


108.2 




U/8 


354.8 




5/8 


49.9 




3/4 


130.7 


32 


7/8 


282.4 


3 


3/8 


30.8 




7/8 


153.6 






324.0 




1/2 


41.7 


18 


5/8 


114.3 




11/8 


365.8 




5/8 


52.9 




3/ 4 


138.1 


33 


7/8 


291.0 


51/2 


1/2 


44.2 




7/8 


162.1 






333.8 




5/8 


56.0 


19 


5/8 


120.4 




U/8 


376.9 




3/4 


68.1 




3/4 


145.4 


34 


7/8 


299.6 


;> 


1/2 


46.6 




7/8 


170.7 






343.7 




5/8 


59.1 


20 


5/8 


126.6 




U/8 


388.0 




3/4 


71.8 




?/4 


152.8 


35 


7/8 


308.1 


! 'V2 


1/2 


49.1 




7/8 


179.3 






353.4 




5/8 


62.1 


21 


5/8 


132.7 




U/8 


399.0 




3/4 


75.5 




3/4 


160.1 


36 


7/8 


316.6 


il 


1/2 


51.5 




7/8 


187.9 






363.1 




5/8 


65.2 


22 


5/8 


138.8 




U/8 


410.0 



The weight of the two flanges may be reckoned = weight of one foot. 



192 



MATERIALS. 



STANDARD THICKNESSES AND WEIGHTS OF CAST-IRON 
PIPE. 





(U. S. Cast-iron Pipe & Fd' 


y Co., 1908.) 






Class A. 

100 ft. Head. 

43 lb. Pressure. 


Class B. 

200 ft. Head. 

86 lb. Pressure. 


side Diam. Ins. 


Thick- 
ness, Ins. 


Wt. per 


Thick- 
ness, Ins. 


Wt. per 




Ft. 


L'gth. 


Ft. 


L'gth. 


3 


0.39 

.42 

.44 

.46 

.50 

.54 

.57 

.60 

.64 

.67 

.76 

.88 

.99 

1.10 

1.26 

1.35 

1.39 

1.62 

1.72 


14.5 

20.0 

30.8 

42.9 

57.1 

72.5 

89.6 

108.3 

129.2 

150.0 

204.2 

291.7 

391.7 

512.5 

666.7 

800.0 

916.7 

1283.4 

1633.4 


175 
240 
370 
515 
685 
870 
1075 
1300 
1550 
1-800 
2450 
3500 
4700 
6150 
8000 
9600 
11000 
15400 
19600 


0.42 

.45 

.48 

.51 

.57 

.62 

.66 

.70 

.75 

.80 

.89 

1.03 

1.15 

1.28 

1.42 

1.55 

1.67 

1.95 

2.22 


16.2 
21.7 
33.3 
47.5 
63.8 
82.1 
102.5 
125.0. 
150.0 
175.0 
233.3 
333.3 
454.2 
591.7 
750.0 
933.3 
1104.2 
1545.8 
2104.2 


194 
260 
400 
570 
765 
985 


4 


6... 


8 


10 


12 


14 


1230 


16.. . 


1500 


18 .. 


1800 


20.... 


2100 i 


24.... *. 


2800 


30 


4000 


36 


5450 


42 


7100 


48 


9000 


54 


11200 


60 


13250 , 


72 


18550 


84 


25250 








Class C. 

300 ft. Head. 

130 lb. Pressure. 


Class D. 

400 ft. Head. 

173 lb. Pressure. 


sideDiam. Ins. 


Thick- 
ness, Ins 


Wt. per 


Thick- 
ness, Ins. 


Wt. per 




Ft. 


L'gth. 


Ft. 


L'gth. 


3 


0.45 

.48 

.51 

.56 

.62 

.68 

.74 

.80 

.87 

.92 

1.04 

1.20 

1.36 

1.54 

1.71 

1.90 

2.00 

2.39 


17.1 

23.3 

35.8 

52.1 

70.8 

91.7 

116.7 

143.8 

175.0 

208.3 

279.2 

400.0 

545.8 

716.7 

908.3 

1141.7 

1341.7 

1904.2 


205 

280 

430 

625 

850 

1100 

1400 

1725 

2100 

2500 

3350 

4800 

6550 

8600 

10900 

13700 

16100 

22850 


0.48 

.52 

.55 

.60 

.68 

.75 

.82 

.89 

.96 

1.03 

1.16 

1.37 

1.58 

1.78 

1.96 

2.23 

2.38 


18.0 

25.0 

38.3 

55.8 

76.7 

100.0 

129.2 

158.3 

191.7 

229.2 

306.7 

450.0 

625.0 

825.0 

1050.0 

1341.7 

1583.3 


216 l 


4 


300 1 


6 


460 \ 


8 


670 lit 


10 


920 1 


12 


1200 


14 . . 


1550 


16... 


1900 


18 


2300 


20 


2750 


24 


3680 1 


30 


5400 1 


36 


7500 


42 


9900 


48 


12600 


54 ... 


16100 


60 

72 


19000 


84 


::: 1 






The above w 
sockets; propor 


eights ar 
tionate al 


i per leng 
owance t( 


th to lay 

) be made 


12 feet, i 
for any v 


ncluding 
ariation. 


1 

i 



THICKNESS OF CAST-IRON WATER-PIPES. 



193 



Standard Thicknesses and Weights of Cast-iron Pipe. 

FOR FIRE-LINES AND OTHER HIGH-PRESSURE SERVICE. 
(U. S. Cast-Iron Pipe & Fd'y Co., 1908.) 



i d 


Class E. 


Class F. 


Class G. 




Class H. 


500 ft. Head. 


600 ft. Head. 


700 ft. Head. 


800 ft iit-i.l 


•3 s 


217 1b. 


260 lb. 


304 lb. 




347 lb. 


•'- c 


Wt. per 


v a 


Wt. per 


v C 


Wt. per 


Jk c ' 


Wt. per 


$1 


IS r f 

rn OB 




z ' 




IS £ 




is •/■ 




Ft. 


L'gth 


Ft. 


L'gth 


Ft. 


L'gth 


Ft. 


L'gth 




c 












C 






c 






i 6 


n 5,s 


41.7 


500 


61 


43.3 


520 


65 


47.1 


565 


69 


49.6 


595 


8 


66 


61.7 


740 


71 


65.7 


790 


75 


70.8 


850 


80 


75.0 


900 


J 10 


74 


86.3 


1035 


80 


92.1 


1105 


86 


100.9 


1210 


.92 


106.7 


1280 


12 


87 


113.8 


1365 


89 


122.1 


1465 


97 


135.4 


1625 


1 04 


143.8 


1725 


14 


Q0 


145.0 


1740 


99 


157.5 


1890 


1 07 


174.2 


2090 


1 16 


186.7 


2240 


16 


98 


179. i 


2155 


1 08 


195.4 


2345 


1 18 


219.2 


2620 


1 7.7 


232.5 


2790 


18 


1 07 


220.4 


2645 


1 17 


238.4 


•2860 


1 78 


267.1 


3205 


1 39 


286.7 


3440 


20 


1 15 


263.0 


3155 


1 27 


286.3 


3435 


1 39 


320.8 


3850 


1 51 


344.6 


4135 


24 


1 31 


359.6 


4315 


1 45 


392.9 


4715 














30 


1 55 


521.7 


6260 


1 73 


585.4 


7025 














36 


1.80 


725.0 


8700 


2.02 


820.0 


9840 















The above weights are per length to lay 12 feet, including standard 
iockets; proportionate allowance to be made for any variation. 

Weight of Underground Pipes. (Adopted by the Natl. Fire Pro- 
action Association, 1905). Weights are not to be less than those specified 
when the normal pressures do not exceed 125 lbs. per sq. in. When the 
lormal pressures are in excess of 125 lbs. heavier pipes should be used. 
The weights given include sockets. 

Pipe, ins 

Weights per foot, lbs 



6 


8 


10 


12 


14 


16 


32 


48 


67 


87 


109 


133 



THICKNESS OF CAST-IRON WATER-PIPES. 

P. H. Baermann, in a paper read before the Engineers' Club of Phila- 
ielphia in 1882, gave twenty different formulas for determining the thick- 
iess of cast-iron pipes under pressure. The formulas are of three classes: 

1. Depending upon the diameter only. 

2. Those depending upon the diameter and head, and which add a con- 
stant. 

3. Those depending upon the diameter and head, contain an additive 
or subtractive term depending upon the diameter, and add a constant. 

I The more modern formulas are of the third class, and are as follows: 

.! = 0.00008/id + O.Old + 0.36 Shedd, No. 1. 

= 0.00006/id + 0.0133d + 0.296 Warren Foundry, No. 2. 

; = 0.000058/id + 0.0152d -I- 0.312 Francis, No. 3. 

= 0.000048/id + 0.013d + 0.32 . Dupuit, - No. 4. 

! = 0.00004/wZ + 0.1 ^d + 0.15 Box, No. 5. 

! = 0.000135/id + 0.4 - O.OOlld Whitman, No. 6. 

J = 0.00006(ft + 230)d + 0.333 - 0.0033d Fanning, No. 7. 

! = 0.00015ftd 4- 0.25 - 0.0052d Meggs, No. 8. 



194 



MATERIALS. 



In which t - thickness in inches, A = head in feet, d = diameter in inches. 
For ft = 100 ft., and d = 10 in., formulae Nos. 1 to 7 inclusive give to from 
0.49 to 0.54 in., but No. 8 gives only 0.35 in. Fanning's formula, now 
(1908) in most common use, gives 0.50 in. 

Rankine (Civil Engineering," p. 72-1) says: "Cast-iron pipes should be 
made of a soft and tough quality of iron. Great attention should be paid 
to molding them correctly, so that the thickness may be exactly uniform 
all round. Each pipe should be tested for air-bubbles and flaws by ring- 
ing it with a hammer, and for strength by exposing it to double the 
intended greatest working pressure." The rule for computing the thick- 
ness of a pipe to resist a given working pressure is t = rp/f, where r is 
the radius in inches, p the pressure in pounds per square inch, and / the 
tensile strength of the iron per square inch. When f = 18,000, and a 
factor of safety of 5 is used, the above expressed in terms of d and hi 
becomes t = 0.5d X 0.433ft ■*- 3600 = 0.00006dft. 

"There are limitations, however, arising from difficulties in casting, and 
by the strain produced by shocks, which cause the thickness to be made 
greater than that given by the above formula." (See also Bursting 
Strength of Cast-iron Cylinders, under "Cast Iron.") 

The most common defect of cast-iron pipes is due to the "shifting oi 
the core," which causes one side of the pipe to be thinner than the other. 
Unless the pipe is made of very soft iron the thin side is apt to be chilled 
in casting, causing it to become brittle and it may contain blow-holes and 
"cold-shots." This defect should be guarded against by inspection oi 
every pipe for uniformity of thickness. 



Safe Pressures and Equivalent Heads of Water for Cast-iron Pipe 
of Different Sizes and Thicknesses. 

(Calculated by F. H. Lewis, from Fanning's Formula.) 





Size of Pipe. 




4" 


6" 


8" 


10" 


12" 


14" 


16" 


18" 


20" 


Thickness. 


*3 




i-3 








3 




3 
h! 




3 




1 




Hi 




J 


































d 












Uh 




Uh 




Uh 




ft 




ft 




ft 




ft 




Uh 




Uh 












































a 




d 
















d 




d 












d 




d 




d 












^ 




d 




5 




d 








TS 












— 




—■ 




— 




— 








-) 








ft 
49 


a; 
112 


ft 
18 


O 
ft 

42 


CD 
ft 


X 


9 
ft 


03 


CD 
ft 




0^ 

ft 




ft 


8) 


ft 


CD 


7/16 


112 


258 


l/ 2 ........ 


224 


516 


124 




74 


171 


44 


101 


24 


55 


















9/16 


336 


774 


199 


458 


130 


300 


89 


205 


62 


143 


42 


97 














5/8 






774 


631 


186 


4?:-) 


13?, 


304 


99 


228 


74 


1 70 


56 


129 


41 


95 






ll/l 6 














177 

224 


516 


137 
174 
212 
249 


316 
401 

488 
574 


106 
138 
170 

202 
234 
266 


316 
392 
465 
538 
612 


84 
112 
140 
168 
196 
224 


194 
258 
323 
387 
452 
516 


66 
91 
116 
141 
166 
191 
216 


152 
210 

267 
325 
382 
440 
497 


51 

74 
96 
119 
14! 
164 
209 
256 


lit 

17( 
221 
27^ 
32! 
37c 
481 
58< 


3/ 4 














13/ 16 














7 /8 


















15 /l6- • • • 


















1 






















1 l/ 8 






















' Vi 

































































THICKNESS OF CAST-IRON WATER-PIPES. 



195 



Safe Pressures, etc., for Cast-iron Pipe. — (Continued.) 



















Size of Pipe. 


















22" 


24" 


27" 


30" 


33" 


36" 


42" 


48" 


60" 


Thickness. 


ja 

h! 




hi 




HH 








h! 




ja 
h1 




,3 

Hi 




ja 




Hi 














































U^ 




l*t 




l=q 


Ti 


Uh 




^ 




(^ 


m 


Uh 




[hh 


■~ 


Uh 










rt 




fl 












C 








fl 




(3 




3 




a 




3 












3 








" 












T5 




T5 








— 




— 
















TJ 


























«( 








rt 




rt 










































Ph 
40 


a 

92 


Ph 
30 


69 


Ph 
19 


64 


Ph 


W 


Ph 


a 


Ph 


W 


Ph- 


a 


Ph 


a 


Ph 


a 


H/16 




3/4 


60 


138 


49 


113 


36 


83 


24 


55 






















13/16 


80 


184 


68 


157 


52 


120 


39 


90 






















7/8 


101 


233 


86 


198 


69 


159 


54 


124 


42 


97 


32 


74 














15/16 


121 


279 


105 


14 ! 


85 


196 


69 


159 


55 


127 


44 


101 














1 


142 
187, 


327 
419 


124 
161 


286 
371 


102 
135 


235 
311 


84 
114 


194 
263 


69 
96 


159 

221 


57 

82 


131 

189 


38 

59 


88 

136 


24 
43 


55 
99 






11/8 




1 1/4 


224 


516 


199 


458 


169 


389 


144 


12 


124 


16 


107 


247 


81 


187 


62 


143 


34 


78 


13/ 8 






237 


"746 


202 


465 


174 


401 


151 


.348 


132 


304 


103 


237 


81 


187 


49 


113 


1 l/ 2 










236 


544 


204 
234 


470 
538 


178 
205 
733 


410 

472 
537 


157 
182 
?07 


3*2 
4.9 

477 


124 
145 
167 


286 
334 

385 


99 
Ufa 

136 


228 
:\ 
313 


64 
79 
94 


147 


1 5/ 8 










18"? 


13/ 4 














?17 


1 7/ 8 


























188 


433 


155 


357 


100 


?51 


2 


























710 


484 


174 


40! 


174 


^86 


2 1/8 

21/4 

21/2 






























193 


^45 


no 


3?n 






























?1? 


488 


|S4 


355 


































184 


474 


2 3/ 4 


































214 


48? 







































Note. — The absolute safe static pressure which may 
be put upon pipe is given by the formula P = 2TS/5D, 
in which formula P is the pressure per square inch; T, 
the thickness of the shell; S, the ultimate strength per 
square inch of the metal in tension; and D, the inside 
diameter of the pipe. In the tables *S is taken as 18,000 
pounds per square inch, with a working strain of one- 
fifth this amount or 3600 pounds per square inch. The 
formula for the absolute safe static pressure then is: 
P = 7200/D. 

It is, however, usual to allow for "water-ram" by 
increasing the thickness enough to provide for 100 
pounds additional static pressure, and, to insure suffi- 
cient metal for good casting and for wear and tear, a 
further increase equal to 0.333 (1 - 0.01 D). 

The expression for the thickness then becomes 



(P + 100)P 



+ 0.333 



- 0.333 (1 






100. 



7200 
and for safe working pressure 

p = ?f°(r- 

The additional section provided as above represents 
an increased value under static pressure for the different 
sizes of pipe as follows (see table in margin). So that 
to test the pipes up to one-fifth of the ultimate strength 
of the material, the pressures in the marginal table 
should be added to the pressure-values given in the 
table above. 



Size 




of 


Lbs. 


Pipe. 




4" 


676 


6 


476 


8 


346 


10 


316 


12 


276 


14 


248 


16 


226 


18 


209 


20 


196 


22 


185 


24 


176 


27 


165 


30 


156 


33 


149 


36 


143 


42 


133 


48 


126 


60 


116 



196 



MATERIALS. 



/ 



CAST-IRON PIPE-FITTINGS. 

Approximate Weights (The Massilon Iron & Steel Co.). 



m 


0) 




Hi 


m 




Ol 


o> 






g 




rg 


P 


4) 


A 


o 





a 


o 


03 


-g 

a 


e 


1 




o 


H 




O 


H 


M 


D 


H 




Q 


H 


3x3 


85 


65 


14x14 


665 


525 


20x12 


900 


800 


36x36 


4160 


3490 


4x4 


115 


90 


14x10 


530 


445 


20x8 


730 


665 


36x30 


3475 


3010 


4x3 


105 


85 


14x6 


390 


350 


20x3 


565 


545 


36x24 


2920 


2585 


6x6 


165 


130 


14x3 


330 


310 


24x24 


1800 


1565 


36x20 


2550 


2315 


6x3 


125 


105 


16x16 


810- 


735 


24x18 


1480 


1280 


36x18 


2370 


2175 


8x8 


290 


230 


16x12 


715 


615 


24x14 


1215 


1085 


36x16 


2240 


2070 


8x6 


230 


195 


16x8 


585 


520 


24x10 


1035 


945 


36x14 


2060 


1930 


8x4 


205 


175 


16x3 


415 


395 


24x6 


840 


800 


36x12 


1940 


1835 


8x3 


185 


165 


18x18 


1055 


860 


24x3 


725 


705 


36x10 


1810 


1730 


10x10 


380 


300 


18x14 


865 


735 


30x30 


2850 


2415 


36x8 


1700 


1635 


10x6 


280 


240 


18x10 


695 


610 


30x20 


2020 


1790 


36x6 


1555 


1515 


10x3 


225 


205 


18x6 


550 


510 


30x16 


1755 


1585 


36x4 


1445 


1415 


12x12 


495 


395 


18x3 


455 


435 


30x12 


1475 


1370 


36x3 


1380 


1360 


12x8 


405 


345 


20x20 


1335 


1100 


30x8 


1255 


1190 








12x3 


275 


255 


20x16 


1 1C0 


935 


30x4 


1030 


1005 









These tables are greatly abridged from the original, many intermediate 
sizes being omitted. 



4) 


Branches. 


a 


B 


ranches. 


J3 


Branches. 


c 


30° 


45° 


60° 


30° 


45° 


60° 


30° 


45° 


60° 


3x3 


70 


70 


60 


14x3 


360 


295 


305 


24x16 


1865 


1520 


1345 


4x4 


115 


95 


85 


16x16 


1185 


910 


815 


24x12 


1500 


1235 


1100 


4x3 


100 


80 


75 


16x12 


885 


710 


635 


24x8 


1175 


1055 


915 


6x6 


180 


145 


130 


16X8 


670 


560 


520 


24x3 


825 


770 


695 


6x3 


135 


105 


100 


16x3 


460 


385 


385 


30x30 


4445 


3390 


2905 


8x8 


310 


250 


230 


18x18 


1415 


1080 


935 


30x20 


3005 


2365 


2220 


8x6 


240 


205 


190 


18x14 


1105 


865 


770 


30x16 


2475 


2025 


1770 


8x3 


135 


160 


150 


18x10 


850 


670 


635 


30x12 


1990 


1695 


1495 


10x10 


450 


370 


320 


18x6 


630 


510 


500 


30x8 


1630 


1400 


1250 


10x6 


300 


255 


235 


18x3 


510 


435 


410 


30x3 


1180 


1125 


960 


10x3 


235 


195 


190 


20x20 


1935 


1455 


1400 


36x36 


6595 


4565 


4115 


12x12 


650 


545 


445 


20x16 


1550 


1190 


1045 


36x24 


4405 


3335 


2990 


12x8 


470 


385 


345 


20x12 


1195 


935 


860 


36x18 


3370 


2695 


2360 


12x3 


300 


255 


240 


20x8 


930 


750 


690 


36x14 


2805 


2340 


2050 


14x14 


830 


650 


565 


20x3 


635 


550 


520 


36x10 


2295 


2040 


1760 


14x10 


625 


505 


455 


24x24 


2795 


2140 


1840 


36x6 


1860 


1610 


1415 


14x6 


450 


365 


355 


24x18 


2035 


1675 


?450 


36x3 


1505 


1360 


1245 



Split Tees. 



3x3 
4x4 



10x8 
10x3 



165 

125 
220 
180 



12x3 
14x8 
14x3 



275 
235 

325 

285 



16x3 
18x8 
18x3 



380 
340 

485 



555 
780 
1130 



1090 
1460 
1420 



CAST-IRON PIPE-FITTINGS. 

Split E 



197 



<B 


Branches. 


s 

-S 

o 

c 


Branches. 


1 
a 


Branches. 


a 


30° 


45° 


60° 


30° 


45° 


60° 


30° 


45° 


60° 


3 

4 
6 


50 
60 

85 


8 
10 


110 
165 


12 
14 


220 
270 


16 

18 


325 
430 


20 

24 


540 
725 


30 
36 


1075 
1405 



































Taper 


Plugs 












3 
4 
6 


7 
10 
20 


8 
10 


25 
40 


12 
14 


60 
80 


16 

18 


• 95 
135 


20 
24 


170 
260 


30 
36 


430 
600 

























4x3 


50 


10x8 


175 


14x12 


295 


16x6 


220 


20x14 


430 


30x24 


865 


6x4 


70 


10x3 


115 


14x8 


220 


18x16 


435 


20x10 


380 


30x18 


825 


6x3 


60 


12x10 


230 


14x4 


165 


18x12 


345 


24x20 


645 


36x30 


1455 


8x6 


100 


12x6 


165 


16x14 


355 


18x8 


280 


24x16 


555 


36x18 


950 


8x3 


55 


12x3 


140 


16x10 


290 


20x18 


520 


24x12 


485 







3x4 


55 


4x14 


210 


8x14 


235 


12x14 


300 


16x18 


455 


20x36 


1310 


3x8 


95 


6x8 


115 


8x18 


320 


12x18 


385 


16x30 


965 


24x30 


940 


3x12 


165 


6x12 


195 


10x12 


245 


12x24 


510 


18x20 


485 


24x36 


1380 


4x6 


75 


6x16 


275 


10x16 


335 


14x16 


375 


18x36 


1220 


30x38 


1475 


4x10 


150 


8x10 


190 


10x20 


410 


14x24 


600 


20x24 


700 









o 


T3 

C 

CD 

o & 


o ^ 

-£2 cd 
cn' 




CD 

a 
'a 
w. 


8 

a o 

p 


>-i a 
o "a 

o 


o 


^a 

o 'a 


f* a 
o a 

o 


a 

6 


> 

m 


3 


50 


40 


35 


75 


50 


355 


50 


55 


65 


70 


20 


35 


4 


60 


50 


45 


105 


70 


370 


70 


75 


85 


95 


25 


45 


6 


95 


70 


60 


145 


115 


395 


95 


105 


120 


125 


40 


60 


8 


155 


115 


100 


210 


190 


450 


160 


175 


205 


210 


60 


75 


10 


215 


160 


130 


360 


295 


485 


200 


235 


270 


290 


85 


100 


12 


290 


210 


170 


450 


420 


575 


265 


300 


380 


425 


110 


17.5 


14 


355 


260 


210 


595 


500 


690 


320 


360 


480 


520 


145 


150 


16 


495 


355 


280 


640 


775 


890 


415 


500 


615 


755 


165 


175 


18 


575 


405 


320 


880 


910 


1080 


475 


565 


735 


875 


235 


200 


20 


745 


515 


410 


1160 


1195 


1190 


580 


725 


950 


1135 


290 


240 


74 


1040 


715 


555 


1590 


1680 


1785 


830 


1000 


1330 


1600 


435 


345 


30 


1580 


1060 


800 


2450 


2345 


2410 


1145 


1470 


2005 


2270 


680 


475 


36 


2230 


1490 


1120 


3540 


3495 


3225 


1600 


2070 


2720 


3315 


1015 


630 



STANDARD PIPE FLANGES (CAST IRON). 

Adopted August, 1894, at a conference of committees of the American 
Society of Mechanical Engineers, and the Master Steam and Hot Water 
Fitters' Association, with representatives of leading manufacturers and 
users of pipe, -^- Trans, A. S. M. E,, xxi, 29. 



198 








MATERIALS. 














The list is divided 


into two 


groups; for medium and high pressures, • 


ti 


e first ranging up 


to 75 lbs 


per square inch, 


and the second up to 


200 lbs. 












■Sjt 


°3. 


03 


m 


.a 


40 












-a 

<u 




I 


6 


3 

a 1 

02 


la 

a 





m 





<D 






Ol 






























a 


I? 
.2 ^ 


o3 • 
v •/, 

zi 

J. z 


rt 


°8 


0) 

s 

03 

Q 


.z-d 
.d ° 


bJO 

d 

J5 


a 

03 

5 

"0 o5 



ffl 
"0 


<x> 


1 


a 

-d* 
ftfl 

d 


d a,. 


03 


H2 oo 


_5 d* 

.r - 


32 


(3 


M 

d 

£5 


dT3 




5-1 

PQ 


— 

i 

s 


5 

"0 


"0 

n 


& d! 

Oi CTi 


2 


0.409 


7/16 


460 


1/8 


6 


5/8 


2 


43/4 


4 


5/8 


2 


82! 


21/2 


.429 


7 16 


550 


1/8 


7 


U/16 


21/ 4 


51/2 


4 


5/8 


21/4 


1051 


3 


.448 


7/16 


690 


1/8 


71/2 


3/4 


21/4 


6 


4 


5/8 


21/2 


1331 


31/2 


.466 


1/2 


700 


1/8 


81/2 


13/16 


21/2 


7 


4 


5/8 




2531 


4 


.486 


1/2 


800 


1/8 


9 


15/16 


21/2 


71/2 


4 


3/ 4 


23/4 


2101 


41/ 2 


.498 


1/2 


900 


1/8 


91/4 


15/16 


23/s 


73/4 


8 


3/4 


3 


143(: 


5 


.525 


1/2 


1000 


1/8 


10 


15/16 


21/2 


81/2 


8 


3/4 


3 


163( 


6 


.563 


9/16 


1060 


1/8 


11 


1 


21/2 


91/2 


8 


3/4 


3 


236( 


7 


.60 


5/8 


1120 


1/8 


121/2 


1 Vie 


23/4 


103/4 


8 


3/4 


31/4 


320( 


8 


.639 


5/8 


1280 


1/8 


131/2 


1 1/8 


23/4 


113/4 


8 


3/ 4 


31/2 


419C 


9 


.678 


11/16 


1310 


3/16 


15 


1 1/8 


3 


131/4 


12 


3/4 


> 


3610 


10 


.713 


3/ 4 


1330 


3/16 


16 


1 3/16 


3 


141/ 4 


12 


7/8 


35/s 


297C: 


12 


.79 


i-Vie 


1470 


3/16 


19 


1 1/4 


31/2 


17 


12 


7/8 


33/4 


428C 


14 


.864 


7/8 


1600 


3/16 


21 


1 3/8 


31/2 


183/4 


12 


1 


41/4 


4280. 


15 


.904 


15/16 


1600 


3/16 


221/4 


1 3/8 


35/s 


20 


16 


1 


41/4 


366C 


16 


.946 


1 


1600 




231/2 


1 7/ie 


33/ 4 


211/4 


16 


1 


41/4 


4210 


18 


1.02 


H/16 


1690 




25 


1 9/16 


31/2 


223/4 


16 


U/8 


43/4 


4540 


20 


1.09 


U/8 


1780 


3/16 


271/2 


1 H/16 


33/ 4 


25 


20 


U/8 


5 


449C 


22 


1.18 


13/16 


1850 


1/4 


291/ 2 


1 13/16 


33/4 


271/4 


20 


U/4 


51/2 


4320 


24 


1.25 


U/4 


1920 


1/4 


31 1/ 2 32 


U/4 1 7/ 8 


3 3/4 4 


291/ 4 291/2 


20 


U/4 


51/0 


513C 


26 


1.30 


15/16 


1980 


1/4 


333/ 4 341/4 


13/8 2 


3 7/8 41/8 


311/4313/4 


24 


U/4 


53/4 


503C 


28 


1.38 


1.3/8 


2040 


1/4 


36 361/2 


17/16 2 l/i 6 


4 41/4 


331/2 34 


28 


U/4 


6 


500C 


30 


1.48 


U/2 


2000 


1/4 


38 383/4 


1 1/2 2 1/8 


4 43/ 8 


35 1/2 36 


28 


13/8 


6I/4 


459C 


36 


1.71 


13/4 


1920 


1/4 


441/2 453/4 


13/4 2 3/ 8 


41/4 47/s 


42 423/4 


32 


13/8 


6I/2 


579C 


42 


1.87 


2 


2100 


1/4 


51 523/4 


1 7/8 2 5/ 8 


41/2 53/s 


481/ 2 491/ 2 


36 


U/2 


71/4 


570C 


48 


2.17 


21/4 


2130 


1/4 


571/2 591/2 


2 2 3/4 


43/4 53/4 


543/ 4 56 


44 


U/2 


73/4 


609C 



Notes. — Sizes up to 24 inches are designed for 200 lbs. or less. 

Sizes from 24 to 48 inches are divided into two scales, one for 200 lbs. 
the other for less. 

The sizes of bolts given are for high pressure. For medium pressures 
the diameters are Vs in. less for pipes 2 to 20 in. diameter inclusive, and 
1/4 in. less for larger sizes, except 48-in. pipe, for which the size of bolt is 
13/8 in. 

When two lines of figures occur under one heading, the single columns 
are for both medium and high pressures. Beginning with 24 inches, the 
left-hand columns are for medium and the right-hand lines are for high 
pressures. 

The sudden increase in diameters at 16 inches is due to the possible 
insertion of wrought-iron pipe, making with a nearly constant width of 
gasket a greater diameter desirable. 

When wrought-iron pipe is used, if thinner flanges than those given 
are sufficient, it is proposed that bosses be used, to bring the nuts up to 
the standard lengths. This avoids the use of a reinforcement around the 
pipe. 

Figures in the 3d, 4th, 5th, and last columns refer only to pipe for 
high pressure. 

In drilling valve flanges a vertical line parallel to the spindles should 
be midway between two holes on the upper side of the flanges. 



STANDARD STRAIGHT-WAY GATE VALVES. 



199 



FLANGE DIMENSIONS, ETC., FOB EXTRA HEAVY ] 
FITTINGS (UP TO 250 LBS. PRESSURE). 

Adopted by a Conference of Manufacturers, June 28, 1901. 



Size of 


Diam. of 


Thickness 


Diameter of 


Number of 


Size of 


Pipe. 


Flange. 


of Flange. 


Bolt Circle. 


Bolts. 


Bolts. 


Inches. 


Inches. 


Inches. 


Inches. 




Inches. 


2 


61/2 


7/8 


5 


4 


5/8 


21/2 


71/2 


1 


5 7/ 8 


4 


3/4 


3 


81/4 


H/8 


65/s 


8 


5/8 


31/2 


9 


13/16 


71/4 


8 


5/8 


4 


10 


11/4 


77/s 


8 


3/4 


41/2 


101/2 


15/16 


8I/2 


8 


3/4 


5 


11 


13/s 


91/4 


8 


3/4 


6 


'21/2 


17/16 


105/ 8 


12 


3/4 


7 


14 


H/2 


H7/8 


12 


7/8 


8 


15 


15/8 


13 


12 


7/8 


9 


16 


13/4 


14 


12 


7/8 


10 


171/2 


17/8 


151/4 


16 


7/8 


12 


20 


2 


173/4 


16 


7/8 


14 


221/2 


21/8 


20 


20 


7/8 


15 


231/2 


23/ie 


21 


20 


1 


16 


25 


21/4 


221/2 


20 


1 


18 


27 


23/ 8 


241/2 


24 


1 


20 


291/2 


21/2 


26 3/4 


24 


H/8 


22 


3U/2 


25/ 8 


28 3/4 


28 


H/8 


24 


34 


23/ 4 


311/4 


28 


H/8 



STANDARD STRAIGHT-WAY GATE VALVES. 

(Crane Co.) 

Iron Body. Brass Trimmings. Wedge Gate. 

Dimensions in Inches: A, nominal size; D, face to face, flanged; C, diam. 
of flanges; D, thickness of flanges; K, end to end, screwed; N, center to 
top of non-rising stem; 0, diam. of wheel; S, center to top of rising stem, 
open; P, size of by-pass; F, end to end, hub; T, diam. of hub; X, number 
of turns to open. 



A 


B 


C 


D 


K 


N 





S 


Y 


P 


X 


U/2 


61/2 


51/4 


9/16 


5 


101/2 


51/2 






6 


2 


7 


6 


5/8 


57/16 


113/4 


51/2 


14 






7 


21/2 


71/2 


7 


H/16 


57/8 


123/4 


51/2 


153/ 4 






8 


3 


8 


71/2 


3/4 


61/8 


141/4 


61/2 


181/2 






101/4 


31/2 


81/2 


8 1/2 


13/16 


61/2 


151/4 


71/2 


203/4 






101/ 8 


4 


9 


9 


15/16 


67/s 


161/4 


9 


231/2 






8 3/4 


41/2 


91/2 


91/4 


15/16 


71/4 


175/s 


9 


243/4 






9 


5 


10 


10 


15/16 


75/ie 


19 


10 


28 






11 


6 


101/2 


11 


1 


73/4 


203/4 


10 


313/4 






125/s 


7 


11 


121/2 


U/16 


8I/4 


23 


12 


371/4 






151/4 


8 


111/2 


131/2 


U/8 


EU/16 


26 


14 


41 






16 


9 


12 


15 


U/8 


91/4 


28 


14 


441/4 






183/4 


10 


13 


16 


13/16 


97/ 8 


301/4 


16 


491/2 






201/2 


12 


14 


19 


U/4 


H5/8 


351/4 


18 


571/4 






241/8 


14 


15 


21 


13/8 




391/4 


20 


66I/9 


191/2 


2 


211/4 


15 


15 


221/4 


13/8 




4U/8 


20 


693/ 4 


21 


2 


3H/2 


16 


16 


231/2 


17/16 




423/4 


22 


743/4 


233/4 


3 


331/4 


18 


17 


25 


19/16 




483/4 


24 


86 


243/4 


3 


351/2 


20 


18 


27 1/2 


1 H/16 




521/2 


24 


91 


2 73/4 


4 


421/4 


22 


19 


291/2 


1 13/16 




551/2 


27 


100 


29 


4 


46 


24 


20 


32 


17/8 




62 


30 


109 


301/2 


4 


50 


26 


23 


341/4 


2 




657/ 8 


30 


1171/2 


32 


4 


65 


28 


26 


351/2 


21/16 




70 


36 


125 


33 


4 


80 


30 


30 


383/4 


21/8 




751/2 


36 


133 


34 


4 


921/2 


36 


36 


453/4 


23/8 




83 




1581/2 


39 


6 


108 



200 



MATERIALS. 



EXTRA HEAVY STRAIGHT-WAT GATE VALVES. 

Ferrosteel. Hard Metal Seats. Wedge Gate. 



A 


5 


K 


C 


D 


N 

83/ 4 


S 



5 


P 


Y 


X 


U/4 


61/2 


51/2 


5 


3/ 4 


105/ 8 


12 


11/2 


71/2 


61/4 


6 


13/1 fi 


9b/« 


121/4 


51/9 






11 


2 


81/2 


7 


61/2 


V/8 


101/9, 


133/4 


61/9 






14 


21/ 2 


91/2 


8 


71/2 


I 


127/8 


16 


71/9 






15 


3 


111/8 


9 


81/4 


1 1/8 


l4b/ 8 


191/9 


9 






14 


31/2 


117/8 


10 


9 


13/16 


151/, 


22 


10 






16 


4 


12 


11 


10 


H/4 


i;3 /4 


241/9 


12 






18 


41/2 


131/4 


121/4 


101/2 


Itylfi 


l83 /4 


27 


12 






21 


5 


15 


131/2 


11 


I 3/8 


201/4 


2y3/ 4 


14 






23 


6 


15 7/s 


157/s 


121/2 


IV/i fi 


23 


341/ 8 


16 


U/4 


13 


28 


7 


I6I/4 


161/4 


14 


IV? 


243/4 


38 


18 


H/ 4 


141/8 


30 


8 


161/2 


I6I/2 


15 


15/8 


283/ 4 


423/4 


20 


IV?, 


157/8 


34 


9 


17 


17 


16 


13/4 


301/, 


47 


20 


H/2 


163/s 


40 


10 


18 


18 


171/2 


17/8 


3i3/ 4 


523/ 4 


22 


11/?, 


167/ s 


39 


12 


193/ 4 




20 


2 


3/1/4 


60 


24 


2 


197/8 


46 


14 


221/2 




221/2 


21/8 


423/4 


67 3/ 4 


24 


2 


205/s 


52 


15 


221/2 




231/2 


23/ « 


423/4 


6/3/ 4 


24 


2 


205/ 8 


52 


16 


24 




25 


21/4 




751/4 


27 


3 


251/4 


60 


18 


26 




27 


23/8 




821/4 


30 


3 


261/9 


67 


20 


28 




291/2 


21/? 




9U/9 


30 


4 


301/9 


74 


22 


291/2 




3H/2 


25/8 




101 


36 


4 


321/4 


82 


24 


31 




34 


23/4 




109 


36 


4 


33 


88 



For dimensions of Medium Valves and Extra Heavy Hydraulic Valves, 
See Crane Company's catalogue. 



FORGED AND ROLLED STEEL FLANGES. 

Dimensions in Inches. (American Spiral Pipe Works, 1908.) 




f A 


> 1 ' 


' 












Standard Companion Flanges. 


Standard Shrink Flanges. 


"3 0> 


■§a 


li ® 


, . 








-Sa 


a 


, . 


*3 


"o . 


S|S 


is 


£ 


.2 <B 

-a fl 


&M 


a 3 


ii^ 


■?s 


*Q 


.2 i> 


ftK 


.gW 


£ 





< 


H 


Q 


Q 


£ 





ffl 


H 


A 


Q 




A 


B 


C 


D 


E 




A 


B 


C 


D 


E 


2 


6 


21/8 


5/8 


1 


31/8 


4 


9 


*3/ 8 


15/16 


23/ir 


5 3/4 


21/9 


7 


21/?, 


H/16 


U/lfi 


35/8 


41/?, 


9 1/4 


47/s 


I'/lR 


21/4 


61/8 


3 


nh 


31,'s 


3/4 


I 1/8 


45/ lfi 


5 


10 


5 7/, fi 


iVifi 


25/ 1fi 


6 7/s 


31/?, 


81/?, 


35/s 


13/16 


13/16 


4 V/8 


6 


11 


61/9 


1 


27/ 16 


7 7/s 


4 


9 


41/8 


15/16 


I 8/1 6 


53/8 


7 


121/9 


yi/9 


11/16 


21/9 


9 


41/9 


9 1/4 


4^/8 


l/<6 


U/4 


5 13/, fi 


8 


131/9 


8 1/9 


11/8 


25/8 


101 


5 


10 


51/8 


15/16 


i*»/tfl 


67/ie 


9 


15 


91/9 


11/8 


23/ 4 


111/8 


6 


11 


63/i 6 


1 


1 V/,6 


'»/l« 


10 


16 


105/8 


is/m 


3 


121/8 


7 


121/9, 


'8/lfl 


11/16 


11/9 


85/8 


12 


19 


125/8 


11/4 


33/s 


147/ 


8 


131/9 


83/, 6 


11/8 


15/8 


9H/16 


14 


21 


13 7/8 


13/8 


33/s 


15 7/8 


9 


15 


93/, 6 


11/8 


13/4 


10 5/8 


15 


221/ 4 


147/8 


13/8 


31/? 


16 


10 


16 


I0b/i 6 


13/16 


IV/8 


1 ! 15/, 6 


16 


231/2 


l5 7/ 8 


17/0 


35/8 


l«?/4 


12 


19 


I2b/ ]fi 


I l/ 4 


21/, 6 


141/8 


18 


25 


177/s 


l»/tfi 


3 V/8 


201/8 


14 


21 


131/2 


13/8 


23/i 6 


15 7/i 6 


20 


271/2 


197/8 


1 U/1G 


41/8 


221/4 



FORGED AND ROLLED STEEL FLANGES. 



201 



FORGED AND ROLLED STEEL FLANGES. 


— Continued 


ExtraHeavy Companion Flanges. 


Extra Heavy High Hub Flanges. 


"o3 <D 


83 rt 


§ 






4 


"3 -a5 

.9 <B' =1 


Is 




13 o 


"3 




B 


O 


pq 


H 


« 


A 


fc 


o 


m 


H 


Q 


Q 




A 


B 


C 


D 


E 




A 


B 


C 


D 


E 


2 


6V9 


21/8 


7/8 


13/8 


33/ 8 


4 


10 


43/8 


U/8 


31/8 


53/4 


21/2 


71/9 


21/?, 


1 


1 Vlfl 


41/16 


41/?, 


101/9, 


47/s 


H/4 


31/4 


6I/4 


3 


81/4 


31/8 


1 


19/16 


4 11/ie 


5 


11 


57/16 


U/4 


31/4 


7 


31/2 


9 


3b/ 8 


U/8 


lb/8 


!>*>/ifl 


6 


121/? 


61/?, 


11/4 


31/4 


715/16 


4 


10 


41/8 


H/8 


13/4 


5 13/ t R 


7 


14 


/I/? 


Itylfi 


33/8 


91/8 


41/2 


101/9, 


45/ 8 


11/4 


U3/fi 


61/4 


8 


15 


81/?, 


13/8 


3V? 


105/i 6 


5 


11 


5 1/s 


H/4 


IV/8 


613/6 


9 


16 


91/?, 


IV/16 


35/8 


113/ 8 


6 


121/9 


63/, 6 


H/4 


2 


/V/8 


10 


171/?, 


105/ 8 


11/?, 


33/4 


125/ 8 


7 


14 


73/46 


1 b/ifi 


21/16 


91/8 


11 


l83/ 4 


H<>/8 


1 »/l 6 


37/8 


135/ 8 


8 


15 


83/| « 


13/8 


23/. 6 


10 1/8 


12 


20 


l25/ 8 


H>/8 


4 


143/4 


9 


16 


93/,fi 


1 Vl6 


21/4 


iia/ifl 


14 


221/9, 


I3V/8 


I 3/4 


43/ 8 


163/i 6 


10 


M 1/9, 


IOb/iB 


U/?, 


23/s 


129/16 


15 


231/3 


147/s 


I 13/16 


41/9 


171/ 4 


12 


20 


I2b/ 1fi 


l*>/8 


29/16 


1 4o/8 


16 


25 


liV/ R 


IV/8 


43/4 


18l/ 2 


14 


221/9, 


131/9, 


13/4 


2H/16 


1 5 13/, 6 


18 


27 


l7V/ 8 


2 


5 


203/4 


15 


231/9, 


141/9, 


1 13/1R 


213/16 


i/a/i« 


20 


291/ ? , 


197/8 


21/4 


Wi 


221/2 


16 


25 


151/2 


IV/8 


31/16 


I8I/4 















Forged Steel Flanges for Riveted Pipe. 

Riveted Pipe Manufacturers' Standard.* 





„ - 


1 1 


*. 

Si 

1 


"Si: 


.2 02 




1® 








•2p2 




3 


6 


5/16 




4 


7/16 


43/4 


16 


2U/4 


5/8 


3/4 


12 


1/? 


191/4 


4 


y 


W16 


9/16 


8 


V/16 


510/16 


18 


231/4 


5/8 


3/4 


16 


5/8 


2U/4 


5 


8 


•V16 


9/16 


8 


7/16 


61b/ifi 


20 


251/ 4 


5/8 


3/4 


16 


5/8 


231/8 


6 


9 


3/8 


9/16 


8 


1/?, 


/'/R 


22 


281/4 


H/16 


3/4 


16 


5/8 


26 


■J 


10 


3/8 


9/16 


8 


v* 


9 


24 


30 


H/16 


V/8 


16 


5/8 


2/3/ 4 


8 


II 


3/8 


S>/8 


8 


i/? 


10 


26 


32 




I 3/8 


24 


3/4 


293/4 


9 


13 


3/8 


t>/8 


8 


V? 


IU/4 


28 


34 




I 3/8 


28 


3/4 


313/4 


10 


14 


3/8 


H/16 


8 


Vl 


121/4 


3U 


36 




I 3/8 


28 


3/4 


333/4 


11 


15 


7/16 




12 


V?, 


133/8 


32 


38 






28 


3/4 


35 3/4 


12 


16 


7/16 


3/4 


12 


V? 


Ul/ 4 


34 


40 






28 


3/4 


373/ 4 


13 


YJ 


7/16 




12 


1/? 


151/4 


36 


42 




U/? 


32 


3/4 


393/ 4 


14 


18 


Vi« 


3/4 


12 


1/?, 


161/4 


40 


46 




IV? 


32 


3/4 


433/4 


15 


19 


«/l6 


3/4 


12 


1/2 


I///16 

















* Flanges for riveted pipe are also made with the outside diameter and 
the drilling dimensions the same as those of the A. S. M. E. standard 
(page 198), and with the thickness as given in the second column of fig- 
ures under "Thickness of Flange" in the above table. 

Curved Forged Steel Flanges are also made for boilers and tanks. 
See catalogue of American Spiral Pipe Works, Chicago. 



202 



MATERIALS. 



The Rockwood Pipe Joint. — The system of flanged joints now in 
common use for high pressures, made by slipping a flange over the pipe, 
expanding the end of the pipe by rolling or peening, and then facing it in 
a lathe, so that when the flanges of two pipes are bolted together the 
bearing of the joint is on the ends of the pipes themselves and not on the 
flanges, was patented by George I. Rockwood, April 5, 1897, No. 580,058, 
and first described in Eng. Rec, July 20, 1895. The joint as made by 
different manufacturers is known by various trade names, as Walmanco, 
Van Stone, etc. 



WROUGHT-IRON (OR STEEL) WELDED PIPE. 

For discussion of the Briggs Standard of Wrought-iron Pipe Dimen- 
sions, see Report of the Committee of the A. S. M. E. in "Standard 
Pipe and Pipe Threads," 1886. Trans., Vol. VIII, p. 29. The diameter 
of the bottom of the thread is derived from the formula D — 

(0.05D + 1.9) X -, in which D = outside diameter of the tubes, and n 

n 
the number of threads to the inch. The diameter of the top of the 

thread is derived from the formula 0.8 - X 2 + d, or 1.6 - 4- d, in which 

n n 

d is the diameter at the bottom of the thread at the end of the pipe. 

{Continued on page 207). 

Forms of Cast-Iron Flanges. (See tables on pages 203 to 206). 




(1) Elbow. (2) 45° (3) Side (4) Long (5) Tee. (6) Side 
Elbow. Outlet Turn Elbow. Outlet T. 

Elbow. 




(7) Single (8) Lateral. (9) Double (10) Double 
Sweep T. Sweep T. Branch 

Elbow. 




(11) Cross. (12) Re- 
ducing 

Cross. 



(13) Re- (14) Red. T (15) Red. (16) Reduc- 
ducing with Side Single ing Lateral. 
Tee. Outlet. Sweep 

Tee. 



STANDARD CAST-IRON FLANGED FITTINGS. 



203 



*o"]2S 


n 


»£ 


— "£ 


1— -<r — 


^ 


»2?§ 


o=og 


— -o 


-1°, 


*r 


GO-*-*" — 


00 


-a 


-a 


— ■* 00 


N 


™<SOv 


: 


S 2 


-a 


^ 


o 


N | 


■2S 


<o sO 


fe 


^S§ 


ooootn 


2 <oin 


-2 


?ff 


00 


0OOM>t 


2 


^m 


— 00 


^|f 


r* 


r^ooGocN 


o£§ 


5oo 


mo 


vOvO 00 00 — 


f« = 


— 00 


*«! 


in 


in t-s. i~%. o oo ■f o 


Sh 00 


mOO 


"*■<*■ r->. t->. o 


1 


ti-o* 


3 00 


iu? 


T 


J^D^C* 


1 


^-Os 


3 ■"»■ 


"^"^ 


s 


^OO 




r^co 


CO ,5- 




<n 


-^ 




m£ 


^ 


" (NO 


S 


0-n.n 




^ 


S^r 




N 


&■ ^-^J- 




L 


'" rf 


cmt 


§ 


oo^r-r 




£jlT> 


-C 


^^■t? 


i 


Iff 




(N^ 




^1 



GGGGGGGGG • G G G 



T3 m3 

■Si's&a 






c3 bjo 
A G 


ft 


& 


O 


M 




5 




0.2 

G ^ 


•< 
£ 


H 


ft 


<| 


O G 


fl 


ft 


t» T3 

G ® 

§ 


P4 

R 


fl 



G Jr g 


A 


H 


S CD 

=35 


ft 




a 


<p .G 


oa 




■& a 


fc 




**a 


O 


H 


© £ ■ 


CA. 


hJ 


> G 




& 




S 










G <" 


R 




- H 


P 




■* & 







•* 33 



fa ° 



f g N _, 






fcfafa 
o o o 



u G G 
.2G<99 

coO<!<PQ 





"T TCMfM 


-* 


1 


M •*> 00 -^ 




~J Q© © 




it 


— cA <n ~ "° S 




op-ff 


On 


<o 


ofl^fll 




25J2J5 


s 


§ 


ir^^^^g 




orso* 


rr 




0>NNO-iAN 




£©£.« 


1 


o 


sg£©-£- 




n-Os^J-^J- 




00 


tONNO mo 


a 
p 

c 

Pi 

c 

IQ 

Ci 

o 
p 

6B 


CNnOcAcO 


On 


NO 


BONO 1AI> 


©Cn — — 


■•o 


1 


^ffvO^lf 


On — ©© 


2 


— 


S 2 ^N^^ 


GOOOO 


*r 


tN 


*iA-N -3- fA 


^ £ OnOn 


1 


o 


vo^r — m ^ — 


P 


^r>SS 


| 


On 




mvoooco 


o 


00 


m — — oo coo 


d 











££ 






nvov© oo v© to>" 



^ o o r>. \o 



0—00 K-nnO 



a d d ri p 


pi d d '■ r 


■ 




■ : : o r A M 






to Face, 
to Face, 
to Face, 
to Face 
aclius Ell 
of Lon 
Flls 


2 -mm: 


"o 
ffl 

- • 



-2 2 bf- 2 -2° += fi ffl^ Jd»- 

ajT-^r^ « c S rf a?Z £ « d <d £P+> 



£0> 






I 3 





s 








1 


& 


^ 


O IA On 




<N 


^ T3 


<N~, - - 




o 








H 








o 


U 








73 


•S2 












ft 








SI 


N T) 















fe 








fi 


s 


-S2 




H 


=> t/i 






ft 


N C 






Q 








ft 

















fz? 








<1 


| 


^- ~j- 






3 S 






h * ' 


~ "g 






©- « 








>z;H 


^ 






Sh 


V 






^ 


73 






H v 


oS t , 




# ri 








, 








^ o 








p> « 


o 














ft£ 


a 


M CM 




«!« u 


"i n f 


-» — ro 




« M 








H tT 








M ^ 








ft H 


O 






ft H 








OP 








o 








^ J "! 


r 5 r 


nj — m 




O^ 
























^ i 


ON 






ss 


V 






pS 


s 


.(N « 




J ^ - 


J M ? 


O CS| 




<! 


T3 






ft 


OO 






















































5 c 


S 00 On — 




o 
w 


NO 




. 


w 


a c 


d a 
























3 


• o 




o 












01 






« 


' e3 


- 


ert 






ft 


"fa 


In 


Uh 








o 


o 




c 














£ 


O g 


dJ 


ss 






°fa£ 


d c CZ 






ca 3 oj 3 




2 K 


N<<p: 


V«9o 




>■ iL 


CQ<J 


< 


p 







HYDRAULIC FERROSTEEL FLANGED FITTINGS. 





i-Tw" ^r^r 




tj- a^ <si -^ — r>. so 
















vOsO c<>i ro, 


(Mm -<r "" in 
















NinNO-'O- 


















CMm™£'~'' § 


tf-Ct^tn 














OOOO 


OONvO-'CN 
cMin <t> t)- 




-SJ S .5 -^-^ 








23- S?"""' '* 
















vO vO GO 00 


2^-^-^^ 




.N.0O JO _« 






"3-Tj-r^r^ 


l^^ — ^ — ^^ 


















CMCMvOO 
















©©mm 


in oo — oo — m v© 


















oooo-tt 


Tt- VO S 00 — 1T\ I" 




































— CM °^0 — m c> 




















cm^cmS 


Off.-0-iftN 
— CM CM CM 




^^m^o 40^ 






OvOCOOO 


























N e -«i 




;?-<! ^j- 






















Ift^^ft 


00 CM — sO — -3- O 
















too^i- 


1^ — *H CM — Tf 00 


















cm jt cm cm 


t^O — CM WM>. 






d d d d 


d d d 


d d d 




















: : ;"S 




































fefefetti 


^«i§ 














§ ® OJ 


fll 


«St.ffl°g 








c 




a 


<1<3fQW 


QH2 




^£ 





fc 


OOOvOOO'- 




« 




w 










H 




ft 




N 






n 


^SmS^ 






pq 


NOOO^O 


H 




M 




w 


Qco*m» 






1 


OO sO ^T CM 00 






K 


vOCMCM — r-s 






H 




& 


^■Noom 


J 




< 


NOMOJ 


X 












w 














00 00 CM vO — 






- 


sOOOCMnO© 






R 








*r^o©ino 


h 




c 
2 


Nmco^-to 


5 


o^roo^r^ 




cm — cm — — 


« 


42 














32 


vCOtNt 


c 


CN ' - '- 


* 


-5-5 






£ 








- 


TTOCM — ^ 


J 


— CM — — 


- 


NCOOO- 


s 


— CM 


X 
£ 


d '■ d d d 






> 




^ 












































-5j 




a 




-& 






12 §§1 







M ® & c 


^ 










/" 




ffe^fe 







/^ 0> *■" ** 

Q y 0> 0) 


H 




3 




"fels 


< 


SS^oo 




a: 


'J2< 


< 


PC 





H I • 

o * ^ 

3 S i 

© 613 C 

3 -S O 

M 
H 

H 
H 









-5^ 














•OT 0> 


— CM 


— CM CM 














O — 
— CM 


jncMvooo 














O00 


mo -or^ 


~ 


' -<N '~ 














00 t^ 


CMI^ ^T^ 


~ 






-5-5 






t^O 




~~ 


— , 




-5 










— 
























-5-5 


.£>~£! -5 42 










"" 


"" 
















00 00 in 


*~ 


~ 










c^O 




"~ 


"~ 




^^2 40^ 






MO 




"~ 




« ■* 


<M TH 00 










CM 00 


vOOOvOTJ- 


N 


"* N 










CMt-N 


vOCOvOfA 


W M 


M TJ< 00 ^n 












mt^inrn 


d d 


d d d d 
























ojo a> 












oj 










































X 


O 












"t 


XI 


























c 




I 

c 


is 






swS^ 




cS* 8 a^ 










u< ; 






<** 


fl oj ^ <S 




x^ 


1s°s 










Ph S3 §5 


g § d 


oil! 


zc 


c 





C 


p: 


O 





206 



MATERIALS. 






asP? 


o^co 


OOO^NIN 


vO vO o -o 


m^rcoo 


Tr^rsO ' 


Not'" 


off- 


atat 


oorar>Tr 


NO*t 


**,££ 


■ntega 


fffw 


* ££ }« 


fff^ 


mc^S^ 


cqtNO-ra 


NOGON 



•«« ° ° 

: ode* 






^r -<i-o 


DC 

H 

H 

g 

p 

Q 

1 

r - 



03 
fe 


oc 

H 

s 


_££ 


5$ s 


Or^t->, 


CO ^5 


vOOvO 


(VlvOvO 


§3^ 


g — ir, 


as* 


&°=^ 


-tst 


gU^ 




JS* 


Jj^ 


2 = «n 


WON 


§oS 


a : : 

2^ 

o o o 

fa w *-« 

■*" a fl 

05 0) 0) 









a? a? a? a) 

£999 



3° °Q 



aj a) a> 5 

AAVdJl 



NATIONAL STANDARD HOSE COUPLINGS. 



207 



{Continued jrom page 202.) The sizes for the diameters at the bottom 
and top of the thread at the end of the pipe are as follows: 



Diam. 


Diam. 


Diam. 


Diam. 


Diam. 


Diam. 


Diam. 


Diam. 


Diam. 


of Pipe, 


at Bot- 


at Top 


of Pipe, 


at Bot- 


at Top 


of Pipe, 


at Bot- 


at Top 


Nomi- 


tom of 


of 


Nomi- 


tom of 


of 


Nomi- 


tom of 


of 


nal. 


Thread. 


Thread. 


nal. 


Thread . 


Thread. 


nal. 


Thread. 


Thread. 


in. 


in. 


in 


m. 


in. 


in. 


in. 


in. 


in. 


Vs 


0.334 


0.393 


21/2 


2.620 


2.820 


8 


8.334 


8.534 


1/4 


.433 


.522 


3 


3.241 


3.441 


9 


9.327 


9.527 


3/8 


.568 


.658 


31/2 


3.738 


3.938 


10 


10.445 


10.645 


1/2 


.701 


.815 


4 


4.234 


4.434 


11 


11.439 


11.639 


3/ 4 


.911 


1.025 


41/2 


4.731 


4.931 


12 


12.433 


12.633 


1 


1.144 


1.283 


5 


5.290 


5.490 


13 


13.675 


13.875 


H/4 


1.488 


1.627 


6 


6.346 


6.546 


14 


14.669 


14.869 


11/2 


1.727 


1.866 


7 


7.340 


7.540 


15 


15.663 


15.863 


2 


2.223 


2.339 















Having the taper, length of full-threaded portion, and the sizes at bot- 
tom and top of thread at the end of the pipe, as given in the table, taps 
and dies can be made to secure these points correctly, the length of the 
imperfect threaded portions on the pipe, and the length the tap is run 
into the fittings beyond the point at which the size is as given, or, in 
other words, beyond the end of the pipe, having no effect upon the 
standard. The angle of the thread is 60°, and it is slightly rounded off at 
top and bottom, so that, instead of its depth being 0.866 its pitch, as is 
the case with a full V-thread, it is 4/ 5 the pitch, or equal to 0.8 -*- n, n 
being the number of threads per inch. 

Taper of conical tube ends, 1 in 32 to axis of tube = 3/ 4 inch to the 
foot total taper. 

NATIONAL STANDARD HOSE COUPLINGS. 

Dimensions in Inches. 




A 


21/2 

1/4 

31/16 

2.8715 

1 

71/2 

7/8 

3.0925 


3 

1/4 

35/ 8 
3.3763 

U/8 

6 

1 
3.6550 


31/2 

1/4 
41/4 
4.0013 
U/8 

6 

1 
4.28 


41/2 

1/4 

5?/ 4 

5.3970 

TS/S 

4 

11/4 
5.80 


B, 


C 


D 


E 


N 


F 


G 





The threads to be of the 60° V. pattern with 0.01 in. cut off the top of 
thread and 0.01 in. left in the bottom of the 21/2-in., 3-in., and 31/2-in. 
couplings, and 0.02 in. in like manner for the 41/2 in. couplings. 
• A = inside diameter of hose couplings, N = number of threads per 
inch. 

DIMENSIONS OF STANDARD WELDED PIPE. 

Referring to the table on the next page, the weights per foot are based 
upon steel weighing 0.2833 ib. per cu. in. and up to and including 15 ins on 
- an average lengtn of 20 ft. in. including the coupling, although shipping 
lengths of small sizes will usually average less than 20 ft. Long. Above 
15 ins. the weignts given are for plain end pipe. All dimensions and 
weights are nominal. The imits of variation in weight are 5 per cent above 
and 5 per cent below. Taper of threads is s/ 4 hi. in the diameter per ft 
length. Weigat of contained water is based on a temperature of 62° F. and 
0.036085 lb. to tne cubic men. 



208 



MATERIALS. 



£ 2 



eg a 



•8di(J 

JO -!»J -Ulf X 

-nob J9^A\ 



•9did jo 

•%j -utf x m 

paufB^uoo 

5u 01I Ti§ -g - n 



•^iLiCj' - ° ^ Li rr "^ "i ,— — - tNu^rMOTr-jr-.in — r^r^omo 1 ^ — — 

? H 3 X ^ S3 £: 3 2£ _ C2 °. °°. — ovc — iNvoooTinrNO^^a 



;} O -J CN £< u-\ — mSdmSM?;- 



J2S2;!^ tlNOr>tK ~ vo <n m o — a \o om<mn * oo oo ^ - co i 
iOOOOOOO — — NmiftvDODOinoiAiMnnlnftS ?S-S-_ _ 



•^oojoiqno 

-uoo 9drd 
jo q^Saai 



5S 



^-NtOOO- 



-i — r^o^j- — rr 



9013 jjng 

\T3U 

■•i9}xg 



-J9JUJ 



a^xg; 



•aj -uit 
J9d adij 
jo m§i3A\. 



,0000000000c 
£o 



NO>v001-0>OOf 



-1 T ir\ vO t~s O* - 



MvOO^CT* 



So- 



o-^-oc^t^r^oor->o^ooor^or^oooooo-^-v©r^ovou 

-N^tNO^NinOOOCOONOOlf\tfMNa>N^ — ■*' T 



30000 C* 






£=>" ' 




















___ 


— CM CS i fi 




.554 
.866 
1.358 
2.164 
2.835 
4.430 
6.492 
9.621 
12.566 
15.904 
19.635 
24.306 


■"«■ 


1 


00 


1 


90.763 
108.434 
127.676 
153.938 
176.715 
201.062 
254.469 
314.159 
380.133 
452.389 


Ft. 
14.200 
10.494 
7.748 
6.141 
4.636 
3.641 
2.768 
2.372 


I 


1.547 
1.245 
1.077 
.949 

.848 


r-. 


3 






00 TT 


WNN^ 


<n 00 vo 



t o om vo a 



^■^OOOtNO^O 



- — NOiNinm — o* r» 



^' , to^^omao'<rrsoo^Doo^o^O'*mwo^c^»o^^oooo^.^^voo^N 

■(OMnNmOtN'0-vO-1100000tiri**N»-fNO 



- — NN(^1'irnntNOvON'<rintsOtAr>ot< 



OvOOUIOOOOOOOOOC 

cs^j"if^oO' — socMr^.sooovocsio^r^ 
[~o' "— — 'NcicKiPlt^OkoV 



^ ^o so 1^, r^. 00 ^ 



•qom J9d 

sprojqx 

JQ'°N 



OflO-OiMmOinTft^vOvOr- 



•p3U 

-J9^UJ 



•JBU 



.\0 ^OO^ CS N'I'OO ' — < 



r\^^rmsoisrsooo- 



^3 



--NN^Ttif 



■Jtmvoooo 



33 



- — — MtSf^rrc^^-if^vOrsOOa.0 — P. 



LAP-WELDED BOILER-TUBES. 



209 



WROUGHT-IRON WELDED TUBES, EXTRA STRONG. 

Standard Dimensions. 

(National Tube Co., 1902.) 



Nominal 
Diameter. 


Actual 

Outside 

Diameter. 


Thickness, 
Extra 
Strong. 


Thickness, 
Double 
Extra 
Strong. 


Actual Inside 

Diameter, 

Extra 

Strong. 


Actual Inside 

Diameter, 

Double Extra 

Strong. 


Inches. 

Vs 


Inches. 
0.405 
0.54 
0.675 
0.84 
1.05 
1.315 
1.66 
1.9 
2.375 
2.875 
3.5 
4.0 
4.5 


Inches. 
0.100 
0.123 
0.127 
0.149 
0.157 
0.182 
0.194 
0.203 
0.221 
0.280 
0.304 
0.321 
0.341 


Inches. 


Inches. 
0.205 
0.294 
0.421 
0.542 
0.736 
0.951 
1.272 
1.494 
1.933 
2.315 
2.892 
3.358 
3.818 


Inches. 


1/4 






3 /8 






1/2 
3/4 

1 

11/4 

1 1/2 

2 

21/2 

3 

31/2 

4 


0.298 
0.314 
0.364 
0.388 
0.406 
0.442 
0.560 
0.608 
0.642 
0.682 


0.244 
0.422 
0.587 
0.884 
1.088 
1.491 
1.755 
2.284 
2.716 
3.136 



STANDARD SIZES, ETC., OF LAP-WELDED CHARCOAL-IRON 
BOILER-TUBES. 

(National Tube Co.) 



1 

5 


a 
5 


~ t 


— » 


Si 
a o> 

is a 


Internal 


External 




2^ 




eta 


1, 




z ~ 

CO 


sa 
3 s 


Area. 


Area. 


r <u c 




©£' . « 

C fc a 


5*1 


in. 


in. 


in. 


in. 


in. 


sq. in. 


sq.ft. 


sq.in. 


sq.ft. 


ft. 


ft. 


ft. 


lb. 


1 


0.810 


.095 


2.545 


3.142 


0.515 


.0036 


0.785 


.0055 


4.479 


3.820 


4.149 


0.90 


11/4 


1.060 


.095 


3.330 


3.927 


0.882 


.0061 


1.227 


.0085 


3.604 


3.056 


3.330 


1.15 


11/2 


1.310 


.095 


4.115 


4.712 


1.348 


.0094 


1.767 


.0123 


2.916 


2.547 


2.732 


1.40 


13/ 4 


1.560 


.095 


4.901 


5.498 


1.911 


.0133 


2.405 


.0167 


2.448 


2.183 


2.316 


1.65 


2 


1.810 


.095 


5.686 


6.283 


2.573 


.0179 


3.142 


.0218 


2.110 


1.910 


2.010 


1.91 


21/4 


2.060 


.095 


6.472 


7.069 


3.333 


.0231 


3.976 


.0276 


1.854 


1.698 


1.776 


2.16 


21/2 


2.282 


.109 


7.169 


7.854 


4.090 


.0284 


4.909 


.0341 


1.674 


1.528 


1.601 


2.75 


23/4 


2.532 


.109 


7.955 


8.639 


5.035 


.0350 


5.940 


.0412 


1.508 


1.389 


1.449 


3.04 


3 


2.782 


.109 


8.740 


9.425 


6.079 


.0422 


7.069 


.0491 


1.373 


1.273 


1.322 


3.33 


31/4 


3.010 


.120 


9.456 


10.210 


7.116 


.0494 


8.296 


.0576 


1.269 


1.175 


1.222 


3.96 


31/2 


3.260 


.120 


10.242 


10.996 


8.347 


.0580 


9.621 


.0668 


1.172 


1.091 


1.132 


4.28 


33/4 


3.510 


.120 


11.027 


11.781 


9.676 


.0672 


1 1 .045 


.0767 


1.088 


1.019 


1.054 


4.60 


4 


3.732 


.134 


11.724 


12.566 


10.939 


.0760 


12.566 


.0873 


1.024 


0.955 


0.990 


5.47 


41/2 


4.232 


.134 


13.295 


14.137 


14.066 


.0977 


15.904 


.1104 


0.903 


0.849 


0.876 


6.17 


5 


4.704 


.148 


14.778 


15.708 


17.379 


.1207 


19.635 


.1364 


0.812 


0.764 


0.788 


7.58 


6 


5.670 


.165 


17.813 


18.850 


25.250 


.1750 


28.274 


.1963 


0.674 


0.637 


0.656 


10.16 


7 


6.670 


.165 


20.954 


21.991 


34.942 


.2427 


38.485 


.2673 


0.573 


0.546 


0.560 


11.90 


8 


7.670 


.165 


24.096 


25.133 


46.204 


.3209 


50.266 


.3491 


0.498 


0.477 


0.488 


13.65 


9 


8.640 


.180 


27.143 


28.274 


58.630 


.4072 


63.617 


.4418 


0.442 


0.424 


0.433 


16.76 


10 


9.594 


.203 


30.141 


31.416 


72.292 


.5020 


78.540 


.5454 


0.398 


0.382 


0.390 


21.00 


11 


10.560 


.220 


33.175 


34.558 


87.583 


.6082 


95.033 


.6600 


0.362 


0.347 


0.355 


25.00 


12 


11.542 


.229 


36.260 


37.699 


104.629 


.7266 


113.098 


.7854 


0.331 


0.318 


0.325 


28.50 


13 


12.524 


.238 


39.345 


40.841 


123.190 


.8555 


132.733 


.9217 


0.305 


0.294 


0.300 


32.06 


14 


13.504 


.248 


42.424 


43.982 


143.224 


.9946 


153.938 


1 .0690 


0.283 


0.273 


0.278 


36.00 


15 


14.482 


.259 


45.497 


47.124 


164.721 


1.1439 


176.715 


1 .2272 


0.264 


0.255 


0.260 


40.60 


16 


15.458 


.271 


48.563 


50.266 


187.671 


1 .3033 


201.062 


1.3963 


0.247 


0.239 


0.243 


45.20 


17 


16.432 


.284 


51.623 


53.407 


212.066 


1.4727 


226.981 


1.5763 


0.232 


0.225 


0.229 


49.90 


18 


17.416 


.292 


54.714 


56.549 


238.225 


1.6543 


254.470 


1.767! 


0.219 


0.212 


0.216 


54.82 


19 


18.400 


.300 


57.805 


59.690 


265.905 


1.8466 283.529 


1.9690 


0.208 


0.201 


0.205 


59.48 


20 


19.360 


.320 


60.821 


62.832 


294.375 


2.0443 314.159 


2.1817 


0.197 


0.191 


0.194 


66.77 


21 


20.320 


.340 


63.837 65.974 324.294 


2.2520'346.361 


2.4053 0.188 


0.182 


0.185 73.40 



210 



COLD-DRAWN SEAMLESS STEEL TUBES. 



c 
PI 

£ 


c3 
0> 
W) 

O 

m 

a; 

C 

H 


~ | 








O 


Otsm 


§£:* SKo 


?4 


3SS 


cfltfll^ ■"*■ "*• •t 


s 








•O 


2S^ 


O ^"OO — ir\<N 


£ 


tNI^r sO 


O — rA vOOOia 


& 








o 


OOO 


rr, t)- Tf tt ^j- u-s 

OOO OOO 


00 


o<Ni^r 


vOOOO N^CO 


£ 






2S 


in — OO 


£-w 


rn©r^ mOJ 


oo 


22£ 


r^o^o 


<si tj-it^ r^o r^ 


;? 






£ So£ 


®gS 


orvivo 


O n-v \0 O <"A O 
-OOm r^Ot^ 


m vOCOO 


ONM 


t*rN 


00 O — C4 -3- -O 






# 










^KK 


££K KK£ 


mou-s mm^ 


inuMn 


^^■rr ^^ts 


oo^O 


— CMro 


tirwo NOOO 






s 






£££ §SS 


O ^j-i^. 


o^i-t^ 


— ^J-00 — tj- — 


^cnc^ ^-.n^ 


r^oooo 


o-o — 


™«-m^ tinN 






£ 




ss 


s§s 55?; 


— oo-r 


0*m 


O -O r*1 O -O O 


™™ 


™«™ ^-^-^ 


* ,OIN 


GO OOO 


OO— «SN^ 


1 




£S2 


— O O 0O*lT\ 


£5;°. 


O vOCN 


cacmo or^^r 


— ™ 


^™ m-r^p 


ininv0 


r^r^oo 


»0>0 O-N 


s 


2 


OOrAOO 


£g£ 1222 


2^2 


22 — 


c<-\ ■* ■<*■ T tt -*■ 

vO — vO — vO ^O 







^•^^ 


vO*IN 


r*. oo oo o o o 


1 


o" 


8^2 


So©3 ^oo^ 


£&£: 


vOOOO 


-* 00 <N! -O O O 





<— C^(N C-JH»irf>i 


cn-fT 


U-MT1VO 


■O^O^ r^oooo 


;? 




8^S 


or^-* r-*.©f 


r^©rr 


££3 


s 


o 




c-qrsXN 


<^<r^ 


^TT 


u-, 


8 


Iks 


t^O^S 


|£<C- O — O 


— vO — 


2^ : 










o 


- 


"-^ 


NNN 


m^ • 








s 


pi. 


SSi 


OMN^O rA CJ> vD 


r<M> • 








































oo$ 

■— °. 

o 


r^o vO 


S!c?S 










































O 




























si 

d 


SSS 


£s§ 










































o 




























KjO 


5S^ 


cQ^S 










































o 




























1 


3-1 


Sf£ 


i? ;? 


ir£r Jr ST ^ 


£L 


««« 


^j- -r -<r • ->r m «"> 



RIVETED IRON PIPE. 



211 



In estimating the effective steam-heating or boiler surface of tubes, 
the surface in contact with air or gases of combustion (whether internal 
or external to the tubes) is to be taken. 

For heating liquids by steam, superheating steam, or transferring heat 
from one liquid or gas to another, the mean surface of the tubes is to be 
taken. 

Outside Area of Tubes. 

To find the square feet of surface, S, in a tube of a given length, L, in 
feet, and diameter, d, in inches, multiply the length in feet by the diam- 
eter in inches and by 0.2618. Or, S = 3 - 14 ^ dL = 0.2618 dL. For the 

diameters in the table below, multiply the length in feet by the figures 
given opposite the diameter. 



Inches, 
Diameter. 


Square Feet 
per Foot 
Length. 


Inches, 
Diameter. 


Square Feet 
per Foot 
Length. 


Inches, 
Diameter. 


Square 
Feet per 

Foot 
Length. 


1/4 


0.0654 


21/4 


0.5890 


5 


1 .3090 


1/2 


.1309 


21/2 


.6545 


6 


1.5708 


3/ 4 


.1963 


23/ 4 


.7199 


7 


1.8326 


1 


.2618 


3 


.7854 


8 


2.0944 


U/4 


.3272 


31/4 


.8508 


9 


2.3562 


11/2 


.3927 


31/2 


.9163 


10 


2.6180 


13/4 


.4581 


3 3/4 


.9817 


11 


2.8798 


2 


.5236 


4 


1.0472 


12 


3.1416 



RIVETED IRON PIPE. 

(Abendroth & Root Mfg. Co.) 

Sheets punched and rolled, ready for riveting, are packed in con- 
venient form for shipment. The following table shows the iron and 
rivets required for punched and formed sheets. 



Number Square Feet of 


^i §r ^ 


Number Square Feet of 


^iljf 


Iron Required to Make 


6& ^» 


Iron Required to Make 




100 Lineal Feet Punched 


100 Lineal Feet Punched 




and Formed Sheets 


and Formed Sheets 


when put Together. 


£ a "^ 


when put Together. 


2c ^ 




Approxima 
Rivets 1 ] 
Required 
Lineal Fee 
and Form 






Diam- 
eter in 
Inches. 


Width 
of Lap 

in 
Inches. 


Square 
Feet. 


Diam- 
eter in 
Inches. 


Width 
of Lap 

in 
Inches. 


Square 
Feet. 


Approxim 
Rivets 1 
Requirec 
Lineal Fe 
and Forr 


3 


1 


90 


1600 


14 


U/2 


397 


2800 


4 


1 


116 


1700 


15 


U/2 


423 


2900 


5 


11/2 


150 


1800 


16 


U/2 


452 


3000 


6 


H/2 


178 


1900 


18 


U/2 


506 


3200 


7 


H/2 


206 


2000 


20 


U/2 


562 


3500 


8 


H/2 


234 


2200 


22 


U/2 


617 


3700 


9 


U/2 


258 


2300 


24 


U/2 


670 


3900 


10 


H/2 


289 


2400 


26 


U/2 


725 


4100 


11 


U/2 


314 


2500 


28 


U/2 


779 


4400 


12 


1 1/2 


343 


2600 


30 


U/2 


836 


4600 


13 


U/2 


369 


2700 


36 


U/2 


998 


5200 



212 



MATERIALS. 



Weight and Strength of Riveted Hydraulic Pipe. 

(Abner Doble Co., San Francisco, 1906.) 
S = Safe head in feet. W = "Weight in pounds. 



Thickne 
















4-in. 


5-in. 




7-m. 


8-in. 


Gauge. 


In. 
















S 


W 


8 


W 


8 


W 


,S' 


W 


8 


W 


18 


0.050 


555 


2.8 


444 


3.5 


370 


4.1 


317 


4.7 


277 


5.3 


16 


.062 


693 


3.7 


555 


4.4 


462 


5.2 


396 


5.9 


346 


6.7 


14 


.078 


866 


4.4 


693 


5.5 


578 


6.4 


495 


7.3 


433 


8.2 


12 


.109 
.140 










.808. 


8.8 


693 


10.0 


606 
777 


11.5 


10 










14.5 




9-in. 


10-in. 


11-in. 


12-in. 


14-in. 


16 


0.062 


308 


7.5 


277 


8.3 


252 


9.0 


231 


9.9 


198 


11.4 


14 


.078 


385 


9.2 


346 


10.2 


314 


11.0 


289 


12.2 


248 


14.0 


12 


.109 


539 


12.6 


485 


14.2 


439 


15.2 


404 


16.7 


346 


19.2 


10 


.140 


693 


16.4 


623 


18.0 


565 


19.3 


519 


21.0 


445 


24.2 


8 


.171 
3/16 






761 
832 


21.5 
23.5 


693 
757 


23.5 
25.5 


635 
693 


25.6 
27.7 


543 
594 


29.3 








31.9 












15-in. 


16-in. 


18-in. 


20-in. 


22-in. 


16 


0.062 


185 


12.0 


173 


12.8 


154 


14.5 


139 


16.0 


126 


17.7 


14 


.078 


231 


14.0 


217 


16.0 


193 


17.8 


173 


19.6 


157 


21.2 


12 


.109 


323 


20.3 


303 


21.5 


270 


24.4 


242 


27.3 


220 


29.2 


10 


.140 


415 


25.7 


388 


27.3 


346 


30.7 


311 


34.5 


283 


37.1 


8 


.171 


507 


30.4 


475 


33.3 


422 


38.4 


380 


41.5 


346 


45.2 




3/16 


555 


34.0 


520 


36.0 


462 


40.5 


416 


45.0 


378 


49.0 




1/4 


739 


45.5 


693 


48.2 


616 


54.1 


555 


59.6 


505 


65 5 




5 /l6 

3/8 
7/16 






866 


60.6 


770 
924 


67.7 
81.3 


693 
831 
970 


74.6 
89.5 
105.0 


631 

757 
883 


81.5 








98.0 












114.5 




24-in. 


26-in. 


30-in. 


36-in. 


42-in. 


14 


0.078 


144 


23.7 


133 


25.5 














12 


.109 


202 


32.5 


186 


34.5 


162 


39.5 


134 


47.7 






10 


.140 


259 


40.5 


239 


43.7 


208 


50.3 


173 


60.0 


148 


69.5 


8 


.171 


317 


49.2 


293 


53.0 


254 


60.5 


211 


75.0 


181 


84.7 




3/16 


346 


53.0 


320 


57.5 


277 


65.5 


231 


79.0 


198 


91.5 




1/4 


462 


71.0 


427 


76.5 


370 


87.5 


308 


105.5 


264 


122.0 




5 /l6 


578 


88.5 


533 


95.5 


462 


109.0 


385 


130.0 


330 


151.0 




3/8 


693 


106.0 


640 


114.5 


555 


130.5 


462 


156.0 


396 


180.5 




Vl 6 


808 


124.5 


747 


134.0 


647 


151.5 


539 


182.5 


462 


211.0 




1/2 


924 


142.0 


854 


153.0 


739 


174.5 


616 


207.0 


528 


240.5 




5/8 
3/4 
7/8 






1066 


191.0 


924 
1108 


220.0 
264.0 


770 
924 
1078 


260.0 
312.5 
366.0 


660 
792 
924 


302.0 








361.5 












424.0 


















48-in. 


54-in. 


60-in. 


66-in. 


72-in. 


8 


0.171 


158 


98.0 


141 


110.0 


127 


121.0 












3/16 


173 


106.0 


154 


119.0 


139 


131.0 


127 


144.5 


115 


158.0 




1/4 


231 


142.0 


205 


159.0 


185 


175.0 


168 


193.0 


154 


211.0 




5 /l6 


289 


177.0 


256 


198.0 


231 


218.0 


210 


239.0 


193 


260.0 




3/8 


346 


212.0 


308 


237.0 


277 


261.0 


252 


286.5 


231 


312.0 




7/16 


404 


249.0 


359 


277.5 


323 


303.0 


294 


334.0 


270 


365.0 




1/2 


462 


284.0 


411 


316.5 


370 


349.0 


336 


382.0 


308 


414.0 




5/8 


578 


354.0 


513 


399.5 


462 


440.0 


420 


480.0 


385 


520.0 




3/- 4 


693 


430.0 


616 


479.5 


555 


528.0 


504 


577.5 


462 


624.0 




7/8 


808 


505.0 


719 


563.5 


647 


620.0 


588 


677.0 


539 


732.0 




1 


924 


582.0 


822 


647.5 


739 


712.0 


672 


777.5 


616 


840.0 



Pipe made of sheet steel plate, ultimate tensile strength 55,000 lbs. per 
sq. in., double-riveted longitudinal joints and single-riveted circular joints. 
Strength of longitudinal joints, 70%. Strain by safe pressure, 1/4 of ulti- 
mate strength. 



SPIRAL RIVETED PIPE. 



213 



WEIGHT OF ONE SQUARE FOOT OF SHEET-IRON FOR 
RIVETED PIPE. 



Thickness by the Birmingham Wire-Gauge. 



No. of 
Gauge. 



Weight 
in Lbs., 
Black. 



Weight 
in Lbs., 


No. of 


Thick- 


Galvan- 
ized. 


Gauge. 


In. 


0.91 


18 


0.049 


1.16 


16 


.065 


1.40 


14 


.083 


1.67 


12 


.10? 



Weight 
in Lbs., 
Black. 



Weight 

in Lbs., 

Galvan- 

zed. 



22 
20 



0.018 
.022 
.028 
.035 



1.82 
2.50 
3.12 
4.37 



2.16 
2.67 
3.34 
4.73 



SPIRAL RIVETED PIPE. 

Approximate Bursting Strength. Pounds per Square Inch. 

(American Spiral Pipe Works.) 



Inside 
Diam. 
Inches. 






Thickness. — U.S. Standard Gauge. 






















No.20. 


No, 18. 


No. 16. 


No. 14. 


No. 12. 


No. 10. 


No, 8. 


No. 6. 


No. 3 
(1/4"). 


3 


1500 


2000 
















4 


1125 


1500 


1875 














5 


900 


1200 


1500 














6 




1000 


1250 


1560 


2170 










7 




860 


1070 


1340 


1860 










8 




750 


935 


1170 


1640 










9 






835 


1045 


1460 










10 






750 


935 


1310 










11 






680 


850 


1200 










12 






625 


780 


1080 


1410 








13 






575 


720 


1010 


1295 








14 






535 


670 


940 


1210 








15 








625 


875 


1125 








16 








585 


820 


1050 


1290 


1520 


1880 


18 








520 


730 


940 


1140 


1360 


1660 


20 








470 


660 


840 


1030 


1220 


1500 


22 








425 


595 


765 


940 


1108 


1364 


24 








390 


540 


705 


820 


1015 


1250 


26 










505 


650 


795 


935 


1154 


28 










470 


605 


735 


870 


1071 


30 










435 


560 


685 


810 


1000 


32 










410 


525 


645 


760 


940 


34 










380 


490 


600 


715 


880 


36 










365 


470 


570 


680 


830 


40 










330 


420 


515 


610 


750 



214 



MATERIALS. 



FORGED STEEL FLANGES FOR RIVETED PIPE. 

(American Spiral Pipe Works.) 



1 . 8 


® m OC 

3ai 


ci"* 3 


Q 0> 





'o^ 


laJ 




<D 


6 & 




*" " 


3 S g 


Isl 


°5 
pq 

3 3/, 6 


fq OH 




.2pq 


| S - 


3-2 C 




35 OKH 


So 
12 


S"o 

•-PQ 


3 


6 


4 3/ 4 


4 


7/16 


16 


211/4 


161/ 4 


191/4 


1/? 


4 


7 


43/16 


>Wl« 


8 


V/16 


18 


231/4 


IS-Vlfi 


2ll/ 4 


16 


5/8 


5 


8 


53/lfi 


61Vt« 


8 


'//in 


20 


25l/ 4 


20o/ 1fi 


231/s 


16 


5/8 


6 


9 


63/16 


r// H 


8 


1/7 


22 


281/4 


223/ 8 


26 


16 


5/8 


7 


10 


73/ 1fi 


9 


8 


i/^ 


24 


30 


243/ 8 


273/4 


16 


5/8 


8 


11 


8 3/ t 6 


10 


8 


V? 


26 


32 


263/ 8 


293/ 4 


24 


3/4 


9 


13 


91/4 


IU/4 


8 


V? 


28 


34 


283/ 8 


3l3/ 4 


28 


3/4 


10 


14 


101/4 


l2 1/ 4 


8 


1/7! 


30 


36 


303/ 8 


333/4 


28 


3/4 


11 


15 


IU/4 


13 3/8 


12 


1/?, 


32 


38 


323/ s 


33 3/ 4 


28 


3/4 


12 


16 


l21/ 4 


14 1/4 


12 


1/?, 


34 


40 


343/ 8 


37 3/ 4 


28 


3/4 


I) 


17 


131/4 


l3 1/ 4 


12 


V? 


36 


42 


3&3/ 8 


393/ 4 


32 


3/4 


14 


18 


141/4 


I6I/4 


12 


1/? 


40 


46 


4l)3/ 8 


433/ 4 


32 


3/4 


13 


19 


ID 1/4 


U''/16 


12 


V2 















BENT AND COILED PIPES. 

(National Pipe Bending Co., New Haven, Conn.) 
Coils and Bends of Iron and Steel Pipe. 



Size of pipe Inches 

Least outside diameter 
of coil Inches 


1/4 
2 


3/8 

21/2 


1/2 
31/2 


3/4 

41/2 


1 
6 


11/4 

8 


11/2 
12 


2 
16 


21/2 
24 


3 

32 


Size of pipe Inches 

Least outside diameter 
of coil Inches 


31/2 
40 


4 

48 


41/2 
52 


5 

58 


6 
66 


7 

80 


8 
92 


9 

105 


10 
130 


12 

156 



Lengths continuous welded up to 3-in. pipe or coupled as desired. 



Coils and Bends of Drawn Brass and Copper Tubing. 



Size of tube, outside diameter. .Inches 
Least outside diameter of coil. .Inches 


1/4 
1 


3/8 
U/2 


V 2 
2 


5/8 
21/2 


3/4 1 
3 4 


11/4 
6 


13/8 
7 


Size of tube, outside diameter. .Inches 
Least outside diameter of coil. .Inches 


I l/ 2 
8 


1 5/8 
9 


13/4 
10 


2 

12 


21/4 
14 


23/s 
16 


21/2 
18 


23/4 
20 



Lengths continuous brazed, soldered, or coupled as desired. 



SEAMLESS BRASS TUBES. 



215 



90° Bends in Iron or Steel Pipe. 

(Whitlock Goil Pipe Co., Hartford, Conn.) 





3 

12 
3 
15 


31/2 
13 

31/ 2 
161/2 


4 
15 

31/2 
I8I/2 


41/2 
17 

4 
21 


5 

20 
4 
24 


6 

23 
4 
27 


7 


8 

30 
5 
33 


9 
36 

5 
41 


10 

42 
6 
48 


f? 




26 
5 
31 


48 


End 


6 




54 






Size pipe, O.D 


14 
60 
7 
67 


16 
70 
7 
77 


18 
80 
7 
87 


20 
90 
8 
98 


22 

100 

8 

108 


24 

110 

8 

118 


26 
120 

10 
130 


28 
140 

10 
150 


30 
160 


End 


10 




170 



















The radii given are for the center of the pipe. "End" means the 
length of straight pipe, in addition to the 90° bend, at each end of the pipe. 
"Center to face" means the perpendicular distance from the center of 
one end of the bent pipe to a plane passing across the other end. 

Flexibility of Pipe Bends. (Valve World, Feb., 1906.) — So far as 
can be ascertained, no thorough attempt has ever been made to determine 
the maximum amount of expansion which a U-loop, or quarter bend, 
would take up in a straight run of pipe having both ends anchored. The 
Crane Company have adopted five diameters of the pipe as a standard 
radius, which come nearer than any other to suiting average requirements, 
and at the same time produce a symmetrical article. Bends shorter than 
this can be made, but they are extremely stiff, tend to buckle in bending, 
and the metal in the outer wall is stretched beyond a desirable point. 

In 1905 the Crane Company made a few experiments with 8-inch U 
and quarter bends to ascertain the amount of expansion they would take 
up. The U-bend was made of steel pipe 0.32 inch thick, weighing 28 lbs. 
per foot, with extra heavy cast-iron flanges screwed on and refaced. It 
was connected by elbows to two straight pipes, N, 67 ft., >S, 82 ft., which 
were firmly anchored at their outer ends. Steam was then let into the 
pipes with results as follows: 



m. 



80 lbs. Expansion, Total 1 7/ 8 

50 lbs. Expansion, iV, 7/ 8) S, H/s. Total 2 

100 lbs. Expansion, JV, 13/i 6 , S, H/2- Total 2H/16 in. 

150 lbs. Expansion, N, U/8, S, 17/ 8 . Total 3 

200 lbs. Expansion, JV, H/2, S, 17/ 8 . Total 33/ 8 



Flange broke. 



Flange broke at 
208 lbs. 



Quarter bend, full weight pipe. Straight pipe 148 ft., one end. 80 lbs. 
Total expansion 13/ 8 . Flange leaked. 

Quarter bend, extra heavy pipe. Expanded 7/ 8 in. when a flange broke. 
Replaced with a new flange, which broke when the expansion was lty 8 in. 



SEAMLESS BRASS TUBE, IRON-PIPE SIZES. 

(For actual dimensions see tables of Wrought-iron Pipe.) 



Nominal 


Weight 


Nom. 


Weight 


Nom. 


Weight 


Nom. 


Weight 


Size. 


per Foot. 


Size. 


per Foot. 


Size. 


per Foot. 


Size. 


per Foot. 


ins. 


lbs. 


ins. 


lbs. 


ins. 


lbs. 


ins. 


lbs. 


1/8 


.25 


3/4 


1.25 


2 


4.0 


4 


12.70 


1/4 


.43 


1 


1.70 


21/2 


5.75 


41/2 


13.90 


3/8 


.62 


U/4 


2.50 


3 


8.30 


5 


15.75 


1/2 


.90 


11/2 


3. 


31/2 


10.90 


6 


18.31 



216 



MATERIALS. 



WEIGHT PER FOOT OF SEA31LESS BRASS TUBES. 

(Waterbury Brass Co., 1908.) 



A.W.G. 4 


6 


8 


10 


12 


14 


16 


18 


20 


22 


.24 


26 


In* 


.20431 


.16202 


.12849 


.10189 




.064084 


.05082 


.04030; 


.03196: 


•025345 


.0201 


.01594 


In.t 

V8 














0.043 


0.039 


0.034 


0.028 


0.024 


0.020 


3/16 












0.090 


.08 


.068 


.057 


.047 


.038 


.032 


1/4 








0.'l74 


0J6 


.14 


.12 


.097 


.080 


.065 


.053 


.043 


5/16 








.25 


.22 


.18 


.15 


.13 


.104 


.084 


.067 


.054 


3/8 






0.36 


.32 


.27 


.23 


.19 


.15 


.126 


.102 


.082 


.066 


1/2 




0.63 


.55 


.47 


.39 


.32 


.26 


.21 


.17 


.139 


.111 


.089 


5/8 


0.99 


.87 


.74 


.61 


.51 


.42 


.34 


.27 


.22 


.174 


.140 


.112 


3/ 4 


1.29 


1.10 


.92 


.76 


.62 


.51 


.41 


.33 


.26 


.211 


.169 


.135 


7/8 


1.58 


1.33 


1.11 


.91 


.74 


.60 


.48 


.39 


.31 


.248 


.198 


.158 


1 


1.88 


1.57 


1.29 


1.06 


.86 


.69 


.56 


.45 


.36 


.285 


.227 


.181 


U/8 


2.17 


1.80 


1.48 


1.20 


.97 


.79 


.63 


.50 


.40 


.321 


.256 




11/4 


2.47 


2.03 


1.66 


1.35 


1.09 


.88 


.70 


.56 


.45 


.358 


.285 




13/8 


2.76 


2.27 


1.85 


1.50 


1.21 


.97 


.78 


.62 


.50 


.395 


.314 




H/2 


3.05 


2.50 


2.03 


1.64 


1.32 


1.06 


.85 


.68 


.54 


.43 


.343 




13/4 


3.64 


2.97 


2.40 


1.94 


1.56 


1.25 


1.00 


.79 


.63 


.50 


.401 




2 


4.23 3.44 2.77 2.23 1.79 1.43 


1.14 .91 .73 


.58 


.459 




A.W.G. 2 


4 


6 


8 


10 


12 


14 


16 


18 


20 


22 


24 


In* 


.25763 


.20431 


.X6202 


.12849 


.0x89 


.080808 


.064084 


.05082 


.040303 


•025347 


.01594 


TnT 
21/4 


5.92 


4.82 


3.90 


3.15 


2.53 


2.02 


1.62 


1.29 


1.03 


0.82 


0.65 




21/2 


6.67 


5.41 


4.37 


3.52 


2.82 


2.26 


1.80 


1.44 


1.14 


.91 




73 




23/4 


7.41 


6.00 


4.84 


3.89 


3.11 


2.49 


1.99 


1.58 


1.26 


1.00 




80 




3 


8.16 


6.59 


5.31 


4.26 


3.41 


2.72 


2.17 


1.73 


1.38 


1.09 




87 




31/4 


8.90 


7.18 


5.77 


4.63 


3.70 


2.96 


2.36 


1.88 


1.49 


1.19 




■ 




31/2 


9.64 


7.77 


6.24 


5.00 


4.00 


3.19 


2.54 


2.02 


1.61 


1.28 


1 


02 




33/4 


10.39 


8.36 


6.71 


5.37 


4.29 


3.42 


2.73 


2.17 


1.72 


1.37 


1 


09 




4 


11.13 


8.95 


7.18 


5.74 


4.58 


3.66 


2.91 


2.32 


1.84 


1.46 


1 


16 




41/4 


11.87 


9.54 


7.64 


6.11 


4.88 


3.89 


3.10 


2.46 


1.96 


1.55 








41/2 


12.62 


10.13 


8.11 


6.48 


5.17 


4.12 


3.28 


2.61 


2.07 


1.64 








43/4 


13.36 


10.72 


8.58 


6.85 


5.47 


4.36 


3.47 


2.76 


2.19 


1.74 








5 


14.10 


11.31 


9.05 


7.22 


5.76 


4.59 


3.65 


2.90 


2.31 


1.83 








51/4 


14.85 


11.90 


9.51 


7.59 


6.05 


4.82 


3.84 


3.05 


2.42 










51/2 


15.59 


12.49 


9.98 


7.97 


6.35 


5.06 


4.02 


3.20 


2.54 










53/4 


16.33 


13.08 


10.45 


8.34 


6.64 


5.29 


4.21 


3.34 


2.65 










6 


17.08 


13.67 


10.92 


8.71 


6.94 


5.52 


4.39 


3.49 


2.77 










6I/4 


17.82 


14.26 


11.38 


9.08 


7.23 


5.76 


4.58 


3.64 












61/ 2 


18.56 


14.84 


11.85 


9.45 


7.52 


5.99 


4.76 


3.78 












63/ 4 


19.31 


15.43 


12.32 


9.82 


7.82 


6.22 


4.95 


3.93 












7 


20.05 


16.02 


12.79 


10.19 


8.1! 


6.46 


5.13 


4.08 












71/4 


20.79 


16.61 


13.25 


10.56 


8.41 


6.69 


5.32 














71/2 


21.54 


17.20 


13.72 


10.93 


8.70 


6.92 


5.50 














73/4 


22.28 


17.79 


14.19 


11.30 


8.99 


7.15 


5.69 














8 


23.03 


18.48 


14.66 11.67 9.29 7.39 5.87 ... 










* Thickness of Wall. t Outside diameter. 


Seamless brass tubes are made from l/s in. to 1 in. outside diameter, 


varying by Vi6in., and from lVsin. to 8 in. outside diameter, varying by 


1/8 in., and in all gauges from No. 2 to No. 26 A. W. G. within the limits 


of the above table. To determine the weight per foot of a tube of a given 


inside diameter, add to the weights given above the weights given below, 


under the corresponding gauge numbers. 


For copper tubing add 5% to the weights given above. 


A.W.G. 2 4 6 8 10 12 14 16 18 20 22 24 26 


Lb.pe 


•ft. 1. 


532 .9( 


37.60 


61 .38 


1 .239 


7.1507 


.0948 . 


0596 .C 


375 .02 


36 .014 


1 .00 


93 


.0059 

i 



WEIGHT OF LEAD PIPE. 



217 



LEAD AND TIN LINED LEAD PIPE. 

(United Lead Co., New York, 1908.) 









m ^ 








jg a 


Cali- 
ber. 


Letter. 


Weight 
per Foot 
and Rod. 




Cali- 
ber. 


Letter. 


Weight 
per Foot. 


.2 2 


3/ 8 in. 


E 


7 lbs. per rod 


5 


1 in. 


E 


1 1/2 lbs. per foot 


10 




D 


I oz. per foot 


6 




D 


2 






11 


•* 


C 


12" " " 


8 




C 


21/2 


' " 




14 


" 


B 


1 lb. " " 


12 




B 


31/4 






17 




A 


1 1/4 " " " 


16 




A 


4 






21 


•« 


AA 


1 1/2 " " " 


19 




AA 


43/4 


' " ' 




24 




AAA 


1 3/4 " " » 


27 




AAA 


6 






30 


7/16 in. 




13oz. " " 

1 lb. " " 




1 V4 in. 


E 
D 


2 

21/2 






10 
12 


1/2 in. 


E 


9 lbs. per rod 


7 




C 


3 






14 




D 


3/4 lb. per foot 


9 




B 


33/ 4 - 






16 




C 


1 " " " 


11 




A 


43/4 






19 


" 


B 


1 1/4 " " " 


13 




AA 


53/4 






25 


" 


Spc'l 


ll/ 2 " " " 


14 




AAA 


63/4 






28 


J " 


A 


13/ 4 " " «« 


16 


U/2 in. 


E 


3 






12 


" 


AA 


2 " " " 


19 




D 


31/2 






14 




Spc'l 


21/ 2 " " " 


23 




C 


41/4 






17 




AAA 


3 ■« ,, « 


25 




B 


5 






19 


5/8 in. 


E 


I 2 " per rod 


8 


" 


A 


6V2 






23 




D 


1 " per foot 


9 


" 


AA 


71/2 






25 


*• 


C 


11/2" " " 


13 




Spc'l 


8 






27 


" 


B 


2 " " " 


16 




AAA 


8 1/2 






28 


" 


A 


21/2 " " " 


20 


13/4 in. 


D 


4 ' 






13 


" 


AA 


23/4 " " " 


22 




C 

B 

Spc'l 

A 


5 ' 

6 * 
6V2; 






17 
19 
21 
23 


3/4 in. 


AAA 

E 


31/ 2 " " «' 
1 " " " 


25 
. 8 










D 


1 1/4 " " " 


10 


" 


AA 


81/ 2 * 






27 


" 


C 


13/4" " » 


12 


" 


AAA 


10 ' 


1 •< 




30 


•' 


Spc'l 


2 " " " 


14 


2 in. 


D 


43/4' 






15 


" 


B 
A 


21/4" " " 
3 .. .. „ 


16 
20 


;; 


C 
B 
A 


6 

7 ' 

8 ' 






18 

22 
25 




AA 


31/2" " " 


23 




AA 


9 ' 






27 




AAA 


43/4 " " " 


30 




AAA 


113/4" " " 


30 



WEIGHT OF LEAD PIPE WHICH SHOULD BE USED FOR A 
GIVEN HEAD OF WATER. 

(United Lead Co., New York, 1908.) 



Head or 
Number 


Pres- 
sure 
per sq. 
inch. 


Caliber and Weight per Foot. 


of Feet 
Fall. 


Letter. 


3/8 inch. 


1/2 inch. 


5/8 inch. 


3/4 inch. 


1 inch. 


11/4 in. 


30 ft. 

50 ft. 

75 ft. 
100 ft. 
150 ft. 
200 ft. 


15 1b. 
25 1b. 
38 1b. 
50 1b. 
75 1b. 
100 lb. 


D 
C 
B 
A 
AA 
AAA 


10 oz. 
12 oz. 
1 lb. 

11/4 lb. 
1 1/2 lb. 
13/4 lb. 


3/4 lb. 
1 lb. 
11/4 lb. 

1 3/4 lb. 

2 lb. 

3 lb. 


1 lb. 
11/2 lb. 

2 lb. 
21/2 lb. 
23/4 lb. 
3 1/2 lb. 


1 1/4 lb. 
13/4 lb. 
21/4 lb. 
3 lb. 
31/2 lb. 
43/4 lb. 


2 lb. 
21/2 lb. 
31/4 lb. 
4 lb. 
43/4 lb. 
6 lb. 


21/2 lb. 
3 lb. 
33/4 lb. 
43/4 lb. 
53/4 lb. 
63/4 lb. 





















218 



MATERIALS. 



To find the thickness of lead pipe required when the head ol 
water is given. (Chad wick Lead Works.) 

Rule. — Multiply the head in feet by size of pipe wanted, expressed 
decimally, and divide *by 750; the quotient will be the thickness re- 
quired, in one-hundredths of an inch. 

Example. — Required thickness of half-inch pipe for a head of 25 
feet. 

25 X 0.50 -*■ 750 = 0.16 inch. 



1 1/2 in., 2 and 3 pounds per foot. 

2 "3 and 4 pounds per foot. 

3 " 31/2, 5, and 6pounds perfoot. 
3V2 " 4 pounds per foot. 



LEAD WASTE-PIPE. 

4 in., 5, 6, and 8 pounds per foot. 
41/2 " 6 and 8 pounds per foot. 

5 " 8, 10, and 12 pounds perfoot. 

6 " 12 pounds per foot. 



COMMERCIAL SIZES OF LEAD AND TIN TUBING. 

1/8 inch. 1/4 inch. 

SHEET LEAD. 

Weight per square foot, 2l/ 2 , 3, 31/ 2 , 4, 4l/ 2 , 5, 6, 8, 9, 10 lb. and upwards. 
Other weights rolled to order. 



BLOCK-TIN PIPE. 



3/g in., 4, 5, 6 and 8 oz. perfoot. 
1/2 " 6, 71/2 and 10 " " 
5/ 8 " 8 and 10 " " 

3/4 " 10 and 12 " " 



U/4 " 

1 1/2 " 



, 15 and 18 oz. perfoot. 
11/4 and 11/2 lb." " 
2 and 21/2 lb. " " 
21/2 and 3 lb. " " 



TIN-LINED AND LEAD-LINED IRON PIPE. 

Iron and steel pipes are frequently lined with tin or lead for use as water 
service pipes, ventilation pipes, and for carrying corrosive liquids. See 
catalogue of Lead Lined Iron Pipe Co., Wakefield, Mass. 



WOODEN STAVE PIPE. 

Pipes made of wooden staves, banded with steel hoops, are made by 
the Excelsior Wooden Pipe Co., San Francisco, in sizes from 10 inches to 
10 feet in diameter, and are extensively used for long-distance piping, 
especially in the Western States. The hoops are made of steel rods with 
upset and threaded ends. When buried below the hydraulic grade line j 
and kept full of water, these pipes are practically indestructible. For the | 
economic design and use of stave pipe see paper by A. L. Adams, Trans. 
A.S.C.E., vol. xli. 





WEIGHT 


PER 


FT. OF 


COPPER RODS, LB. 








(Waterbury Brass Co., 1908.) 






In. 


Round. 


Square. 


In. 


Round . 


Square. 


In. 


Round. 


Square. 


1/8 


0.047 


0.060 


11/8 


3.831 


4.88 


21/8 


13.668 


17.42 


1/4 


.189 


.241 


U/4 


4.723 


6.01 


21/4 


15.325 


19.51 


3/8 


.426 


.542 


13/8 


5.723 


7.24 


23/8 


17.075 


21.74 


v% 


.757 


.964 


11/2 


6.811 


8.67 


2l/ 2 


18.916 


24.09 


5/8 


1.182 


1.51 


15/8 


7.993 


10.18 


25/8 


20.856 


26.56 


3/4 


1.703 


2.17 


13/4 


9.27 


11.80 


23/4 


22.891 


29.05 


7/8 


2.318 


2.95 


17/8 


10.642 


13.55 


27/8 


25.019 


31.86 


1 


3.03 


3.86 


2 


12.108 


15.42 


3 


27.243 


34.69 



To find the weight of octagon rod, multiply the weight of round rod by 
1.084. 

To find the weight of hexagon rod, multiply the weight of round rod by 
1.12. 



WEIGHT OF COPPER AND BRASS WIRE AND PLATES. 219 



ooo^-ooNoo^OtNT-aiNin^ 






-Ovt^in^r^tNCM — , OOC 



MO 
'So 



- '5 |Q o rj t> oj 

3 O O O O O 00 



•'O'^tsoo'rotmNNmooo-om'O^l " u-, 
C^rr^tA— O^ O^ — vONOa*0\OP p l , 00 , T0 1 iA 

QOOlflNOtMntN OOOrslXvOirMTl'^TAf^rr : w 

ii fN (N CN CN — — — — O O O O O O O © O !0 -^ 'T 

^ooooooooooooooooooog .£> & 



Z6 



& £ 



£-a 

O PI 

s3 



£- 



0<f\— O00tANtO>nMeoO*B0>O001"t0C 

K vom*ovtno»Msov- momoO'l-Of^T — 



->o^vOT -, r-'rcsioo<N — vo>ooo>o«tM» 



o — t^t-^u-ifStsoor^ooifsr^-^-o^inoo — m n o> -o in oo N 

-a>^ooomcoinm>ooinN^ , oiAvOooiNmuM)0'0\oo> 



i-JorsOOOfnoom-a-tNintt^Nf- 



,lftO00ifM'iatA'tNtO»O' , tO>N' 

°TOO — mom(NOr- "- — 






■J o^ r> O T tA tf»> 









^N — TNOOarnO^^fOvOOO-OMinOa'O 
3-^TA0NO(NT-^-00t^.a0O^OO00<Np^00ON 

^No»>0'<tN-oo^oo^.^Olf^^n'r'r^M 

-1NN------0000000000 



so — N^'tmvoiNooo'O- 



220 



MATERIALS. 



WEIGHT OF SHEET AND BAR BRASS. 



Thickness, 


Sheets 


Square 


Round' 


Thickness, 


Sheets 


Square 


Round 


Side or 


per 


Bars 1 


Bars 1 


Side or 


per 


Bars 1 


Bars 1 


Diam., 


sq ft., 


ft. long, 


ft. long. 


Diam., 


sq. ft., 


ft. long, 


ft. long, 


Inches. 


Lbs. 


Lbs. 


Lbs. 


Inches. 


Lbs. 


Lbs. 


Lbs. 


1/16 


2.72 


0.014 


0.011 


1 Vl6 


46.32 


4.10 


3.22 


1/8 


5.45 


.056 


.045 


1 1/8 


49.05 


4.59 


3.61 


3/16 


8.17 


.128 


.100 


1 3/i 6 


51.77 


5.12 


4.02 


1/4 


10.90 


.227 


.178 


1 1/4 


54.50 


5.67 


4.45 


5/16 


13.62 


.355 


.278 


1 5/i 6 


57.22 


6.26 


4.91 


3/8 


16.35 


.510 


.401 


1 3/ 8 


59.95 


6.86 


5.39 


7/16 


19.07 


.695 


.545 


1 7/16 


62.67 


7.50 


5.89 


1/2 


21.80 


.907 


.712 


1 1/2 


65.40 


8.16 


6.41 


9/16 


24.52 


1.15 


.902 


1 9/16 


68.12 


8.86 


6.95 


5/8 


27.25 


1.42 


1.11 


1 5/ 8 


70.85 


9.59 


7.53 


11/16 


29.97 


1.72 


1.35 


1 H/16 


73.57 


10.34 


8.12 


3/4 


32.70 


2.04 


1.60 


1 3/4 


76.30 


11.12 


8.73 


13/16 


35.42 


2.40 


1.88 


1 13/16 


79.02 


11.93 


9.36 


7/8 


38 15 


2.78 


2.18 


1 7/ 8 


81.75 


12.76 


10.01 


15/16 


40.87 


3.19 


2.50 


1 15/16 


84.47 


13.63 


10.70 


1 


43.60 


3.63 


2.85 


2 


87.20 


14.52 


11.40 



WEIGHT OF ALUMINUM SHEETS, SQUARE AND ROUND BARS. 

(Specific Gravity 2.68; 1 cu. in. = 0.0973 lb.) 



Thickness 


Sheets 


Round 


Square 


Thickness 


Sheets 


Round 


Square 


or 


per 


Bars 


Bars 


or 


per 


Bars 


Bars 


Diameter, 


Sq.Ft., 


per Ft., 


per Ft., 


Diameter, 


Sq.Ft., 
Lbs. 


per Ft., 


per Ft., 


Inches. 


Lbs 


Lbs. 


Lbs. 


Inches. 


Lbs. 


Lbs. 


1/16 


0.876 


0.004 


0.005 


3/4 


10.508 


0.516 


0.657 


1/8 


1.751 


.014 


.018 


7/8 


12.260 


.702 


.894 


1/4 


3.503 


.057 


.073 


1 


14.011 


.917 


1.168 


3/8 


5.254 


-129 


.164 


11/4 


17.514 


1.433 


1.824 


1/2 


7.006 


.229 


.292 


11/2 


21.017 


2.063 


2.627 


5/8 


8.757 


.358 


.456 


2 


28.022 


3.668 


4.671 



For further particulars regarding aluminum, see pp. 174, 357. 



SCREW-THREADS, WHITWORTH 


(ENGLISH) STANDARD. 


d 


4 


i 


,d 


s 


4 


g 


JS 


a 


4 






















a 


Ph 


s 


P4 


Q 


Oh 


s 


(U 


Q 


s 


1/4 


20 


5/8 


11 


1 


8 


13/4 


5 


3 


3V? 


5/16 


18 


U/16 


11 


H/8 


y 


17/8 


41/2 


31/4 


31/4 


3/8 


16 


3/4 


10 


11/ 4 


7 


2 


41/2 


31/2 


31/4 


7/16 


14 


13/16 


10 


13/8 


6 


21/4 


4 


33/4 


3 


1/2 


12 


7/8 


9 


11/2 


6 


21/2 


4 


4 


3 


9/16 


12 


15/16 


9 


15/8 


i> 


23/4 


31/2 







In the Whitworth or English system the angle of the thread is 55 
degrees, and the point and root of the thread are rounded to a radius of 
0.1373 X pitch. The depth of the thread is 0.6403 X pitch. 











SCREW- 


rHREADS. 








221 


SCREW-THREADS, SEIXERS OR U. S. STANDARD. 


Bolts and Threads. 


Hex. Nuts and Heads. 




ffl 

i 




"SJS 
1? 


"o 

is 


cS O " 


OT3 OB 

5*1 


M M 

£ ° 


i 

ft-g 
J* 


1 


QJ3 






1°' 


s 

. Ins. 


H 


5 


? 


< 


< OB 


W 


w 


Hi 


H 


H 


yA 




Ins. 


Ins. 






Ins. 


Ins. 


Ins. 


Ins. 


Ins. 




1/4 


20 


0.185 


0.0062 


0.049 


0.027 


1/2 


7/16 


37/64 


1/4 


3/16 


7/10 


5/16 


18 


.240 


.0074 


.077 


.045 


19/32 


17/32 


11/16 


5/16 


1/4 


1°/12 


3/8 


16 


.294 


.0078 


.110 


.068 


11/16 


5/8 


51/64 


3/8 


5/16 


63/64 


7/16 


14 


.344 


.0089 


.150 


.093 


25/32 


23/32 


9/10 


7/16 


3/8 


17/64 


1/2 


13 


.400 


.0096 


.196 


.126 


7/8 


13/16 


1 


1/2 


7/16 


1 15/64 


9/16 


12 


.454 


.0104 


.249 


.162 


i < V 32 


29/3 2 


11/8 


9/16 


1/2 


1 23/ 6 4 


5/8 


11 


.507 


.0113 


.307 


.202 


H/16 


1 


17/32 


5/8 


9/16 


11/2 


3/ 4 


10 


.620 


.0125 


.442 


.302 


H/4 


'3/16 


17/16 


3/ 4 


11/16 


1 4 9/64 


7/8 


9 


.731 


.0138 


.601 


.420 


17/16 


13/8 


1 21/32 


7/8 


13/16 


21/32 


1 


8 


.837 


.0156 


.785 


.550 


15/ 8 


'9/16 


17/8 


1 


15/16 


219/64 


J 1/8 


7 


.940 


.0178 


.994 


.694 


1 13/ ia 


I3/4 


23/32 


11/8 


11/16 


29/ie 


1/4 


7 


1.065 


.0178 


1.227 


.893 


2 


1 15/16 


25/16 


11/4 


13/16 


253/64 


3/8 


6 


1.160 


.0208 


1.485 


1.057 


23/ie 


21/8 


217/32 


'3/8 


15/16 


33/32 


1/2 


6 


1.284 


.0208 


1.767 


1.295 


23/ 8 


25/i 6 


23/4 


U/2 


17/16 


323/64 


5/8 


51/2 


1.389 


.0227 


2.074 


1.515 


29/16 


21/2 


231/32 


15/8 


19/16 


35/8 


13/4 


5 


1.491 


.0250 


2.405 


1.746 


23/ 4 


211/16 


33/16 


13/4 


1 H/I6 


357/64 


17/g 


5 


1.616 


.0250 


2.761 


2.051 


215/ie 


27/8 


313/32 


17/8 


1 13/16 


45/32 


2 


41/2 


1.712 


.0277 


3.142 


2.302 


31/8 


31/16 


35/8 


2 


1 15/16 


427/ 6 4 


21/4 


41/2 


1.962 


.0277 


3.976 


3.023 


31/2 


37/i 6 


4Vl6 


21/4 


23/ 16 


461/64 


21/2 


4 


2.176 


.0312 


4.909 


3.719 


37/ 8 


313/16 


41/2 


21/2 


27/i 6 


531/64 


23/4 


4 


2.426 


.0312 


5.940 


4.620 


41/4 


43/ie 


429/32 


23/4 


2U/16 


6 


3 


31/2 


2.629 


.0357 


7.069 


5.428 


45/s 


89 /i6 


53/s 


3 


215/ie 


617/32 


31/4 


31/2 


2.879 


.0357 


8.296 


6.510 


5 


415/16 


5*3/16 


31/4 


33/16 


71/16 


31/2 


31/4 


3.100 


.0384 


9.621 


7.548 


53/s 


55 /l6 


67/64 


31/2 


3 7/16 


739/64 


33/4 


3 


3.317 


.0413 


11.045 


8.641 


53/4 


511/16 


621/32 


33/4 


3U/16 


81/8 


4 


3 


3.567 


.0413 


12.566 


9.993 


61/8 


6 Vl6 


73/32 


4 


315/16 


841/ 6 4 


41/4 


27/ 8 


3.798 


.0435 


14.186 


11.329 


6 1/2 

67/ 8 

71/4 

75/s 

8 

83/ 8 

83/4 

91/8 


67 /l6 


79/16 


41/4 


43/16 


93/i 6 


41/2 


23/ 4 


4.028 


.0454 


15.904 


12.743 


6l3/i 6 


731/32 


41/2 


47/16 


93/ 4 


43/4 


25/ 8 


4.256 


.0476 


17.721 


14.226 


73 /l6 


813/32 


43/4 


4H/16 


IOI/4 


5 


21/2 


4.480 


.0500 


19.635 


15.763 


7 9/16 


827/3 2 


5 


415/ie 


1049/ 6 4 


51/4 


21/2 


4.730 


.0500 


21.648 


17.572 


713/16 


99/32 


51/4 


5 3/i 6 


1 1 23/ e4 


5l/ 2 


23/s 


4.953 


.0526 


23 . 758 


19.267 


85/i 6 


923/32 


51/2 


57/i 6 


117/8 


53/4 


23/ 8 


5.203 


.0526 


25.967 


21.262 


8H/16 


05/32 


53/4 


5H/16 


123/s 


6 


21/4 


5.423 


.0555 


28.274 23.098 


91/16 


019/32 


6 


515/16 


1215/16 



In 1864 a committee of the Franklin Institute recommended the adop- 
tion of the system of screw-threads and bolts which was devised by Mr. 
William Sellers of Philadelphia. This system is now in general use in 
the United States, and it is commonly called the United States Standard. 

The rule for proportioning the thread is as follows: Divide the pitch, 
or, what is the same thing, the side of the thread, into eight equal parts; 
take off one part from the top and fill in one part in the bottom of the 
thread ; then the flat top and bottom will equal one-eighth of the pitch, 
the wearing surface will be three-quarters of the pitch, and the diameter 
of screw at bottom of the thread will be expressed by the formula, 
diam. of bolt - (1.299 -^ no. of threads per inch). 

For a sharp V-thread with angle of 60 degrees the formula is, 
diam. of bolt - (1.733 -5- no. of threads per inch). 

The angle of the thread in the Sellers system is 60 degrees. 



222 



MATERIALS. 



Thickness of Nuts and Bolt Heads. — In the above table the thickness 
of nuts and heads (rough) is given as equal to the diameter of the bolt. 
Many manufacturers make the thickness of nuts about 7/ 8) and of bolt 
heads 3/ 4 , of the diam. of the bolt. 

Automobile Screws and Nuts. — The Association of Licensed Auto- 
mobile M'f'rs (1906) adopted standard specifications for hexagon head 
screws, castle and plain nuts known as the A.L.A.M. standard. Material 
to be steel, elastic limit not less than 60,000 lbs. per sq. in., tensile strength 
not less than 100,000 lbs. per sq. in. U. S. Standard thread is used, the 
threaded portion of screws being li/ 2 times the diameter. The castle nut 
has a boss on the upper surface with six slots for a locking pin through 
the bolt. 

Standard Automobile Screws, Castle and Plain Nuts. 

All dimensions in inches. P = pitch, or number of threads per inch. 
d = diam. of cotter pin. P -*■ 8 = flat top. 




D 


P 


B 


Ai 


H 


K 


/ 


A 


c 


E 


d 


1/4 


28 


3/8 


7/32 


3/16 


Vlfi 


3/3? 


9/32 


3/3? 


5/64 


1/16 


Wir 


24 


}/2 . 


17/64 


15/64 


1/lfi 


Vlk 


21/64 


3/32 


5/64 


1/16 


3/8 


24 


9/16 


2V64 


9 /32 


3/32 


1/8 


13/32 


1/8 


1/8 


3/3? 


V/16 


20 


U/16 


3/8 


21/64 


3 /32 


1/8 


29/64 


1/8 


1/8 


3/3? 


V? 


20 


3/4 


7/16 


3 /8 


3/37! 


1/8 


9/16 


3/16 


1/8 


3/3? 


«/1« 


18 


7/8 


3V64 


27/64 


3/32 


1/8 


39/64 


3/16 


5 /32 


1/8 


5/8 


18 


15/16 


35/64 


15/32 


3/39, 


VS 


23/32 


1/4 


5/3? 


1/8 


H/tfi 


16 


1 


19/32 


33/64 


3/3? 


1/8 


49/64 


1/4 


5/32 


1/8 


3/4 


16 


»l/8 


21/32 


9/16 


3/3?, 


1/8 


13/16 


V4 


5 /32 


1/8 


7/8 


14 


H/4 


49/64 


21/32 


3/3? 


1/8 


29/32 


1/4 


5/32 


1/8 


1 


14 


17/16 


7/8 


3/4 


3/32 


1/8 


1 


1/4 


5 /32 


1/8 



INTERNATIONAL STANDARD THREAD (METRIC SYSTEM). 

P = pitch, = 1 — no. of threads per millimeter. 

Depth of thread = 0.6495 P. 

Flat top and bottom of thread = one-eighth pitch. 

Diam. at bottom of thread = diam. of bolt - 1.299 P. 
Diam., mm. 6 7 8 9 10 11 12 14 16 18 20 22 24 27 
Pitch, mm. 1.0 1.0 1.25 1.25 1.5 1.5 1.75 2. 2. 2.5 2.5 2.5 3. 3. 
Diam., mm. 30 33 36 39 42 45 48 52 56 60 64 68 72 76 80 
Pitch, mm. 3.5 3.5 4. 4. 4.5 4.5 5. 5. 5.5 5.5 6. 6. 6.5 6.5 7. 

BRITISH ASSOCIATION STANDARD THREAD. 

The angle between the threads is 471/2°. The depth of the thread is 
0.6 X the pitch. The tops and bottoms of the threads are rounded with 
a radius of 2/n of the pitch. 

Number 1 2 3 4 5 6 

Diameter, mm 6.0 5.3 4.7 4.1 3.64 3.2 2.8 

Pitch, mm 1.00 0.90 0.81 0.73 0.66 0.59 0.53 



SIZE OF ROUGH IRON FOR U. S. STANDARD BOLTS. 223 



Number 7 

Diameter, mm 2.5 

Pitch, mm 0.48 



0.43 



9 


10 


12 


14 


19 


1.9 


1.7 


1.3 


1.0 


.79 


0.39 


0.35 


0.28 


0.23 


0.19 



LIMIT GAUGES FOR IRON FOR SCREW-THREADS. 

In adopting the Sellers, or Franklin Institute, or United States Stand- 
ard, as it is variously called, a difficulty arose from the fact that it is 
the habit of iron manufacturers to make iron over-size, and as there are 
no over-size screws in the Sellers system, if iron is too large it is necessary 
to cut it away with the dies. So great is this difficulty, that the practice 
of making taps and dies over-size has become very general. If the 
Sellers system is adopted it is essential that iron should be obtained of the 
correct size, or very nearly so. Of course no high degree of precision is 
possible in rolling iron, and when exact sizes were demanded, the ques- 
tion arose how much allowable variation there should be from the true 
size. It was proposed to make limit-gauges for inspecting iron with two 
openings, one larger and the other smaller than the standard size, and 
then specify that the iron should enter the large end and not enter the 
small one. The following table of dimensions for the limit-gauges was 
adopted by the Master Car-Builders' Association in 1883. 



Size of 


Large 


Small 


Differ- 


Size of 


Large 


Small 


Differ- 


Iron. 


End of 


End of 


Iron. 


End of 


End of 


In. 


Gauge. 


Gauge. 




In. 


Gauge. 


Gauge. 




1/4 


0.2550 


0.2450 


0.010 


5/8 


0.6330 


0.6170 


0.016 


5 /l6 


0.3180 


0.3070 


0.011 


3/ 4 


0.7585 


0.7415 


0.017 


3/8 


0.3810 


0.3690 


0.012 


7/8 


0.8840 


0.8660 


0.018 


7/16 


0.4440 


0.4310 


0.013 


1 


1.0095 


0.9905 


0.019 


V2 


0.5070 


0.4930 


0.014 


H/8 


1.1350 


1.1150 


0.020 


9 /l6 


0.5700 


0.5550 


0.015 


H/4 


1.2605 


1.2395 


0.021 



Caliper gauges with the above dimensions, and standard reference 
gauges for testing them, are made by the Pratt & Whitney Co. 

THE MAXIMUM VARIATION IN SIZE OF ROUGH IRON 
FOR U. S. STANDARD BOLTS. 

Am. Mach., May 12, 1892. 

By the adoption of the Sellers or U. S. Standard, thread taps and dies 
keep their size much longer in use when flatted in accordance with this 
system than when made sharp "V", though it has been found advisable 
in practice in most cases to make the taps of somewhat larger outside 
diameter than the nominal size, thus carrying the threads further towards 
the V-shape and giving corresponding clearance to the tops of the threads 
when in the nuts or tapped holes. 

Makers of taps and dies often have calls for taps and dies, U. S. Stand- 
ard, "for rough iron." 

An examination of rough iron will show that much of it is rolled out of 
round to an amount exceeding the limit of variation in size allowed. 

In view of this it may be desirable to know what the extreme varia- 
tion in iron may be, consistent with the maintenance of U. S. Standard 
threads, i.e., threads which are standard when measured upon the angles, 
the only place where it seems advisable to have them fit closely. Mr. 
Chas. A. Bauer, the general manager of the Warder, Bushnell & Glessner 
Co., at Springfield, Ohio, in 1884 adopted a plan which may be stated as 
follows: All bolts, whether cut from rough or finished stock, are stand- 
ard size at the bottom and at the sides or angles of the threads, the vari- 
ation for fit of the nut and allowance for wear of taps being made in the 
machine taps. Nuts are punched with holes of such size as to give 85 
per cent of a full thread, experience showing that the metal of wrought 
nuts will then crowd into the threads of the taps sufficiently to give 
practically a full thread, while if punched smaller some of the metal will 
be cut out by the tap at the bottom of the threads, which is of course 
undesirable. Machine taps are made enough larger than the nominal 



224 



MATERIALS. 



to bring the tops of the threads up sharp, plus the amount allowed for 
fit and wear of taps. This allows the iron to be enough above the nomi- 
nal diameter to bring the threads up full (sharp) at top, while if it is 
small the only effect is to give a flat at top of threads; neither condition 
affecting the actual size of the thread at the point at which it is intended 
to bear. Limit gauges are furnished to the mills, by which the iron is 
rolled, the maximum size being shown in the third column of the table 
The minimum diameter is not given, the tendency in rolling being nearly 
always to exceed the nominal diameter. 

In making the taps the threaded portion is turned to the size given in 
the eighth column of the table, which gives 6 to 7 thousandths of an inch 
allowance for fit and wear of tap. Just above the threaded portion of the 
tap a place is turned to the size given in the ninth column, these sizes 
being the same as those of the regular U. S. Standard bolt, at the bottom 
of the thread, plus the amount allowed for fit and wear of tap; or, in other 
words, d' = U. S. Standard d + (Z)' — D). Gauges like the one in the 
cut, Fig. 75, are furnished for this sizing. In finishing the threads of the 




Fig. 75. 



tap a tool is used which has a removable cutter finished accurately to 
gauge by grinding, this tool being correct U. S. Standard as to angle, 
and flat at the point. It is fed in and the threads chased until the flat 
point just touches the portion of the tap which has been turned to size 
§'. Care having been taken with the form of the tool, with its grinding 
on the top face (a fixture being provided for this to insure its being ground 
properly), and also with the setting of the tool properly in the lathe, the 
result is that the threads of the tap are correctly sized without further 
attention. 

STANDARD SIZES OF SCREW-THREADS FOR BOLTS 
AND TAPS. 

(Chas. A. Bauer.) 



A 


n 


D 


d 


h 


/ 


D'-D 


D' 


d' 


H 






Inches 


Inches 


Inches 


Inches 


Inches 


Inches 


Inches 


Inches 


1/4 


20 


0.2608 


0.1855 


0.0379 


0.0062 


0.006 


0.2668 


0.1915 


0.2024 


&/10 


18 


0.3245 


0.2403 


0.0421 


0.0070 


0.006 


0.3305 


0.2463 


0.2589 


3/8 


16 


0.3885 


0.293S 


0.0474 


0.0078 


0.006 


0.3945 


0.2998 


0.3139 


7/1*5 


14 


0.4530 


0.3447 


0.0541 


0.0089 


0.006 


0.4590 


0.3507 


0.3670 


V? 


13 


0.5166 


0.4000 


0.0582 


0.0096 


0.006 


0.5226 


0.4060 


0.4236 


«/lfi 


12 


0.5805 


0.4543 


0.0631 


0.0104 


0.007 


0.5875 


0.4613 


0.4802 


5 /s 


11 


0.6447 


0.5069 


0.0689 


0.0114 


0.007 


0.0517 


0.5139 


0.5346 


3/4 


10 


0.7717 


0.6201 


0.0758 


0.0125 


0.007 


0.7787 


0.6271 


0.6499 


7/R 


9 


0.8991 


0.7307 


0.0842 


0.0139 


0.007 


0.9061 


0.7377 


0.7630 


1 


8 


1.0271 


0.8376 


0.0947 


0.0156 


0.007 


1.0341 


0.8446 


0.8731 


11/8 


7 


1.1559 


0.9394 


0.1083 


0.0179 


0.007 


1.1629 


0.9464 


0.9789 


11/4 


7 


1.2809 


1.0644 


0.1083 


0.0179 


0.007 


1.2879 


1.0714 


1.1039 



A — nominal diameter of bolt. 
D = actual diameter of bolt. 
d = diameter of bolt at bottom of 

thread. 
n = number of threads per inch. 
/ = flat of bottom of thread. 
h = depth of thread. 



D' and d' = diameters of tap. 

H = hole in nut before tapping. 

D = A + 0.2165/n. 

d = A- 1.29904/n. 

h = 0.7577/n = (D - d)/2. 

f = 0.125/w. 

H = D'_i^? = .D'-o.85(2ft). 



STANDARD SET-SCREWS AND CAP-SCREWS. 225 



STANDARD SET-SCREWS AND CAP-SCREWS. 

American, Hartford, and Worcester Machine-Screw Companies. 
(Compiled by W. S. Dix, 1895.) 



(See tables below) 

Diameter of screw 

Threads per inch 

Size of tap drill * 



(A) 


(B) 


(C) 


(D) 


(E) 


(F) 


1/8 


3/16 


1/4 


Wifi 


3/8 


7/16 


40 


24 


20 


18 


16 


14 


No. 43 


No. 30 


No. 5 


17/64 


21/64 


3/8 


(H) 


(I) 


(J) 


(K) 


(L) 


(M) 


9/16 


Ws 


3/ 4 


V/8 


1 


1 


12 


11 


10 


9 


8 


7 


31/64 


17/32 


21/32 


49/64 


7/8 


63/64 



(G) 

1/2 

12 

27/64 



Diameter of screw. 
Threads per inch . . 
Size of tap drill * . . . 



(N) 

IV 

7 

H/8 



* For cast iron. For numbers of twist-drills, see page 30. 



Set-screws. 


Hex. Head Cap-screws. 


Sq. Head Cap-screws. 


Short 

Diam. 

of Head. 


Long 
Diam. 
ofH'd. 


Lengths 
(under 
Head). 


Short 
Diam. 

of 
Head. 


Long 
Diam. 

of 
Head. 


Lengths 
(under 
Head). 


Short 
Diam. 

of 
Head. 


Long 
Diam. 

of 
Head. 


Lengths 
(under 
Head)... 


(C) 1/4 

(D) 5/i6 

(E) 3/ 8 

(F) 7/ie 

(G) 1/2 
(H) 9/ 16 
(I) S/g 
(J) 3/4 
(K) 7/s 
(L) 1 
(M) H/8 
(N) H/4 


0.35 

.44 

.53 

.62 

.71 

.80 

.89 

1.06 

1.24 

1.42 

1.60 

1.77 


3/ 4 to 3 

3/4 to 3 1/ 4 
3/ 4 to 31/ 2 
3/ 4 to 33/4 
3/ 4 to 4 
3/ 4 to 41/4 
3/4 to 41/2 

1 to 43/ 4 

1 1/4 to 5 

1 1/2 to 5 

1 3/ 4 to 5 
2 to 5 


7/16 
1/2 
9 /l6 
5/8 
3/4 
13/16 
7/8 
1 

U/8 
U/4 
13/8 
1 1/2 


0.51 
.58 
.65 
.72 
.87 
.94 
1.01 
1.15 
1.30 
1.45 
1.59 
1.73 


3/4 to 3 

3/4 to 3 1/4 
3/4 to 3 1/ 2 
3/ 4 to 3 3/ 4 
3/ 4 to 4 
3/ 4 to 41/4 

1 to 41/2 
1 1/4 to 43/4 
1 1/2 to 5 

1 3/ 4 to 5 

2 to 5 
2 to 5 


3/8 

7/16 

1/2 

9 /l6 

5/8 

11/16 

3/4 

7/8 

U/8 

11/4 

13/ 8 

H/2 


0.53 

.62 

.71 

.80 

.89 

.98 

1.06 

1.24 

1.60 

1.77 

1.95 

2.13 


3/ 4 to 3 
3/4 to 3 1/ 4 
3/4 to 3 1/ 2 
3/4 to 33/ 4 
3/ 4 to 4 
3/4 to 41/4 

1 to 41/2 
1 1/4 to 43/ 4 
1 1/2 to 5 

1 3/ 4 to 5 

2 to 5 
21/4 to 5 



Round and Fillister Head 
Cap-screws. 


Flat Head Cap-screws. 


Button-head Cap- 
screws. 


Diam. of 
Head. 


Lengths 

(under 

Head). 


Diam. of 
Head. 


Lengths 

(including 

Head). 


Diam. of 
Head. 


Lengths 
(under 
Head). 


(A) 3/ie 

(B) 1/4 

(C) 3/8 

(D) 7/ie 

(E) 9/16 

(F) 5/8 

(G) 3/4 
(H) 13/16 
(I) 7/ 8 
(J) 1 
(K) U/8 
(L) 1 1/4 


3/ 4 to 21/2 
3/4 to 23/4 
3/4 to 3 
3/ 4 to 31/4 
3/ 4 to 3 1/2 
3/ 4 to 33/ 4 
3/4 to 4 

1 to 41/4 
U/4 to 41/2 
1 1/2 to 43/4 
1 3/ 4 to 5 

2 to 5 


1/4 
3/8 

15/32 
5/8 
3/4 

13/16 
7/8 
1 

U/8 

13/8 


3/4 to 1 3/4 
3/4 to 2 
3/ 4 to 21/4 
3/ 4 to 23/4 
3/ 4 to 3 

1 to 3 
1 1/4 to 3 
1 1/2 to 3 
1 3/ 4 to 3 

2 to 3 


7/32 (-225) 
5/16 
7/16 
9/16 
5/8 
3/4 
13/16 
15/16 

U/4 


3/4 to 13/4 
3/4 to 2 
3/4 to 21/ 4 
3/ 4 to 21/2 
3/4 to 23/ 4 
3/4 to 3 
1 to 3 

1 1/4 to 3 

1 1/2 to 3 

1 3/ 4 to 3 



Threads are U. S. Standard. Cap-screws are threaded 3/ 4 length up 
to and including 1 inch diameter X 4 inches long, and 1/2 length above. 
Lengths increase by 1/4 inch each regular size between the limits given. 
Lengths of heads, except flat and button, equal diameter of screws. 

The angle of the cone of the flat-head screw is 76 degrees, the sides 
making angles of 52 degrees with the top. 



226 



MATERIALS. 



THE ACME SCREW THREAD. 

The Acme Thread is an adaptation of the commonly used style of worm j 
thread and is intended to take the place of the square thread. It is a 
little shallower than the worm thread, but the same depth as the square !' 
thread and much stronger than the latter. The angle of the thread is 29°. 

The various parts of the Acme Thread are obtained as follows: 

Width of point of tool for screw or tap thread = 
(0.3707 -*- No. of Threads per in.) - 0.0052. 

Width of screw or nut thread = 0.3707 -s- No. of Threads per in. 

Diam. of Tap = Diam. of Screw + 0.020. 

: Diam. of Screw- XT „ „„ r^, 1 ,^ ._ + 0.020. 



Diam. of Tap or ) 
Screw at Root J 



Depth of Thread = (1 



No. of Threads per in. 
- 2 X No. of Threads per in.) + 0.010. 



MACHINE SCREWS.— A. £.M.#. Standard. 

The American Society of Mechanical Engineers (1907) received a report 
on standard machine screws from its committee on that subject. The 
included angle of the thread is 60 degrees and a flat is made at the top 
and bottom of the thread of one-eighth the basic diameter. A uniform 
increment of 0.013 inch exists between all sizes from to 10 and 0.026 
inch in the remaining sizes. The pitches are a function of the diameter 
as expressed by the formula 

Threads per inch = D + 002 m 

The minimum tap conforms to the basic standard in all respects except 
diameter. The difference between the minimum tap and the maximum 
screw provides an allowance for error in pitch and for wear of the tap in 
service. 

A. S. M. E. STANDARD MACHINE SCREWS. 
(Corbin Screw Corporation.) 



Size. 


Outside Diameters. 


Pitch Diameters. 


Root Diameters. 




Out. 




















No. 


Dia. 

and 


Mini- 


Maxi- 


Dif- 
fer- 


Mini- 


Maxi- 


Dif- 
fer- 


Mini- 


Maxi- 


Dif- 




Thds. 


mum. 


mum. 




mum. 


mum. 




mum. 


mum. 










ence. 






ence. 






ence. 




per In. 























0.060-80 


0.0572 


0.060 


0.0028 


0.0505 


0.0519 


0.0014 


0.0410 


0.0438 


0.0028 


I 


.073-72 


.070 


.073 


.003 


.0625 


.064 


.0015 


.052 


.055 


.0030 


2 


.086-64 


.0828 


.086 


.0032 


.0743 


.0759 


.0016 


.0624 


.0657 


.0033 


3 


.099-56 


.0955 


.099 


.0035 


.0857 


.0874 


.0017 


.0721 


.0758 


.0037 


4 


.112-48 


. 1082 


.112 


.0038 


.0966 


.0985 


.0019 


.0807 


.0849 


.0042 


5 


.125-44 


.1210 


.125 


.0040 


.1082 


.1102 


.0020 


.0910 


.0955 


.0045 


6 


.138-40 


.1338 


.138 


.0042 


.1197 


.1218 


.0021 


.1007 


.1055 


.C048 


7 


.151-36 


.1466 


.151 


.0044 


.1308 


.1330 


.0022 


.1097 


.1149 


.0052 


8 


.164-36 


.1596 


.164 


.0044 


.1438 


.146 


.0022 


.1227 


.1279 


.0052 


9 


.177-32 


.1723 


.177 


.0047 


.1544 


.1567 


.0023 


.1307 


.1364 


.0057 


10 


.190-30 


.1852 


.190 


.0048 


.166 


.1684 


.0024 


.1407 


.1467 


.0060 


12 


.216-28 


.2111 


.216 


.0049 


.1904 


.1928 


.0024 


.1633 


.1696 


.0063 


14 


.242-24 


.2368 


.242 


.0052 


.2123 


.2149 


.0026 


.1808 


.1879 


.0071 


16 


.268-22 


.2626 


.268 


.0054 


.2358 


.2385 


.0027 


.2014 


.209 


.0076 


18 


.294-20 


.2884 


.294 


.0056 


.2587 


.2615 


.0028 


.2208 


.229 


.0082 


20 


.320-20 


.3144 


.320 


.0056 


.2847 


.2875 


.0028 


.2468 


.255 


.0082 


22 


.346-18 


.3402 


.346 


.0058 


.3070 


.3099 


.0029 


.2649 


.2738 


.0089 


24 


.372-16 


.366 


.372 


.0060 


.3284 


.3314 


.0030 


.281 


.2908 


.0098 


26 


.398-16 


.392 


.398 


.0060 


.3544 


.3574 


.0030 


.307 


.3168 


.0098 


28 


.424-14 


.4178 


.424 


.0062 


.3745 


.3776 


.0031 


.3204 


.3312 


.0108 


30 


.450-14 


.4438 


.450 


.0062 


.4005 


.4036 


.0031 


.3464 


.3572 


.0108 



A. S. M. E. STANDARD TAPS. 



227 



A.S.M.E. STANDARD TAPS. 

(Corbin Screw Corporation.) 



Size. 


Outside Diameters. 


Pitch Diameters. 


Root Diameters. 


























Tap 


























Out. 




















Drill 


No. 


Dia. 

and 
Thds. 

per 
Inch. 


Mini- 
mum. 


Maxi- 
mum. 


Dif- 
fer- 
ence. 


Mini- 
mum. 


Maxi- 
mum. 


Dif- 
fer- 
ence. 


Mini- 
mum. 


Maxi- 
mum. 


Dif- 
fer- 
ence. 


Di- 
am- 
eters. 





0.060-80 


0.0609 


0.0632 


0.0023 


0.0528 


0.0538 


0.001 


0.0447 


0.0466 


0.0019 


0.0465 


1 


.073-72 


.074 


.0765 


.0025 


.065 


.066 


.001 


.056 


.058 


.002 


.0595 


2 


.086-64 


.0871 


.0898 


.0027 


.0770 


.0781 


.0011 


.0668 


.0689 


.0021 


.070 


3 


.099-56 


.1002 


.1033 


.0031 


.0886 


.0897 


.0011 


.077 


.0793 


.0023 


.0785 


4 


.112-48 


.1133 


.1168 


.0035 


.0998 


.101 


.0012 


.0852 


.0887 


.0025 


.089 


5 


.125-44 


.1263 


.1301 


.0038 


.1116 


.1129 


.0013 


.0968 


.0995 


.0027 


.0995 


6 


.138-40 


.1394 


.1435 


.0041 


.1232 


.1246 


0014 


.1069 


.1097 


.0028 


.110 


7 


.151-36 


.1525 


.1569 


.0044 


.1345 


.1359 


.0014 


.1164 


.1193 


.0029 


.120 


8 


.164-36 


.1655 


.1699 


.0044 


.1475 


.1489 


.0014 


.1294 


.1323 


.0029 


.136 


9 


.177-32 


.1786 


.1835 


.0049 


.1583 


.1598 


.0015 


.138 


.1411 


.0031 


.1405 


10 


.190-30 


.1916 


.1968 


.0052 


.170 


.1716 


.0016 


.1483 


.1515 


.0032 


.152 


12 


.216-28 


.2176 


.2232 


.0056 


.1944 


.1961 


.0017 


.1712 


.1745 


.0033 


.173 


14 


.242-24 


.2438 


.250 


.0062 


.2167 


.2184 


.0017 


.1897 


.1932 


.0035 


.1935 


16 


.268-22 


.2698 


.2765 


.0067 


.2403 


.2421 


.0018 


.2108 


.2144 


.0036 


.213 


18 


.294-20 


.2959 


.3031 


.0072 


.2634 


.2652 


.0018 


.2309 


.2346 


.0037 


.234 


20 


.320-20 


.3219 


.3291 


.0072 


.2894 


.2912 


.0018 


.2569 


.2606 


.0037 


.261 


22 


.346-18 


.3479 


.3559 


.0080 


.3118 


.3138 


.0020 


.2757 


.2796 


.0039 


.281 


24 


.372-16 


.374 


.3828 


.0088 


.3334 


.3354 


.0020 


.2928 


.2968 


.004C 


.2968 


26 


.398-16 


.400 


.4088 


.0088 


.3594 


.3614 


.002C 


.3188 


.3228 


.004C 


.323 


28 


.424-14 


.4261 


.4359 


.0098 


.3797 


.3818 


.0021 


.3333 


.3374 


.0041 


.339 


30 


.450-14 


.4521 


.4619 


.0098 


.4057 


.4078 


.0021 


.3593 


.3634 


.0041 


.368 



SPECIAL TAPS. 



1 


0.073-64 


0.0741 


0.0768 


0.0027 


0.064 


0.0651 


0.0011 


0.0538 


0.0559 


0.0021 


0.055 


2 


.086-56 


.0872 


.0903 


.0031 


.0756 


.0767 


.0011 


.064 


.0663 


.0023 


.067 


3 


.099-48 


.1003 


.1038 


.0035 


.0868 


.088 


.0012 


.0732 


.0757 


.0025 


.076 


4 


.112-40 


.1134 


.1175 


.0041 


.0972 


.0986 


.0014 


.0809 


.0837 


.0028 


.082 




36 


.1135 


.1179 


.0044 


.0955 


.0969 


.0014 


.0774 


.0803 


.0029 


.081 


5 


.125-40 


.1264 


.1305 


.0041 


.1102 


.1116 


.0014 


.0939 


.0967 


.C028 


.098 




36 


.1255 


.1309 


.0044 


.1085 


.1099 


.0014 


.0904 


.0933 


.0029 


.0935 


6 


.138-36 


.1395 


.1439 


.0044 


.1215 


.1229 


.0014 


.1034 


.1063 


.0029 


.1065 




32 


.1396 


.1445 


.0049 


.1193 


.1208 


.0315 


.099 


.1021 


.0031 


.1015 


7 


.151-32 


.1526 


.1575 


.0049 


.1323 


.1338 


.0315 


.112 


.1151 


.0031 


.116 




30 


.1526 


.1578 


.0052 


.131 


.1326 


.0016 


.1093 


.1125 


.0032 


.113 


8 


.164-32 


.1656 


.1705 


.0049 


.1453 


.1468 


.0015 


.125 


.1281 


.0031 


.1285 




30 


.1656 


.1708 


.0052 


.144 


.1456 


.0016 


.1223 


.1255 


."032 


.1285 


9 


.177-30 


.1786 


.1838 


.0052 


.1569 


.1585 


.0016 


.1353 


.1385 


.0032 


.1405 




24 


.1788 


.185 


.0962 


.1517 


.1534 


.0017 


.1247 


.1282 


.0035 


.1285 


10 


.190-32 


.1916 


.1965 


.0049 


.1713 


.1728 


.0015 


.151 


.1541 


.0031 


.154 




24 


.1918 


.198 


.:062 


.1647 


.1664 


.0017 


.1377 


.1412 


.0035 


.1405 


12 


.216-24 


.2178 


.224 


.0062 


.1907 


. 1 ?24 


.0017 


.1637 


.1672 


.C035 


.166 


14 


.242-20 


.2439 


.2511 


.0072 


.2114 


.2132 


.0018 


.1789 


.1826 


.0037 


.182 


16 


.268-20 


.2699 


.2771 


.0072 


.2374 


.2392 


.0018 


.2049 


.2086 


.0037 


.209 


18 


.294-18 


.2959 


.3039 


.0080 


.2598 


.2618 


.0020 


.2237 


.2276 


.0039 


.228 


20 


.320-18 


.3219 


.3299 


.0080 


.2858 


.2878 


.0020 


.2497 


.2536 


.0039 


.257 


22 


.346-16 


.348 


.3568 


.0088 


.3074 


.3094 


.0020 


.2668 


.2708 


.0040 


.272 


24 


.372-18 


.3739 


.3819 


.0080 


.3378 


.3398 


.0020 


.3017 


.3056 


.0039 


.3125 


26 


.398-14 


.4001 


.4099 


.0098 


.3537 


.3558 


.0021 


.3073 


.3114 


.0041 


.316 


28 


.424-16 


.426 


.4348 


.0088 


.3854 


.3874 


.0020 


.3448 


.3488 


.0040 


.348 


30 


.450-16 


.452 


.4608 


.0088 


.4114 


.4134 


.0020 


.3708 


.3748 


.0040 


.377 



228 



MATERIALS. 



DIMENSIONS OF MACHINE SCREW HEADS, A.S.M.E. 
STANDARD. 




ROUND HEAD. 

(2) 



H3 



OVAL. FILLISTER FLAT FILLI8- 
HEAD. TER HEAD. 

(3) (4) 



Dimensions. 



A=Diam.ofBody. D 
B = Diameter of 

Head, and r ad. 

of oval (3). 
C = H eight of i a-O.OC 

Head or Side > — ■ _ on 

of Head (3). ) 1 - 739 
E= Width of Slot, 1/3C 
F= Height of ) 

Head (3). J 



Width of Slot = 0.173 A + 0.015. 

(1) (2) (3) (4) 

2A-0.008 1.85A- 0.005 1.64A-0.009 1.64A- 0.009 



0.7A 0.66A-0.002 0.66A- 0.002. 
V2C+O.OI 1/ 2 F I/2C 
0.134B]+C 



A 


B 


B 


B 


C! 


C 


C 


D 

0~025~ 


E 


E 


E 


E 


F 


(1) 


(2) 

106 


(3,4) 


(1) 


(2) 


(3,4) 


(1) 


(2) 

oToTT 


(3) 


(4) 

0.019 


(3) 


0.060 


11?. 


0.0894 


029 


042 


0.0376 


0.010 


0.025 


0.0496 


073 


138 


130 


.1107 


.037 


.051 


.0461 


.028 


.012 


.035 


.030 


023 


.0609 


086 


164 


154 


.132 


,045 


,060 


.0548 


.030 


.015 


.040 


.036 


027 


.0725 


099 


190 


178 


.153 


052 


069 


.0633 


.032 


.017 


.044 


.042 


.032 


.0838 


.112 


.216 


.202 


.1747 


.060 


.078 


.0719 


.034 


.020 


.049 


.048 


.036 


.0953 


.125 


242 


226 


.196 


067 


087 


.0805 


.037 


022 


.053 


.053 


.040 


.1068 


,138 


262 


250 


.217 


075 


096 


.089 


.039 


.025 


.058 


.059 


.044 


.1180 


.151 


294 


274 


.2386 


,082 


.105 


.0976 


.041 


.027 


.062 


.065 


.049 


.1296 


.164 


320 


298 


.2599 


090 


114 


.1062 


.043 


.030 


.067 


.071 


053 


.1410 


.177 


.346 


.322 


.2813 


.097 


.123 


.1148 


.046 


.032 


.071 


.076 


.057 


.1524 


.190 


372 


346 


.3026 


.105 


133 


.1234 


.048 


.035 


.076 


.082 


062 


.1639 


.216 


424 


394 


.3452 


.120 


.151 


.1405 


,052 


.040 


.085 


.093 


070 


.1868 


242 


472 


443 


.3879 


.135 


169 


.1577 


.057 


.045 


.094 


.105 


.079 


.2097 


268 


.528 


491 


.4305 


.150 


.187 


.1748 


.061 


.050 


.103 


.116 


.087 


.2325 


294 


.580 


.539 


.4731 


.164 


.205 


.192 


.066 


.055 


.112 


.128 


.096 


.2554 


320 


632 


587 


.5158 


179 


224 


.2092 


.070 


.060 


.122 


.140 


104 


.2783 


.346 


682 


635 


.5584 


.194 


.242 


.2263 


.075 


.065 


.131 


.150 


.113 


.3011 


„372 


.732 


,683 


.601 


.209 


.260 


.2435 


.079 


.070 


.140 


.162 


.122 


.3240 


.398 


.788 


.731 


.6437 


.224 


.278 


.2606 


.084 


.075 


.149 


.173 


.130 


.3469 


.424 


.840 


.779 


.6863 


.239 


.296 


.2778 


.088 


.080 


.158 


.185 


.139 


.3698 


.450 


.892 


.827 


.727 


.254 


.315 


.295 


.093 


.085 


.167 


.201 


.147 


.4024 





WEIGHT OF 
WEIGHT OF 


100 BOLTS WITH SQUARE 

100 BOLTS WITH SQUARE 

(Hoopes & Townsend.) 


HEADS. 
HEADS. 


220 




am. 
3hes. 


1/4 


5/16 


3/8 


7/16 


1/2 


9/16 


5/8 


3/4 


7/8 


1 


H/8 


11/4 


13/8 


11/2 


13/4 


2 I 


agth. 
ches. 

H/2 

2 

21/2 

3 

31/2 

4 

41/2 

51/2 

6 

61/ 2 

7 
'71/2 

8 

9 
10 
II 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 


lbs. 
3.9 
4.6 
5.4 
6.2 
6.9 
7.6 
8.3 
9.0 
9.7 
10.4 
11.1 
11.8 
12.5 
13.2 


lbs. 
6.2 
7.2 
8.2 
9.3 
10.4 
11.5 
12.6 
13.7 
14.8 
15.9 
17.0 
18.1 
19.2 
20.3 


lbs. 
9.7 
11.3 
12.9 
14.5 
16.1 
17.7 
19.2 
20.7 
22.2 
23.7 
25.2 
2o.7 
28.2 
29.7 
33.1 
36.5 
40.0 
43.5 


lbs. 
14.7 
16.5 
18.5 
20.5 
22.6 
24.7 
26.8 
28.9 
31.0 
33.1 
35.2 
37.3 
39.4 
41.5 
45.7 
49.9 
54.1 
58.3 


lbs. 
20.4 
22.4 
25.0 
27.8 
30.6 
33.4 
36.2 
39.0 
41.8 
44.6 
47.4 
50.2 
53.1 
56.0 
61.5 
67.0 
72.5 
78.0 
83.5 
89.0 
94.5 
100.0 
105.5 
111.0 
116.5 
122.0 


lbs. 

26.0 
29.0 
32.2 
35.4 
38.7 
42.0 
45.3 
48.6 
51.9 
55.2 
58.5 
61.8 
65.1 
68.5 
75.2 
81.9 
88.7 
95.5 
102.3 
109.1 
116.0 
123.0 
130.0 
137.0 

144:0 

151.0 


lbs. 
37.0 
39.9 
44.1 
48.3 
52.5 
56.7 
60.9 
65.1 
69.2 
73.4 
77.6 
81.8 
86.0 
90.0 
98.0 
106.3 
114.6 
122.9 
131.2 
139.5 
148.0 

156:5 

165.0 
173.5 
182.0 
190.5 
198.0 
206.0 
215.0 
224.0 


lbs. 
58.0 
63.2 
69.0 
75.2 
81.4 
87.6 
93.8 
100.0 
106.1 
112.2 
118.3 
124.4 
130.5 
136.6 
148.8 
161.0 
173.2 
184.4 
196.6 
208.8 
221.0 
233.2 
245.4 
257.6 
269.8 
282.0 
294.0 
306.0 
318.0 
330.0 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


97.7 
105.6 
113.8 
122.0 
130.2 
138.4 
146.6 
154.9 
163.2 
171.5 
179.8 
187.1 
195.4 
212.0 
229.0 
246.0 
263.0 
280.0 
297.0 
314.0 
331.0 
348.0 
365.0 
382.0 
399.0 
416.0 
437.0 
454.0 
470.0 


145 
153 
163 
174 
185 
196 
207 
218 
229 
240 
251 
262 
273 
295 
317 
339 
361 
383 
405 
427 
449 
471 
493 
515 
537 
559 
581 
603 
625 


























240 
253 
267 
281 
295 
309 
323 
337 
351 
365 
379 
407 
435 
463 
491 
519 
547 
575 
603 
631 
659 
687 
715 
743 
771 
799 
827 
855 


309 
325 
342 
359 
376 
394 
412 
430 
448 
466 
484 
518 
552 
586 
620 
655 
690 
725 
760 
795 
830 
865 
900 
935 
970 
1005 
1040 
1075 


350 
370 
390 
410 
430 
450 
470 
490 
510 
530 
550 
590 
630 
670 
710 
751 
793 
835 
877 
919 
961 
1003 
1045 
1087 
1129 
1171 
1213 
1?Vi 


480 
500 
520 
545 
570 
595 
620 
645 
670 
695 
725 
775 
825 
875 
925 
975 
1025 
1075 
1125 
1175 
1225 
1275 
1325 
1375 
1425 
1475 
1525 
157S 










800 
833 
866 
900 
934 
968 
1002 
1036 
1070 
1138 
1206 
1274 
1342 
1410 
1478 
1548 
1616 
1684 
1752 
1820 
1888 
1956 
2024 
2092 
2160 
??7fi 


1370 
1414 
1458 
1502 
1546 
1590 
1634 
1722 






1810 






1898 






1986 






2074 










2162 










2250 










2338 










2426 










2514 










2602 










2690 










2778 














2866 














2954 














3042 














3130 





























ROUND HEAD RIVETS. 














Approximate Number in One Pound. (Garland Nut & Rivet Co.) 


si 


7/16 


3/8 


5/13 


1/4 


7/32 


3/16 


r, /32 


1/8 


- - 


7/16 


3/8 


5/16 


1/4 


7/32 


3/16 


f) /32 


1/8 


CJ 


















3^ 


















3/s 






68 


103 


145 


184 


194 


204 


13/8 


10 l/o 


15 


22 


34 


46 


65 


76 


87 


v? 




31 


51 


80 


108 


155 


165 


175 


1 3/,, 


10 


14 


21 


32 


43 


62 


72 


81 


5/8 




28 


45 


70 


94 


135 


148 


160 


17/s 


91/o 


13 


20 


30 


41 


58 


69 




3/ 4 


17 


24 


39 


63 


84 


119 


132 


144 


2 


9 


12 


19 


29 


39 


55 


67 




7/8 


15 


22 


35 


56 


75 


106 


121 


135 


21/1 


81/4 


11 


17 


27 


35 


49 






1 


14 


20 


32 


50 


68 


96 


111 


126 


2 l/o 


73/ 4 


10 


16 


24 


32 


45 






H/8 


13 


19 


30 


46 


62 


88 


102 


116 


23/.« 


71/4 


9 


14 


22 


29 


42 






U/4 


12 


18 


28 


43 


57 


81 


94 


108 


3 


63/ 4 


8 


13 


20 


21 


39 






13/8 


111/9 


17 


26 


40 


53 


74 


87 


100 


i 1/9 


6 


7 


11 


18 


lb 


34 






H/2 


11 


16 


24 


37 


50 


69 


81 


93 


4 


5 


6 


10 


16 


20 


30 







Small rivets are made to fit holes of their rated size; the actual diameter 
may vary slightly from the decimals given below: 

Size 3/32 7/ 64 l/ 8 9/64 6/33 U/ M 3/ 16 

Approx. diam 094 .109 .125 .140 .155 .170 .185 

Size 7/32 1/4 9 /32 5 / 16 3/ 8 7/ 16 

Approx. diam 215 .245 .275 .305 .365 .425 



230' 



MATERIALS. 





With United 


TRACK BOLTS. 

States Standard Hexagon Nuts. 






Wt.of 

Rail. 

Lb. per 

Yard. 


Bolts. 


Nuts. 


No. in 
Keg, 
200 
Lb. 


Kegs 
per 
Mile. 


Wt. of 

Rail. 

Lbs. per 

Yard. 




Nuts. 


No. in 
Keg, 
200 
Lb. 

375 
410 
435 
465 
715 
760 
800 
820 


Kegs 
per 
Mile. 


45 to 85 | 


3/ 4 x41/4 

3/ 4 x4 

3/4X33/4 

3/4X31/2 

3/4x31/4 

3/4 X 3 


11/4 
U/4 
U/4 
11/4 
U/4 
U/4 


230 
240 
254 
260 
266 
283 


6.3 
6. 

5.7 
5.5 
5.4 
5.1 


30 to 40 J 
20 to 30 J 


U/16 
U/16 
U/16 
U/16 

7/8 
7/8 
7/8 
7/8 


4. 
3.7 
3.3 
3.1 

2. 
2. 
2. 
2. 



WROUGHT WASHERS, MANUFACTURERS' STANDARD. 

(Upson Nut Co., Cleveland, 1906.) 



Diam. 


Hole. 


Thick- 
ness 
B.W.G. 


Bolt. 


No. in 
200 Lb. 


Diam. 


Hole. 


Thick- 
ness 
B.W.G. 


Bolt. 


No. in 
200 Lb 


In. 


In. 


No. 


In. 




In. 


In. 


No. 


In. 




»/ifi 


1/4 


18 


3/16 


85200 


21/? 


1 V16 


9 


1 


1200 


3/4 


W1R 


16 


1/4 


34800 


23/4 


11/4 


9 


U/8 


888 


7/8 


a/« 


16 


5/16 


26200 


3 


13/8 


9 


U/4 


900 


1 


7/lfi 


14 


3/8 


14400 


31/4 


U/9, 


8 


13/ 8 


600 


U/4 


V? 


14 


7/16 


8400 


31/2 


15/8 


8 


11/2 


570 


m 


a/16 


12 


1/2 


5800 


33/4 


13/ 4 


8 


15/8 


460 


11/2 


Vr 


12 


9/16 


4600 


4 


17/8 


8 


13/4 


432 


13/4 


11/16 


10 


5/8 


2600 


41/4 


2 


8 


17/8 


366 


2 


13/1 fl 


10 


3/4 


2200 


41/2 


21/8 


8 


2 


356 


21/4 


l°/l6 


9 


7/8 


1600 



















SIZES OF CAST WASHERS. 










(Upson Nut Co., Cleveland, 1906.) 






Diam. 


Hole. 


Thick. 


Bolt. 


Weight. 
Lbs. 


Diam. 


Hole. 


Thick. 


Bolt. 


Weight. 
Lbs. 


In. 


In. 


In. 


In. 




In. 


In. 


In. 


In. 




21/4 


5/8 


H/16 


1/2 


1/2 


4 


11/ 8 


15/16 


1 


15/ 8 


23/4 


3/4 


3/4 


5/8 


5/8 


41/2 


U/4 


1 


U/8 


21/4 


3 


7/8 


13/16 


3/4 


3/4 


5 


13/ 8 


U/8 


U/4 


3 


31/2 


1 


7/8 


7/8 


U/4 


6 


13/4 


U/4 


11/2 


5 



TURNBUCKLES. 



231 



CONE-HEAD BOILER RIVETS, Vf EIGHT PER 100. 

. (Hoopes & Townsend.) 



Diam., in., 
Scant. 


1/2 


9 /l6 


5/8 


H/16 


3/4 


13/16 


7/8 


1 


11/8* 


11/4* 


Length. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


3/4 inch 


8.75 
9.35 
10.00 
10.70 
11.40 
12.10 


13.7 
14.4 
15.2 
16.0 
16.8 
17.6 


16.20 
17.22 
18.25 
19.28 
20.31 
21.34 
















7/8 " 
















1 


2K70 
23.10 
24.50 
25.90 


'26:55 
28.00 
29.45 
30.90 












1 1/8 " 












11/4 " 


37.0' 
38.6 


"'46' 

48 


'"60" 
63 






'3/8 " 


'95' 




11/2 " 


12.80 


18.4 


22.37 


27.30 


32.35 


40.2 


50 


65 


98 


" 133 * 


15/8 " 


13.50 


19.2 


23.40 


28.70 


33.80 


41.9 


52 


67 


101 


137 


13/4 " 


14.20 


20.0 


24.43 


30.10 


35.25 


43.5 


54 


69 


104 


141 


17/8 " 


14.90 


20.8 


25.46 


31.50 


36.70 


45.2 


56 


71 


107 


145 


2 


15.60 


21.6 


26.49 


32.90 


38.15 


47.0 


58 


74 


110 


149 


21/8 " 


16.30 


22.4 


27.52 


34.30 


39.60 


48.7 


60 


77 


114 


153 


21/4 " 


17.00 


23.2 


28.55 


35.70 


41.05 


50.3 


62 


80 


118 


157 


23/8 " 


17.70 


24.0 


29.58 


37.10 


42.50 


51.9 


64 


83 


121 


161 


21/2 " 


18.40 


24.8 


30.61 


38.50 


43.95 


53.5 


66 


86 


124 


165 


25/8 " 


19.10 


25.6 


31.64 


39.90 


45.40 


55.1 


68 


89 


17,7 


169 


23/ 4 " 


19.80 


26.4 


32.67 


41.30 


46.85 


56.8 


70 


92 


130 


173 


27/8 " 


20.50 


27.2 


33.70 


42.70 


48.30 


58.4 


72 


95 


133 


177 


3 


21.20 


28.0 


34.73 


44.10 


49.75 


60.0 


74 


98 


137 


181 


31/4 " 


22.60 


29.7 


36.79 


46.90 


52.65 


63.3 


78 


103 


144 


189 


31/2 " 


24.00 


31.5 


38.85 


49.70 


55.55 


66.5 


82 


108 


151 


197 


33/4 " 


25.40 


33.3 


40.91 


52.50 


58.45 


69.8 


86 


113 


158 


205 


4 


26.80 


35.2 


42.97 


55.30 


61.35 


73.0 


90 


118 


165 


2'3 


41/4 " 


28.20 


36.9 


45.03 


58.10 


64.25 


76.3 


94 


124 


172 


221 


41/2 " 


29.60 


38.6 


47.09 


60.90 


67.15 


79.5 


98 


130 


179 


229 


43/4 " 


31.00 


40.3 


49.15 


63.70 


70.05 


82.8 


102 


136 


186 


237 


5 


32.40 


42.0 


51.27 


66.50 


72.95 


86.0 


106 


142 


193 


245 


51/4 " 


33.80 


43.7 


53.27 


69.20 


75.85 


89.3 


110 


148 


200 


254 


51/2 " 


35.20 


45.4 


55.33 


72.00 


78.75 


92.5 


114 


154 


206 


263 


53/4 «' 


36.60 


47.1 


57.39 


74.80 


81.65 


95.7 


118 


160 


212 


272 


6 


38.00 


48.8 


59.45 


77.60 


84.55 


99.0 


122 


166 


218 


281 


6I/2 " 


40.80 


52.0 


63.57 


83.30 


90.35 


105.5 


130 


177 


231 


297 


7 


43.60 


55.2 


67.69 


88.90 


95.15 


112.0 


138 


188 


245 


314 


Heads 


5.50 


8.40 


11.50 


13.20 


18.00 


23.0 


29.0 


38.0 


56.0 


77.5 



* These two sizes are calculated for exact diameter. 



TURNBUCKLES. 

(Cleveland City Forge and Iron Co.) 
Standard sizes made with right and left threads. D = 



outside diameter 




of screw. A = length in clear between heads = 6 ins. for all sizes, 
B = length of tapped heads = 1 1/2 D nearly. C = 6 ins. + 3 D nearly. 



232 



MATERIALS. 



TINNERS' RIVETS. FLAT HEADS. 

Garland Nut & Rivet Co. 



gd 


a a 


is 

■ o 


sfri 


.g 


k 


I s 


-g 
M • 

C S3 




ia 


to • 

S3.C 


0> . 


Q 


h1 


£ 


.Q 


1-} 


fc~ 


Q 


^ 


£~ 


Q 


Hi 


£- 


0.070 


Vs 


4 oz. 


0.115 


13/fi 4 


1 lb. 


0.160 


5/16 


3 lbs. 


0.225 


7/16 


8 


.080 


9/64 


6 


.120 


7/3? 


H/4 


.163 


*V«4 


31/2 


.230 


^9/64 


9 


.090 


5/32 


8 


.125 


15/fi 4 


H/?, 


.173 


11/3?, 


4 


.233 


l°/32 


10 


.094 


U/(M 


10 


.133 


1/4 


13/4 


.185 


8/8 


5 


.253 


1/2 


12 


.101 


3 /l6 


12 


.140 


17/64 


2 


.200 


&/«4 


6 


.275 


33/ fi4 


14 


.109 


3/16 


14 


.147 


9/32 


21/2 


.215 


13/32 


7 


.293 


l>/32 


16 



MATERIAL REQUIRED FOR ONE MILE OF SINGLE TRACK 
RAILROAD. 

(American Bureau of Inspection and Tests, 1908.) 
Cross Ties. 



33-Foot Rail. 


30-Foot Rail. 


Spacing of 
Ties, Center 
to Center. 


Ties per 
Rail. 


Ties per Mile. 


Ties per Rail. 


Ties per Mile. 


20 
18 
16 


3200 
2880 
2560 


18 
16 
14 


3168 
2816 
2464 


1 ft. 6 in. 

1 " 9 " 

2 " " 



Weight per 

Yard. 

Lb. 


Gross Tons 
Per Mile. 


Weight per 

Yard. 

Lb. 


Gross Tons 
Per Mile. 


Weight per 

Yard. 

Lb. 


Gross Tons 
per Mile. 


100 
90 
85 
80 
75 
72 
70 


1571/7 
1413/ 7 
133 4/ 7 
125 5/ 7 
1176/7 
1131/7 
110 


67 
65 
60 
56 
52 
50 
45 


1052/7 
1021/7 
942/7 
88 

815/7 
78 4/7 
705/ 7 


40 
35 
30 
25 
20 
16 
12 


626/7 
55 

471/7 
392/7 
313/7 
251/7 
I86/7 


Decimal 1 
5/ 7 =0.714. 


Equivalent fo 
B/7 = 0.857. 


r i/ 7 = 0.143 


2/ 7 = 0.286. 


3/ 7 = 0.429. 


4/ 7 = 0.571. 



233 



To find gross tons per mile of track multiply weight of rail (pounds per 
yard) by 11 and divide by 7. To find feet of rail per gross ton divide 6720 
by weight of rail per yard. 

Splices and Bolts. 



Length of Rails 
Used. 


Number of Joints 
or Rails. 


Number of Bolts 

Using Four-Hole 

Splices. 


Number of Bolts 

Using Six-Hole 

Splices. 


33 ft. 
30 " 


320 
352 


1280 
1408 


1920 
2112 



Spikes. 





°o 


Kegs per Mile (4 Spikes to a Tie). 




Using 33-Ft. 


Using 30-Ft. 






Under Head. 


»03 


Rails. 


Rails. 


No 






20 I 18 1 16 


18 | 16 I 14 


£6 




< 


Ties per Rail. 


Ties per Rail. 




$"£ 


6 x5/ 8 


260 


49.2 


44.3 


39.4 


48.7 


43.3 


37.9 


40.6 


Hi 


6 X9/16 


350 


36.6 


32.9 


29.3 


36.2 


32.2 


28.2 


30.2 


w - 


51/2X5/ 8 


290 


44.1 


39.7 


35.3 


43.7 


38.8 


34.0 


36.4 


g»s 


51/2X 9 /16 


375 


34.1 


30.7 


27.3 


33.8 


30.0 


26.3 


28.2 




5 X9/1 6 


400 


32.0 


28.8 


25.6 


31.7 


28.2 


24.6 


26.4 


* 


5 Xl/2 


450 


28.5 


25.6 


22.8 


28.2 


25.0 


21.9 


23.5 


"E 


41/2X1/2 


530 


24.2 


21.8 


19.3 


23.9 


21.3 


18.6 


19.9 





41/ 2 x7/i6 


680 


18.8 


17.0 


15.1 


18.6 


16.6 


14.5 


15.5 


M 




12800 


11520 


10240 


12672 


11264 


9856 


10560 









WROUGHT SPIKES. 

Number of Nails in Keg of 150 Pounds. 



Length, 
Inches. 


1/4 in. 


5 /l6 in- 


3 /8in. 


Length, 
Inches. 


1/4 in. 


5 /l6 in. 


3 /8 in. 


7 /l6in. 


1/2 in 


3 


2250 
1890 
1650 
1464 
1380 
1292 






7 
8 
9 
10 
11 
12 


1161 


662 
635 
573 


482 
455 
424 
391 


445 
384 
300 
270 
249 
236 


306 


31/2 
4 

41/2 


1208 
1135 
1064 
930 

868 


"742' 
570 


256 
240 
222 






203 


6 








180 



For sizes and weights of wire spikes see Steel Wire Nails, page 235. 

BOAT SPIKES. 

Number in Keg of 200 Pounds. 



Length. 


1/4 


5/16 


3/8 


1/2 




2375 
2050 
1825 








5 " 


1230 
1175 
990 

880 


940 
800 
650 
600 

525 

475 




6 " 


450 


7 " 


375 


8 " .... 




335 


9 " 




300 


10 " 






275 



234 



MATERIALS. 



LENGTH 


AND 


NUMBER 


OF 


CUT 


NAILS TO 


THE POUND. 


Size. 


a 
1-1 


a 



a 
a 




O 





c 


6 
a 


73 

m 


a 

'1 
O 


n 



5 

O 

H 


03 

M 

» 




3/ 4 


3/4 In. 












sou 

500 
376 
224 
180 










7/ 8 


7/8 

1 

11/4 

11/2 

13/4 

2 

21/4 

21/2 

23/4 

3 

31/4 

31/2 

4 

.41/2 

51/2 
6 




















2d 


800 

480 

288 

200 

168 

124 

88 

70 

58 

44 

34 

23 

18 

14 

10 

8 






1100 
720 
523 
410 
268 
188 
146 
130 
102 
76 
62 
54 


1000 

760 

368 










3d 














4d 






398 








5d 








130 
96 

82 
68 




6d 


95 

74 
62 
53 
46 
42 
38 
33 
20 


84 
64 
48 
36 
30 
24 
20 
16 






224 


126 
98 
75 
65 
55 
40 
27 




7d 








8d 






128 
110 
91 
71 

54 
40 
33 
27 




9d 








lOd 








28 


12d 








16d 








22 


20d 






141/ 2 
121/2 

91/2 

8 


30d 










40d 














50d 
















60d 


















6 





DIMENSIONS OF 


WOOD SCREWS. 




No. 


Threads 
per In. 


Diam. of 
Body. 


Lengths. 


No. 


Threads 
per In. 


Diam. of 
Body. 


Lengths, 






In. 


In. 






In. 


In. 


2 


56 


0.0842 


3/16-1/2 


12 


20, 24 


0.2158 


3/8-13/4 


3 


48 


.0973 


3 /l6- 5 /8 


14 


20, 24 


.2421 


3/8-2 


4 


32, 36, 40 


.1105 


3/16-3/4 


16 


16, 18, 20 


.2684 


3/8-21/4 


5 


32, 36, 40 


. 1 236 


3/16-7/8 


18 


16, 18 


.2947 


1/2-21/2 


6 


30, 32 


.1368 


3/16-1 


20 


16, 18 


.3210 


1/2-23/4 


7 


30, 32 


.1500 


1/4-1 1/8 


22 


16, 18 


.3474 


1/2-3 


8 


30, 32 


.1631 


1/4-1 1/4 


24 


14, 16 


.3737 


1/2-3 


9 


24, 30, 32 


.1763 


1/4-13/8 


26 


14, 16 


.4000 


3/4-3 


10 


24, 30, 32 


.1894 


1/4-1 1/2 


28 


14, 16 


.4263 


7/3-8 










30 


14, 16 


.4520 


13- 



WEIGHTS AND 


DIMENSIONS OF LAG SCREWS. 


Length in 
Inches. 


Diameter in Inches. 


3/8 
Lb. per 100. 


7/16 
Lb. per 100. 


1/2 
Lb. per 100. 


5/8 
Lb. per 100. 


3/ 4 
Lb. per 100. 


H/2 


6.88 
7.50 
8.25 
9.25 
9.62 
10.82 
11.50 
13.31 
14.82 
16.50 
17.37 
18.82 










13/ 4 


11.75 
12.62 
12.88 
13.28 
16.62 
18.18 
18.88 
19.50 
21.25 
23.56 
25.31 


16.88 
17.18 
18.07 
19.18 
22.00 
24.00 
26.82 
28.25 
30.37 
33.88 
35.37 
38.94 
44.37 






2 






21/4 






21/0 






3 


34.07 
35.88 
39.25 
42.62 
47.75 
51.62 
55.12 
61.88 
68.75 
77.00 
90.00 




31/2 




4 


64 00 


41/2 


67 88 


5 : 2 


71 37 


51/2 


79 37 


6... 


86.62 


7 


92.75 


8 






97.50 


9 






108.75 


10 








124.75 



STEEL WIRE NAILS. 



235 



GO 










T3T3X3'w5-C'O-CJ'C-dX)'0T5T3-d 
tm>OMO»oN>oooooo 

— — — CNr^TirtvO 


•saqouj 'q^Sua^j 




•S85[ldg 8JJAV 
















• -^-*^r3 — — 2°° 


•Surajq 
































•ooo'Bqo^ 














r^. r^ ir> rr^ Q\ Q\ \C 
















• 8T Suiqg 










?4 


§SlE~z s 
















Sugoog paqj-Bg 




SS^S 


















•Sm^is 






T 


§ 


22° 


















e3 
O . 


>> 

> 














\0 — or^^oiTMn-^-f^Cvlc^ — — — 


M. 

3 














tN^NNNISOm — 00 — t^m 


O 
ffl 


>> 

> 

K 














<T 


<N 


vO ■TftANO 










1 














CO 




O : MOB|0 










•spB-igSniJOOfj 
















"A f^ O^ O^ ^O iA 1" d 










•xog paqJT3g 

puB q-joorag 

puB 'Suisbq 






o 
o 


^ 3 -q- tj- rQ £5 — — 






qajj^g 


\0 vom o oo o r>. ■ 
T o r-* o vO o m • 




















•8UIJ 


N-COO 




o • 




















•gtnqstui j paqj-sg 
puB qaoouig 






1 


o 


tOO>COaN-nON 
OOOOl^OONN — ©^ \C 










•80U8J 










• ^ n aoo >c in t tn m 










•qouyio 










TTmr^ovooocsior^ 










•sp-Bjg pu-e 

Sft'B^J UOTIIUIOQ 






00 


CO 


-^55oo>«*tmN'-'-- 


•saqouj 'q^Suaq; 


— — — — — — {Mr^CN!Cvlr<* 1 r<-\rA^l-" , Tir\mvO 




CO 








: 


i 


c 

= 






— 


- 


X 


00O> 


i 


o 


a 


I 


-z 







236 



NUMBER OF WIRE NAILS PER POUND. 



M 

l-l 


a | 


»5!<£j4?\ ;:."'.;::;: 








These approximate numbers are an average only, 
and the figures given may be varied either way by 
changes in the dimensions of the heads or points. 
Brads and no-head nails will run more to the pound 
than the table shows, and large or thick-headed 
nails will run less. 


= | 


f^-*mso i i i* : i : i i i 








© 


t^in*NO. i i ''■ ''■ 








o> 


Tfin*ts»o ; ; 








CO | 


>nloco- ::::::: 








- 1 


vONOOO^ — f^lACO 








* 1 


SOOO — r^tnco — inu. • • • 








in 1 


ooa — rnmoo — mom — O • 








"f 1 


O>Orntr\O^00mO'»OinC 








" ! 


o-^*o»tn>o-is^NNam 






1 


Ntn^O^MOOi^f\^0* — ONt^ 




«' 


f in o^ N ia o if\ — o i^ o» m m rsco vO 
• — « — i — NNrnr^^tirnriOCOOr^tMA 


^ 


^Ntfl>00>ONOOO'NO'm1-1 , tO ■ • 










N 


O-OONOOintANinvOrA^NI-OOOOO-O • 
CN cm cs m en tj- m vcin oo o <N in o -o m m r> r~^ • 










I 


OONO^iAO^OOtAON 
minNN^-O-UMO-tNcnOOOinOMS 












NaoOI-OO-NOinoOiAOi^NW^-OOoMO 
NNrOtinvOtM»0-tANOOrMAtM»vOMNr> 








> 


^tinNONinO>ONinCO-0>OM»-^'OinfriO 






- 


57 

65 

76 

90 

106 

123 

149 

172 

207 

248 

314 

411 

536 

710 

876 

1143 

1558 

2069 

2667 

3750 

4444 




£ 


100 
120 
141 
164 
200 
229 
276 
333 
418 
548 
714 
947 
1168 
1523 
2077 
2758 
3556 
5000 
5926 
7618 


£ 


169 
197 
?39 
275 
331 
397 
502 
658 
857 
1136 
1402 
1828 
2495 
3310 
4267 
6000 
7111 
9143 


£ 


211 
247 
299 
345 
414 
496 
628 
822 
1072 
1420 
1752 
2280 
3116 
4138 
5334 
7500 
8888 
11428 


£ 








5 0>^*»«NNOON 








-i — ^-Mfl^iANO'-m 








> 














3$$2SS8£8 










CO 














9 

'1 


8g 


es" To 


222E 


vOlNOOO 


c 






1 



PROPERTIES OF STEEL WIRE. 



PROPERTIES OF STEEL WIRE. 

(John A. Roebling'sISons Co., 1908.) 



No., 


Diam., 

in. 


Area, 
square 
inches. 


Breaking 
strain, 100, 
000 lb. per 

sq. inch. 


Weight 


n pounds. 


Feet in 
2000 lb. 


Roebling 
Gauge. 


Per 

1000ft. 


Per 
mile. 


000000 


0.460 


0.166191 


16,619 


558.4 


2,948 


3,582 


00000 


0.430 


0.145221 


14,522 


487.9 


2,576 


4,099 


0000 


0.393 


0.121304 


12,130 


407.6 


2,152 


4,907 


000 


0.362 


0.102922 


10,292 


345.8 


1,826 


5,783 


00 


0.331 


0.086049 


8,605 


289.1 


1,527 


6,917 





0.307 


0.074023 


7,402 


248.7 


1,313 


8,041 


1 


0.283 


0.062902 


6,290 


211.4 


1,116 


9,463 


2 


0.263 


0.054325 


5,433 


182.5 


964 


10,957 


3 


0.244 


0.046760 


4,676 


157.1 


830 


12,730 


4 


0.225 


0.039761 


3,976 


133.6 


705 


14,970 


5 


0.207 


0.033654 


3,365 


113.1 


597 


17,687 


6 


0.192 


0.028953 


2,895 


97.3 


514 


20,559 


' 7 


0.177 


0.024606 


2,461 


82.7 


437 


24,191 


8 


0.162 


0.020612 


2,061 


69.3 


366 


28,878 


9 


148 


0.017203 


1,720 


57.8 


305 


34,600 


10 


0.135 


0.014314 


1,431 


48.1 


254 


41,584 


11 


0.120 


0.011310 


1,131 


38.0 


201 


52,631 


12 


0.105 


0.008659 


866 


29.1 


154 


68,752 


13 


0.092 


0.006648 


665 


22.3 


118 


89,525 


14 


0.080 


0.005027 


503 


16.9 


89.2 


118,413 


15 


0.072 


0.004071 


407 


13.7 


72.2 


146,198 


16 


0.063 


0.003117 


312 


10.5 


55.3 


191,022 


17 


0.054 


0.002290 


229 


7.70 


40.6 


259,909 


18 


0.047 


0.001735 


174 


5.83 


30.8 


343,112 


19 


0.041 


0.001320 


132 


4.44 


23.4 


450,856 


20 


0.035 


0.000962 


96 


3.23 


17.1 


618,620 


21 


0.032 


0.000804 


80 


2.70 


14.3 


740,193 


22 


0.028 


0.000616 


62 


2.07 


10.9 


966,651 


23 


0.025 


0.000491 


49 


1.65 


8.71 




24 


0.023 


0.000415 


42 


1.40 


7.37 




25 


0.020 


0.000314 


31 


1.06 


5.58 




26 


0.018 


0.000254 


25 


0.855 


4.51 




27 


0.017 


0.000227 


23 


.763 


4.03 




28 


0.016 


0.000201 


20 


.676 


3.57 




29 


0.015 


0.000177 


18 


.594 


3.14 




30 


0.014 


0.000154 


15 


.517 


2.73 




31 


0.0135 


0.000143 


14 


.481 


2.54 




32 


0.013 


0.000133 


13 


.446 


2.36 




33 


0.011 


0.000095 


9.5 


.319 


1.69 




34 


0.010 


0.000079 


7.9 


.264 


1.39 




35 


0.0095 


0.000071 


7.1 


.238 


1.26 




36 


0.009 


0.000064 


6.4 


.214 


1.13 





The above table was calculated on a basis of 483.84 lb. per cu. ft. for steel 
wire. Iron wire is a trifle lighter. The breaking strains are calculated for 
100,000 lb. per sq. in. throughout, simply for convenience, so that the 
breaking strains of wires of any strength per sq. in. may be quickly deter- 
mined by multiplying the values given in the tables by the ratio between 
the strength per square inch and 100,000. Thus, a No. 15 wire, with a 

strength per sq. in. of 150,000 lb., has a breaking strain of 407 X ] 5 ° 



■■ 610.51b. 



' 100,000 



238 



MATERIALS. 



GALVANIZED IRON WIRE FOR TELEGRAPH AND 
TELEPHONE LINES. 

(Trenton Iron Co.) 
Weight per Mile-Ohm. — This term is to be understood as dis- 
tinguishing the resistance of material only, and means the weight of such 
material required per mile to give the resistance of one ohm. To ascer- 
tain the mileage resistance of any wire, divide the " weight per mile- 
ohm" by the weight of the wire per mile. Thus in a grade of Extra 
Best Best, of which the weight per mile-ohm is 5000, the mileage resist- 
ance of No. 6 (weight per mile 525 lbs.) would be about 91/2 ohms; and 
No. 14 steel wire, 6500 lbs. weight per mile-ohm (95 lbs. weight per mile), 
would show about 69 ohms. 

Sizes of Wire used in Telegraph and Telephone Lines. 

No. 4. Has not been much used until recently; is now used on 
important lines where the multiplex systems are applied. 

No. 5. Little used in the United States. 

No. 6. Used for important circuits between cities. 

No. 8. Medium size for circuits of 400 miles or less. 

No. 9. For similar locations to No. 8, but on somewhat shorter cir- 
cuits; until lately was the size most largely used in this country. 

Nos. 10, 11. For shorter circuits, railway telegraphs, private lines, 
police and fire-alarm lines, etc. 

No. 12. For telephone lines, police and fire-alarm lines, etc. 

Nos. 13, 14. For telephone lines and short private lines; steel wire is 
used most generally in these sizes. 

The coating of telegraph wire with zinc as a protection against oxida- 
tion is now generally admitted to be the most efficacious method. 

The grades of line wire are generally known to the trade as "Extra 
Best Best'' (E. B. B.), "Best Best" (B. B.), and "Steel." 

"Extra Best Best" is made of the very best iron, as nearly pure as 
any commercial iron, soft, tough, uniform, and of very high conduc- 
tivity, its weight per mile-ohm being about 5000 lbs. 

The " Best Best" is of iron, showing in mechanical tests almost as 
good results as the E. B. B., but is not quite as soft, and somewhat lower 
in conductivity; weight per mile-ohm about 5700 lbs. 

The "Steel" wire is well suited for telephone or short telegraph lines, 
and the weight per mile-ohm is about 6500 lbs. 

The following are (approximately) the weights per mile of various 
sizes of galvanized telegraph wire, drawn by Trenton Iron Co.'s gauge: 
No. 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14. 

Lbs. 720, 610, 525, 450, 375, 310, 250, 200, 160, 125, 95. 

TESTS OF TELEGRAPH WIRE. 

The following data are taken from a table given by Mr. Prescott relat- 
ing to tests of E. B. B. galvanized wire furnished the Western Union 
Telegraph Co. 







Wei 


? ht. 




Resist 


ance. 


Ratio of 
Breaking 


Size 


Diam., 
Inch. 






Length. 

Feet 

per 
pound. 


Temp. 75.8° Fahr. 


of 


Grains 


Pounds 


Weight to 


Wire 


Feet 


Ohms 


Weight 






per foot. 


per mile. 


per ohm 


per mile. 


per mile. 


4 


0.238 


1043.2 


886.6 


6.00 


958 


5.51 




5 


.220 


891.3 


673.0 


7.85 


727 


7.26 




6 


.203 


758.9 


572.2 


9.20 


618 


8.54 


3.05 


7 


.180 


596.7 


449.9 


11.70 


578 


10.86 


3.40 


8 


.165 


501.4 


378.1 


14.00 


409 


12.92 


3.07 


9 


.148 


403.4 


304.2 


17.4 


328 


16.10 


3.38 


10 


.134 


330.7 


249.4 


21.2 


269 


19.60 


3.37 


11 


.120 


265.2 


200.0 


26.4 


216 


24.42 


2.97 


12 


.109 


218.8 


165.0 


32.0 


179 


29.60 


3.43 


14 


083 


126.9 


95.7 


55.2 


104 


51.00 


3.05 



" PLOUGH "-STEEL WIRE. 



239 



Joints in Telegraph Wires. — The fewer the joints in a line the 
better. All joints should be carefully made and well soldered over, for 
a bad joint may cause as much resistance to the electric current as several 
miles of wire. 





SPECIFICATIONS 


FOR GALVANIZED 


IRON WIRE. 






Issued by the British Postal Telegraph Authorities. 


Weight 
Mile 


per 


Diameter. 


Tests for Strength and 
Ductility. 


ID 43 

rd a 


6 














































c 






T3 

a 

T3 




SO +5 


'5 
H ■ 


SO 


^o 


M 


,5 


?1 


"C to 




Allowed. 


w. 


Allowed. 




c = 


1«2 

S+3 


1 




.5 




II X 


■= 






u 




ffl 


'A 


W fn 




w t; 


IS 


rt 




a* 
& 


d 


03 


3 


d 


03 


d 


d 


§'53 


oil 


d 


x 


ll 


3 


§ 


tf 


m 


§ 


^ 


§ 


i-T 


3 


^ 


i 


§ 


O 


lb. 


lb. 


lb. 


mils. 


mils. 


mils. 


lb. 




lb. 




lb 








800 


767 


833 


242 


23; 


24/ 


2480 


15 


2550 


14 


2620 


n 


6.75 


5400 


600 


571 


629 


209 


204 


214 


1860 


17 


1910 


16 


1960 


is 


9.00 


5400 


430 


424 


477 


181 


176 


186 


1390 


19 


1425 


18 


1460 


17 


12.00 


5400 


400 


377 


424 


l/l 


166 


176 


1240 


21 


1270 


20 


1300 


19 


13.50 


5400 


200 


190 


213 


121 


118 


125 


620 


30 


638 


28 


655 


26 


27.00 5400 



STRENGTH OF PIANO-WIRE. 

The average strength of English piano-wire is given as follows by 
Webster, Horsfals & Lean: 



Size,_ 

Music- wire 

Gauge. 


Equivalent 

Diameters, 

Inch. 


Ultimate 

Tensile 

Strength, 

Pounds. 


Size, 
Music- wire 

Gauge. 


Equivalent 

Diameters, 

Inch. 


Ultimate 
Tensile 

Strength, 
Pounds. 


12 
13 
14 
15 

16 
17 


0.029 
.031 
.033 
.035 
.037 
.039 


225 
250 
285 
305 
340 
360 


18 
19 
20 
21 
22 


0.041 
.043 
.045 
.047 
.052 


395 
425 
500 
540 
650 



These strengths range from 300,000 to 340,000 lbs. per sq. in. The 
composition of this wire is as follows: Carbon, 0.570; silicon, 090- 
sulphur, 0.011; phosphorus, 0.018; manganese, 0.425. 

" PLOUGH "-STEEL WIRE. 

The term "plough," given in England to steel wire of high quality 
was derived from the fact that such wire is used for the construction of 
ropes used for ploughing purposes. It is to be hoped that the term will 
not be used in this country, as it tends to confusion of terms. Plough- 
steel is known here in some steel-works as the quality of plate steel used 
for the mold-boards of ploughs, for which a very ordinary grade is 
good enough. 

Experiments by Dr. Percy on the English plough-steel (so-called) 
gave the following results: Specific gravity, 7.814; carbon, 0.828 per 
cent; manganese, 0.587 per cent; silicon, 0.143 per cent; sulphur, 0.009 
per cent: phosphorus, nil; copper, 0.030 per cent. No traces of chro- 
mium, titanium, or tungsten were found. The breaking strains of the 
wire were as follows: 

Diameter, inch 0.093 0.132 0.159 0.191 

Pounds per sq. inch . . 344,960 257,600 224,000 201,600 
The elongation was only from 0.75 to 1.1 per cent. 



240 



COPPER WIRE TABLE. 



*3l 



S£8aSS?9SSSSSR8ffiSS|2§§|RSgg||§||||§|| 



>p?sl 



OK>6"fNO«>O0P00O 



SsfSEIISssSa^S 



S — O OOOO OO OQOOOOQpOOOQOOoSOOOdO 

i§ssg§§s§ss§sssllsg§gss§s§ssss 



1B'TON--Oars-iA!nnlNO > 0-NiAt>-0>6tO'00'0 > 0-NNJ«)2 

^i — oooooooo£ : - - " : - : • ■'■'. ; - ". ooooooooooo 

3 © O © O © O O O O O O O O © © O O O O © © © © © O © © © © © © © © © © © 






O£00NN r^i^TOOOOO — C 

00(N^>OmtSO'<S-<M<AOOmOI^'q 






•> — vOr^©r^r^<M-"T^c>rvi'«t-ir" 1 aov©»^ir\t^©Tt-GO»r%fnC'ie>r>. , !rcvico'«raO\0 — c>f^>oc>GC 

iANtinar^NNt^'<rOOtnNiftN^'^S^OO^^"NflOinO^>ON , OiA— O C'l'T *© — 

rq r*.' oo — ' •■J- u-i o eW f\ — ' T — r-i oo oo r^ <s u-.' wi' so «i' •* o- wi t' n •» r*i ir> -*' — ' -o o-' c>>\oVi i>« <«i a 
— — — — — <S{slr>l{"JW«*ir>>©t>.00O© — r^^e>£j<QeJ>f > 



£°i82?£ 



0^t>.©i*-iOO©C>>OrjONsOCqHaO^-fi)r>.0>ir>0*r> 



_ jS©rjcoS| 



■Z 8 

Srs it c 

5 s 


54.78 
70.72 
89.45 
109.55 
122.48 
141.43 
158.12 
173.21 
187.09 
200.00 
212.14 
223.61 
234.53 
244.95 
254196 
264.58 
273.87 
282.85 
291.55 
300.00 
308.23 
316.23 
331 .67 
346.42 
360.56 
374.17 
387.30 
400.00 
412.32 
424.27 
435.89 
447.22 
469.05 
489.90 
509.91 
529.16 
547.73 
565 69 
583.10 
600.00 




^«ON'C'Coo'ei0 9.N«NO--©ooifi-<e»ONNo«on«*obi«N«-wm 


N oo vO m — — — © oo <> "J 2} © i»» t> «s ^ £ **» e> >£ ^ u> » © N >» ir\ r>» oo e* © <S f» «"> ws m «* fi! "T 

— ■— — — — — — — — — — — — r4rSCv»<s|tM?5<s£l«*><«M*\<*»WS'«"»'* 



ii||l|||||||l|||i||||p|||||l|||l||||||l 



£31 
u»5 



9C ^£SS^9?9SSSSSi;.8SS$8Sgg§SSg8Sg§||'||§|| 



BARE AND INSULATED COPPER WIRE. 



241 



Sizes, Weights and Strengths of Hard-Copper Telegraph and 
Telephone Wire. 

(J. A. Roebling's Sons Co., 1908.) 



02 


_d 


5 
-2 




ance, ln- 
ational 
s per mile 
°F. 


x. size, 
ing gauge 
B.B.iron 
of equal 
ance. 




d 


a 




of C £ . 


x. size, 
ing gauge 
B.B.iron 
of equal 
ance. 


W "• 








"S H SR 




^ -! 




<D 




.sEJh 


°J2 • "E 


So 

02 


S 




2 = 




^W £-p 


1 « 

so 

32 


rt 

5 


f" 


zi ■'- 
- =. 

pq 




9 


0.114 


208 


653 


4.39 


2 


13 


0.072 


83 


274 


11.01 


6 1/2 


10 


0.102 


166 


340 


5.49 


3 


14 


0.064 


65 


220 


13.94 


8 


11 


0.091 


132 


426 


6.90 


4 


15 


0.057 


52 


174 


17.57 


9 


12 


0.081 


103 


334 


8.70 


6 


16 


0.051 


42 


139 


21.95 


10 



In handling this wire the greatest care should be observed to avoid 
kinks, bends, scratches, or cuts. Joints should be made only with 
Mclntire connectors. On account of its conductivity being about five 
times that of E. B. B. iron wire, and its breaking strength over three 
times its weight per mile, copper may be used of which the section is 
smaller and the weight less than an equivalent iron wire, allowing a 
greater number of wires to be strung on the poles. Besides this advan- 
tage, the reduction of section materially decreases the electrostatic 
capacity, while its non-magnetic character lessens the self-induction of 
the line, both of which features tend to increase the possible speed of 
signaling in telegraphing, and to give greater clearness of enunciation 
over telephone lines, especially those of great length. 



Weight of Bare and Insulated Copper Wire, Pounds. 

(John A. Roebling's Sons Co., 1908.) 





Weight per 


1000 Feet, Solid. 




Weight 


per Mile, Solid 








Weather- 








Weather- 






i 


v proof. 


s s ° 


bi 

a 


6 


proof. 




hi) 


■So 


J2 • 

3 3 


S'8 


3"0 
3 '3 


|| 


-9 => 


m 


pq 


Qpq 


Hpq 


^(^Pm 


w pq 


PQ 


Qpq 


Hpq 


E^Ph 
4550 


ojpq 


0000 


641 


723 


767 


862 


925 


3384 


3817 


4050 


4890 


000 


509 


587 


629 


710 


760 


2687 


3098 


3320 


3750 


4020 


00 


403 


467 


502 


562 


600 


2127 


2467 


2650 


2970 


3170 





320 


377 


407 


462 


495 


1689 


1989 


2150 


2440 


2610 


1 


253 


294 


316 


340 


365 


1335 


1553 


1670 


1800 


1930 


2 


202 


239 


260 


280 


300 


1066 


1264 


1370 


1480 


1585 


3 


159 


185 


199 


230 


270 


840 


977 


1050 


1220 


1425 


4 


126 


151 


164 


190 


220 


665 


795 


865 


1000 


1160 


5 


100 


122 


135 


155 


190 


528 


646 


710 


820 


1000 


6 


79 


100 


112 


127 


160 


417 


529 


590 


670 


840 


8 


50 


66 


75 


85 


110 


264 


349 


395 


450 


580 


9 


39 


54 


62 






206 


283 


325 






10 


32 


46 


53 


60 


80 


169 


241 


280 


315 


420 


12 


20 


30 


35 


42 


55 


106 


158 


185 


220 


290 


14 


\2A 


20 


25 


30 


40 


66 


107 


130 


160 


210 


16 


7.9 


16 


20 


24 


30 


42 


83 


105 


130 


160 


18 


4.t 


12 


16 


19 


24 


25 


64 


85 


100 


130 


20 


3.1 


9 


12 






16 


48 


65 







MATERIALS. 



Stranded Copper Feed Wire, Weight in Pounds. 

(John A. Roebling's Sons Co., 1908.) 





Weight 


per 1000 Feet. 


Weight per Mile. 




Weather- 








Weather- 










proof 








proof 






















"^ 5rt 




03 

a3o!§ 


03 

c3 

PQ 


3:2 

QPQ 


~2 


a % 

- "> 2 
£js:pm 


a 


a5 

o3 

pq 


03 . 

3 a 


11 

C u 




PQ 

| 

53 


2,000,000 


6100 


6690 


7008 




7540 


32208 


35323 


37000 




39800 


1,750,000 


5338 


5894 


6193 




6700 


28184 


31119 


32700 




35400 


1,500,000 


4575 


5098 


5380 




5830 


24156 


26915 


28400 




30800 


1,250,000 


3813 


4264 


4508 




4940 


20132 


22516 


23800 




20000 


1,000,000 


3050 


3456 


3674 


3860 


3980 


16104 


18246 


19400 


20400 


26100 


900,000 


2745 


3127 


3332 


3520 


3640 


14493 


16513 


17600 


18600 


11000 


800,000 


2440 


2799 


2992 


3180 


3280 


12883 


14779 


15800 


16800 


19200 


750,000 


2288 


2635 


2822 


3000 


3100 


12080 


13913 


14900 


15850 


17300 


700,000 


2135 


2471 


2650 


2820 


2920 


11272 


13045 


14000 


14900 


16300 


600,000 


1830 


2093 


2235 


2350 


2460 


9662 


11052 


11800 


12400 


15400 


500,000 


1525 


1765 


1894 


1990 


2080 


8052 


9318 


10000 


10500 


13100 


450,000 


1373 


1601 


1724 


1820 


1900 


7249 


8452 


9100 


9600 


10000 


400,000 


1220 


1436 


1553 


1650 


1700 


6441 


7584 


8200 


8700 


9000 


350,000 


1068 


1248 


1345 


1440 


1500 


5639 


6589 


7100 


7600 


7900 


300,000 


915 


1083 


1174 


1270 


1310 


4831 


5721 


6200 


6700 


6900 


250,000 


762 


907 


985 


1060 


1120 


4023 


4788 


5200 


5600 


5900 


B.&S. 

Gauge. 

0000 






















645 


745 


800 


900 


960 


3405 


3935 


4220 


4750 


5070 


000 


513 


604 


653 


735 


785 


2708 


3190 


3450 


3880 


4150 


00 


406 


482 


522 


583 


625 


2143 


2544 


2760 


3080 


3300 





322 


388 


424 


480 


510 


1700 


2051 


2240 


2530 


2700 


1 


255 


303 


328 


355 


380 


1346 


1599 


1735 


1870 


2000 


2 


203 


246 


270 


290 


335 


1071 


1301 


1425 


1540 


1770 


3 


160 


190 


206 


240 


280 


844 


1004 


1090 


1270 


1480 


4 


127 


155 


170 


195 


230 


670 


820 


900 


1030 


1220 


5 


101 


126 


140 


160 


195 


533 


668 


740 


845 


1030 


6 


80 


103 


115 


132 


165 


422 


544 


610 


695 


870 


8 


50 


68 


78 


87 


105 


264 


359 


410 


460 


555 



Approximate Rules for the Resistance of Copper Wire. — The 

resistance of any copper wire at 20° C. or 68° F., according to Matthies- 

sen's standard, is R = — '■— , in which R is the resistance in inter- 
national ohms, I the length of the wire in feet, and d its diameter in mils. 
(1 mil = l/ioooinch.) 

A No. 10 Wire, A.W.G., 0.1019 in. diameter (practically 0.1 in.), 
1000 ft. in length, has a resistance of 1 ohm at 68° F. and weighs 31.4 
lbs. 

If a wire of a given length and size by the American or Brown & 
Sharpe gauge has a certain resistance, a wire of the same length and 
three numbers higher has twice the resistance, six numbers higher four 
times the resistance, etc. 

Wire gauge, A.W.G. No 

Relative resistance 

section or weight . 

See wire table, A.W.G. , under Electrical Engineering. 



000 1 


4 


7 


10 


16 8 


4 


2 


1 


1/16 1/8 


1/4 


1/2 


1 



13 16 19 22 

1/2 1/4 1/8 Vl6 



WIRES OF DIFFERENT METALS AND ALLOYS. 243 



SPECIFICATIONS FOR HARD-DRAWN COPPER WIRE. 

The British Post Office authorities require that hard-drawn copper 
wire supplied to them shall be of the lengths, sizes, weights, strengths, 
and conductivities as set forth in the annexed table. 



Weight 


per Statute 


Approximate Equiv- 


C 


£ 


-g'S J 3' ; 


i° 


Mile. 


alent Diameter, mils. 






»^rt a 


■s® 
















0) - 
















■a'H 

a o3 

so 


a 

3 

a 

'5 


B 
3 
B 

1 


03 
-3 

CI 

03 


B 
3 
B 
'B 

i 


B 
3 

a 
1 


c 

i 


3 m 
a. s 

'3 £ 


3 13 >fe 
3^o 

.aggs 

oj o3|> c3 


a-g£ 
1^ 


, 100 


971/2 


1021/2 


79 


78 


80 


330 


30 


9.10 


50 


150 


1461/4 


1533/ 4 


97 


951/2 


98 


490 


25 


6.05 


50 


200 


195 


205 


112 


IIOI/2 


1131/4 


650 


20 


4.53 


50 


400 


390 


410 


158 


1551/2 


160 1/4 


1300 


10 


2.27 


50 



WIRES OF DIFFERENT METALS AND ALLOYS. 

(J. Bucknall Smith's Treatise on Wire.) 

Brass Wire is commonly composed of an alloy of 1 3/4 to 2 parts of 
copper to one part of zinc. The tensile strength ranges from 20 to 40 
tons per square inch, increasing with the percentage of zinc in the alloy. 

German or Nickel Silver, an alloy of copper, zinc, and nickel, is 
practically brass whitened by the addition of nickel. It has been drawn 
into wire as fine as 0.002 inch diameter. 

Platinum wire may be drawn into the finest sizes. On account of its 
high price its use is practically confined to special scientific instruments 
and electrical appliances in which resistances to high temperature, 
oxygen, and acids are essential. It expands less than other metals 
when heated. Its coefficient of expansion being almost the same as 
that of glass permits its being sealed in glass without fear of cracking the 
latter. It is therefore used in incandescent electric lamps. 

Phosphor-bronze Wire contains from 2 to 6 per cent of tin and 
from 1/20 to 1/8 per cent of phosphorus. The presence of phosphorus is 
detrimental to electric conductivity. 

" Delta-metal " wire is made from an alloy of copper, iron, and zinc. 
Its strength ranges from 45 to 62 tons per square inch. It is used for 
some kinds of wire rope, also for wire gauze. It is not subject to de- 
posits of verdigris. It has great toughness, even when its tensile 
strength is over 60 tons per square inch. 

Aluminum Wire. — Specific gravity 0.268. Tensile strength only 
about 10 tons per square inch. It has been drawn as fine as 11,400 
yards to the ounce, or 0.042 grain per yard. 

Aluminum Bronze, 90 copper, 10 aluminum, has high strength and 
ductility; is inoxidizable, sonorous. Its electric conductivity is 12.6 
per cent. 

Silicon Bronze, patented in 1882 by L. Weiler of Paris, is made as 
follows: Fluosilicate of potash, pounded glass, chloride of sodium and 
calcium, carbonate of soda and lime, are heated in a plumbago crucible, 
and after the reaction takes place the contents are thrown into the 
molten bronze to be treated. Silicon-bronze wire has a conductivity of 
from 40 to 98 per cent of that of copper wire and four times more than 
that of iron, while its tensile strength is nearly that of steel, or 28 to 55 
tons per square inch of section. The conductivity decreases as the ten- 
sile strength increases. Wire whose conductivity equals 95 per cent of 
that of pure copper gives a tensile strength of 28 tons per square inch, 
but when its conductivity is 34 per cent of pure copper, its strength is 
50 tons per square inch. It is being largely used for telegraph wires. 
It has great resistance to oxidation. 

Ordinary Drawn and Annealed Copper Wire has a strength of from 
15 to 20 tons per square inch. 



244 



MATERIALS. 



Composed of 



WIRE ROPES. 
STANDARD HOISTING ROPE. 

} Strands and a Hemp Center, 19 Wires to the Strand. 
(John A. Roebling's Sons Co., 1908.) 



See also pamphlets of John A. Roebling's Sons Co., Trenton Iron Co., 
A. Leschen & Sons Rope Co., and other makers. 



SWEDISH IRON. 



03 

s 


01 


' s .s 


jO 




HI 

5odS 


"3 o 

.2 ID 




.5 


'3 


jP 




*!§ 

| 60 G 
O.S£ 


0> 

.2 a? 

3 0) 


0) 

2 


1 

Q 


a 
a 


a 


O to 

£;s2 


03 02 

£ 60 £ 

J2.2-2 




0) 
T3 


| 


a° 


a 


O co 

£ 6J0C 
flfl o 


H 


<! 


S 


< 


<! 


a 


H 


3 


-< 


«! 


5 


s 




23/4 


85/s 


11.95 


114 


22.8 


16 


8 


i 


3 


1.58 


iy 


3.40 


51/4 




21/, 


/7/ 8 


9.85 


95 


18.9 


15 


9 


7/8 


23/4 


1.20 


13 


2.60 


41/2 


1 


21/ 4 


>l/8 


8.00 


78 


15.60 


13 


10 


3/4 


21/4 


0.89 


97 


1.94 


4 


2 


2 


6I/4 


6.30 


62 


12.40 


12 


101/4 


b/8 


2 


0.62 


6.8 


1.36 


31/2 


3 


13/4 


!>l/ ? 


4.85 


48 


9.60 


10 


101/2 


y/ifi 


IS/4 


0.50 


5.5 


1.10 


23/ 4 


4 


1 V8 


3 


4.15 


42 


8.40 


81/9, 


103/4 


1/9 


U/?, 


0.39 


4.4 


0.88 


21/4 


5 


U/ ? 


43/ 4 


3.55 


36 


7.20 


71/9 


10a 


V/1B 


H/4 


0.30 


3.4 


0.68 


2 


5 V* 


13/s 


41/4 


3.00 


31 


6.20 


7 


106 


3/8 


H/8 


0.22 


2.5 


0.50 


H/2 


6 


U/4 


4 


2.45 


25 


5.00 


61/9 


\0c 


W16 


1 


0.15 


1.7 


0.34 


1 


y 


H/8 


31/2 


2.00 


21 


4.20 


6 


lOrf 


1/4 


3/ 4 


0.10 


1.2 


0.24 


3/4 



CAST STEEL. 





23/ 4 


85/s 


11.95 


228 


45.6 


10 


8 


i 


3 


1.58 


34 


6.80 


4 






77/ 8 


9.85 


190 


37.9 


91/9 


9 


■7/8 


23/ 4 


1.20 


26 


5.20 


31/ 2 


1 


21/4 


A/8 


8.00 


156 


31.2 


8 V? 


10 


3/ 4 


21/4 


0.89 


19.4 


3.88 


3 


2 


2 


6I/4 


6.30 


124 


24.8 


8 


101/4 


*>/8 


2 


62 


13.6 


2.72 


21/4 


3 


13/4 


51/?, 


4:85 


96 


19.2 


71/4 


101/9 


»/lB 


13/4 


0.50 


11.0 


2.20 


13/4 


4 


lb/8 


5 


4.15 


84 


16.8 


6I/4 


l03/ 4 


i/„ 


11/9, 


0.39 


8.8 


1.76 


H/2 


5 


11/, 


43/ 4 


3.55 


72 


14.4 


53/ 4 


10a 


V/lfi 


U/4 


0.30 


6.8 


1.36 


U/4 


51/2 


l3/ 8 


41/4 


3.00 


62 


12.4 


51/? 


106 


3/8 


11/8 


0.22 


5.0 


1.00 




6 


H/4 


4 


2.45 


50 


10.0 


5 


m 


*>/m 


1 


0.15 


3.4 


0.68 


2/3 


y 


H/8 


31/2 


2.00 


42 


8.40 


41/2 


10rf 


1/4 


3/4 


0.10 


2.4 


0.48 


1/2 



.This rope is almost universally employed for hoisting purposes on 
account of its flexibility. It is made of 6 strands, each of which is 
formed by twisting 19 wires together, and a hemp core or center. Some- 
times the hemp center is replaced by a wire strand, which adds from 7 
to 10 per cent to the strength of the rope; but the wear on the center is 
as great as on the outside strands, and its use is not generally advised. 
This rope is very pliable, and will wind on moderate-sized drums and 
pass over reasonably small sheaves without injury. Where it is possi- 
ble, drums and sheaves larger than those indicated in the lists should 
be adopted, particularly when high speeds are employed or when the 
working strain is greater than one-fifth of the breaking strain, as the 
bending of a rope around a sheave is more destructive the heavier the 
strain on the rope and the smaller the sheave. The working strains for 
these tables have been calculated at about one-fifth the breaking strains. 
It is necessary, however, in some cases, — where the speed of the rope is 
- to take it at one-eighth or one-tenth of the breaking strain, 



TRANSMISSION OR HAULAGE ROPE. 



245 



Before deciding upon iron or steel for ropes, it is better to have advice 
from the manufacturers of wire rope. 

In substituting steel for iron, it is well to use the same size of rope, 
thereby taking full advantage of the increased wearing capacity of steel 
over iron. The best steel is the only one to use, as inferior grades are 
not as serviceable as good iron, because the constant vibrations to which 
ropes are subjected cause the poor steel to become brittle and unsafe. 

TRANSMISSION OR HAULAGE ROPE. 

Composed of 6 Strands and a Hemp Center, 7 Wires to the Strand. 

SWEDISH IRON. 







.a 




MO 

.a§ 


MO 

eg 


a 






.a 




MO 
.So 


,ai 


a 


a 


.a 

o 

a 


a 

3 
o 

'3 

X 

O 


a 


O 03 


O w 

a."* 3 


24 

o of 


5 
3 

3 
03 


| 


a 

'3 
o 


2 

05 

a 


ffl o 

x.a" 


13 tS 

O 03 

tsg 

fig- 


„ > 


2 


a 
a 


% 


ow£ 


2w2 


.as 


g 


a 


■+i 


#$2 


-2w£ 


.as 


H 


Q 


< 


< 


< 


§ 


H 


Q 


< 


b 


< 


<J 


s 


11 


1V-, 


43/ 4 


3.55 


34 


6.80 


13 


19 


5/8 


2 


0.62 


6.6 


1.32 


51/i 


12 


13/8 


41/4 


3.00 


29 


5.80 


12 


2U 


9/16 


13/4 


0.50 


5.3 


1.06 


41A> 


13 


U/4 


4 


2.45 


24 


4.80 


103/4 


21 


V? 


HA. 


0.39 


4.2 


0.84 


4 


14 


11/8 


31/9 


2.00 


20 


4.00 


91/9 


22 


■Vlfl 


U/4 


0.30 


3.3 


0.66 


31/ 4 


15 


1 


3 


1.58 


16 


3.20 


8I/2 


23 


3/8 


H/8 


0.22 


2.4 


0.48 


23/,, 


16 


7/8 


23/4 


1.20 


12 


2.40 


71/9, 


24 


•>Mfi 


1 


0.15 


1.7 


0.34 


2 I'm 


\1 


3/ 4 


21/4 


0.89 


9.3 


1.86 


63/4 


2b 


9/3? 


V* 


0.125 


1.4 


0.28 


21/4 


Id 


H/16 


21/8 


0.75 


7.9 


1.58 


6 

















CAST STEEL. 



11 


11/9 


43/ 4 


3.55 


68 


13.6 


81/9, 


19 


5/8 


2 


0.62 


13.2 


2.64 


31/9 


12 


13/ 8 


41/4 


3.00 


58 


11.6 


8 


20 


9/16 


I 3/ 4 


0.50 


10.6 


2.12 


3 


13 


U/4 


4 


2.45 


48 


9.60 


71/4 


21 


1/9 


I 1/., 


0.39 


8.4 


1.68 


21/9 


14 


U/8 


31/9 


2.00 


40 


8.00 


6I/4 


22 


'','16 


11/4 


0.30 


6.6 


1.32 


21/,, 


15 


1 


3 


1.58 


32 


6.40 


53/4 


23 


3/8 


11/8 


0.22 


4.8 


0.96 


?, 


16 


7/8 


23/ 4 


1.20 


24 


4.80 


5 


24 


5/1 fi 


1 


0.15 


3.4 


0.68 


I3/4 


17 


3/4 


21/4 


0.89 


18.6 


3.72 


41/2 


25 


9/3- 


7/8 


0.125 


2.8 


0.56 


11/o 


18 


H/16 


21/8 


0.75 


15.8 


3.16 


4 

















This rope is much stiffer than standard hoisting rope. It is made of 
6 strands, each of which is composed of 7 wires, and a hemp core or 
center. It may have, if it is desired, a wire center, which adds from 7 
to 10 per cent to its strength, but it is then open to the objections 
already noted on page 226. The wires of this variety of rope are 1 2/3 
times greater in diameter than those of the standard hoisting rope, 
and hence the rope is much less pliable, and will not bend around as 
small sheaves. It is well adapted for haulages and transmissions, 
because the wires are large and are not quickly worn through. It will 
resist the rough usage of mine haulages and the great wear due to pass- 
ing over a large number of pulleys and rollers. The wires are fewer in 
number, however, and a greater factor of safety is desirable than for 
hoisting rope, because the breakage of one or two wires takes away con- 
siderable amount of the total strength. In using steel, instead of iron 
rope, it is necessary to have the best quality. For transmissions, the 
sizes from li/s in. diameter down give excellent satisfaction, when prop- 
erly selected. Both the regular and Lang constructions are extensively 
used for haulages and inclined planes. 



246 



MATERIALS. 



PLOUGH-STEEL ROPE. 

Composed of 6 Strands and a Hemp Center. 

19 WIRES TO THE STRAND. 







,3 




bjjo 
So 


Mo 

• So 


s 

3 






.s 




M§ 


Mo 


s 


^ 




g 




J2^>, 


-fifCS 


P*> 


h - 




n 






JiJtN 


«*i 






3 


J2 


















O m 


B 

3 


.9 




h a 


£§ 

0)"* 3 


"3 oj" 

g S3 


a 

3 


.g 


_Sh 




fn 3 
ffl ° 




°> 


0> 


I 


o 


ft 


x.S 


JO 3 


s i- 


£ 


| 


X 

S 


ft 


O 03 • 


,Q 3 


2 u 


F, 


a 


-4 


Sm£ 


-2££ 


.So 


03 


ft 


-J 


$n£ 


-2r/5£ 


.S o 


H 


P 


<J 


£ 


<J 


<J 


§ 


H 


P 


^ 


£ 


<! 


k<! 


3 




23/4 


85/r 


11.95 


305 


61.0 


11 


8 


1 


3 


1.58 


44 


8.80 


41/4 




21/ ? 


77/s 


9.85 


254 


50.8 


10 


9 


7/8 


23/4 


1.20 


34 


6.80 


33/4 


1 


21/4 


71/8 


8.00 


208 


41.6 


9 


10 


3/4 


2l/ 4 


0.89 


25 


5.00 


31/9 


2 


2 


61/4 


6 30 


165 


33.0 


8 


101/4 


O/S 


2 


62 


18 


3.60 


3 


5 


l3/ 4 


5l/ ? 


4.85 


128 


25.6 


71/9 


101/9 


9/16 


l3/ 4 


0.50 


14.5 


2.90 


21/9 


4 


I&/8 


5 


4 15 


111 


22.2 


6 


103/4 


1/9 


11/9 


0.39 


11.4 


2.28 


2 


5 


ll/o 


43/4 


3.55 


96 


19.2 


51/9 


10a 


7/tt 


11/4 


0.30 


8.85 


1.77 


11/, 


1)1/9 


l3/ 8 


41/4 


3.00 


82 


16.4 


»V4 


10& 


3/8 


H/8 


0.22 


6.55 


1.31 


1 


6 


11/4 


4 


2,45 


67 


13.4 


5 


10c 


Wl6 


1 


15 


4.50 


0.90 


7/ s 


7 


H/8 


31/2 


2.00 


56 


11.2 


41/2 


lOd 


1/4 


3/4 


0.10 


3.00 


0.60 


2/3 



7 WIRES TO THE STRAND. 



11 


11/9 


43/4 


3 55 


91 


18.2 


81/ 2 


19 


5/fl 


2 


0.62 


17 


3.40 


3 


12 


13/8 


/1/4 


3.00 


78 


15.6 


8 


20 


9/16 


13/4 


0.50 


14 


2.80 


23/4 


13 


U/4 


4 


2.45 


64 


12.8 


71/ 4 


21 


!/•> 


11/9 


0.39 


11 


2.20 


21/9 


14 


H/8 


31/9, 


2.00 


53 


10.6 


61/4 


22 


V/16 


H/4 


0.30 


8.55 


1.71 


2 


15 


1 


3 


1.58 


42 


8.40 


51/9 


23 


3/8 


11/8 


0.22 


6.35 


1.27 


11/9 


16 


7/8 


23/4 


1.20 


32 


6.40 


5 


24 


■V16 


1 


0.15 


4.35 


0.87 


H/4 


17 


3/4 


21/4 


0.89 


24 


4.80 


4 


25 


Ufa 


'7/8 


0.125 


3.65 


0.73 


1 


18 


H/16 


21/8 


0.75 


21 


4.20 


31/2 

















Plough-steel wire is made of high grade of crucible steel, and will 
stand a strain of from 95 to 175 tons per sq. in. Plough-steel ropes are 
used instead of cast-steel or iron where it is necessary to reduce the 
dead weight, as, for instance, with heavy or extremely long ropes when 
the weight of the rope is a large item. They are also employed when 
the load on the rope of an existing plant has been materially Increased 
and the sheaves and drums cannot be altered to meet the new require- 
ments. In this case a plough-steel rope of the same size can be used 
with an increase in strength of 50 to 100 per cent. Plough-steel is, 
therefore, applicable to conditions involving great wear and rough 
usage. It is advisable to reduce all bends to a minimum and to use 
somewhat larger drums and sheaves than are suitable for the ordinary 
cast-steel rope, having a strength of 60 to 80 tons per sq. in. It is well 
to obtain advice upon the adaptability of plough-steel ropes before 
using them. 

" LANG LAY » ROPE. 

In wire rope, as ordinarily made, the component strands are laid up 
into rope in a direction opposite to that in which the wires are laid into 
strands; that is, if the wires in the strands are laid from right to left, 
the strands are laid into rope from left to right. In the "Lang Lay," 
sometimes known as "Universal Lay," the wires are laid into strands 
and the strands into rope in the same direction; that is, if the wire is laid 
in the strands from right to left, the strands are also laid into rope from 
right to left. Its use has been found desirable under certain conditions 



GALVANIZED IRON WIRE ROPE. 



247 



and for certain purposes, mostly for haulage plants, inclined planes, and 
street railway cables, although it has also been used for vertical hoists 
in mines, etc. Its advantages are that it is somewhat more flexible 
than rope of the same diameter and composed of the same number of 
wires laid up in the ordinary manner; and (especially) that owing to the 
fact that the wires are laid more axially in the rope, longer surfaces of 
the wire are exposed to wear, and the endurance of the rope is thereby 
increased. (Trenton Iron Co.) 

CABLE-TRACTION ROPES. 

According to English practice, cable-traction ropes, of about 31/2 in' 
circumference, are commonly constructed with six strands of 7 or 15 
wires, the lays in the strands varying from, say, 3 in. to 31/2 in., and 
the lays in the ropes from, say, 7 1/2 in. to 9 in. In the United States, how- 
ever, strands of 19 wires are generally preferred, as being more flexible; 
but, on the other hand, the smaller external wires wear out more rapidly. 
The Market-street Street Railway Company, San Francisco, has used 
ropes 11/4 in. diam., composed of six strands of 19 steel wires, weighing 
21/2 lb. per foot, the longest continuous length being 24,125 ft. The 
Chicago City Railroad Co. has employed cables of identical construction, 
the longest length being 27,700 ft. On the New York and Brooklyn 
Bridge cable-railway steel ropes 11,500 ft. long, containing 114 wires, 
have been used. 

GALVANIZED IRON WIRE ROPE. 

For Ships' Rigging and Derrick Guys. 
Composed of 6 Strands and a Hemp Center, 7 or 12 Wires to the Strand. 



2 




J2 


4a2 


r 2& 


2' 




,fl 


Mi 


- a o 1 


^ 


.2 


4»" 


. UJ rA 


.2|h_c 


t3 


a 


J 


w »i 


r <3 M 


£ 


2 

3 


OS 


O GO 


d m C 





2 

3 


a 


p 52 


d a 


< 





s 


a-2-S 


b 


£2 
< 


5 


js* 


< 


O 


13/4 


51/2 


4.85 


44 


11 


1 


3 


1.44 


13 


53/4 


UV16 


51/4 


4.40 


40 


101/2 


v/s 


23/4 


1.21 


11 


51/4 


1 5/8 


5 


4.00 


36 


10 


13/16 


21/2 


1.00 


9.0 


5 


1 V? 


43/4 


3.60 


32 


91/2 


3/4 


21/4 


0.81 


7.3 


43/4 


1 V/16 


41/2 


3.25 


29 


9 


t»/R 


2 


0.64 


5.8 


41/2 


1 3/ 8 


41/4 


2.90 


26 


8 1/2 


9/16 


13/4 


0.49 


4.4 


33/4 


1 1/4 


4 


2.55 


23 


8 


1/7 


11/2 


0.36 


3.2 


3 


1 3/ 1fi 


33/4 


2.25 


20 


71/2 


V/16 


11/4 


0.25 


2.3 


21/2 


U/8 


31/2 


1.95 


18 


6 1/2 


3/8 


U/8 


0.20 


1.8 


21/4 


1 Vl6 


31/4 


1.70 


15 


6 


Wl6 


I 


0.16 


1.4 


2 








5 St 


RANDS, ' 


* WlR 


esEach 








9 /32 


7/8 


0.123 


1.1 


13/4 


7/32 


5/8 


0.063 


0.56 


11/4 


1/4 


3/4 


0.090 


0.81 


11/2 


3/16 


1/2 


0.040 


0.36 


U/8 



Galvanized wire rope has almost entirely superseded manila rope for 
shrouds and stays aboard ship. It is cheaper in first cost, is not affected 
by weather, and does not stretch and contract with changes in atmos- 
pheric conditions; on the other hand, it is quite as elastic as manila rope. 
It is only 1/5 or 1/6 as large by bulk as a manila rope of equal strength, 
and offers only half as much surface to the wind, and weighs less. It is 
much less liable to accidents by cutting or chafing. 

If galvanized rope of greater strength than that shown in the table 
is desired, galvanized open hearth, cast-steel or plough-steel wire rope 
can be obtained. 



248 



MATERIALS. 



STEEL FLAT ROPES. 

(J. A. Roebling's Sons Co.) 

Steel-wire Flat Ropes are composed of a number of strands, alter- 
nately twisted to the right and left, laid alongside of each other, and 
sewed together with soft iron wires. These ropes are used at times in 
place of round ropes in the shafts of mines. They wind upon them- 
selves on a narrow winding-drum, which takes up less room than one 
necessary for a round rope. The soft-iron sewing-wires wear out sooner 
•than the steel strands, and then it becomes necessary to sew the rope 
with new iron wires. 



_fl 


s 


lS8 


i 


.5 


J" 


J) -r 




a a) 
-3 


a 






03 

a 


"11 




M . 


O oa • 


Sofii 


-fl.H 


.fl 


2 M O! 


i a 


g.S3£ 


s^oQw 


§£ 


- 5)^5 




=3^02^, 


£ 


< 


<! 


£ 


£ 


<9*> 


< 


3/8X2 


1.19 


18 


3.6 


1/2 x 3 


2.38 


36 


7.2 


3/8X21/2 


1.86 


28 


5.6 


1/2X31/2 


2.97 


45 


9.0 


3/8X3 


2.00 


30 


6.0 


1/2X4 


3.30 


50 


10. a 


3/8 X 31/2 


2.50 


38 


7.6 


1/2X41/2 


4.00 


60 


12.0 


3/8 X 4 


2.86 


43 


8.6 


1/2 x 5 


4.27 


64 


12.8 


3/8 X 41/ 2 


3.12 


47 


9.4 


1/2X51/2 


4.82 


72 


14.4 


3/8X5 


3.40 


50 


10.0 


1/2 X 6 


5.10 


77 


15.4 


3/8 X 51/2 


3.90 


55 


11.0 


1/2X7 


5.90 


89 


17.8 



GALVANIZED STEEL CABLES. 

For Suspension Bridges. (Roebling's.) 
Composed of 6 Strands — With Wire Center. 







Approx. 






Appro. 






Appro. 


Diam., 


Wt. per 
foot, 


Breaking 
Strain, 


Diam., 


Wt. per 
foot, 


Break- 
ing 


Diam., 


Wt. per 
foot, 


Break- 
ing 




lb. 


tons 
(20001b.). 




lb. 


Strain, 
tons. 




lb. 


Strain, 
tons. 


23/ 4 


12.7 


310 


21/4 


6.52 


208 


13/4 


5.10 


124 


25/ 8 


11.6 


283 


21/8 


7.60 


185 


15/8 


4.34 


106 


21/2 


10.5 


256 


2 


6.73 


164 


11/2 


3.70 


90 


2S/ 8 


9.50 232 


17/8 


5.90 


144 


13/8 


3.10 


75 



GALVANIZED CAST-STEEL YACHT RIGGLNG. 

6 Strands and a Hemp Center. 7 or 19 Wires to the Strand. 



i 




J2 


o3 ,£ 


I1| 

£18 


i 

03 




£ 




111 

£ag 


3 


.s 


£ 


n-SS 


fl 


.£ 


£ 




o^| 


O 


s 


ft 




S^ 


2 


a 


01 

a 


°&^ 


N* 


ft . 


w 




ft bH fl 




a . 






awfl 


O oj o< 


ac 





£ 


ft A 9, 


glw 


as 





£ 


ac 


s §w 


H/4 


4 


2 55 


53 


13 


5/8 


2 


0.64 


14.0 


6 


13/16 


33/ 4 


2.25 


47 


12 


9/16 


13/4 


0.49 


10.8 


51/4 


11/8 


3l/„ 


1.95 


41 


11 


1/2 


11/2 


0.36 


8.1 


43/4 


11/16 


31/4 


1.70 


36 


10 


15/32 


13/8 


0.30 


6.8 


41/2 


1 


3 


1.44 


31 


9 


7/16 


11/4 


0.25 


5.7 


41/4 


7/8 


23/4 


1.21 


26 


8 1/2 


3/8 


H/8 


0.20 


4.5 


33/4 


13/16 


21/9 


1.00 


22 


8 


5/16 


1 


0.16 


3.7 


3 


3/4 


21/4 


0.81 


17.6 


7 













GALVANIZED STEEL HAWSERS. 



249 



GALVANIZED STEEL-WIRE STRAND. 

For Smokestack Guys, Signal Strand, etc. 

(J. A. Roebling's Sons Co., 1908.) 
This strand is composed of 7 wires, twisted together into a single strand. 



Diam., in. 


Wt. per. 
1000 ft., lb. 


Approx. 
Breaking 
Strain, lb. 


Diam., in. 


Wt. per 
1000 ft. 


Approx. 
Breaking 
Strain, lb. 


I/9 


510 
415 
295 
210 
125 


8500 
6500 
5000 
3800 
2300 


7/39 


95 
75 
55 
32 
20 


1800 


7/ 16 


3/ 16 


1400 


3 /8 ••• 


0/39 


900 


5 /l6 


l/ 8 


500 


1/4 . 


3/ 32 


400 









Galvanized strand is made on application of wire of any strength from 
60,000 lb. to 350,000 lb. per sq. in. When used to run over sheaves or 
pulleys the use of soft-iron stock is advisable. 

FLEXIBLE STEEL-WIRE HAWSERS. 

These hawsers are extensively used. They are made with six strands of 
twelve wires each, hemp centers being inserted in the individual strands as 
well as in the completed rope. The material employed is crucible cast 
steel, galvanized, and guaranteed to fulfill Lloyd's requirements. They 
are only one-third the weight of hempen hawsers, and are sufficiently 
pliable to work round any bitts to which hempen rope of equivalent 
strength can be applied. 

13-inch tarred Russian hemp hawser weighs about 39 lbs. per fathom. 

10-inch white manila hawser weighs about 20 lbs. per fathom. 

1 1/8-inch stud chain weighs about 68 lbs. per fathom. 

4-inch galvanized steel hawser weighs about 12 lbs. per fathom. 

Each of the above named has about the same tensile strength. 

GALVANIZED STEEL HAWSERS. 

For Mooring, Sea or Lake Towing. 

Composed of 6 Strands and a Hemp Center, each Strand consisting of 
12 Wires and a Hemp Core or of 37 Wires. 







Wt. per 


ft., lb. 


Approx. Breaking Strain, 
tons (2000 lb.). 


Approx. 


Circum., 














Diam., in. 


m. 


12-Wire 


37-Wire 


12-Wire 


37-Wire 






Strand. 


Strand. 


Strand. 


Strand. 


21/16 


6 1/2 


4.56 


6.76 


83 


179 


2 


6 1/4 


4.20, 


6.25 


77 


166 


1 15/ 16 


6 


3.88 


5.76 


71 


155 


1 13/16 


53/4 


3.56 


5.29 


66 


142 


13/4 


51/2 


3.25 


4.85 


61 


131 


1 H/I6 


51/4 


2.95 


4.41 


57 


120 


15/8 


5 


2.70 


4.00 


53 


109 


11/2 


43/4 


2.42 


3.60 


45 


99 


17/16 


41/2 


2.18 


3.24 


42 


90 


13/s 


41/4 


1.94 


2.90 


39 


81 


11/4 


4 


1.72 


2.55 


32 


72 


13/16 


33/ 4 


1.51 


2.25 


29 


62 


11/8 


31/2 


1.32 


1.95 


27 


55 


11/16 


31/4 


1.14 


1.69 


24 


46 


1 


3 


.97 


1.44 


21.5 


40 


7/8 


23/4 


.81 


1.21 


16.4 


34 


13/16 


21/2 


.67 


1.00 


14.4 


28 


3/4 

r 


21/4 


.54 


.81 


12.3 


23 















250 MATERIALS. 

Notes on the Use of Wire Rope. (J. A. Roebling's Sons Co.) 
(See also notes under various tables of wire ropes.) 

Several kinds of wire rope are manufactured. The most pliable 
variety contains nineteen wires to the strand. The ropes with twelve 
wires and seven wires in the strand are stiffer, and are better adapted for 
standing rope, guys, and rigging. Orders should state the use of the 
rope, and advice will be given. 

Wire rope is as pliable as new hemp rope of the same strength; the 
former will therefore run over the same-sized sheaves and pulleys as the 
latter. But the greater the diameter of the sheaves, pulleys, or drums, 
the longer wire rope will last. The minimum size of drum is given in 
the table. Experience has demonstrated that the wear increases with 
the speed. It is, therefore, better to increase the load than the speed. 

Wire rope must 'not be coiled or uncoiled like hemp rope. — When 
mounted on a reel, the latter should be mounted on a spindle or flat 
turn-table to pay off the rope. When forwarded in a small coil, without 
reel, roll -it over the ground like a wheel, and run off the rope in that 
wav. All untwisting or kinking must be avoided. 

To preserve wire rope, apply raw linseed -oil with a piece of sheepskin, 
wool inside; or mix the oil with equal parts of Spanish brown or lamp- 
black. 

To preserve wire rope under water or under ground, take mineral or 
vegetable tar, and add one bushel of fresh-slacked lime to one barrel of 
tar, which will neutralize the acid. Boil it well, and saturate the rope 
with the hot tar. To give the mixture body, add some sawdust. 

The grooves of cast-iron pulleys and sheaves should be filled with 
well-seasoned blocks of hard wood, set on end, to be renewed when 
worn out. This end-wood will save wear and increase adhesion. The 
smaller pulleys or rollers which support the ropes on inclined planes 
should be constructed on the same plan. When large sheaves run at 
high velocity, the grooves should be lined with leather, set on end, or 
with India rubber. This is done in the case of sheaves used in the 
transmission of power between distant points by means of rope, which 
frequently runs at the rate of 4000 feet per minute. 



Locked Wire Rope. 

Fig. 77 shows what is known as the Patent Locked Steel Wire Rope 
made by the Trenton Iron Co. It is claimed to wear two to three times 




as long as an ordinary wire rope of equal diameter and of like material, 
with an increased life for sheaves and rollers. Sizes made are from 1/2 
to 2 inches diameter, with a minimum diameter of sheave of 4 and 12 
feet respectively. 



251 



CHAINS. 

Weight per Foot, Proof Test and Breaking Weight. 

(Pennsylvania Railroad Specifications, 1903.) 



Nominal 

Diameter 

of Wire. 

Inches. 



5/32 
3/16 
3/16 

V4 
5/16 
3/8 
3/8 
7/16 
7/16 
1/2 
1/2 
5/8 
5/8 
3/4 
3/4 
7/8 
1 
1 

H/8 
H/4 
U/2 
13/4 
2 



Description, 



Twisted chain . 



Perfection twisted chain 
Straight-link chain. 



Crane chain 

Straight-link chain . . . 

Crane chain 

Straight-link chain . . . 

Crane chain 

Straight-link chain . . . 

Crane chain 

Straight-link chain . . . 
Crane chain 



Straight-link chain . 
Crane chain 



Maximum 

Length of 

100 Links 

Inches. 



1031/ 8 
96l/ 4 
l5ll/ 4 
102 
1143/ 4 
1143/4 
1135/ 8 
1271/ 2 
1261/4 
153 
1511/2 
1781/9 
176 3/4 
204 
202 
2521/2 
277 ?/ 4 
2801/-, 
303 
3531/2 
4165/ 8 
4793/ 4 
5551/ 2 



\\ eight 



Lbs. 



0.20 
0.35 
0.27 
0.70 
1.10 
1.60 
1.60 
2.07 
2.07 
2.50 
2.60 
4.08 
4.18 
5.65 
5.75 
7.70 
9.80 
9.80 
12.65 
15.50 
22.50 
30.00 
39.00 



Proof 
Test. 
Lbs. 



1,600 
2,500 
3,600 
4,140 
4,900 
5,635 
6,400 
7,360 
10,000 
11,500 
14,400 
16,560 
22,540 
29,440 
25,600 
38,260 
46,000 
66,240 
90, 1 60 
117,760 



Breaking 

Weight. 
Lbs. 



3,200 
5,000 
7,200 
8,280 
9,800 
11,270 
12,800 
14,720 
20,000 
23,000 
28,800 
33,120 
45,080 
58,880 
51,200 
76,520 
92,000 
132,480 
180,320 
235,520 



A.11 chain must stand the proof 
ft. long out of each 200 ft. is 



Elongation of all sizes, 10 per cent 
test without deformation. A piece 
tested to destruction. 

British Admiralty Proving Tests of Chain Cables. — Stud-links. 
Minimum size in inches and 16ths. Proving test in tons of 2240 lbs. 
Min. Size: ft I i§ i if 1 1th H 1 r 3 s H li 6 s If 
Test, tons: 8* 10.1 11.9 13f 15f 18 20.3 22f 25A 28.1 31 34 
Min. Size: 1 T 7 H 1* 1 T 9 6 IS Ui 1* Ul If lit 2 2| 
Test, tons: 37 5 3 5 40£ 43 9 47| 51* 55.1 59.1 63* 67JJ 72 81* 

Wrought-iron Chain Cables. — The strength of a chain link is less 
than twice that of a straight bar of a sectional area equal to that of one 
side of the link. A weld exists at one end and a bend at the other, each 
requiring at least one heat, which produces a decrease in the strength. 
The report of the committee of the U. S. Testing Board (1879), on tests 
of wrought-iron and chain cables, contains the following conclusions. 
That beyond doubt, when made of American bar iron, with cast-iron 
studs, the studded link is inferior in strength to the unstudded one. 

" That when proper care is exercised in the selection of material, a varia- 
tion of 5 to 17 per cent of the strongest may be expected in the resistance 
of cables. Without this care, the variation may rise to 25 per cent. 

"That with proper material and construction the ultimate resistance of 
the chain may be expected to vary from 155 to 170 per cent of that of the 
bar used in making the links, and show an average of about 163 per cent. 

"That the proof test of a chain cable should be about 50 per cent of 
the ultimate resistance of the weakest link." 

The decrease of the resistance of the studded below the unstudded 
cable is probably due to the fact that in the former the sides of the link 
do not remain parallel to each other up to failure, as they do in the latter. 
The result is an increase of stress in the studded link over the unstudded 
in the proportion of unity, to the secant of half the inclination of the 
sides of the former to each other. 

From a great number of tests of bars and unfinished cables, the commit- 
tee considered that the average ultimate resistance, and proof tests of 
chain cables made of the bars, whose diameters are given, should be 
such as are shown in the accompanying table. 



252 



MATERIALS. 



ULTIMATE RESISTANCE AND PROOF TESTS OF CHAIN CABLES. 


Diam. 
of 
Bar. 


Average resist. 
= 163% of Bar. 


Proof Test. 


Diam. 

of 
Bar. 


Average resist. 
= 163% of Bar. 


Proof Test. 


Inches. 


Pounds. 


Pounds. 


Inches. 


Pounds. 


Pounds. 


1 


71,172 


33,840 


19/16 


162,283 


77,159 


11/16 


79,544 


37,820 


15/8 


174,475 


82,956 


U/8 


88,445 


42,053 


1 11/16 


187,075 


88,947 


13/16 


97,731 


46,468 


13/4 


200,074 


95,128 


U/4 


107,440 


51,084 


1 13/16 


213,475 


101,499 


1 5 /16 


117,577 


55,903 


17/8 


227,271 


108,058 


13/ 8 


128,129 


60,920 


1 15/16 


241,463 


114,806 


17/16 


139,103 


66,138 


2 


256,040 


121,737 


H/2 


150,485 


71,550 









Pitch, Breaking, Proof and Working Strains of Chains. 

(Bradlee & Co., Philadelphia.) 



1/4 

5/16 

3/8 

7/16 

1/2 

8/16 

5/8 

H/16 

3/4 

13/16 

7/8 

15/16 

H/16 

U/8 

13/16 

U/4 

15/16 

13/8 

17/16 

11/2 

19/16 

13/ 4 

2 

21/ 4 

21/2 

2 3/4 

3 



25 /32 
27/32 
31/32 
15/32 
1 H/32 
1 15/3 2 
1 23/3 2 
1 13/16 
1 15/16 
21/16 
23/ie 
27/i 6 
21/2 
25/ 8 
23/4 
31/16 
31/8 
33/8 
39/i 6 
3H/16 
37/8 
4 

43/ 4 
53/4 
63/4 
7 

71/4 
73/4 



3/4 
1 

U/2 
2 

21/2 
33/io 
41/10 
5 

62/io 
67/io 
83/s 
9 

101/9 

12 

135/s 

137/io 

16 

161/-> 

191/4 

197/io 

23 

25 

31 

40 

523/4 

641/2 

73 

86 



15/16 

U/8 

15/16 

U/2 

1 13/16 

2 

23/16 

23/ 8 

29/ie 

23/4 

215/ie 

33/i 6 

33/8 

39/ie 

313/i 6 

4 

43/ie 

43/ 8 

49/ie 

43/ 4 

51/8 

55/ie 

57/s 

63/4 

75/8 

83/s 

91/8 

97/8 



D. B. G. Special Crane. 



1,932 

2,898 
4,186 
5,796 
7,728 
9,660 
11,914 
14,490 
17,388 
20,286 
22,484 
25,872 
29,568 
33,264 
37,576 
41,888 
46,200 
50,512 
55,748 
60,368 
66,528 
70,762 
82,320 
107,520 
136,080 
168,000 
193,088 
217,728 



3,864 
5,796 
8,372 
11,592 
15,456 
19,320 
23,828 
28,9 
34,776 
40,572 
44,968 
51,744 
59,136 
66,538 
75,152 
83,776 
92,400 
101,024 
111,496 
120,736 
133,056 
141,524 
164,640 
215,040 
272,160 
336,000 
386,176 
435,456 



1,288 
1,932 
2,790 
3,864 
5,152 
6,440 
7,942 
9,660 
11,592 
13,524 
14,989 
17,248 
19,712 
22,176 
25,050 
27,925 
30,800 
33,674 
37,165 
40,245 
44,352 
47,174 
54,880 
71,680 
90,720 
112,000 
128,725 
145,152 



1,680 
2,520 
3,640 
5,040 
6,720 
8,400 
10,360 
12,600 
15,120 
17,640 
20,440 
23,520 
26,880 
30,240 
34,160 
38,080 
42,000 
45,920 
50,680 
54,880 
60,480 
65,520 



<~ 



3,360 
5,040 
7,280 
10,080 
13,440 
16,800 
20,720 
25,200 
30,240 
35,280 
40,880 
47,040 
53,760 
60,480 
68,320 
76,160 
84,000 
91,840 
101,360 
109,760 
120,960 
131,140 



1,12 
1,68 
2,420 
3,360 
4,487 
5,600 
6,900 
8,400 
10,087 
11,760 
13,620 
15,680 
17,927 
20,160 
22,770 
25,380 
28,003 
30,617 
33,780 
36,583 
40,327 
43,187 



The distance from center of one link to center of next is equal to the 
inside length of link, but in practice 1/32 in. is allowed for weld. This is 
approximate, and where exactness is required, chain should be made so. 

For Chain Sheaves. — The diameter, if possible, should be not less 
than thirty times the diameter of chain used. 

Example. — For 1-inch chain use 30-inch sheaves. 



SIZES OF FIRE-BRICK. 



253 





9x4^x2)^ , 

9-inch straight ... 9 X 4 1/2 X 2 V 2 inches. 

Soap 9x21/4X21/2 

Checker 9X3 X3 

'Kev \ NO. 1 Split 9X41/2X1V4 

_!___— -} No. 2 Split 9X41/2X2 

-^7aH- 2 T Jamb 9 X 4V 2 X 2 1/2 

: -"-' — -'- No. 1 key 9 X 21/2 thick X 4V 2 to 4 inches 

wide. 112 bricks to circle 12 feet inside 
diam. 

No. 2 key 9 X 2V 2 thick X 41/2 to 3V 2 inches 

Wedge \ wide. 65 bricks to circle 6 ft. inside diam. 

x No. 3 key 9 X 21/2 thick X4i/ 2 to 3 inches wide. 

41 bricks to circle 3 ft. inside diam. 
* - g-^ No. 4 key 9X2 1/2 thick X 4 V 2 to 2 1/4 inches 

wide. 26 bricks to circle IV2 ft. inside diam. 

v No. 1 wedge (or bullhead) 9 X 4 1/2 wide 2 XV2 

Arch \ to 2 in. thick, tapering lengthwise. 

7 102 bricks to circle 5 ft. inside diam. 

:4>$x (2>£:1K/ No. 2 wedge 9 X 41/2 X 21/2 to 1 1/2 in. thick. 

/ 63 bricks to circle 21/2 ft. inside diam. 

■ ' No. 1 arch 9 X 4V 2 X 2V 2 to 2 in. thick, 

tapering breadthwise. 72 bricks to circle 4 ft. 
inside diam. 
,No.l Skew\ No. 2 arch 9 X 4l/ 2 X 2i/ 2 to 1 1/ 2 . 

42 bricks to circle 2 ft. inside diam. 
No. 1 skew 9 to 7 X 41/2 to 2V 2 . 

( m*Ui*ZX / Bevel on one end. 

'■ No. 2 skew 9 X 2i/ 2 X 4V 2 to 2i/ 2 . 

Equal bevel on both edges. 

~ __. — \ No. 3 skew 9 X 2i/ 2 X 4i/ 2 to H/ 2 . 

jno.^ sKew \ Taper on one edge. 

/ 24-inch circle 8 1/4 to 5i/ 8 X 4V 2 X 2l/ 2 . 

*2tex(il4-2Xt Edges curved, 9 bricks line a 24-inch circle. 

n I 36-inch circle 83/ 4 ,to 6i/ 2 X 4i/ 2 X 2i/ 2 . 

-* 13 bricks line a 36-inch circle. 

48-inch circle. ... 83/ 4 to 71/4X 4i/ 2 X 2i/ 2 . 
17 bricks line a 48-inch circle. 
No 3 Skew — \ 13 1/2-inch straight . . 13 1/2 X 2 1/ 2 X 6. 

131/2-inch key No. 1, 13i/ 2 X 2 1/2 X 6 to 5 inch. 
2Xx(i\4-U£Y 1 90 bricks turn a 12-ft. circle. 

' * . 2-2/ 3 1/2-inch key No. 2, 1 3 1/2 X 2 1/2 X 6 to 4 3/ 8 inch. 

52 bricks turn a 6-ft. circle. 
in. Cirdfl Bridge wall, No. 1, 13 X 6V2X 6. 

~~S% -\ Bridge wall, No. 2, 13 X 6 1/2 X 3. 

\ Mill tile 18, 20, or 24 X 6 X 3. 

^\ M \ Stock-hole tiles ... 18, 20, or 24 X 9 X 4. 
1 18-inch block .... 18X9X6. 

Flat back 9 X 6 X 2 1/2. 

Flat back arch ... 9 X 6 X 3 1/2 to 21/2. 

22-inch radius, 56 bricks to circle. 
CuDoia^^ Locomotive tile. . .32 X 10 X 3. I 36 X 8 X 3. 
34 X 10 X 3. 40 X 10 X 3. 

34 X 8 X 3. I 
Tiles, slabs, and blocks, various sizes 12 to 30 
in. long, 8 to 30 in. wide, 2 to 6 in. thick. 
Cupola brick, 4 and 6 in. high, 4 and 6 in. radial width, to line shells 
23 to 66 in. diameter. 

A 9-inch straight brick weighs 7 lb. and contains 100 cubic inches. 
( = 120 lb. per cubic foot. Specific gravity 1.93.) 

One cubic foot of wall requires 17 9-inch bricks, one cubic yard re- 
quires 460. Where keys, wedges, and other "shapes" are used, add 10 
per cent in estimating the number required. 

One ton of fire-clay should be sufficient to lay 3000 ordinary bricks. 
To secure the best results, fire-bricks should be laid in the same clay 




254 



MATERIALS. 



from which they are manufactured. It should be used as a thin paste, 
and not as mortar. The thinner the joint the better the furnace wall. 
In ordering bricks, the service for which they are required should be 
stated. 

NUMBER OF FIRE-BRICK REQUIRED FOR VARIOUS 
CIRCLES. 



Diam. 


Key Bricks. 


Arch Bricks. 


Wedge Bricks. 


of 
Circle. 


d 


d 


c 


d 


*3 

o 


c 

Iz; 


d 
5 




o 


d 


d 


.5 

ON 


"3 

o 
H 


ft. in. 
1 6 


25 
17 
9 








25 
30 
34 
38 
42 
46 
51 
55 
59 
63 
67 
71 
76 
80 
84 

92 
97 
101 
105 
109 
113 
117 


















2 


13 
25 
38 
32 
25 
19 
13 
6 






42 
31 
?,1 






42 
49 
57 
64 
72 
80 
87 
95 
102 
110 
117 
125 
132 
140 
147 
155 
162 
170 
177 
185 
193 










2 6 






18 
36 
54 
72 
72 
72 
72 
72 
72 
72 
72 
72 
72 

72 
72 
72 
72 
72 


15 
23 
30 
38 
45 
53 
60 
68 
75 
83 
90 
98 
105 
113 
121 


60 

48 
36 
24 
12 






60 


3 






20 
40 
59 
79 
98 
98 
98 
98 
98 
98 
98 
98 
98 
98 
98 
98 
98 
98 
98 


"8" 

15 

23 

30 

38 

46 

53 

61 

68 

76 

83 

91 

98 
106 


68 


3 6 

4 

4 6 

5 

5 6 

6 


10 

21 
32 
42 
53 
63 
58 
52 
47 
42 
37 
31 
26 
21 
16 
11 
5 


' 9 " 

19 

29 

38 
47 

66 

76 

85 

94 
104 
113 
113 


1 


) 


76 
83 
91 
98 
106 
113 


6 6 






121 


7 






128 


7 6 






136 


8 






144 


8 6 






151 


9 






159 


9 6 






166 


10 






174 


10 6 






181 


11 






189 


11 6 






196 


12 






204 


12 6 



































For larger circles than 12 feet use 113 No. 1 Key, and as many 9-inch 
brick as may be needed in addition. 



WEIGHTS OF LOGS, LUMBER, ETC. 



Weight of Green Logs to Scale 1000 Feet, Board Measure. 



Yellow pine (Southern) 8,000 to 10 

Norway pine (Michigan) 7,000 to 8 

White nine rMichiearrt i off of stum P 7 - 000 to 7 

wnite pine (.Micmgan) J QUt of water 7000 to 

White pine (Pennsylvania), bark off 5,000 to 

Hemlock (Pennsylvania), bark off 6,000 to 7,000 ' 

Four acres of water are required to store 1,000,000 feet of logs. 



000 lb. 
000 " 
,000 " 
,000 " 
,000 " 



Weight of 1000 Feet of Lumber, Board Measure. 



Yellow or Norway pine Dry, 3,000 lb. 

White pine " 2,500" 



Green, 5, 

4', 



0001b. 
,000 " 



ANALYSES OF FIRE CLAYS. 



255 



Weight of 1 Cord of Seasoned Wood, 138 Cu. Ft. per Cord. 

Hickory or sugar maple 4 500 lb 

White oak 3,850 " 

Beech, red oak or black oak 3,250 " 

Poplar, chestnut or elm , . 2,350 " 

Pine (white or Norway) 2,000 " 

Hemlock bark, dry 2,200 " 



ANALYSES OF FIRE CLAYS. 



Brand. 


73 

'3 
< 

u 

H 


6 


c n 
go 




O 

s 


O 
6 

S 

3 


.2 

93 


C 
o 


q 

73 

c 

X< 


H 

o ft 
Eh 


o 
i-1 






50.46 
56.80 
44.40 
56.15 
55.87 
56.80 
67.84 
68.01 
48.35 
44.80 
51.50 
63.18 
44.61 
45.26 
67.47 
73.82 


35.90 
30.08 
33.56 
33.30 
41.39 
30.08 
21.83 
24.09 
36.37 
39.00 
44.85 
23.70 
38.01 
37.85 
19.33 
15.88 


12.744 
10.50 
14.575 
9.68 

Y.W 

5.98 
3.03 
10.56 
14.70 
1.94 
6.87 
13.63 
13.30 
10.45 
6.45 


1.50 
1.12 
1.08 
0.59 
1.60 
1.67 
1.57 
1.01 
2.00 
0.30 
0.33 
1.20 
1.25 
2.03 
2.56 
2.95 


0.13 


1 
02 Trop.fi 


1.65 
1.92 
1.47 
0.88 
2.79 
3.97 
4.33 
4.02 
4.73 




Mt. Savage 2 


1.15 
1.53 




0.80 
0.247 




Mt. Savage 3 


Tr. 
0.17 
0.40 


0.11 
0.12 
0.30 




Strasburg, O 


0.45 
1.15 


0.29 

2.30 

2.24 


0.20 




Woodbridge, N. J. . 


0.28 
3.01 
0.07 
0.20 
0.23 
0.17 
0.08 
0.08 
0.41 
Tr. 


0.24 




Clearfield Co., Pa. . 


L46 

1.02 


0.12 
1.00 
1.15 
0.47 
0.41 
0.02 
0.07 
Tr. 


2.54 












Clinton Co., Pa. ... 

Clarion Co., Pa 

Farrandsville, Pa. . 
St. Louis Co., Mo.. . 
Stourbridge, Eng. . . 


2.52 
1.74 
1.26 
1.07 
0.90 


4.55 
3.47 
3.59 
5.14 

3.85 


SO 2 0.l9 
6.20 



1 Mass. Inst, of Technology 1871. 2 Report on Clays of New Jersey. 
Prof. G. H. Cook, 1877. 3 Second Geological Survey of Penna., 1878, 
* Dr. Otto Wuth (2 samples), 1885. 6 Flint clay from Clearfield and 
Cambria counties, Pa., average of hundreds of analyses by Harbison- 
Walker Refractories Co., Pittsburg, Pa. 6 Same material calcined. All 
other analyses from catalogue of Stowe-Fuller Co., 1907. 



Refractoriness of Some American Fire-Brick. — (R. F. Weber, 
A. I. M. E., 1904.) Prof. Heinrich Ries notes that the fusibility of New 
Jersey brick is influenced largely by its percentage of silica, but also in 
part by the texture of the clay. It was found that the fusion-point of 
almost any of the New Jersey fire-bricks could be reduced four or five 
cones by grinding the brick sufficiently fine to pass through a 100-mesb 
sieve. 

Mr. Weber draws the conclusion from his tests of 44 bricks that it is 
evident that the refractoriness of a fire-brick depends on the total quan- 
tity of fluxes present, the silica percentage and the coarseness of grain; 
moreover, chemical analysis alone cannot be used as an index of the 
refractoriness except within rather wide limits. The following table 
shows the composition, fusion-point, and physical properties of six most 
refractory and of five least refractory of the 44 bricks. 



256 



MATERIALS. 





Locality. 


Si0 2 . 


AI2O3. 


FesOs- 


Ti0 2 . 


13 

< 


i 


°.2 

" 2 3 

flrv. 

O 


1 .. 




Per 

cent. 

51.59 

54.90 

53.05 

93.57 

44.77 

68.70 

61.28 

74.83 

67.19 

60.76 

60.58 


Per 

cent. 
38.26 
38.19 
41.16 
2.53 
43.08 
20.75 
27.13 
16.40 
25.05 
31.66 
32.49 


Per 

cent. 
1.84 
2.18 
2.65 
0.62 
2.78 
1.20 
2.90 
3.26 
2.83 
5.67 
2.25 


Per 
cent. 
1.97 
1.55 
1.80 
0.27 
2.54 
5.54 
1.37 
0.77 
0.71 
1.58 
1.69 


Per 
cent. 
6.34 
3.18 
1.34 
3.01 
6.83 
3.81 
7.31 
4.74 
4.22 
0.33 
2.99 


Per 
cent. 
10.25 
6.91 
5.79 
3.90 
12.15 
10.55 
11.58 
8.77 
7.76 
7.58 
6.93 


No. 
32 to 33 


2.... 
3.... 
4 .. 


Kentucky 

Pennsylvania 


32 to 33 
32 to 33 
32 to 33 


5 ... 




31 to 32 


6.... 




31 to 32 


40.... 
41.... 
42 


Pennsylvania 

Pennsylvania. 


26 
26 
26 


43 ... . 




26 


44.... 


Kentucky 


26 



1 Fairly uniform, angular flint-clay particles, constituting body of 
brick. Largest pieces 5 to 6 mm. in diameter. White. 

2 Coarse-grained: angular pieces of flint-clay as large as 9 mm. Aver- 
age 4 to 5 mm. Light buff. 

3 Coarse, angular flint-clay particles, varying from 1 to 5 mm. in 
diameter. Average 4 to 5 mm. Buff. 

4 Fine-grained quartz particles. Largest 2 to 3 mm. in diameter. 
White. 

6 Medium grain; flint-clay particles, fairly uniform in size, 3 to 4 mm. 
Light buff. 

6 Coarse grain; quartz particles, 4 to 5 mm. in diameter, forming 
about 50 per cent of brick. White., 

40 Fine grain; small, white flint-clay particles, not over 2 mm. in 
diameter and not abundant. Buff. 

41 Medium grain; pieces of quartz with pinkish color and angular flint- 
clay particles. About 3 mm. in diameter. Buff. 

42 Fine grain; even texture. Few coarse particles. Brown. 

43 Fine grain; some particles as large as 1 to 2 mm. in diameter. Buff. 

44 Angular, dark-colored, flinty-clay particles. Maximum size 5 mm. 
Throughout a reddish-brown matrix. 

SLAG BRICKS AND SLAG BLOCKS. 

Slag bricks are made by mixing granulated basic slag and slaked lime, 
molding the mixture in a brick press or by hand, and drying. The silica 
in the slag ranges from 22.5% to 35%; the alumina andiron oxide together, 
from 16.1% to 21%; the lime, from 40% to 51.5%. The granulated slag 
is dried and pulverized. Powdered slaked lime is added in sufficient quan- 
tity to bring the total calcium oxide in the mixture up to about 55%. 
Usually a small amount of water is added. The mixture is then molded 
into shape, and the bricks are then dried for six to ten days in the open 
air. Slag bricks weigh less than clay bricks of equal size, require less 
mortar in laying up, and are at least equal to them in crushing strength. 

Slag blocks are made by running molten slag direct from the furnaces 
into molds. If properly made, they are stronger than slag bricks. They 
are, however, impervious to air and moisture; and on that account 
dwellings constructed of them are apt to be damp. Their chief uses are 
for foundations or for paving blocks. The properties required in a slag 
paving block, viz: density, resistance to abrasion, toughness, and rough- 
ness of surface, vary with the chemical composition of the slag, the 
rapidity of cooling, and the character of the molds used. Blocks cast in 
sand molds, and heavily covered with loose sand, cool slowly, and give 
much better results than those cast in iron molds. — E. C. Eckel, Eng. 
News, April 30, 1903. 



MAGNESIA BRICKS. 257 

MAGNESIA BRICKS. 

"Foreign Abstracts" of the Institution of Civil Engineers, 1893, gives a 
paper by C. Bischof on the production of magnesia bricks. The material 
most in favor at present is the magnesite of Styria, which, although less 
pure considered as a source of magnesia than the Greek, has the property 
of fritting at a high temperature without melting. 

At a red heat magnesium carbonate is decomposed into carbonic acid 
and caustic magnesia, which resembles lime in becoming hydrated and 
recarbonated when exposed to the air, and possesses a certain plasticity, 
so that it can be moulded when subjected to a heavy pressure. By long- 
continued or stronger heating the material becomes dead-burnt, giving a 
form of magnesia of high density, sp. gr. 3.8, as compared with 3.0 in the 
plastic form, which is unalterable in the air but devoid of plasticity. A 
mixture of two volumes of dead-burnt with one of plastic magnesia can 
be moulded into bricks which contract but little in firing. Other binding 
materials that have been used are: clay up to 10 or 15 per cent; gas-tar, 
perfectly freed from water, soda, silica, vinegar as a solution of magnesium 
acetate which is readily decomposed by heat, and carbolates of alkalies 
or lime. Among magnesium compounds a weak solution of magnesium 
chloride may also be used. For setting the bricks lightly burnt, caustic 
magnesia, with a small proportion of silica to render it less refractory, is 
recommended. The strength of the bricks may be increased by adding 
iron, either as oxide or silicate. If a porous product is required, sawdust 
or starch may be added to the mixture. When dead-burnt magnesia is 
used alone, soda is said to be the best binding material. See also papers 
by A. E. Hunt, Trans. A. I. M. E., xvi, 720, and by T. Egleston, Trans. 
A. I. M.E., xiv, 458. 

The average composition of magnesite, crude and calcined, is given as 
follows by the Harbison- Walker Refractories Co., Pittsburg (1907). 

Grecian. Styrian. 

Crude. Calcined. Crude. Calcined. 

Carbonate of magnesia 97.00% 92.50% . 

Magnesia 94.00% 85.50% 

Silica 1.25 2.75 1.50 3.00 

Alumina 0.40 0.70 0.50 1.00 

Iron Oxide 0.40 0.80 3.90 8.00 

Lime 0.75 1.50 1.25 2.50 

Loss 0.40 0.50 

100.05 100.15 99.65 100.50 

With the calcined Styrian magnesite of the above analysis it is not 
necessary to use a binder either for making brick or for forming the 
bottom of an open-hearth furnace. 

ASBESTOS. 

The following analyses of asbestos'are given by J. T. Donald, Eng. and 
M. Jour., June 27, 1891. 

Canadian. 
Italian. Broughton. Templeton. 

Silica 40.30% 40:57% 40.52% 

Magnesia 43.37 41.50 42.05 

Ferrous oxide 87 2.81 1.97 

Alumina 2.27 .90 2.10 

Water 13.72 13.55 13.46 

100.53 99.33 100.10 

Chemical analysis throws light upon an important point in connection 
with asbestos, i.e., the cause of the harshness of the fibre of some varieties. 
Asbestos is principally a hydrous silicate of magnesia, i.e., silicate of mag- 
nesia combined with water. When harsh fibre is analyzed it is found to 
contain less water than the soft fibre. In fibre of very fine quality from 
Black Lake analysis showed 14.38% of water, while a harsh-fibred sample 
gave only 11.70%. If soft fibre be heated to a temperature that will drive 
off a portion of the combined water, there results a substance so brittle 
that it may be crumbled between thumb and finger. There is evidently 
some connection between the consistency of the fibre and the amount of 
water in its composition. 



258 STRENGTH OF MATERIALS. 



STRENGTH OF MATERIALS. 

Stress and Strain. — There is much confusion among writers on 
strength of materials as to the definition of these terms. An external 
force applied to a body, so as to pull it apart, is resisted by an internal 
force, or resistance, and the action of these forces causes a displacement 
of the molecules, or deformation. By some writers the external force is 
called a stress, and the internal force a strain; others call the external 
force a strain, and the internal force a stress; this confusion of terms is 
not of importance, as the words stress and strain are quite commonly 
used synonymously, but the use of the word strain to mean molecular 
displacement, deformation, or distortion, as is the custom of some, is a 
corruption of the language. See Engineering News, June 23, 1892. 
Some authors in order to avoid confusion never use the word strain in 
their writings. Definitions by leading authorities are given below. 

Stress. — A stress is a force which acts in the interior of a body, and 
resists the external forces which tend to change its shape. A deformation 
is the amount of change of shape of a body caused by the stress. The 
word strain is often used as synonymous with stress, and sometimes it is 
also used to designate the deformation. (Merriman.) 

The force by which the molecules of a body resist a strain at any point 
is called the stress at that point.. 

The summation of the displacements of the molecules of a body for a 
given point is called the distortion or strain at the point considered. 
(Burr.) 

Stresses are the forces which are applied to bodies to bring into action 
their elastic and cohesive properties. These forces cause alterations of 
the forms of the bodies upon which they act. Strain is a name given to 
the kind of alteration produced by the stresses. The distinction between 
stress and strain is not always observed, one being used for the other. 
(Wood.) 

The use of the word stress as synonymous with "stress per square inch," 
or with "strength per square inch," should be condemned as lacking in 
precision. 

Stresses are of different kinds, viz.: tensile, compressive, transverse, tor- 
sional, and shearing stresses. 

A tensile stress, or pull, is a force tending to elongate a piece. A com- 
pressive stress, or push, is a force tending to shorten it. A transverse stress 
tends to bend it. A torsional stress tends to twist it. A shearing stress 
tends to force one part of it to slide over the adjacent part. 

Tensile, compressive, and shearing stresses are called simple stresses. 
Transverse stress is compounded of tensile and compressive stresses, and 
torsional of tensile and shearing stresses. 

To these five varieties of stresses might be added tearing stress, which is 
either tensile or shearing, but in which the resistance of different portions 
of the material are brought into play in detail, or one after the other, 
instead of simultaneously, as in the simple stresses. 

Effects of Stresses. — The following general laws for cases of simple 
tension or compression have been established by experiment (Merriman) : 

1. When a small stress is applied to a body, a small deformation is pro- 
duced, and on the removal of the stress the body springs back to its original 
form. For small stresses, then, materials may be regarded as perfectly 
elastic. 

2. Under small stresses the deformations are approximately proportional 
to the forces or stresses which produce them, and also approximately pro- 
portional to the length of the bar or body. 

3. When the stress is great enough a deformation is produced which is 
partly permanent, that is, the body does not spring back entirely to its 
original form on removal of the stress. This permanent part is termed a 
set. In such cases the deformations are not proportional to the stress. 

4. When the stress is greater still the deformation rapidly increases and 
the body finally ruptures. 

5. A sudden stress, or shock, is more injurious than a steady stress or 
than a stress gradually applied. 



ELASTIC LIMIT AND YIELD POINT. 259 

Elastic Limit. — The elastic limit is defined as that load at which 
the deformations cease to be proportional to the stresses, or at which 
the rate of stretch (or other deformation) begins to increase. It is also 
defined as the load at which a permanent set first becomes visible. The 
last definition is not considered as good as the first, as it is found that with 
some materials a set occurs with any load, no matter how small, and that 
with others a set which might be called permanent vanishes with lapse of 
time, and as it is impossible to get the point of first set without removing 
the whole load after each increase of load, which is frequently inconven- 
ient. The elastic limit, defined, however, as that stress at which the 
extensions begin to increase at a higher rate than the applied stresses, 
usually corresponds very nearly with the point of first measurable per- 
manent set. 

Apparent Elastic Limit. — Prof. J. B. Johnson (Materials of Con- 
struction, p. 19) defines the " apparent elastic limit " as " the point on the 
•stress diagram [a plotted diagram in which the ordinates represent loads 
and the abscissas the corresponding elongations] at which the rate of 
deformation is 50% greater than it is at the origin," [the minimum rate]. 
An equivalent definition, proposed by the author, is that point at which 
the modulus of extension (length X increment of load per unit of section 
■*- increment of elongation) is two thirds of the maximum. Fcr steel, 
with a modulus of elasticity of 30,000,000, this is equivalent to that 
point at which the increase of elongation in an 8-inch specimen for 1000 
lbs. per sq. in. increase of load is 0.0004 in. 

Yield-point. — The term yield-point has recently been introduced into 
the literature of the strength of materials. It is defined as that point at 
which the rate of stretch suddenly increases rapidly with no increase of 
the load. The difference between the elastic limit, strictly defined as 
the point at which the rate of stretch begins to increase, and the yield- 
point, may in some cases be considerable. This difference, however, will 
not be discovered in short test-pieces unless the readings of elongations 
are made by an exceedingly fine instrument, as a micrometer reading to 
0.0001 inch. In using a coarser instrument, such as calipers reading to 
1/100 of an inch, the elastic limit and the yield-point will appear to be 
simultaneous. Unfortunately for precision of language, the term yield- 
point was not introduced until long after the term elastic limit had been 
almost universally adopted to signify the same physical fact which is now 
defined by the term yield-point, that is, not the point at which the first 
change in rate, observable only by a microscope, occurs, but that later 
point (more or less indefinite as to its precise position) at which the 
increase is great enough to be seen by the naked eye. A most convenient 
method of determining the point at which a sudden increase of rate of 
stretch occurs in short specimens, when a testing-machine in which the 
pulling is done by screws is used, is to note the weight on the beam at 
the instant that the beam "drops." During the earlier portion of the 
test, as the extension is steadily increased by the uniform but slow rota- 
tion of the screws, the poise is moved steadily along the beam to keep it 
in equipoise; suddenly a point is reached at which the beam drops, and 
will not rise until the elongation has been considerably increased by the 
further rotation of the screws, the advancing of the poise meanwhile 
being suspended. This point corresponds practically to the point at which 
the rate of elongation suddenly increases, and to the point at which 
an appreciable permanent set is first found. It is also the point 
which has hitherto been called in practice and in text-books the elastic 
limit, and it will probably continue to be so called, although the use of 
the newer term " yield-point " for it, and the restriction of the term elastic 
limit to mean the earlier point at which the rate of stretch begins to 
increase, as determinable only by micrometric measurements, is more 
precise and scientific. In order to obtain the yield-point by the drop of 
the beam with approximate accuracy, the screws of the testing machine 
must be run very slowly as the yield-point is approached, so as to cause 
an elongation of not more than, say, 0.005 in. per minute. 

In tables of strength of materials hereafter given, the term elastic limit 
is used in its customary meaning, the point at which the rate of stress has 
begun to increase as observable by ordinary instruments or by the drop of 
the beam. With this definition it is practically synonymous with yield- 
point. 



260 STRENGTH OF MATERIALS. 

Coefficient (or Modulus) of Elasticity. — This is a term express- 
ing the relation between the amount of extension or compression of a mate- 
rial and the load producing that extension or compression. 

It is defined as the load per unit of section divided by the extension per 
unit of length. 

Let P be the applied load, k the sectional area of the piece, I the length 
of the part extended, A the amount of the extension, and E the coefficient 
of elasticity. Then P -*- k = the load on a unit of section; A -*- I = the 
elongation of a unit of length. 

7? = Z u. * = U. 

k ' I k\ 

The coefficient of elasticity is sometimes defined as the figure express- 
ing the load which would be necessary to elongate a piece of one square' 
inch section to double its original length, provided the piece would not 
break, and the ratio of extension to the force producing it remained con- 
stant. This definition follows from the formula above given, thus: 
If k = one square inch, I and A each = one inch, then E = P. 

Within the elastic limit, when the deformations are proportional to the 
stresses, the coefficient of elasticity is constant, but beyond the elastic 
limit it decreases rapidly. 

In cast iron there is generally no apparent limit of elasticity, the defor- 
mations increasing at a faster rate than the stresses, and a permanent 
set being produced by small loads. The coefficient of elasticity therefore 
is not constant during any portion of a test, but grows smaller as the load 
increases. The same is true in the case of timber. In wrought iron and 
steel, however, there is a well-defined elastic limit, and the coefficient of 
elasticity within that limit is nearly constant. 

Resilience, or Work of Resistance of a Material. — Within the 
elastic limit, the resistance increasing uniformly from zero stress to the 
stress at the elastic limit, the work done by a load applied gradually is 
equal to one half the product of the final stress by the extension or other 
deformation. Beyond the elastic limit, the extensions increasing more 
rapidly than the loads, and the strain diagram (a plotted diagram showing 
the relation of extensions to stresses) approximating a parabolic form, the 
work is approximately equal to two thirds the product of the maximum 
stress by the extension. 

The amount of work required to break a bar, measured usually in inch- 
pounds, is called its resilience; the work required to strain it to the elastic 
limit is called its elastic resilience. (See below.) 

Under a load applied suddenly the momentary elastic distortion is 
equal to twice that caused by the same load applied gradually. 

When a solid material is exposed to-percussive stress, as when a weight 
falls upon a beam transversely, the work of resistance is measured by the 
product of the weight into the total fall. 

Elastic Resilience. — In a rectangular beam tested by transverse 
stress, supported at the ends and loaded in the middle, 



3 I 

in which, if P is the load in pounds at the elastic limit, R = the modulus of 
transverse strength, or the stress on the extreme fibre, at the elastic limit, 
E = modulus of elasticity, A = deflection, I, b, and d = length, breadth, 
and depth in inches. Substituting for P in (2) its value in (1), A= 1/6 Rl 2 
+ Ed. 

The elastic resilience = half the product of the load and deflection = 
1/2 P A, and the elastic resilience per cubic inch = 1/2 PA -r- Ibd. 

Substituting the values of P and a, this reduces to elastic resilience per 
1 R 2 
cubic inch= rr. tt > which is independent of the dimensions; and therefore 

18 hi 
the elastic resilience per cubic inch for transverse strain may be used as a 
modulus expressing one valuable quality of a material. 



ELEVATION OP THE ELASTIC LIMIT. 261 

Similarly for tension: Let P = tensile stress in pounds per square inch 
at the elastic limit; e = elongation per unit of length at the elastic limit: 
E = modulus of elasticity = P -*■ e; whence e = P + E. 

1 P 2 

Then elastic resilience per cubic inch = 1/2 Pe = ^ jjr 

Elevation of Ultimate Resistance and Elastic Limit. — It was 

first observed by Prof. R. H. Thurston, and Commander L. A. Beardslee, 
U. S. N., independently, in 1873, that if wrought iron be subjected to a 
stress beyond its elastic limit, but not beyond its ultimate resistance, and 
then allowed to "rest" for a definite interval of time, a considerable 
increase of elastic limit and ultimate resistance may be experienced. In 
other words, the application of stress and subsequent "rest" increases 
the resistance of wrought iron. This "rest" may be an entire release 
from stress or a simple holding the test-piece at a given intensity of 
stress. 

Commander Beardslee prepared twelve specimens and subjected them 
to a stress equal to the ultimate resistance of the materia], without 
breaking the specimens. These were then allowed to rest, entirely free 
from stress, from 24 to 30 hours, after which they were again stressed 
until broken. The gain in ultimate resistance by the rest was found to 
vary from 4.4 to 17 per cent. 

This elevation of elastic and ultimate resistance appears to be peculiar 
to iron and steel; it has not been found in other metals. 

Relation of the Elastic Limit to Endurance under Repeated 
Stresses (condensed from Engineering, August 7, 1891). — When engi- 
neers first began to test materials, it was soon recognized that if a speci- 
men was loaded beyond a certain point it did not recover its original 
dimensions on removing the load, but took a permanent set; this point 
was called the elastic limit. Since below this point a bar appeared to 
recover completely its original form and dimensions on removing the 
load, it appeared obvious that it had not been injured by the load, and 
hence the working load might be deduced from the elastic limit by using 
a small factor of safety. 

Experience showed, however, that in many cases a bar would not carry 
safely a stress anywhere near the elastic limit of the material as deter- 
mined by these experiments, and the whole theory of. any connection 
between the elastic limit of a bar and its working load became almost 
discredited, and engineers employed the ultimate strength only in deduc- 
ing the safe working load to which their structures might be subjected. 
Still, as experience accumulated it was observed that a higher factor of 
safety was required for a live load than for a dead one. 

In 1871 Wohler published the results of a number of experiments on 
bars of iron and steel subjected to live loads. In these experiments the 
stresses were put on and removed from the specimens without impact, 
but it was, nevertheless, found that the breaking stress of the materials 
was in every case much below the statical breaking load. Thus, a bar 
of Krupp's axle steel having a tenacity of 49 tons per square inch broke 
with a stress of 28.6 tons per square inch, when the load was completely 
removed and replaced without impact 170,000 times. These experiments 
were made on a large number of different brands of iron and steel, and 
the results were concordant in showing that a bar would break with an 
alternating stress of only, say, one third the statical breaking strength of 
the material, if the repetitions of stress were sufficiently numerous. At 
the same time, however, it appeared from the general trend of the experi- 
ments that a bar would stand an indefinite number of alternations of 
stress, provided the stress was kept below the limit. 

Prof. Bauschinger defines the elastic limit as the point at which stress 
ceases to be sensibly proportional to extension, the latter being measured 
with a mirror apparatus reading to 1/5000 of a millimetre, or about 
1/100000 in. This limit is always below the yield-point, and may on 
occasion be zero. On loading a bar above the yield-point, this point 
rises with the stress, and the rise continues for weeks, months, and 

Eossibly for years if the bar is left at rest under its load. On the other 
and, when a bar is loaded beyond its true elastic limit, but below its 
yield-point, this limit rises, but reaches a maximum as the yield-point is 
approached, and then falls rapidly, reaching even to zero. On leaving 
the bar at rest under a stress exceeding that of its primitive breaking- 



262 STRENGTH OF MATERIALS. 

down point the elastic limit begins to rise again, and may, if left a suffi- 
cient time, rise to a point much exceeding its previous value. 

A bar has two limits of elasticity, one for tension and one for com- 
pression. Bauschinger loaded a number of bars in tension until stress 
ceased to be sensibly proportional to deformation. The load was then 
removed and the bar tested in compression until the elastic limit in this 
direction had been exceeded. This process raises the elastic limit in 
compression, as would be found on testing the bar in compression a second 
time. In place of this, however, it was now again tested in tension, when 
it was found that the artificial raising of the limit in compression had 
lowered that in tension below its previous value. By repeating the 
process of alternately testing in tension and compression, the two limits 
took up points at equal distances from the line of no load, both in tension 
and compression. These limits Bauschinger calls natural elastic limits 
of the bar, which for wrought iron correspond to a stress of about 8V2 tons 
per square inch, but this is practically the limiting load to which a bar 
of the same material can be strained alternately in tension and com- 
pression, without breaking when the loading is repeated sufficiently often, 
as determined by Wohler's method. 

As received from the rolls the elastic limit of the bar in tension is above 
the natural elastic limit of the bar as defined by Bauschinger, having been 
artificially raised by the deformations to which it has been subjected in 
the process of manufacture. Hence, when subjected to alternating 
stresses, the limit in tension is immediately lowered, while that in com- 
pression is raised until they both correspond to equal loads. Hence, in 
Wohler's experiments, in which the bars broke at loads nominally below 
the elastic limits of the material, there is every reason for concluding that 
the loads were really greater than true elastic limits of the material. 
This is confirmed by tests on the connecting-rods of engines, which work 
under alternating stresses of equal intensity. Careful experiments on 
old rods show that the elastic limit in compression is the same as that in 
tension, and that both are far below the tension elastic limit of the 
material as received from the rolls. 

The common opinion that straining a metal beyond its elastic limit 
injures it appears to be untrue. It is not the mere straining of a metal 
beyond one elastic limit that injures it, but the straining, many times 
repeated, beyond its two elastic limits. Sir Benjamin Baker has shown 
that in bending a shell plate for a boiler the metal is of necessity strained 
beyond its elastic limit, so that stresses of as much as 7 tons to 15 tons 
per square inch may obtain in it as it comes from the rolls, and unless the 
plate is annealed, these stresses will still exist after it has been built into 
the boiler. In such a case, however, when exposed to the additional 
stress due to the pressure inside the boiler, the overstrained portions of 
the plate will relieve themselves by stretching and taking a permanent 
set, so that probably after a year's working very little difference could be 
detected in the stresses in a plate built into the boiler as it came from the 
bending rolls, and in one which had been annealed, before riveting into 
place, and the first, in spite of its having been strained beyond its elastic 
limits, and not subsequently annealed, would be as strong as the other. 



Resistance of Metals to Repeated Shocks. 

More than twelve years were spent by Wohler at the instance of the 
Prussian Government in experimenting upon the resistance of iron and 
steel to repeated stresses. The results of his experiments are expressed 
in what is known as Wohler's law, which is given in the following words 
in Dubois's translation of Weyrauch: 

" Rupture may be caused not only by a steady load which exceeds the 
carrying strength, but also by repeated applications of stresses, none of 
which are equal to the carrying strength. The differences of these stresses 
are measures of the disturbance of continuity, in so far as by their increase 
the minimum stress which is still necessary for rupture diminishes." 

A practical illustration of the meaning of the first portion of this law 
may be given thus: If 50,000 pounds once applied will just break a bar 
of iron or steel, a stress very much less than 50,000 pounds will break it 
if repeated sufficiently often. 



STRESSES DUE TO SUDDEN FORCES AND SHOCKS. 263 

This is fully confirmed by the experiments of Fairbairn and Spangenberg, 
as well as those of Wohler; and, as is remarked by Weyrauch, it may be 
considered as a long-known result of common experience. It partially 
accounts for what Mr. Holley has called the "intrinsically ridiculous 
factor of safety of six." 

Another "long-known result of experience" is the fact that rupture may 
be caused by a succession of shocks or impacts, none of which alone would 
be sufficient to cause it. Iron axles, the piston-rods of steam hammers, 
and other pieces of metal subject to continuously repeated shocks, 
invariably break after a certain length of service. They have a "life" 
which is limited. 

Several years ago Fairbairn wrote: " We know that in some cases 
wrought iron subjected to continuous vibration assumes a crystalline 
structure, and that the cohesive powers are much deteriorated, but we 
are ignorant of the causes of this change." We are still ignorant, not 
only of the causes of this change, but of the conditions under which it 
takes place. Who knows whether wrought iron subjected to very slight 
continuous vibration will endure forever? or whether to insure final 
rupture each of the continuous small shocks must amount at least to a 
certain percentage of single heavy shock (both measured in foot-pounds), 
which would cause rupture with one application? Wohler found in test- 
ing iron by repeated stresses (not impacts) that in one case 400,000 
applications of a stress of 500 centners to the square inch caused rupture, 
while a similar bar remained sound after 48,000,000 applications of a 
stress of 300 centners to the square inch (1 centner = 110.2 lbs.). 

Who knows whether or not a similar law holds true in regard to repeated 
shocks? Suppose that a bar of iron would break under a single impact of 
1000 foot-pounds, how many times would it be likely to bear the repetition 
of 100 foot-pounds, or would it be safe to allow it to remain for fifty years 
subjected to a continual succession of blows of even 10 foot-pounds each? 

Mr. William Metcalf published in the Metallurgical Review, Dec, 1877, 
the results of some tests of the life of steel of different percentages of 
carbon under impact. Some small steel pitmans were made, the specifi- 
cations for which required that the unloaded machine should run 41/2 
hours at the rate of 1200 revolutions per minute before breaking. 

The steel was all of uniform quality, except as to carbon. Here are the 
results. The 

0.30 C. ran 1 h. 21 m. Heated and bent before breaking. 

0.49 C. " 1 h. 28 m. 

0.53 C. " 4 h. 57 m. Broke without heating. 

0.65 C. " 3 h. 50 m. Broke at weld where imperfect. 

0.80 C. " 5 h. 40 m. 

0.84 C. " 18 h. 

0.87 C. Broke in weld near the end. 

0.96 C. Ran 4.55 m., and the machine broke down. 

Some other experiments by Mr. Metcalf confirmed his conclusion, viz. 
that high-carbon steel was better adapted to resist repeated shocks and 
vibrations than low-carbon steel. 

These results, however, would scarcely be sufficient to induce any 
engineer to use 0.84 carbon steel in a car-axle or a bridge-rod. Further 
experiments are needed to confirm or overthrow them. 

(See description of proposed apparatus for such an investigation in the 
author's paper in Trans. A. I. M. E., vol. viii, p. 76, from which the above 
extract is taken.) 

Stresses Produced by Suddenly Applied Forces and Shocks. 

(Mansfield Merriman, R. R. & Eng. Jour., Dec, 1889.) 

Let P be the weight which is dropped from a height h upon the end of a 
bar, and let y be the maximum elongation which is produced. The work 
performed by the falling weight, then, is W = P(h + y), and this must 
equal the internal work of the resisting molecular stresses. The stress in 
the bar, which is at first 0, increases up to a certain limit Q, which is 
greater than P; and if the elastic limit be not exceeded the elongation 
increases uniformly with the stress, so that the internal work is equal to 



264 STRENGTH OF MATERIALS, 

the mean stress 1/2 Q multiplied by the total elongation y, or TF=i/2 QV- 
Whence, neglecting the work that may be dissipated in heat, 

V2 Qy = Ph + Py. 
If e be the elongation due to the static l oad P, within the elastic limit 
y = -pe; whence Q = P (l + y 1 + 2 -Y which gives the momentary 
maximu m stres s. Substituting this value of Q, there results y = e 
(l + y 1 + 2 -J, which is the value of the momentary maximum elon- 
gation. 

A shock results when the force P, before its action on the bar, is moving 
with velocity, as is the case when a weight P falls from a height h. The 
above formulas show that this height h may be small if e is a small quan- 
tity, and yet very great stresses and deformations be produced. For 
instance, let h = 4e, then Q = 4P and y = 4e; also let h — 12e, then 
Q = 6P and y = 6e. Or take a wrought-iron bar 1 in. square and 5 ft. 
long: under a steady load of 5000 lbs. this will be compressed about 0.012 
in., supposing that no lateral flexure occurs; but if a weight of 5000 lbs. 
drops upon its end from the small height of 0.048 in. there will be produced 
the stress of 20,000 lbs. 

A suddenly applied force is one which acts with the uniform intensity P 
upon the end of the bar, but which has no velocity before acting upon it. 
This corresponds to the case of h = in the above formulas, and gives 
Q = 2P and y = 2e for the maximum stress and maximum deforma- 
tion. - Probably the action of a rapidly moving train upon a bridge 
produces stresses of this character. For a further discussion of this 
subject, in which the inertia of the bar is considered, see Merriman's 
Mechanics of Materials, 10th ed., 1908. 

Increasing the Tensile Strength of Iron Bars by Twisting them. 
— Ernest L. Ransome of San Francisco obtained a patent, in 1888, for 
an "improvement in strengthening and testing wrought metal and steel 
rods or bars, consisting in twisting the same in a cold state. . . . Any 
defect in the lamination of the metal which would otherwise be concealed 
is revealed by twisting, and imperfections are shown at once. The 
treatment may be applied to bolts, suspension-rods or bars subjected to 
tensile strength of any description." 

Jesse J. Shuman (Am. Soc. Test. Mat., 1907) describes several series of 
experiments on the effect of twisting square steel bars. Following are 
some of the results: 
Soft Bessemer steel bars 1/2 in. square. Tens. Strength, plain bar, 60,400 c 

No. of turns per foot 3 43/ 4 5 53/ 4 57/ 8 

Yield point, lbs. per sq. in 65,600 72,400 84,800 84,000 80,800 

Ult. strength " " " " ....83,200 89,600 92,000 90,000 88,800 

Elongation in 8 in., % 10 5.75 6.25 7.5 3.75 

Bessemer, 0.25 carbon, 1/2 in. sq. Tens, strength, plain bar, 75,000. 

No. of turns per foot 3 41/2 47/ 8 5 5 1/2 

Yield point, lbs. per sq. in 83,600 83,200 88,800 84,200 84,200 

Ult. strength " " " " 99,600 99,200 104,000 102,000 100,800 

Elongation in 8 in., % 8 4.5 4 5.75 6 

Bars of each grade twisted off when given more turns than stated. 
Soft Bessemer, square bars, different sizes. 

Size, in. sq 1/4 3 /8 V2 5 /8 3/ 4 7/ 8 1 1 1/ 8 1 1/4 

No. of turns per ft 4 3 1/2 3 21/4 1 1/2 1 V4 1 7 /s 3 /4 

Yield point, increase %* Ill 82 64 83 85.5 77 82 64 ^59 

Ult. strength " %* 37 38.6 41 33.5 34.3 29.7 22.8 20.1 28.9 

Mr. Schuman recommends that in twisting bars for reinforced concrete, 
in order not to be in danger of approaching the breaking point, the num- 
ber of turns should be about half the number at which the steel is at its 
maximum strength, which for Bessemer of about 60,000 lbs. tensile 
strength means one complete twist in 8 to 10 times the size of the bar. 

Steel bars strengthened by twisting are largely used in reinforced 
concrete. . 

* Average of two tests each.] 



TENSILE STRENGTH. 



265 



TENSILE STRENGTH. 

The following data are usually obtained in testing by tension in a testing- 
machine a sample of a material of construction: 

The load and the amount of extension at the elastic limit. 

The maximum load applied before rupture. 

The elongation of the piece, measured between gauge-marks placed a 
stated distance apart before the test; and the reduction of area at the 
point of fracture. 

The load at the elastic limit and the maximum load are recorded in 
pounds per square inch of the original area. The elongation is recorded 
as a percentage of the stated length between the gauge-marks, and the 
reduction of area as a percentage of the original area. The coefficient of 
elasticity is calculated from the ratio the extension within the elastic 
limit per inch of length bears to the load per square inch producing that 
extension. 

On account of the difficulty of making accurate measurements of the 
fractured area of a test-piece, and of the fact that elongation is more 
valuable than reduction of area as a measure of ductility and of resilience 
or work of resistance before rupture, modern experimenters are abandoning 
the custom of reporting reduction of area. The data now calculated 
from the results of a tensile test for commercial purposes are: 1. Tensile 
strength in pounds per square inch of original area. 2. Elongation per 
cent of a stated length between gauge-marks, usually 8 inches. 3. Elastic 
limit in pounds per square inch of original area. 

The short or grooved test specimen gives with most metals, especially 
with wrought iron and steel, an apparent tensile strength much higher 
than the real strength. This form of test-piece is now almost entirely 
abandoned. Pieces 2 in. in length between marks are used for forgings. 

The following results of the tests of six specimens from the same 1/4-in. 
steel bar illustrate the apparent elevation of elastic limit and the changes 
in other properties due to change in length of stems which were turned 
down in each specimen to 0.798 in. diameter. (Jas. E. Howard, Eng. 
Congress 1893, Section G.) 



Description of Stem. 



1.00 in. long 

0.50 in. long 

0.25 in. long 

Semicircular groove, 0.4 

in. radius 

Semicircular groove, 1/8 

in. radius 

V-shaped groove 



Elastic Limit, 
Lbs. per Sq. In. 



64,900 
65,320 
68,000 

75,000 

86,000, about 
90,000, about 



Tensile Strength, 
Lbs. per Sq. In. 


Contraction of 
Area, per cent. 


94,400 
97,800 
102,420 


49.0 
43.4 
39.6 


116,380 


31.6 


134,960 
117,000 


23.0 
Indeterminate. 



Test plates made by the author in 1879 of straight and grooved test- 
pieces of boiler-plate steel cut from the same gave the following results: 

5 straight pieces, 56,605 to 59,012 lbs. T. S. Aver. 57,566 lbs. 

4 grooved " 64,341 to 67,400 " " " 65,452 " 

Excess of the short or grooved specimen, 21 per cent, or 12,114 lbs. 

Measurement of Elongation. — In order to be able to compare 
records of elongation, it is necessary not only to have a uniform length of 
section between gauge-marks (say 8 inches), but to adopt a uniform 
method of measuring the elongation to compensate for the difference 
between the apparent elongation when the piece breaks near one of the 
gauge-marks, and when it breaks midway between them. The following 
method is recommended (Trans. A.S.M. E., vol. xi, p. 622): 



266 STRENGTH OF MATERIALS. 

Mark on the specimen divisions of 1/2 inch each. After fracture measure 
from the point of fracture the length of 8 of the marked spaces on each 
fractured portion (or 7 + on one side and 8 + on the other if the fracture 
is not at one of the marks). The sum of these measurements, less 8 
inches, is the elongation of 8 inches of the original length. If the fracture 
is so near one end of the specimen that 7 + spaces are not left on the 
shorter portion, then take the measurement of as many spaces (with the 
fractional part next to the fracture) as are left, and for the spaces lacking 
add the measurement of as many corresponding spaces of the longer 
portion as are necessary to make the 7 4- spaces. 

• Shapes of Specimens for Tensile Tests. — The shapes shown in 
Fig. 78 were recommended by the author in 1882 when he was connected 
with the Pittsburgh Testing Laboratory. They are now in most general 
use; the earlier forms, with 5 inches or less in length between shoulders, 
being almost entirely abandoned. 

f< 16-'to-20" : 



Y 16- f to-2Q- H 



No. 1. Square or flat bar, as 
rolled. 



No. 2. Round bar, as rolled. 



No. 3. Standard shape for 
flats or squares. Fillets 
1/2 inch radius. 

No. 4. Standard shape for 
rounds. Fillets 1/2 inch 
radius. 

No. 5. Government shape 
formerly used for marine 
boiler-plates of iron. Not 
recommended, as results 
are generally in error. 



Fig. 78. 



Precautions Required in making Tensile Tests. — The testing- 
machine itself should be tested, to determine whether its weighing 
apparatus is accurate, and whether it is so made and adjusted that 
in the test of a properly made specimen the line of strain of the testing- 
machine is absolutely in line with the axis of the specimen. 

The specimen should be so shaped that it will not give an incorrect 
record of strength. 

It should be of uniform minimum section for not less than eight inches 
of its length. Eight inches is the standard length for bars. For forgings 
and castings and in special cases shorter lengths are used; these show 
greater percentages of elongation, and the length between gauge marks 
should therefore always be stated in the record. 

Regard must be had to the time occupied in making tests of certain 
materials. Wrought iron and soft steel can be made to show a higher 
than their actual apparent strength by keeping them under strain for a 
great length of time. 

In testing soft alloys, copper, tin, zinc, and the like, which flow under 
constant strain, their highest apparent strength is obtained by testing 
them rapidly. In recording tests of such materials the length of time 
occupied in the test should be stated. 

For very accurate measurements of elongation, corresponding to incre- 
ments of load during the tests, the electric contact micrometer, described 
in Trans. A. S. M. E., vol. vi. p. 479, will be found convenient. When 
readings of elongation are then taken during the test, a strain diagram 
may be plotted from the reading, which is useful in comparing the quali- 
ties of different specimens. Such strain diagrams are made automatically 
by the new Olsen testing-machine, described in Jour. Frank. Inst. 1891. 

The coefficient of elasticity should be deduced from measurement 



COMPRESSIVE STRENGTH. 267 

observed between fixed increments of load per unit section, say between 
2000 and 12,000 pounds per square inch or between 1000 and 11,000 
pounds instead of between and 10,000 pounds. 



COMPRESSIVE STRENGTH. 

What is meant by the term "compressive strength" has not yet been 
settled by the authorities, and there exists more confusion in regard to 
this term than in regard to any other used by writers on strength of 
materials. The reason of this may be easily explained. The effect of a 
compressive stress upon a material varies with the nature of the material, 
and with the shape and size of the specimen tested. While the effect of a 
tensile stress is to produce rupture or separation of particles in the direc- 
tion of the line of strain, the effect of a compressive stress on a piece of 
material may be either to cause it to fly into splinters, to separate into 
two or more wedge-shaped pieces and fly apart, to bulge, buckle, or bend, 
or to flatten out and utterly resist rupture or separation of particles. A 
piece of speculum metal (copper 2, tin 1) under compressive stress will 
exhibit no change of appearance until rupture takes place, and then it 
will fly to pieces as suddenly as if blown apart by gunpowder. A piece 
of cast iron or of stone will generally split into wedge-shaped fragments. 
A piece of wrought iron will buckle or bend. A piece of wood or zinc 
may bulge, but its action will depend upon its shape and size. A piece 
of lead will flatten out and resist compression till the last degree; that is, 
the more it is compressed the greater becomes its resistance. 

Air and other gaseous bodies are compressible to any extent as long as 
they retain the gaseous condition. Water not confined in a vessel is com- 
pressed by its own weight to the thickness of a mere film, while when 
confined in a vessel it is almost incompressible. 

It is probable, although it has not been determined experimentally, 
that solid bodies when confined are at least as incompressible as water. 
When they are not confined, the effect of a compressive stress is not only 
to shorten them, but also to increase their lateral dimensions or bulge 
them. Lateral stresses are therefore induced by compressive stresses. 

The weight per square inch of original section required to produce any 
given amount or percentage of shortening of any material is not a constant 
quantity, but varies with both the length and the sectional area, with the 
shape of the sectional area, and with the relation of the area to the length. 
The "compressive strength" of a material, if this term be supposed to 
mean the weight in pounds per square inch necessary to cause rupture, 
may vary with every size and shape of specimen experimented upon. 
Still more difficult would it be to state what is the " compressive strength" 
of a material which does not rupture at all, but flattens out. Suppose we 
are testing a cylinder of a soft metal like lead, two inches in length and 
one inch in diameter, a certain weight will shorten it one per cent, another 
weight ten per cent, another fifty per cent, but no weight that we can 
place upon it will rupture it, for it will flatten out to a thin sheet. What, 
then, is its compressive strength? Again, a similar cylinder of soft 
wrought iron would probably compress a few per cent, bulging evenly 
all around; it would then commence to bend, but at first the bend would 
be imperceptilbe to the eye and too small to be measured. Soon this 
bend would be great enough to be noticed, and finally the piece might be 
bent nearly double, or otherwise distorted. What is the "compressive 
strength" of this piece of iron? Is it the weight per square inch which 
compresses the piece one per cent or five per cent, that which causes the 
first bending (impossible to be discovered), or that which causes a per- 
ceptible bend? 

As showing the confusion concerning the definitions of compressive 
strength, the following statements from different authorities on the 
strength of wrought iron are of interest. 

Wood's Resistance of Materials states, "Comparatively few experiments 
have been made to determine how much wrought iron will sustain at the 
point of crushing. Hodgkinson gives 65,000, Rondulet 70,800, Weisbach 
72,000, Rankine 30,000 to 40,000. It is generally assumed that wrought 



268 STRENGTH OF MATERIALS. 

iron will resist about two thirds as much crushing as to tension, but the 
experiments fail to give a very definite ratio." 

The following values, said to be deduced from the experiments of Major 
Wade, Hodgkinson, and Capt. Meigs, are given by Haswell: 



American wrought iron 127,720 1 

" (mean) 85,500 

Fnriteh " " i 65,200 ! 

English { 40,000 



Stoney states that the strength of short pillars of any given material, all 
having the same diameter, does not vary much, provided the length of 
the piece is not less than one and does not exceed four or five diameters, 
and that the weight which will just crush a short prism whose base equals 
one square inch, and whose height is not less than 1 to 11/2 and does not 
exceed 4 or 5 diameters, is called the crushing strength of the material. 
It would be well if experimenters would all agree upon some such definition 
of the term "crushing strength," and insist that all experiments which 
are made for the purpose of testing the relative values of different materials 
in compression be made on specimens of exactly the same shape and size. 
An arbitrary size and shape should be assumed and agreed upon for this 
purpose. The size mentioned by Stoney is definite as regards area of 
section, viz., one square inch, but is indefinite as regards length, viz., 
from one to five diameters. In some metals a specimen five diameters 
long would bend, and give a much lower apparent strength than a speci- 
men having a length of one diameter. The words "will just crush" are 
also indefinite for ductile materials, in which the resistance increases 
without limit if the piece tested does not bend. In such cases the weight 
which causes a certain percentage of compression, as five, ten, or fifty per 
cent, should be assumed as the crushing strength. 

For future experiments on crushing strength three things are desirable: 
First, an arbitrary standard shape and size of test specimen for comparison 
of all materials. Secondly, a standard limit of compression for ductile 
materials, which shall be considered equivalent to fracture in brittle 
materials. Thirdly, an accurate knowledge of the relation of the crushing 
strength of a specimen of standard shape and size to the crushing strength 
of specimens of all other shapes and sizes. The latter can only be secured 
by a very extensive and accurate series of experiments upon all kinds of 
materials, and on specimens of a great number of different shapes and 
sizes. 

The author proposes, as a standard shape and size, for a compressive 
test specimen for all metals, a cylinder one inch in length, and one half 
square inch in sectional area, or 0.798 inch diameter; and for the limit of 
compression equivalent to fracture, ten per cent of the original length. 
The term "compressive strength," or "compressive strength of standard 
specimen," would then mean the weight per square inch required to 
fracture by compressive stress a cylinder one inch long and 0.798 inch 
diameter, or to reduce its length to 0.9 inch if fracture does not take 
place before that reduction in length is reached. If such a standard, or 
any standard size whatever, had been used by the earlier authorities on 
the strength of materials, we never would have had such discrepancies 
in their statements in regard to the compressive strength of wrought 
iron as those given above. 

The reasons why this particular size is recommended are: that the 
sectional area, one-half square inch, is as large as can be taken in the ordi- 
nary testing-machines of 100,000 pounds capacity, to include all the 
ordinary metals of construction, cast and wrought iron, and the softer 
steels; and that the length, one inch, is convenient for calculation of 
percentage of compression. If the length were made two inches, many 
materials would bend in testing, and give incorrect results. Even in cast 
iron Hodgkinson found as the mean of several experiments on various 
grades, tested in specimens 3/ 4 inch in height, a compressive strength per 
square inch of 94,730 pounds, while the mean of the same number of 
specimens of the same irons tested in pieces H/2 inches in height was 



COLUMNS, PILLARS, OR STRUTS. 269 

only 88,800 pounds. The best size and shape of standard specimen 
should, however, be settled upon only after consultation and agreement 
among several authorities. 

The Committee on Standard Tests of the American Society of Mechan- 
ical Engineers say (vol. xi, p. 624): 

"Although compression tests have heretofore been made on diminutive 
sample pieces, it is highly desirable that tests be also made on long pieces 
from 10 to 20 diameters in length, corresponding more nearly with actual 
practice, in order that elastic strain and change of shape may be deter- 
mined by using proper measuring apparatus. 

" The elastic limit, modulus or coefficient of elasticity, maximum and 
ultimate resistances, should be determined, as well as the increase of 
section at various points, viz., at bearing surfaces and at crippling point. 

" The use of long compression-test pieces is recommended, because the 
investigation of short cubes or cylinders has led to no direct application 
of the constants obtained by their use in computation of actual structures, 
which have always been and are now designed according to empirical for- 
mulas obtained from a few tests of long columns." 



COLUMNS, PILLARS, OR STRUTS. 

Notation. — P = crushing weight in pounds; d = exterior diameter 
in inches; a = area in square inches; L = length in feet; I = length in 
inches; S = compressive stress, lbs. per sq. in.; E = modulus of elasticity 
in tension or compression; r = least radius of gyration; $, an experimental 
coefficient. 

For a short column centrally loaded S = P/a, but for a long column 
which tends to bend under load, the stress on the concave side is greater, 
and on the convex side less than P/a. 



Hodgkinson's Formula for Columns. 

Both ends rounded, the Both ends flat, the length 

m„A ,-vf rui,,™™ length of the column of the column exceed- 

ivinaoi column. exceeding 15 times its ing 30 times its diam- 

diameter. eter. 



W3-55 

P = 98,920 j— j 



Solid cylindrical col- 1 

umns of cast iron . . . ) 
Solid cylindrical col- \ 

umns of wrought iron ) 

These formulae apply only in cases in which the length is so great that 
the column breaks by bending and not by simple crushing. Hodgkinson's 
tests were made on small columns, and his results are not now con- 
sidered reliable. 

Euler's Formula for Long Columns. 

P/a = it 2 E (r/l) 2 for columns with round or hinged ends. For columns 
with fixed ends, multiply by 4; with one end round and the other fixed, 
multiply by 21/4; for one end fixed and the other free, as a post set in the 
ground, divide by 4. P is the load which causes a slight deflection: a 
load greater than P will cause an increase of deflection until the column 
fails by bending. The formula is now little used. 

Christie's Tests (Trans. A. S. C. E. 1884; Merriman's Mechanics 
of Materials). — About 300 tests of wrought-iron struts were made, the 
quality of the iron being about as follows: tensile strength per sq. in., 
49,600 lbs., elastic limit 32,000 lbs., elongation 18% in 8 ins. 



270 



STRENGTH OP MATERIALS. 



The following table gives the average results. 



Ratio I It 
Length to 
Least Ra- 
dius of 
Gyration. 


Ultimate Load, P/a, in Pounds per Square Inch. 


Fixed Ends. 


Flat Ends. 


Hinged Ends. 


Round Ends. 


20 
40 
60 
80 
100 
120 
140 
160 
180 
200 
220 
240 
260 
280 
300 
320 
360 
400 


46,000 
40,000 
36,000 
32,000 
30,000 
28,000 
25,500 
23,000 
20,000 
17,500 
15,000 
13,000 
11,000 
10,000 
9,000 
8,000 
6,500 
5,200 


46,000 
40,000 
36,000 
32,000 
29,800 
26,300 
23,500 
20,000 
16,800 
14,500 
12,700 
11,200 
9,800 
8,500 
7,200 
6,000 
4,300 
3,000 


46,000 

40,000 

36,000 

31,500 

28,000 

24,300 

21,000 

16,500 

12,800 

10,800 

8,800 

7,500 

6,500 

5,700 

5,000 

4,500 

3,500 

2,500 


44,000 

36,500 

30,500 

25,000 

20,500 

16,500 

12,800 

9,500 

7,500 

6,000 

5,000 

4,300 

3,800 

3,200 

2,800 

2,500 

1,900 

1,500 



The results of Christie's tests agree with those computed by Euler's 
formula for round-end columns with llr between 150 and 400, but 
differ widely from them in shorter columns, and still more widely in 
columns with fixed ends. 

Rankine's Formula (sometimes called Gordon's), S = — f 1 +<£ (-) ) 

or — = — — , /T/ .„ • Applying Rankine's formula to the results of 

a 1+0 (l/ry 
experiments, wide variations are found in the values of the empirical 
coefficient <£. Merriman gives the following values, which are extensively 
employed in practice. 

Values of 4> for Rankine's Formula. 



Material. 


Both Ends 
Fixed. 


Fixed and 
Round. 


Both Ends 
Round. 




1/3,000 
1 /5,000 
1/36,000 
1 /25.000 


1.78/3,000 
1.78/5,000 
1 .78/36,000 
1.78/25,000 


4/3,000 




4/5,000 


Wrought Iron 

Steel 


4/36,000 
4/25,000 







The value to be taken for 5 is the ultimate compressive strength of the 
material for cases of rupture, and the allowable compressive unit stress 
for cases of design. 

Burr gives the following values as commonly taken for S and <f>. 

For solid wrought-iron columns, S = 36,000 to 40,000, <j> = 1/36,000 to 
1/40,000. 

For solid cast-iron columns, S = 80,000, <b = 1/6,400. 

IP 

For hollow cast-iron columns, P/a = 80,000 -r 1 + ™ -g (d — outside 



diam. in inches;. 



800 c 



COLUMNS, PILLARS, OR STRUTS. 271 

The coefficient of l 2 /d 2 is given by different writers as 1/400, 1/500, 
1/600 and 1/800. (See Strength of Cast-iron Columns, below.) 

Sir Benjamin Baker gives for mild steel, £ = 67,000 lbs., = 1/22,400; 
for strong steel, S = 114,000 lbs., <j> = 1/14,400. Prof. Burr considers 
these only loose approximations. (See Straight-line Formula, below). 

For dry timber, Rankine gives *S = 7200 lbs., 4> = 1/3000. 

The Straight-line Formula. — The results of computations by Euler's 
or Rankine's formulas give a curved line when plotted on a diagram 
with values of l/r as abscissas and value of P la as ordinates. The average 
results of experiments on columns within the limits of l/r commonly 
used in practice, say from 50 to 200, can be represented by a straight line 
about as accurately as by a curve. Formulas derived from such plotted 
lines, of the general form P la = S - C l/r, in which C is an experimental 
coefficient, are in common use, but Merriman says it is advisable that the 
use of this formula should be limited to cases in which the specifications 
require it to be employed, and for rough approximate computations. 
Values of S and C given by T. H. Johnson are as follows: 

F H R F H R 

Wrought Iron: 

S =42,000 lbs., C = 128, 157, 203; limit of l/r = 218, 178, 138 
Structural Steel: 

5=52,500" C = 179, 220, 284; " " " 195,159,123 
Cast Iron: 5=80,000" C = 438, 537, 693; " " " 122, 99, 77 
Oak, flat ends: 

S = 5,400 " C = 28; " " " 128 

F, flat ends; H, hinged ends; R , round ends. 

Merriman says: "The straight-line formula is not suitable for investi- 
gating a column, that is for determining values of 5 due to given loads, 
because S enters the formula in such a manner as to lead to a cubic 
equation when it is the only unknown quantity. It may be used .to find 
the safe load for a given column to withstand a given unit stress, or to 
design a column for a given load and unit stress. When so used, it is 
customary to divide the values of S and C given in the table by an 
assumed factor of safety. For example, Cooper's specifications require 
that the sectional area a for a medium-steel post of a through railroad 
bridge shall be found from P la = 17,000 - 90 l/r lbs. per sq. in., in 
which P is the direct dead-load compression on the post plus twice the 
live-load compression; the values of S and C here used are a little less 
than one-third of those given in the table for round ends." 

Working Formulae for Wrought-iron and Steel Struts of Various 
Forms. — Burr gives the following practical formulas: 

p = Ultimate %^$j^ 
Kind of Strut. lb^ner^'in ] /5 Ultimate, 



Flat-end iron channels and I-beams . . . 40000 - 1 10 - (5) 8000 - 22 - (6) 

r r 

Flat-end mild-steel angles 52000-180- (7) 10400-36- (8) 

Flat-end high-steel angles 76000-290 - (9) 15200-58- (10) 

r r 

Pin-end solid wrought-iron columns . . . 32000 - 80 -] 6400 - 16-1 

* (ID r j\(X2) 

d) 6400 - 55 d) 



ir ' l 

32000- 277 -U 6400-55 



" 




20 " " 
40 " " 
20 " " 


~ 


200 
200 
200 


I 
d 




6 and - 
a 


= 


65 



272 STRENGTH OF MATERIALS. 



Equations (1) to (4) are to be used only between - =40 and - = 

(5) and (6) " " " " 

" (7) to (10) " " " " 

(11) and (12) " " " " 



Built Columns (Burr). — Steel columns, properly made, of steel 
ranging in specimens from 65,000 to 73,000 lbs. per square inch, should 
give a resistance 25 to 33 per cent in excess of that of wrought-iron 
columns with the same value of I -j- r, provided that ratio does not exceed 
140. 

The unsupported width of a plate in a compression member should not 
exceed 30 times its thickness. 

In built columns the transverse distance between centre lines of rivets 
securing plates to angles or channels, etc., should not exceed 35 times the 
plate thickness. If this width is exceeded, longitudinal buckling of the 
plate takes place, and the column ceases to fail as a whole, but yields in 
detail. 

The thickness of the leg of an angle to which latticing is riveted should 
not be less than 1/9 of the length of that leg or side if the column is purely 
a compression member. The above limit may be passed somewhat in stiff 
ties and compression members designed to carry transverse loads. 

The panel points of latticing should not be separated by a greater dis- 
tance than 60 times the thickness of the angle-leg to which the latticing 
is riveted, if the column is wholly a compression member. 

The rivet pitch should never exceed 16 times the thickness of the 
thinnest metal pierced by the rivet, and if the plates are very thick it 
should -never nearly equal that value. 

Burr gives the following general principles which govern the resistance 
of built columns: 

The material should be disposed as far as possible from the neutral axis 
of the cross-section, thereby increasing r; 

There should be no initial internal stress; 

The individual portions of the column should be mutually supporting; 

The individual portions of the column should be so firmly secured to 
each other that no relative motion can take place, in order that the 
column may fail as a whole, thus maintaining the original value of r. 

Stoney says: "When the length of a rectangular wrought-iron tubular 
column does not exceed 30 times its least breadth, it fails by the bulging or 
buckling of a short portion of the plates, not by the flexure of the pillar 
as a whole." 



WORKING STRAINS ALLOWED IN BRIDGE MEMBERS. 

Theodore Cooper gives the following in his Bridge Specifications: 
Compression members shall be so proportioned that the maximum load 
shall in no case cause a greater strain than that determined by the follow- 
ing formula: 

„ 8000 „ a • x, 

for square-end compression members; 



for compression members with one pin and one square 
end; 

for compression members with pin-bearings; 



p = 


1 


+ 


I 2 

40,000 r 2 
8000 


1 


+ 


I 2 


p = 


30,000 r 2 
8000 


1 


+ 


I 2 
20,000 r 2 



WORKING STRAINS ALLOWED IN BRIDGE MEMBERS. 273 

(These values may be increased in bridges over 150 ft. span. See 
Cooper's Specifications.) 

P = the allowed compression per square inch of cross-section; 
I = the length of compression member, in inches; 
r = the least radius of gyration of the section in inches. 

No compression member, however, shall have a length exceeding 25 
times its least width. 

Tension Members, — All parts of the structure shall be so proportioned 
that the maximum loads shall in no case cause a greater tension than the 
following (except in spans exceeding 150 feet): 

Pounds per 
sq. in. 

On lateral bracing 15,000 

On solid rolled beams, used as cross floor-beams and stringers .... 9,000 

On bottom chords and main diagonals (forged eye-bars) 10,000 

On bottom chords and main diagonals (plates or shapes), net section 8,000 

On counter rods and long verticals (forged eye-bars) 8,000 

On counter and long verticals (plates or shapes), net section 6,500 

On bottom flange of riveted cross-girders, net section 8,000 

On bottom flange of riveted longitudinal plate girders over 20 ft. 

long, net section 8,000 

On bottom flange of riveted longitudinal plate girders under 20 ft. 

long, net section 7,000 

On floor-beam hangers, and other similar members liable to sudden 

loading (bar iron with forged ends) 6,000 

On floor-beam hangers, and other similar members liable to sudden 

loading (plates or shapes), net section 5,000 

Members subject to alternate strains of tension and compression shall be 
proportioned to resist each kind of strain. Both of the strains shall, how- 
ever, be considered as increased by an amount equal to 8/ 10 of the least of 
the two strains, for determining the sectional area by the above allowed 
strains. 

The Phoenix Bridge Co. (Standard Specifications, 1895) gives the follow- 
ing: 

The greatest working stresses in pounds per square inch shall be as 
follows : 

Tension. 

Steel. Iron. 

p_ 8 , 5 oo \i + " in - s f ess 1 , P,ates 7 P- 7,000 Tl + "in. ^1 
L Max. stressj shapes net. |_ Max. stressj 

8,500 pounds. Floor-beam hangers, forged ends 7,000 pounds. 

7,500 " Floor-beam hangers, plates or shapes, net 

section 6,000 

10,000 " Lower flanges of rolled beams 8,000 

20,000 " Outside fibres of pins 15,000 

30,000 " Pins for wind-bracing 22,500 

20,000 " Lateral bracing 15,000 

Shearing. 

9,000 pounds. Pins and rivets 7,500 pounds. 

Hand-driven rivets 20% less unit stresses. 
For bracing increase unit stresses 50%. 
6,000 pounds. Webs of plate girders 5,000 pounds. 

Bearing. 

16 000 pounds. Projection semi-intrados pins and rivets, 12,000 pounds. 
Hand-driven rivets 20 % less unit stresses. For 
bracing increase unit stresses 50%. 



274 STRENGTH OF MATERIALS. 



Compression. 

Lengths less than forty times the least radius of gyration, P previously 
found. See Tension. 

Lengths more than forty times the least radius of gyration, P reduced 
by following formulae: 

p 

For both ends fixed, b — ^ 



1 + 
For one end hinged, b = 



36,000 r 2 
P 



For both ends hinged, b -- 



24,000 r 2 
P 



18,000 r 2 



P = permissible stress previously found (see Tension); b = allowable 
working stress per square inch; I = length of member in inches; r = least 
radius of gyration of section in inches. No compression member, how- 
ever, shall have a length exceeding 45 times its least width. 

Pounds per 
sq. in. 

In counter web members 10,500 

In long verticals 10,000 

In all main-web and lower-chord eye-bars 13,200 

In plate hangers (net section) 9,000 

In tension members of lateral and transverse bracing 19,000 

In steel-angle lateral ties (net section) 15,000 

For spans over 200 feet in length the greatest allowed working stresses 
per square inch, in lower-chord and end main-web eye-bars, shall be taken 



10,000 ( 



min. total stress x 
max. total stress/ 



whenever this quantity exceeds 13,200. 

The greatest allowable stress in the main-web eye-bars nearest the centre 
of such spans shall be taken at 13,200 pounds per square inch; and those 
for the intermediate eye-bars shall be found by direct interpolation 
between the preceding values. 

The greatest allowable working stresses in steel plate and lattice girders 
and rolled beams shall be taken as follows: 

Pounds per 
sq. in. 

Upper flange of plate girders (gross section) 10,000 

Lower flange of plate girders (net section) 10,000 

In counters and long verticals of lattice girders (net section) 9,000 
In lower chords and main diagonals of lattice girders (net 

section) 10,000 

In bottom flanges of rolled beams 10,000 

In top flanges of rolled beams 10,000 



THE STRENGTH OF CAST-IRON COLUMNS. 

Hodgkinson's experiments (first published in Phil. Trans. Royal Socy., 
1840, and condensed in Tredgold on Cast Iron, 4th ed., 1846), and Gordon's 
formula, based upon them, are still used (1898) in designing cast-iron col- 
umns. They are entirely inadequate as a basis of a practical formula 
suitable to the present methods of casting columns. 

Hodgkinson's experiments were made on nine "long" pillars, about 71/2 
ft. long, whose external diameters ranged from 1.74 to 2.23 in., and 
average thickness from 0.29 to 0.35 in., the thickness of each column also 
varying, and on 13 "short" pillars, 0.733 ft. to 2.251 ft. long, with exter- 



THE STRENGTH OF CAST-IRON COLUMNS. 



275 



nal diameters from 1.08 to 1.26 in., all of them less than 1/4 in. thick. 
The iron used was Low Moor, Yorkshire, No. 3, said to be a good iron, not 
very hard, earlier experiments on which had given a tensile strength of 
14,535 and a crushing strength of 109,801 lbs. per sq. in. Modern cast- 
iron columns, such as are used in the construction of buildings, are very- 
different in size, proportions, and quality of iron from the slender "long" 
pillars used in Hodgkinson's experiments. There is usually no check, by 
actual tests or by disinterested inspection, upon the quality of the material. 
The tensile, compressive, and transverse strength of cast iron varies 
through a great range (the tensile strength ranging from less than 10,000 
to over 40,000 lbs. per sq. in.), with variations in the chemical composition 
of the iron, according to laws which are as yet very imperfectly under- 
stood, and with variations in the method of melting and of casting. 
There is also a wide variation in the strength of iron of the same melt 
when cast into bars of different thicknesses. 

Another difficulty in obtaining a practical formula for the strength of 
cast-iron columns is due to the uncertainty of the quality of the casting, 
and the danger of hidden defects, such as internal stresses due to unequal 
cooling, cinder or dirt, blow-holes, "cold-shuts," and cracks on the inner 
surface, which cannot be discovered by external inspection. Variation 
in thickness, due to rising of the core during casting, is also a common 
defect. 

In addition to these objections to the use of Gordon's formula, for cast- 
iron columns, we have the data of experiments on full-sized columns, 
made by the Building Department of New York City (Eng'g News, Jan. 13 
and 20, 1898). Ten columns in all were tested, six 15-inch, 190 1/4 inches 
long, two 8-inch, 160 inches long, and two 6-inch, 120 inches long. The 
tests were made on the large hydraulic machine of the Phoenix Bridge Co., 
of 2,000,000 pounds capacity, which was calibrated for frictional error by 
the repeated testing within the elastic limit of a large Phoenix column, 
and the comparison of these tests with others made on the government 
machine at the Watertown Arsenal. The average frictional error was 
calculated to be 15.4 per cent, but Engineering News, revising the data, 
makes it 17.1 per cent, with a variation of 3 per cent either way from the 
average with different loads. The results of the tests of the columns are 
given below. 

TESTS OF CAST-IRON COLUMNS. 









Thickness. 


Breaking 


Load. 


Num- 
ber. 


Diam. 
Inches. 


























Max. 


Min. 


Average. 


Pounds. 


Pounds 
per Sq. In. 


1 


15 


1 




1 


1,356,000 


30,830 


2 


15 


15/16 




11/8 


1,330,000 


27,700 


3 


15 


H/4 




11/8 


1,198,000 


24,900 


4 


151/8 


17/32 




H/8 


1,246,000 


25,200 


5 


15 


1 H/16 




1 H/64 


1,632,000 


32,100 


6 


15 


11/4 


11/8 


13/16 


2,082,000 + 


40,400 + 


7 


73/ 4 to8l/ 4 


H/4 


5/8 


1 


651,000 


31,900 


8 


8 


13/32 




13/64 


612,800 


26,800 


9 


61/16 


15/32 


11/8 


19/64 


400,000 


22,700 


10 


63/32 


H/8 


H/16 


17/64 


455,200 


26,300 



Column No. 6 was not broken at the highest load of the testing 
machine. 

Columns Nos. 3 and 4 were taken from the Ireland Building, which 
collapsed on August 8, 1895; the other four 15-inch columns were made 
from drawings prepared by the Building Department, as nearly as possible 
duplicates of Nos. 3 and 4. Nos. 1 and 2 were made by a foundry in New 
York with no knowledge of their ultimate use. Nos. 5 and 6 were made 



276 



STRENGTH OP MATERIALS. 



by a foundry in Brooklyn with the knowledge that they were to be tested. 
Nos. 7 to 10 were made from drawings furnished by the Department. 
Applying Gordon's formula, as used by- the Building Department, 

s = ~ i - !!"* to tnese columns gives for the breaking strength per square 



inch of the 15-inch columns 57,143 pounds, for the 8-inch columns 40,000 
pounds, and for the 6-inch columns 40,000. The strength of columns Nos. 
3 and 4 as calculated is 128 per cent more than their actual strength; their 
actual strength is less than 44 per cent of their calculated strength; and 
the factor of safety, supposed to be 5 in the Building Law, is only 2.2 for 
central loading, no account being taken of the likelihood of eccentric 
loading. 

Prof. Lanza, Applied Mechanics, p. 372, quotes the records of 14 
tests of cast-iron mill columns, made on the Watertown testing-machine in 
1887-88, the breaking strength per square inch ranging from 25,100 to 
63,310 pounds, and showing no relation between the breaking strength 
per square inch and the dimensions of the columns. Only 3 of the 14 
columns had a strength exceeding 33,500 pounds per square inch. The 
average strength of the other 1 1 was 29,600 pounds per square inch. Prof. 
Lanza says that it is evident that in the case of such columns we cannot 
rely upon a crushing strength of greater than 25,000 or 30,000 pounds 
per square inch of area of section. 

He recommends a factor of safety of 5 or 6 with these figures for crush- 
ing strength, or 5000 pounds per square inch of area of section as the 
highest allowable safe load, and in addition makes the conditions that 
the length of the column shall not be greatly in excess of 20 times the 
diameter, that the thickness of the metal shall be such as to insure a good 
strong casting, and that the sectional area should be increased if necessary 
to insure that the extreme fibre stress due to probable eccentric loading 
shall not be greater than 5000 pounds per square inch. 

Prof. W. H. Burr (Eng'g News, June 30, 1898) gives a formula derived 
from plotting the results of the Watertown and Phoenixville tests, above 
described, which represents the average strength of the columns in pounds 
per square inch. It is p = 30,500 - 160 lid. It is to be noted that this 
is an average value, and that the actual strength of many of the columns 
was much lower. Prof. Burr says: "If cast-iron columns are designed 
with anything like a reasonable and real margin of safety, the amount of 
metal required dissipates any supposed economy over columns of mild 
steel." 

Square Columns. — Square cast-iron columns should be abandoned. 
They are liable to have serious internal strains from difference in con- 
traction on two adjacent sides. John F. Ward, Eng. News, Apr. 16, 1896. 

Safe Load, in Tons of 2000 Lbs., for Round Cast-iron Columns, 
with Turned Capitals and Bases. 

Loads being not eccentric, and length of column not exceeding 20 times 
the diameter. Based on ultimate crushing strength of 25,000 lbs. per 
sq. in. and a factor of safety of 5. 



Thick- 












Diameter, Inches. 










ness, 
Inches. 


6 


7 


8 


9 


10 


11 


13 


13 


14 


15 


16 


18 


5/8 
3/ 4 

Vs 

11/8 


26.4 
30.9 
35.2 
39.2 


31.3 
36.8 
42.1 
47.1 


42.7 
48.9 
55.0 
60.8 


48.6 
55.8 
62.8 
69.6 
76.1 


54.5 
62.7 
70.7 
78.4 
85.9 
93.1 


69.6 

78.5 
87.2 
95.7 
103.9 


76.5 
86.4 
96.1 
105.5 
114.7 
123.7 


94.2 
104.9 
115.3 
125.5 
135.5 


102.1 
113.8 
125.2 
136.3 
147.3 
168.4 


110.0 
122.6 
135.0 
147.1 
159.0 
182.1 
204.2 


131.4 
144.8 
157.9 
170.8 
195.8 
219.9 




11/ 4 






164.4 


1 3 /8 








179.5 


1V2 










194.4 


13/ 4 














223.3 


2 


















251.3 

























THE STRENGTH OF CAST-IRON COLUMNS. 277 

For lengths greater than 20 diameters the allowable loads should be 
decreased. How much they should be decreased is uncertain, since suffi- 
cient data of experiments on full-sized very long columns, from which a 
formula for the strength of such columns might be derived, are as yet 
lacking. There is, however, rarely, if ever, any need of proportioning 
cast-iron columns with a length exceeding 20 diameters. 



Safe Loads in Tons of 2000 Pounds for Cast-iron Columns. 

(By the Building Laws of New York City, Boston, and Chicago, 1897.) 





New York. 
( 8a 


Boston. 
5 a 


Chicago. 
5 a 


Square columns . . . 


I * + 500d 2 
( 8a 


I 2 
1 + 1067d 2 

5a 


1 + 800 d 2 
5a 


Round columns . . . 


■ < I 2 
I 1 + 400¥ 2 


1 +-^- 
800 d 2 


I 2 
1 + 600 d 2 



a = sectional area in square inches; Z= unsupported length of column 
in inches; d = side of square column or thickness of round column in 
inches. 

The safe load of a 15-inch round column 11/2 inches diameter, 16 feet 
long, according to the laws of these cities would be, in New York, 361 tons; 
in Boston, 264 tons; in Chicago, 250 tons. 

The allowable stress per square inch of area of such a column would be, 
in New York, 11,350 pounds; in Boston, 8300 pounds; in Chicago, 7850 
pounds. A safe stress of 5000 pounds per square inch would give for the 
safe load on the column 159 tons. 

Strength of Brackets on Cast-iron Columns. — The columns tested 
by the New York Building Department referred to above had brackets 
cast upon them, each bracket consisting of a rectangular shelf sup- 
ported by one or two triangular ribs. These were tested after the 
columns had been broken in the principal tests. In 17 out of 22 cases the 
brackets broke by tearing a hole in the body of the column, instead of by 
shearing or transverse breaking of the bracket itself. The results were 
surprisingly low and very irregular. Reducing them to strength per 
square inch of the total vertical section through the shelf and rib or ribs, 
they ranged from 2450 to 5600 lbs., averaging 4200 lbs., for a load con- 
centrated at the end of the shelf, and 4100 to 10,900 lbs., averaging 8000 
lbs., for a distributed load. (Eng'g News, Jan. 20, 1898.) 

Maximum Permissible Stresses in columns used in buildings. 
(Building Ordinances of City of Chicago, 1893.) 

For riveted or other forms of wrought-iron columns: 

I = length of column in inches; 
r = least radius of gyration in inches; 
■"■ ' 36000 r 2 a= area °f column in square inches. 

For riveted or other steel columns, if more than 60 r in length: 

s = 17,000 - 521. 

r 

If less than 60 r in length: S = 13,500 a. 
For wooden posts: 

no. a = area of post in square inches; 

d = least side of rectangular post in inches; 



I 2 
1 + o£7Tw2 I = len £tb of P° st in inches, 

Jbua ( 600 for white or Norway pine; 

J 800 for oak; 
900 for long-leaf yellow pine. 



278 STRENGTH OF MATERIALS. 

ECCENTRIC LOADING OF COLUMNS. 

In a given rectangular cross-section, such as a masonry joint under 
pressure, the stress will be distributed uniformly over the section only 
when the resultant passes through the centre of the section; any deviation 
from such a central position will bring a maximum unit pressure to one 
edge and a minimum to the other; when the distance of the resultant 
from one eige is one third of the entire width of the joint, the pressure at 
the nearer edge is twice the mean pressure, while that at the farther edge 
is zero, and that when the resultant approaches still nearer to the edge 
the pressure at the farther edge becomes less than zero; in fact, becomes 
a tension, if the material (mortar, etc.) there is capable of resisting tension. 
Or, if, as usual in masonry joints, the material is practically incapable of 
resisting tension, the pressure at the nearer edge, when the resultant 
approaches it nearer than one third of the width, increases very rapidly 
and dangerously, becoming theoretically infinite when the resultant 
reaches the edge. 

With a given position of the resultant relatively to one edge of the joint 
or section, a similar redistribution of the pressures throughout the section 
may be brought about by simply adding to or diminishing the width of 
the section. 

Let P = the total pressure on any section of a bar of uniform thickness. 
w = the width of that section = area of the section, when thickness = 1 . 
p = P/w = the mean unit pressure on the section. 

M = the maximum unit pressure on the section. 

m = the minimum unit pressure on the section. 

d = the eccentricity of the resultant = its distance from the centre of 
the section. 

Then M = p (l + ^) and m = p (l - ^V 

When d = ~ w then M = 2p and m = O. 
b 

When d is greater than 1 /6 w, the resultant in that case being less than 
one third of the width from one edge, p becomes negative. (J. C. Traut- 
wine, Jr., Engineering News, Nov. 23, 1893.) 

Eccentric Loading of Cast-iron Columns. — Prof. Lanza writes 
the author as follows: The table on page 276 applies when the result- 
ant of the loads upon the column acts along its central axis, i.e., passes 
through the centre of gravity of every section. In buildings and other 
constructions, however, cases frequently occur when the resultant load 
does not pass through the centre of gravity of the section; and then the 
pressure is not evenly distributed over the section, but is greatest on the 
side where the resultant acts. (Examples occur when the loads on 
the floors are not uniformly distributed.) In these cases the outside 
fibre stresses of the column should be computed as follows, viz.: 
Let P = total pressure on the section; 

d = eccentricity of resultant = its distance from the centre of 

gravity of the section; 
A = area of the section, and / its moment of inertia about an axis in 
its plane, passing through its centre of gravity, and perpendic- 
ular to d\ 
c\ = distance of most compressed and ci = that of least compressed 

fibre from above stated axis; 
si = maximum and S2 = minimum pressure ner unit of area. Then 

P , (Pd)ci , P (Pd)c2 

Si = a + -r~ and S2 = i--t— 

Having assumed a certain trial section for the column to be designed, si 
should be computed, and, if it exceed the proper safe value, a different 
section should be used for which si does not exceed this value. 

The proper safe value, in the case of cast-iron columns whose ratio of 
length to diameter does not greatly exceed 20, is 5000 pounds per square 
inch when the eccentricity used in the computation of si is liable to occur 
frequently in the ordinary uses of the structure; but when it is one which 
can only occur in rare cases the value 8000 lbs. per sq. in. may be used. 

A long cap on a column is more conducive to the production of eccen- 
tricity of loading than a short one, hence a long cap is a source of weakness. 



MOMENT OF INERTIA AND RADIUS OF GYRATION. 279 

MOMENT OF INERTIA AND RADIUS OF GYRATION. 

The moment of inertia of: a section is the sum of the products of 
each elementary area of the section into the square of its distance from an 
assumed axis of rotation, as the neutral axis. 

Assume the section to be divided into a great many equal small areas, 
a, and that each such area has its own radius, r, or distance from the 
assumed axis of rotation, then the sum of all the products derived by 
multiplying each a by the square of its r is the moment of inertia, I, or 
7 = 2 ar 2 , in which 2 is the sign of summation. 

For moment of inertia of the weight or mass of a body see Mechanics. 

The radius of gyration of the section equals the square root of the 
quotient of the moment of inertia divided by the area of the section. If 
R = radius of gyration, I = moment of inertia and A = area 

R =^TJa. I/A = R*. 

The center of gyration is the point where the entire area might be 
concentrated and have the same moment of inertia as the actual area. 
The distance of«this center from the axis of rotation is the radius of 



d = diameter, or outside diameter; di = inside diameter; b = breadth; 
h = depth; bi, hi, inside breadth and depth; 

Solid rectangle I = Vnbh 3 ; Hollow rectangle I = i/uibh 3 - bihi 3 ); 
Solid square I = V12& 4 ; Hollow square I =-- 1/12(0* — bi*); 
Solid cylinder I = Ve^d 4 ; Hollow cylinder / = i/ei^Cd 4 — di 4 ). 

Moment of Inertia about any Axis. — If 6 = breadth and h = 
depth of a rectangular section its moment of inertia about its central 
axis (parallel to the breadth) is 1/12 bh 3 ; and about one side is 1/3 bh 3 . If 
a parallel axis exterior to the section is taken, and d = distance of this 
axis from the farthest side and di = its distance from the nearest side, 
[d — di = h), the moment of inertia about this axis is 1/3 b (d 3 — di 3 ). 

The moment of inertia of a compound shape about any axis is equal to 
the sum of the moments of inertia, with reference to the same axis, of all 
the rectangular portions composing it. 

Moment of Inertia of Compound Shapes. (Pencoyd Iron 
Works.) — The moment of inertia of any section about any axis is equal 
to the I about a parallel axis passing through its centre of gravity + (the 
area of the section X the square of the distance between the axes). 

By this rule, the moments of inertia or radii of gyration of any single 
sections being known, corresponding values may be obtained for any 
combination of these sections. 

E. A. Dixon (Am. Mack., Dec. 15, 1898) gives the following formula for 
the moment of inertia of any rectangular element of a built up beam: 
/ = V3 (h 3 — hi 3 )b, I = moment of inertia about any axis parallel to the 
neutral axis, h = distance from the assumed axis to the farthest fiber, 
hi = distance to nearest fiber, b = breadth of element. The sum of the 
moments of inertia of all the elements, taken about the center of gravity 
or neutral axis of the section, is the moment of inertia of the section. 

The polar moment of inertia of a surface is the sum of the products 
obtained by multiplying each elementary area by the square of its dis- 
tance from the center of gravity of the surface; it is equal to the sum of 
the moments of inertia taken with respect to two axes at right angles to 
each other passing through the center of gravity. It is represented by 
/. For a solid shaft J = 1/32 *d 4 ; for a hollow shaft, J = 1/32 Jt(d i - di 4 ), 
in which d is the outside and d the inside diameter. 

The polar radius of gyration, R p = \/J/A, is defined as the radius of 
a circumference along which the entire area might be concentrated and 
have the same poiar moment of inertia as the actual area. 

For a solid circular section R p 2 = i/8D 2 ; for a hollow circular sec- 
tion R p 2 = i/ 8 (cZ 2 + di 2 ). 

Moments of Inertia and Radius of Gyration for Various Sec- 
tions, and their Use in the Formulas for Strength of Girders and 
Columns. — The strength of sections to resist strains, either as 
girders or as columns, depends not only on the area but also on the 
form of the section, and the property of the section which forms the 



280 STRENGTH OP MATERIALS. 

basis of the constants used in the formulas for strength of girders and 
columns to express the effect of the form, is its moment of inertia about 
its neutral axis. The modulus of resistance of any section to transverse 
bending is its moment of inertia divided by the distance from the neutral 
axis to the fibres farthest removed from that axis; or 

Section modulus = Moment of inertia 



Distance of extreme fibre from axis c 

Moment of resistance = section modulus X unit stress on extreme fibre. 

Radius of Gyration of Compound Shapes. — In the case of a 
pair of any shape without a web the value of R can always be found with- 
out considering the moment of inertia. 

The radius of gyration for any section around an axis parallel to another 
axis passing through its centre of gravity is found as follows: 

Let r = radius of gyration around axis through centre of gravity; R -- 
radius of gyration ar ound an other axis parallel to above; d = distance 
between axes: R = ^d 2 + r 2 . , 

When r is small, R may be taken as equal to d without material error. 

Graphical 31ethod for Finding Radius of Gyration. — Benj. F. 
La Rue, Eng. News, Feb. 2, 1893, gives a short graphical method for 
finding the radius of gyration of hollow, cylindrical, and rectangular 
columns, as follows: 

For cylindrical columns: 

Lay off to a scale of 4 (or 40) a right-angled triangle, in which the base 
equals the outer diameter, and the altitude equals the inner diameter 
of the column, or vice versa. The hypothenuse, measured to a scale of 
unity (or 10), will be the radius of gyration sought. 

This depends upon the formula 



G= Viiom. of inertia -*- Area = 1/4 ^D 2 + d 2 
in which A = area and D = diameter of outer circle, a = area an d d = 
diameter of inner circle, and G = radius of gyration. \^D 2 + d 2 is the 
expression for the hypothenuse of a right-angled triangle, in which D and 
d are the base and altitude. 

The sectional area of a hollow round column is 0.7854(Z> 2 — d 2 ). By 
constructing a right-angled triangle in which D e quals the hypothenuse 
and d equals the altitude, the base will equal VD 2 — d 2 . Calling the 
value of this expression for the base B, the area will equal 0.7854J5 2 . 

Value of G for square columns: 

Lay off as before, but using a scale of 10, a right-angled triangle of which 
the base equals D or the side of the outer square, and the altitude equals d , 
the side of the inner square. With a scale of 3 measure the hypothenuse, 
which will be, approximately, the radius of gyration. 

This process for square columns gives an excess of slightly more than 
4%. By deducting 4% from the result, a close approximation will be 
obtained. 

A Very close result is also obtained by measuring the hypothenuse with 
the same scale by which the base and altitude were laid off, and multiplying 
by the decimal 0.29; more exactly, the decimal is 0.28867. 

The formula is 



V- 



Mom. of inertia 1 



= 7y= ^D 2 + d 2 , = 0.28867 V ' D 2 + d 2 ' 



This may also be applied to any rectangular column by using the lesser 
diameters of an unsupported column, and the greater diameters if the 
column is supported in the direction of its least dimensions. 

ELEMENTS OF USUAL SECTIONS. 

Moments refer to horizontal axis through centre of gravity. This table 
is intended for convenient application where extreme accuracy is not 
important. Some of the terms are only approximate; those marked * are 
correct. Values for radius of gyration in flanged beams apply to standard 
minimum sections only. A = area of section; b = breadth; h = depth; 
D = diameter. 



ELEMENTS OF USUAL SECTIONS. 



281 



Shape of Section. 


Moment 
of Inertia. 


Section 
Modulus. 


Square of 

Least 
Radius of 

Cyration. 


Least 
Radius of 
Gyration. 


- 


— - 


4 

"7 


Solid Rect- 
angle. 


bh 3 * 
12 


bh 2 * 
6 


(Least side) 2 * 


Least side * 


12 


3.46 


.-b- 








Hollow Rect- 
angle. 


12 


bht-bjij* 

6/i 


h 2 +h t 2 * 
12 




- 


m 


r 


h+h 1 
4.89 


-*-h 







Solid Circle. 


1/64 nD* 
= 0.0491 D 4 


1/32 *D 3 
= 0.0982 Z) 3 


D 2 * 
16 


D* 
4 


t 5 ^! 


Hollow Circle. 
A, area of 
large section ; 
a, area of 
small section. 


AD 2 -ad 2 
16 


.4D 2 -ad 2 


D 2 +d 2 * 
16 


D+d 


8D 


5.64 


m 


Solid Triangle. 


bh? ■ 
36 


fc/t 2 
24 


The least of 
the two ; 
h 2 b 2 
T8° r 24 


The least 

of the two ; 

h b 

4.24 ° r 4.9 






Even Angle. 


Ah? 
10.2 


7.2 


b 2 
25 










b 
5 








'-6-H 






e 


Uneven Angle. 


Ah 2 
9.5 


.4/i 
6.5 


(hb) 2 


hb 


I3(/i 2 +fe 2 ) 


2.6(h+b) 


-e 


Even Cross. 


.4 ft 2 
19 


.4/i 
9.5 


h 2 
22.5 


h 
4.74 




o 


Even Tee. 


Ah 2 
11.1 


.4/i 
8 


6 2 
22.5 


6 
4.74 








c 


fert 


I Beam. 


Ah 2 
6.66 


Ah 
3.2 


6 2 
21 


b 
4.58 




Channel. 


.4/i 2 
7.34 


J/i 
3.67 


b 2 
12.5 




3 


:i ! v 


6 
3.54 


° 


m 


Deck Beam. 


Ah 2 
6.9 


Ah 
4 


6 2 
36.5 


b 
6 















luneyen angle, — -= ; even tee, 77-5 ; deck beam, — ; all other shapes 
given in the table, - or — • 



282 STRENGTH OF MATERIALS. 



TRANSVERSE STRENGTH. 

In transverse tests the strength of bars of rectangular section is found to 
vary directly as the breadth of the specimen tested, as the square of its 
depth, and inversely as its length. The deflection under any load varies 
as the cube of the length, and inversely as the breadth and as the cube'of 
the depth. Represented algebraically, if S = the strength and D the 
deflection, I the length, b the breadth, and d the depth, 

a . bd 2 ,~. I 3 

S varies as — - and D vanes as t—- 
I ba 3 

For the purpose of reducing the strength of pieces of various sizes to 
a common standard, the term modulus of rupture (represented by R) is 
used. Its value is obtained by experiment on a bar of rectangular section 
supported at the ends and loaded in the middle and substituting numerical 
values in the following formula: 

p 3 PI 
K 2bd*' 

in which P = the breaking load in pounds, I = the length in inches, b the 
breadth, and d the depth. 

The modulus of rupture is sometimes defined as the strain at the instant 
of rupture upon a unit of the section which is most remote from the neu- 
tral axis on the side which first ruptures. This definition, however, is 
based upon a theory which is yet in dispute among authorities, and it is 
better to define it as a numerical value, or experimental constant, found 
by the application of the formula above given. 

From the above formula, making I 12 inches, and b and d each 1 inch, it 
follows that the modulus of rupture is 18 times the load required to break 
a bar one inch square, supported at two points one foot apart, the load 
being applied in the middle. 

_ ~ . . „ . . ,, span in feet X load at middle in lbs. 

Coefficient ot transverse strength = . ^—r—. — : — r — ——5 — -r-. — : — - — - , 

breadth in inches X(depthininches) 2 ' 

* . = — th of the modulus of rupture. 

Fundamental Formulae for Flexure of Beams (Merriman). 

Resisting shear = vertical shear; 

Resisting moment = bending moment; 

Sum of tensile stresses = sum of compressive stresses; 

Resisting shear = algebraic sum of all the vertical components of the 
internal stresses at any section of the beam. 

If A be the area of the section and S $ the shearing unit stress, then 
resisting shear = AS S ; and if the vertical shear = V, then V= ASs. 

The vertical shear is the algebraic sum of all the external vertical forces 
on one side of the section considered. It is equal to the reaction of one 
support, cousidered as a force acting upward, minus the sum of all the 
vertical downward forces acting between the support and the section. 

The resisting moment = algebraic sum of all the moments of the inter- 
nal horizontal stresses at any section with reference to a point in that 

section, = — • in which S = the horizontal unit stress, tensile or com- 

c 
pressive as the case may be, upon the fibre most remote from the neutral 
axis, c = the shortest distance from that fibre to said axis, and / = the 
moment of inertia of the cross-section with reference to that axis. 

The bending moment M is the algebraic sum of the moment of the 
external forces on one side of the section with reference to a point in that 
section = moment of the reaction of one support minus sum of moments 
of loads between the support and the section considered. 



The bending moment is a compound quantity = product of a force by 
the distance of its point of application from the section considered, the 
distance being measured on a line drawn from the section perpendicular 
to the direction of the action of the force 



TRANSVERSE STRENGTH OF BEAMS. 



283 



















"n 


























S. &q 












o 
I" 1 


£i^ 


fe|S £1^ 


l|5 


mloo 


*IS 


aP*Psi 


& l 5 f 








-I0O -j^ 


i 1 * 


+ 

ft. 


Q,|S 


feir 


' Oslo 5 


Mil 




Q 






































o 










-1™ 










"S ^ 




















S3 u. 


















m 














-■I >-S 1 








o " 


«|« 


03|« Q*|« 


3|« 


S|« 


ai|° 


*j|« o-|o ^ 


«|° 


03 

o 


§ tf 




































s 


c 




II II 


ii 


11 


II 




ii 


11 


o3 


1 . 








~o 






ft^ 




ffl 




£ 


fe £ 


s 


"C^ 


ft^ 


£ fe 


"^T^ 


S 




§co 




— Its _ i^r 


_ . 


— |0O 


-|0C 


-l-O lc 


^ IcA 


— |0O 




So 








+ 




1- 


" > 






"3 








ft. 






-CL- 






1 








^riS 






tA |00 






ou 








CO l^ 1 










s 

o3 
0) 

PQ 


o o 


SIS 


s ^ tt; ^ 


LA 1^ 

^ IcA 


— ICO 
+ 


-12 


-i 

-1 


C CO 

- z 

a d 


§ 


00 

d 




03 










-I-* 










3 


















M 


CUD 


-6 


Ik 


nu «u 


HU 


S|~ 


2U 


N l ^1 




^3 | 


o3 


o3 

o 


§1 


Oil 51 


SI 


Oil 


Oil 


ok>S 




oil 


o> 


J 


— i>o 


^_ iff, (N ]rA 


■* ItO 


"^ IcA 


^T I (A 


Oil <vjl 




^IrA 


£ 


be 


II 


II II 


II 


|| 


II 


II 1 




II 




3 


ft. 


&S ^ 


fe 


^ 


ft, 


ft, £ 




f^. 




0) 








+ 












ffl 








eg 


































^ 














>3 
















d 






































iO 


M 


1 =3 








■3 






O 








00 
01 

03 

a 


o 


"3 3 






O 
"ol 


s 






X2 T3* 








s s 

« .2 


"o3 

o3 
O 


XJ o3 

■'g q 


> 

1 




3 
■3 „ 

X3 T3 


03 

o 


1 -c 

ft o- 


"£ «^ 

° c 
a c 

ft o 


a 

- 










O 


"S o3 




X c 


m *" 


_o 




c3 
O 
S3 

o 

fa 


o 


-3 -a 

1 ts 


T3 

03 


3 O 

o3 - 


S3 
0) 

o 

JO 


fa 1 

% 1 

o3 7 


o ^ 


| 
o 






"o3 
T3 


-! o 


o 


O 3 


"ol 
T3 


CQ = 
a? a 


03 « 


3 _ 






S 


a S 


1 


l| 


X 


£ E 


M 1 


I 








03 3 


03 


o3 






.H — 


o3 






fc 




W • 02 


<r 




02 




fa 


cr 


a 


2 fa 




a 


2 



284 



STRENGTH OF MATERIALS. 



Concerning the formula, M = SI/c, p. 282, Prof. Merriman, Eng. News, 
July 21, 1894, says: The formula quoted is true when the unit-stress S on 
the part of the beam farthest from the neutral axis is within the elastic limit 
of the material. It is not true when this limit is exceeded, because then 
the neutral axis does not pass through the center of gravity of the cross- 
section, and because also the different longitudinal stresses are not pro- 
portional to their distances from that axis, these two requirements being 
involved in the deduction of the formula. But in all cases of design the 
permissible unit-stresses should not exceed the elastic limit, and hence 
the formula applies rationally, without regarding the ultimate strength 
of the material or any of the circumstances regarding rupture. Indeed, 
so great reliance is placed upon this formula that the practice of testing 
beams by rupture has been almost entirely abandoned, and the allowable 
unit-stresses are mainly derived from tensile and compressive tests. 



APPROXIMATE GREATEST SAFE LOADS IN LBS. ON STEEL 

BEAMS. (Pencoyd Iron Works.) 

Based on fiber strains of 16,000 lbs. for steel. (For iron the loads should 
be one-eighth less, corresponding to a fibre strain of 14,000 lbs. per square 
inch.) Beams supported at the ends and uniformly loaded. 

L = length in feet between supports; a = interior area in square 
A = sectional area of beam in square inches; 

inches; d = interior depth in inches. 

D = depth of beam in inches. w = working load in net tons. 



Shape of 


Greatest Safe Load in Pounds. 


Deflection in Inches. 


Section. 


Load in 
Middle. 


Load 
Distributed. 


Load in 
Middle. 


Load 
Distributed. 


Solid Rect- 


890 A D 
L 


1780AD 
L 


wL 3 
32AD 2 


wL 3 


angle. 


52AD 2 


Hollow 


890 (A D-ad) 
L 


1780( A D-ad) 
L 


wL 3 


wL 3 


Rectangle. 


32( AD 2 -ad 2 ) 


52(AD 2 -ad 2 ) 


Solid 

Cylinder. 


667AD 
L 


\333AD 
L 


wL 3 
24 AD 2 


wU 
3SAD 2 


Hollow 


667 (A D-ad) 
L 


\333(AD-ad) 
L 


wL 3 


wL 3 


Cylinder. 


24( A D-'-aa 2 ) 


38(AD 2 -ad 2 ) 


Even- 
legged 
Angle or 
Tee. 


885AD 
L 


1770AD 
L 


wL s 
32 AD 2 


wL 3 
52AD 2 


Channel or 
Z bar 


1525AD 
L 


3050 AD 
L 


wL 3 
53AD* 


wL 3 
85AD 2 


Deck 


\380AD 
L 


2760AD 
L 


wL 3 


wL 3 


Beam. 


50 AD 2 


80 AD 2 


I Beam. 


1695 AD 
L 


3390AD 
L 


iv L 3 
58 AD- 


wTJ 
95 A D- 


I 


II 


III 


IV 


V 



The above formula} for the strength and stiffness of rolled beams of 
various sections are intended for convenient application in cases where 
strict accuracy is not required, 



TRANSVERSE STRENGTH OF BEAMS. 



■285 



The rules for rectangular and circular sections are correct, while those 
for the flanged sections are approximate, and limited in their application 
to the standard shapes as given in the Pencoyd tables. When tne section 
of any beam is increased above the standard minimum dimensions, the 
flanges remaining unaltered, and the web alone being thickened, the ten- 
dency will be for the load as found by the rules to be in excess of the 
actual; but within the limits that it is possible to vary any section in the 
rolling, the rules will apply without any serious inaccuracy. 

The calculated safe loads will be approximately one half of loads that 
would injure the elasticity of the materials. 

The rules for d ©flection apply to any load below the elastic limit, or 
less than double the greatest safe load by the rules. 

If the beams are long without lateral support, reduce the loads for the 
ratios of width to span as follows: 

Proportion of Calculated Load 
forming Greatest Safe Load. 



Length of Beam. 




20 times flange width. 


Whole calculated load 


30 " 


9-10 


40 " 


8-10 


50 " 


7-10 


60 " 


6-10 


70 " 


5-10 



These rules apply to beams supported at each end. For beams supported 
otherwise, alter the coefficients of the table as described below, referring 
to the respective columns indicated by number. 



Changes of Coefficients for Special Forms of Beams. 



Kind of Beam. 


Coefficient for Safe 
Load. 


Coefficient for Deflec- 
tion. 


Fixed at one end, loaded 
at the other. 


One fourth of the coeffi- 
cient, col. II. 


One sixteenth of the co- 
efficient of col. IV. 


Fixed at one end, load 
evenly distributed. 


One fourth of the coeffi- 
cient of col. III. 


Five forty-eighths of the 
coefficient of col. V. 


Both ends rigidly fixed, 
or a continuous beam, 
with a load in middle. 


Twice the coefficient of 
col. II. 


Four times the coeffi- 
cient of col. IV. 


Both ends rigidly fixed, 
or a continuous beam, 
with load evenly dis- 
tributed. 


One and one-half times 
the coefficient of col. 
III. 


Five times the coefficient 
of col. V. 



Formulae for Transverse Strength of Beams. — - Referring to table 
in page 283, 

P = load at middle; 
W = total load, distributed uniformly; 
I = length, b = breadth, d = depth, in inches; 

E = modulus of elasticity; 

R = modulus of rupture, or stress per square inch of extreme fiber; 

/ = moment of inertia; 

c = distance between neutral axis and extreme fibre. 
For breaking load of circular section, replace bd 2 by 0.59d 3 . 



286 



STRENGTH OF MATERIALS. 



The value of R at rupture, or the modulus of rupture (see page 268), 
is about 60,000 for structural steel, and about 110,000 for strong steel. 
(Merriman.) 

For cast iron the value of R varies greatly according to quality. Thurs- 
ton found 45,740 and 67,980 in No. 2 and No. 4 cast iron, respectively. 

For beams fixed at both ends and loaded in the middle, Barlow, by 
experiment, found the maximum moment of stress = 1/6 PI instead of 
1/8 PI, the result given by theory. Prof. Wood (Resist. Matls. p. 155) 
says of this case: The phenomena are of too complex a character to admit 
of a thorough and exact analysis, and it is probably safer to accept the 
results of Mr. Barlow in practice than to depend upon theoretical results. 



BEAMS OF UNIFORM STRENGTH THROUGHOUT THEIR 
LENGTH. 

The section is supposed in all cases to be rectangular throughout. The 
beams shown in plan are of uniform depth throughout. Those shown in 
elevation are of uniform breadth throughout. 

B = breadth of beam. D = depth of beam. 






Fixed at one end, loaded at the other2 
curve parabola, vertex at loaded end ; BD 
proportional to distance from loaded end- 
The beam may be reversed, so that the 
upper edge is parabolic, or both edges may 
be parabolic. 

Fixed at one end, loaded at tne other; 
triangle, apex at loaded end ; BD 2 propor- 
tional to the distance from the loaded end. 

Fixed at one end; load distributed; tri- 
angle, apex at unsupported end ; BD 2 pro- 
portional to square of distance from unsup- 
ported end. 

Fixed at one end; load distributed; 
curves two parabolas, vertices touching 
each other at unsupported end; BD 2 
proportional to distance from unsupported 
end. 

Supported at both ends; load at any one 
point; two parabolas, vertices at the 
points of support, bases at point loaded; 
BD 2 proportional to distance from nearest 
point of support. The upper edge or 
both edges may also be parabolic. 

Supported at both ends; load at any one 
point; two triangles, apices at points of 
support, bases at point loaded; BD 2 pro- 
portional to distance from the nearest 
point of support. 

Supported at both ends; load distri- 
buted; curves two parabolas, vertices at 
the middle of the beam; bases centre line 
of beam; BD 2 proportional to product of 
distances from points of support. 

Supported at both ends; load distri- 
buted; curve semi-ellipse; BD 2 propor- 
tional to the product of the distances 
from the points of support. 



PROPERTIES OF ROLLED STRUCTURAL STEEL. 287 



PROPERTIES OF ROLLED STRUCTURAL STEEL. 

Explanation of Tables of the Properties of I-Beams, Channels, 
Angles, Z-Bars, Tees, Trough and Corrugated Plates. 

(The Carnegie Steel Co.) 

The tables for I-beams and channels are calculated for all standard 
weights to which each pattern is rolled. The tables for angles are cal- 
culated for the minimum intermediate and maximum weights of the 
various shapes, while the properties of Z-bars are given for thicknesses 
differing by Vi6 inch. For tees, each shape can be rolled to one weight 
only. 

Columns headed C in the tables for I-beams and channels give coeffi- 
cients by the help of which the safe uniformly distributed load may be 
readily determined. To do this, divide the coefficient given by the span 
or distance between supports in feet. 

If a section is to be selected (as will usually be the case), intended to 
carry a certain load for a length of span already determined on,_ascertain 
the coefficient which this load and span will require, and refer to the table 
for a section having a coefficient of this value. The coefficient is obtained 
by multiplying the load, in pounds uniformly distributed, by the span 
length in feet. 

In case the load is not uniformly distributed, but is concentrated at the 
middle of the span, multiply the load by 2, and then consider it as uni- 
formly distributed. The deflection will be 8/ 10 of the deflection for the 
latter load. 

For other cases of loading obtain the bending moment in foot-pounds; 
this multiplied by 8 will give the coefficient required. 

If the loads are quiescent, the coefficients for a fiber stress of 16,000 

gounds per square inch for steel may be used; but if moving loads are to 
e provided for, a coefficient of 12,500 pounds should be taken. Inas- 
much as the effects of impact may be very considerable (the stresses pro- 
duced in an unyielding inelastic material by a load suddenly applied being 
double those produced by the same load in a quiescent state), it will 
sometimes be advisable to use still smaller fiber stresses than those given 
in the tables. In such cases the coefficients may be determined by 
^ proportion. Thus, for a fiber stress of 8000 pounds per square inch the 
coefficient will equal the coefficient for 16,000 pounds fiber stress, from 
the table, divided by 2. 

The section moduli are used to determine the fiber stress per square 
inch in a beam, or other shape, subjected to bending or transverse stresses, 
by simply dividing the bending moment expressed in inch-pounds by the 
section modulus. 

In the case of T-shapes with the neutral axis parallel to the flange, there 
will be two section moduli, and the smaller is given. The fiber stress cal- 
culated from it will, therefore, give the larger of the two stresses in the 
extreme fibers, since these stresses are equal to the bending moment 
divided by the section modulus of the section. 

For Z-bars the coefficient (C) may be applied for cases where the bars 
are subjected to transverse loading, as in the case of roof-purlins. 

For angles, there will be two section moduli for each position of the 
neutral axis, since the distance between the neutral axis and the extreme 
fibers has a different value on one side of the axis from what it has on the 
other. The section modulus given in the table is the smaller of these two 
values. 

Column headed X, in the table of the properties of standard channels, 
giving the distance of the center of gravity of channel from the outside 
of web, is used to obtain the radius of gyration for columns or struts con- 
sisting of two channels latticed, for the case of the neutral axis passing 
through the center of the cross-section parallel to the webs of the channels, 
This radius of gyration is equal to the distance between the center of 
gravity of the channel and the center of the section, i.e., neglecting the 
moments of inertia of the channels around their own axes, thereby intro- 
ducing a slight error on the side of safety. 

(For much other important information concerning rolled structural 
shapes, see the " Pocket Companion" of The Carnegie Steel Co., Pittsburg, 
Pa., price $2.) 



288 



STRENGTH OF MATERIALS. 



Properties of Carnegie Standard I-Beams — Steel. 















, 


i -+j«*-i 


, 


1 -^42 


— i n 


^o 










• 




ip 


3 a o 

.3.33 


J go 
ill 


0-" IB 






| 
02 


PQ 
"8 

Q 
in. 


o 

o 

En 

tu 

ft 

1 

53 
lbs. 


d 

.2 

o 

<d 
02 


i 

OJ 

M 

a 

'M 
H 


PI 


Moment of Inert 
tral Axis Co 
with Center 
Web. 


«Of) 

<$ H > 


|ll 
f &o 

o oj 

III 

m 


£ o . 

'S j ft 

o 




sq.in. 


in. 


in 


/ 


If 


r 


r' 


S 


c* 


B] 




100 


29.41 


0.75 




2380.3 


48.56 


9.00 


1.28 


198.4 


2115800 






95 


27.94 


0.69 


7.19 


2309.6 


47.10 


9.09 


1.30 


192.5 


2052900 


>• 




90 


26.47 


0.63 


7.13 


2239.1 


45.70 


9.20 


1.31 


186.6 


1 990300 


" 




85 


25.00 


0.57 


7.07 


2168.6 


44.35 


9.31 


1.33 


180.7 


1 927600 


« 




80 


23.32 


0.50 


7.00 


2087.9 


42.86 


9.46 


1.36 


174.0 


1855900 


B2 


20 


100 


29.41 


33 


7.28 


1655.8 


52.65 


7.50 


1.34 


165.6 


1766100 






95 


27.94 


0.81 


721 


1606.8 


50.78 


7.58 


1.35 


160.7 


1713900 






90 


26.47 


0.74 


7.14 


1557.8 


48.98 


7.67 


1.36 


155.8 


1661600 






85 


25.00 


0.66 


7.06 


1508.7 


47.25 


7.77 


1.37 


150.9 


1 609300 






80 


23.73 


0.60 


7.00 


1466.5 


'45.81 


7.86 


1.39 


146.7 


1 564300 


B3 


20 


75 


22.06 


0.65 


6.40 


1268.9 


30.25 


7.58 


1.17 


126.9 


1353500 






70 


20.59 


0.58 


6.33 


1219.9 


29.04 


7.70 


1.19 


122.0 


1301200 






65 


19.0S 


0.50 


6.25 


1169.6 


27.86 


7.83 


1.21 


117.0 


1247600 


B80 


18 


70 


20.59 


0.72 


6.26 


921.3 


24.62 


6.69 


1.09 


102.4 


1091900 






65 


19.12 




6.18 


881.5 


23.47 


6.79 


1.11 


97.9 


1044800 






60 


17.65 


0.56 


6.10 


841.8 


22.38 


6.91 


1.13 


93.5 


997700 






55 


15.93 


0.46 


6.00 


795.6 


21.19 


7.07 


1.15 


88.4 


943000 


B4 


15 


100 


29.41 


1.18 


6.77 


900.5 


50.98 


5.53 


1.31 


120.1 


1280700 






95 


27.94 


1 .09 


6,68 


872.9 


48.37 


5.59 


1.32 


116.4 


1241500 






90 


26.47 


9.99 


6.58 


845.4 


45.91 


5.65 


1.32 


112.7 


1202300 






85 


25.00 




, 18 


817.8 


43.57 


5.72 


1.32 


109.0 


1163000 


" 




80 


23.81 


0.81 


6.40 


795.5 


41.76 


5.78 


1.32 


106.1 


1131300 


J5 


15 


75 


22.05 


0.88 


6.29 


691.2 


30.68 


5.60 


1.18 


92.2 


983000 






70 


20.59 


0.78 


6.19 


663.6 


29.00 


5.68 


1.19 


88.5 


943800 






65 


19.12 


0.69 


6.10 


636.0 


27.42 


5.77 


1.20 


84.8 


904600 






60 


17.67 


0.59 


6.00 


609.0 


25.96 


5.87 


1.21 


81.2 


866100 


$7 


15 


55 


16.18 




5.75 


511.0 


17.06 


5.62 


1.02 


68.1 


726800 






50 


14.71 


0.56 


5.65 


483.4 


16.04 


5.73 


1.04 


64.5 


687500 






45 


13.24 


0.46 


5.55 


455.8 


15.00 


5.87 


1.07 


60.8 


648200 






42 


12.48 


0.41 


5.50 


441.7 


14.62 


5.95 


1.08 


58.9 


628300 


38 


12 


55 


16.18 


0.82 


5.61 


321.0 


17.46 


4.45 


1.04 


53.5 


570600 






50 


14.71 


0.70 


5.49 


303.3 


16.12 


4.54 


1.05 


50.6 


539200 






45 


13.24 


0.58 


5.37 


285.7 


14.89 


4.65 


1.06 


47.6 


507900 






40 


11.84 


0.46 


5.25 


268.9 


13.81 


4.77 


1.08 


44.8 


478100 


S? 


12 


35 


10.29 


0.44 


5.09 


228.3 


10.07 


4.71 


0.99 


38.0 


405800 






31.5 


9.26 


0.35 


5.00 


215.8 


9.50 


4.83 


1.01 


36.0 


383700 


311 


10 


40 


11.76 


0.75 


5.10 


158.7 


9.50 


3.67 


0.90 


31.7 


338500 






35 


10.29 


0.60 


4.95 


146.4 


8.52 


3.77 


0.91 


29.3 


312400 






30 


8.82 


0.4 b 


4.81 


134.2 


7.65 


3.90 


0.93 


26.8 


286300 






25 


7.37 


0.31 


4.66 


122.1 


6.89 


4.07 


0.97 


24.4 


260500 


313 


9 


35 


10.29 


0.73 


4.77 


111.8 


7.31 


3.29 


0.84 


24.8 


265000 






30 


8.82 


0.57 


4.61 


101.9 


6.42 


3.40 


0.85 


22.6 


241500 






25 


7.35 


0.41 


4.45 


91.9 


5.65 


3.54 


0.S8 


20.4 


217900 






21 


6.31 


0.29 


4.33 


84.9 


5.16 


3.67 


0.90 


18.9 


201300 


315 


8 


25.5 


7.50 


0.54 


4.27 


68.4 


4.75 


3.02 


0.80 


17.1 


182500 






23 


6.76 


0.45 


4.18 


64.5 


4.39 


3.09 


0.81 


16.1 


1 72000 






20.5 


6.03 


9 36 


4.09 


60.6 


4.07 


3.17 


0.82 


15.1 


161600 






18 


5.33 


0.27 


4.00 


56.9 


3.78 


3.27 


0.84 


14.2 


151700 



* This coefficient used for buildings; for bridges use 12,500 pounds per 
square inch, or multiply value in this column by 0.78125. 



PROPERTIES OF ROLLED STRUCTURAL STEEL. 289 



Properties of Carnegie 


Standard I-Beams — 


Steel. 


Conti 


nued. 
















3 c ° 


§ =■ U 


M 


"c5 o 


eg 


c 

c 


S 

i' 

w 

ft 

2 


"o 

o 

ft 

i 


S3 

_o 

01 

W 
'o 
o> 

< 


t 




St! 

•J ft° 

0) 0> cS 

o>_ +J 

m 


a> 53 

-"8 fl 

Si 

ill 

3 


d § 53 
.2ftO 
ts 53 ■£ 

r 


ego" 
.2-2 © 

>> ^ 

S3 
I- 1 


3 u 
Oi e« 

S Is 
o Bo 

.2. £-3 

5 


c 

©<,_ 

£ ° 
o to • 

S 53 ^ 
O 




in. 


lbs. 


sq.ra. 


in. 


in. 


/ 


/' 


/ 


c* 


H17 


7 


20 


5.88 


46 


3.87 


42.2 


3.24 


2.68 


0.74 


12.1 


128600 






17.5 


5.15 


035 


3.76 


39 2 


2.94 


2.76 


0.76 


11.2 


1 1 9400 


" 




15 


4.42 


0.25 


3.66 


36.2 


2.67 


2.86 


0.78 


10.4 


110400 


H19 


6 


l71/ 4 


5.07 


0.48 


3.58 


26.2 


2.36 


2.27 


0.68 


8.7 


93100 






143/^ 


4.34 


35 


3 45 


24.0 


2.09 


2.35 


0.69 


8.0 


85300 


" 




121/^ 


3.61 


23 


3.33 


21.8 


1.85 


2.46 


072 


7.3 


77500 


R21 


5 


143/^ 


4.34 


0.50 


3.29 


15.2 


1.70 


1.87 


0.63 


6.1 


64600 






121/4 


3.60 


0.36 


3.15 


13.6 


1.45 


1.94 


0.63 


5.4 


58100 




" 


93/„ 


2 87 


21 


3 00 


12.1 


1.23 


2.05 


0.65 


4.8 


51600 


B23 


4 


105 


3.09 


41 


2 88 


7.1 


1.01 


1.52 


0.57 


3.6 


38100 






9.5 


2.79 


0.34 


2.81 


6.7 


0.93 


1.55 


0.58 


3.4 


36000 


" 




8.5 


2.50 


0.26 


2.73 


6.4 


0.85 


1.59 


0.58 


3.2 


33900 


" 


" 


7.5 


2.21 


19 


2 66 


6.0 


0.77 


1.64 


0.59 


3.0 


31800 


B77 


3 


75 


2.21 


36 


2 52 


2.9 


0.60 


1.15 


0.52 


1.9 


20700 






65 


1.91 


26 


2 42 


2.7 


53 


1.19 


0.52 


1.8 


19100 


" 




5.5 


1.63 


0.17 


2.33 


2.5 


0.46 


1.23 


0.53 1 1.7 


17600 



Lightest weight in each section is standard ; others are special. 

L = safe loads in pounds, uniformly distributed; I = span in feet. 
M = moments of forces in foot-pounds; C = coefficient given above. 

L = ~ ; M = | ; C = LI =8 M = ^ ; / = fiber stress. 





Properties of Carnegie 


Trough Plates — 


Steel. 




Section 
Index. 


Size, in 
Inches. 


Weight 
per 
Foot. 


Area 

of Sec- 
tion. 


Thick- 
ness in 
Inches. 


Moment of 

Inertia, 

Neutral 

Axis 

Parallel to 
Length. 


Section 
Modulus, 
Axis as 
before. 


Radius 
of Gyra- 
tion, 
Axis as 
before. 


M10 

Mil 
M12 
M13 
M14 


91/2X33/4 
91/2X33/4 
91/2X33/4 
91/2X33/4 
91/2X33/4 


lb. 
16.32 
18.02 
19.72 
21.42 
23.15 


sq. in. 
4.8 
5.3 
5.8 
6.3 
6.8 


1/2 
9/16 

5/8 
U/16 

3/4 


/ 
3.68 
4.13 
4.57 
5.02 
5.46 


S 

1.38 
1.57 
1.77 
1.96 
2.15 


0.91 
0.91 
0.90 
0.90 

0.90 



Properties of Carnegie Corrugated Plates 



ed Plates 


— Steel. 


Moment of 




Inertia, 


Section 


Neutral 


Modulus, 


Axis 


Axis as 


Parallel to 


before. 


Length. 




/ 


8 


0.64 


0.80 


0.95 


1.13 


1.25 


1.42 


4.79 


3.33 


5.81 


3.90 


6.82 


4.46 



Section 
Index. 



M30 
M31 
M32 
M33 
M34 
M35 



Size, in 
Inches. 



83/4 XI 1/2 
83/4 XI 9/16 
8 3/4 XI 5/s 
12 3/ ]6 X23/ 4 
123/ 16 X213/ 10 
123/ l6 x27/ 8 



Weight 


Area 


Thick- 


per 


of Sec- 


ness in 


Foot. 


tion. 


Inches. 


lb. 


sq. in. 




8.01 


2.4 


1/4 


10.10 


3.0 


5/16 


12.00 


3.5 


3/8 - 


17.75 


5.2 


% 


20.71 


6.1 


7/16 


23.67 


7.0 


1/2 



Radius 
of Gyra- 
tion, 
Axis as 
before. 



0.52 
0.57 
0.62 
0.96 
0.98 
0.99 



STRENGTH OF MATERIALS. 



- * ^ "S 



^- 


2s 


com 

— vO 


N 


o 




t^ON 


^■cn 


3 


1.14 
1.06 
0.99 
0.94 
0.88 
0.84 
0.80 
0.76 


in 


ON— 1 


vOO 

int' 




s 


som 


CSJCS 




oo t>. vq in ■* <rv N N 


vO 


^ 

N- 


r>vd 


T 




n-'cA 


incvj 


00 


r>. oo N oo m T * m 
r>. m tj- n — © O; oq 

IN <N tN «N IN f-i — ' — ' 




jQ 


^ro 


o> 
oq 


o 

<3 


so'ifi 


NO 

o>q 




T 00 mm r>. — vO m 


00 


j£5 

00 




T 
GO 

d 


CO 
On' 


COIN 


ON 
vo'nO 


S 


NvDtO-0>a- 

■^ o t->. i- (N ov r» vq 

ifMn'tV^CMflfl 



n«MOwoi-«M 



— — OO OO < 



r>vD l^. 00 OvO —IN c 



ivors»o>o- 



Jv — Ov NOvOC 

-r> in ovmcnc 



t^tl-l-tAf 



o o Ov oo oo r«. r-> vc -o vO 






"fr Ov fs OO — in (N o 

\u — in i— rs.<^Ov\Orn — oOvO"^ 

O ©' Ov Ov oo' oo K. r>.' r> t>.' vd \d vd 



q m <n ov 

- O O Ov Ov Ov 00 00 00 l>«° 



> so tsooao • 



2o 








6.18 
.4.17 
.2.44 
.0.94 
9.63 
8.48 
7.45 
6.53 
5.71 
4.96 
4.28 
3.66 
3.09 
2.57 


2.08 
1.64 
1.22 
0.83 
0.47 


0.13 
9.82 
9.52 
9.24 
8.98 
8.73 






O 
vO 


6.09 
3.31 
0.93 
8.87 
7.07 
5.47 
4.06 
2.79 
1.65 
0.62 
9.68 
8.83 
8.04 
7.32 


6.66 
6.04 
5.47 
4.93 
4.43 


3.97 
3.53 
3.12 
2.74 
2.37 
2.03 






o 

00 


47.14 
43.51 
40.40 
37.71 
35.35 
33.27 
31.42 
29.77 
28.28 
26.94 
25.71 
24.59 
23.57 
22.63 


.1.76 
'0.95 
>0.20 
9.51 
8.86 


8.25 
7.68 
7.14 
6.64 
6.16 
5.71 







- ov r>« vo -<r m cv 



co oo O Ov Ov o 



nrvi — © OOvoo oor>.rN 



oo vO r> t oo — if 

— — 0C - 

m'o'ir 

vOvOir 



J O Ov Ov Ov O ( 



!_; 


xj 


dOOOOvOOOO-O'tOaoOintsN 
mmcslooommoOT — — cove- 


Ov^nTOO 
vOm — OOv 


fOM 
OO — 


0> — 00 
CNinr-N 


^r 


o 

00 


rs— vo — oot- oOvO^TMOoor^ 
NN>0»OinininvTvftttnvc^ 


inTcocviO 
commence 


CMtNCs] 


I^NvOin 
CSINCM 












Nt^tmvOtsooO'O- (Nro-^-in 

_, ____^_ fslfNJ , Nf sj f M< N 


vONCOOvO 
CM <N CN CM CO 




fmvo 


.23 <u 


«g.a 











PROPERTIES OF ROLLED STRUCTURAL STEEL. 291 



,_; 




O O 


o 


CO 


CN 


CO 


in 


tN 


o 


o 
















en 


^ jQ 1 t> tT 


en 


cs 


tN 


*" 


— 


— — o 














• 




t> oo 


IT. 


o 


O 


tN 


o 


tN O xO 


ir 


tN 


— o 








^r 


E£ 


(N CO 


xO 


in 


en 


en 


eN 


<N , 


"~ 


"" 


— o 








• 


IP! 


xO en 


m 


„_ 


*r 


<N 


en 










^r 


en 


N - 


*. 




o -<r 


o 


CO 


o 


in 


^r 


en en CN 


tN 


N 


"" "* 


"~ 


"" 


' 


^ 


™. 43" 


O in 


CO 


_ 


o 


CO 


T 


t*o 


T 


O 


r^ t 


IN 


o 


00 sO 










o 




xO 


Xltt 














<o 


- 






"" 






















■ 


£ 


(N r^ 


in 


en 


sO 


_ 


_ 


^ 


m vO 


O 


en 


eo ^r 


_ 


CO 


m en 






-* o 




r^ 








so m 




T 














T en 




























































42 


f> — 


o 


^ 


r^ 


<N 


m 


mo 


^ 


r^ 


o 


en r> 


(N 


CO 


T — 






O eN 






Of) 






o o 




V2 




m T 


"* 






CO 


£ 




^ 


IN 




"" 




" 


















43 


m o 


_ 


IT. 


o 


_ 


o 


O O en 


O 


o 


o eg 


vO 


O 


vO 00 






O m 






T 


o 


xO 


tj- — o 


f> 








m 


T en 


0> 


<N 






en 


tN 


tN 




" ~ 














CJ r> BJ . 

U « £ "£ 




























ri S g 8 


in xO 


r^ 


CD 


r> 


r> 




fN en -^r 










o 


— IN 


•2 & g& 
























tN 


tN eN 


S*«g.s 






























43 


— T 


en 


xO 


CN 


o 


o 


Nm 0> 


■* 


t> 


m <n O 


■o 


en 


— o* 




00 m 






o 


o 








T 


-* T en 




en 


en tN 


b 






























































xO t^ 


xO 


— 


c 


en 


CO 


vO vO 


r^ 


O 


en 


r>. — i>. 


en 


On 


vO en 


M * 


— ' 42 


xO eN 


O 


^ 


£ 


2 


~ 


o o 


CO 


^ 


^ 


vO sO^ 


"" 


^r 


-<r ■* 


eN 


































<n en 


■* 


en 


r> 


in 


CO 


(N O 


CO 


o 


o 


en t^ — 


vO 


— 


r> en 








"* 




a> 


xO 


T 




O 


CT> 


o 




vO 


vO 








m eN 


<N 


tN 
























^r 
































43 


xO in 


— 


O 


m 


r> 


■* 


T t> N 


o 


o 


o — 


en 


*c 


o 


m O 










tr 




ON 


i^ in ^r 






o o 


O 


CO 


CO 


r>, t*s 












nj 


IN 




















HJ 


■<af 






























4 12 2 


fN 


m 


CO 


o 


1^ 


ON* 


o 


■* 


0,00 


O 


O 


en O 


























O Ox 


- 


o ho « 


T 


en 


en 




CN 


CS (N — 






--J- 








42 


-o o 


t^ 


en 


tN 


tN 


o> 


en en C^ 


■>T 


^5- 


V© — 


r^ 


m 


T 


in xO 






















O 00 








en tN 












^r 








CM 


CN 












. 






























42 


in oo 




o 


CO 


o 




— \0 ^r 






^r — t> 


O 


o 
















o 


vO en — 


O 




sO m en 


eN 




— o 




m 


vo m 


^r 


T 




en 


cm 


N N N 














































4J5 


o oo 








tN 




vO CN en 


CO 


NO 


r> O m 






00 Ox 
















T — CO 






— O 00 






^r en 








xO 




t 


^xt 








(M 










^ 


xO 






























v£) vO 


cc 


un 


— 


— 


en 


en — in 


en 


vO 


NO- 


in 


o 


xO ■* 




42 












on 


en O m 




O 






o 














xD 




^r 






n) 


CS tN tN 








































CO 
































O CO 








tN 




tt T5- — 


■* 










— xO 




42 










N- 


i^ 


— vO (N 


on 




N 0>N 






CN O 










co 




xo 




in TT ^T 














t 


O 




























cn 






























«jc^ 








































Ox O — 




en 


til* 




CO 


Ox O 


i§ £ g-fa 














— es es 






CN fS CN 




































5 ^ 


» 3 fi 

3 OQ ■- 



































2 e. 

O ^ 



0X'J2 — 
oOO 



yi 



>43^ 



cp O 3 



,9P 






■a 

fa o'O 



292 



STRENGTH OF MATERIALS. 



Properties of Carnegie Standard Channels — Steel. 













"3 ° 


"H ^ 


3 3 


h-B 


"3° 


o§ 


>_d 


1 

1 
j 


o 

o 

fa 

I 

1 
1 


c 
,o 

<u 

m 
"o 

< 


a 
IS 


0) 

M 

C 


flj 

1-1 So 

Hi 


30 

M go 
«- 03 o> 


gls 
111 

&PhO 
'■B S O 


m & 


3 fc. 

*| 

3 c a 
H P. c 

73 £7 CD 

- : 


"§0 

8 ° 

M « a 
•4^02 w 

•sfeft 



0^ 
<B73 

if 

So 
g| 


in. 


lbs. 


sq. in. 


in. 


in. 


/ 


r 


r' 


S 


c* 


X 


15 


55. 


16.18 


0.82 


3.82 


430.2 


12.19 


5.16 


0.868 


57.4 


611900 


0.823 




50. 


14.71 


0.72 


3.72 


402.7 


11.22 


5.23 


0.873 


53.7 


572700 


0.803 




45. 


13.24 


0.62 


3.62 


375.1 


10.29 


5.32 


0.882 


50.0 


533500 


0.788 




40. 


11.76 


0.52 


3.52 


347.5 


9.39 


5.43 


0.893 


46.3 


494200 


0.783 


" 


35. 


10.29 


0.43 


3.43 


320.0 


8.48 


5.58 


0.908 


42.7 


455000 


0.789 


" 


33. 


9.90 


0.40 


3.40 


312.6 


8.23 


5.62 


0.912 


41.7 


444500 


0.794 


12 


40. 


11.76 


0.76 


3.42 


197.0 


6.63 


4.09 


0.751 


32.8 


350200 


0.722 


" 


35. 


10.29 


0.64 


3.30 


179.3 


5.90 


4.17 


0.757 


29.9 


318800 


0.694 


" 


30. 


8.82 


0.51 


3.17 


161.7 


5.21 


4.28 


0.768 


26.9 


287400 


0.677 




25. 


7.35 


0.39 


3.05 


144.0 


4.53 


4.43 


0.785 


24.0 


256100 


0.678 


" 


20.5 


6.03 


0.28 


2.94 


128.1 


3.91 


4.61 


0.805 


21.4 


227800 


0.704 


10 


35. 


10.29 


0.82 


3.18 


115.5 


4.66 


3.35 


0.672 


23.1 


246400 


0.695 


" 


30. 


8.82 


0.68 


3.04 


103.2 


3.90 


3.42 


0.672 


20.6 


220300 


0.651 




25. 


7.35 


0.53 


2.89 


91.0 


3.40 


3.52 


0.680 


18.2 


194100 


0.620 


" 


20. 


5.88 


0.38 


2.74 


78.7 


2.85 


3.66 


0.696 


15.7 


168000 


0.609 




15. 


4.46 


0.24 


2.60 


66.9 


2.30 


3.87 


0.718 


13.4 


142700 


0.639 


9 


25. 


7.35 


0.62 


2.82 


70.7 


2.98 


3.10 


0.637 


15.7 


167600 


0.615 


" 


20. 


5.88 


0.45 


2.65 


60.8 


2.45 


3.21 


0.646 


13.5 


144100 


0.585 


" 


15. 


4.41 


0.29 


2.49 


50.9 


1.95 


3.40 


0.665 


11.3 


120500 


0.590 


" 


131/4 


3.89 


0.23 


2.43 


47.3 


1.77 


3.49 


0.674 


10.5 


112200 


0.607 


8 


2H/4 


6.25 


0.58 


2.62 


47.8 


2.25 


2.77 


0.600 


11.9 


127400 


0.587 




183/4 


5.51 


0.49 


2.53 


43.8 


2.01 


2.82 


0.603 


11.0 


116900 


0.567 




161/4 


4.78 


0.40 


2.44 


39.9 


1.78 


2.89 


0.610 


10.0 


106400 


0.556 


" 


133/4 


4.04 


0.31 


2.35 


36.0 


1.55 


2.98 


0.619 


9.0 


96000 


0.557 




1H/4 


3.35 


0.22 


2.26 


32.3 


1.33 


3.11 


0.630 


8.1 


86100 


0.576 


7 


193/4 


5.81 


0.63 


2.51 


33.2 


1.85 


2.39 


0.565 


9.5 


101100 


0.583 


" 


171/4 


5.07 


0.53 


2.41 


30.2 


1.62 


2.44 


0.564 


8.6 


92000 


0.555 




143/4 


4.34 


0.42 


2.30 


27.2 


1.40 


2.50 


0.568 


7.8 


82800 


0.535 




121/4 


3.60 


0.32 


2.20 


24.2 


1.19 


2.59 


0.575 


6.9 


73700 


0.528 




93/4 


2.85 


0.21 


2.09 


21.1 


0.98 


2.72 


0.586 


6.0 


66800 


0.546 


6 


15.5 


4.56 


0.56 


2.28 


19.5 


1.28 


2.07 


0.529 


6.5 


69500 


0.546 




13. 


3.82 


0.44 


2.16 


17.3 


1.07 


2.13 


0.529 


5.8 


61600 


0.517 


" 


10.5 


3.09 


0.32 


2.04 


15.1 


0.88 


2.21 


0.534 


5.0 


53800 


0.503 




8. 


2.38 


0.20 


1.92 


13.0 


0.70 


2.34 


0.542 


4.3 


46200 


0.517 


5 


11.5 


3.38 


0.48 


2.04 


10.4 


0.82 


1.75 


0.493 


4.2 


44400 


0.508 




9. 


2.65 


0.33 


1.89 


8.9 


0.64 


1.83 


0.493 


3.5 


37900 


0.481 


" 


6.5 


1.95 


0.19 


1.75 


7.4 


0.48 


1.95 


0.498 


3.0 


31600 


0.489 


4 


71/4 


2.13 


0.33 


1.73 


4.6 


0.44 


1.46 


0.455 


2.3 


24400 


0.463 


" 


61/4 


1.84 


0.25 


1.65 


4.2 


0.38 


1.51 


0.454 


2.1 


22300 


0.458 




51/4 


1.55 


0.18 


1.58 


3.8 


0.32 


1.56 


0.453 


1.9 


20200 


0.464 


3 


6. 


1.76 


0.36 


1.60 


2.1 


0.31 


1.08 


0.421 


1.4 


14700 


0.459 




5. 


1.47 


0.26 


1.50 


1.8 


0.25 


1.12 


0.415 


1.2 


13100 


0.443 


" 


4. 


1.19 


0.17 


1.41 


1.6 


0.20 


1.17 


0.409 


1.1 


11600 


0.443 



* Used for buildings; for bridges use 12,500 pounds, or multiply coeffi- 
cient in this column by 0.78125. 

L = safe load in pounds, uniformly distributed; I = span in feet; 
M = moment of forces in foot-pounds; C = coefficient given above. 

• 7 " r - 7 • * - T 7 - ° ■*' - ^ ; /,= fiber stress. 



L = 



M = £■ ; C ■■ 



LI ■- 



\M -- 



12 ' 



PROPERTIES OF ROLLED STRUCTURAL STEEL. 



293 



vOen — ©O00 rvNvOOu 

— . — : —. — . P °. °. °. °. °. °. °. °. °. °. °. 
dddddd ddddd dddoo 



•<r •■*• ^ ttwc 



ooooo ooooo ooooo 



oooooo ooooo ooooo ooooo 



DOOO OOOOO 



vOeNJO^O^ren eN - 
CN CN — — — ; — — - 

o'do'do'd o'c 



^ o 00 oo t> 



ooooo 



ooooo ooooo 



oooooo ooooo ooooo ooooo 



lUgl8A4. UT 8SB9J0UI •£ © vO en © 00 
x i- • • en en eN cn cn — 

•q T ^j9Aajojppv ooo'doo 



ooooo ooooo ooooo 



u 


Sa 


6.68 
5.57 
4.77 
4.18 
3.71 
3.34 


3.04 
2.78 
2.57 
2.39 
2.23 


2.09 
1.96 
1.86 
1.76 
1.67 


ONinof 


•q|A.i8Aa'jojppv 


eNm©vO en- 
Ten en eN CN eN 

do" oo'o'd 


0.19 

0.18 
0.16 
0.15 
0.14 


0.13 
0.12 
0.11 
0.11 
0.11 


0.10 
0.10 
0.09 
0.09 
0.08 


U 

GO 




8.61 

7.18 
6.15 
5.38 
4.78 
4.31 


— on 
On in 


-oors 


2.69 
2.53 
2.39 
2.27 
2.15 


2.05 
1.96 
1.87 
1.79 
1.72 



•^tjSraAi. m as-eajoiiT 


T 


— OOOt^vO 


mTeneNeN 


0.11 
0.11 
0.10 
0.10 
0.09 


0.09 
0.09 
0.08 
0.08 
0.08 


•qjA\i8A8 jo j ppy 


' "d 


d ©" d o" © 


d ©' © © d 


U 




3 


OooeN — JT 


— ocNm — 


vO m -T cn <N 


vOcnOrAN 
— ©©On CO 


ON 


m'£ 


: : : : :m 


mi-1-Tm 


enencnCNeN 


eNcseNeNCN 


tNfNCN 



\0 in T ■>»■ en 



^<N — — © ©OONONQN 



•qj AJ8A9 


joippy 


: : : : .^ 

•© 


© © © © © 


© © © © © 


© d ©' © © 


o'dc'oo 


u 

© 


— j§ 


! '. '. '. !»• 


6.49 
5.95 
5.49 
5.10 
4.76 


4.46 
4.20 
3.96 
3.76 
3.57 


3.40 
3.24 
3.10 
2.97 

2.85 


■"3- -3- m vO 00 
r>. vo m t en 



•qj AjaAa'-ioj ppy ' 


en 

© 


0.29 
0.26 
0.24 
0.23 
0.21 


© 00 00 f> vO 

© © © © © 


mTTTrenen 
© © © © © 


© ©' © © © 


U 


Si 


ON 

en 


10.35 
9.49 
8.76 
8.14 
7.59 


7.12 
6.70 
6.33 
5.99 
5.70 


5.42 
5.18 
4.95 
4.75 
4.56 


4.38 
4.22 
4.07 
3.93 
3.80 


-juSiaAi ux aseajatri 
•qj ^t8A8joj ppy 


ON 

©' 


0.35 
0.33 
0.30 
0.28 
0.26 


0.24 
0.23 
0.22 
0.21 
0.20 


ON GO t^ vO O 
©' © © © © 


in t tj- m en 

© ©odd 


U 


en j§ 


CN 


20.20 
18.52 
17.10 
15.87 
14.82 


13.89 
13.07 
12.35 
11.70 
11.11 


10.58 
10.10 
9.66 
9.26 
8.89 


8.55 
8.23 
7.94 
7.66 
7.41 


•^aaj m 
uaaA^aq 


s^joddng 
aou^siQ 


m vo t>ooON©» 


— cNenTm 


vONCOOO 


— eNenTm 

fNMfNCSCN 


^rsoooo 
cN<N(NfNen 



STRENGTH OF MATERIALS. 



Properties of Carnegie T-Shapes. — Steel. 





















1 

132 
>> 

So 

| 






s 

bO 

"8 


d 

m 
t 


V ■ 

u M 
Gv 

$ g 


~1 

So 

*-> ® * 
goo 

0+ .>t-i 


3° So 

^ M ?3 

m «'£ 


<> 
C ^ 8 
O M-2 

J 11 


SJOD 

8 Oy- 

og MO 


Hi 

III 

2S 
1^ 


xg . 
<•& g 
.p "8 » 

3.5£ 

Sg£ 


:>efric. of Strength for Fibe 
Stress of 12,0001b. per sq. in. 
Neutral Axis thro' C. of G 
Parallel to Flange. 


B3 


£ 


< 


Q*~ 


s 


j 


& 


§ 


w 


^ 


O 


in. 


lb. 


sq.in. 


in. 


/ 


s 


r 


/' 


S' 


r' 


c 


5 X3 


13.6 


3.99 


0.75 


2.6 


1.18 


0.82 


5.6 


2.22 


1.19 


9410 


5 X21/2 


11.0 


3.24 


0.65 


1.6 


0.86 


0.71 


4.3 


1.70 


1.16 


6900 


41/2X31/2 


15.9 


4.65 


1.11 


5.1 


2.13 


1.04 


3.7 


1.65 


0.90 


17020 


41/2X3 


8.6 


2.55 


0.73 


1.8 


0.81 


0.87 


2.6 


1.16 


1.03 


6490 


41/2X3 


10.0 


3.00 


0.75 


2.1 


0.94 


0.86 


3.1 


1.38 


1.04 


7540 


41/2X21/2 


8.0 


2.40 


0.58 


1.1 


0.56 


0.69 


2.6 


1.16 


1.07 


4520 


41/2X21/2 


9.3 


2.79 


0.60 


1.2 


0.65 


0.68 


3.1 


1.38 


1.08 


5220 


4 X5 


15.7 


4.56 


1.56 


10.7 


3.10 


1.54 


2.8 


1.41 


0.79 


24800 


4 X5 


12.3 


3.54 


1.51 


8.5 


2.43 


1.56 


2.1 


1.06 


0.78 


19410 


4 X4i/ 2 


14.8 


4.29 


1.37 


8.0 


2.55 


1.37 


2.8 


1.41 


0.81 


20400 


4 X4i/ 2 


11.6 


3.36 


1.31 


6.3 


1.98 


1.38 


2.1 


1.06 


0.80 


15840 


4 X4 


13.9 


4.02 


1.18 


5.7 


2.02 


1.20 


2.8 


1.40 


0.84 


16170 


4 X4 


10.9 


3.21 


1.15 


4.7 


1.64 


1.23 


2.2 


1.09 


0.84 


13100 


4 X3 


9.3 


2.73 


0.78 


2.0 


0.88 


0.86 


2.1 


1.05 


0.88 


7070 


4 X21/ 2 


8.7 


2.52 


0.63 


1.2 


0.62 


0.69 


2.1 


1.05 


0.92 


4980 


4 x2i/ 2 


7.4 


2.16 


0.60 


1.0 


0.55 


0.70 


1.8 


0.88 


0.91 


4380 


4 X2 


7.9 


2.31 


0.48 


0.60 


0.40 


0.52 


2.1 


1.05 


0.96 


3180 


4 X2 


6.7 


1.95 


0.51 


0.54 


0.34 


0.51 


1.8 


0.88 


0.95 


2700 


31/2X4 


12.8 


3.75 


1.25 


5.5 


1.98 


1.21 


1.89 


1.08 


0.72 


15870 


31/2X4 


10.0 


2.91 


1.19 


4.3 


1.55 


1.22 


1.42 


0.81 


0.70 


12380 


31/2X31/2 


11.9 


3.45 


1.06 


3.7 


1.52 


1.04 


1.89 


1.08 


0.74 


12160 


31/2X31/2 


9.3 


2.70 


1.01 


3.0 


1.19 


1.05 


1.42 


0.81 


0.73 


9530 


31/2X3 


11.0 


3.21 


0.88 


2.4 


1.13 


0.87 


1.88 


1.08 


0.77 


9050 


31/2X3 


8.7 


2.49 


0.83 


1.9 


0.88 


0.88 


1.41 


0.81 


0.75 


7040 


31/2X3 


7.7 


2.28 


0.78 


1.6 


0.72 


0.89 


1.18 


0.68 


0.76 


5790 


3 X4 


11.9 


3.48 


1.32 


5.2 


1.94 


1.23 


1.21 


0.81 


0.59 


15480 


3 X4 


10.6 


3.12 


1.32 


4.8 


1.78 


1.25 


1.09 


0.72 


0.60 


14270 


3 X4 


9.3 


2.73 


1.29 


4.3 


1.57 


1.26 


0.93 


0.62 


0.59 


12540 


3 X31/2 


11.0 


3.21 


1.12 


3.5 


1.49 


1.06 


1.20 


0.80 


0.62 


11910 


3 X31/2 


9.8 


2.88 


1.11 


3.3 


1.37 


1.08 


1.31 


0.88 


0.68 


10990 


3 X3 


10.1 


2.94 


0.93 


2.3 


1.10 


0.88 


1.20 


0.80 


0.64 


8780 


3 X3 


9.0 


2.67 


0.92 


2.1 


1.01 


0.90 


1.08 


0.72 


0.64 


8110 


3 X3 


7.9 


2.28 


0.88 


1.8 


0.86 


0.90 


0.90 


0.60 


0.63 


6900 


3 X2l/ 2 


7.2 


2.10 


0.71 


1.1 


0.60 


0.72 


0.89 


0.60 


0.66 


4800 


23/4X2 


7.4 


2.16 


0.53 


1.1 


0.75 


0.71 


0.62 


0.45 


0.54 


6000 


21/2X3 


7.2 


2.10 


0.97 


1.8 


0.87 


0.92 


0.54 


0.43 


0.51 


6960 


21/2X23/4 


6.8 


1.98 


0.87 


1.4 


0.73 


0.84 


0.66 


0.53 


0.58 


5860 


21/2X21/2 


6.5 


1.89 


0.76 


1.0 


0.59 


0.74 


0.52 


0.42 


0.53 


4700 


2 1/2 X HA 


3.0 


0.84 


0.29 


0.094 


0.09 


0.31 


0.29 


0.23 


0.58 


710 


21/4X21/4 


5.0 


1.44 


0.69 


0.66 


0.42 


0.68 


0.33 


0.30 


0.48 


3360 


2 X2 


4.4 


1.26 


0.63 


0.45 


0.33 


0.60 


0.23 


0.23 


0.43 


2610 


2 X 1 1/2 


3.2 


0.90 


0.42 


0.16 


0.15 


0.42 


0.18 


0.18 


0.45 


1200 


13/4Xl3/ 4 


3.2 


0.90 


0.54 


0.23 


0.19 


0.51 


0.12 


0.14 


0.37 


1540 


H/2XH/2 


2.6 


0.75 


0.42 


0.15 


0.14 


0.49 


0.08 


0.10 


0.34 


1150 


H/4XI 1/4 


2.1 


0.60 


0.40 


0.08 


0.10 


0.36 


0.05 


0.07 


0.27 


760 


1 XI 


1.3 


0.36 


0.32 


0.03 


0.05 


0.29 


0.02 


0.04 


0.21 


370 



Some light weight T's of the smaller sizes are omitted. 



PROPERTIES OF ROLLED STRUCTURAL STEEL. 



295 



Properties of Carnegie Standard and Special Angles with Equal 

Legs. Minimum, Intermediate, and Maximum Thicknesses 

and Weights. 





















8 











3 G£ 


gOp 

3 js 


3 G*> 


ir.- 




0) 

xi 
C 


I 



U 

•2 a 


3 rt « 


't, ^ 




.2 s . .■ 

£■£'> 1 


i 6 |i 


• 


7 


Cm 




■8*1 




l§ 1 


Cl ,« tH ffl 


3-gSl 


a 
o 

1 

S 


a 
a 

13 


a 
1 






oment of 
tral Axis 
ter of G 
to Flang 


action Mc 
Axis thri 
Gravity 
Flange. - 


adius of ( 
tral Axis 
ter of G 
to Flang 




S 


H 


1 


< 


S 


§ 


CO 


« 


J 


8 X8 


I 1/8 


56.9 


16.73 


2.41 


97.97 


17.53 


2.42 


1.55 


8 X8 


13/16 


42.0 


12.34 


2.30 


74.71 


13.11 


2.46 


1.57 


8 X8 


1/2 


26.4 


7.75 


2.19 


48.63 


8.37 


2.50 


1.58 


6 X6 


1 


37.4 


11.00 


1.86 


35.46 


8.57 


1.80 


1.16 


6 X6 


11/16 


26.5 


7.78 


1.75 


26.19 


6.17 


1.83 


1.17 


6 X6 


3/8 


14.9 


4.36 


1.64 


15.39 


3.53 


1.88 


1.19 


*5 X5 


1 


30.6 


9.00 


1.61 


19.64 


5.80 


1.48 


0.96 


*5 X5 


11/16 


21.8 


6.42 


1.50 


14.68 


4.20 


1.51 


0.97 


*5 X5 


3/8 


12.3 


3.61 


1.39 


8.74 


2.42 


1.56 


0.99 


4 X4 


13/16 


19.9 


5.84 


1.29 


8.14 


3.01 


1.18 


0.77 


4 X4 


9/16 


14.3 


4.18 


1.21 


6.12 


2.19 


1.21 


0.78 


4 X4 


5 /l6 


8.2 


2.40 


1.12 


3.71 


1.29 


1.24 


0.79 


3V2X31/2 


13/16 


17.1 


5.03 


1.17 


5.25 


2.25 


1.02 


0.67 


31/2X31/2 


9/16 


12.4 


3.62 


1.08 


3.99 


1.65 


1.05 


0.68 


31/2X31/2 


5/16 


7.2 


2.09 


0.99 


2.45 


0.98 


1.08 


0.69 


3 X3 


5/8 


11.5 


3.36 


0.98 


2.62 


1.30 


0.88 


0.57 


3 X3 


7/16 


8.3 


2.43 


0.91 


1.99 


0.95 


0.91 


0.58 


3 X3 


1/4 


4.9 


1.44 


0.84 


1.24 


0.58 


0.93 


0.59 


*2 3/ 4 x2 3/4 


1/2 


8.5 


2.50 


0.87 


1.67 


0.89 


0.82 


0.52 


*2 3/4X23/ 4 


3/8 


6.6 


1.92 


0.82 


1.33 


0.69 


0.83 


0.53 


*2 3/4X2 3/4 


1/4 


4.5 


1.31 


0.78 


0.93 


0.48 


0.85 


0.55 


21/2X21/2 


1/2 


7.7 


2.25 


0.81 


1.23 


0.73 


0.74 


0.47 


21/2X21/2 


3/8 


5.9 


1.73 


0.76 


0.98 


0.57 


0.75 


0.48 


21/2X21/2 


3/16 


3.1 


0.90 


0.69 


0.55 


0.30 


0.78 


0.49 


*2 1/4X2 1/4 


1/2 


6.8 


2.00 


0.74 


0.87 


0.58 


0.66 


0.48 


*2 1/4X2 1/4 


3/8 


5.3 


1.55 


0.70 


0.70 


0.45 


0.67 


0.43 


*2 1/4X2 1/4 


3/16 


2.8 


0.81 


0.63 


0.39 


0.24 


0.70 


0.44 


2 X2 


7/16 


5.3 


1.56 


0.66 


0.54 


0.40 


0.59 


0.39 


2 X2 


5/16 


4.0 


1.15 


0.61 


0.42 


0.30 


0.60 


0.39 


2 X2 


3/16 


2.5 


0.72 


0.57 


0.28 


0.19 


0.62 


0.40 


13/4X13/4 


7/16 


4.6 


1.30 


0.59 


0.35 


0.30 


0.51 


0.33 


13/4X13/4 


5/16 


3.4 


1.00 


0.55 


0.27 


0.23 


0.52 


0.34 


13/4X13/4 


3/16 


2.2 


0.62 


0.51 


0.18 


0.14 


0.54 


0.35 


H/2XH/2 


3/8 


3.4 


0.99 


0.51 


0.19 


0.19 


0.44 


0.29 


II/2XH/2 


1/4 


2.4 


0.69 


0.47 


0.14 


0.134 


0.45 


0.29 


II/2XH/2 


1/8 


1.3 


0.36 


0.42 


0.08 


0.070 


0.46 


0.30 


II/4XH/4 


5/16 


2.4 


0.69 


0.42 


0.09 


0.109 


0.36 


0.23 


II/4XH/4 


1/4 


2.0 


0.56 


0.40 


0.077 


0.091 


0.37 


0.24 


II/4XH/4 


1/8 


1.1 


0.30 


0.35 


0.044 


0.049 


0.38 


0.25 


1 XI 


1/4 


1.5 


0.44 


0.34 


0.037 


0.056 


0.29 


0.19 


1 XI 


3/16 


1.2 


0.34 


0.32 


0.030 


0.044 


0.30 


0.19 


1 XI 


1/8 


0.8 


0.24 


0.30 


0.022 


0.031 


0.31 


0.20 


* 7/s X 7/ 8 


3/16 


1.0 


0.29 


0.29 


0.019 


0.033 


0.26 


0.18 


* 7/s X 7/ 8 


1/8 


0.7 


0.21 


0.26 


0.014 


0.023 


0.26 


0.19 


3/4 X 3/ 4 


3/16 


0.9 


0.25 


0.26 


0.012 


0.024 


0.22 


0.16 


3/4 x 3/4 1 


1/8 


0.6 


0.17 ' 


0.23 1 


0.009 


0.017 


0.23 


0.17 



Angles marked * are special. 



296 



STRENGTH OF MATERIALS. 



Properties of Carnegie Standard and Special Angles with 

Unequal Legs; Minimum, Intermediate, and Maximum 

Thicknesses, and Weights. 



8 








Moment of 


Section 


Radius of Gyra- 


i 

c 

1 


1 

O 

O 


■g a 


Inertia. — /. 


Modul 


as.— S 


tion. — r. 


C 

T 

1 


o3 Si) 

Ph C 

O 




=3 M 

Ph a 





o3 M 

Ph C 



o3 -2 
Png 


. a 


m 


a> «; 


a; 1- 1 


<o • 


< . 


<Jo • 


< • 


<lo . 


<o ■ 


%.$ 






CO CD 


-^ <d 


-£ CD 


+j <u 


■H CD 


-U CD 


+3 CD 


tiQ 


I 

6 


2 


a 3 

MO 
'53 Ph 


03 a 1 

CDCB 


.-3 M 

?3_ C 


— bJO 




13 M 


=3_ a 


.-5 M 

?3_ C 


§3 


Q 


H 


£ 


< 

6.02 


A. 92 


39.96 


1.79 


£ 


I 


2.58 


£ 


8 X31/2 


n/20 


20.5 


7.99 


0.90 


0.74 


♦7 X31/2 


1 


32.3 


9.50 


7.53 


45.37 


2.96 


10.58 


0.89 


2.19 


0.88 


*7 X31/2 


3/ 4 


24.9 


7.31 


6.08 


35.99 


2.31 


8.22 


0.91 


2.22 


0.88 


*7 X31/2 


7/16 


15.0 


4.40 


3.95 


22.56 


1.47 


5.01 


0.95 


2.26 


0.89 


6 X4 


1 


30.6 


9.00 


10.75 


30.75 


3.79 


8.02 


1.09 


1.85 


0.85 


6 X4 


11/16 


21.8 


6.41 


8.11 


22.82 


2.76 


5.78 


1.13 


1.89 


0.86 


6 X4 


3/8 


12.3 


3.61 


4.90 


13.47 


1.60 


3.32 


1.17 


1.93 


0.88 


6 X31/2 


1 


28.9 


8.50 


7.21 


29.24 


2.90 


7.83 


0.92 


1.85 


0.74 


6 X3V2 


11/16 


20.6 


6.06 


5.47 


21.74 


2.11 


5.65 


0.95 


1.89 


0.75 


6 X31/2 


3/8 


11.7 


3.42 


3.34 


12.86 


1.23 


3.25 


0.99 


1.94 


0.77 


*5 X4 


7/8 


24.2 


7.11 


9.23 


16.42 


3.31 


4.99 


1.14 


1.52 


0.84 


*5 X4 


5 /8 


17.8 


5.23 


7.14 


12.61 


2.48 


3.73 


1.17 


1.55 


0.84 


*5 X4 


3/8 


11.0 


3.23 


4.67 


8.14 


1.57 


2.34 


1.20 


1.59 


0.86 


5 X31/2 


7/8 


22.7 


6.67 


6.21 


15.67 


2.52 


4.88 


0.96 


1.53 


0.75 


5 X31/2 


5/8 


16.8 


4.92 


4.83 


12.03 


1.90 


3.65 


0.99 


1.56 


0.75 


5 X31/2 


5/16 


8.7 


2.56 


2.72 


6.60 


1.02 


1.94 


1.03 


1.61 


0.76 


5 X3 


13/16 


19.9 


5.84 


3.71 


13.98 


1.74 


4.45 


0.80 


1.55 


0.64 


5 X3 


9/16 


14.3 


4.18 


2.83 


10.43 


1.27 


3.23 


0.82 


1.58 


0.65 


5 X3 


5/16 


8.2 


2.40 


1.75 


6.26 


0.75 


1.89 


0.85 


1.61 


0.66 


♦41/2X3 


13/16 


18.5 


5.43 


3.60 


10.33 


1.71 


3.62 


0.81 


1.38 


0.64 


*4i/2X3 


9/16 


13.3 


3.90 


2.75 • 


7.75 


1.25 


2.64 


0.85 


1.41 


0.64 


♦41/2X3 


5/16 


7.7 


2.25 


1.73 


4.69 


0.76 


1.54 


0.88 


1.44 


0.66 


♦4 X31/2 


13/16 


18.5 


5.43 


5.49 


7.77 


2.30 


2.92 


1.01 


1.19 


0.72 


♦4 X31/2 


9/16 


13.3 


3.90 


4.17 


5.86 


1.68 


2.15 


1.03 


1.23 


0.72 


♦4 X31/2 


5/16 


7.7 


2.25 


2.59 


3.56 


1.01 


1.26 


1.07 


1.26 


0.73 


4 X3 


13/16 


17.1 


5.03 


3.47 


7.34 


1.68 


2.87 


0.83 


1.21 


0.64 


4 X3 


9/16 


12.4 


3.62 


2.66 


5.55 


1.23 


2.09 


0.86 


1.24 


0.64 


4 X3 


5/16 


7.2 


2.09 


1.65 


3.38 


0.74 


1.23 


0.89 


1.27 


0.65 


• 31/2X3 


13/16 


15.8 


4.62 


3.33 


4.98 


1.65 


2.20 


0.85 


1.04 


0.62 


31/2X3 


5/16 


6.6 


1.93 


1.58 


2.33 


0.72 


0.96 


0.90 


1.10 


0.63 


31/2X21/2 


11/16 


12.5 


3.65 


1,72 


4.13 


0.99 


1.85 


0.67 


1.06 


0.53 


31/2X21/2 


1/4 


4.9 


1.44 


0.78 


1.80 


0.41 


0.75 


0.74 


1.12 


0.54 


♦31/4X2 


9/16 


9.0 


2.64 


0.75 


2.64 


0.53 


1.30 


0.53 


1.00 


0.44 


♦31/4X2 


1/4 


4.3 


1.25 


0.40 


1.36 


0.26 


0.63 


0.57 


1.04 


0.45 


3 X21/2 


9/16 


9.5 


2.78 


1.42 


2.28 


0.82 


1.15 


0.72 


0.91 


0.52 


3 X21/2 


1/4 


4.5 


1.31 


0.74 


1.17 


0.40 


0.56 


0.75 


0.95 


0.53 


♦3 X2 


1/2 


7.7 


2.25 


0.67 


1.92 


0.47 


1.00 


0.55 


0.92 


0.43 


♦3 X2 


1/4 


4.1 


1.19 


0.39 


1.09 


0.25 


0.54 


0.57 


0.95 


0.43 


21/2X2 


1/2 


6.8 


2.00 


0.64 


1.14 


0.46 


0.70 


0.56 


0.75 


0.42 


21/2X2 


3/16 


2.8 


0.81 


0.29 


0.51 


0.20 


0.29 


0.60 


0.79 


0.43 


♦21/4XU/2 


1/2 


5.6 


1.63 


0.26 


0.75 


0.26 


0.54 


0.40 


0.68 


0.39 


♦21/4XU/2 


3/8 


4.4 


1.27 


0.21 


0.61 


0.20 


0.42 


0.41 


0.69 


0.39 


♦21/4XU/2 


3/16 


2.3 


0.67 


0.12 


0.34 


0.11 


0.23 


0.43 


0.72 


040 


♦2 X 1 3/ 8 


1/4 


2.7 


0.78 


0.12 


0.37 


0.12 


0.23 


0.39 


0.63 


0.30 


♦2 X 1 % 


3/16 


2.1 


0.60 


0.09 


0.24 


0.09 


0.18 


0.40 


0.63 


031 


♦13/8X1 


1/4 


1.9 


0.53 


0.04 


0.09 


0.05 


0.09 


0.27 


0.41 


22 


♦13/sXl 


1/8 1 


1.0 


0.28 


0.02 


0.051 0.03 


0.06 


0.29 


0.44 


0.22 



Angles marked * are special. A few of the smaller intermediate sizes 
are omitted, 



PROPERTIES 


OF 


ROLLED 


STRUCTURAL STEEL. 297 


Safe Loads (Tons, 2000 Lb.) Uniformly Distributed for 


Carnegie 


Standard and Special Angl 


es With Equal Legs. 


Size of Angle. 


Distance between Supports in Feet. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


8 X8 XI 1/8 
8 X8 XV2 


93.49 
44.64 


46.74 
22.32 


31.16 

14.88 


23.37 
11.16 


18.70 
8.93 


15.58 
7.44 


13.36 
6.38 


11.69 
5.58 


10.39 
4.96 


9.35 
4.46 


6 X6 XI 
6 X6 X3/ 8 
*5 X5 XI 
*5 X5 X3/8 


45.72 
18.82 
30.91 
12.91 


22.86 
9.41 

15.45 
6.45 


15.24 
6.27 

10.30 
4.30 


11.43 
4.70 
7.73 
3.23 


9.14 
3.76 
6.18 
2.58 


7.62 
3.14 
5.15 
2.15 


6.53 
2.69 
4.42 
1.84 


5.72 
2.35 
3.86 
1.61 


5.08 
2.09 
3.43 
1.43 


4.57 
1.88 
3.09 
1.29 


4 X4 X WIG 
4 X4 X 5 /i6 

31/2X31/2X13/16 
31/2X31/2X5/16 


16.05 
6.88 

12.00 
5.20 


8.03 

3.44 
6.00 
2.60 


5.35 

2.29 
4.00 
1.73 


4.01 
1.72 
3.00 
1.30 


3.21 
1.38 
2.40 
1.04 


2.68 
1.15 
2.00 
0.87 


2.29 
0.98 
1.71 
0.74 


2.01 
0.86 
1.50 
0.65 


1.78 
0.76 
1.33 
0.58 


1.61 
0.69 
1.20 
0.52 


3 X3 X5/ 8 
3 X3 Xi/4 

*2 3/4X2 3/4 X 1/2 
*2 3/4X2 3/4X1/4 


6.93 
3.09 

4.75 
2.56 


3.47 
1.55 
2.37 
1.28 


2.31 
1.03 
1.58 
0.85 


1.73 
0.77 
1.19 
0.64 


1.39 

0.62 
0.95 
0.51 


1.16 
0.52 
0.79 
0.43 


0.99 
0,44 
0.68 
0.37 


0.87 
0.39 
0.59 
0.32 


0.77 
0.34 
0.53 
0.28 


0.69 
0.31 
0.47 
0.26 


21/2X21/2X1/2 
2V2X21/2X3/16 
*2 1/4X21/4XV2 
*21/ 4 X21/4X3/16 


3.89 
1.61 
3.09 
1.30 


1.95 
0.81 
1.55 
0.65 


1.29 
0.54 
1.03 
0.43 


0.97 
0.40 
0.77 
0.32 


0.78 
0.32 
0.62 
0.26 


0.65 
0.27 
0.52 
0.22 


0.56 
0.23 
0.44 
0.19 


0.49 
0.20 
0.39 
0.16 


0.43 
0.18 
0.34 
0.14 


0.39 
0.16 
0.31 
0.13 


2 X2 X7/16 
2 X2 X3/i6 
13/4X13/4X7/16 
13/4X13/4X3/16 


2.13 
1.01 
1.60 
0.75 


1.07 
0.51 
0.80 
0.37 


0.71 
0.34 
0.53 
0.25 


0.53 
0.25 
0.40 
0.19 


0.43 
0.20 
0.32 
0.15 


0.36 
0.17 
0.27 
0.12 


0.30 
0.14 
0.23 
0.11 


0.27 
0.13 
0.20 
0.093 


0.24 
0.11 
0.18 
0.083 


0.21 
0.10 
0.16 
0.075 


11/2X11/2X3/8 
II/2XII/2XV8 
11/4X1 1/4 X.5/16 
11/4X1 I/4XV8 


1.01 
0.38 
0.58 
0.26 


0.51 
0.19 
0.29 
0.13 


0.34 
0.13 
0.19 
0.087 


0.25 
0.096 
0.150 
0.065 


0.20 
0.077 
0.120 
0.052 


0.17 
0.064 
0.097 
0.044 


0.14 
0.055 
0.083 
0.037 


0.130 
0.048 
0.073 
0.033 


0.110 
0.043 
0.065 
0.029 


0.100 
0.038 
0.058 
0.026 


1 XI Xl/4 
1 XI XV8 


0.30 
0.17 


0.15 

0.083 


0.100 
0.055 


0.075 
0.041 


0.060 
0.033 


0.050 
0.028 


0.043 
0.024 


0.037 
0.021 


0.033 
0.018 


0.030 
0.017 


* 7/ 8 X 7/ 8X 3/ 16 

* 7/ 8 X 7/8X1/8 
3/4 X 3/ 4 X3/i6 
3/4 X 3/4X1/8 


0.18 
0.12 
0.13 
0.091 


0.088 
0.061 
0.064 
0.045 


0.059 
0.041 
0.043 
0.030 


0.044 
0.031 
0.032 
0.023 


0.035 
0.025 
0.026 
0.018 


0.029 
0.020 
0.021 
0.015 


0.025 
0.018 
0.018 
0.013 


0.022 
0.015 
0.016 
0.011 


0.020 
0.014 
0.014 
0.010 


0.018 
0.012 
0.013 
0.009 



Safe loads given include weight of angle. Maximum fiber stress, 
16,000 pounds per square inch. Neutral axis through center of gravity 
parallel to one leg. Angles marked * are s 



298 



STRENGTH OF MATERIALS. 



Safe Loads in Tons (2000 Lb.) Uniformly Distributed for Stand- 
ard Carnegie Angles with Unequal Legs. 









(Short Leg Vertical.) 












Distance between Supports in Feet. 


























1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


6 x4 xl 


20 21 


10.11 


6.74 


5.05 


4.04 


3.37 


2.89 


2.53 


2.25 


2 02 


6 x4 x3/ 8 


8,53 


4.27 


2.84 


2.13 


1.71 


1.42 


1.22 


1.07 


0.95 


85 


6 x3l/ 2 xl 


15.47 


7.74 


5.16 


3.87 


3.09 


2.58 


2.21 


1.93 


1.72 


1 55 


6 x3i/ 2 x3/ 8 


6,56 


3.28 


2.19 


1.64 


1.31 


1.09 


0.94 


0.82 


0.73 


66 


5 x3l/ 2 x7/ 8 


13,44 


6.72 


4.48 


3.36 


2.69 


2.24 


1.92 


1.68 


1.49 


1 14 


5 X 3 1/2X5/16 


5,44 


2.72 


1.81 


1.36 


1.09 


0.91 


0.78 


0.68 


0.60 


54 


5 x3 xi3/ 16 


9 28 


4.64 


3.09 


2.32 


1.86 


1.55 


1.33 


1.16 


1.03 


0.93 


5 x3 x'/ie 


4,00 


2.00 


1.33 


1.00 


0.80 


0.67 


0.57 


0.50 


0.44 


0.40 


4 x3 xl3/ 16 


8 96 


4.48 


2.99 


2.24 


1.79 


1 <9 


1.28 


1.12 


1.00 


0.90 


4 x3 x"Vi6 


3.95 


1.97 


1.32 


0.99 


0.79 


0.65 


0.56 


0.49 


0.44 


0.39 


3 1/ 2 X 3 xl3/ 16 


8.80 


4.40 


2.93 


2.20 


1.76 


1.47 


1.26 


1.10 


0.98 


0.88 


31/ 3 x3 X5/ 16 


3 84 


1.92 


1.28 


0.96 


0.77 


0.64 


0.55 


0.48 


0.43 


38 


3l/ 2 x2l/ 2 x ll/i 6 


5 28 


2.64 


1.76 


1.32 


1.06 


0.88 


0.75 


0.66 


0.59 


53 


31/2X21/2 X l/ 4 


2 19 


1.09 


0.73 


0.55 


0.44 


0.36 


0.31 


0.27 


0.24 


22 


3 X21/ 2 x9/ 16 


4.37 


2.19 


1.46 


1.09 


0.87 


0.73 


0.62 


0.55 


0.49 


44 


3 x 21/2x1/4 


2.13 


1.07 


0.71 


0.53 


0.43 


0.36 


0.30 


0.27 


0.24 


0.21 


2l/ 2 x2 xl/2 


2.45 


1.23 


0.82 


0.61 


0.49 


0.41 


0.35 


0.31 


0.27 


0.25 


21/2X2 X3/ 16 


1.07 


0.53 


0.36 


0.27 


0.21 


0.18 


0.15 


0.13 


0.12 


0.11 



Safe loads given include weight of angle. Maximum fiber stress, 
16,000 lb. persq. in. Neutral axis through center of gravity parallel to 
long leg. 

Safe Loads in Tons (2000 Lb.) Uniformly Distributed for Stand- 
ard Carnegie Angles with Unequal Legs. 

(Long Leg Vertical.) 









Distance between Supports in 


Feet. 






Size of Angle. 
























1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


6 x4 x 1 


42,77 


21.39 


14 26 


10.69 


8.55 


7.13 


6.11 


5.35 


4.75 


4 28 


6 x4 x3/ 8 


17,71 


8.85 


5 90 


4.43 


3.54 


2.95 


2.53 


2.21 


1.97 


1 77 


6 x3l/ 2 x 1 


41.76 


20.88 


13 92 


10.44 


8.35 


6.96 


5.97 


5.22 


4,64 


4.18 


6 x3i/ 2 x3/ 8 


17.33 


8.67 


5.78 


4.33 


3.47 


2.89 


2.48 


2.17 


1.93 


1 73 


5 x31/ 2 x7/ 8 


26.03 


13.01 


8.68 


6.51 


5.21 


4.34 


3.72 


3.25 


2.89 


2 60 


5 X3l/ 2 X5/ 16 


10.35 


5.18 


3.45 


2.59 


2.07 


1.73 


1.48 


1.29 


1.15 


1 04 


5 x3 xl3/ 16 


23 73 


11.87 


7 91 


5.93 


4.75 


3.96 


3.39 


2.97 


2.64 


7, 37 


5 x3 x5/i 6 


10 08 


5.04 


3 36 


2.52 


2.02 


1.68 


1.44 


1.26 


1.12 


1 01 


4 X3 X 13/i 6 


15.31 


7.65 


5 10 


3.83 


3.06 


2.55 


2.19 


1.91 


1.70 


1 53 


4 X3 x5/i 6 


6.56 


3.28 


2.19 


1.64 


1.31 


1.10 


0.94 


0.82 


0.73 


66 


31/2X3 X 13/i 6 


11.73 


5.87 


3.91 


2.93 


2.35 


1.96 


1.68 


1.47 


1.30 


1 17 


31/2X3 x5/i 6 


3.12 


2.56 


1.71 


1.28 


1.02 


0.85 


0.73 


0.64 


0.57 


0.51 


3 1/ 2 X21/ 2 X11/16 


9 87 


4.93 


3 29 


2.47 


1.97 


1.64 


1.41 


1.23 


1.10 


99 


31/2X21/2X1/4 


4 00 


2.00 


1.33 


1.00 


0.80 


0.67 


0.57 


0.50 


0.44 


40 


3 X2i/ 2 x9/ 16 


6.13 


3.07 


2.04 


1.53 


1.23 


1.02 


0.88 


0.77 


0.68 


61 


3 x 21/3x1/4 


2.99 


1.50 


1.00 


0.75 


0.60 


0.50 


0.43 


0.37 


0.33 


0.30 


21/2X2 Xl/ 2 


3 73 


1.87 


1 24 


0.93 


0.75 


0.62 


0.53 


0.47 


0.41 


37 


21/2X2 X3/i 6 


1.55 


0.77 


0.52 


0.39 


0.31 


0.26 


0.22 


0.19 


0.17 


0.16 



Safe loads given include weight of angle. Maximum fiber stress, 
16,000 lb. per sq. in. Neutral axis through center of gravity parallel to 
short leg. 



PROPERTIES OF ROLLED STRUCTURAL STEEL. 299 



Properties of Carnegie Z-Bars. 













.2 i 


■a a 


fi 


•pfl 


+=■ i 


*-' m 


to bb 


33 aS 














n <v 


rf a; 




§o 


SB a 


J3 CG 


t 
a 


12 


1 


o 

o 

03 

1 


.2 

Xfl 
C3 


. G 

.go 

m 


if 


«»3 

Pn 

Jo 

5 c « 


<3 

is 

V o 

£0 

,/0 

log 

1~* 


£ & 

Ph 

• SO 
pi 

O"o£ 

J-91 


o 2"^ 
PI 


35 
o| 

O £ 
3 


?'6J 

t,<N'Pn a 
^ to<J 03 

§cq-.S£ 


Q 


? 


E- 


s 


< 


§ 


§ 


02 


03 


cd 


tf 


P3 


o 


in. 


in. 


in. 


lb. 


sq.in. 


/ 


I 


s 


s 


r 


r 


r 


c 


) 


31/2 


3/8 


15.6 


4.59 


25.32 


9.11 


8.44 


2.75 


2.35 


1.41 


0.83 


67,500 


>Vl6 


3 9/16 


7/16 


18.3 


5.39 


29.80 


10.95 


9.83 


3.27 


2.35 


1.43 


0.84 


78,600 


>Vs 


35/8 


1/2 


21.0 


6.19 


34.36 


12.87 


11.22 


3.81 


2.36 


1.44 


0.84 


89,800 


5 


31/2 


9/16 


22.7 


6.68 


34.64 


12.59 


11.52 


3.91 


2.28 


1.37 


0.81 


92,400 


3Vl6 


3 9/16 


5/8 


25.4 


7.46 


38.86 


14.42 


12.82 


4.43 


2.28 


1.39 


0.82 


102,600 


>Vs 


3 5/8 


11/16 


28.0 


8.25 


43.18 


16.34 


14.10 


4.98 


2.29 


1.41 


0.84 


112,800 


s 


31/2 


3/ 4 


29.3 


8.63 


42.12 


15.44 


14.04 


4.94 


2.21 


1.34 


0.81 


112,300 


s Vie 


3 9/i 6 


13/16 


31.9 


9.40 


46.13 


17.27 


15.22 


5.47 


2.22 


1.36 


0.82 


121,800 


51/8 


3 5/8 


7/8 


34.6 


10.17 


50.22 


19.18 


16.40 


6.02 


2.22 


1.37 


0.83 


131,200 


5 


31/4 


5/16 


11.6 


3.40 


13.36 


6.18 


5.34 


2.00 


1.98 


1.35 


0.75 


42,700 


i Vie 


3 5/ie 


3/8 


13.9 


4.10 


16.18 


7.65 


6.39 


2.45 


1.99 


1.37 


0.76 


51,100 


>Vs 


3 3/ 8 


7/16 


16.4 


4.81 


19.07 


9.20 


7.44 


2.92 


1.99 


1.38 


0.77 


59,500 




31/ 4 


1/2 


17.9 


5.25 


19.19 


9.05 


7.68 


3.02 


1.91 


1.31 


0.74 


61,400 


'Vie 


3 5/i 6 


9/16 


20.2 


5.94 


21.83 


10.51 


8.62 


3.47 


1.91 


1.33 


0.75 


69,000 


>Vs 


3 3/8 


5 /8 


22.6 


6.64 


24.53 


12.06 


9.57 


3.94 


1.92 


1.35 


0.76 


76,600 




31/4 


11/16 


23.7 


6.96 


23.68 


11.37 


9.47 


3.91 


1.84 


1.28 


0.73 


75,800 


1 1/16 


3 5/ie 


3/4 


26.0 


7.64 


26.16 


12.83 


10.34 


4.37 


1.85 


1.30 


0.75 


82,700 


'1/8 


3 3/ 8 


13/16 


28.3 


8.33 


28.70 


14.36 


11.20 


4.84 


1.86 


1.31 


0.76 


89,600 


\ 


31/16 


V4 


8.2 


2.41 


6.28 


4.23 


3.14 


1.44 


1.62 


1.33 


0.67 


25,100 


H/16 


31/8 


5/16 


10.3 


3.03 


7.94 


5.46 


3.91 


1.84 


1.62 


1.34 


0.68 


31,300 


»V 8 


3 3/ie 


3/8 


12.4 


3.66 


9.63 


6.77 


4.67 


2.26 


1 62 


1.36 


0.69 


37,400 


1 


31/16 


7/16 


13.8 


4.05 


9.66 


6.73 


4.83 


2.37 


1.55 


1.29 


0.66 


38,600 


H/ie 


31/8 


1/2 


15.8 


4.66 


11.18 


7.96 


5.50 


2.77 


1.55 


1.31 


0.67 


44,000 


♦1/8 


3 3/ie 


9/16 


1.7.9 


5.27 


12.74 


9.26 


6.18 


3.19 


1.55 


1.33 


0.69 


49,400 


\ 


3Vl6 


5/8 


18.9 


5.55 


12.11 


8.73 


6.05 


3.18 


1.48 


1.25 


0.66 


48,400 


i Vie 


31/8 


11/16 


20.9 


6.14 


13.52 


9.95 


6.65 


3.58 


1.48 


1.27 


0.67 


53,200 


H/8 


3 3/16 


3/4 


23.0 


6.75 


14.97 


11.24 


7.26 


4.00 


1.49 


1.29 


0.69 


58,100 




2H/16 


1/4 6.7 


1.97 


2.87 


2.81 


1.92 


1.10 


1.21 


1.19 


0.55 


15,400 


Vl6 


2 3/4 


5/16 8.4 


2.48 


3.64 


3.64 


2.38 


1.40 


1.21 


1.21 


0.56 


19,000 


> 


211/16 


3/8 9.7 


286 


3.85 


3.92 


2.57 


1.57 


1.16 


1.17 


0.55 


2,6000 


Vl6 


23/ 4 


7/16 11.4 


3.36 


4.57 


4.75 


2.98 


1.88 


1.17 


1.19 


0.56 


23,800 




2 11/16 


1/2 12.5 


3.69 


4.59 


4.85 


3.06 


1.99 


1.12 


1.15 


0.55 


24,500 


1/16 


23/4 


9/16 J 


14.2 


4.18 


5.26 


5.70 


3.43 


2.31 


1.12 


1.17 


0.56 


27,400 



300 



STRENGTH OF MATERIALS. 



D 


mensions of 6, 8 


, and 


10-Inch Carnegie 


Z-Bar Columns. 


%~ 


A. 


B. 


C. 


D. 


c^ 
































^ 


6 


8 


10 


6 


8 


10 


6 


8 


10 


6 


8 


10 


h^ 


in. 


in. 


in. 


in. 

31/s 


m. 

41/8 


m. 


in. 

5 9/, 6 


m. 

67/ 16 


in. 


in. 

31/8 


in. 

35/s 


in. 


in. 
!'4 


123/4 


155/ 16 






5/16 


I27/ S 


153/8 


b H/i 6 


3V/ m 


4v/ m 


55/ 3 9, 


i»/lfl 


6 V/! o 


69/ 1R 


31/8 


3 5/8 


35/8 


3/8 


I2b/ H 


151/2 


613/10 


3 3/ 1fi 


45/16 


51/4 


5V/ 1fi 


bV/ 1R 


69/16 


31/s 


35/8 


3i>/8 


7/10 


I2H/1 


3 151/16 


blb/16 


3 9/3? 


47/3? 


5H/3? 


jV/lfi 


61/4 


6»/lfl 


31/8 


3 5/8 


35/8 


1/7 


!27/ 1fi 


153/16 


l61/ ? 


31/4 


45/ifi 


51/4 


5ty|fi 


61/4 


63/8 


31/8 


35/8 


35/ 8 


9/10 


12 9/10 


15 5/ 16 


I6b/ S 


311/32 


4l3/ 3? 


5 U/3? 


55/ 16 


61/4 


63/ 8 


31/8 


35/ 8 


35/ 8 


B/8 




14 7/ 8 


I 6 3/ 4 




4 5/, o 


5 7/10 




61/16 


6 3/8 




3 5/8 


35/ 8 


11/16 




15 


I63/ S 




413/JW 


5 H/3? 




61/16 


63/ 1fi 




35/s 


35/ a 


3/4 




151/8 


\bl/ ?l 




41/2 


5V/io 




61/16 


63/,o 




35/ 8 


3W8 


13/10 






165/ 8 




... 517/3 2 






63/16 






35/ 8 


c3 

IS 


E. 


F. 


G. 


H. 


I. 


6 


8 


10 


6 


8 and 


6 


8 


10 


6 


Sand 


6 


8 


10 




m. 


iii. 


in. 


in. 


10 in. 


in. 


in. 


in. 


in. 


10 in. 


in. 


m. 


in. 


1/4 


3 


Mh 




15/8 


17/8 


211/10 


31/16 




8V ? , 


10 


31/4 


41/4 




W10 


3 


»v, 


31/. 


15/8 


IV/8 


23/4 


31/8 


31/4 


81/7, 


10 


33/s 


43/8 


5t>/l6 


3/8 


3 




31/' 


15/8 


IV/8 


2H/10 


33/ 16 


35/ 16 


8V ? 


10 


33/8 


41/?, 


5V/ 1f , 


Vw 


3 


Jl/o 


3V- 


1 5/8 


Wh 


23/4 


31/16 


3 3/8 


81/9 


10 


31/2 


4V/ 16 


59/m 


i/?, 


3 


U/ ? 


31/- 


15/8 


IV/8 


2H/16 


31/8 


31/ 4 


81/9 


10 


31/2 


49/ 16 


5 V? 


9/16 


3 


1 


3V- 


15/8 


IV/8 


23/ 4 


3 8/10 


3 5/! 6 


81/9 


10 


35/s 


4H/16 


5 5/ 8 


*»/« 




ii/., 


3 1/- 




IV/8 




31/16 


3 3/8 




10 




45/ 8 


53/ 4 


11/10 




il/9 


3 1/. 




IV/8 




31/8 


3 1/4 




10 




43/ 4 


5H/16 


3/4 
13/16 


::: 


51/2 


3V: 
31/3 




IV/8 
17/8 




3 3/ie 


3 5/ie 
3 3/s 




10 
10 




47/ 8 


513/ie 
515/16 



fi in m] I 4 z " bars - 3 " 3 Vie in- deep, 

o-in. coi. | x web plate 6 in x tMck Qf z _ bars> 

a in onl i 4. Z-bars, 4.-4 1/s in. deep, 

s-in. coi. 1 1 web plate 7 in x thick _ of z _ bars _ 

i n in nni 1 4 Z-bars, 5-51/s in. deep, 

lU-m. coi. y 1 web plate 7 in x thick# of z-bars. 

All rivets or bolts 3/ 4 inch diameter. 

Dimensions of 14-Inch Carnegie Z-Bar Columns. 






A. Inches. 


B. Inches. 


•R8 


d 




® s 


d 


d 




d 


d 




>£ 


• S on 


3-° 




S • 


■s'h 


e? "» 


^co 


M 2 


x4 


w-.Q 


XN 


xj 


xii 


-^ o3 


xjS 


xj 


SiM 


%** 


XN 


<?.s 


> N 


>^ 


XN 


<CS3 


^N3 


H 


vO 


vO 


vO 


vO 


o 


^o 


^O 


vO 


3/8 


199/i 6 


197/16 


199/is 


193/ 4 


627/3, 


63/4 


627/32 


615/10 


7/16 


1911/ie 


191/2 


195/ 8 


1913/iG 


baa/a,. 


6 13/1R 


6 29/32 


7 


1/9 


193/4 


195/s 


193/4 


197/g 


Mi/r> 


67/8 


631/39 


7Vie 


9/16 


197/s 


193/4 


197/s 


20 


> 1/37 


615/ifi 


7Vs? 


71/8 


5/8 


1915/i 6 


1913/ 16 


1915/ie 


201/ie 


/ 3/39 


7 


73/3? 


73/ie 


11/16 


201/16 


197/s 


201/ie 


201/g 


>5/39 


71/16 


7 5/ s? 


71/4 


3/4 


201/8 


20 


201/s 


201/4 


/''/m 


71/8 


yv/jw 


7b/i« 


13/10 


201/4 


201/ie 


203/ 16 


20 5/i 6 


^9/39 


/3/ 1fi 


yy/37 


73/g 


7/8 


205/ 16 


201/s 


201/4 


20 7/i 6 


' H/32 


71/4 


^ H/32 


77/16 



^.i=d 




1 Web Plate, 8 in.X thick, of Z-bars. 

2 Side Plates 14 in. wide 4 Z-bars. 



PROPERTIES OF ROLLED STRUCTURAL STEEL. 301 



Notes on Tables of Z-Bar and Channel Columns. 

(Carnegie Steel Co., 1903.) 

The tables of safe loads for steel Z-bar and channel columns are com- 
piled on the basis of an allowable stress per square inch of 12,000 pounds, 
with a factor of safety of 4 for lengths of 90 radii and under and an allow- 
able stress deduced from the formula 17,100 — 57 I -s- r for lengths greater 
than 90 radii; I = length in feet; r = radius of gyration in inches. Calcu- 
lations are made by means of Gordon's formula, modified for steel. The 
values used in these tables should be used only where the loads are mostly 
statical and equal or nearly so on opposite sides of the column. If the 
eccentricity is great or the load subject to sudden changes the values 
should be reduced according to circumstances. The safe loads given in 
the tables on channel columns range in value from I -*- r= 90 to about 

1 -r- r = 125. The size and spacing of lattice bars of channel columns 
should be proportioned to the sections composing the column. They 
should not be less than 11/2 inch X 5 /i6 inch for 6-inch channels; 13/4 X 5 /ie 
inch for 7- and 8-inch channels; 2 X 5/i 6 inch for 9- and 10-inch channels; 

2 X 3 /8 inch for 12-inch channels. 

Safe Loads in Tons (2000 Lb.) on Carnegie Z-Bar Columns 
(Square Ends). 

Dimensions and form of columns given in tables, p. 300. 
6-INCH Z-BAR COLUMN. 



Length 
of 

Col. 
Feet. 








Thiol 


mess of Metal, 


Inch. 






1/4 


5/ie 


3/S 


7/16 


1/2 


9/16 


5/8 


11/16 


3/4 


13/16 


r (min) 


= 1.86 
55.9 


1.90 


1.88 


1.93 


1.90 


1.95 










12 

and under 


70.3 


81.6 


95.8 


105.7 


119.8 










14 


55.7 


70.3 


81.6 


95. e 


105.7 


.119.6 










16 


52.3 


66.5 


76.6 


91.3 


99.9 


114.8 










18 


48.fi 


62.3 


71.7 


85.6 


93.6 


107.fi 










20 


45.4 


58.1 


66.7 


79.9 


87.2 


iocs 










22 


42.0 


53.9 


61.8 


74.3 


80.9 


93 .e 










24 


38.6 


49.7 


56.9 


68.6 


74.6 


86.fi 










26 


35.2 


45.5 


51.9 


63.0 


68.2 


79.8 










28 


31.7 


41.3 


47.0 


57.3 


61.9 


72.8 










30 


28.3 


37.1 


42.0 


51.7 


55.5 


65.8 
















8- 


[NCH 


Z-BAR 


COLL 


MN. 






r (min) 


= 2.47 
67.5 


2.52 


2.57 


2.49 


2.55 


2.60 


2.52 


2.58 


2.63 




18 


84.8 


102.4 


114.2 


131.2 


148.5 


157.5 


174.3 


191.2 




20 


65.0 


82.5 


100.5 


110.5 


128.2 


146.4 


153.3 


171.3 


189.6 




22 


61.9 


78 7 


95.9 


105.3 


122.4 


139.9 


146.2 


163.5 


181.3 




24 


58.8 


74.8 


91.3 


100.1 


116.5 


133.4 


139.1 


155.8 


173.0 




26 


55.7 


71.0 


86.8 


94.8 


110.6 


126.9 


132.0 


148.1 


164.7 




28 


52.6 


67.1 


82.3 


89.6 


104.7 


120.3 


124.8 


140.4 


156.4 




30 


49.4 


63.3 


77.7 


84.4 


93.8 


113.8 


117.7 


132.7 


148.2 




32 


46.3 


59.5 


73.2 


79.2 


93.0 


107.3 


110.6 


125.0 


139.9 




34 


43.2 


55.6 


68.7 


74.0 


87.1 


100.8 


103.5 


117.3 


131.6 




36 


40.1 


51.8 


64.1 


68.7 


81.2 


94.3 


96.4 


109.6 


123.3 




38 


37.0 


48.0 


59.6 


63.5 


75.3 


87.8 


89.4 


101.9 


115.0 




40 


33.9 


44.1 


55.0 


58.3 


69.5 


81.3 


82.2 


94.2 


106.7 





302 



STRENGTH OF MATERIALS. 



Safe Loads in Tons (2000 Lb.) on Carnegie Z-Bar Columns 
(Square Ends). (Continued) 

10-INCH Z-BAR COLUMN. 



r (min) 


= 


3.08 
94.7 


3.13 


3.18 


3.10 


3.15 


3.21 


3.13 


3.18 


3.25 


22 






114.2 


133.9 


147.0 


166 2 


185.6 


196.0 


214.9 


234.0 


24 








92.8 


112.6 


133.1 


144.6 


164.8 


185.3 


193.6 


213.9 


234.0 


26 








89.3 


108.6 


128.3 


139.2 


158.7 


178.7 


186.5 


206.2 


226.6 


28 








85.8 


104.4 


123.5 


133.8 


152.7 


172.1 


179.3 


198.5 


218.4 


30 








82.3 


100.2 


118.7 


128.4 


146.7 


165.5 


172.2 


190.8 


210.2 


32 








78.8 


96.1 


113.8 


123.0 


140.7 


158.9 


165.0 


183.1 


202.0 


34 








75.3 


91.9 


109.1 


117.6 


134.7 


152.3 


157.9 


175.4 


193.8 


36 








71.8 


87.8 


104.3 


112.2 


128.7 


145.7 


150.7 


167.8 


185.6 


38 








68.3 


83.6 


99.5 


106.8 


122.7 


139.1 


143.6 


160.0 


177.4 


40 








64.8 


79.4 


94.7 


101.4 


116.7 


132.5 


136.5 


152.3 


169.1 


42 








61.3 


75.3 


89.9 


96.0 


110.6 


125.9 


129.4 


144.6 


160.9 


44 








57.7 


71.1 


85.1 


90 6 


104 6 


119.3 


122.2 


136.9 


152.7 


46 








54.2 


67.0 


80.3 


85.2 


98.6 


112.7 


115.1 


129.2 


144.5 


48 








50.7 


62.8 


75.5 


79.8 


926 


106.1 


107.9 


121.5 


136.3 


50 








47.2 


58.6 


70.7 


74.4 


86.6 


99.5 


100.8 


113.8 


128.1 



Safe Load in Tons (2000 Lb.) on 14-Inch Carnegie Z-Bar 
Columns (Square Ends). 

Dimensions and form of column given in table, p. S00. 

Section: 4 Z-bars 6l/ 8 X U/i6 in- 1 Web Plate 8 X U/i6 in. 2 Side Plate 
14 in. wide. 





vO 


<3 


in 


in 


Tf 


t 


m 


■^r 


rs 




o a 


cn a 




3; a 


o a 


o a 


<s a 


oo C 


-r q 




































n . 




<N " 




II £ 


II g* 


II §? 


II cr 


II 5* 


II O" 


II g 1 


II O* 


II a 1 

So 


Length of 


do 


®<x> 




jC 


So 


SoO 


Jm 


®r^ 




^£ 


£© 


"S£ 


i^' 


tf^O 




fflO* 






in Feet. 


£ 


PLl 10 


Ph ,| 


An^ 


S' 


(^m 


^7 


Ph^ 


Ph 




x~£ 


J^ 


X;5 


»VQ 


x-° 


y=2 


X-0 


x£ 


.00 II 

x£ 




T 


t 


•* 


<♦ 


1- 


T 


T 


f 


T 


r (min.) = 


3.80 


3.81 


3.82 


3.82 


3.83 


3.84 


3.85 


3.85 


3.85 


28 
and under 


294.0 


304.5 


315.0 


325.5 


336.0 


346.5 


357.0 


367.5 


378.0 


30 


286.6 


297.2 


307.7 


318.3 


328.9 


339.5 


350.0 


360.4 


370.9 


32 


277.8 


288.1 


298.3 


308.6 


3189 


329.2 


339.4 


349.5 


359.7 


34 


269.0 


278.9 


288.9 


298.9 


308.9 


318.9 


328.8 


338.6 


348.6 


36 


260.1 


269.8 


279.5 


289.2 


298.9 


308.6 


318.2 


327.7 


337.4 


38 


251.3 


260.7 


270.1 


279.5 


289.0 


298.3 


307.6 


316.8 


326.2 


40 


242.5 


251.6 


260.7 


269.7 


278.9 


288.0 


297.0 


306.0 


315.0 


42 


233.7 


242.5 


251.3 


260.1 


269.0 


277.8 


286.4 


295.1 


303.8 


44 


224.9 


233.3 


241.9 


250.4 


258.9 


267.4 


275.8 


284.2 


292.3 


46 


216.0 


224.3 


232.4 


240.7 


249.0 


257.2 


265.2 


273.3 


281.6 


48 


207.2 


215.1 


223.0 


230.9 


238.9 


246.9 


254.6 


262.4 


270.5 


50 


198.4 


206.0 


213.6 


221.3 


229.0 


236.5 


244.0 


251.5 


259.1 



PROPERTIES OF ROLLED STRUCTURAL STEEL. 303 



Safe Load in Tons (2000 Lb.) on 14-Inch Carnegie Z-Bar 

Columns (Square Ends). (Continued) 

Section: 4 Z-bars 6 X 3/4 in. 1 Web Plate 8 X 3/ 4 in. 2 Side Plates 1 4 in . wide. 





■a- 


* 


m 


^r 


CN 


eg 


— 


— 


















o a 


m C 


o . 










o 5 
























<N . 










II » 


II & 


ll Sf 


II o- 


ll 5* 


II & 


II CO 


II S* 


7 °* 


Length of 
Column 


!-■ 


^S 


as"* 


ta ' 




$00 


fa""* 


QJ^ 


K>© 


in Feet. 


S H 


%ll 


E || 


&H J 


S ii 


53 II 


Ph ii 


Pw^ 


E ii 




OT-J2 


^_Q 




TO _Q 


W ,£3 


3 -Q 


m _Q 


2 JD 


c?:2 


















X" 


X 




T 


T 


Z 


^r 


2 


^r 


2 


■a- - 


2 


r (min.) = 


3.75 


3.76 


3.77 


3.78 


3.79 


3.80 


3.80 


3.81 


3.82 


28 
and under 


306 


316.5 


327.0 


337.5 


348.0 


358.5 


369.0 


379.5 


390.0 


30 


296.7 


307.2 


317.8 


328.3 


338.9 


349.4 


359.9 


370.5 


381.1 


32 


287.4 


297.6 


307.9 


318.2 


328.4 


338.7 


348.9 


359.1 


369.4 


34 


278.1 


288.0 


298.0 


308.0 


318.0 


327.9 


337.8 


347.8 


357.8 


36 


268.8 


278.4 


288.2 


297.9 


307.4 


317.2 


326.8 


336.4 


346.1 


38 


259.5 


268.8 


278.3 


287.7 


297.0 


306.4 


315.7 


325.1 


334.5 


40 


250.2 


2593 


268.4 


277.5 


286.5 


295.6 


304.7 


313.7 


322.8 


42 


240.9 


249.7 


258.5 


267.3 


276.1 


284.8 


293.6 


302.4 


311.2 


44 


231.6 


240.1 


248.6 


257.1 


265.6 


274.1 


282.5 


291.0 


299.6 


46 


222.4 


230.5 


238.7 


246.9 


255.1 


263.4 


271.5 


279.7 


287.9 


48 


213.0 


220.9 


228.8 


236.8 


244.7 


252.6 






276.2 


50 


203.7 


211.3 


219.0 


226.6 


234.2 


241.8 






264.6 



Section: 4 Z-bars 61/ieX 13 /l6 in. 1 Web Plate 8 X 13/16 in. 2 Side Plates 
14 in. wide. 





■o 


in 


in 


^r 


■*r 


en 


en 


<N 


OJ 












o 












00 


O 


& 


o 


o 




<N 


Ol 


en 




1-a 


II .s 


7 


k U 


" fi- 
ll - 5 


l ii-s 


•;-a 


°H -S 


N a' 

II"! 


Length of 


S3? 


CD d* 


g.S 


1 ST 


8i" 


£ cr 


s £f 


cS g* 


o* 


Column 


s^o 


3^ 


e3 a 1 


— 0O 


cjvO 


rim 


o3 — . 


^ao 


1$o 


in Feet. 


&£ 


Phvo 


5" 


Pna>" 


QLi — 


Sen 


ss 


Ph'O 


Eg 

jw II 
























xS 


x£ 


x II 


05 -Q 
X — 


X-Q 


X-' 


x£ 


x£ 


x:2 




■* 


t 


"■*■ 


1- 


^r 


■a- 


-<r 


■* 


f 


(min.) = 


3.73 


3.74 


3.75 


3.76 


3.77 


3.78 


3.78 


3.79 


3.80 


26 

and under 


327.5 


338.0 


348.5 


359.0 


369.5 


380.0 


390.5 


401.0 


411.5 


28 


326.7 


337.5 


348.5 


359.0 


369.5 


380.0 


390.5 


401.0 


411.5 


30 


316.7 


827.2 


337.7 


348.3 


358.9 


369.5 


380.0 


390.6 


401.1 


32 


306.6 


318.0 


327.2 


337.4 


347.7 


358.0 


368.2 


378.5 


388.8 


34 


296.6 


306.6 


316.6 


326.5 


336.5 


346.5 


356.4 


366.4 


376.4 


36 


286.7 


296.4 


306.0 


315.7 


325.3 


335.0 


344.7 


354.3 


364.0 


38 


276.7 


236.0 


295.4 


304.8 


314.2 


323.6 


332.9 


342.3 


351.7 


40 


266.6 


275.7 


284.8 


293.9 


303.0 


312.1 


321.2 


330.3 


339.3 


42 


256.6 


265.5 


274.3 


283.0 


291.8 


300.6 


309.4 


318.2 


327.0 


44 


246.6 


255.2 


263.6 


272.2 


280.6 


289.2 


297.6 


306.1 


314.6 


46 


236.6 


244.9 


253.0 


261.3 


269.5 


277.7 


285.8 


294.0 


302.3 


48 


226 7 


234.6 


242.5 


250.4 


258.3 


266.2 


274.1 


282.0 


290.0 


50 


216.6 


224.3 


231.9 


239.5 


247.1 


254.8 


262.3 


269.9 


277.6 



304 



STRENGTH OF MATERIALS. 



Safe Load in Tons (2000 Lb.) on 14-Inch Carnegie Z-Bar 
Columns (Square Ends). (Continued) 

Section: 4 Z-bars 61/8 X7/ 8 in. 1 Web Plate 8X7/8 in. 2 Side Plates 14 in. wide. 





0O 


00 


r^ 


r^ 


vO 


vO 


m 


ir\ 


■<r 








On" 










On' 






2d 


o 


O . 


?3 d 


Sd 


N.d 


c3 d 


(N d 


J5.s 






*!? d" 
















Length of 


03 °" 


Is 1 


w & 


|? 


II ^ 


to O* 






II £ 


Column 


^ 00 


^°" 


J^. 


r ^^ t - 


eSiW 


^S 


"cloo' 


-S^ - 


"S«m* 


in Feet. 


E«" 


£<£ 


Pnso 


ss 


£<= 


PhS 


E^ 


ss 


S^ 




x£ 


x£ 




Sll 


x£ 


2 || 

x~' 


xfi 


X- 


x~' 




<«■ 


T 


t 


^r 


f 


^ 


■>r 


T 


*r 


r (min.) = 


3.71 


3.72 


3.73 


3.74 


3.75 


3.76 


'3.77 


3.77 


3.78 


26 
and under 


349.1 


359.6 


370.1 


380.6 


391.1 


401.6 


412.1 


422.6 


433.1 


28 


347.4 


358.3 


369.1 


380.0 


390.9 


401.6 


412.1 


422.6 


433.1 


30 


336.7 


347.2 


357.9 


368.4 


378.9 


389.5 


400.1 


410.7 


421.2 


32 


326.0 


336.3 


346.6 


356.8 


367.1 


377.3 


387.6 


397.9 


408.2 


34 


315.3 


325.2 


335.2 


345.2 


355.1 


365.2 


375.2 


385.1 


395.1 


36 


304.5 


314.2 


324.0 


333.6 


343.3 


353.0 


362.7 


372.4 


382.0 


38 


293.8 


303.2 


312.6 


322.0 


331.4 


340.8 


350.2 


359.6 


369.0 


40 


283.1 


292.2 


301.3 


310.4 


319.5 


328.6 


337.7 


346.8 


355.9 


42 


272.3 


281.2 


290.0 


298.8 


307.6 


316.4 


325.2 


334.0 


342.8 


44 


261.6 


270.2 


278.7 


287.2 


295.7 


304.2 


312.7 


321.2 


329.8 


46 


250.9 


259.1 


267.4 


275.6 


283.8 


292.1 


300.3 


308.5 


316.7 


48 


240.2 


248.1 


256.1 


264.0 


272.0 


279.8 


287.8 


295.7 


303.6 


50 


229.5 


237.1 


244.8 


252.4 


260.0 


267.6 


275.3 


283.0 


290.6 



PKOPERTIES OF ROLLED STRUCTURAL STEEL. 305 



Dimensions of and Safe Loads on Carnegie Channel 
Columns, Tons (2000 Lb.). 

Column comprises 2 Channels Latticed or with 2 Side 
Plates. ' (Square Ends.) 



h 


x> 
a 


-o 1 
55 8 




15 
o 






















^ 


?« 






















w 




5,5 


o . 




So 

o 

a 


§ 


o 

M x 


T3 


5 


x> 


01 


5 


XI 

5 


s 


5 


5 


s 


3 


^ 


£ 


pq 


6 


^ 


h-1 


■51 


<~ 


M~ 


2.32 


2.32 


2.32 


2.32 


^~ 


s? 














2.33 


2.32 


2.32 


2.32 


2.32 














16 


28 6 


52.6 


58.6 


64.6 


70.6 


76.6 


82 6 


88 6 


94 6 














18 


28 1 


51.7 


57.5 


63.^ 


69.3 


75.2 


81 1 


87 f 


92 9 






8 


8 


3 7/ 8 


53/4 


20 


26 7 


49.1 


54.7 


60.3 


65.fi 


71.4 


77.( 


82 6 


88.2 














22 


25 3 


46,5 


51.6 


57.1 


62.4 


67,7 


73 f 


78.2 


83.5 




6 








24 


23.9 


43.9 


48.9 


53.9 


58.9 


63.9 


68.9 


73.9 


78.9 












r = 


2.00 


2.12 

"847 
84.2 


2.13 


2.14 


2.15 


2.16 


2.17 


2.18 


2.18 












14 
16 


54.7 
53 


90.7 
90 4 










96 7 


107.7 


108 7 


1)4 7 


120 7 


126 7 






15.5 


8 


»"'/« 


53/ 4 


18 


49.9 


79.7 85.6 


91 5 


97. A 


103 3 


109.2 


115.1 


121.0 














20 


46.8 


75.1 80.7 


86 4 


92 ,0 


97 6 


103 2 


mjt 


114.^ 














22 




70.51 75.9 


81.2 


86.5 


91.8 


97.1 


102.5 


107.8 














r = 


3.11 


3.03 


3.02 


3.01 


3.00 


2.99 


2.98 


2.98 


2.97 














































22 


40.2 


70 2 


77 7 


85 2 


92,7 


100.7 


107.7 


115 2 


122 7 














24 


39 6 


68 4 


75 5 


82 7 


89 8 


97 


104 1 


111 7, 


118 4 






Hl/4 


10 


.l/o 


71/9 


26 


33.1 


65 7 


72 6 


794 


86,3 


93.1 


100,1 


106 8 


1137 














28 


36 6 


63.1 


69 7 


76 2 


82 8 


89 3 


95 9 


107 4 


109 




8 










30 


35.2 


60.5 66.7 


73 


79 2 


85 5 


91 a 


98 


104.2 












r = 


2.77 


2.83 


2.84 


2.84 


2.84 


2.84 


2.84 


2.85 


2.85 1 












20 


75 


135 


142 5 


150 


157 5 


165 


172 5 


180 


187.5 . . . 












22 


72 9 


132 6 


140 


147 5 


154 9 


162 3 


169 8 


177 2 


184.7 ... 




211/4 


10 


51/9, 


71/9 


24 


69.8 


27 2 


134 3 


141 5 


148 6 


1557 


162,9 


l ;o,o 


177.1 ... 












26 


66.7 


21 7 


128 6 


135 4 


142.3 


149.1 


155.9 


162.8 


169.6 












28 


63.7 


116.3 


122.9 


129.4 


136.0 


142.5 


149.0 


155.6 


162.1 














r = 


3.87 




3.74 


3.72 


3.70 


3.68 


3.67 


3.65 


3.64 


3.63 












26 








107 5 


1165 


17.5 5 


134 5 


143 5 


152 5 


161 5 












28 


53 5 




98 5 


107 


1157 


124 4 


133 1 


141 8 


150 5 


159?. 












30 


52 6 




95 3 


103 7 


1122 


120 5 


128 9 


137,3 


145.7 


154 2 




15 


12 


7 


91/2 


32 


51 




92 3 


1004 


108 6 


1167 


124 8 


132.9 


141.0 


149.1 










34 


49 5 




89 3 


97.1 


105.0 


112,8 


120.6 


128.4 


136.2 


144.0 












36 


47.9 




86 3 


93 8 


101 4 


108 9 


1164 


123 9 


131 4 


139,0 


n 










38 


46.3 




83.3 


90.5 


97.8 


105.0J 


112.2 


119.4 


126.7 


133.9 










•I 


8 


dl 


8 


.8 


rif 


.8 


4 


















•2 o3 




— o3 


03 


























SE 


| S 


.SP-i 


^Ah 


^5 


§s 


s^ 












r~ 


3.35 




3.45 


3.45 


3.45 


3.45 


3.45 


3.45 


3.45 


3.45 












~?T 


123 5 




?40l 


249~5 


258~5 


2673 


2853 


3033 


3273 


339.5 












76 


121 3 




239 3 


248 2 


257.2 


266.2 


284.1 


302.1 


320.0 


338.0 












78 


117 I 




731 3 


740 


7.48 7 


257 3 


274 7 


292.1 


309.4 


326.8 




35 


12 


/ 


yi/ 2 


30 


112.9 




723 3 


731 7 


7,40 1 


748 5 


265 2 


282.0 


298.8 


315.5 












3? 


108 7 




715 4 


2?3 5 


731 6 


239 6 


255.8 


272.0 


288.1 


304.3 












34 


104 5 




207 4 


7.15 7. 


7.7.3 


730 8 


246 3 


262.0 


277.5 


293.1 








36 




. . . 199.5 


207.0 


214.5 


222.0 


236.9 


251.9 


266.9 


28 1. s> 



To above weights of column shaft add weights of rivets and lattice bars. 



306 



STRENGTH OF MATERIALS. 



Dimensions of and Safe Loads on Carnegie Channel 
Columns, Tons (3000 Lb.). 



Column comprises 2 Channels Latticed or with 2 Side 
Plates. (Square Ends.) 



c 


"53 


t3 






























a 


"^ i 






o 






















°~? 
































O 


o . 
J:2 


' 3 I 


s 


c 

6_ 


o 

if -: 
^ 


& 


"S 

5 


o> 

5 


s 


5 


"5 
5 


5 


o> 

5 


c3 

to 














r = 


4.61 




4.40 


4.38 


4.35 


4.33 


4.32 


4.30 


4.29 


4.27 












1>2 






124.9 


T35~4 


145.9 


15674 


166^9 


17774 


187.9 


198.4 












34 


72.4 




123.0 


133.0 


142.9 


152.9 


162.8 


172.8 


182.8 


192.7 












36 


70.9 




119.7 


129.4 


139.1 


148.8 


158.4 


168.1 


177.8 


187.4 


12 


201/2 


14 


8I/4 


11 1/4 


38 


69.1 




116.5 


125.9 


135.3 


144.6 


154.0 


163.4 


172.8 


182.1 












40 


67.3 




113.3 


122.4 


131.5 


140.5 


149.6 


158.7 


167.8 


176.8 












42 


65.5 




110.0 


118.8 


127.6 


136.4 


145.2 


154.0 


162.8 


171.5 












44 


63.7 




106.8 


115.3 


123.8 


132.3 


140.8 


149.3 


157.8 


166.2 
















S 


E 


5 


5 


s 


5 


■5 


5 
















"eg 

1-3 




,a> 




; 


rt" 


rt- 


jj- 


dr 

















— - — 


— — — 


— =i — 






























r = 


4.09 


4.12 


4.11 


4.11 


4.11 


4.10 


4.10 


4.10 


4.09 














30 


141.1 


277.6 


233.1 


293.6 


309.1 


330.1 


351.1 


372.1 


393.1 














32 


133.2 


272.6 


232.8 


293.0 


303.2 


323.7 


344.1 


364.6 


385.0 














34 


134.2 


264.9 


274.8 


284.8 


294.7 


314.5 


334.4 


354.2 


374.1 




12 


40 


14 


8I/4 


111/4 


36 


130.3 


257.2 


266.8 


276.5 


286.1 


305.4 


324.6 


343.9 


363.1 














33 


126.3 


249.5 


258.8 


268.2 


277.5 


296.2 


314.9 


333.5 


352.2 





































































To above weights of column shaft, add weights of rivets and lattice bars. 



Bethlehem "Special," "Girder" and "H" Steel Beams. These 
beams are rolled on the Grey universal beam mill, and have wider 
flanges than the standard American forms of I-beams, which are rolled 
in grooved rolls. The special I-beams from 8 to 24 in. in depth have 
the same section modulus or coefficient of strength as the standard 
forms, but on account of putting a larger proportion of metal in the 
flanges they are 10% lighter. For equal weights of sections they have 
a coefficient of strength about 5% greater than the standard shapes. 
The 26, 28 and 30-in. beams are respectively equal in coefficient of 
strength to two 20-in. 65 lb., two 20-in. 80 lb., and two 24-in. 80 lb. 
standard beams. 

The girder beams from 8 to 24 in. in depth have a coefficient of 
strength equal to that of two standard I-beams of minimum weight of 
the same depth, but weigh 121/2% less than the two combined. 

The rolled H, or column sections are designed especially for columns of 
buildings. All shapes having the same section number are rolled from 
the same main rolls without change. Thus the 12-in. H column is rolled 
in 35 different weights, the sectional areas ranging from 11.76 to 79.06 
sq. in. 

The flanges of the special and girder beams have a uniform slope of 
12V2%, and the flanges of the H sections a uniform slope of 2%. 



PROPERTIES OF BETHLEHEM GIRDER BEAMS. 



307 



The tables of special and girder beams give the sections and weights 
usually rolled. Intermediate and heavier weights may be obtained 
by special arrangement. The table of H columns gives only the minimum 
and maximum weights for each section number. Many intermediate 
weights are regularly made. 

The coefficients of strength given in the tables are based on a maxi- 
mum fiber stress of 16,000 lb. per sq. in., which is allowable for quies- 
cent loads, as in buildings. For moving loads the fiber stress of 12,500 
lb. per sq. in. should be used, and the coefficients reduced proportion- 
ately. For suddenly applied loads, as in railroad bridges, they should 
be still further reduced. For a fiber stress of 8000 lb. per sq. in. the 
coefficients would be one half those given in the tables. 

For further information see handbook of Structural Steel Shapes, 
Bethlehem Steel Co., South Bethlehem, Pa., 1907. 



PROPERTIES OF BETHLEHEM GIRDER BEAMS. 



8 

03 


o 

o 


O (B 
1| 

< 


'o . 


be 

a 

s 

o o 
G 

rG 1 "" 1 

T3 


Neutral Axis 
Perpendicular to 
Web at Center. 


Coeffic'nts of Strength 

for Fiber Stz-ess of 

~ 16,000 Lbs. per Sq. 

In. for Buildings. 


rj O • 
x = — 

!£" 

X G 
o3 O 


Neutral 
Axis Coinci- 
dent with 
Center Line 
of Web. 


Q 


G oj 
CD •- 

1 s 

I 


3 >>G 

IS'l 

r 


s 


a os 

§ ° v 

V 




30 

30 


200.0 
175.0 


58.85 
51.35 


0.75 

.68 


15.00 
12.00 


9154.7 
7851.8 


12.47 
12.37 


610.3 
523.5 


6,510,000 
5,583,500 


95.2 
81.1 


599.7 

346.4 


3.19 
2.60 


28 
28 


180.0 
162.5 


52.98 
47.81 


.69 
.65 


14.35 
12.00 


7269.0 
6465 . 1 


11.72 
11.63 


519.2 
461.8 


5,538,200 
4,925,800 


81.3 
73.8 


507.6 
328.2 


3.09 
2.62 


26 
26 


160.0 
150.0 


47.00 
44.13 


.63 
.62 


13.60 
12.00 


5618.7 
5200.4 


10.93 
10.86 


432.2 
400.0 


4,610,200 
4,267,000 


68.3 
66.6 


414.5 
306.5 


2.97 
2.63 


24 
24 


140.0 
120.0 


41.03 
35.31 


.56 
.51 


13.00 
12.00 


4241.9 
3630.7 


10.17 

10.14 


353.5 
302.6 


3,770,700 
3,227,200 


54.9 
46.5 


338.3 
240.0 


2.87 
2.61 


20 
20 


140.0 
112.0 


41.28 
32.88 


.64 
.52 


12.50 
12.00 


2938.3 
2368.9 


8.44 
8.49 


293.8 
236.9 


3,134,200 
2,526,700 


62.4 
45.6 


334.3 
232.8 


2.85 
2.66 


18 


92.0 


27.09 


.47 


11.50 


1595.3 


7.67 


177.3 


1,890,800 


37.1 


172.4 


2.52 


15 

15 
15 


140.0 
104.0 
73.0 


41.28 
30.58 
21.52 


.80 
.60 

.42 


11.75 
11.25 
10.50 


1591.5 
1219.7 
886.5 


6.21 
6.32 
6.42 


212.2 
162.6 
118.2 


2,263,500 
1,734,700 
1,260,900 


67.3 
47.4 
28.8 


319.2 
203.3 
116.6 


2.78 
2.58 
2.33 


12 

12 


70.0 
55.0 


20.60 
16.12 


.445 
.35 


10.00 
9.75 


540.9 
432.0 


5.12 
5.18 


90.2 
72.0 


961,600 
768,000 


28.0 

19.7 


109.5 
76.1 


2.31 
2.17 


10 
9 
8 


44.0 
38.0 
32.5 


12.95 
11.18 
9.52 


.30 
.29 

.28 


9.00 
8.50 
8.00 


244.3 
169.8 
113.9 


4.34 
3.90 
3.46 


48.9 
37.7 

28.5 


521,200 
402,500 
303,800 


14.3 
12.8 
11.4 


53.6 

40.7 
30.3 


2.03 
1.91 
1.78 



W = Safe load in pounds uniformly distributed including weight of beam. 
L = Span in feet. M = Moment offerees in foot-pounds. /= fiber stress, 
W= C/L; M = C/8 ; C = WL = 8 M = 2/ 3 fS, 



308 



STRENGTH OF MATERIALS. 



Properties of Bethlehem Sp2cial I Beams. 



s 

ffl i 


o 

o ■ 


O <u 

0) fl 

02 h-1 

< 


o 

H 


a 


Neutral Axis 
Perpendicular to 
Web at Center. 


Coeffic'ntsof Strength 

for Fiber Stress of 

O 16,000 Lbs. per Sq. 

In. for Buildings. 


02.S 

3 0-^ 
cS go 


Neutral 
Axis Coin- 
cident with 
Center Line 

of Web. 


° c 

03 

Q 


<x> .5 

o o> 

i 


r 


.0,3 . 

z : ~ 

S 


1 i 
i' 


2 >A 
r' 


30 

28 
26 
24 


120.0 
105.0 
90.0 
84.0 


35.25 
31.04 
26.63 
24.79 


0.52 
.48 
.44 

.45 


10.00 
9.60 
9.15 
8.85 


5271 
4089 
3043 
2392 


12.23 
11.43 
10.71 
9.82 


351.4 
292.1 
234.1 
199.3 


3,748,200 
3,115,700 
2,496,900 
2,125,900 


48.7 
41.5 
34.9 
36.3 


149.7 
122.6 
93.4 
82.0 


2.11 
1.98 
1.87 
1.82 


24 
24 


82.0 
72.0 


24.33 
21.21 


.50 
.37 


8.83 
8.70 


2240 
2091 


9.60 
9.93 


186.7 
174.2 


1,991,600 
1,858,100 


43.8 
24.4 


71.1 
67.7 


1.71 
1.79 


20 
20 


82.0 
72.0 


24.23 
21.43 


.57 
.43 


8.51 
8.37 


1561 
1468 


8.03 
8.28 


156.1 
146.8 


1,665,400 
1,565,800 


51.5 
32.7 


71.5 
67.6 


1.72 
1.78 


20 
20 
20 
20 


68.0 
63.0 
60.0 
58.5 


19.95 

18.55 
17.65 
17.15 


.49 
.42 
.375 
.35 


7.69 
7.62 
7.58 
7.55 


1270 
1223 
1193 
1176 


7.98 
8.12 
8.22 
8.28 


127.0 
122.3 
119.3 
117.6 


1,354,600 
1,304,500 
1,272,600 
1,254,800 


40.4 
31.1 
25.3 

22.2 


45.7 
44.3 
43.4 
43.0 


1.51 
1.54 
1.57 

1.58 


18 
18 
18 


58.5 
52.5 
48.5 


17.29 
15.40 
14.23 


.48 
.373 
.31 


7.47 
7.37 
7.30 


883.6 
832.9 
801.3 


7.15 
7.35 
7.50 


98.2 
92.5 
89.0 


1,047,500 
987,200 
949,800 


37.4 
24.8 
17.4 


35.9 
34.4 
33.4 


1.44 
1.49 
1.53 


15 


72.0 


21.27 


.54 


7.15 


797.9 


6.13 


106.4 


1,134,800 


41.2 


55.1 


1.61 


15 
15 


64.0 
54.0 


18.85 
15.85 


.60 
.40 


7.20 
7.00 


666.8 
610.5 


5.95 
6.21 


88.9 
81.4 


948,100 
868,100 


46.6 
26.5 


40.8 
37.2 


1.47 
1.53 


15 
15 
15 


46.0 
42.0 
38.0 


13.46 
12.41 
11.21 


.43 
.36 

.28 


6.81 
6.74 
6.66 


484.6 
464.9 
442.4 


5.99 
6.12 
6.28 


64.6 
62.0 
59.0 


689,200 
661,200 
629,200 


29.1 
22.1 
14.2 


24.2 
23.4 
22.5 


1.34 
1.37 
1.42 


12 


36.0 


10.63 


.31 


6.30 


270.2 


5.04 


45.0 


480,300 


16.2 


20.4 


1.38 


12 
12 


31.0 
28.5 


9.13 
8.41 


.31 

.25 


6.16 
6.10 


225.2 
216.6 


4.97 
5.07 


37.5 
36.1 


400,300 
385,000 


16.0 
11.2 


14.7 
14.2 


1.27 
1.30 


10 
10 
10 


27.5 
24.5 
22.5 


8.05 
7.15 
6.65 


34 
.25 
.20 


5.94 
5.85 
5.80 


134.6 
127.1 
122.8 


4.09 
4.22 
4.27 


26.9 
25.4 
24.6 


287,300 
271,300 
262,000 


16.7 
10.6 
7.3 


11.7 
11.1 
10.8 


1.20 
1.24 
1.27 


9 
9 
9 


23.0 
21.0 
19.0 


6.76 
6.22 
5.68 


.31 
.25 
.19 


5.50 

5.44 
5.38 


92.4 

88.8 
85.1 


3.70 
3.78 
3.87 


20.5 
19.7 

18.9 


219,100 
210,300 
201,800 


13.8 
10.0 
6.5 


8.5 
8.2 
7.9 


1.12 
1.15 
1.18 


8 
8 
8 


21.25 
18.00 
16.25 


6.25 
5.37 
4.81 


.36 
.25 
.18 


5.37 
5.26 
5.19 


64.7 
60.0 
57.0 


3.22 
3.34 

3.44 


16.2 
15.0 
14.3 


172,500 
160,000 
152,000 


15.3 
9.5 
5.7 


6.8 
6.4 
6.1 


1.05 
1.09 
1.12 



W =Safe load in pounds uniformly distributed including weight of beam. 
L = Span in feet. M= Moment of forces in foot-pounds. / = fiber stress. 
C = Coefficients given in the table. 
W =C/L; M = CIS; C = WL = 8M = 2/ 3 /£. 



PROPERTIES OF BETHLEHEM GIRDER BEAMS. 



309 



Dimensions and Properties of Bethlehem Rolled Steel. 
14-Ineh H Columns. 

Table greatly condensed from original.* 





3" 


Dimensions in 


a 


Axis Perpen. to 


Axis Center of 


fl3 






Inches. 


2 »3 


Web. 




Web. 


J2 
B 
3 

3 

o 

01 

m 


18 

o§3 

1- 
'53^ 






oj"S 








.3 
a 

CD 

Q 


03 M 




i— * 

3 0j 


is 


3 

Jl 


.2 
- * 


B ® 

O 3 


.2-2 


It 


H14s 


42.6 


133/ 8 


V? 


8.00 


0.33 


12.53 


400.8 


59.9 


5.66 


43.6 


10.9 


1.87 


93.7 


14 


13/16 


13.00 


.51 


27.56 


1004.7 


143.5 


6.04 


288.5 


44.4 


3.24 


H14 


98.8 


14 


13/1 fi 


14.00 


.51 


29.06 


1070.6 


153.0 


6.07 


355.9 


50.8 


3.50 


162.2 


15 


I -Vie 


14.31 


.82 


47.71 


1894.0 


252.5 


6.31 


625.1 


87.4 


3.62 


H14a 


164.4 


15 


1 5/1 B 


14 57 


87, 


48 36 


1924.7 


256.6 


6 32 


659.8 


90.6 


3.69 


222.3 


157/ 8 


1 3/ 4 


14.84 


1.09 


65.39 


2774.5 


349.5 


6.51 


936.6 


126.2 


3.78 


H14b 


230.8 


16 


1 13/1 fi 


14 88 


1 13 


67 89 


2905.9 


363.2 


6 55 


978.7 


131.5 


3.80 


291.2 


167/ 8 


2 1/4 


15.16 


1.41 


85.63 


3897.7 


462.0 


6.75 


1290.7 


170.3 


3.88 



13-Inch H Columns. 



41.2 
86.6 


123/g 
13 


1/2 
13/16 


8.00 
12.04 


0.33 
.51 


12.12 

25.48 


334.5 
793.6 


54.1 
122.1 


5.25 
5.58 


43.2 
229.9 


10.8 
38.2 


91.5 
150.5 


13 
14 


13/16 
1 5/16 


13.00 
13.31 


.51 
.82 


26.93 
44.27 


847.9 
1511.4 


130.5 
215.9 


5.61 

5.84 


286.7 
504.9 


44.1 
75.9 


156.4 
219.8 


14 
15 


1 5/ie 
1 13/16 


14.00 
14.31 


.82 

1.13 


45.99 
64.64 


1581.6 
2404.9 


225.9 
320.7 


5.86 
6.10 


585.1 
870.2 


83.6 
121.6 


226.5 
285.9 


15 

157/ 8 


1 13/16 

2 1/4 


14.88 
15.16 


1.13 
1.41 


66.62 
84.09 


2492.7 
3361.9 


332.4 
423.6 


6.12 
6.32 


975.8 
1287.6 


131.2 
169.9 



12-Inch H Columns. 



40.0 
73.4 


111/2 
12 


1/2 
3/4 


8.00 
11.04 


0.33 
.47 


78.0 
132.5 


12 
13 


3/4 
11/4 


12.00 
12.31 


.47 
.78 


138.1 
197.1 


13 
14 


11/4 
13/4 


13.00 
13.31 


.78 
1.09 


204.9 
268.8 


14 
15 


13/4 

21/4 


14.00 
14.32 


1.09 
1.41 



11.76 
21.60 



40.61 
57.96 



60.27 
79.06 



282.1 
572.8 



1198.8 
1862.2 



1950.8 
2777.0 



41.9 
95.5 



102.6 
175.6 



184.4 
266.0 



278.7 
370.3 



42.8 
163.7 



446.4 
676.6 



784.8 
1086.2 



* Only the minimum and maximum weights of each section number 
are given here. The original table gives many intermediate weights. 



310 



STRENGTH OF MATERIALS. 



Dimensions and Properties of Bethlehem Rolled Steel. 
11-Ineh H Columns. 



J2 


o 

01 o 

'o £ 
•g ft 

'IS 


Dimensions in 
Inches. 






Axis 


Perpen. to 

Web. 


Axis 


Center of 
Web. 


a 
m 


ft 
& 




8) 

«° 

8.00 
10.03 

11.00 
11.31 

12.00 
12.32 


0.32 
.43 

.43 

.74 

.74 

1.06 


%£ 

v If 

as 
£L M 

234.1 
401.2 

434.6 
843.1 

889.4 
1417.0 


3 

"S o 
l § 

44.1 
73.0 

79.0 
140.5 

148.2 
218.0 


oo 






11 


HI1 s 

H1I 

Hlla 


38.4 
61.3 

65.5 
115.5 

120.9 
175.8 


I05/ 8 
11 

11 
12 

12 
13 


1/2 
U/16 

H/16 
• 3 /l6 

1 3/ie 
Hl/16 


11.30 

18.02 

19.26 
33.98 

35.54 
51.70 


4.55 
4.72 

4.75 
4.98 

5.00 

5.24 


42.4 
112.6 

147.0 
280.7 

333.5 
517.9 


10.6 

22.4 

26.7 
49.6 

55.6 
84.1 


1.94 
2.50 

2.76 
2.87 

3.06 
3.17 











10-Inch H Columns. 










HlOs 


37.2 
50.6 


9 3/ 4 
10 


1/2 
5/8 


8.00 
9.04 


0.32 
.40 


10.95 

14.88 


192.0 
272.5 


39.4 
54.5 


4.19 

4.28 


41.9 
75.1 


,0.5 
16.6 


1.96 
2.25 


H10 


54.1 
99.7 


10 

11 


5/8 
H/8 


10.00 
10.31 


.39 
.70 


15.91 
29.32 


296.8 
'607.0 


59.4 
110.4 


4.32 
4.55 


100.4 
201.7 


20.1 
39.1 


2.51 
2.62 


HlOa 


104.7 
155.2 


11 

12 


H/8 
15 /8 


11.00 
11.32 


.70 

1.02 


30.80 
45.64 


643.6 
1053.6 


117.0 
175.6 


4.57 
4.80 


243.7 
387.2 


44.3 
68.4 


2.81 
2.91 











9-Inch H Columns. 










H9s 


28.8 
40.6 


8 3/ 4 
9 


7/16 
9/16 


7.00 
8.04 


0.28 
.36 


8.46 
11.95 


119.3 
177.0 


27.3 
39.3 


3.76 
3.85 


24.7 
47.6 


7.0 
11.8 


1.71 
2.00 


H9 


43.8 
85.3 


9 
10 


9/16 
U/16 


9.00 
9.32 


.35 
.67 


12.88 
25.08 


194.7 
424.6 


43.3 
84.9 


3.89 
4.11 


65.9 
140.9 


14.6 
30.2 


2.26 
2.37 


H9a 


90.0 
135.6 


10 
11 


U/16 
19/16 


10.00 
10.31 


.67 
.98 


26.46 
39.87 


452.6 
762.8 


90.5 
138.7 


4.14 
4.38 


173.1 
281.6 


34.6 
54.6 


2.56 
2.66 



8-Inch H Columns. 



27.7 
31.8 


77/g 
8 


7/16 

1/2 


7.00 
7.04 


0.28 
.32 


8.15 
9.35 


93.6 
109.1 


23.8 
27.3 


3.39 
3.42 


24.4 
28.5 


7.0 
8.1 


34.6 
71.6 


8 
9 


1/2 
1 


8.00 
8.32 


.31 
.63 


10.17 
21.05 


121.5 
285.6 


30.4 
63.5 


3.46 
3.68 


41.1 
94.4 


10.3 

22.7 


76.0 
117.1 


9 
10 


1 

11/2 


9.00 
9.31 


.63 
.94 


22.35 
34.45 


306.8 
535.9 


68.2 
107.2 


3.70 
3.94 


118.9 
199.3 


26.4 
42.8 



TORSIONAL STRENGTH. 311 



TORSIONAL STRENGTH, 

Let a horizontal shaft of diameter = d be fixed at one end, and at the 
other or free end, at a distance = I from the fixed end, let there be fixed 
a horizontal lever arm with a weight = P acting at a distance = a from 
the axis of the shaft so as to twist it; then Pa = moment of the applied 
force. 

Resisting moment = twisting moment = SJ/c, in which S = unit 
shearing resistance,. J = polar moment of inertia of the section with 
respect to the axis,- and c = distance of the most remote fiber from the 
axis, in a cross-section. For a circle with diameter d 

c = 1/2 d; 




StITp 

3 s; ^=y-s" 



For hollow sMafts of external diameter d and internal diameter d lt 
Pa = 0.1963 ,, * S; d 



For a rectangular bar in which b and d are the long and short sides of 
the rectangle, Pa = 0.2222 bd 2 S; and for a square bar with side d, Pa = 
0.2222 d s S. (Merriman, "Mechanics of Materials," 10th ed.) 

The above formulae are based on the supposition that the shearing 
resistance at any point of the cross-section is proportional to its distance 
from the axis; but this is true only within the elastic limit. In mate- 
rials capable of flow, while the particles near the axis are strained within 
the elastic limit those at some distance within the circumference may be 
strained nearly to the ultimate resistance, so that the total resistance is 
something greater than that calculated by the formulae. For working 
strength, however, the formulae may be used, with S taken at the safe 
working unit resistance. 

The ultimate torsional shearing resistance S is about the same as the 
direct shearing resistance, and may be taken at 20,000 to 25,000 lbs. per 
square inch for cast iron, 45,000 lbs. for wrought iron, and 50,000 to 
150,000 lbs. for steel, according to its carbon and temper. Large factors 
of safety should be taken, especially when the direction of stress is re- 
versed, as in reversing engines, and when the torsional stress is com- 
bined with other stresses, as is usual in shafting. (See "Shafting.") 

Elastic Resistance to Torsion. — Let I = length of bar being 
twisted, d = diameter, P = force applied at the extremity of a lever arm 
of length = a, Pa = twisting moment, G = torsional modulus of elas- 
ticity, 6 = angle through which the free end of the shaft is twisted, 
measured in arc of radius = 1. 

For a cylindrical shaft, 

_ n6Gd\ ._ 32 Pal . 32 Pal . 32 

Fa -"32T' d -~nd*G' G -~e^F' v- 10 - 186 - 
If a = angle of torsion in degrees, 

_a^. 180 6 180 X 32 Pal _ 583.6 Pal 

~ 180' a it nWG d 4 G 

The value of G is given by different authorities as from 1/3 to 2/5 of E, 
the modulus of elasticity for tension. For steel it is generally taken as 
12,000,000 lbs. per sq. in. 



312 STRENGTH OF MATERIALS. 



COMBINED STRESSES. 

Combined Tension and Flexure. — Let A = the area of a bar 
subjected to both tension and flexure, P = tensile stress applied at the 
ends, P -5- A = unit tensile stress, S = unit stress at the fiber on the 
tensile side most remote from the neutral axis, due to flexure alone, then 
maximum tensile unit stress = (P -s- A) + S. A beam to resist com- 
bined tension and flexure should be designed so that (P -f- A) \ + S shall 
not exceed the proper allowable working unit stress. 

Combined Compression and Flexure. — If P -s- A = unit stress 
due to compression alone, and S = unit compressive stress at fiber most 
remote from neutral axis, due to flexure -alone, then maximum compres- 
sive unit stress = (P -h A) + S. 

Combined Tension (or Compression) and Shear. — If applied 
tension (or compression) unit stress = p, applied shearing unit stress = v, 
then from the combined action of the two forces 

Max. S = ± vV+ V4P 2 , Maximum shearing unit stress; 
Max. t = V2P+^v 2 4- 1/4P 2 , Maximum tensile (or compressive) unit stress. 
Combined Flexure and Torsion. — If S = greatest «unit stress due 
to flexure alone, and S s = greatest torsional shearing. unit stress due to 
torsion alone, then for the combined stresses 

Max. tension or compression unit stress t = V2S 4- V ' S s 2 + 1/1S 2 ; 
Max. shear s = ±^S S 2 + 1/4SP. 

Equivalent bending moment = 1/2 M 4- 1/2 ^ M 2 + T 2 , where M = bending 
moment and T= torsional moment. 

Formula for diameter of a round shaft subjected to transverse load 
while transmitting a given horse-power (see also Shafts of Engines): 



31 , 16 ./A 



16 M , 16 JM 2 , 402,500,000/7 2 

d 3 = — h -r Vt ^ 9 ' 

* n 2 n 2 



where M = maximum bending moment of the transverse forces in 
pound-inches, H = horse-power transmitted, n = No. of revs, per minute, 
and t = the safe allowable tensile or compressive working strength of 
the material. 

Gues t's For mula for maximum tension or compression unit stress is 
t = *SS S 2 +S 2 {Phil. Mag., July, 1900). It is claimed by many writers to 
be more accurate th an Ran kine's formula, given above. Equivalent 
bending moment = v'mHP. (Eng'g., Sept. 13 and 27, 1907; July 10, 
1908; April 23, 1909.) 

Combined Compression and Torsion. — For a vertical round shaft 
carrying a load and also transmitting a given horse-power, the result- 
ant maximum compressive unit stress 

7id z " n 2 d 2 rM* 

in which P is the load. From this the diameter d may be found when t 
and the other data are given. 

Stress due to Temperature. — Let I = length of a bar, A = its sec- 
tional area, c = coefficient of linear expansion for one degree, t = rise or 
fall in temperature in degrees, E = modulus of elasticity, A the change 
of length due to the rise or fall t; if the bar is free to expand or contract, 
A = dl. 

If the bar is held so as to prevent its expansion or contraction the 
stress produced by the change of temperature = S = ActE. The fol- 
lowing are average values of the coefficients of linear expansion for a 
change in temperature of one degree Fahrenheit: 

For brick and stone a = 0.0000050, 

For cast iron a = 0.0000056, 

For wrought iron and steel.. ..(=0.0000065. 



STRENGTH OF FLAT PLATES. 313 



The stress due to temperature should be added to or subtracted from 
the stress caused by other external forces according as it acts to increase 
or to relieve the existing stress. 

What stress will be caused in a steel bar 1 inch square in area by a 
change of temperature of 100° F.? S = ActE = 1 X 0.0000065 X 100 X 
30,000,000 = 19,500 lbs. Suppose the bar is under tension of 19,500 
lbs. between rigid abutments before the change in temperature takes 
place, a cooling of 100° F. will double the tension, and a heating of 100° 
will reduce the tension to zero. 



STRENGTH OF FLAT PLATES. 

For a circular plate supported at the edge, uniformly loaded, according 
to Grashof, 

5r 2 , t/ErZp 6 ft 2 

For a circular plate fixed at the edge, uniformly loaded, 



t/2£5- p , 

▼ 3 / ' p 



_w.. 

' 3f 2 i 



in which / denotes the working stress; r, the radius in inches; t, the thick- 
ness in inches; and p, the pressure in pounds per square inch. 
For mathematical discussion, see Lanza, "Applied Mechanics." 
Lanza gives the following table, using a factor of safety of 8, with ten- 
sile strength of cast iron 20,000, of wrought iron 40,000, and of steel 80,000: 

Supported. Fixed. 

Cast iron t = 0.0182570 r Vp t = 0.0163300 r ^p_ 

Wrought iron t = 0.0117850 r \ / p_ t = 0.^)105410 r ^p 

Steel t = 0.0091287 r Vp t = 0.0081649 r ^p 

For a circular plate supported at the edge, and loaded with a concen- 
trated load P applied at a circumference the radius of_ which is r : 



\6 7 / Ttt* Ttt" 




- = 10 20 30 40 


50; 


c = 4.07 5.00 5.53 5.92 


6.22; 


f=V /cP p = ^. 





The above formulse are deduced from theoretical considerations, and 
give thicknesses much greater than are generally used in steam-engine 
cylinder-heads. (See empirical formulae under Dimensions of Parts of 
Engines.) The theoretical formula seem to be based on incorrect or 
incomplete hypotheses, but they err in the direction of safety. 

Thickness of Flat Cast-iron Plates to resist Bursting Pressures. 
■ — ■ Capt. John Ericsson (Church's Life of Ericsson) gave the following 
rules: The proper thickness of a square cast-iron plate will be obtained 
by the following: Multiply the side in feet (or decimals of a foot) by 
1/4 of the pressure in pounds and divide by 850 times the side in inches; 
the quotient is the square of the thickness in inches. 

For a circular plate, multiply 11-14 of the diameter in feet by 1/4 of 
the pressure on the plate in pounds. Divide by 850 times 11-14 of the 
diameter in inches. [Extract the square root.] 



314 STRENGTH OF MATERIALS. 



Prof. Wm. Harkness, Eng'g News, Sept. 5, 1895, shows that these rules 
can be put in a more convenient form, thus: For square plates T = 
0.00495 S Vp, and for circular plates T = 0.00439 flVp, where T = 
thickness of plate, S = side of the square, D = diameter of the circle, 
and p = pressure in lbs. per sq. in. Professor Harkness, however, 
doubts the value of the rules, and says that no satisfactory theoretical 
solution has yet been obtained. 

The Strength of Unstayed Flat Surfaces. — Robert Wilson 
(Eng'g, Sept. 24, 1877) draws attention to the apparent discrepancy 
between the results of theoretical investigations and of actual experi- 
ments on the strength of unstayed flat surfaces of boiler-plate, such as 
the unstayed flat crowns of domes and of vertical boilers. 

On trying to make the rules given by the authorities agree with the 
results of his experience of the strength of unstayed flat ends of cylin- 
drical boilers and domes that had given way after Ion? use, Mr. Wilson 
was led to believe that the rules give the breaking strength much lower 
than it actually is. He describes a number of experiments made by 
Mr. Nichols of Kirkstall, which gave results varying widely from each 
other, as the method of supporting the edges of the plate was varied, 
and also varying widely from the calculated bursting pressures, the 
actual results being in all cases very much the higher. Some conclusions 
drawn from these results are: 

1. Although the bursting pressure has been found to be so high, boiler- 
makers must be warned against attaching any importance to this, since 
the plates deflected almost as soon as any pressure was put upon them 
and sprang back again on the pressure being taken off. This springing 
of the plate in the course of time inevitably results in grooving or chan- 
neling, which, especially when aided by the action of the corrosive acids 
in the water or steam, will in time reduce the thickness of the plate, and 
bring about the destruction of an unstayed surface at a very low pressure. 

2. Since flat plates commence to deflect at very low pressures, they 
should never be used without stays; but it is better to dish the plates 
when they are not stayed by flues, tubes, etc. 

3. Against the commonly accepted opinion that the limit of elasticity 
should never be reached in testing a boiler or other structure, these ex- 
periments show that an exception should be made in the case of an un- 
stayed flat end-plate of a boiler, which will be safer when it has assumed 
a permanent set that will prevent its becoming grooved by the continual 
variation of pressure in working. The hydraulic pressure in this case 
simply does what should have been done before the plate was fixed, 
that is, dishes it. 

4. These experiments appear to show that the mode of attaching by 
flange or by an inside or outside angle-iron exerts an important influence 
on the manner in which the plate is strained by the pressure. 

When the plate is secured to an angle-iron, the stretching under pres- 
sure is, to a certain extent, concentrated at the line of rivet-holes, and 
the plate partakes rather of a beam supported than fixed round the edge. 
Instead of the strength increasing as the square of the thickness, when 
the plate is attached by an angle-iron, it is probable that the strength 
does not increase even directly as the thickness, since the plate gives 
way simply by stretching at the rivet-holes, and the thicker the plate, 
the less uniformly is the strain borne by the different layers of which the 
plate may be considered to be made up. When the plate is flanged, the 
flange becomes compressed by the pressure against the body of the plate, 
and near the rim, as shown by the contrary flexure, the inside of the plate 
is stretched more than the outside, and it may be by a kind of shearing 
action that the plate gives way along the line where the crushing and 
stretching meet. 

5. These tests appear to show that the rules deduced from the theo- 
retical investigations of Lame\ Rankine, and Grashof are not confirmed 
by experiment, and are therefore not trustworthy. 

The rules of Lame, etc., applv only within the elasiic limit. (Eng'g, 
Dec. 13, 1895.) 

Unbraced Wrought-iron Heads of Boilers, etc. (The Locomo- 
tive, Feb., 1890). — Few experiments have been made on the strength 
of flat heads, and our knowledge of them comes largely from theory. 
Experiments have been made on small plates Vi6 of an inch thick, 



STRENGTH OF FLAT PLATES. 315 

yet the data so obtained cannot be considered satisfactory when we 
consider the far thicker heads that are used in practice, although the 
results agreed well with Rankine's formula. Mr. Nichols has made ex- 
periments on larger heads, and from them he has deduced the following 
rule: "To find the proper thickness for a flat unstayed head, multiply 
the area of the head by the pressure per square inch that it is to bear 
safely, and multiply this by the desired factor ot safety (say 8): then 
divide the product by ten times the tensile strength of the material 
used for the head." His rule for finding the bursting pressure when the 
dimensions of the head are given is: "Multiply the thickness of the end- 
plate in inches by ten times the tensile strength of the material used, 
and divide the product by the area of the head in inches." 

In Mr. Nichols's experiments the average tensile strength of the iron 
used for the heads was 44,800 pounds. The results he obtained are 
given below, with the calculated pressure, by his rule, for comparison. 

1. An unstayed flat boiler-head is 341/2 inches in diameter and 9/ ]6 
inch thick. What is its bursting pressure? The area of a circle 341/2 
inches in diameter is 935 square inches: then 9/i6 x 44,800 X 10 = 
252,000, and 252,000 -*- 935 = 270 pounds, the calculated bursting 
pressure. The head actually burst at 280 pounds. 

2. Head 341/2 inches in diameter and 3/ 8 inch thick. The area = 935 
square inches; then, 3/ 8 x 44,800 X 10 = 168,000, and 168,000 +- 935 
= 180 pounds, calculated bursting pressure. This head actually burst 
at 200 pounds. 

3. Head 26 1/4 inches in diameter, and 3/ 8 inch thick. The area 541 
square inches; then, 3/ 8 x 44,800 X 10 = 168,000, and 168,000 -^ 541 
= 311 pounds. This head burst at 370 pounds. 

4. Head 28 1/2 inches in diameter and 3/ 8 inch thick. The area = 638 
square inches; then, 3/ 8 x 44,800 X 10 = 168,000, and 168,000 -*- 638 
= 263 pounds. The actual bursting pressure was 300 pounds. 

In the third experiment, the amount the plate bulged under different 
pressures was as follows: 

At pounds per sq. in. . 
Plate bulged 



10 


20 


40 


80 


120 


140 


170 


200 


L/32 


1/16 


1/8 


1/4 


3/8 


1/2 


5/8 


3/4 



The pressure was now reduced to zero, and the end sprang back 3/ 16 
inch, leaving it with- a permanent set of 9/ 16 inch. The pressure of 
200 lbs. was again applied on 36 separate occasions during an interval of 
five days, the bulging and permanent set being noted on each occasion, 
but without any appreciable difference from that noted above. 

The experiments described were confined to plates not widely different 
in their dimensions, so that Mr. Nichols's rule cannot be relied upon for 
heads that depart much from the proportions given in the examples. 

Strength of Stayed Surfaces. — A flat plate of thickness t is sup- 
ported uniformly by stays whose distance from center to center is a, 
uniform load p lbs. per square inch. Each stay supports pa 2 lbs. The 
greatest stress on the plate is 



' 9P ' 

For additional matter on this subject see strength of Steam Boilers. 

Stresses in Steel Plating due to Water-pressure, as in plating of 
vessels and bulkheads {Engineering, May 22, 1891, page 629). 

Mr. J. A. Yates has made calculations of the stresses to which steel 
plates are subjected by external water-pressure, and arrives at the 
following conclusions: 

Assume 2a inches to be the distance between the frames or other 
rigid supports, and let d represent the depth m feet, below the surface 
of the water, of the plate under consideration, t = thickness of plate in 
inches, D the deflection from a straight line under pressure in inches, 
and P = stress per square inch of section. 

For outer bottom and ballast-tank plating, a = 420 t/d, D should not 
be greater than 0.05 X 2 a/12, and P/2 not greater than 2 to 3 tons; 
while for bulkheads, etc., a = 2352 t/d, D should not be greater than 



316 



STRENGTH OF MATERIALS. 



0.1 X 2 a/ 12, and P/2 not greater than 7 tons. To illustrate the appli- 
cation of these formulae the following cases have been taken: 



For Outer Bottom, etc. 


For Bulkheads, etc. 


Thick- 


Depth 


Spacing of 


Thick- 


Depth of 
Water. 


Maximum Spac- 


ness of 


below 


Frames should 


ness of 


ing of Rigid 


Plating. 


Water. 


not exceed 


Plating. 


Stiff en ers. 


in. 


ft. 


in. 


in. 


ft. 


ft. in. 


V2 


20 


About 2 1 


1/2 


20 


9 10 


1/2 


10 


" 42 


3/8 


20 


7 4 


3/8 


18 


" 18 


3/8 


10 


14 8 


3/8 


9 


" 36 


1/4 


20 


4 10 


1/4 


10 


" 20 


1/4 


10 


9 8 


1/4 


5 


" 40 


1/8 


10 


4 10 



It would appear that the course which should be followed in stiffening 
bulkheads is to fit substantially rigid stiffening frames at comparatively 
wide intervals, and only work such light angles between as are necessary 
for making a fair job of the bulkhead. 



SPHERICAL SHELLS AND DOMED BOILER-HEADS. 

To find the Thickness of a Spherical Shell to resist a given 
Pressure. — Let d = diameter in inches, and p the internal pressure 
per square inch. The total pressure which tends to produce rupture 
around the great circle will be V4^d' 2 p. Let *S' = safe tensile stress per 
square inch, and t the thickness of metal in inches; then the resistance 
to the pressure will be ndt S. Since the resistance must be equal to the 
pressure, 

1/4 7td 2 p = 7tdtS. Whence t = £| . 

The same rule is used for finding the thickness of a hemispherical head 
to a cylinder, as of a cylindrical boiler. 

Thickness of a Domed Head of a Boiler. — If S = safe tensile 
stress per square inch, d = diameter of the shell in inches, and t = thick- 
ness of the shell, t = pd h- 25; but the thickness of a hemispherical 
head of the same diameter is t = pd -*- AS. Hence if we make the 
radius of curvature of a domed head equal to the diameter of the boiler, 

we shall have t = -j~ = -^ , or the thickness of such a domed head 

will be equal to the thickness of the shell. 



THICK HOLLOW CYLINDERS UNDER TENSION. 

Lamp's formula, which is generally used, gives 



f ( h + p \h 
l \\T^p) 



h = P : 



t = thickness; n= inside and ri = outside radius; 
h = maximum allowable hoop tension at the 

interior of the cylinder; 
p = intensity of interior pressure; 
s = tension at the exterior of the cylinder. 



•■ p - 



2n 2 



STEEL ROLLERS AND BALLS. 317 



Example: Let maximum unit stress at the inner edge of the annulus 
= 8000 lbs. per square inch, radius of cylinder = 4 inches, interior 
pressure = 4000 lbs. per square inch. Required the thickness and the 
tension at the exterior surface. 

s = p 9 2n , = 4000 X .J? X \ 6 g = 4000 lbs. per sq. in. 
T2 2 — TV 48-16 

For short cast-iron cylinders, such as are used in hydraulic presses, it is 
doubtful if the above formulae hold true, since the strength of the cylindri- 
cal portion is reinforced by the end. In that case the strength would be 
higher than that calculated by the formula. A rule used in practice 
for such presses is to make the thickness = Vio of the inner circum- 
ference, for pressures of 3000 to 4000 lbs. per square inch. 

Hooped Cylinders. — For very high pressures, as in large guns, hoops 
or outer tubes of forged steel are shrunk on inner tubes, thus bringing a 
compressive stress on the latter which assists in resisting the tension due 
to the internal pressure. For discussion of Lame's, and other formulae 
for built-up guns, see Merriman's "Mechanics of Materials." 

THIN CYLINDERS UNDER TENSION. 

Let p = safe working pressure in lbs. per sq. in.; 
d = diameter in inches; 

T = tensile strength of the material, lbs. per sq. in.; 
t = thickness in inches; 
/ = factor of safety ; 
c = ratio of strength of riveted joint to strength of solid plate. 




14,000 



The above represents the strength resisting rupture along a longitudinal 
seam. For resistance to rupture in a circumferential seam, due to 

pressure on the ends of the cylinder, we have ^-r— = — ^ — ; 

4Ttc 

whence p = —rz — • 

Or the strength to resist rupture around a circumference is twice as great 
as that to resist rupture longitudinally; hence boilers are commonly 
single-riveted in the circumferential seams and double-riveted in the 
longitudinal seams. 

CARRYING CAPACITY OF STEEL ROLLERS AND BALLS. 

Carrying Capacity of a Steel Roller between Flat Plates. — (Merri- 
man, Mech. of Matls.) Let S = maximum safe unit stress of the mate- 
rial, I = length of the roller in inches, d = diameter, E = modulus of 
elasticity, W = load, then W =2/ s idS (2 S/£)i Taking w = W/l, 
and S = 15,000 and E = 30,000,000 lbs. per sq. in. for steel the formula 
reduces to w = 316 d. Cooper's specifications for bridges, 1901, gives 
w = 300 d. (The rule given in some earlier specifications, w = 1200 V<2, 
is erroneous.) The formula assumes that only the roller is deformed by 
the load, but experiments show that the plates also are deformed, and 
that the formula errs on the side of safety. Experiments by Crandall 



318 STRENGTH OF MATERIALS. 

and Marston on steel rollers of diameters from 1 to 16 in. show that 
their crushing loads are closely given by the formula W = 880 Id. (See 
Roller Bearings.) 

Spherical Rollers. — With the same notat ion as above, d being the 
diameter of the sphere, S = ^WElV.i nd?\ W = 1/4 nd 2 S 2 /E. The 
diameter of a sphe re to ca rry a given load with an allowable unit- 
stress S is d = 2 \/WE/xS 2 . This rule assumes that there is no de- 
formation of the plates between which the sphere acts, hence it errs on 
the side of safety. (See Ball Bearings.) 

RESISTANCE OF HOLLOW CYLINDERS TO COLLAPSE. 

Fairbairn's empirical formula {Phil. Trans., 1858) is 

p = 9,675,600 ^ (1) 

where p = pressure in lbs. per square inch, t = thickness of cylinder, 
d = diameter, and I = length, all in inches; or, 

p = 806,300 j^, if Lis in feet .... (2) 

He recommends the simpler formula 



Id 



(3) 



as sufficiently accurate for practical purposes, for tubes of considerable 
diameter and length. 

The diameters of Fairbairn's experimental tubes were 4, 6, 8, 10, and 
12 inches, and their lengths ranged between 19 and 60 inches. 

His formula (3) was until about 1 908 generally accepted as the basis of 
rules for strength of boiler-flues. In some cases, however, limits were 
fixed to its application by a supplementary formula. 

Lloyd's Register contains the following formula for the strength of 
circular boiler-flues, viz., 

P- 8 -^- (4) 

The English Board of Trade prescribes the following formula for cir- 
cular flues, when the longitudinal joints are welded, or made with riveted 
butt-straps, viz., 

= 90.000 t 2 

(L+l)d {o) 

For lap-joints and for inferior workmanship the numerical factor may 
be reduced as low as 60,000. 

The rules of Lloyd's Register, and those of the Board of Trade, pre- 
scribe further, that in no case the value of P must exceed 800 t/d. (6) 

In formulae (4), (5), (6) P is the highest working pressure in pounds 
per square inch, t and d are the thickness and diameter in inches, L is 
the length of the flue in feet measured between the strengthening rings, 
in case it is fitted with such. Formula (4) is the same as formula (3), 
with a factor of safety of 9. In formula (5) the length L is increased 
by 1; the influence which this addition has on the value of P is, of 
course, greater for short tubes than for long ones. 

Nystrom has deduced from Fairbairn's experiments the following 
formula for the collapsing strength of flues: 

4 TV 

P = 7-' (7) 

rfVL 
where p, t, and d have the same meaning as in formula (1), L is the length 
in feet, and T is the tensile strength of the metal in pounds per square 
inch. 

If we assign to T the value 50,000, and express the length of the flue in 
inches-, equation (7) assumes the following form, viz., 

V = 692,800 -!—-- • (8) 

dVl 



RESISTANCE OF HOLLOW CYLINDERS. 319 

Nystrom considers a factor of safety of 4 sufficient in applying his formula. 
(See " A New Treatise on Steam Engineering," by J. W. Nystrom, p. 106.) 

Formulae (1), (4), and (8) have the common defect that they make the 
collapsing pressure decrease indefinitely with increase of length, and 
vice versa. 

D. K. Clark, in his "Manual of Rules," etc., p. 696, gives the dimen- 
sions of six flues, selected from the reports of the Manchester Steam- 
Users Association, 1862-69, which collapsed while in actual use in boil- 
ers. These flues varied from 24 to 60 inches in diameter, and from 
3/i6 to 3 8 inch in thickness. They consisted of rings of plates riveted 
together, with one or two longitudinal seams, but all of them unfortified 
by intermediate flanges or strengthening rings. At the collapsing pres- 
sures the flues experienced compressions ranging from 1.53 to 2.17 tons, 
or a mean compression of 1.82 tons per square inch of section. From 
these data Clark deduced the following formula "for the average resist- 
ing force of common boiler-flues," viz., 

p . (2 («|0?_5oo) (9) 

where p is the collapsing pressure in pounds per square inch, and d and t 
are the diameter and thickness expressed in inches. 

Clark (S. E., vol. i. p. 643) says : The resistance to collapse of plain- 
riveted flues is directly as the square of the thickness of the plate, and 
inversely as the square of the diameter. The support of the two ends 
of the flue does not practically extend over a length of tube greater than 
twice or three times the diameter. The collapsing pressure of long 
tubes is therefore practically independent of the length. Instances of 
collapsed flues of Cornish and Lancashire boilers collated by Clark, 
showed that the resistance to collapse of flues of 3/ 8 -inch plates, 18 to 
43 feet long, and 30 to 50 inches diameter, varied as the 1.75 power of 
the diameter. Thus, 

for diameters of 30 35 40 45 50 inches, 

the collapsing pressures were 76 58 45 37 30 lbs. per sq. in. 

for 7/ 16 -inch plates the collapsing 

pressures were 60 49 42 lbs. per sq. in. 

C. R. Roelker, in Van Nostrand's Magazine, March, 1881, says that 
Nystrom's formula, (8), gives a closer agreement of the calculated with 
the actual collapsing pressures in experiments on flues of every descrip- 
tion than any of the other formulae. 

For collapsing pressures of plain iron flue-tubes of Cornish and Lanca- 
shire steam-boilers, Clark gives: 

200,000 P 

For short lengths the longitudinal tensile resistance may be effective in 
augmenting the resistance to collapse. Flues efficiently fortified by 
flange-joints or hoops at intervals of 3 feet may be enabled to resis't 
from 50 lbs. to 60 lbs. or 70 lbs. pressure per square inch more than 
plain tubes, according to the thickness of the plates. 

(For strength of Segmental Crowns of Furnaces and Cylinders see 
Clark, S. E., vol. i. pp. 649-651 and pp. 627, 628.) 

Formula for Corrugated Furnaces (Eng'g, July 24, 1891, p. 102). — 
As the result of a series of experiments on the resistance to collapse 
of Fox's corrugated furnaces, the Board of Trade and Lloyd's Register 
altered their formulas for these furnaces in 1891 as follows: 

Board of Trade formula is altered from 



T = thickness in inches; 
D = mean diameter of furnace; 
WP = working pressure in pounds per square inch. 



WP. 



320 STRENGTH OF MATERIALS. 

Lloyd's formula is altered from 

1000 X {T - 2) _ 1234 X (T - 2) 

D ■ D 

T = thickness in sixteenths of an inch; 
D = greatest diameter of furnace; 
WP = working pressure in pounds per square inch. 

Stewart's Experiments. — Prof. Reid T. Stewart (Trans. A.S.M.E., 

xxvii, 730) made two series of tests on Bessemer steel lap-welded tubes 
3 to 10 ins. diam. One series was made on tubes 85/ 8 in. outside diam. 
with the different commercial thicknesses of wall, and in lengths of 21/2, 
5, 10, 15 and 20 ft. between transverse joints tending to hold" the tube in 
a circular form. A second series was made on single lengths of 20 ft. 
Seven sizes, from 3 to 10 in. outside diam., in all the commercial thick- 
nesses obtainable, were tested. The tests showed that all the old for- 
mulae were inapplicable to the wide range of conditions found in modern 
practice. The principal conclusions drawn from the research are as 
follows: 

1. The length of tube, between transverse joints tending to hold it 
in circular form, has no practical influence upon the collapsing pressure 
of a commercial lap-welded tube so long as this length is not less than 
about six diameters of tube. 

2. The formulae, based upon this research, for the collapsing pres- 
sures of modern lap-welded Bessemer steel tubes, for all lengths greater 
than six diameters, are as follows: 



p= 1,000 (1 - yi -1600^,) (a) 

P =• 86,670 I - 1386 (B) 

Where P = collapsing pressure, pounds per sq. inch, d = outside 
diameter of tube in inches, t = thickness of wall in inches. 

Formula A is for values of P less than 581 pounds, or for values of - 

less than 0.023, while formula B is for values greater than these. When 
applying these formula?, to practice, a suitable factor of safety must be 
applied. 

3. The apparent fibre stress under which the different tubes failed 
varied from about 7000 lbs. for the relatively thinnest to 35,000 lbs. 
per sq. in. for the relatively thickest walls. Since the average yield 
point of the material was 37,000 and the tensile strength 58,000 lbs. 
per sq. in., it would appear that the strength of a tube subjected to a 
fluid collapsing pressure is not dependent alone upon either the elastic 
limit or ultimate strength of the material constituting it. The element 
of greatest weakness in a tube is its departure from roundness, even 
when this departure is relatively small. 

The table on the following page is a condensed statement of the principal 
results of the tests. 

Rational Formulae for Collapse of Tubes. (S. E. Slocum, Eng'g, t 

Jan. 8, 1909.) 
Heretofore designers have been forced to rely either upon the anti- 
quated experiments of Fairbairn, which were known to be in error by 
as much as 100% in many cases, or else to apply the theoretical formu- 
lae of Love and others, without knowing how far the assumptions on 
which these formulae are based are actually realized. 

A rational formula for thin tubes under external pressure, due to A. E. H. 
Love, is 

P = [2E/(1 -m*)](t/D)*, ....... (1) 

in which P = collapsing pressure in lbs. per sq. in. 

E = modulus of elasticity in lbs. per sq. in. 

m = Poisson's ratio of lateral to transverse deformation. 

t = thickness of tube wall in ins. 
D = external tube diameter in ins. 



RESISTANCE OF HOLLOW CYLINDERS. 



321 



Collapsing Pressure of Lap-Welded Steel Tubes. 
Outside Diameter, 85/ 8 In.; Length of Pipe, 20 Ft. 



Thick- 


Length, 


Bursting 
Pressure, 


Aver- 


Outside 

Diam. 

In. 


Thick- 


Bursting 


Aver- 


In. 


Ft. 


Lbs. per 
Sq. In. 


age. 


ness. 


Pressure. 


age. 


0.176 


2.21 


815-1085 


977 


3 


0.112 


1550-2175 


1860 


0.180 


4.70 


525-705 


792 


3 


0.143 


2575-3350 


2962 


0.181 


10.08 


455-650 


565 


3 


0.188 


3700-4200 


4095 


0.184 


14.71 


425-610 


548 


4 


0.119 


860-1030 


964 


0.185 


19.72 


450-625 


536 


4 


0.175 


2050-2540 


2280 


0.212 


2.21 


1240-1353 


1314 


4 


0.212 


3075-3375 


3170 


0.212 


4.70 


805-975 


907 


4 


0.327 


5425-5625 


5560 


0.217 


10.50 


700-960 


841 


6 


0.130 


450-640 


524 


0.219 


12.79 


750-1115 


905 


6 


0.167 


715-1110 


928 


0.268 


2.14 


1475-2200 


1872 


6 


0.222 


1200-2075 


1797 


0.274 


4.64 


1345-2030 


1684 


6 


0.266 


1750-2890 


2441 


0,272 


9.64 


1150-1908 


1583 


7 


0.160 


515-675 


592 


0.273 


14.64 


1250-1725 


1485 


7 


0.242 


1525-1850 


1680 


0.268 


19.64 


1250-1520 


1419 


7 


0.279 


1835-2445 


2147 


0.311 


2.16 


2290-2490 


2397 


8.64 


0.185 


450-625 


536 


0.306 


4.64 


1795-2325 


2073 


8.66 


0.268 


1250-1520 


1419 


0.306 


9.64 


1585-2055 


1807 


8.67 


0.354 


1830-2180 


2028 


0.309 


14.64 


1520-2025 


1781 


10 


0.165 


210-240 


225 


0.302 


19.75 


1575-1960 


1762 


10 


0.194 


305-425 


383 










10 


0.316 


1275-1385 


1319 












Collapsing Pressure of Lap- Welded Steel Tubes (Lbs. per Sq. In.) 
Calculated by Stewart's Formulae. 









Outside Diameters, 


Inches 












2 In. 


21/2 
In. 


3 In. 


4 In. 


5 In. 


6 In. 


7 In. 


8 In. 


9 In. 


10 In. 


11 In. 


0.10 


2947 

3814 
4671 
5548 


2081 
2774 
3468 
4161 


1503 
2081 
2659 
3236 


781 
1214 
1647 
2081 
















0.12 


694 
1041 
1387 


400 
636 
925 












0.14 


400 
595 


286 
400 


217 

297 






0.16 


232 


187 


0.18 


6414 


4854 


3814 


3514 


1734 


1214 


843 


564 


400 


306 


244 


0.20 


7281 


5548 


4392 


2947 


2081 


1503 


1090 


781 


542 


400 


314 


0.22 


8148 


6241 


4970 


3381 


2427 


1792 


1338 


997 


733 


525 


400 


0.24 


9014 


6934 


5548 


3814 


2774 


2081 


1586 


1214 


935 


694 


512 


0.26 


9881 


7628 


6125 


4248 


3121 


2370 


1833 


1431 


1118 


867 


633 


0.28 




8321 


6703 


4681 


3468 


2669 


2081 


1647 


1310 


1041 


820 


0.30 




9014 


7281 


5114 


3814 


2947 


2328 


1864 


1503 


1214 


978 


0.32 




9708 


7859 


5548 


4161 


3236 


2576 


2081 


1696 


1387 


1135 


0.34 






8437 
9014 
9592 


5981 
6414 
6848 
7281 
7714 
8148 
8581 
9014. 
9448 


4508 
4854 
5201 
5548 
5894 
6241 
6588 
6934 
7281 


3525 
3814 
4103 
4392 
4681 
4970 
5259 
5543 
5887 


2824 
3071 
3319 
3567 
3814 
4062 
4309 
4557 
4805 


2297 
2514 
2731 
2947 
3164 
3381 
3598 
3814 
4031 


1888 
2081 
2273 
2466 
2659 
2851 
3044 
3236 
3429 


1561 
1734 
1907 
2081 
2254 
2427 
2601 
2774 
2947 


1293 


36 






1450 


38 






1608 


0.40 






i766 


0.42 








1923 


0.44 








2081 


46 








2238 


48 








2396 


0.50 








2554 













322 STRENGTH OF MATERIALS. 

For thick tubes a special case of Lame's general formula is 

P = 2u[(t/D) - (t/DT-], (2) 

in which u = ultimate compressive strength in lbs. per sq. in. 

The average values of the elastic constants are for steel, E = 30,000,000, 
m = 0.295, u = 40,000; and for brass, E = 14,000,000, m = 0.357, 
u = 11,000. 

Hence, for thin steel tubes, P = 65,720,000 (t/D) 3 (3) 

For thick steel tubes, P = 80,000 [(t/D) - (t/D) 2 ] .... (4) 

For thin brass tubes, P = 32,090,000 (t/D) 3 (5) 

For thick brass tubes, P = 22,000 [(t/D) - (t/D) 2 ] .... (6) 

It is desirable to introduce a correction factor C in (1) which shall 
allow for the average ellipticity and variation in thickness. The cor- 
rection for ellipticity = d = (D m in/2>max) 3 , and that for variation in 
thickness = C 2 = (tmin/^aver.) 3 . From Stewart's twenty-five experiments 
C t = 0.967 and Ci = 0.712. The correction factor C = C x Ci = 0.69; 
and (1) becomes 

P = C [2 22/(1 - m 2 )](t/D) 3 (7) 

in which C = 0.69 for Stewart's lap-welded steel flues, t = average 
thickness in ins., and D = maximum diameter in ins. 

The empirical formulas obtained by Carman (Univ. of Illinois, Bull. 
No. 17, 1906), are for thin cold-drawn seamless steel tubes, 

P = 50,200,000 (t/D) 3 , 
and for thin seamless brass tubes, 

P = 25,150,000 (t/D) 3 . 

Carman assigns 0.025 as the upper limit of t/D for thin tubes and 0.03 
as the lower limit of t/D for thick tubes. Stewart assigns 0.023 as the 
limit of t/D between thin and thick tubes. 

Comparing these with (3) and (5), it is evident that they correspond 
to a correction factor of 0.76 for the steel tubes and 0.78 for the brass 
tubes. Since Carman's experiments were performed on seamless drawn 
tubes, while Stewart used lap-welded tubes, it might have been antici- 
pated that the latter would develop a smaller percentage of the theo- 
retical strength for perfect tubes than the former. 

Formula (2) for thick tubes when corrected for ellipticity and varia- 
tion in thickness reads 

P = 2u c C(t/D)[l - C(t/D)] (8) 

in which t = average thickness, and C = d, Ci, C t being equal to 

Dmin/Dmax: C 2 = Average /Urn- 

From Stewart's experiments, average ellipticity C t = 0.9874, and 
average variation in thickness C 2 = 0.9022; .\ C = 0.9874 X 0.5022 
= 0.89. 

We have then, for thick lap-welded steel flues, 

P = 2w c 0.89 (t/D) [1 - 0.89 (t/D)] 
and for thin lap-welded steel flues, 

P = 0.69 [2 E/(l - m?)} (t/D) 3 
in which E = 30,000,000, m = 0.295, and u c = 38,500 lbs. per sq. in. 

The experimental data of Stewart and Carman have made it possible 
to correct the rational formulas of Love and Lame" to conform to actual 
conditions; and the result is a pair of supplementary formulas (7) and 
(8), which cover the. entire range of materials, diameters, and thicknesses 
for long tubes of circular section. All that now remains to be done is 
the experimental determination of the correction constants for other 
types of commercial tubes than those already tested. 

HOLLOW COPPER BALLS. 

Hollow copper balls are used as floats in boilers or tanks, to control 
feed and discharge valves, and regulate the water-level. 

They are spun up in halves from sheet copper, and a rib is formed on 
one half. Into this rib the other half fits, and the two are then soldered 
or brazed together. In order to facilitate the brazing, a hole is left on 
one side of the ball, to allow air to pass freely in or out; and this hole is 



HOLDING-POWER OF NAILS, SPIKES, AND SCREWS. 323 

made use of afterwards to secure the float to its stem. The original 
thickness of the metal may be anything up to about Vi6 of an inch, if 
the spinning is done on a hand lathe, though thicker metal may be used 
when special machinery is provided for forming it. In the process of 
spinning, the metal is thinned down in places by stretching; but the 
thinnest place is neither at the equator of the ball (i.e., along the rib) 
nor at the poles. The thinnest points lie along two circles, passing 
around the ball parallel to the rib, one on each side of it, from a third 
to a half of the way to the poles. Along these lines the thickness may 
be 10, 15, or 20 per cent less than elsewhere, the reduction depending 
somewhat on the skill of the workman. 

The Locomotive for October, 1891, gives two empirical rules for deter- 
mining the thickness of a copper ball which is to work under an external 
pressure, as follows: 

... _ diameter in inches X pressure in pounds per sq. in. 

1. lluckness 16,000 

_ _, . , diameter X ^pressure 

2. Thickness = t^ttt^ 

1240 

These rules give the same result for a pressure of 166 lbs. only. Ex- 
ample: Required the thickness of a 5-inch copper ball to sustain 

Pressures of 50 100 150 166 200 250 lbs.per sq.in. 

Answer by first rule. . ..0156 .0312 .0469 .0519 .0625 .0781 inch. 
Answer by second rule .0285 .0403 .0494 .0518 .0570 .0637 " 

HOLDING-POWER OF NAILS, SPIKES, AND SCREWS. 

(A. W. Wright,. Western Society of Engineers, 1881.) 
Spikes. ■ — Spikes driven into dry cedar (cut' 18 months): 

Size of spikes 5 X 1/4 in. sq. 6 X 1/4 . 6 X 1/2 5 X3/8 

Length driven in 41/4 in. 5 in. 5 in. 4 1/4 in. 

Pounds resistance to drawing. Av'ge. lbs. 857 821 1691 1202 

From fi to Q tests earh (Max. " 1159 923- 2129 1556 

*rom b to 9 tests eacn j Min .. ?66 76Q n2Q 68? 

A. M. Wellington found the force required to draw spikes 9/i6 X 9 /i6 in., 
driven 41/4 inches into seasoned oak, to be 4281 lbs. ; same spikes, etc., 
in unseasoned oak, 6523 lbs. 

" Professor W. R. Johnson found that a plain spike 3/ 8 inch square 
driven 33/s inches into seasoned Jersey yellow pine or unseasoned chest- 
nut required about 2000 lbs. force to extract it; from seasoned white 
oak about 4000 and from well-seasoned locust 6000 lbs." 

Experiments in Germany, by Funk, give from 2465 to 3940 lbs. (mean 
of many experiments about 3000 lbs.) as the force necessary to extract a 
plain 1/2-inch square iron spike 6 inches long, wedge-pointed for one inch 
and driven 41/2 inches into white or yellow pine. When driven 5 inches 
the force required was about V10 part greater. Similar spikes 9/ 16 inches 
square, 7 inches long, driven 6 inches deep, required from 3700 to 6745 
lbs. to extract them from pine; the mean of the results being 4S73 lbs. 
In all cases about twice as much force was required to extract them 
from oak. The spikes were all driven across the grain of the wood. 
When driven with the grain, spikes or nails do not hold with more than 
half as much force. 

Boards of oak or pine nailed together by from 4 to 16 tenpenny com- 
mon cut nails and then pulled apart in a direction lengthwise of the 
boards, and across the nails, tending to break the latter in two by a 
shearing action, averaged about 300 to 400 lbs. per- nail to separate 
them, as the result of many trials. 

Resistance of Drift-bolts in Timber. — Tests made by Rust and 
Coolidge, in 1878. 

White Norway 
Pine. Pine. 

1 in. square iron drove 30 in. in i5/i6-in. hole, lbs 26,400 19,200 

1 in. round " " 34 " " i3/i 6 -in. " " 16,800 18,720 

1 in. square " " 18 " " i5/i 6 -in. " " 14,600 15,600 

1 in. round ". " 22 " " i3/i 6 -in. " " 13,200 14,400 



324 STRENGTH OP MATERIALS. 



Holding-power of Bolts in White Pine. (Eng'g News, Sept. 26, 1891.) 

Round. Square. 
Lbs. Lbs. 

Average of all plain 1-in. bolts 8224 8200 

Average of all plain bolts, 5/ 8 to 1 1/ 8 in 7805 8110 

Average of all bolts 8383 8598 

Round drift-bolts should be driven in holes 13/ 16 of their diameter, and 
square drift-bolts in holes whose diameter is 14/16 of the side of the square. 

Force required to draw Screws out of Norway Pine. 

1/2" diam. drive screw 4 in. in wood. Power required, average 2424 lbs. 

" 4 threads per in. 5 in. in wood. " " 2743 " 

" D'blethr'd,3perin.,4in. in " " " 2730 " 

Lag-screw, 7 per in., 11/2 "" " " 1465 " 

6 " " 21/2 " " " " " 2026 " 

1/2 inch R.R. spike 5 "" " " " 2191 " 

Force required to draw Wood Screws out of Dry Wood. — Tests 
made by Mr. Bevan. The screws were about two inches in length, 0.22 
diameter at the exterior of the threads, 0.15 diameter at the bottom, the 
depth of the worm or thread being 0.035 and the number of threads in one 
inch equal 12. They were passed through pieces of wood half an inch 
in thickness and drawn out by the weights stated: Beech, 460 lbs.; ash, 
790 lbs.; oak, 760 lbs.; mahogany, 770 lbs.; elm, 665 lbs.; sycamore, 
830 lbs. 

Tests of Lag-screws in Various Woods were made by A. J. Cox, 
University of Iowa, 1891: 

Kind of Wood Size Hole Length JSjx No 

Kind 01 w 00a. gcrew _ ^tioie in Tie. i| s Tests. 

Seasoned white oak 5/ 8 in. 1/2 in. 41/2 in. 8037 3 

" 9/ 16 " 7/ 16 " 3 " 6480 1 

" 1/2 " 3 /8 " 41/2 " 8780 2 

Yellow-pine stick 5/ 8 " i/ 2 " 4 " 3800 2 

White cedar, unseasoned. .. . 5/ 8 " 1/2 " 4 " 3405 2 

Cut versus Wire Nails. • — Experiments were made at the Watertown 
Arsenal in 1893 on the comparative direct tensile adhesion, in pine and 
spruce, of cut and wire nails. The results are stated by Prof. W. H. Burr 
as follows: 

There were 58 series of tests, ten pairs of nails (a cut and a wire nail 
in each) being used. The tests were made in spruce wood in most in- 
stances. The nails were of all sizes, from li/s to 6 in. in length. In 
every case the cut nails showed the superior holding strength by a large 
percentage. In spruce, in nine different sizes of nails, both standard 
and light weight, the ratio of tenacity of cut to wire nail was about 
3 to 2. With the" finishing" nails the ratio was roughly 3.5 to 2. With 
box nails (H to 4 inches long) the ratio was roughly 3 to 2. The mean 
superiority in spruce wood was 61%. In white pine, cut nails, driven 
with taper along the grain, showed a superiority of 100%, and with 
taper across the grain of 135%. Also when the nails were driven in the 
end of the stick, i.e., along the grain, the superiority of cut nails was 
100%, or the ratio of cut to wire was 2 to 1. The total of the results 
showed the ratio of tenacity to be about 3.2 to 2 for the harder wood, 
and about 2 to 1 for the softer, and for the whole taken together the 
ratio was 3.5 to 2. 

Nail-holding Power of Various Woods. — Tests at the Watertown 
Arsenal on different sizes of nails from 8d. to 60d., reduced to holding 
power per sq. in. of surface in wood, gave average results, in pounds, 
as follows: white pine, wire, 167; cut, 495. Yellow pine, wire, 318; cut, 
662. White oak, wire, 940; cut, 1216. Chestnut, cut, 683. Laurel, 
wire, 651; cut, 1200. 



STRENGTH OF WROUGHT IRON BOLTS. 



325 



Experiments by F. W. Clay. (Eng'g News, Jan. 11, 1894.) 

w™^i f Tenacity of 6d nails > 

wooa - Plain. Barbed. Blued. Mean. 

White pine 106 94 135 111 

Yellow pine 190 130 270 196 

Basswood 78 132 219 143 

White oak 226 300 555 360 

Hemlock 141 201 319 220 

STRENGTH OF WROUGHT IRON BOLTS. 

(Computed by A. F. Nagle.) 







Dia. 


Dia. 


No. 


of 




Thr. 


Root. 


V9, 


13 


0.400 


9/16 


12 


0.454 


5/8 


11 


0.507 


3/4 


10 


0.620 


7/8 


9 


0.731 


1 


8 


0.337 


H/8 


7 


0.940 


U/4 


7 


1.065 


13/8 


6 


1.160 


11/2 


6 


1.284 


15/8 


51/2 


1.389 


13/ 4 


5 


1.491 


17/8 


5 


1.616 


2 


41/2 


1.712 


21/ 4 


41/2 


1.962 


21/9, 


4 


2.176 


23/ 4 


4 


2.426 


3 


31/2 


2.629 


31/7 


31/4 


3.100 


4 


3 


3.567 



Area 

at 
Root. 



0.126 
0.162 
0.202 
0.302 
0.420 
0.550 
0.694 
0.893 
1.057 
1.295 
1.515 
1.746 
2.051 
2.302 
3.023 
3.719 
4.620 
5.428 
7.548 
9.963 



Stress upon Bolt upon Basis of 



per 
Sq. In. 



378 

486 

606 

906 

1,260 

1,650 

2,082 

2,679 

3,171 

3,885 

4,545 

5,238 

6,153 

6,906 

9,069 

11,157 

13,860 

16,284 

22,644 

29,889 



4,000 
lb. 



504 

648 

808 

1,208 

1,680 

2,200 

2,776 

3,572 

4,228 

5,180 

6,060 

6,984 

8,204 

9,208 

12,092 

14,876 

18,480 

21,712 

30,192 

39,852 



5,000 
lb. 



630 

810 

1,010 

1,510 

2,100 

2,750 

3,470 

4,465 

- 5,285 

6,475 

7,575 

8,730 

10,255 

11,510 

15,165 

18,595 

23,100 

27,140 

37,740 

49,815 



7,500 
lb. 



945 

1,215 

1,515 

2,265 

3,150 

4,125 

5,205 

6,698 

7,927 

9,712 

11,362 

13,095 

15,382 

17,265 

22,672 

27,892 

34,650 

40,710 

56,610 

74,722 



10,000 
lb. 



1,260 

1,620 

2,020 

3,020 

4,200 

5,500 

6,940 

8,930 

10,570 

12,950 

15,150 

17,460 

20,510 

23,020 

30,230 

37,190 

46,200 

54,280 

75,480 

99,630 



6,400 

8,200 

10,200 

15,200 

21,100 

27,500 

34,500 

44,000 

52,000 

63,000 

74,000 

84,000 

99,000 

110,000 

143,000 

174,000 

214,000 

248,000 

337,000 

433,000 



The U. S. or Sellers System of Screw Threads is used in the above table. 

The "Probable Breaking Load" is based upon wrought iron running from 
51,000 lbs. per sq. in. for 1/2 inch diam. down to 43,500 lbs. for 4 in. diam. 

For soft steel bolts add 20% to this column. 

When it is known what load is to be put upon a bolt, and the judgment 
of the engineer has determined what stress is safe to put upon the iron, 
look down in the proper column of said stress until the required load is 
found. The area at the bottom of the thread will give the equivalent 
area of a flat bar to that of the bolt. 

Effect of Initial Strain in Bolts. — Suppose that bolts are used to 
connect two parts of a machine and that they are screwed up tightly 
before the effective load comes on the connected parts. Let Pi = the 
initial tension on a bolt due to screwing up, and Pi = the load after- 
wards added. The greatest load may vary but little from Pi or Pi, 
according as the former or the latter is greater, or it may approach the 
value Pi 4- Pi, depending upon the relative rigidity of the bolts and of 
the parts connected. Where rigid flanges are bolted together, metal to 
metal, it is probable that the extension of the bolts with any additional 
tension relieves the initial tension, and that the total tension is Pi or Pi, 
but in cases where elastic packing, as india rubber, is interposed, the 
extension of the bolts may very little affect the initial tension, and the 
total strain may be nearly Pi 4- Pi. Since the latter assumption is 
more unfavorable to the resistance of the bolt, this contingency should 
usually be provided for. (See Unwin, " Elements of Machine Design," 
for demonstration.) 



326 



STRENGTH OF MATERIALS. 



Forrest E. Cardullo (Machinery' 1 s Reference Series No. 22, 190S) states 
the effect of initial stress in bolts due to screwing them tight as follows: 

1. When the bolt is more elastic than the material it compresses, the 
stress in the bolt is either the initial stress or the force applied, whichever 
is greater. 

2. When the material compressed is more elastic than the bolt, the 
stress in the bolt is the sum of the initial stress and the force applied. 

Experiments on screwing up 1/2, 3 /4, 1 and 11/4 in. bolts showed that the 
stress produced is often sufficient to break a 1/2-in. bolt, and that the stress 
varies about as the square of the diameter. From these experiments 
Prof. Cardullo calculates what he calls the "working section" of a bolt as 
equal to its area at the root of the thread, less the area of a 1/2-in. bolt 
at the root of the thread times twice the diameter of the bolt, and gives 
the following table based on this rule. 





Working Strength of Bolts. 


U. S. Standard Threads. 


^ 


"3 £ 


A 




j 


<- 


j 


\ 


„. 


~o 


c3 




"0 




*o 


*o 


*5 03 


"O rn 


m 


-^ 3 


02 g 


ffl 73 


W 03 


W03 


W 03 


m 1 


W-3 


"o 


8 g* 


^*G 

3 


1=1 




a 


■Si 




<U 03 


■**& A 


bOeo 


^ 03 


-3 _: 


•B eU 


£°m 


^ a »5 


^ & 03 


si 

.S-S 


«3 $ « 

£H.S 


•§3 


5o » 




eg £ 

£^02 


£«02 


MO S 


Mo a 

CO E 

03.RJ += 

£-02 


Q 


< 




02 


02 


02 


02 


02 


02 


1/2 


0.126 























5/8 


0.202 


0.044 


220 


264 


308 


352 


440 


528 


3/4 


0.302 


0.113 


565 


678 


791 


904 


1,130 


1,356 


7/8 


0.420 


0.200 


1,000 


1,200 


1,400 


1,600 


2,000 


2,400 


1 


0.550 


0.298 


1,490 


1,788 


2,086 


2,384 


2,980 


3,476 


11/8 


0.694 


0.411 


2,055 


2,466 


2,877 


3,288 


4,110 


4,932 


11/4 


0.893 


0.578 


2,890 


3,468 


4,046 


4,624 


5,780 


6,936 


13/8 


1 .057 


0.710 


3,550 


4,260 


4,970 


5,680 


7,100 


8,520 


11/3 


1.295 


0.917 


4,585 


5,502 


6,419 


7,336 


9,170 


10,504 


15/8 


1.515 


1.105 


5,525 


6,630 


7,735 


8,840 


11,050 


13,260 


13/ 4 


1.746 


1.305 


6,525 


7,830 


9,135 


10,440 


13,050 


15,660 


17/8 


2.051 


1.578 


7,890 


9,468 


11,046 


12,624 


15,780 


18,936 


2 


2.302 


1.798 


8,990 


10,788 


12,586 


14,384 


17.980 


21,576 


21/4 


3.023 


2.456 


12,280 


14,736 


17,192 


19,648 


24,560 


29,472 


21/ 2 


3.719 


3.089 


15,445 


18,534 


21,623 


24,712 


30,890 


37,068 


23/4 


4.620 


3.927 


19,635 


23,562 


27,489 


31,416 


39,270 


47,124 


3 


5.428 


4.672 


23,360 


28,032 


32,704 


37,376 


46,720 


56,064 


31/4 


6.510 


5.690 


28,450 


34,140 


39,830 


45,520 


56,900 


68,280 


31/2 


7.548 


6.666 


33,330 


39,996 


46,664 


53,328 


66,660 


79,992 



The stresses on bolts caused by tightening the nuts by a wrench may 
be calculated as follows: Let L = the effective length of the wrench in 
inches, P = the force in pounds applied at the distance L, n = no. of 
threads per inch of the bolt, T = total tension on the bolt if there were 
no friction, then T = 2 nnLP. Wilfred Lewis, Trans. A. S. M. E., gives 
for the efficiency of a bolt E = 1 -5- (1 + nd), where d = external diameter 
of the screw. T X E = 2 nnLP -h (1 + nd) is the tension corrected 
for friction. It also expresses the load that can be lifted by screwing a 
nut on a bolt or a bolt into a nut. 

STRENGTH OF CHAINS. 

Formulas for Safe Load on Chains. — Writing the formula for the safe 
load on chains P = Kd 2 , P in pounds, d in inches, the following figures for 
K are given by the authorities named. 

Open link Stud link 

Unwin 13,440; 11,200* 20,160 

Weisbach 13,350 17,800 

Bach 13,750; 11,000* 16,500; 13,200* 

* The lower figures are for much used chain, subject, frequently to the 
maximum load. G. A Goodenough and L. E. Moore, Univ. of Illinois 



STAND-PIPES AND THEIR DESIGN. 327 



STAND-PIPES AND THEIR DESIGN. 

(Freeman C. Coffin, New England Water Works Assoc, Eng. News, 
March 16, 1893.) See also papers bv A. H. Howland, Eng. Club of Phil., 
1887; B. F. Stephens, Amer. Water Works Assoc., Eng. Neivs, Oct. 6 
and 13, 1888; W. Kiersted, Rensselaer Soc. of Civil Eng.,. Eng'g Record, 
April 25 and May 2, 1891, and W. D. Pence, Eng. News, April and May, 
1894; also, J. N. Hazlehurst's " Towers and Tanks for Water Works." 

The question of diameter is almost entirely independent of that of 
height. The efficient capacity must be measured by the length from the 
high-water line to a point below which it is undesirable to draw the 
water on account of loss of pressure for fire-supply, whether that point 
is the actual bottom of the stand-pipe or above it. This allowable 
fluctuation ought not to exceed 50 ft., in most cases. This makes the 
diameter dependent upon two conditions, the first of which is the amount 
of the consumption during the ordinary interval between the stopping and 
starting of the pumps. This should never draw the water below a point that 
will give a good fire stream and leave a margin for still further draught 
for fires. The second condition is the maximum number of fire streams 
and their size which it is considered necessary to provide for, and the 
maximum length of time which they are liable to have to run before the 
pumps can be relied upon to reinforce them. 

Another reason for making the diameter large is to provide for stability 
against wind-pressure when empty. 

The following table gives the height of stand-pipes beyond which they 
are not safe against wind-pressures of 40 and 50 lbs. per square foot. 
The area of surface taken is the height multiplied by one half the 
diameter. 

Diameter, feet 20 25 30 35 

Max. height, wind 40 lbs 45 70 150 

" 50 " 35 55 80 160 

Any form of anchorage that depends upon connections with the side 
plates near the bottom is unsafe. By suitable guys the wind-pressure is 
resisted by tension in the guys, and the stand-pipe is relieved from 
wind strains that tend to overthrow it. The guys should be attached to 
a band of angle or other shaped iron that completely encircles the tank, 
and rests upon some sort of bracket or projection, and not be riveted to 
the tank. They should be anchored at a distance from the base equal 
to the height of the point at which they are attached, if possible. 

The best plan is to build the stand-pipe of such diameter that it will 
resist the wind by its own stability. 

Thickness of the Side Plates. 

The pressure on the sides tending to rupture the plates by tension, due 
to the weight of the water, increases in direct ratio to the height, and 
also to the diameter. The strain upon a section 1 inch in height at any 
point is the total. strain at that point divided by two — for each side is 
supposed to bear the strain equally. The total pressure at any point is 
equal to the diameter in inches, multiplied by the pressure per square 
inch, due to the height at that point. It may be expressed as follows: 

H = height in feet, and / = factor of safety; 
d = diameter in inches; 
V = pressure in lbs. per square inch; 
0.434 = p for 1 ft. in height; 

s = tensile strength of material per square inch; 
T = thickness of plate. 

Bulletin, No. 18, 1907, after an extensive theoretical and experimental 
investigation, find that these values give maximum stresses in the external 
fibers of from 26,400 to 40,320 lbs. per sq. in., which they consider much 
too high for safety. Taking 20,000 as a permissible maximum stress, 
they give the formulse for safe load P = 8000 d 2 for open links and 
P = 10,000 d 2 for stud links. Thev say that the stud link will within 
the elastic limit bear from 20 to 25% more load than the open link, but 
that the ultimate strength of the stud link is probably less than that of the 
open link. See also tables of Size and Strength of Chains, page 251. 



328 STRENGTH OF MATERIALS. 

Then the total strain on each side per vertical inch 

= 0.434 Hd = pd . OAteHdf _ pdf 

2 2 ' 2s 2s ' 

Mr. Coffin takes / = 5, not counting reduction of strength of joint, 
equivalent to an actual factor of safety of 3 if the strength of the riveted 
joint is taken as 60 per cent of that of the plate. 

• The amount of the wind strain per square inch of metal at any joint 
can be found by the following formula, in which 

H = height of stand-pipe in feet above joint; 
T = thickness of plate in inches; 
p = wind-pressure per square foot; 
W = wind-pressure per foot in height above joint; 
W = Dp where D is the diameter in feet; 
. m = average leverage or movement about neutral axis 
or central points in the circumference; or, 
m = sine. of 45°, or 0.707 times the radius in feet. 

Then the strain per square inch of plate 
(Hiv) f 



circ. in ft. X mT 

Mr. Coffin gives a number of diagrams useful in the design of stand- 
pipes, together with a number of instances of failures, with discussion 
of their probable causes. 

Mr. Kiersted's paper contains the following: Among the most promi- 
nent strains a stand-pipe has to bear are: that due to the static pressure 
of the water, that due to the overturning effect of the wind on i:ti empty 
stand-pipe, and that due to the collapsing effect, on the upper rings, of 
violent wind storms. 

For the thickness of metal to withstand safely the static pressure of 
water, let t = thickness of the plate iron in inches; H = height of stand- 
pipe in feet; D = diameter of stand-pipe in feet. 

Then, assuming a tensile strength of 48,000 lbs. per square inch, a 
factor of safety of 4, and efficiencv of double-riveted lap-joint equaling 
0.6 of the strength of the solid plate, t = 0.00036 H X D; H = 10,000 t 
-H3.6D; which will give safe heights for thicknesses up to 5/ 8 to 3/ 4 of an 
irich. The same formula may also apply for greater heights and thick- 
nesses within practical limits, if the joint efficiency be increased by triple 
riveting. 

The conditions for the severest overturning wind strains exist when 
the stand-pipe is empty. 

Formula for wind-pressure of 50 pounds per square foot, whenrf = 
diameter of stand- pipe in inches; x = any unknown height of stand- 
pipe; x = VgOTzdt = 15.85 ^dt. 

Failures of Stand-pipes. — A list showing 23 important failures 
inside of nine years is given in a paper by Prof. W. D. Pence, Eng'g 
News, April 5, 12, 19 and 26, May 3, 10 and 24, and June 7, 1894. His 
discussion of the probable causes of the failures is most valuable. 

Water Tower at Yonkers, N.Y. — This tower, with a pipe 122 feet 
high and 20 feet diameter, is described in Engineering News, May 18, 1892. 

The thickness of the lower rings is n/i6 of an inch, based on a tensile 
strength of 60,000 lbs. per square inch of metal, allowing 65% for the 
strength of riveted joints, using a factor of safety of 31/2 and adding a 
constant of l/g inch. The plates diminish in thickness by Vl6 inch to 
the last four plates at the top. which are 1/4 inch thick. 

The contract for steel requires an elastic limit of at least 33,000 lbs. 
per square inch ; an ultimate tensile strength of from 56,000 to 66,000 lbs. 
per square inch; an elongation in 8 inches of at least 20%, and a reduc- 
tion of area of at least 45%. The inspection of the work was made by the 
Pittsburgh Testing Laboratorv. According to their report the actual 
conditions developed were as follows: Elastic limit from 34,020 to 39,420; 



WROUGHT-IRON AND STEEL WATER PIPES. 



329 



the tensile strength from 58,330 to 65,390; the elongation in 8 inches 
from 221/2 to 32%; reduction in area from 52.72 to 71.32%; 17 plates 
out of 141 were rejected in the inspection. 

The following table is calculated by Mr. Kiersted's formulae. The 
stand-pipe is intended to be self-sustaining; that is, without guys or 
stiffeners. 

Heights of Stand-pipes for Various Diameters and Thicknesses of 
Plates. 



Thickness 
of Plate 
in Frac- 
tions of 
an Inch. 

3/i 6 










Diameters in Feet. 












5 

50 
55 
60 
70 
75 
80 
85 


6 
55 


7 
60 


8 
65 


9 

55 
65 
75 
90 
100 
110 
115 
125 
130 


10 

50 
60 
70 
85 
100 
115 
120 
130 
135 
145 
150 


12 

35 
50 
55 
70 
85 
100 
115 
130 
145 
155 
165 


14 


15 


16 


18 


20 


25 


7/32 


40 
50 
60 
75 
85 
100 
110 
120 
135 
145 
160 


40 

45 
55 
70 
80 
90 
100 
115 
125 
135 
150 
160 










V4 

5/16 

3/8 

7/16 

1/2 

9/l 6 


65 

75 
80 
90 
95 


70 

80 
90 
95 
100 


75 
85 
95 
100 
110 
115 


40 
50 
65 
75 
85 
95 
105 
120 
130 
140 
150 
160 


35 
45 
55 
65 
75 
85 
95 
105 
115 
125 
135 
145 
155 


35 
40 
50 
60 
70 
80 
85 
95 
105 
110 
120 
130 
140 


25 
35 
40 
45 
55 
60 


5/ 8 








65 


11/16 










75 


3/ 4 












80 


13/i 6 












90 


17/ 8 
















95 


•Vi ...... 


















105 


1 




















110 



























Heights to nearest 5 feet. Rings are to build 5 feet vertically. 



WROUGHT -IRON AND STEEL WATER-PD?ES. 

Riveted Steel Water-pipes (Engineering News, Oct. 11, 1890, and 
Aug. 1, 1891). — The use of riveted wrought-iron pipe has been common 
in the Pacific States for many years, the largest being a 44-inch conduit 
in connection with the works of the Spring Valley Water Co., which 
supplies San Francisco. The use of wrought iron and steel pipe has been 
necessary in the West, owing to the extremely high pressures to be with- 
stood and the difficulties of transportation. As an example: In connec- 
tion with the water supply of Virginia City and Gold Hill, Nev., there 
was laid in 1872 an 11 1/2-inch riveted wrought-iron pipe, a part of which , 
is under a head of 1720 feet. 

In the East, an important example of the use of riveted steel water 
pipe is that of the East Jersey Water Co., which supplies the city of 
Newark. The contract provided for a maximum high service supply of 
25,000,000 gallons daily. In this case 21 miles of 48-inch pipe was laid, 
some of it under 340 feet head. The plates from which the pipe is made 
are about 13 feet long by 7 feet wide, open-hearth steel. Four plates 
are used to make one section of pipe about 27 feet long. The pipe is 
riveted longitudinally with a double row, and at the end joints with a 
single row of rivets. Before being rolled into the trench, two of the 
27-feet lengths are riveted together, thus diminishing the number of 
joints to be made in the trench and the extra excavation to give room 
for joining. 

The thickness of the plates varies with the pressure, but only three 
thicknesses are used, 1/4 , 5/i 6 , and 3/ 8 inches, the pipe made of these 
thicknesses having a weight of 160, 185, and 225 lbs. per foot, respec- 
tively. At the works all the pipe was tested to pressure IV2 times that 
to which it is to be subjected when in place. 

An important discussion of the design of large riveted steel pipes to 



330 STRENGTH OF MATERIALS. 

resist not only the internal pressure but also the external pressure from 
moist earth in which thev are laid, together uith notes on the design of f 
pipe 18 ft. diam. t,000 ft. long for the Ontario Water Power Co., Niagari 
Falls, by Joseph Mayer, will be found in Eng. News, April 26, 1906. 



a 



STRENGTH OF VARIOUS MATERIALS. EXTRACTS FROM 
KIRKALDY'S TESTS. 

The publication, in a book by W. G. Kirkaldy, of the results of many 
thousand tests made during a quarter oL.a century by his father, David 
Kirkaldy, has made an important contribution to our knowledge con- 
cerning the range of variation in strength of numerous materials. A 
condensed abstract of these results was published in the American Ma- 
chinist, May 11 and 18, 1893, from which the following still further con- 
densed extracts are taken: \ 

The figures for tensile and compressive strength, or, as Kirkaldy calls 
them, pulling and thrusting stress, are given in pounds per square inch of 
original section, and for bending strength in pounds of actual stress or 
pounds per BD 2 (breadth X square of depth) for length of 36 inches 
between supports. The contraction of area is given as a percentage of 
the original area, and the extension as a percentage in a length of 10 
inches, except when otherwise stated. The abbreviations T. S., E. L., 
Contr., and Ext. are used for the sake of brevity, to represent tensile 
strength, elastic limit, and percentages of contraction of area, and elon- 
gation, respectively. 

Cast Iron. —44 tests: T. S. 15,468 to 28,740 pounds; 17 of these 
were unsound, the strength ranging from 15,468 to 24,357 pounds. 
Average of all, 23,805 pounds. 

Thrusting stress, specimens 2 inches long, 1.34 to 1.5 in. diameter; 
43 tests, all sound, 94,352 to 131,912; one, unsound, 93,759; average of 
all, 113,825. 

Bending stress, bars about 1 in. wide by 2 in. deep, cast on edge. 
Ultimate stress 2876 to 3854; stress per BD 2 = 725 to 892; average, 
820. Average modulus of rupture, R, = 3/ 2 stress per BD 2 X length, 
= 44,280. Ultimate deflection, 0.29 to 0.40 in.; average, 0.34 inch. 

Other tests of cast iron, 460 tests, 16 lots from various sources, gave 
results with total range as follows: Pulling stress, 12,688 to 33,616 
pounds; thrusting stress, 66,363 to 175,950 pounds; bending stress, per 
BD 2 , 505 to 1128 pounds; modulus of rupture, R, 27,270 to 61,912. 
Ultimate deflection, 0.21 to 0.45 inch. 

The specimen which was the highest in thrusting stress was also the 
highest in bending, and showed the greatest deflection, but its tensile 
strength was only 26,502. 

The specimen with the highest tensile strength had a thrusting stress of 
143,939 and a bending strength, per BD 2 , of 979 pounds with 0.41 de- 
flection. The specimen lowest in T. S. was also lowest in thrusting and 
bending, but gave 0.38 deflection. The specimen which gave 0.21 deflec- 
tion had T. S., 19,188; thrusting, 104,281; and bending, 561. 

Iron Castings. — 69 tests; tensile strength, 10,416 to 31,652; thrust- 
ing stress, ultimate per square inch, 53,502 to 132,031. 

Channel Irons. — Tests of 18 pieces cut from channel irons. T. S. 
40,693 to 53,141 pounds per square inch; contr. of area from 3.9 to 
32.5%. Ext. in 10 in. from 2.1 to 22.5%. The fractures ranged all the 
way from 100% fibrous to 100% crystalline. The highest T. S., 53,141, 
with 8.1% contr. and 5.3% ext., was 100% crystalline;' the lowest T. S., 
40,693, with 3.9 contr. and 2.1% ext., was 75% crystalline. All the 
fibrous irons showed from 12.2 to 22.5% ext., 17.3 to 32.5 contr., and 
T. S. from 43,426 to 49,615. The fibrous irons are therefore of medium 
tensile strength and high ductility. The crystalline irons are of variable 
T. S., highest to lowest, and low ductility. 

Lowraoor Iron Bars. — Three rolled bars 21/2 inches diameter; ten- 
sile tests: elastic, 23,200 to 24,200; ultimate, 50,875 to 51,905; contrac- 
tion, 44.4 to 42.5; extension, 29.2 to 24.3. Three hammered bars, 41/2 
inches diameter, elastic 25,100 to 24,200; ultimate, 46,810 to 49,223; 
contraction, 20.7 to 46.5; extension, 10.8 to 31.6. Fractures of all, 100 
per cent fibrous. In the hammered bars the lowest T. S. was accom- 
panied by lowest ductility. 



kirkaldy's tests. 



331 



Iron Bars, Various. — Of a lot of 80 bars of various sizes, some 
rolled and some hammered (the above Lowmoor bars included), the 
lowest T. S. (except one) 40, SOS pounds per square inch, was shown by 
the Swedish "hoop L" bar 31/4 inches diameter, rolled. Its elastic limit 
was 19,150 pounds; contraction 68.7% and extension 37.7% in 10 
inches. It was also the most ductile of all the bars tested-, and was 100% 
fibrous. The highest T. S., 60,780 pounds, with elastic limit, 29,400; 
contr., 36.6; and ext., 24.3%, was shown by a " Farnley " 2-inch bar, 
rolled. It was also 100%* fibrous. The lowest ductility 2.6% contr., 
and 4.1% ext., was shown by a 33/ 4 -inch hammered bar, without brand. 
It also had the lowest T. S., 40,278 pounds, but rather high elastic limit, 
25,700 pounds. Its fracture was 95% crystalline. Thus of the two bars 
showing the lowest T. S., one was the most ductile and the other the 
least ductile in the whole series of 80 bars. 

Generally, high ductility is accompanied by low tensile strength, as in 
the Swedish bars, but the Farnley bars showed a combination of high 
ductility and high tensile strength. 

Locomotive Forgings, Iron. — 17 tests average, E. L., 30,420; 
T. S., 50,521; contr., 36.5: ext. in 10 inches, 23.8. 

Broken Anchor Forging?, Iron. — 4 tests: average, E. L., 23,825; 
T. S., 40,083; contr., 3.0; ext. in 10 inches, 3.8. 

Kirkaldy places these two irons in contrast to show the difference 
between good and bad work. The broken anchor material, he says, is 
of a most treacherous character, and a disgrace to any manufacturer. 

Iron Plate Girder. — Tensile tests of pieces cut from a riveted iron 
girder after twenty years' service in a railway bridge. Top plate, aver- 
age of 3 tests, E. L., 26,600; T. S., 40,806; contr., 16.1; ext. in 10 inches, 
7.8. Bottom plate, average of 3 tests, E. L., 31,200; T. S., 44,288; 
contr., 13.3; ext. in 10 inches, 6.3. Web-plate, average of 3 tests, E. L., 
28,000; T. S., 45,902: contr., 15.9; ext. in 10 inches, 8.9. Fractures 
all fibrous. The results of 30 tests from different parts of the girder 
prove that the iron has undergone no change during twenty years of use. 

Steel Plates. — Six plates 100 inches long, 2 inches wide, thickness 
various, 0.36 to 0.97 inch. T. S., 55,4S5 to 60,805; E. L., 29,600 to 33,200; 
contr., 52.9 to 59.5; ext., 17.05 to 18.57. 

Steel Bridge Links. — 40 links from Hammersmith Bridge, 1886. 





Fracture. 




T. S. 


E. L. 


Contr. 


Ext. in 
100 in. 


Silky. 


Gran- 
ular. 




67,294 
60,753 
75,936 
64,044 
63,745 
65,930 
63,980 


38,294 
36,030 
44,166 
32,441 
38,118 
36,792 
39,017 


34.5% 
30.1 
31.2 
34.7 
52.8 
40.8 
6.0 


14.11% 
15.51 
12.42 
13.43 
15.46 
17.78 
6.62 


30% 
15 
30 
100 
35 





Lowest T. S 

Highest T.S. and E. L.. . . 

Lowest E. L 

Greatest Contraction 

Greatest Extension 

Least Contr. and Ext 


70% 
85 
70 

65 
100 



The ratio of elastic to ultimate strength ranged from 50.6 to 65.2 per 
cent; average, 56.9 per cent. 

Extension in lengths of 100 inches. At 10,000 lbs. per sq. in., 0.018 to 
0.024; mean, 0.020 inch; at 20,000 lbs. per sq. in., 0.049 to 0.063; mean, 
0.055 inch; at 30,000 lbs. per sq. in., 0.083 to 0.100; mean, 0.090; set at 
30,000 pounds per sq. in., to 0.0G2; mean, 0. 

The mean extension between 10,000 to 30,000 lbs. per sq. in. increased 
regularly at the rate of 0.007 inch for each 2000 lbs. per sq. in. increment 
of strain. This corresponds to a modulus of elasticity of 28,571,429. 
The least increase of extension for an increase of load of 20,000 lbs. per 
sq. in., 0.065 inch, corresponds to a modulus of elasticity of 30,769,231, 
and the greatest, 0.076 inch, to a modulus of 26,315,789. 

Steel Rails. — Bending tests, 5 feet between supports, 11 tests of flange 
rails 72 pounds per yard, 4.63 inches high. 



332 



STRENGTH OF MATERIALS. 



Elastic stress 
Pounds. 
Hardest. . . 34,200 
Softest .... 32,000 

Mean 32,763 

All uncracked at 



Ultimate stress. Deflection at 50,000 



Pounds. 
60,960 
56,740 
59,209 
inches deflection. 



Pounds. 
3.24 ins. 
3.76 " 
3.53 " 



Ultimate 

Deflection. 

8 ins. 



Pulling tests of pieces cut from same rails. Mean results. 

Elastic Ultimate Contraction of 

Stress. Pounds. area of frac- Extension 

per sq. in. per sq. in. ture. in 10 ins. 

Top of rails 44,200 83,110 19.9% 13.5% 

Bottom of rails 40,900 77,820 30.9% 22.8% 



Steel Tires. — Tensile tests of specimens cut from steel tires. 



Krupp Steel. — 262 Tests. 



Highest . 

Mean 

Lowest. . 



E. L. 

69,250 
52,869 
41,700 



T. S. 
119,079 
104,112 

90,523 



Contr. 
31 9 
29.5 
45.5 



Ext. in 

5 inches. 

18.1 

19.7 

23.7 



Vickers, Sons & Co. — 70 Tests. 



Highest . 
Mean. . . . 
Lowest. . 



E. L. 

58,600 
51,066 
43,700 



T. S. 
120,789 
101,264 

87,697 



Contr. 
11.8 
17.6 
24.7 



Ext. in 

5 inches. 

8.4 

12.4 

16.0 



Note the correspondence between Krupp's and Vickers' steels as to 
tensile strength and elastic limit, and their great difference in contrac- 
tion and elongation. The fractures of the Krupp steel averaged 22 per 
cent silky, 78 per cent granular; of the Vicker steel, 7 per cent silky, 
93 per cent granular. 



Steel Axles. — Tensile tests of specimens cut from steel axles. 



Highest . 
Mean 
Lowest. . 



E. L. 

49,800 
36,267 
31,800 

Vickers, Sons & 



Highest . 
Mean . . . 
Lowest. . 



E. L. 

42,600 
37,618 
30,250 



Tree Co. — 157 Tests. 






Ext. in 


T. S. Contr. 


5 inches. 


99,009 21.1 


16.0 


72,099 33.0 


23.6 


61,382 34.8 


25.3 


Co. — 125 Tests. 






Ext. in 


T. S. Contr. 


5 inches. 


83,701 18.9 


13.2 


70,572 41.6 


27.5 


56,388 49.0 


37.2 



The average fracture of Patent Shaft and Axle Tree Co. steel was 33 
per cent silky, 67 per cent granular. 

The average fracture of Vickers' steel was 88 per cent silky, 12 per 
cent granular. 

Steel Propeller Shafts. — Tensile tests of pieces cut from two shafts, 
mean of four tests each. Hollow shaft, Whitvvorth, T. S., 61,290; E. L., 
30,575; contr., 52.8; ext. in 10 inches, 28.6. Solid shaft, Vickers', T. S., 
46,870; E. L., 20,425; contr., 44.4; ext. in 10 inches, 30.7. 

Thrusting tests, Whitworth, ultimate, 56,201; elastic, 29,300; set at 
30,000 lbs., 0.18 per cent; set at 40,000 lbs., 2.04 per cent; set at 50,000 
lbs., 3.82 per cent. 

Thrusting tests, Vickers', ultimate, 44,602; elastic, 22,250; set at 
30,000 lbs., 2.29 per cent; set at 40,000 lbs., 4.69 per cent. 



kirkaldy's tests. 333 



Shearing strength of the Whitworth shaft, mean of four tests, 40,654 
lbs. per square inch, or 66.3 per cent of the pulling stress. Specific 
gravity of the Whitworth steel, 7.867; of the Vickers', 7.856. 

Spring Steel. — Untempered, 6 tests, average, E. L., 67,916: T. S., 
115,668; contr., 37.8: ext. in 10 inches. 16.6. Spring steel untem- 
pered, 15 tests, average, E. L., 38,785; T. S., 69,496; contr., 19.1; ext. 
in 10 inches, 29.8. These two lots were shipped for the same purpose, 
viz., railway carriage leaf springs. 

Steel Castings. —44 tests, E. L., 31,816 to 35,567: T. S., 54,928 to 
63,840; contr., 1.67 to 15.8; ext., 1.45 to 15.1. Note the great varia- 
tion in ductility. The steel of the highest strength was also the most 
ductile. 

Riveted Joints, Pulling Tests of Riveted Steel Plates, Triple Riv- 
eted Lap Joints, Machine Riveted, Holes Drilled. 

Plates, width and thickness, inches: 
13.50X0.25 13.00X0.51 11.75X0.78 12.25X1.01 14.00X0.77 
Plates, gross sectional area square inches: 

3.375 6.63 9.165 12.372 10.780 

Stress, total, pounds: 

199,320 332,640 423,180 528,000 455,210 

Stress per square inch of gross area, joint: 

59,058 50,172 46,173 42,696 42,227 

Stress per square inch of plates, solid: 

70,765 65,300 64,050 62,280 68,045 

Ratio of strength of joint to solid plate: 

83.46 76.83 72.09 68.55 62.06 

Ratio net area of plate to gross: 

73.4 65.5 62.7 64.7 72.9 

Where fractured: 

plate at plate at plate at plate at rivets 

holes. holes. holes. holes. sheared 

Rivets, diameter, area and number: 

0.45, 0.159, 24 0.64, 0.321, 21 0.95, 0.708, 12 1.08, 0.916, 12 0.95,0.708, 12 
Rivets, total area: 

3.816 6.741 8.496 10.992 8.496 

Strength of Welds. — Tensile tests to determine ratio of strength of 
weld to solid bar. 

Iron Tie Bars. — 28 Tests. 

Strength of solid bars varied from 43,201 to 57,065 lbs. 

Strength of welded bars varied from 17,816 to 44,586 lbs. 

Ratio of weld to solid varied from 37.0 to 79.1% 

Iron Plates. — 7 Tests. 

Strength of solid plate from 44,851 to 47,481 lbs. 

Strength of welded plate from 26,442 to 38,931 lbs. 

Ratio of weld to solid 57.7 to 83.9% 

Chain Links. — 216 Tests. 

Strength of solid bar from 49,122 to 57,875 lbs. 

Strength of welded bar from 39,575 to 48,824 lbs. 

Ratio of weld to solid ■ 72.1 to 95.4% 

Iron Bars. — Hand and Electric Machine Welded. 

32 tests, solid iron, average 52,444 

17 " electric welded, average 46,836 ratio 89.1% 

19 " hand " " 46,899 " 89.3% 

Steel Bars and Plates. — 14 Tests. 

Strength of solid 54,226 to 64,580 

Strength of weld 28,553 to 46,019 

Ratio weld to solid 52.6 to 82.1% 

The ratio of weld to solid in all the tests ranging from 37.0 to 95.4 is 
proof of the great variation of workmanship in welding. 



334 



STRENGTH OF MATERIALS. 



Cast Copper. —4 tests, average, E. L., 5900; T. S., 24,781; contr., 
24.5; ext., 21.8. 

Copper Plates. —As rolled, 22 tests, 0.26 to 0.75 in. thick; E. L., 9766 
to 18,650; T. S., 30,993 to 34,281; contr., 31.1 to 57.6; ext., 39.9 to 
52.2. The variation in elastic limit is due to difference in the heat at 
which the plates were finished. Annealing reduces the T. S. only about 
1000 pounds, but the E. L. from 3000 to 7000 pounds. 

Another series, 0.38 to 0.52 in. thick; 148 tests, T. S., 29,099 to 31,924; 
contr., 28.7 to 56.7; ext. in 10 inches, 28.1 to 41.8. Note the uniformity 
in tensile strength. 

Drawn Copper. — 74 tests (0.88 to 1.08 inch diameter); T. S., 31,634 
to 40,557; contr., 37.5 to 64.1; ext. in 10 inches, 5.8 to 48.2. 

Bronze from a Propeller Blade. — ■ Means of two tests each from 
center and edge. Central portion (sp. gr. 8.320), E. L., 7550; T. S., 
26,312; contr., 25.4; ext. in 10 inches, 32.8. Edge portion (sp. gr. 
8.550). E. L., 8950; T. S., 35,960; contr., 37.8; ext. in 10 inches, 47.9. 

Cast German Silver. — 10 tests: E. L., 13,400 to 29,100; T. S., 
23,714 to 46,540; contr., 3.2 to 21.5; ext. in 10 inches, 0.6 to 10.2. 

Thin Sheet Metal. — Tensile Strength. 

German silver, 2 lots 75,816 to 87,129 

Bronze, 4 lots 73,380 to 92,086 

Brass, 2 lots 44,398 to 58,188 

Copper, 9 lots 30,470 to 48,450 

Iron, 13 lots, lengthway 44,331 to 59,484 

Iron, 13 lots, crossway 39,838 to 57,350 

Steel, 6 lots 49,253 to 78,251 

Steel, 6 lots, crossway 55,948 to 80,799 



Wire Ropes. 

Selected Tests Showing Range of Variation. 



Description. 



Galvanized. . 
Ungalvanized 
Ungalvanized 
Galvanized . . . 
Ungalvanized 
Ungalvanized 
Galvanized. . . 
Galvanized. . . 
Galvanized. . . 
Ungalvanized 
Ungalvanized 
Ungalvanized 
Galvanized. . . 
Galvanized. . . 
Ungalvanized 
Ungalvanized 
Galvanized . . . 
Galvanized. . 
Ungalvanized 
Galvanized . . 
Galvanized. . 



<B 








C 


a^ 






aj 




















. c 

O Bi 




7.70 


53.00 


6 


19 


0.1563 


7.00 


53.10 


7 


19 


0.1495 


6.38 


42.50 


7 


19 


0.1347 


7.10 


37.57 


6 


30 


0.1004 


6.18 


40.46 


7 


19 


0.1302 


6.19 


40.33 


7 


19 


0.1316 


4.92 


20.86 


6 


30 


0.0728 


5.36 


18.94 


6 


12 


0. 1 1 04 


4.82 


21.50 


6 


7 


0. 1 693 


3.65 


12.21 


6 


19 


0.0755 


3.50 


12.65 


7 


7 


0.122 


3.82 


14.12 


6 


7 


0.135 


4.11 


11.35 


6 


12 


0.080 


3.31 


7.27 


6 


17. 


0.068 


3.02 


8.62 


6 


7 


0.105 


2.68 


6.26 


6 


6 


0.0963 


2.87 


5.43 


6 


12 


0.0560 


2.46 


3.85 


6 


12 


0.0472 


1.75 


2.80 


6 


7 


0.0619 


2.04 


2.72 


6 


12 


0.0378 


1.76 


1.85 


6 


12 


0.0305 



Hemp Core. 



Main 
Main and Strands 

Wire Core 

Main and Strands 

Wire Core 

Wire Core 

Main and Strands 

Main and Strands 

Main 

Main 
Wire Core 

Main 
Main and Strands 
Main and Strands 

Main 
Main and Strands 
Main and Strands 
Main and Strands 

Main 
Main and Strands 

Main 



IP 

P«2 



339,780 
314,860 
295,920 
272,750 
268,470 
221,820 
190,890 
136,550 
129,710 
110,180 
101,440 
98,670 
75,110 
55,095 
49,555 
41,205 
38,555 
28,075 
24,552 
20,415 
14,634 



kirkaldy's tests. 335 



Wire. — Tensile Strength. 

German silver, 5 lots 81,735 to 92,224 

Bronze, 1 lot 78,049 

Brass, as drawn, 4 lots 81,114 to 98,578 

Copper, as drawn, 3 lots 37,607 to 46,494 

Copper annealed, 3 lots 34,936 to 45,210 

Copper (another lot), 4 lots 35,052 to 62,190 

Copper (extension 36.4 to 0.6%). 

Iron, 8 lots 59,246 to 97,908 

Iron (extension 15.1 to 0.7%). 

Steel, 8 lots „ „ 103,272 to 318,823 

. The steel of 318,823 T. S. was 0.047 inch diam., and had an extension of 
only 0.3 percent; that of 103,272 T. S. was 0.107 inch diam., and had an 
extension of 2.2 per cent. One lot of_0.044 inch diam. had 267,114 T. S., 
and 5.2 per cent extension. 

Hemp Ropes* I. T n tarred. — 15 tests of ropes from 1.53 to 6.90 inches 
circumference, weighing 0.42 to 7.77 pounds per fathom, showed an 
ultimate strength of from 1670 to 33,808 pounds, the strength per fathom 
weight varying from 2872 to 5534 pounds. 

Hemp Ropes, Tarred. — 15 tests of ropes from 1.44 to 7.12 inches 
circumference, weighing from 0.38 to 10.39 pounds per fathom, showed 
an ultimate strength of from 1046 to 31,549 pounds, the strength per 
fathom weight varying from 1767 to 5149 pounds. 

Cotton Ropes. — 5 ropes, 2.48 to 6.51 inches circumference, 1.08 to 
8.17 pounds per fathom. Strength 30S9 to 23,258 pounds, or 2474 to 
3346 pounds per fathom weight. 

Manila Ropes. — 35 tests: 1.19 to 8.90 inches circumference, 0.20 to 
11.40 pounds per fathom. Strength 1280 to 65,550 pounds, or 3003 to 
7394 pounds per fathom weight. 

Belting. 

No. of Tensile strength 

lots. per square inch. 

11 Leather, single, ordinary tanned 3248 to 4824 

4 Leather, single, Helvetia 5631 to 5944 

7 Leather, double, ordinary tanned : 2160 to 3572 

8 Leather, double Helvetia 4078 to 5412 

6 Cotton, solid woven 5648 to 8869 

14 Cotton, folded, stitched 4570 to 7750 

1 Flax, solid, woven 9946 

1 Flax, folded, stitched 6389 

6 Hair, solid, woven 3852 to 5159 

2 Rubber, solid, woven 4271 to 4343 

Canvas. — 35 lots: Strength, lengthwise, 113 to 408 pounds per inch; 
crossways, 191 to 468 pounds per inch. 

The grades are numbered 1 to 6, but the weights are not given. The 
strengths vary considerably, even in the same number. 

Marbles. — Crushing strength of various marbles. 38 tests, 8 kinds. 
Specimens were 6-inch cubes, or columns 4 to 6 inches diameter, and 6 
and 12 inches high. Range 7542 to 13,720 pounds per square inch. 

Granite. — Crushing strength, 17 tests: square columns 4X4 and 
6 X 4, 4 to 24 inches high, 3 kinds. Crushing strength ranges 10,026 to 
13,271 pounds per square inch. (Very uniform.) 

Stones. — (Probably sandstone, local names only given.) 11 kinds, 42 
tests, 6X6, columns 12, 18 and 24 inches high. Crushing strength 
ranges from 2105 to 12,122. The strength of the column 24 inches long 
is generally from 10 to 20 per cent less than that of the 6-inch cube. 

Stones. — (Probably sandstone) tested for London & Northwestern 
Railwav. 16 lots, 3 to 6 tests in a lot. Mean results of each lot ranged 
from 3785 to 11,956 pounds. The variation is chiefly due to the stones 
being from different lots. The different specimens in each lot gave 
results which generally agreed within 30 per cent. 



336 



STRENGTH OF MATERIALS. 



Bricks. — Crushing strength, 8 lots; 6 tests in each lot; mean results 
ranged from 1835 to 9209 pounds per square inch. The maximum 
variation in the specimens of one lot was over 100 per cent of the 
lowest. In the most uniform lot the variation was less than 20 per 
cent. 

Wood. — Transverse and Thrusting Tests. 



Pitch pine. 

Dantzic fir . . 

English oak 

American white oak . . 



Sizes abt. in 
square. 



11 1/2 to 121/2 
12 to 13 

41/2 X 12 
41/2 X 12 







S= 


Span, 


Ultimate 


LW 


inches. 


Stress. 


4BD 2 




45,856 


1096 


144 


to 


to 




80,520 


1403 




37,948 


657 


144 


to 


to 




54,152 


790 




32,856 


1505 


120 


to 


to 




39,084 


1779 




23,624 


1190 


120 


to 


to 




26,952 


1372 



5438 
2478 



3423 
2473 



4437 
2656 



Demerara greenheart, 9 tests (thrusting) 8169 to 10,785 

Oregon pine, 2 tests 5888 and 7284 

Honduras mahogany, 1 test 6769 

Tobasco mahogany, 1 test 5978 

Norway spruce, 2 tests 5259 and 5494 

American yellow pine, 2 tests 3875 and 3993 

English ash, 1 test 3025 

Portland Cement. — (Austrian.) Cross-sections of specimens 2 X 21/2 
inches for pulling tests only; cubes, 3X3 inches for thrusting tests; 
weight, 98.8 pounds per imperial bushel; residue, 0.7 per cent with 
sieve 2500 meshes per square inch; 38.8 per cent by volume of water 
required for mixing; time of setting, 7 days; 10 tests to each lot. The 
mean results in lbs. per sq. in. were as follows: 

Cement Cement 1 Cement, 1 Cement, 1 Cement, 

alone, alone, 2 Sand, 3 Sand, 4 Sand, 

Age. Pulling. Thrusting. Thrusting. Thrusting. Thrusting. 

10 days 376 2910 893 407 228 

20 days 420 3342 1023 494 275 

30 days 451 3724 1172 594 338 

Portland Cement. — Various samples pulling tests, 2 X 21/2 inches 
cross-section, all aged 10 days, 180 tests; ranges 87 to 643 pounds per 
square inch. 

TENSILE STRENGTH OF WIRE. 

(From J. Bucknall Smith's Treatise on Wire.) 

Tons per sq. Pounds per 
in. sectional sq. in. sec- 
area, tional area. 

Black or annealed iron wire 25 56,000 

Bright hard drawn 35 78,400 

Bessemer, steel wire 40 89,600 

Mild Siemens-Martin steel wire 60 134,000 

High carbon ditto (or "improved") 80 179,200 

Crucible cast-steel "improved" wire 100 224,000 

"Improved" cast-steel "plough" 120 268,800 

Special qualities of tempered and improved 

cast steel wire may attain 150 to 170 336,000 to 380,800 



MISCELLANEOUS TESTS OF MATERIALS. 



337 



MISCELLANEOUS TESTS OF MATERIALS. 
Reports of Work of the Watertown Testing-machine in 1883. 

TESTS OF RIVETED JOINTS, IRON AND STEEL PLATES. 







5 










-S O CD 


A * 


43' 




5 

1 


> 

CD'" 

5 


J 

Co 

Stem 

%^£ 

B £ » 
•2-g G 
Qg~ 

3 
P4 


'oi'o 


> 

d 

6 


"o-S 

s 


Tensile Streng 

Joint in Net Se 

tion of Plate p 

square inch, 

pounds. 


biS5 
£ <a G 

G-g.G 


«fH G 

o <u 

&° 

.£Ph 


* 


3/8 


H/16 


3/4 


101/2 


13/4 


39,300 


47,180 


47.0 t 


* 


3/8 


H/16 


3/4 


101/2 


6 


13/4 


41,000 


47,180 


49.0 J 


* 


1/9 


3/4 


13/16 


10 


5 


2 


35,650 


44,615 


45.6 X 


* 


V? 


3/4 


13/16 


10 


5 


2 


35,150 


44,615 


44.9 J 


* 


3/8 


11/16 


3/4 


10 


5 


2 


46,360 


47,180 


59.9 § 


* 


3/8 


H/16 


3/4 


10 


5 


2 


46,875 


47,180 


60.5 § 


* 


1/9 


3/4 


.13/16 


10 


5 


2 


46,400 


44,615 


59.4 § 


* 


!/•> 


3/4 


13/16 


10 


5 


2 


46,140 


44,615 


59.2 § 


* 


5/8 


1 


H/16 


101/2 


4 


25/ 8 


44,260 


44,635 


57.2 § 


* 


5/8 


1 


1-1/16 


101/2 


4 


25/ 8 


42,350 


44,635 


54.9 § 


* 


3/4 


U/8 


13/16 


11 .9 


4 


2.9 


42,310 


46,590 


52.1 § 


* 


3/4 


U/8 


13/16 


11 .9 


4 


2.9 


41,920 


46,590 


51.7 § 


* 


3/8 


3/4 


13/16 


101/2 


6 


13/4 


61,270 


53,330 


59.5 t 


t 


3/8 


3/4 


13/16 


101/2 


6 


13/4 


60,830 


53,330 


59.1 % 


t 


1/9 


15/16 


1 


10 


5 


2 


47,530 


57,215 


40.2 X 


t 


1/9 


15/16 


1 


10 


5 


2 


49,840 


57,215 


42.3 X 


t 


3/8 


H/16 


3/4 


10 


5 


2 


62,770 


53,330 


71.7 § 


t 


3/8 


H/16 


3/4 


10 


5 


2 


61,210 


53,330 


69.8 § 


t 


1/9 


15/16 


1 


10 


5 


2 


68,920 


57,215 


57.1 § 


t 


1/9 


15/16 


1 


10 


5 


2 


66,710 


57,215 


55.0 § 


t 


5/8 


1 


H/16 


91/2 


4 


23/g 


62,180 


52,445 


63.4 § 


t 


5/8 


1 


H/16 


91/2 


4 


23/ 8 


62,590 


52,445 


63.8 § 


t 


3/4 


U/8 


13/16 


10 


4 


21/2 


54,650 


51,545 


54.0 § 


t 


3/4 


U/8 


13/16 


10 


4 


21/2 


54,200 


51,545 


53.4 § 



t Steel. 



X Lap-joint. 



§ Butt-joint. 



The efficiency of the joints is found by dividing the maximum tensile 
stress on the gross sectional area of plate by the tensile strength of the 
material. 



COMPRESSION TESTS OF 3 X 


3 INCH WROUGHT-IRON BARS. 


Length, inches. 


Tested with Two 
Pin Ends, Pins U/2 
in. Diana. Com- 
pressive Strength, 
lbs. per sq. in. 


Tested with Two 
Flat Ends. Com- 
pressive Strength, 
lbs. per sq. in. 


Tested with One 
Flat and One Pin 
End. Compressive 
Strength, lbs. per 
sq. in. 




(28,260 
\ 3 1 ,990 
(26,310 
\ 26,640 
( 24,030 
\ 25,380 
( 20,660 
1 20,200 
( 16,520 
X 17,840 
( 13,010 
X 15,700 
















60 














90 


VoVs 
oooo 


(25,120 


120 


< 22,450 
(21,870 



























338 



STRENGTH OF MATERIALS, 



Tested 
Ends. 



with Two Pin 
Length of Bars 



Diameter Comp 

of Pins. per sq. : 

7/ 8 inch 16 

1 1/8 inches 17, 

17/s " 21 

.21/4 " ....: 



. Str., 
n., lbs. 
250 
740 

400 

210 



COMPRESSION OF WROUGHT-IRON COLUMNS, 
BOX AND SOLID WEB. 

ALL TESTED WITH PIN ENDS. 



Columns made of 



6-inch channel, solid web 

6 " " " " 

6 " " " " 

8 " " " " 

8 " " " " 

8-inch channels, with 5/ig-in. continuous 

plates ." 

5/i6-inch continuous plates and angles.. 

Width of plates, 12 in., 1 in. and 7.35 in 
7/i6-inch continuous plates and angles.. 

Plates 1 2 in. wide 

8-inch channels, latticed 

8 " " " 

8 " " " 

8-inch channels, latticed, swelled sides . . 



10-inch channels, latticed, swelled sides. 
10 " " " 

io " •• 'I 

* 10-inch channels, latticed one side; con 
tinuous plate one side 

t 10-inch channels, latticed one side; con 
tinuous plate one side 



10.0 
15.0 
20.0 
20.0 



26.8 
13.3 
20.0 
26.8 
13.4 
20.0 
26.8 
16.8 
25.0 
16.7 
25.0 

25.0 

25.0 



9.83 f 
9.977 
9.762 
16.281 
16.141 

19.417 

16.163 

20.954 
7.628 
7.621 
7.673 
7.624 
7.517 
7.702 
1 1 .944 
12.175 
12.366 
1 1 .932 

17.622 

17.721 



432 

592 

755 

1,290 

1,645 

1,940 

1,765 

2,242 

679 

924 

1,255 

684 

921 

1,280 

1,470 

1,926 

1,549 

1,962 

1,848 

1,827 






30,220 
21,050 
16,220 
22,540 
17,570 

25,290 

28,020 

25,770 
33,910 
34,120 
29,870 
33,530 
33,390 
30,770 
33,740 
32,440 
31,130 
32,740 

26,190 

17,270 



* Pins in center of gravity of channel bars and continuous plate, 1.63 
inches from center line of channel bars. 

t Pins placed in center of gravity of channel bars. 



TENSILE TEST OF SIX STEEL EYE-BARS. 

COMPARED WITH SMALL TEST INGOTS. 

The steel was made by the Cambria Iron Company, and the eye-bar 
heads made by Keystone Bridge Company by upsetting and hammering. 
All the bars were made from one ingot. Two test pieces, 3/ 4 _inch round, 
rolled from a test-ingot, gave elastic limit 48,040 and 42,210 pounds; 
tensile strength, 73,150 and 69,470 pounds, and elongation in 8 inches, 
22.4 and 25.6 per cent respectively. The ingot from which the eye-bars 
were made was 14 inches square, rolled to billet, 7X6 inches! The 
eye-bars were rolled to 6 1/2 X 1 inch. Chemical tests gave carbon 0.27 
to 0.30; manganese, 0.64 to 0.73; phosphorus, 0.074 to 0.09S. 



MISCELLANEOUS TESTS OF IRON AND STEEL. 339 



Gauged 


Elastic 


Tensile 


Elongation 


Length, 


limit, lbs. 


strength per 


per cent, in 


inches. 


per sq. in. 


sq. in., lbs. 


Gauged Length. 


160 


37,4S0 


67,800 


15.8 


160 


36,650 


64,000 


6.96 


160 




71,560 


8.6 


200 


37,600 


68,720 


12.3 


200 


35,810 


65,850 


12.0 


200 


33,230 


64,410 


16.4 


200 


37,640 


6S,290 


13.9 



The average tensile strength of the 3/4-inch test pieces was 71,310 lbs., 
that of the eye-bars 67,230 lbs., a decrease of 5.7%. The average elastic 
limit of the test pieces was 45,150 lbs., that of the eye-bars 36,402 lbs., a 
decrease of 19.4%. The elastic limit of the test pieces was 63.3% of 
the ultimate strength, that of the eve-bars 54.2% of the ultimate strength. 

Tests of 11 full-sized eye bars, 15 X 1 1/4 to 2i/i 6 in., 20.5 to 21.4 ft. long 
between centers of pins, made bv the Phoenix Iron Co., are reported in 
Eng. News, Feb. 2, 1905. The average T.S. of the bars was 58,300 lbs. 
per sq. in., E.L., 32,800. The average T.S. of small specimens was 
63,900, E.L., 37,000. The T.S. of the full-sized • bars averaged 8.8% 
and the E.L. 12.1% lower than the small specimens. 

EFFECT OF COLD-DRAWING ON STEEL. 

Three pieces cut from the same bar of hot-rolled steel: 

1. Original bar, 2.03 in. diam., gauged length 30 in., tensile strength 

55,400 lbs. per square in.; elongation 23.9%. 

2. Diameter reduced in compression dies (one pass) .094in.; T. S. 70,420; 

el. 2.7% in 20 in. 

3. " " " " " " " 0.222in.;T.S. 81,890; 

el. 0.075 % in 20 in. 
Compression test of cold-drawn bar (same as No. 3), length 4 in., diam. 
1.808 in.: Compressive strength per sq. in., 75,000 lbs.; amount of com- 
pression 0.057 in.; set 0.04 in. Diameter increased by compression to 
1.821 in. in the middle; to 1.813 in. at the ends. 



MISCELLANEOUS TESTS OF IRON AND STEEL. 

Tests of Cold-rolled and Cold-drawn Steel, made by the Cambria 
Iron Co. in 1897, gave the following results (averages of 12 tests of each) : 

E. L. T. S. El. in 8 in. Red. 

Before coid-rolling 35,390 59,980 28.3% 58.5% 

After cold-rolling 72,530 79,830 9.6% 34.9%, 

After cold-drawing 76,350 83,860 8.9% 34.2% 

The original bars were 2 in. and 7/ 8 in. diameter. The test pieces cut 
from the bars were 3/ 4 in. diam., IS in. long. The reduction in diameter 
from the hot-rolled to the cold-rolled or cold-drawn bar was 1/16 in. in 
each case. 

Cold Rolled Steel Shafting (Jones & Laughlins) m/i6in. diam. — 
Torsion tests of 12 samples gave apparent outside fiber stress, calculated 
from maximum twisting moment, 70,700 to 82,900 lbs. per sq. in.; fiber 
stress at elastic limit, 32,500 to 38,800 lbs. per sq. in.; shearing modulus 
of elasticity, 11,800,000 to 12,100,000; number of turns per foot before 
fracture, 1.60 to 2.06. — Tech. Quar., vol. xii, Sept., 1899. 

Torsion Tests on Cold Rolled Shafting. — {Tech. Quar. XIII, No. 3, 
1900, p. 229.) 14 tests. Diameter about 1.69 in. Gauged length, 40 to 
50 in. Outside fiber stress at elastic limit, 28,610 to 33,590 lbs. per sq. 
in.; apparent outside fiber stress at maximum load, 67,980 to 77,290. 
Shearing modulus of elasticity, 11,400,000 to 12,030,000 lbs. per sq. in. 
Turns per foot between jaws at fracture, 0.413 to 2.49. 

Torsion Tests on Refined Iron. — 13/ 4 in. diam. 14 tests. Gauged 
length, 40 ins. Outside fiber stress at elastic limit, 12,790 to 19,140 lbs. 
per sq. in.; apparent outside fiber stress at maximum load, 45,350 to 
58,340. Shea?ing modulus of elasticity, 10,220,000 to 11,700,000. Turns 
per foot betwem jaws at fracture, 1.08 to 1.42. 



340 



STRENGTH OF MATERIALS. 



Tests of Steel Angles with Riveted End Connections. (F. P. 

McKibbin, Proc. A.S.T.M., 1907.) — The angles broke through the rivet 
holes in all cases. The strength developed ranged from 62.5 to 79.1% 
of the ultimate strength of the gross area, or from 73.9 to 92% of the 
calculated strength of the net section at the rivet holes. 

SHEARING STRENGTH. 

H. V. Loss in American Engineer and Railroad Journal, March and 
April, 1893, describes an extensive series of experiments on the shearing 
of iron and steel bars in shearing machines. Some of his results are: 

Depth of penetration at point of maximum resistance for soft steel 
bars is independent of the width, but varies with the thickness. If 
d = depth of penetration and t = thickness, d_= 0.3£ for a flat knife, 
d = 0.25t for a 4° bevel knife, and d = 0.16 Vjs f or an 8° bevel knife. 
The ultimate pressure per inch of width in flat steel bars is approxi- 
mately "0,000 lbs. X t. The energy consumed in foot-pounds per inch 
width of steel bars is, approximately: 1" thick, 1300 ft. -lbs.; IV2", 
2500; 13/4", 3700; 1W, 4500; the energy increasing at a slower rate than 
the square of "the thickness. Iron angles require more energy than steel 
angles of the same size; steel breaks while iron has to be cut off. Few 
hot-rolled steel the, resistance per square inch for rectangular sections 
varies from 4400 lbs. to 20,500 lbs., depending partly upon its hardness 
and partly upon the size of its cross-area, which latter element indirectly 
but greatly indicates the temperature, as the smaller dimensions require 
a considerably longer time to reduce them down to size, which time 
again means loss of heat. 

It is not probable that the resistance in practice can be brought very 
much below the lowest figures here given — viz., 4400 lbs. per square 
inch — as a decrease of 1000 lbs. will henceforth mean a considerable 
increase in cross-section and temperature. 

Relation of Shearing to Tensile Strength of Different 31etals. 
E. G. Izod, in a paper presented to the Institution of Mechl. Engrs. 
{Am. Mac.h., Jan. 18, 1906), describes a series of tests on bars and plates 
of different metals. The specimens were firmly clamped on two steel 
plates with opposed shearing edges 4 ins. apart, and a shearing block, 
which was a sliding fit between these edges, was brought down upon 
the specimen, so as to cut it in double shear, by a testing machine. 





a 


b 


• 




a 


6 


c 


Cast iron. A 


9.7 
13.4 
11.3 

33.1 

13.4 

19.7 
12.1 
7.5 
16.0 


12.5 

2.2 

8.0 
7.8 
6.5 
35.0 


152 
111 
122 

60 

128 

93 
103 
126 

74 


Rolled phosphor- 


39.5 
6.4 
12.7 
26.0 

26.9 
24.9 
42.1 
56.3 
61.3 


11,7 

25.5 
9.6 

22.5 

34.7 
43.0 
26.0 
15.0 
11.0 


61 






70 


Cast aluminum- 
bronze 

Cast phosphor- 


Aluminum alloy 

Wrought t-iron bar. . 
Mild-steel,0.14 car- 


59 
75 

78 


Cast phosphor- 


Crucible steel, 0.12 C 
0.48 C 


74 
68 




0.71 C. . . 


65 




0.77 C 


6? 


Yellow brass 







a. Tensile strength of the metal, gross tons per sq. in.; 6. elongation 
in 2 in.%; c. ratio shearing -r- tensile strength. The results seem to 
point to the fact that there is no common law connecting the ultimate 
shearing stress with the ultimate tensile stress, the ratio varying greatly 
with different materials. The test figures from crystalline materials, 
such as cast iron or those with very little or no elongation, seem to indicate 
that the ultimate shear stress exceeds the ultimate tensile stress by as 
much as 20 or 25%, while from those with a fairly high measure of 
ductility, the ultimate shear stress may be anything from to 50% less 
than the ultimate tensile stress. 

For shearing strength of rivets, see pages 407 and 412, 



STRENGTH OF IRON AND STEEL PIPE. 



341 



STRENGTH OF IRON AND STEEL PIPE. 

Tests of Strength and Threading of Wrought-Iron and Steel 
Pipe. T. N. Thomson, in Proc. Am. Soc. Heat and Vent. Engineers, 
vol. xii., p. 80, describes some experiments on welded wrought iron and 
steel pipes. Short rings of 6-in. pipe were pulled in the direction of a 
diameter so as to elongate the ring. Four wrought iron rings broke at 
2400, 3000, 3100 and 4100 lbs. and four steel rings at 5300 (defective 
weld) 18,000, 29,000 and 35,000 lbs. Another series of 9 tests each 
were tested so as to show the tensile strength of the metal and of the 
weld. The average strength of the metal was, iron, 34,520, steel, 61,850 
lbs. The strength of the weld in iron ranged from 49 to 84, averaging 
71 per cent of the strength of the metal, and in steel from 50 to 93, 
averaging 72%. 

A large number of iron and steel pipes of different sizes were tested by- 
twisting, the force being applied at the end of a three-foot lever. The 
average pull on the steel pipes was: 1/2 in. pipe, 109 lbs.; 1 in., 172 lbs.; 
IV2 in., 300 lbs.; number of turns in 6 ft. length, respectively, 15, 8 and 
51/2- Per cent failed in weld, 0, 13 and 13 respectively. For different 
lots of iron pipe the average pull was: 1/2 in., 68, 81 and 65 lbs.; 1 in., 
154, 136, 107 lbs.; 1 1/2 in. 256, 250, 258 lbs. The number of turns in 
6 feet for the nine lots were respectively, 41/2, 53/4, 21/2; 6 1/4, 31/2. 21/2; 
41/2, 31/2, 21/4. The failures in the weld ranged from 33 to 100% in the 
different lots. 

The force required to thread ll/4-in. pipe with two forms of die was 
tested by pulling on a lever 21 ins. long. The results were as follows: 

Old form of die, iron pipe. . 83 to 87 lbs. pull, steel pipe 100 to 111 lbs. 
Improved die, iron pipe 58 to 62 lbs. pull, steel pipe, 60 to 65 lbs. 

Mr. Thomson gives the following table showing approximately the 
steady pull in pounds required at the end of a 16-in. lever to thread 
twist and split iron and steel pipe of small sizes: 





To Thread with Oiled 
Dies. 


To 
Twist 
Lbs. 


To 
Split 
Lbs. 


Safety 
Margin 
Lbs. 




New 
Rake 
Dies. 


New 
Com- 
mon 
Dies. 


Old 

Com- 
mon 
Dies. 


1/2 in. steel 


34 
27 
44 
44 
69 
62 


56 
33 
60 
51 
111 
106 


60 
49 
91 
73 
124 
116 


122 
102 
150 
140 

286 
273 


152 
110 

240 
176 
420 
327 


74 
46 


3/4 in. steel 


112 




81 


1 in. steel 

1 in. iron 


259 
173 



The margin of safety is computed by adding 30% to the pull required 
to thread with the old dies and subtracting the sum from the pull re- 
quired to split the pipe. If the mechanic pulls on the dies beyond the 
limit, due to imperfect dies, or to a hard spot in the pipe, he will split 
the pipe. 

Old Boiler Tubes used as Columns. (Tech. Quar. XIII, No. 3, 
1900, p. 225.) Thirteen tests were made of old 4-in. tubes taken from 
worn-out boilers. The lengths were from 6 to 8 ft., ratio l/r 53 to 71, 
and thickness of metal 0.13 to 0.18 in. It is not stated whether the tubes 
were iron or steel. The maximum load ranged from 34,600 to 50,000 
lbs., and the maximum load per sq. in. from 17,100 to 27,500 lbs. Six 
new tubes also were tested, with maximum loads 55,600 to 64,800 lbs., 
and maximusa loads per sq. in. 31,600 to 38,100 lbs. The relation of 
the strength p^r sq. in. of the old tubes to the ratio l/r was very variable, 
being expressed approximately by the formula S = 41,000 — €00 l/r 
± 5000. That of the new tubes is approximately S = 52,000 - 300 l/r 
± 2000. 



342 STRENGTH OF MATERIALS. 



HOLDING-POWER OF BOILER-TUBES EXPANDED INTO 
TUBE-SHEETS. 

Experiments by Chief Engineer W. H. Shock, U. S. N., on brass tubes, 
21/2 inches diameter, expanded into plates 3/ 4 inch thick, gave results 
ranging from 5850 to 46,000 lbs. Out of 48 tests 5 gave figures under 
10,000 lbs., 12 between 10,000 and 20,000 lbs., 18 between 20,000 and 
30,000 lbs., 10 between 30,000 and 40,000 lbs., and 3 over 40,000 lbs. 

Experiments by Yarrow & Co., on steel tubes, 2 to 21/4 inches diameter, 
gave results similarly varying, ranging from 7900 to 41,715 lbs., the 
majority ranging from 20,000 to 30,000 lbs. In 15 experiments on 
4 and 5 inch tubes the strain ranged from 20,720 to 68,040 lbs. Beading 
the tube does not necessarily give increased resistance, as some of the 
lower figures were obtained with beaded tubes. (See paper on Rules 
Governing the Construction of Steam Boilers, Trans. Engineering Con- ' 
gress, Section G, Chicago, 1893.) 

The Slipping Point of Rolled Boiler-Tube Joints. 

(O. P. Hood and G. L. Christensen, Trans. A. S. M. E., 1908). , 

When a tube has started from its original seat, the fit may be no longer 
continuous at all points and a leak may result, although the ultimate 
holding power of the tube may not be impaired. A small movement of 
the tube under stress is then the preliminary to a possible leak, and it 
is of interest to know at what stress this slipping begins. 

As results of a series of experiments with tube sheets of from 1/? in. 
to 1 in. in thickness and with straight and tapered tube seats, the authors 
found that the slipping point of a 3-in. 12-gage Shelby cold-drawn tube 
rolled into a straight, smooth machined hole in a 1-in. sheet occurs with 
a pull of about 7,000 lbs. The frictional resistance of such tubes is about 
750 lbs. per sq. in. of tube-bearing area in sheets 5/ 8 in. and 1 in. thick. 

Various degrees of rolling do not greatly affect the point of initial slip, 
and for higher resistances to initial slip other resistance than friction must 
be depended upon. Cutting a 10-pitch square thread in the seat, about 
0.01 in. deep will raise the slipping point to three or four times that in a 
smooth hole. In one test this thread was made 0.015 in. deep in a sheet 
1 in. thick, giving an abutting area of about 1.4 sq. in., and a resistance 
to initial slip of 45,000 lbs. The elastic limit of the tube was reached at 
about 34,000 lbs. 

Where tubes give trouble from slipping and are required to carry an 
unusual load, the slipping point can be easily raised by serrating the tube 
seat by rolling with an ordinary flue expander, the rolls of which are 
grooved about 0.007 in. deep and 10 grooves to the inch. One tube 
thus serrated had its slipping point raised between three and four times 
its usual value. 

METHODS OF TESTING THE HARDNESS OF METALS. 

BrinelPs Method. J. A. Brinell, a Swedish engineer, in 1900 pub- 
lished a method for determining the relative hardness of steel which has 
come into somewhat extensive use. A hardened steel ball, 10 mm. 
(0.3937 in.), is forced with a pressure of 3000 kg. (6614 lbs.) into a flat 
surface on the sample to be tested, so as to make a slight spherical in- 
dentation, the diameter of which may be measured by a microscope or 
the depth by a micrometer. The hardness is defined as the quotient 
of the pressure by the area of the indentation. From the measurement 
the "hardness number" is calculated by one of the following /ormulse: 



H = K (r 4- Vr* - R*) -5- 2 n rR*, or H = K -f- 2 n rd. 

K = load, = 3000 kg., r = radius of ball, = 5 mm., R = radius and 
d = depth of indentation. 

The following table gives the hardness number corresponding to 
different values of R and d. 



STRENGTH OF GLASS. 



343 



R 


H 


R 


H 


R 


H 


d 


H 


d 


H 


d 


H 


1.00 


955 


2.40 


398 


3.80 


251 


2.00 


946 


3.20 


364 


4.60 


170 


1.20 


796 


2.60 


367 


4.00 


239 


2.10 


857 


3.40 


321 


4.80 


156 


1.40 


682 


2.80 


341 


4.20 


227 


2.20 


782 


3.60 


286 


5.00 


143 


1.60 


597 


3.00 


318 


4.40 


217 


2.40 


652 


3.80 


255 


5.50 


116 


1.80 


531 


3.20 


298 


4.60 


208 


2.60 


555 


4.00 


228 


6.00 


95 


2.00 


477 


3.40 


281 


4.80 


199 


2.80 


477 


4.20 


207 


6.50 


80 


2.20 


434 


3.60 


265 


4.95 


193 


3.00 


' 418 


4.40 


187 


6.95 


68 



The hardness of steel, as determined by the Brinell method, has a 
direct relation to the tensile strength, and is equal to the product of a 
coefficient, C, into the hardness number. Experiments made in Sweden 
with annealed steel showed that when the impression was made trans- 
versely to the rolling direction, with H below 175, C = 0.362; with H 
above 175, C = 0.344. When the impression was made in the rolling 
direction, with H below 175, C = 0.354; with H above 175, C = 0.324. 
The product, C X H, or the tensile strength, is expressed in kilograms 
per square millimeter. 

Electro-magnetic Method. — Several instruments have been de- 
vised for testing the hardness of steel by electrical methods. According 
to Prof. D. E. Hughes (Cass. Mag., Sept., 1908), the magnetic capacity 
of iron and steel is directly proportional to the softness, and the resist- 
ance to a feeble external magnetic force is directly as the hardness. The 
electric conductivity of steel decreases with the increase of hardness. 
(See Electric Conductivity of Steel, p. .) 

The Scleroscope. — This is the name of an instrument invented by 
A. F. Shore for determining the hardness of metals. It consists chiefly 
of a vertical glass tube in which slides freely a small cylinder of very 
hard steel, pointed on the lower end, called the hammer. This hammer 
is allowed to fall about 10 inches onto the sample to be tested, and the 
distance, it rebounds is taken as a measure of the hardness of the sample. 
A scale on the tube is divided into 140 equal parts, and the hardness is 
expressed as the number on the scale to which the hammer rebounds. 
Measured in this way the hardness of different substances is as follows: 
Glass, 130; porcelain, 120; hardest steel, 110; tool steel, 1% C, may be 
as low as 31; mild steel, 0.5 C, 26 to 30; gray castings, 39; wrought 
iron, 18; babbitt metal, 4 to 10; soft brass, 12; zinc, 8; copper, 6; 
lead, 2. (Cass. Mag., Sept., 1908.) 



STRENGTH OF GLASS. 

(Fairbairn's "Useful Information for Engineers," Second Series.) 

Best Common Extra 
Flint Green White Crown 
Glass. 

Mean specific gravity 3.078 

Mean tensile strength, lbs. per sq. in., bars 2,413 

do. thin plates 4,200 

Mean crush'g strength, lbs. p. sq. in., cyl'drs 27,582 

do. cubes 13,130 

The bars in tensile tests were about 1/2 inch diameter. The crushing 
tests were made on cylinders about 3/ 4 inch diameter and from 1 to 2 
inches high, and on cubes approximately 1 inch on a side. The mean 
transverse strength of glass, as calculated by Fairbairn from a mean 
tensile strength of 2560 lbs. and a mean compressive strength of 30,150 
lbs. per sq. in., is, for a bar supported at the ends and loaded in the 
middle, w = 3140 bd 2 /l, in which w = breaking weight in lbs., b = 
breadth, d = depth, and I = length, in inches. Actual tests will prob- 
ably show wide variations in both directions from the mean calculated 
strength. 



Glass. 


Glass. 


2.528 
2,896 
4,800 
39,876 
20,206 


2.450 
2,546 
6,000 
31,003 
21,867 



344 



STRENGTH OF MATERIALS. 



STRENGTH OF ICE. 

Experiments at the University of Illinois in 1895 (The Technograph, 
vol. ix) gave 620 lbs. per sq. in. as the average crushing strength of cubes 
of manufactured ice tested at 23° F., and 906 lbs. for cubes tested at 
14° F. Natural ice, at 12° F., tested with the direction of pressure parallel 
to the original water surface, gave a mean of 1070 lbs., and tested with 
the pressure perpendicular to this surface 1845 lbs. The range of varia- 
tion in strength of individual pieces is about 50% above and below the 
mean figures, the lowest and highest figures being respectively 318 and 
2818 lbs. per sq. in. The tensile strength of 34 samples tested at 19 to 
23° F. was from 102 to 256 lbs. per sq. in. 

STRENGTH OF COPPER AT HIGH TE31PERATURES. 

The British Admiralty conducted some experiments at Portsmouth 
Dockyard in 1877, on the effect of increase of temperature on the tensile 
strength of copper and various bronzes. The copper experimented upon 
was in rods 0.72 in. diameter. 

The following table shows some of the results: 



Temperature, 
Fahr. 


Tensile Strength 
in lbs. per sq. in. 


Temperature, 
Fahr. 


Tensile Strength 
in lbs. per sq. in. 


Atmospheric 
100° 
200° 


23,115 
23,366 
22,110 


300° 
400° 
500° 


21,607 
21,105 
19,597 



Up to a temperature of 400° F. the loss of strength was only about 
10 per cent, and at 500° F. the loss was 16 per cent. The temperature of 
steam at 200 lbs. pressure is 382° F., so that according to these experi- 
ments the loss of strength at this point would not be a serious matter. 
Above a temperature of 500° the strength is seriously affected. 



STRENGTH OF TIMBER. 

Strength of Long-leaf Pine (Yellow Pine, Pinus Palustris) from 
Alabama (Bulletin No. 8, Forestry Div., Dept. of Agriculture, 1893. 
Tests by Prof. J. B. Johnson). 

The following is a condensed table of the range of results of mechani- 
cal tests of over 2000 specimens, from 26 trees from four different sites 
in Alabama; reduced to 15 per cent moisture: 



Specific gravity . , 
Transverse strength, 



3WL 

h 2bh? 

do. do. at elast. limit 

Mod. of elast., thous. lbs. 

Relative elast. resilience, 

inch-pounds per cub. in. 

Crushing endwise, str. 

per sq. in.-lbs 

Crushing across grain, 

strength per sq. in., lbs. 

Tensile strength per sq. 

in 

Shearing strength (with 
grain) , mean per sq . in . 









Av'g 
of all 
Butt 


Butt Logs. 


Middle Logs. 


Top Logs. 








Logs. 


0.449 to 1 .039 


0.575 to 0.859 


0.484 to 0.907 


0.767 


4,762 to 16,200 


7,640 to 17,128 


4,268 to 15,554 


12,614 


4,930 to 13,110 
l,119to 3,117 


5,540 to 11,790 
1,136 to 2,982 


2,553 to 11,950 
842 to 2,697 


9,460 
1,926 


0.23 to 4.69 


1.34 to 4.21 


0.09 to 4.65 


2.98 


4,781 to 9,850 


5,030 to 9,300 


4,587 to 9,100 


7,452 


675 to 2,094 


656 to 1,445 


584 to 1,766 


1,598 


8,600 to 31,890 


6,330 to 29,500 


4, 170 to 23,280 


17,359 


464 to 1,299 


539 to 1,230 


484 to 1,1 56 


866 



Some of the deductions from the tests were as follows: 

1. With the exception of tensile strength a reduction of moisture is 
accompanied by an increase in strength, stiffness, and toughness. 

2. Variation in strength goes generally hand-in-hand with specific 
gravity. ■ 



STRENGTH OF TIMBER. 345 

3. In the first 20 or 30 feet in height the values remain constant; then 
occurs a decrease of strength which amounts at 70 feet to 20 to 40 per 
cent of that of the butt-log. 

4. In shearing parallel with the grain and crushing across and par- 
allel with the grain, practically no difference was found. 

5. Large beams appear 10 to 20 per cent weaker than small pieces. 

6. Compression tests endwise seem to furnish the best average state- 
ment of the value of wood, and if one test only can be made, this is the 
safest, as was also recognized by Bauschinger. 

7. Bled timber is in no respect inferior to unbled timber. 

The figures for crushing across the grain represent the load required to 
cause a compression of 15 per cent. The relative elastic resilience, in 
inch-pounds per cubic inch of the material, is obtained by measuring 
the area of the plotted strain-diagram of the transverse test from the 
origin to the point in the curve at which the rate of deflection is 50 per 
cent greater than the rate in the earlier part of the test where the dia- 
gram is a straight line. This point is arbitrarily chosen since there is 
no definite "elastic limit " in timber as there is in iron. The "strength 
at the elastic limit" is the strength taken at this same point. Timber 
is not perfectly elastic for any load if left on any great length of time. 

The long-leaf pine is found in all the Southern coast states from North 
Carolina to Texas. Prof. Johnson says it is probably the strongest timber 
in large sizes to be had in the United States. In small selected speci- 
mens, other species, as oak and hickory, may exceed it in strength and 
toughness. The other Southern yellow pines, viz., the Cuban, short- 
leaf and the loblolly pines are inferior to the long-leaf about in the ratios 
of their specific gravities; the long-leaf being the heaviest of all the 
pines. It averages (kiln-dried) 48 pounds per cubic foot, the Cuban 47, 
the short-leaf 40, and the loblolly 34 pounds. 

Strength of Spruce Timber. — The modulus of rupture of spruce 
is given as follows by different authors: Hatfield, 9900 lbs. per square 
inch; Rankine, 11,100; Laslett, 9045; Trautwine, 8100; Rodman, 6168. 
Trautwine advises for use to deduct one-third in the case of knotty and 
poor timber. 

Prof. Lanza, in 25 tests of large spruce beams, found a modulus of 
rupture from 2995 to 5666 lbs.; the average being 4613 lbs. These 
were average beams, ordered from dealers of good repute. Two beams 
of selected stock, seasoned four years, gave 7562 and 8748 lbs. The 
modulus of elasticity ranged from 897,000 to 1,588,000, averaging 
1,294,000. 

Time tests show much smaller values for both modulus of rupture and 
modulus of elasticity. A beam tested to 5800 lbs. in a screw machine 
was left over night, and the resistance was found next morning to have 
dropped to about 3000, and it broke at 3500. 

Prof. Lanza remarks that while it was necessary to use larger factors 
of safety, when the moduli of rupture were determined from tests with 
smaller pieces, it will be sufficient for most timber constructions, except 
in factories, to use a factor of four. For breaking strains of beams, he 
states that it is better engineering to determine as the safe load of a 
timber beam the load that will not deflect it more than a certain fraction 
of its span, say about 1/300 to 1/400 of its length. 

Expansion of Timber Due to the Absorption of Water. 

(De Volson Wood, A. S. M. E., vol. x.) 

Pieces 36 X 5 in., of pine, oak, and chestnut, were dried thoroughly, 
and then immersed in water for 37 days. 

The mean per cent of elongation and lateral expansion were: 

Pine. Oak. Chestnut. 

Elongation, per cent 0.065 0.085 0.165 

Lateral expansion, per cent ... . 2.6 3.5 3.65 

Expansion of Wood by Heat. — Trautwine gives for the expansion, 
of white pine for 1 degree Fahr. 1 part in 440,530, or for 180 degrees 
1 part in 2447, or about one-third of the expansion of iron. 



346 



STRENGTH OF MATERIALS. 



TESTS OF AMERICAN WOODS. (Watertown Arsenal Tests, 1883.) 

In all cases a large number of tests were made of each wood. Mini- 
mum and maximum results only are given. All of the test specimens 
had a sectional area of 1.575 X 1.575 inches. The transverse test speci- 
mens were 39.37 inches between supports, and the compressive test 
specimens were 12.60 inches long. Modulus of rupture calculated from 

3 PI 
formula R = ~prj, ; P = load in pounds at the middle, I = length, in 

inches, b = breadth, d — depth: 



Name of Wood. 


Transverse Tests. 
Modulus of 
Rupture. 


Comp 

Para 

Grain, 

per squ 

Min. 


ression 
llel to 
pounds 
are inch. 




Min. 


Max. 


Max. 


Cucumber tree {Magnolia acuminata) . 
Yellow poplar white wood (Lirioden- 


7,440 

6,560 

6,720 

9,680 
8,610 

12,200 
8,310 
7,470 

10,190 
9,830 

10,290 
5,950 
5,180 

10,220 
8,250 

6,720 

4,700 
8,400 
14,870 
11,560 
7,010 
9,760 
7,900 
5,950 
13,850 

11,710 

8,390 
6,310 
5,640 
9,530 
5,610 
3,780 

9,220 
9,900 
7,590 

8,220 
10,080 


12,050 

11,756 

11,530 

20,130 
13,450 
21,730 
16,800 
11,130 
14,560 
14,300 
18,500 
15,800 
10,150 
13,952 
15,070 

11,360 

11,740 
16,320 
20,710 
19,430 
18,360 
18,370 
18,420 
12,870 
18,840 

17,610 
13,430 
9,530 
15,100 
10,030 
11,530 
10,980 

21,060 
11,650 
14,680 

17,920 
16,770 


4,560 

4,150 

3,810 

7,460 
6,010 
8,330 
5,830 
5,630 
6,250 
6,240 
6,650 
4,520 
4,050 
6,980 
4,960 

4,960 

5,480 
6,940 
7,650 
7,460 
5,810 
4,960 
4,540 
3,680 
5,770 

5,770 

3,790 
2,660 
4,400 
5,060 
3,750 
2,580 

4,010 
4,150 
4,500 

4,880 
6,810 


7,410 
5,790 


White wood, Basswood (Tilia Ameri- 
cana) 

Sugar-maple, Rock-maple (Acer sac- 


6,480 
9,940 


Red maple (Acer rubrum) 

Locust (Robinia pseudacacia) 

Wild cherry (Primus serotina) 

Sweet gum (Liquidambar styraciflua) . 

Dogwood (Cornus florida) 

Sour gum, Pepperidgd(Nyssa sylvatica) 
Persimmon (Diospyros Virginiana) . . 
White ash (Fraxunis Americana) .... 
Sassafras (Sassafras officinale) 


7,500 
1 1 ,940 
9,120 
7,620 
9,400 
7,480 
8,080 
8,830 
5,970 
8,790 


White elm (Ulmus Americana) 

Sycamore; Button wood (Platanus 


8,040 
7,340 


Butternut; white walnut (Juglans 


6,810 


Black walnut (Juglans nigra) 

Shellbark hickory (Carya alba) 


8,850 
10,280 
8,470 




9,070 




8,970 


Black oak (Quercus tinctoria) 

Chestnut (Castanea vulgaris) 


8,550 
6,650 
7,840 


Canoe-birch, paper-birch (Betula pa- 


8,590 


Cottonwood (Popidus monilifera) .... 

White cedar ( Thuja occidentalis) 

Red cedar (Juniperus Virginiana) . . . 
Cypress (Saxodium Distichum) 


6,510 
5,810 
7,040 
7,140 
5,600 




4,680 




10,600 




5,300 


Hemlock (Tsuga Canadensis) 


7,420 
9,800 


Tamarack (Larix Americana) 


10,700 



THE STRENGTH OF BRICK, STONE, ETC. 



347 



Shearing Strength of American Woods, adapted for Pins or 
Tree-nails. 

J. C. Trautwine {Jour. Franklin Inst.). (Shearing across the grain.) 



per 


sq. in. 


per 


sq. in. 


Ash 


.6280 


Hickory 


. 6045 


Beech 


5223 


Hickory 


. 7285 


Birch 


.5595 


Maple 


. 6355 


Cedar (white) 


1372 


Oak 


. 4425 




1519 


Oak (live) 


8480 


Cedar (Central American) . . . 


3410 


Pine (white) 


. 2480 


Cherry 


2945 


Pine (Northern yellow) 


. 4340 


Chestnut 


1536 


Pine (Southern yellow) 


. 5735 


Dogwood 


6510 


Pine (very resinous yellow) . . 


. 5053 


Ebony 


7750 


Poplar 


. 4418 


Gum 


5890 


Spruce 


. 3255 


Hemlock 


2750 


Walnut (black) 


. 4728 


Locust 


7176 


Walnut (common) 


. 2830 



Transverse Tests of Pine and Spruce Beams. {Tech. Quar. XIII, 
No. 3, 1900, p. 226.) — Tests of 37 hard pine beams, 4 to 10 ins. wide, 6 to 
12 ins. deep, and 8 to 16 ft. length between supports, showed great varia- 
tions in strength. The modulus of rupture of different beams was as 
follows: 1, 2970; 4, 4000 to 5000; 1, 5510; 1, 6220; 9, 7000 to 8000; 8, 
8000 to 9000; 4, 9000 to 10,000; 5, 10,000 to 11,000; 3, 11,000 to 12,000; 
1, 13,600. 

Six tests of white pine beams gave moduli of rupture ranging from 
1840 to 7810; and eighteen tests of spruce beams from 2750 to 7970 lbs. 
per sq. in. 

Drying of Wood. -- Circular 111, U. S. Forest Service, 1907. Sticks 
of Southern loblolly pine 11 to 13 inches diameter, 9 to 10 ft. long, were 
weighed every two weeks until seasoned, to find the weight of water 
evaporated. The loss, per cent of weight, was as follows: 

Weeks 2 4 6 8 10 12 14 16 

Loss per cent of green wood 16 21 26 31 32 34 35 35 

Preservation of Timber. — U. S. Forest Service, Circular 111, 1907, 
discusses preservative treatment of timber by different methods, namely, 
brush treatment with creosote and with carbolinium; open tank treat- 
ment with salt solution, zinc chloride solution; and cylinder treatment 
with zinc chloride solution and creosote. 

The increased life necessary to pay the cost of these several preserva- 
tive treatments is respectively: 6, 16, 7, 13, 41, 27, and 55%. The 
results of the experiments prove that it will pay mining companies to 
peel their timber, to season it for several months and to treat it with a 
good preservative. Loblolly and pitch pine have been most success- 
fully preserved by treatment with creosote in an open tank. 

Circular No. 151 of the Forest Service describes experiments on the 
best method of treating loblolly pine cross-arms of telegraph poles. The 
arms after being seasoned in air are placed in a closed air-tight cylinder, 
a vacuum is applied sufficient to draw the oil (creosote, dead oil of coal 
tar) from the storage tank into the treating cylinder. Sufficient pres- 
sure is then applied to force the oil into the heartwood portion of the 
timber, and continued until the desired amount of oil is absorbed, then a 
vacuum is maintained until the surplus oil is drawn from the sapwood. 
It is recommended that heartwood should finally contain about 6 lbs. 
of oil per cubic foot, and sapwood about 10 lbs. The preliminary bath 
of live steam, formerly used, has been found unnecessary. Much valu- 
able information concerning timber treatment and its benefits is con- 
tained in the several circulars on the subject issued by the Forest 
Service. 

THE STRENGTH OF BRICK, STONE, ETC. 

A great advance has recently (1895) been made in the manufacture 
of brick, in the direction of increasing their strength. Chas. P. Chase, in 
Engineering News, says: "Taking the tests as given in standard engi- 
neering books eight or ten years ago, we find in Trautwine the strength of 
brick given as 500 to 4200 lbs. per sq. in. Now, taking recent tests in 



348 



STRENGTH OF MATERIALS. 



experiments made at Watertown Arsenal, the strength ran from 5000 to 
22,000 lbs. per sq. in. In the tests on Illinois paving-brick, by Prof. 
I. O. Baker, we find an average strength in hard paving brick of over 
5000 lbs. per square inch. The average crushing strength of ten varie- 
ties of paving-brick much used in the West, I find to be 7150 lbs. to the 
square inch." 

A test, of brick made by the dry-clay process at Watertown Arsenal, 
according to Paving, showed an average compressive strength of 3972 lbs. 
per sq. in. In one instance it reached 4973 lbs. per sq. in. A test was 
made at the same place on a "fancy pressed brick." The first crack 
developed at a pressure of 305,000 lbs., and the brick crushed at 364,300 
lbs., or 11,130 lbs. per sq. in. This indicates almost as great compressive 
strength as granite paving-blocks, which is from 12,000 to 20,000 lbs. 
per sq. in. 

The three following notes on bricks are from Trautwine's Engineer's 
Pocket-book: 

Strength of Brick. — 40 to 300 tons per sq. ft., 622 to 4668 lbs. per 
sq. in. A soft brick will crush under 450 to 600 lbs. per sq. in., or 30 to 
40 tons per square foot, but a first-rate machine-pressed brick will stand 
200 to 400 tons per sq. ft. (3112 to 6224 lbs. per sq. in.). 

Weight of Bricks. — Per cubic foot, best pressed brick, 150 lbs.; 
good pressed brick, 131 lbs.; common hard brick, 125 lbs.; good common 
brick, 118 lbs.; soft inferior brick, 100 lbs. 

Absorption of Water. — A brick will in a few minutes absorb 1/2 to 
3/4 lb. of water, the last being 1/7 of the weight of a hand-molded one, 
or 1/3 of its bulk. 

Tests of Bricks, full size, on flat side. (Tests made at Watertown 
Arsenal in 1883.) — The bricks were tested between flat steel buttresses. 
.Compressed surfaces (the largest surface) ground approximately flat. 
The bricks were all about 2 to 2.1 inches thick, 7.5 to 8.1 inches long, 
and 3.5 to 3.76 inches wide. Crushing strength per square inch: One 
lot ranged from 11,056 to 16,734 lbs.; a second, 12,995 to 22,351; a 
third, 10,390 to 12,709. Other tests gave results from 5960 to 10,250 
lbs. per sq. in. 

Tests of Brick. (Tech. Quar., 1900.) — Different brands of brick tested 
on the broad surfaces, and on edge, gave results as follows, lbs. per sq. in. 



(Tech. 


Quar. 


XII, No 


. 3, 1899.) 38 tests. 






No. 
Test. 


Aver- 
age. 


Maxi- 
mum. 


Mini- 
mum. 


Per cent Wai 
Absorbed. 


er 


On broad surface 
Bay State, light hard 

Same, tested on edge . . 

On broad surface 
Dover River, soft 


71 

67 

38 

36 

36 

36 

36 

16 
16 


7039 
6241 

5350 

8070 

2190 

3600 

5360 

7940 
6430 


11,240 
10,840 

8630 

10,940 

3060 

4950 

8810 

9770 
10,230 


3587 
3325 

3930 

5850 

1370 

2080 

3310 

6570 
3830 


15.15 to 19.3av. 
13.67 to 18.2 " 

14.0 to 18.6 " 

4.7 to 10.1 " 

!7.8 to 22.0 " 

16.6 to 23.4 " 

8.3 to 16.7 " 

7.6 to 12.9 " 
6.2 to 18.7 " 


7.5 
7.4 

11 6 


Dover River, hard 


7 


Central N. Y., soft 


19.9 


Central N. Y., me- 
dium burned 

Central N. Y., hard 


18.6 
12 5 


Another lot,* hard 


10 6 


Same,* tested on edge 


11.4 



Brand not named. 



The per cent water absorbed in general seemed to have a relation to 
the strength, the greatest absorption corresponding to the lowest strength, 
and vice versa, but there were many exceptions to the rule. 



THE STRENGTH OF BRICK, STONE, ETC. 349 

Strength of Common Red Brick. — Tests of 67 samples of Hudson 
River macnine-molded brick were made by I. H. Woolson, Eng. News. 
April 13, 1905. The crushing strength, in lbs. per sq. in., of 15 pale biick 
ranged from 1607 to 4546, average 3010; 44 medium, 2080 to 8944, av. 
4080; 8 hard brick, 2396 to 6420, av. 4960. Five -Philadelphia pressed 
brick gave from 3524 to 9425, av. 6361. The absorption ranged from 
8.7 to 21.4% by weight. The relation of absorption to strength varied 
greatly, but on the average there was an increase of absorption up to 
3000 lbs. per sq. in. crushing strength, and beyond that a decrease. 

The Strongest Brick ever tested at the Watertown Arsenal was a 
paving brick from St. Louis, Mo., which showed a compressive strength 
of 3S,446 lbs. per sq. in. The absorption was 0.21% by weight and 
0.5% by volume. The sample was set on end, and measured 2.45 X 3.06 
ins. in cross section. — Eng. News, Mar. 14, 1907. 

Crushing Strength of Masonry Materials. (From Howe's "Re- 
taining-Wafls.") — 

tons per sq. ft. tons per sq. ft. 

Brick, best pressed . 40 to 300 Limestones and marbles 250 to 1000 

Chalk 20 to 30 Sandstone 150 to 550 

Granite 300 to 1200 Soapstone 400 to 800 

Strength of Granite. — The crushing strength of granite is commonly 
rated at 12,000 to 15,000 lbs. per sq. in. when tested in two-inch cubes, 
and only the hardest and toughest of the commonly used varieties reach 
a strength above 20,000 lbs. Samples of granite from a quarry on the 
Connecticut River, tested at the Watertown Arsenal, have shown a 
strength of 35,965 lbs. per sq. in. (Engineering News, Jan. 12, 1893). 

Ordinary granite ranges from 20,000 to 30,000 lbs. compressive strength 
per sq. in. A granite from Asheville, N.C., tested at the Watertown 
Arsenal, gave 51,900 lbs. — Eng. News, Mar. 14, 1907. 

Strength of Avondale, Pa., Limestone. (Engineering Nei»*, 
Feb. 9, 1893.) — Crushing strength of 2-in. cubes: light stone 12,112, 
gray stone 18,040, lbs. per sq. in. 

Transverse test of lintels, tool-dressed, 42 in. between knife-edge bear- 
ings, load with knife-edge brought upon the middle between bearings: 

Gray stone, section 6 in. wide X 10 in. high, broke under a load of 20,950 lbs. 

Modulus of rupture 2,200 " 

Light stone, section SV4 in. wide X10 in. high, broke under. . . 14,720 " 

Modulus of rupture 1,170 " 

Absorption. — Gray stone 0.051 of 1 % 

Light stone 0.052 of 1% 

Tests of Sand-lime Brick. (I. H. Woolson, Eng. News, June 14, 
1906). — Eight varieties of brick in lots of 300 to 800 were received from 
different manufacturers. They were tested for transverse strength, on 
supports 7 in. apart, loaded in the middle: and half bricks were tested by 
compression, sheets of heavy fibrous paper being inserted between the 
specimen and the plates of the testing machine to insure an even bearing. 
Tests were made on the brick as received, and on other samples after 
drying at about 150° F. to constant weight, requiring from four to six 
days. The moisture in two bricks of each series was determined, and 
found to range from 1 to 10%, average 5.9%. The figures of results 
given below are the averages of 10 tests in each case. Other bricks of 
each lot were tested for absorption by being immersed 1/2 in. in water for 
48 hours, for resistance to 20 repeated freezings and thawings, and for 
resistance to fire by heating them in a fire testing room, the bricks being 
built in as 8-in. walls, to 1700° F. and maintaining that temperature 
three hours, then cooling them with a li/8-in. stream of cold water from 
a hydrant. Transverse and compressive tests were made after these 
treatments. The results given below are averages of five tests, except in 
the case of the bricks tested after firing, in which two samples are averaged. 

Effect of the Fire Test. — Several large cracks developed in both 
the sand-lime and the clay brick walls during the test. These were no 
worse in one wall than in the other. With the exception of surface 
deterioration the walls were solid and in good condition. After they 



350 



STRENGTH OF MATERIALS. 



were cooled the inside course of each wall was cut through and specimens 
of each series secured for examination and test. It was difficult to 
secure whole bricks, owing to the extreme brittleness. 

In general the bricks were affected by fire about half way through. 
They were all brittle and many of them tender when removed from the 
wall. With the sand-lime brick, if a brick broke the remainder had to be 
chiseled out like concrete, whereas a clay brick under like conditions 
would chip out easily. The clay brick were so brittle and full of cracks 
that the wall could be broken down without trouble. The sa'nd-lime 
bricks adhered to the mortar better, were cracked less, and were not so 
brittle. 



Designation of Brick. 


A 

272 


B 


C 


D 


E 


F 


G 


Modulus of ) 
Rupture J 


As received 


424 


377 


262 


190 


301 


365 


Dried 


320 


505 


406 


334 


197 


570 


494 




Increase, % 


15.0 


16.0 


7.1 


21.5 


3.5 


47.2 


26.2 




Wet 


248 


349 


345 


241 


243 


250 


485 


" 


After fire 


17 


57 


20 


32 


•24 


27 


37 






Compressive ) 


As received 


1875 


2300 


2871 


1923 


1610 


2460 


2669 


Strength, | 


Dried 


2604 


2772 


3240 


2476 


1870 


3273 


3190 


lbs. per sq. in. ) 


Increase, % 


30.2 


17.1 


20.7 


22.3 


13.5 


24.8 


16.3 




Wet 


1611 


2174 


2097 


1923 


1108 


2063 


2183 




After freez- 


















ing 


1596 


1619 


2265 


1174 


1167 


1851 


1739 




After fire 1807 


2814 


2573 


2069 


1089 


2051 


4885 


% of lime in brick 


b 


10 


5 


41/* 


41/7 


5 


8 


Pressure for hardening, lbs.. . . 


120 


135 


150 


125 


120 


150 


125 


Hours in hardening, lbs 


10 


8 


7 


10 


10 


7 


10 



Transverse Strength of Flagging. 

(N. J. Steel & Iron Co.'s Book.) 
Experiments made by R. G. Hatfield and Others. 

6 = width of the stone in inches; d = its thickness in inches; I — dis- 
tance between bearings in inches. 

The breaking loads in tons of 2000 lbs., for a weight placed at the center 
of the space, will be as follows: 



bd 2 
I 

Bluestone flagging 0.744 

Quincy granite 0.624 

Little Falls freestone 0.576 

Belleville, N. J., freestone. . 0.480 
Granite (another quarry). . . 0.432 
Connecticut freestone 0.312 



X 



bd 2 
I 



X 



Dorchester freestone 0.264 

Aubigny freestone 0.216 

Caen freestone 0.144 

Glass 1.000 

Slate 1.2 to 2.7 



Thus a block of Quincy granite 80 inches wide and 6 inches thick, 
resting on beams 36 inches in the clear, would be broken by a load resting 

80 X 36 
midway between the beams = — — — X 0.624 »= 49.92 tons, 
oo 



STRENGTH OF LIME AND CEMENT MORTAR. 

{Engineering, October 2, 1891.) 

Tests made at the University of Illinois on the effects of adding cement 
to lime mortar. In all the tests a good quality of ordinary fat lime was 
used, slaked for two days in an earthenware jar, adding two parts by 
weight of water to one of lime, the loss by evaporation being made up 



VARIOUS MATERIALS. 



351 



by fresh additions of water. The cements used were a German Port- 
land, Black Diamond (Louisville), and Rosendale. As regards fineness 
of grinding, 85 per cent of the Portland passed through a No. 100 sieve, 
as did 72 per cent of the Rosendale. A fairly sharp sand, thoroughly 
washed and dried, passing through a No. 18 sieve and caught on a No. 30, 
was used. The mortar in all cases consisted of two volumes of sand to 
one of lime paste. The following results were obtained on adding 
various percentages of cement to the mortar: 



Tensile Strength, pounds per square inch. 



Age { 


4 


7 


14 


21 


28 


50 


84 


Days. 


Days. 


Days. 


Days. 


Days. 


Days. 


Days. 




4 
5 


8 
81/2 


10 
91/2 


13 
12 


18 
17 


21 
17 


26 


20 per cent Rosendale 


18 


20 " " Portland. 


5 


81/2 


14 


20 


25 


24 


26 


30 " " Rosendale 


7 


11 


13 


181/ 2 


21 


221/2 


23 


30 " " Portland. 


8 


16 


18 


22 


25 


28 


27 


40 " " Rosendale 


10 


12 


I6I/2 


211/2 


221/9 


24 


36 


40 " " Portland. 


27 


39 


38 


43 


47 


59 


57 


60 " " Rosendale 


9 


13 


20 


16 


22 


221/2 


23 


60 " " Portland. 


45 


58 


55 


68 


67 


102 


78 


80 " " Rosendale 


12 


I8I/2 


221/2 


27 


29 


3H/2 


33 


80 " " Portland. 


87 


91 


103 


124 


94 


210 


145 


100 " " Rosendale 


18 


23 


26 


31 


34 


46 


48 


100 " " Portland. 


90 


120 


146 


152 


181 


205 


202 



Tests of Portland Cement. 

(Tech, Quar. XIII. No. 3, 1900, p. 236.) 





IDay. 


2 Days. 


14 Days 


1 Mo. 


2Mos. 


6 Mos. 


1 Year. 


Neat cement: 
Tension, lbs. 
per sq. in... 


268-312 
( 8650 
{ to 
( 10,250 

56-75 
( 1200 
\ to 
( 1585 


454-532 
13,080 

to 
14,860 

79-92 
1750 
to 
1885 


780-820 
23,640 

to 
34,820 

185-211 
3780 
to 
4420 


915-920 
211-230 


950-1100 
34,000 

to 
38,500 

217-240 
7850 
to 
8250 


1036-1190 


996-1248 
36,150 

to 
50,000 


Compression, 
lbs. per sq. in 




3 sand, 1 cem. 
Tens 


300-382 


280-383 




8000 


3 sand, 1 cem. 




to 


Comp. 




10,000 









MODULI OF ELASTICITY OF VARIOUS MATERIALS. 

The modulus of elasticity determined from a tensile test of a bar of any 
material is the quotient obtained by dividing the tensile stress in pounds 

f)er square inch at any point of the test by the elongation per inch of 
ength produced by that stress; or if P = pounds of stress applied, 
K = the sectional area, I = length of the portion of the bar in which the 
measurement is made, and A. = the elongation in that length, the modu- 
lus of elasticity E = — ■*• - = — • The modulus is generally measured 

A ( /1A 

within the elastic limit only, in materials that have a well-defined elastic 
limit, such as iron and steel, and when not otherwise stated the modulus 
is understood to be the modulus within the elastic limit. Within this 
limit, for such materials the modulus is practically constant for any 
given bar, the elongation being directly proportional to the stress. In 



352 STRENGTH OF MATERIALS. 

other materials, such as cast iron, which have no well-defined elastic 
limit, the elongations from the beginning of a test increase in a greater 
ratio than the stresses, and the modulus is therefore at its maximum near 
the beginning of the test, and continually decreases. The moduli of 
elasticity of various materials have already been given above in treating 
of these materials, but the following table gives some additional values 
selected from different sources: 

Brass, cast ' 9,170,000 

Brass wire 14,230,000 

Copper 15,000,000 to 18,000,000 

Lead 1,000,000 

Tin, cast 4,600,000 

Iron, cast 12,000,000 to 27,000,000 (?) 

Iron, wrought 22,000,000 to 29,000,000 (?) 

Steel 28,000,000 to 32,000,000 (see below) 

Marble 25,000,000 

Slate 14,500,000 

Glass 8,000,000 

Ash 1,600,000 

Beech 1,300,000 

Birch 1,250,000 to 1,500,000 

Fir 869,000 to 2,191,000 

Oak 974,000 to 2,283,000 

Teak 2,414,000 

Walnut 306,000 

Pine, long-leaf (butt-logs) . 1,119,000 to 3,117,000 Avge. 1,926,000 

The maximum figures given by some earlv writers for iron and steel, 
viz., 40,000,000 and 42,000,000, are undoubtedly erroneous. The modulus 
of elasticity of steel (within the elastic limit) is remarkably constant, 
notwithstanding great variations in chemical analysis, temper, etc. It 
rarely is found below 29,000,000 or above 31,000,000. It is generally 
taken at 30,000,000 in engineering calculations. Prof. J. B. Johnson, 
in his report on Long-leaf Pine, 1893, says: "The modulus of elasticity 
is the most constant and reliable property of all engineering materials. 
The wide range of value of the modulus of elasticity of the various metals 
found in public records must be explained by erroneous methods of 
testing." 

In a tensile test of cast iron by the author (Van Nostrand's Science 
Series, No. 41, page 45), in which the ultimate strength was 23,285 lbs. 
per sq. in., the measurements of elongation were made to 0.0001 inch, 
and the modulus of elasticity was found to decrease from the beginning 
of the test, as follows: At 1000 lbs. per sq. in., 25,000,000: at 2000 lbs., 
16,666,000; at 4000 lbs., 15,384,000; at 6000 lbs., 13,636,000; at 8000 
lbs., 12,500,000; at 12,000 lbs., 11,250,000; at 15,000 lbs., 10,000,000; 
at 20,000 lbs., 8,000 000; at 23,000 lbs., 6,140,000. 



FACTORS OF SAFETY. 

A factor of safety is the ratio in which the load that is just sufficient to 
overcome instantly the strength of a piece of material is greater than the 
greatest safe ordinary working load. (Rankine.) 

Rankine gives the following "examples of the values of those factors 
which occur in machines": 

Dead Load, Live Load, Live Load, 

Greatest. Mean. 

Iron and steel 3 6 from 6 to 40 



Timber 4 to 5 

Masonry 4 



The great factor of safety, 40, is for shafts in millwork which transmit 
very variable efforts. 



FACTORS OF SAFETY. 353 

Unwin gives the following " factors of safety which have been adopted 
in certain cases for different materials." They "include an allowance 
for ordinary contingencies." 

, Live Load. > 

Dead In Temporary In Permanent In Structures 
Load. Structures. Structures, subj. to Shocks. 
Wrought iron and steel 3 4 4 to 5 10 

Cast iron 3 4 5 10 

Timber 4 10 

Brickwork .... 6 .... 

Masonry 20 20 to 30 

Unwin says that "these numbers fairly represent practice based on 
experience in many actual cases, but they are not very trustworthy." 

Prof. Wood in his "Resistance of Materials" says: "In regard to the 
margin that should be left for safety, much depends upon the character 
of the loading. If the load is simply a dead weight, the margin may be 
comparatively small; but if the structure is to be subjected to percus- 
sive forces or shocks, the margin should be comparatively large on account 
of the indeterminate effect produced by the force. In machines which 
are subjected to a constant jar while in use, it is very difficult to deter- 
mine the proper margin which is consistent with economy and safety. 
Indeed, in such cases, economy as well as safety generally consists in 
making them excessively strong, as a single breakage may cost much 
more than the extra material necessary to fully insure safety." 

For discussion of the resistance of materials to repeated stresses and 
shocks, see pages 261 to 264. 

Instead of using factors of safety, it is becoming customary in designing 
to fix a certain number of pounds per square inch as the maximum stress 
which will be allowed on a piece. Thus, in designing a boiler, instead of 
naming a factor of safety of 6 for the plates and 10 for the stay-bolts, the 
ultimate tensile strength of the steel being from 50,000 to 60,000 lbs. per 
sq. in., an allowable working stress of 10,000 lbs. per sq. in. on the plates 
and 6000 lbs. per sq. in. on the stay-bolts may be specified instead. So 
also in the use of formulae for columns (see page 271) the dimensions of a 
column are calculated after assuming a maximum allowable compressive 
stress per square inch on the concave side of the column. 

The factors for masonry under dead load as given by Rankine and by 
Unwin, viz., 4 and 20, show a remarkable difference, which may possibly 
be explained as follows: If the actual crushing strength of a pier of 
masonry is known from direct experiment, then a factor of safety of 4 is 
sufficient for a pier of the same size and quality under a steady load ; 
but if the crushing strength is merely assumed from figures given by the 
authorities (such as the crushing strength of pressed brick, quoted above 
from Howe's Retaining Walls, 40 to 300 tons per square foot, average 
170 tons), then a factor of safety of 20 may be none too great. In this 
case the factor of safety is really a "factor of ignorance." 

The selection of the proper factor of safety or the proper maximum unit 
stress for any given case is a matter to be largely determined by the 
judgment of the engineer and by experience. No definite rules can be 
given. The customary or advisable factors in many particular cases will 
be found where these cases are considered throughout this book. In 
general the following circumstances are to be taken into account in the 
selection of a factor: 

1. When the ultimate strength of the material is known within narrow 
limits, as in the case of structural steel when tests of samples have been 
made, when the load is entirely a steady one of a known amount, and 
there is no reason to fear the deterioration of the metal by corrosion, the 
lowest factor that should be adopted is 3. 

2. When the circumstances of 1 are modified by a portion of the load 
being variable, as in floors of warehouses, the factor should be not less 
than 4. 

3. When the whole load, or nearly the whole, is apt to be alternately 
put on and taken off, as in suspension rods of floors of bridges, the factor 
should be 5 or 6. 

4. When the stresses are reversed in direction from tension to com- 
pression, as in some bridge diagonals and parts of machines, the factor 
should be not less than 6. 



351 STRENGTH OF MATERIALS. 

5. When the piece is subjected to repeated shocks, the factor should be 
not less than 10. 

6. When the piece is subject to deterioration from corrosion the section 
should be sufficiently increased to allow for a definite amount of corrosion 
before the piece be so far weakened by it as to require removal. 

7. When the strength of the material, or the amount of the load, or 
both are uncertain, the factor should be increased by an allowance suffi- 
cient to cover the amount of the uncertainty. 

8. When the strains are of a complex character and of uncertain 
amount, such as those in the crank-shaft of a reversing engine, a very 
high factor is necessary, possibly even as high as 40, the figure given by 
Rankine for shafts in millwork. 

Formulas for Factor of Safety. — (F. E. Cardullo, Ma^h'y, Jan,. 

1906.) The apparent factor of safety is the product of four factors, or, 

F = a X b X c X d. 

a is the ratio of the ultimate strength of the material to its elastic limit, 
rot the yield point, but the true elastic limit within which the material is, 
in so far as we can discover, perfectly elastic, and takes no permanent set. 
Two reasons for keeping the working stress within this limit are: (1) that 
the material will rupture if strained repeatedly beyond this limit; and 
(2) that the form and dimensions of the piece would be destroyed under 
the same circumstances. 

'the second factor, 6, is one depending upon the character of the stress 
produced within the material. The experiments of Wohler proved that 
the repeated application of a stress less than the ultimate strength of a 
material would rupture it. Prof. J. B. Johnson's formula for the relation 
between the ultimate strength and the "carrying strength" under con- 
ditions of variable loads is as follows: 

/ = U + (2 - Vi/P), 
where / is the "carrying strength" when the load varies repeatedly 
between a maximum value, p, and a minimum value, pi, and U is the 
ultimate strength of the material. The quantities p and pi have plus 
signs when they represent loads producing tension, and minus signs when 
they represent loads producing compression. 

If the load is variable the factor b must then have a value, 
b = U/f = 2 - pi/p. 

Taking a load varying between zero and a maximum, 
pi/p = 0, and 6 = 2— pi/p = 2. 

Taking a load that produces alternately a tension and a compression 
equal in amount, 

p' = — p and pi/p = — 1, and 6 = 2— pi/p = 2 — (— 1) = 3. 

The third factor, c, depends upon the manner in which the load is applied 
to the piece. When the load is suddenly applied c = 2. When not all 
of the load is applied suddenly, the factor 2 is reduced accordingly. If 
a certain fraction of the load, n/m, is suddenly applied, the factor is 
1 + n/m. 

The last factor, d, we may call the "factor of ignorance." All the 
other factors have provided against known contingencies; this provides 
against the unknown. It commonly varies in value between IV2 and 3, 
although occasionally it becomes as great as 10. It provides against 
excessive or accidental overload, unexpectedly severe service, unreliable 
or imperfect materials, and all unforeseen contingencies of manufacture 
or operation. When we know that the load will not be likely to be 
increased, that the material is reliable, that failure will not result dis- 
astrously, or even that the piece for some reason must be small or light, 
this factor will be reduced to its lowest limit, 1 1/2. When life or property 
would be endangered by the failure of the piece, this factor must be made 
larger. Thus, while it is IV2 to 2 in most ordinary steel constructions, 
it is rarely less than 2 1/2 for steel in a boiler. 

The reliability of the material in a great measure determines the value 
of this factor. For instance, in all cases where it would be 1 1/2 for mild 
steel, it is made 2 for cast iron. It will be larger for those materials 
subject to internal strains, for instance for complicated castings, heavy 



THE MECHANICAL PROPERTIES OF CORK. 355 

forgings, hardened steel, and the like, also for materials subject to hidden 
detects, such as internal haws in lorgings, spongy places in castings, etc. 
It will be smaller tor ductile and larger tor brittle materials. It will be 
smaller as we are sure that the piece lias received uniform treatment, and 
as the tests we have give more uniform results and more accurate : ndi- 
cations of the real strength and quality of the pjece itself. In fixing the 
factor d, the designer must depend on his judgment, guided by the general 
rules laid down. 

Table of Factors of Safety. 

The following table may assist in a proper choice of the factor of safety 
It shows the value of the four factors for various materials and conditions 
of service. 

Class of Service or Materials. r ~~a~ h^°c d~~^ F 

Boilers 2 1 1 21/4-3 4 1/ 2 - 6 

Piston and connecting rods for double- 
acting engines 1 1/ 3 -2 3 2 1 1/ 2 13 1/2-I8 

Piston and connecting rod for single-acting 

engines 1 1/2-2 2 2 1 1/ 2 9 -12 

Shaft carrying bandwheel, flv-wheel, or 

'armature 1 1/>-2 3 I 1 l/ 2 63/ 4 - 9 

Lathe spindles 2 2 2 1 1/ 2 12 

Mill shafting. 2 3 22 24 

Steel work in buildings 2 I 1 2 4 

Steel work in bridges 2 1 I 21/ 2 5 

Steel work for small work 2 1 2 1 1/ 2 6 

Cast iron wheel rims 2 1 110 20 

Steel wheel rims i 2 1 I 4 8 

Materials. Minimum Values. 

Cast iron and other castings , 2 1 12 4 

Wrought iron or mild steel. 2 1 1 1 1/ 2 3 

Oil tempered or nickel steel 1 1/2 1 I I V2 2 1/4 

Hardened steel 1 1/2 1 1 2 3 

Bronze and brass, rolled or forged 2 1 1 1 1/2 3 

THE MECHANICAL PROPERTIES OF CORK. 

Cork possesses qualities which distinguish it from all other solid or 
liquid bodies, namely, its power of altering its volume in a very marked 
degree in consequence of change of pressure. It consists, practically, 
of an aggregation of minute air-vessels, having thin, water-tight, and 
very strong walls, and hence, if compressed, the resistance to compression 
rises in a manner more like the resistance of gases than the resistance of 
an elastic solid such as a spring. In a spring the pressure increases in 
proportion to the distance to which the spring is compressed, but with 
gases the pressure increases in a much more rapid manner; that is, in- 
versely as the volume which the gas is made to occupy. But from the 
permeability of cork to air, it is evident that, if subjected to pressure in 
one direction only, it will gradually part with its occluded air by effusion, 
that is, by its passage through the porous walls of the cells in which it is 
contained. The gaseous part of cork constitutes 53% of its bulk. Its 
elasticity has not only a very considerable range, but it is very persistent. 
Thus in the better kind of corks used in bottling the corks expand the 
instant they escape from the bottles. This expansion may amount to 
an increase of volume of 75%, even after the corks have been kept in a 
state of compression in the bottles for ten years. If the cork be steeped 
in hot water, the volume continues to increase till it attains nearly three 
times that which it occupied in the neck of the bottle. 

When cork is subjected to pressure a certain amount of permanent 
deformation or "permanent set" takes place very quickly. This prop- 
erty is common to all solid elastic substances when strained beyond their 
elastic limits, but with cork the limits are comparatively low. Besides 
the permanent set, there is a certain amount of sluggish elasticity — that 
is, cork on being released from pressure springs back a certain amount 
at once, but the complete recovery takes an appreciable time. 



356 STRENGTH OF MATERIALS. 

Cork which had been compressed and released in water many thousand 
times had not changed its molecular structure in the least, and had con- 
tinued perfectly serviceable. Cork which has been kept under a pressure 
of three atmospheres for many weeks appears to have shrunk to from 
80% to 85% of its original volume. — Van Nostrand's Eng'g Mag., 1886, 
xxxv. 307. 

VULCANIZED INDIA-RUBBER. 

The specific gravity of a rubber compound, or the number of cubic 
inches to the pound, is generally taken by buyers as a correct index of 
the value, though in reality such is often very far from being the case. 
In the rubber works the qualities of the rubber made vary from floating, 
the best quality, to densities corresponding to 11 or 12 cu. in. to the 
pound, the latter densities being in demand by consumers with whom 
price appears to be the main consideration. Such densities as these can 
only be obtained by utilizing to the utmost the quality that rubber 
exhibits of taking up a large bulk of added matters. — Eng'g, 1897. 

Lieutenant L. Vladomiroff, a Russian naval officer, has recently carried 
out a series of tests at the St. Petersburg Technical Institute with view 
■ to establishing rules for estimating the quality of vulcanized india- 
rubber. The folio wng, in brief, are the conclusions arrived at, recourse 
being had to physical properties, since chemical analysis did not give 
any reliable result: 1. India-rubber should not give the least sign of 
superficial cracking when bent to an angle of 180 degrees after five hours 
of exposure in a closed air-bath to a temperature of 125° C. The 
test-pieces- should be 2.4 inches thick. 2. Rubber that does not contain 
more than half its weight of metallic oxides should stretch to five times 
its length without breaking. 3. Rubber free from all foreign matter, 
except the sulphur used in vulcanizing it, should stretch to at least seven 
times its length without rupture. 4. The extension measured immedi- 
ately after rupture should not exceed 12% of the original length, with 
given dimensions. 5. Suppleness may be determined by measuring the 
percentage of ash formed in incineration. This may form the basis for 
deciding between different grades of rubber for certain purposes. 6. Vul- 
canized rubber should not harden under cold. These rules have been 
adopted for the Russian navy. — Iron Age, June 15, 1893. 

Singular Action of India Rubber under Tension. — R. H. Thurston, 
Am. Mach., Mar. 17, 1898, gives a diagram showing the stretch at dif- 
ferent loads of a piece of partially vulcanized rubber. The results trans- 
lated into figures are: 

Load, lbs 30 50 80 120 150 200 320 430 

Stretch per in. of 

length, in 0.5 1. 2.2 4 5 6 7 7.5 

Stretch per 10 lbs. in- 
crease of load 0.17 0.25 0.4 0.45 0.33 0.20 0.08 0.04 

Up to about 30% of the breaking load the rubber behaves like a soft 
metal in showing an increasing rate of stretch with increase of load, 
then the rate of stretch becomes constant for a while and later decreases 
steadily until before rupture it is less than one-tenth of the maximum. 
Even when stretched almost to rupture it restores itself very nearly to 
its original dimensions on removing the load, and gradually recovers a 
part of the loss of form at that instant observable. So far as known, 
no other substance shows this curious relation of stretch to load. 

Rubber Goods Analysis. Randolph Boiling. {Iron Age, Jan. 28, 1909.) 

The loading of rubber goods used in manufacturing establishments 
with zinc oxide, lead sulphate, calcium sulphate, etc., and the employ- 
ment of the so-called "rubber substitutes" mixed with good rubber call for 
close inspection of the works chemist in order to determine the value of 
the samples and materials received. The following method of analysis is 
recommended: 

Thin strips of the rubber must be cut into small bits about the pize of 
No. 7 shot. A half gram is heated in a 200 c.c. flask with red fuming 
nitric acid on the hot plate until all organic matter has been decomposed, 
and the total sulphur is determined by precipitation as barium sulphate. 
The difference between the total and combined sulphur gives the per 
cent that has been used for vulcanization. Free sulphur indicates either 
that improper methods were used in vulcanizing or that an excessive 



ALUMINUM — ITS PROPERTIES AND USES. 357 

per cent of substitutes was employed. Following is a scheme for the 
analysis of india-rubber articles: 

1. Extraction with acetone: A. Solution: Resinous constituents of 
india-rubber, fatty oils, mineral oils, resin oils, solid hydrocarbons, resins 
free sulphur. B. Residue. , 

2. Extraction with pyridine: C. Extract: Tar, pitch, bituminous 
bodies, sulphur in above. D. Residue. 

3. Extraction with alcoholic potash: E. Extract: Chlorosulphide sub- 
stitutes, sulphide substitutes, oxidized (blown) oils, sulphur in substitutes, 
chlorine in substitutes. F. Residue. 

4. Extraction with nitro-naphthalene: G. Extract: India-rubber, sul- 
phur in india-rubber, chlorine in india-rubber, the total of the above 
three estimated by loss. H. Residue. 

5. Extraction with boiling water: I. Extract: Starch (farina), dextrine. 
K. Residue: Mineral matter, free carbon, fibrous materials, sulphur in 
inorganic compounds. 

6. Separate estimations: Total sulphur, chlorine in rubber. 

NICKEL. 

Properties of Nickel.— (F. L. Sperry, Tran. A. I.M. E., 1895.) Nickel 
has similar physical properties to those of iron and copper. It is less malle- 
able and ductile than iron, and less malleable and more ductile than 
copper. It alloys with these metals in all proportions. It has nearly 
the same specific gravity as copper, and is slightly heavier than iron. 
It melts at a temperature of about 2900° to 3200° F. A small percentage 
of carbon in metallic nickel lowers its melting-point perceptibly. Nickel 
is harder than either iron or copper; is magnetic, but will not take a 
temper. It has a grayish-white color, takes a fine polish, and may be 
rolled easily into thin plates or drawn into wire. It is unappreciably 
affected by atmospheric action, or by salt water. Commercial nickel is 
from 98 to 99 per cent pure. The impurities are iron, copper, silicon, 
sulphur, arsenic, carbon, and (in some nickel) a kernel of unreduced 
oxide. It is not difficult to cast, and acts like some iron in being cold- 
short. Cast bars are likely to be porous or spongy, but, after hammer- 
ing or rolling, are compact and tough. 

The average results of several tests are as follows: Castings, tensile 
strength, 85,000 lbs. per sq. in., elongation, 12%; wrought nickel, T. S., 
96,000, El., 14%; wrought nickel, annealed, T. S., 95,000, El., 23%; 
hard rolled, T. S., 78,000, El., 10%. (See also page 473.) 

Nickel readily takes up carbon, and the porous nature of the metal is 
undoubtedly due to occluded gases. According to Dr. Wedding, nickel 
may take up as much as 9% of carbon, which may exist either as amor- 
phous or as graphitic carbon. 

Dr. Fleitmann, of Germany, discovered that a small quantity of pure 
magnesium would free nickel from occluded gases and give a metal 
capable of being drawn or rolled perfectly free from blow-holes, to such 
an extent that the metal may be rolled into thin sheets 3 feet in width. 
Aluminum or manganese may be used equally as well as a purifying 
agent; but either, if used in excess, serves to make the nickel very much 
harder. Nickel will alloy with most of the useful metals, and generally 
adds the qualities of hardness, toughness, and ductility. 

ALUMINUM — ITS PROPERTIES AND USES. 

(By Alfred E. Hunt, Pres't of the Pittsburgh Reduction Co.) 
The specific gravity of pure aluminum in a cast state is 2.58; in rolled 
bars Of large section it is 2.6; in very thin sheets subjected to high com- 
pression under chilled rolls, it is as much as 2.7. Taking the weight of a 
given bulk of cast aluminum as 1, wrought iron is 2.90 times heavier; struc- 
tural steel, 2.95 times; copper, 3.60; ordinary high brass, 3.45. Most wood 
suitable for use in structures has about one third the weight of aluminum, 
which weighs 0.092 lb. to the cubic inch. 

Pure aluminum is practically not acted upon by boiling water or steam. 
Carbonic oxide or hydrogen sulphide does not act upon it at any tempera- 
ture under 600° F. It is not acted upon by most organic secretions. 

Hydrochloric acid is the best solvent for aluminum, and strong solutions 
of caustic alkalies readily dissolve it. Ammonia has a slight solvent action, 
and concentrated sulphuric acid dissolves aluminum upon heating, with 
evolution of sulphurqus acid gas, Dilute sulphuric acid acts but slowly on 



358 STRENGTH OF MATERIALS, 

the metal, though the presence of any chlorides in the solution allows rapid 
decomposition. Nitric acid, either concentrated or dilute, has very littie 
action upon the metal, and sulphur has no action unless the metal is at a 
red heat. Sea-water has very little effect on aluminum. Strips of the 
metal placed on the sides of a wooden ship corroded less than 1/1000 inch 
after six months' exposure to sea-water, corroding less than copper sheets 
similarly placed. 

In malleability pure aluminum is only exceeded by gold and silver. In 
ductility it stands seventh in the series, being exceeded by gold, silver, 
platinum, iron, very soft steel, and copper. Sheets of aluminum have been 
rolled down to a thickness of 0.0005 inch, and beaten into leaf nearly as 
thin as gold leaf. The metal is most malleable at a temperature of between 
400° and 600° F., and at this temperature it can be drawn down between 
rolls with nearly as much draught upon it as with heated steel. It has also 
been drawn down into the very finest wire. By the Mannesmann process 
aluminum tubes have been made in Germany. 

Aluminum stands very high in the series as an electro-positive metal, and 
contact with other metals should be avoided, as it would establish a gal- 
vanic couple. 

The electrical conductivity of aluminum is only surpassed by pure 
copper, silver, and gold. With silver taken at 100 the electrical conduc- 
tivity of aluminum is 54.20; that of gold on the same scale is 78; zinc is 
29.90; iron is only 16, and platinum 10.60. Pure aluminum has no polar- 
ity, and the metal in the market is absolutely non-magnetic. 

Sound castings can be made of aluminum in either dry or "green" sand 
moulds, or in metal "chills." It must not be heated much beyond its 
melting-point, and must be poured with care, owing to the ready absorp- 
tion of occluded gases and air. The shrinkage in cooling is 17/64 inch per 
foot, or a little more than ordinary brass. It should be melted in plumbago 
crucibles, and the metal becomes molten at a temperature of 1215° F. 

The coefficient of linear expansion, as tested on s/g-inch round aluminum 
rods, is 0.00002295 per degree centigrade between the freezing and boiling 
point of water. The mean specific heat of aluminum is higher than that of 
any other metal, excepting only magnesium and the alkali metals. From 
zero to the melting-point it is 0.2185; water being taken as 1, and the latent 
heat of fusion at 28.5 heat units. The coefficient of thermal conductivity 
of unannealed aluminum is 37.96; of annealed aluminum, 38.37. As a 
conductor of heat alumnium ranks fourth, being exceeded only by silver, 
copper, and gold. 

Aluminum, under tension, and section for section, is about as strong as 
cast iron. The tensile strength of aluminum is increased by cold rolling or 
cold forging, and there are alloys which add considerably to the tensile 
strength without increasing the specific gravity to over 3 or 3.25. 

The strength of commercial aluminum is given in the following table as 
the result of many tests: 

Elastic Limit Ultimate Strength Percentage 
per sq. in. in per sq. in. in of Reduct'n 

Form. Tension, Tension, of Area in 

lbs. lbs. Tension. 

Castings 6,500 15,000 15 

Sheet 12,000 24,000 35 

Wire 16,000-30,000 30,000-65,000 60 

Bars 14,000 28,000 40 

The elastic limit per square inch under compression in cylinders, with 
length twice the diameter, is 3500. The ultimate strength per square inch 
under compression in cylinders of same form is 12,000. The modulus of 
elasticity of cast aluminum is about 11,000,000. It is rather an open metal 
in its texture, and for cylinders to stand* pressure an increase in thickness 
must be given to allow for this porosity. Its maximum shearing stress in 
castings is about 12,000, and in forgings about 16,000, or about that of pure 
copper. 

Pure aluminum is too soft and lacking in tensile strength and rigidity for 
many purposes. Valuable allovs are now being made which seem to give 
great promise for the future. They are alloys containing from 2% to 7% 
or 8% of copper, manganese, iron, and nickel. 

Plates and bars of these alloys have a tensile strength of from 40,000 to 



ALUMINUM — ITS PROPERTIES AND USES. 359 

50,000 pounds per square inch, an elastic limit of 55% to 60% of the 
ultimate tensile strength, an elongation of 20% in 2 inches, and a 
red tCtio.i of area of 25 f . 

This metal is especially capable of withstanding the punishment and 
distortion to which structural material is ordinarily subjected. Some 
aluminum alloys have as much resilience and spring as the hardest of hard- 
drawn brass. 

Their specific gravity is about 2.80 to 2.85, where pure aluminum has a 
specific gravity of 2.72. 

In castings, more of the hardening elements are necessary in order to give 
the maximum stiffness and rigidity, together with the strength and duc- 
tility of the metal; the favorite alloy material being zinc, iron, manganese, 
and copper. Tin added to the alloy reduces the shrinkage, and alloys of 
aluminum and tin can be made which have less shrinkage than cast iron. 

The tensile strength of hardened aluminum-alloy castings is from 20,000 
to 25,000 pounds per square inch. 

Alloys of aluminum and copper form two series, both valuable. The 
first is aluminum bronze, containing from 5% to 11 1/2% of aluminum; and 
the second is copper-hardened aluminum, containing from 2% to 15% of 
copper. Aluminum-bronze is a very dense, fine-grained, and strong alloy, 
having good ductility as compared with tensile strength. The 10% bronze 
in forged bars will give 100,000 lbs. tensile strength per square inch, with 
60,003 lbs. elastic limit per square inch, and 10% elongation in 8 inches. 
The 5 % to 7 1/2% bronze has a specific gravity of 8 to 8.30, as compared with 
7.50 for the 10% to 11 1/2% bronze, a tensile strength of 70,000 to 80,000 
lbs., an elastic limit of 40,000 lbs. per square inch, and an elongation of 
30% in 8 inches. 

Aluminum is used by steel manufacturers to prevent the retention of 
the occluded gases in the steel, and thereby produce a solid ingot. The 
proportions of the dose range from 1/2 lb. to several pounds of aluminum 
per ton of steel. Aluminum is also used in giving extra fluidity to steel 
used in castings, making them sharper and sounder. Added to cast iron, 
aluminum causes the iron to be softer, free from shrinkage, and lessens the 
tendency to "chill." 

With the exception of lead and mercury, aluminum unites with all 
metals, though it unites with antimony with great difficulty. A small 
percentage of silver whitens and hardens the metal, and gives it added 
strength ; and this alloy is especially applicable to the manufacture of fine 
instruments and apparatus. The following alloys have been found 
recently to be useful in the arts: Nickel-aluminum, composed of 20 parts 
nickel to 80 of aluminum; rosine, made of 40 parts nickel, 10 parts silver, 
30 parts aluminum, and 20 parts tin, for jewellers' work ; mettaline, made 
of 35 parts cobalt, 25 parts aluminum, 10 parts iron, and 30 parts copper, 
The aluminum-bourbouze metal, shown at the Paris Exposition of 1889, 
has a specific gravity of 2.9 to 2.96, and can be cast in very solid shapes, as 
it has very little shrinkage. From analysis the following composition is 
deduced: Aluminum, 85.74%; tin, 12.94%; silicon, 1.32%; iron, none. 

The metal can be readily electrically welded, but soldering is still not 
satisfactory. The high heat conductivity of the aluminum withdraws the 
heat of the molten solder so rapidly that it "freezes" before it can flow 
sufficiently. A German solder said to give good results is made of 80% 
tin to 20% zinc, using a flux composed of 80 parts stearic acid, 10 parts 
chloride of zinc, and 10 parts of chloride of tin. Pure tin, fusing at 250° C, 
has also been used as a solder. The use of chloride of silver as a flux has 
been patented, and used with ordinary soft solder has given some success. 
A pure nickel soldering-bit should be used, as it does not discolor aluminum 
as copper bits do. 

Aluminum Wire. — Tension tests. Diam. 0.128"in. 14 tests. E.L. 
12,509 to 19,100; T. S. 25,800 to 26,900 lbs. per sq. in.: el. 0.30 to 1.02% 
in 48 ins.; Red. of area. 75.0 to 83.4%. Mod. of el. 8,800,000 to 
10,700,000. — Tech. Quar., xii, 1899. 

Aluminum Rod. — Torsion tests. 10 samples, 0.257 in. diam. Appar- 
ent outride fiber stress, lbs. per sq. in. 15,900 to 18,300 lbs. per sq. in. 
11 samples, 0.367 in. diam. Apparent outside fiber stress, 18,400 to 
19,200. 10 samples, 0.459 in. diam. Apparent outside fiber stress, 20,700 
to 21,500 lbs. per sq. in. The average number of turns per inch for the 
three series were respectively, 1.58 to 3.65; 1.20 to 2.64; 0.87 to 1.06. 
Ibid. 



360 



ALLOYS. 

AIXOYS OF COPPER ANI> TIN. 

(Extract from Report of IT. g. Test Board.*) 





Mean 


Corn- 


A . 






*r 


03 fl 


a 


Torsion 




position by 


"S.S 
c . 


la 


*d 


l-s 


£ J2 


'". 


Tests. 


0/ 

£ 


Analysis. 




Oft.S 


D 03 05 

ill 

a o a 


- a 


bjo Mas 

c a a 


a ■ M 

'Hog 


, . 


Cop- 
per. 


Tin. 


=11 

m 








H 


H 


w 


H 


Q 


O 


< 


1 


100. 




27,800 


14,000 


6.47 


29,848 


bent. 


42,000 


143 


153 


la 


100. 




12,760 


11,000 


0.47 


21,251 


2.31 


39,000 


65 


40 


2 


97.89 


1 .90 


24,580 


10,000 


13.33 






34,000 


150 


317 


3 


96.06 


3.76 


32,000 


16,000 


14.29 


33,232 


bent. 


42,048 


157 


247 


4 


94.11 


5.43 








38,659 










5 


92.11 


7.80 


28,540 


19,000 


"5.53 


43,731 




42,000 


160 


126* 


6 


90.27 


9.58 


26,860 


15,750 


3.66 


49,400 




38,000 


175 


114 


7 


88.41 


11.59 








60,403 










8 


87.15 


12.73 


29,430 


20,000 


3.33 


34,531 


4.00 


53,000 


182 


IOO' 


9 


82.70 


17.34 








67,930 


0.63 








10 


80.95 


18.84 


32,980 




' 0.04 


56,715 


0.49 


78,000 


190 


16* 


1! 


77.56 


22.25 






0. 


29,926 


0.16 








12 


76.63 


23.24 


22,6 io 


22,6 io 


0. 


32,210 


0.19 


114,000 


122 


'3.4 


13 


72.89 


26.85 






0. 


9,512 


0.05 








14 


69.84 


29.88 


5,585 


5,585 


0. 


12,076 


0.06 


147,000 


"is 


T.5 


15 


68.58 


31.26 






0. 


9,152 


0.04 








16 


67.87 


32.10 






0. 


9,477 


0.05 








17 


65.34 


34.47 


2,201 


2,201 


0. 


4,776 


0.02 


84,700 


*i6 


T 


18 


56.70 


43.17 


1,455 


1,455 


0. 


2,126 


0.02 








19 


44.52 


55.28 


3,010 


3,010 


0. 


4,776 


0.03 


35,800 


"23 


"1" 


20 


34.22 


65.80 


3,371 


3,371 


0. 


5,384 


0.04 


19,600 


17 


2 


21 


23.35 


76.29 


6,775 


6,775 


0. 


12,408 


0.27 








22 


15.08 


84.62 








9,063 


0.86 


6,500 


'23 


25" 


23 


11.49 


88.47 


6,380 


3', 500 


4.io 


10,706 


5.85 


10,100 


23 


62 


24 


8.57 


91.39 


6,450 


3,500 


6.87 


5,305 


bent. 


9,800 


23 


132 


25 


3.72 


96.31 


4,780 


2,750 


12.32 


6,925 




9,800 


23 


220 


26 


0. 


100. 


3,505 




35.51 


3,740 




6,400 


12 


557 



* The tests of the alloys of copper and tin and of copper and zinc, the 
results of which are published in the Report of the U. S. Board appointed 
to test Iron, Steel, and other Metals, Vols. I and II, 1879 and 1881, were 
made by the author under direction of Prof. R. H. Thurston, chairman of 
the Committee on Alloys. See preface to the report of the Committee, 
in Vol. I. 

Nos. la and 2 were full of blow-holes. 

Tests Nos. 1 and la show the variation in cast copper due to varying 
conditions of casting. In the crushing tests Nos. 12 to 20, inclusive, 
crushed and broke under the strain, but all the others bulged and flattened 
out. In these cases the crushing strength is taken to be that which 
caused a decrease of 10% in the length. The test-pieces were 2 in. long 
and 5/ 8 in. diameter. The torsional tests were made in Thurston's torsion- 
machine, on pieces 5/ 8 in. diameter and 1 in. long between heads. 

Specific Gravity of the Copper-tin Alloys. — The specific gravity 
of copper, as found in these tests, is 8.874 (tested in turnings from the 
ingot, and reduced to 39.1° F.). The alloy of maximum sp. gr. 8.956 
contained 62.42 copper, 37.48 tin, and all the alloys containing less than 



ALLOYS OF COPPER AND TIN. 361 

37% tin varied irregularly in sp. gr. between 8.65 and 8.93, the density- 
depending not on the composition, but on the porosity of the casting. It 
is probable that the actual sp. gr. of all these alloys containing less than 
37% tin is about 8.95, and any smaller figure indicates porosity in the 
specimen. 

From 37% to 100% tin, the sp. gr. decreases regularly from the maxi- 
mum of 8.956 to that of pure tin, 7.293. 



Note on the Strength of the Copper-tin Alloys. 

The bars containing from 2% to 24% tin, inclusive, have considerable 
strength, and all the rest are practically worthless for purposes in which 
strength is required. The dividing line between the strong and brittle 
alloys is precisely that at which the color changes from golden yellow to 
silver-white, viz., at a composition containing between 24% and 30% of 
tin. 

It appears that the tensile and compressive strengths of these alloys are 
in no way related to each other, that the torsional strength is closely pro- 
portional to the tensile strength, and that the transverse strength may de- 
pend in some degree upon the compressive strength, but it is much more 
nearly related to the tensile strength. The modulus of rupture, as ob- 
tained by the transverse tests, is, in general, a figure between those of 
tensile and compressive strengths per square inch, but there are a few 
exceptions in which it is larger than either. 

The strengths of the alloys at the copper end of the series increase 
rapidly with the addition of tin till about 4% of tin is reached. The 
transverse strength continues regularly to increase to the maximum, till 
the alloy containing about 17^% of tin is reached, while the tensile and 
torsional strengths also increase, but irregularly, to the same point. This 
irregularity is probably due to porosity of the metal, and might possibly 
be removed by any means which would make the castings more compact. 
The maximum is reached at the alloy containing 82.70 copper, 17.34 tin, 
the transverse strength, however, being very much greater at this point 
than the tensile or torsional strength. From the point of maximum 
strength the figures drop rapidly to the alloys containing about 27.5% of 
tin, and then more slowly to 37.5%, at which point the minimum (or 
nearly the minimum) strength, by all three methods of test, is reached. 
The alloys of minimum strength are found from 37.5% tin to 52.5% tin. 
The absolute minimum is probably about 45% of tin. 

From 52.5% of tin to about 77.5% tin there is a rather slow and irregu- 
lar increase in strength. From 77.5% tin to the end of the series, or all 
tin, the strengths slowly and somewhat irregularly decrease. 

The results of these tests do not seem to corroborate the theory given 
by some writers, that peculiar properties are possessed by the alloys 
which are compounded of simple multiples of their atomic weights or 
chemical equivalents, and that these properties are lost as the com- 
positions vary more or less from this definite constitution. It does 
appear that a certain percentage composition gives a maximum strength 
and another certain percentage a minimum, but neither of these com- 
positions is represented by simple multiples of the atomic weights. 

There appears to be a regular law of decrease from the maximum to 
the minimum strength which does not seem to have any relation to the 
atomic proportions, but only to the percentage compositions. 

Hardness.— The pieces containing less than 24 % of tin were turned in 
the lathe without difficulty, a gradually increasing hardness being noticed, 
the last named giving a very short chip, and requiring frequent sharpening 
of the tool. 

With the most brittle alloys it was found impossible to turn the test- 
pieces in the lathe to a smooth surface. No. 13 to No. 17 (26.85 to 34.47 
tin) could not be cut with a tool at all. Chips would fly off in advance 
of the tool and beneath it, leaving a rough surface; or the tool would 
sometimes, apparently; crush off portions of the metal, grinding it to 
powder. Beyond 40 % tin the hardness decreased so that the bars could 
be easily turned. 



362 



ALLOYS. 



ALLOYS OF COPPER AND ZINC. (U. S. Test Board.) 











Elastic 


T 


v 




Torsional 




Mean Com- 
position by 


Tensile 


Limit 
%of 




verse 
Test 
Modu- 
lus of 
Rup- 
ture. 


i^s 


Crush- 
ing 
Str'gth 
per sq. 
in., lbs. 


Tests. 








No. 


Analysis. 


Str'gth, 
lbs. per 
sq. in. 


B reak- 
ing 

Load, 
lbs. per 

sq. in. 


! J 

o ti 


.2 h 1 


o c • 






Cop- 
per. 


Zinc. 




1 


97.83 


1.88 


27,240 












130 


357 


2 


82,93 


16.98 


32,600 


26.1 


26.7 


23, 1 97 


Bent 




155 


329 


3 


81.91 


17.99 


32,670 


30.6 


31.4 


21,193 






166 


345 


4 


77.39 


22.45 


35,630 


20.0 


35.5 


25,374 






169 


311 


5 


76.65 


23.08 


30,520 


24.6 


35.8 


22,325 




42,000 


165 


267 


6 


73.20 


26.47 


31,580 


23.7 


38.5 


25,894 






168 


293 


7 


71.20 


28.54 


30,510 


29.5 


29.2 


24,468 






164 


269 


8 


69.74 


30.06 


28,120 


28.7 


20.7 


26,930 






143 


202 


9 


66.27 


33.50 


37,800 


25.1 


37.7 


28,459 


" 




176 


257 


10 


63.44 


36.36 


48,300 


32.8 


31.7 


43,216 






202 


230 


11 


60.94 


38.65 


41,065 


40.1 


20.7 


38,968 




75,000 


194 


202 


12 


58.49 


41.10 


50,450 


54.4 


10.1 


63,304 






227 


93 


13 


55.15 


44.44 


44,280 


44.0 


15.3 


42,463 




78,000 


209 


109 


14 


54.86 


44.78 


46,400 


53.9 


8.0 


47,955 






223 


72 


15 


49.66 


50.14 


30,990 


54.5 


5.0 


33,467 


1.26 


1 1 7,400 


172 


38 


16 


48.99 


50.82 


26,050 


100 


0.8 


40,189 


0.61 




176 


16 


17 


47.56 


52.28 


24, 1 50 


100 


0.8 


48,471 


1.17 


1 2 i ,000 


155 


13 


18 


43 36 


56.22 


9,170 


100 




17,691 


0.10 




88 


2 


19 


41.30 


58.12 


3,727 


100 




7,761 


0.04 




18 


2 


20 


32.94 


66.23 


1,774 


100 




8,296 


0.04 




29 


1 


21 


29.20 


70.17 


6,414 


100 




16,579 


0.04 




40 


2 


22 


20.81 


77.63 


9,000 


100 


0.2 


22,972 


0.13 


52J52 


65 


1 


23 


12.12 


86.67 


12,413 


100 


0.4 


35,026 


0.31 




82 


3 


24 


4.35 


94.59 


18,065 


100 


0.5 


26,162 


0.46 




81 


22 


25 


Cast. 


Zinc. 


5,400 


75 


0.7 


7,539 


0.12 


22,000 


37 


142 



Variation in Strength of Gun-bronze, and Means of Improving 
the Strength. — The figures obtained for alloys of from 7.8% to 12.7% 
tin, viz., from 26,860 to 29,430 pounds, are much less than are usually 
given as the strength of gun-metal. Bronze guns are usually east under 
the pressure of a head of metal, which tends to increase the strength and 
density. The strength of the upper part of a gun casting, or sinking 
head, is not greater than that of the small bars which have been tested 
in these experiments. The following is an extract from the report of 
Major Wade concerning the strength and density of gun-bronze (1850): 
■ — Extreme variation of six samples from different parts of the same 
gun (a 32-pound er howitzer): Specific gravitv, 8.487 to 8.835: tenacity, 
26,428 to 52,192. Extreme variation of all the samples tested: Specific 
gravity, 8.308 to 8.850; tenacity, 23,108 to 54,531. Extreme variation of 
all the samples from the gun heads: Specific gravity, 8.308 to 8.756; 
tenacity, 23,529 to 35,484. 

Major Wade says: The general results on the quality of bronze as it is 
found in guns are mostly of a negative character. They expose defects 
in density and strength, develop the heterogeneous texture of the metal 
in different parts of the same gun, and show the irregularity and un- 
certainty of quality which attend the casting of all guns, although made 
from similar materials, treated in like manner. 

Navy ordnance bronze containing 9 parts copper and 1 part tin, tested 
at Washington, D.C., in 1875-6, showed a variation in tensile strength 
from 29,800 to 51,400 lbs. per square inch, in elongation from 3% to 
58%, and in specific gravity from 8.39 to 8.88. 

That a great improvement may be made in the density and tenacity 
of gun-bronze by compression has been shown by the experiments of 
Mr. S. B. Dean in Boston, Mass., in 1869, and by those of General 
Uchatius in Austria in 1873. The former increased the density of the 



ALLOYS OF COPPER, TIN AND ZINC. 



363 



metal next the bore of the gun from 8.321 to 8.875, and the tenacity 
from 27,238 to 41,471 pounds per square inch. The latter, by a similar 
process, obtained the following figures for tenacity: 

Pounds per sq. in. 

Bronze with 10% tin 72,053 

Bronze with 8% tin 73,958 

Bronze with 6% tin 77,656 



ALLOTS OF COPPER, TIN, AND ZINC. 

(Report of U. S. Test Board, Vol. II, 1881.) 



No. 
in 


Analysis, 
Original Mixture. 


Transverse 
Strength. 


Tensile 
Strength per 
square inch. 


Elongation 
per cent in 
5 inches. 


Re- 
port. 


Cu. 


Sn. 


Zn. 


Modulus 
of 
Rup- 
ture. 


Deflec- 
tion, 
ins. 


A. 


B. 


A. 


B. 


72 


90 


5 


5 


41,334 


2.63 


23,660 


30,740 


2.34 


9.68 


5 


88.14 


1.86 


10 


31,986 


3.67 


32,000 


33,000 


17.6 


19.5 


70 


85 


5 


10 


44,457 


2.85 


28,840 


28,560 


6.80 


5.28 


71 


85 


10 


5 


62,470 


2.56 


35,680 


36,000 


2.51 


2.25 


89 


85 


12.5 


2.5 


62,405 


2.83 


34,500 


32,800 


1.29 


2.79 


88 


82.5 


12.5 


5 


69,960 


1.61 


36,000 


34,000 


0.86 


0.92 


77 


82.5 


15 


2.5 


69,045 


1.09 


33,600 


33,800 




0.68 


67 


80 


5 


15 


42,618 


3.88 


37,560 


32,300 


■ 11.6 


3.59 


68 


80 


10 


10 


67, 1 1 7 


2.45 


32,830 


31,950 


1.57 


1.67 


69 


80 


15 


5 


54,476 


0.44 


32,350 


30,760 


0.55 


0.44 


86 


77.5 


10 


12.5 


63,849 


1.19 


35,500 


36,000 


1.00 


1.00 


87 


77.5 


12.5 


10 


61,705 


0.71 


36,000 


32,500 


0.72 


0.59 


63 


75 


5 


20 


55,355 


2.91 


33,140 


34,960 


2.50 


3.19 


85 


75 


7.5 


17.5 


62,607 


1.39 


33,700 


39,300 


1.56 


1.33 


64 


75 


10 


15 


58,345 


0.73 


35,320 


34,000 


1.13 


1.25 


65 


75 


15 


10 


51,109 


0.31 


35,440 


28,000 


0.59 


0.54 


66 


75 


20 


5 


40,235 


0.21 


23,140 


27,660 


0.43 




83 


72.5 


7.5 


20 


51,839 


2.86 


32,700 


34,800 


3.73 


3.78 


84 


72.5 


10 


17.5 


53,230 


0.74 


30,000 


30,000 


0.48 


0.49 


59 


70 


5 


25 


57,349 


1.37 


38,000 


32,940 


2.06 


0.99 


82 


70 


7.5 


22.5 


48,836 


0.36 


38,000 


32,400 


0.84 


0.40 


60 


70 


10 


20 


36,520 


0.18 


33,140 


26,300 


0.31 




61 


70 


15 


15 


37,924 


0.20 


33,440 


27,800 


0.25 




62 


70 


20 


10 


15,126 


0.08 


17,000 


12,900 


0.03 




» 


67.5 


2.5 


30 


58,343 


2.91 


34,720 


45,850 


7.27 


3.09 


67.5 


5 


27.5 


55,976 


0.49 


34,000 


34,460 


1.06 


0.43 


75 


67.5 


7.5 


25 


46,875 


0.32 


29,500 


30,000 


0.36 


0.26 


B 


65 


2.5 


32.5 


56,949 


2.36 


41,350 


38,300 


3.26 


3.02 


65 


5 


30 


51,369 


0.56 


37,140 


36,000 


1.21 


0.61 


56 


65 


10 


25 


27,075 


0.14 


25,720 


22,500 


0.15 


0.19 


57 


65 


15 


20 


13,591 


0.07 


6,820 


7,231 






58 


65 


20 


15 


11,932 


0.05 


3,765 


2,665 






79 


62.5 


2.5 


35 


69,255 


2.34 


44,400 


45,000 


2 . 1 5 


2.Y9 


78 


60 


2.5 


37.5 


69,508 


1.46 


57,400 


52,900 


4.87 


3.02 


52 


60 


5 


35 


46,076 


0.28 


41,160 


38,330 


0.39 


0.40 


53 


60 


10 


30 


24,699 


0.13 


21,780 


21,240 


0.15 




54 


60 


15 


25 


18,248 


0.09 


18,020 


12,400 






12 


58.22 


2.30 


39.48 


95,623 


1.99 


66,500 


67,600 


3J3 


3.' 15 


3 


58.75 


8.75 


32.5 


35,752 


0.18 


Broke 


before te 


st; very 


brittle 


4 


57.5 


21.25 


21.25 


2,752 


0.02 


725 


1,300 






73 


55 


0.5 


44.5 


72,308 


3.05 


68,900 


68,900 


9.43 


2.88 


50 


55 


5 


40 


38,174 


0.22 


27,400 


30,500 


0.46 


0.43 


51 


55 


10 


35 


28,258 


0.14 


25,460 


18,500 


0.29 


0.10 


49 


50 


5 


45 


20,814 


0.11 


23,000 


31,300 


0.66 


0.45 



364 



The transverse tests were made in bars 1 in. square, 22 in. between 
supports. The tensile tests were made on bars 0.798 in. diam. turned 
from the two halves of the transverse-test bar, one half bein6 marked A 
and the other B. 

Ancient Bronzes. — The usual composition of ancient bronze was 
the same as that of modern gun-metal — 90 copper, 10 tin; but the 
proportion of tin varies from 5% to 15%, and in some cases lead has 
been found. Some ancient Egyptian tools contained 88 copper, 12 tin. 

Strength of the Copper-zinc Alloys. — The alloys containing less 
than 15% of zinc by original mixture were generally defective. The 
bars were full of blow-holes, and the metal showed signs of oxidation. 
To insure good castings it appears that copper-zinc alloys should con- 
tain more than 15% of zinc. 

From No. 2 to No. 8 inclusive, 16.98 to 30.06% zinc the bars show a 
remarkable similarity in all their properties. They have all nearly the 
same strength and ductility, the latter decreasing slightly as zinc 
increases, and are nearly alike in color and appearance. Between Nos. 8 , 
and 10, 30.06 and 36.36% zinc, the strength by all methods of test 
rapidly increases. Between No. 10 and No. 15, 36.36 and 50.14% zinc, 
there is another group, distinguished by high strength and diminished 
ductility. The alloy of maximum tensile, transverse and torsional 
strength contains about 41 % of zinc. 

The alloys containing less than 55% of zinc are all yellow metals. 
Beyond 55% the color changes to white, and the alloy becomes weak and 
brittle. Between 70% and pure zinc the color is bluish gray, the brit- 
tleness decreases and the strength increases, but not to such a degree as 
to make them useful for constructive purposes. 

Difference between Composition by Mixture and by Analysis. — 
There is in every case a smaller percentage of zinc in the average analy- 
sis than in the original mixture, and a larger percentage of copper. The 
loss of zinc is variable, but in general averages from 1 to 2%. 

Liquation or Separation of the Metals. ■ — In several of the bars a 
considerable amount of liquation took place, analysis showing a differ- 
ence in composition of the two ends of the bar. In such cases the 
change in composition was gradual from one end of the bar to the other, 
the upper end in general containing the higher percentage of copper. 
A notable instance was bar No. 13, in the above table, turnings from the 
upper end containing 40.36% of zinc, and from the lower end 48.52%. 

Specific Gravity. — The specific gravity follows a definite law, vary- 
ing with the composition, and decreasing with the addition of zinc. 
From the plotted curve of specific gravities the following mean values 
are taken: 

Per cent zinc 10 20 30 40 50 60 70 80 90 100 

Specific gravity . . . 8.80 8.72 8.60 8.40 8.36 8.20 8.00 7.72 7.40 7.20 7.14 

Graphic Representation of the Law of Variation of Strength of 
Copper-Tin'-Zinc Alloys. — In an equilateral triangle the sum of the 
perpendicular distances from any point within it to the three sides is 
equal to the altitude. Such a triangle can therefore be used to show 
graphically the percentage composition of any compound of three parts, 
such as a triple alloy. Let one side represent copper, a second tin, 
and the third zinc, the vertex opposite each of these sides representing 
100 of each element respectively. On points in a triangle of wood rep- 
resenting different alloys tested, wires were erected of lengths propor- 
tional to the tensile strengths, and the triangle then built up. with plaster 
to the height of the wires. The surface thus formed has a characteristic 
topography representing the variations of strength with variations of 
composition. The cut shows the surface thus made. The vertical 
section to the left represents the law of tensile strength of the copper-tin 
alloys, the one to the right that of tin-zinc alloys, and the one at the 
rear that of the copper-zinc alloys. The high point represents the 
strongest possible alloys of the three metals. Its composition is copper 
55, zinc 43, tin 2, and its strength about 70,000 lbs. The high ridge from 
this point to the point of maximum height of the section on the left is 
the line of the strongest alloys, represented by the formula zinc 4- (3 X tin) 
= 55. 

All alloys Iving to the rear of the rid^e. containing more copper and 
less tin or zinc are alloys of greater ductility than those on the line of 



ALLOYS OF COPPER, TIN AND ZINC. 



365 



maximum strength, and are the valuable commercial alloys; those in 
front on the declivity toward the central valley are brittle, and those in 
the valley are both brittle and weak. Passing from the.valley toward the 
section at the right the alloys lose their brittleness and become soft, the 
maximum softness being at tin=100, but they remain weak, as is shown 
by the low elevation of the surface. This model was planned and con- 
structed by Prof. Thurston in 1877. (See Trans. A. S C E., 1881. 
Report of the U. S. Board appointed to test Iron, Steel etc , vol. ii, 
Washington, 1881, and Thurston's Materials of Engineering vol iii.) 




Fig. 79. 

The best alloy obtained in Thurston's research for the U. S. Testing 
Board has the composition, copper 55, tin 0.5, zinc 44.5. The tensile 
strength in a cast bar was 68,900 lbs. per sq. in., two specimens giving 
the same result; the elongation was 47 to 51. per cent in 5 inches. 
Thurston's formula for copper-tin-zinc alloys of maximum strength 
(Trans. A. S. C. E., 1881) is z + 3 t = 55, in which z is the percentage of 
zinc and t that of tin. Alloys proportioned according to this formula 
should have a strength of about 40,000 lbs. per sq. in. + 500 2. The 
formula fails with alloys containing less than 1 per cent of tin. 

The following would be the percentage composition of a number of 
alloys made according to this formula, and their corresponding tensile 
strength in castings: 









Tensile 








Tensile 


Tin. 


Zinc. 


Copper. 


Strength, 
lbs. per 
sq. in. 


Tin. 


Zinc. 


Copper. 


Strength 
lbs. per 
sq. in. 


1 


52 


47 


66,000 


8 


31 


61 


55,500 


2 


49 


49 


64,500 


9 


28 


63 


54,000 


3 


46 


51 


63,000 


10 


25 


65 


52,500 


4 


43 


53 


61,500 


12 


19 


69 


49,500 


5 


40 


55 


60,000 


14 


13 


73 


46,500 


6 


37 


57 


58,500 


16 


7 


77 


43,500 


7 


34 


59 


57,000 


18 


1 


81 


40,500 



366 



These alloys, while possessing maximum tensile strength, would in 
general be too hard for easy working by machine tools. Another series 
made on the formula z + 4t = 50 would have greater ductility, together 
with considerable strength, as follows, the strength being calculated as 
before, tensile strength in lbs. per sq. in. = 40,000 + 500 z. 









Tensile 








Tensile 


Tin. 


Zinc. 


Copper. 


Strength, 
lbs. per 
sq. in. 


Tin. 


Zinc. 


Copper. 


Strength, 
lbs. per 
sq. in. 


1 


46 


53 


63,000 


7 


22 


71 


51,000 


2 


42 


56 


61,000 


8 


18 


74 


49,000 


3 


38 


59 


59,000 


9 


14 


77 


47,000 


4 


34 


62 


57,000 


10 


10 


80 


45,000 


5 


30 


65 


55,000 


11 


6 


83 


43,000 


6 


26 


68 


53,000 


12 


2 


86 


41,000 



Composition of Alloys in E very-day Use in Brass Foundries. 

(American Machinist.) 





Cop- 
per. 


Zinc. 


Tin. 


Lead. 




Admiralty metal . . 


lbs. 
87 

16 
16 

64 

32 

20 

16 
60 

92 
90 

16 
50 


lbs. 
5 

...£.. 

8 
1 

1 

*40" 

3 

50 


lbs. 
8 

4 

4 
3 

H/2 
21/2 


lbs. 

" "i/2 ' 
4 

1 


For parts of engines on 
board naval vessels. 

Bells for ships and factories. 

For plumbers, ship and house 
brass work. 

For bearing bushes for shaft- 
ing. 

For pumps and other hydrau- 
lic purposes. 

Castings subjected to steam 
pressure. 

For heavy bearings. 


Brass (yellow) 

Bush metal 


Steam metal 

Hard gun metal. . . 


Phosphor bronze . . 


8phc 
10 


s. tin 


nuts are forged, valve spin- 
dles, etc. 

For valves, pumps and gen- 
eral work. 

For cog and worm wheels, 
bushes, axle bearings, slide 
valves, etc. 

Flanges for copper pipes. 

Solder for the above flanges. 















Admiralty Metal, for surface condenser tubes where sea water is used 
for cooling, Cu, 70; Zn, 29; Sn, 1. Power, June 1, 1909. 

Gurley's Bronze. — 16 parts copper, 1 tin, 1 zinc, 1/2 lead, used by 
W & L. E. Gurley of Troy for the framework of their engineer's transits. 
Tensile strength 41,114 lbs. per sq. in., elongation 27% in 1 inch, sp. gr. 
8.696. (W. J. Keep, Trans, A, I, M, E., 1890.) 



ALLOYS OF COPPER, TIN, AND ZINC, 



367 



Composition of Various Grades of Rolled Brass, Etc 




Trade Name. 


Copper. 


Zinc. 


Tin. 


Lead. 


Nickel. 




61.5 

60 

662/3 

80 

60 

60 

662/3 

6H/2 


38.5 

40 

331/3 

20 

40 

40 

331/3 

201/2 


Ti/2 


Ti/2 

11/2 to 2 




















Drill rod 










18 







The above table was furnished by the superintendent of a mill in Connec- 
ticut in 1894. He says: While each mill has its own proportions for various 
mixtures, depending upon the purposes for which the product is intended, 
the figures given are about the average standard. Thus, between cartridge 
brass with 331/3 per cent zinc and common high brass with 38 1/2 per cent 
zinc, there are any number of different mixtures known generally as " high 
brass," or specifically as "spinning brass," "drawing brass," etc., wherein 
the amount of zinc is dependent upon the amount of scrap used in the 
mixture, the degree of working to which the metal is to be subjected, etc. 



Useful Alloys of Copper, Tin, and Zinc. 

(Selected from numerous sources.) 



U. S. Navy Dept. journal boxes ) _ 

and guide-gibs J 

Tobin bronze 

Naval brass 

Composition, U. S. Navy 

Brass bearings (J. Rose) 

Gun metal 



Tough brass for engines 

Bronze for rod-boxes (Lafond) 

" " pieces subject to shock 

Red brass parts 

" v " per cent 

Bronze for pump casings (Lafond).. 
" " eccentric straps. 

" shrill whistles 

" " low-toned whistles 

Art bronze, dull red fracture 

Gold bronze 

Bearing metal 



English brass of a.d. 1504 . 



Copper. 


Tin. 


182.8 


1 
13.8 


58.22 


2.30 


62 


I 


88 


10 


(64 


8 


187.7 


11.0 


92.5 


5 


91 


7 


87.75 


9.75 


85 


5 


83 


2 


(13 
1 76.5 


2 


11.8 


82 


16 


83 


15 


20 


1 


87 


4.4 


88 


10 


84 


14 


80 


18 


81 


17 


97 


2 


89.5 


2.1 


89 


8 


89 


21/2 


86 


14 


851/4 


123/4 


80 


18 


79 


18 


74 


91/2 


64 


3 



1/4 parts. 

3.4 per cent. 
39.48 " " 
37 " " 

2 " " 

1 parts. 

1 .3 per cent 

2.5 " " 

2 ." " 

2.5 " " 
10 " " 
15 " «' 

2 parts. 
11 .7 per cent. 

2 slightly malleable. 

1.50 0.50 lead. 

1 1 

4.3 4.3 " 

2 

2 

2.0 antimony. 

2.0 " 

1 

5.6 2.8 lead. 

81/2 

"l" 

2 

21/2 1/2 lead. 

91/2 7 lead. 
291/2 3 1/2 lead. 



368 



" Steam-metal." Alloys of copper and zinc are unsuitable for steam 
valves and other like purposes, since their strength is greatly reduced at 
high temperatures, and they appear to undergo a deterioration by con- 
tinued heating. Alloys of copper with from 10 to 12% of tin, when cast 
without oxidation are good steam metals, and a favorite alloy is what is 
known as "government mixture," 88 Cu, 10 Sn, 2 Zn. It has a tensile 
strength of about 33,000 lbs. per sq. in., when cold, and about 30,600 lbs. 
when heated to 407° F., corresponding to steam of 250 lbs. pressure. 

Tobin Bronze. — This alloy is practically a sterro or delta metal with 
the addition of a small amount of lead, which tends to render copper 
softer and more ductile. (F. L. Garrison, J. F. I., 1891.) 

The following analyses of Tobin bronze were made by Dr. Chas. B. 
Dudley: 




Test Bar 

(Rolled), per 

cent. 



Copper. 
• Zinc. . . 
Tin.... 
Iron. . 
Lead. . . 



61.20 
37.14 
0.90 
0.18 
0.35 



Dr. Dudley writes. " We tested the test bars and found 78,500 tensile 
strength with 40V2% elongation in two inches, and 15% in eight inches. 
This high tensile strength can only be obtained when the metal is manip- 
ulated. Such high results could hardly be expected with cast metal." 

The original Tobin bronze in 1875, as described by Thurston, Trans. 
A. S. C. E., 1881, had copper 58.22, tin 2.30, zinc 39.48. As cast it had a 
tenacity of 66.000 lbs. per sq. in., and as rolled 79,000 lbs.; cold rolled it 
gave 104,000 lbs. 

A circular of Ansonia Brass & Copper Co. gives the following: — The 
tensile strength of six Tobin bronze one-inch round rolled rods, turned 
down to a diameter of 5/8 of an inch, tested by Fairbanks, averaged 79,600 
lbs. per sq. in., and the elastic limit obtained on three specimens aver- 
aged 54,257 lbs. per sq. in. 

At a cherry-red heat Tobin bronze can be forged and stamped as 
readily as steel. Bolts and nuts can be forged from it, either by hand 
or by machinery. Its great tensile strength, and resistance to the corro- 
sive action of sea-water, render it a most suitable metal for condenser 
plates, steam-launch shafting, ship sheathing and fastenings, nails, hull 
plates for steam yachts, torpedo and life boats, and ship deck fittings. 

The Navy Department has specified its use for certain purposes in the 
machinery of the new cruisers. Its specific gravity is 8.071. The 
weight of a cubic inch is 0.291 lb. 



Special Alloys. (Engineering, March 24, 1893.) 
Japanese Alloys for art work: 





Copper. 


Silver. 


Gold. 


Lead. 


Zinc. 


Iron. 


Shaku-do 

Shibu-ichi 


94.50 

67.31 


1.55 
32.07 


3.73 
traces. 


0.11 
0.52 


trace. 


trace. 



Gilbert's Alloy for cera-perduta process, for casting in plaster-of- 
paris. 

Copper 91.4 Tin 5.7 Lead 2.9 Very fusible. 



ALLOYS OF COPPER, TIN, AND LEAD. 369 

COPPER-ZINC-IRON ALLOYS. 

(F. L. Garrison, Jour. Frank. Inst., June and July, 1891.) 

Delta Metal. — This alloy, which was formerly known as sterro-metal, 
is composed of about 60 copper, from 34 to 44 zinc, 2 to 4 iron, and 1 to 2 
tin. 

The peculiarity of all these alloys is the content of iron, which appears 
to have the property of increasing their strength to an unusual degree. 
In making delta metal the iron is previously alloyed with zinc in known 
and definite proportions. When ordinary wrought-iron is introduced 
into molten zinc, the latter readily dissolves or absorbs the former, and 
will take it up to the extent of about 5% or more. By adding the zinc- 
iron alloy thus obtained to the requisite amount of copper, it is possi- 
ble to introduce any definite quantity of iron up to 5% into the copper 
alloy. Garrison gives the following as the range of composition of 
copper-zinc-iron, and copper-zinc-tin-iron alloys: 

I. II. 

Per cent. Per cent. 

Iron 0.1 to 5 Iron 0.1 to 5 

Copper 50 to 65 Tin 0.1 to 10 

Zinc .49.9 to 30 Zinc 1.8 to 45 

Copper 98 to 40 

The advantages claimed for delta metal are great strength and tough- 
ness. It produces sound castings of close grain. It can be rolled and 
forged hot, and can stand a certain amount of drawing and hammering 
when cold. It takes a high polish, and when exposed to the atmosphere 
tarnishes less than brass. 

When cast in sand delta metal has a tensile strength of about 45,000 
pounds per square inch, and about 10% elongation; when rolled, ten- 
sile strength of 60,000 to 75,000 pounds per square inch, elongation 
from 9% to 17% on bars 1.128 inch in diameter and 1 inch area. 

Wallace gives the ultimate tensile strength 33,600 to 51,520 pounds 
per square inch, with from 10% to 20% elongation. 

Delta metal can be forged, stamped and rolled hot. It must be forged 
at a dark cherry-red heat, and care taken to avoid striking when at a 
black heat. 

According to Lloyd's Proving House tests, made at Cardiff, December 
20, 1887, a half-inch delta metal-rolled bar gave a tensile strength of 
88,400 pounds per square inch, with an elongation of 30% in three 
inches. 

ALLOYS OF COPPER, TIN, AND LEAD. 

G. H. Clamer, in Castings, July, 1908, describes some experiments on 
the use of lead in copper alloys. A copper and lead alloy does not make 
what would be called good castings; by the introduction of tin a more 
homogeneous product is secured. By the addition of nickel it was found 
that more than 15% of lead could be used, while maintaining tin at 8 to 
10%, and also that the tin could be dispensed with. A good alloy for 
bearings was then made without nickel, containing Cu 65, Sn 5, Pb 30. 
This alloy is largely sold under the name of "plastic bronze." If the 
matrix of tin and copper were so proportioned that the tin remained 
below 9% then more than 20% of lead could be added with satisfactory 
results. As the tin is decreased more lead may be added. (See Bear- 
ing Metal Alloys, below.) 

The Influence of Lead on Brass. — E. S. Sperry, Trans. A.I.M.E., 
1897. As a rule, the lower the brass (that is, the lower in zinc) the 
more difficult it is to cut. If the alloy is made from pure copper and 
zinc, the chips are long and tenacious, and a slow speed must be em- 
ployed in cutting. For some classes of work, such as spinning or car- 
tridge brass, these qualities are essential, but for others, such as clock 
brass or screw rod, they are almost prohibitory. To make an alloy 
which will cut easily, giving short chips, the best method is the addition 
of a small percentage of lead. Experiments were made on alloys con- 



370 



taining different percentages of lead. The following is a condensed 
statement of the chief results: 

Cu, 60; Zn, 30: Pb, 10. Difficult to obtain a homogeneous alloy. 
Cracked badly on rolling. 

Cu, 60; Zn, 35; Pb, 5. Good cutting qualities but cracked on rolling. 

Cu, 60; Zn, 37.5: Pb, 2.5. Cutting qualities excellent, but couid 
only be hot-rolled or forged with difficulty. 

Cu, 60; Zn, 38.75; Pb, 1.25. Cutting qualities inferor to those of 
the alloy containing 2.5% of lead, but superior to those of pure brass. 

Cu, 60; Zn, 40. Perfectly homogeneous. Rolls easily at a cherry 
red heat, and cracks but slightly in cold rolling. Chips long and tena- 
cious, necessitating a slow speed in cutting. 

Tensile tests of these alloys gave the following results: 



Copper, % 
Zinc, % . . . 
Lead, % . . 



T. S. per sq. in.* . . 
Elonga. in 1 in.,% . 
Elonga. in 8 in.,%. 
Red. of area, %.. . . 



P.R.. 



60.0 



92% 



60.0 
37.5 
2.5 



65% 



60.0 
35.0 
5.0 



61% 



60.0 
30.0 
10.0 



* Thousands of pounds. C, casting; A, annealed sheet; H, hard 
rolled sheet; P. R., possible reduction in rolling. 

The use of tin, even in small amounts, hardens and increases the ten- 
sile strength of brass, which is detrimental to free turning. Mr. Sperry 
gives analyses of several brasses which have given excellent results in 
turning, all included within the following range: Cu, 60 to 66%, Zn, 38 
to 32%, Pb, 1.5 to 2.5%. For cartridge-brass sheet, anything over 
0.10% of lead increases the liability of cracking in drawing. 



PHOSPHOR-BRONZE AND OTHER SPECIAE BRONZES. 

Phosphor-bronze. — In the year 1868, Montefiore & Kunzel of Liege. 
Belgium, found by adding small proportions of phosphorus or "phos- 
phoret of tin or copper" to copper that the oxides of that metal, nearly 
always present as an impurity, more or less, were deoxidized and the 
copper much improved in strength and ductility, the grain of the frac- 
ture became finer, the color brighter, and a greater fluidity was attained. 

Three samples of phosphor-bronze tested by Kirkaldy gave: 

Elastic limit, lbs. per sq. in 23,800 24,700 16,100 

Tensile strength, lbs. per sq. in. . 52,625 46,100 44,448 
Elongation, per cent 8.40 1.50 33.40 

The strength of phosphor-bronze varies like that of ordinary bronze 
according to the percentages of copper, tin, zinc, lead, etc., in the alloy. 

Phosphor-bronze Rod. — Torsion tests of 20 samples, 1/4 in. diam. 
Apparent outside fiber stress, 77,500 to 86,700 lbs. per sq. in.; average 
number of turns per inch of length, 0.76 to 1.50. — Tech. Quar., vol. xii, 
Sept., 1899. 

Penn. R. R. Co.'s Specifications for Phosphor-bronze (1902). — 
The metal desired is a homogeneous alloy of copper, 79.70; tin, 10.00; 
lead, 9.50; phosphorus, 0.80. Lots will not be accepted if samples do 
not show tin, between 9 and 11%: lead, between 8 and 11%; phos- 
phorus, between 0.7 and 1%; nor if the metal contains a sum total of 
other substances than copper, tin, lead, and phosphorus in greater quan- 
tity than 0.50 per cent. (See also p. 381.) 



ALUMINUM ALLOYS. 



371 



Deoxidized Bronze. — This alloy resembles phosphor bronze some- 
what in composition and also delta metal, in containing zinc and iron. 
The following analysis gives its average composition: Cu, 82.67; Sn, 12.40; 
Zn, 3.23; Pb, 2.14; Fe, 0.10; Ag, 0.07; P, 0.005. 



Comparison of Copper, 
Wires. 


Silicon-bronze, and Phosphor-bronze 

(Engineering, Nov. 23, 1883.) 


Description of Wire. 


Tensile Strength. 


Relative Conductivity. 




39,827 lbs. per sq. in. 

41,696 " " " " 
108,080 " " " " 
102,390 " " " " 




Silicon bronze (telegraph) 

" (telephone) 

Phosphor bronze (telephone) . . 


96 " " 
34 " " 

26 " " 



Silicon Bronze. (Aluminum World, May, 1897.) 

The most useful of the silicon bronzes are the 3% (97% copper, 3% 
silicon) and the 5% (95% copper, 5% silicon), although the hardness 
and strength of the alloy can be increased or decreased at will by 
increasing or decreasing silicon. A 3% silicon bronze has a tensile 
strength, in a casting, of about 55,000 lbs. per sq. in., and from 50% to 
60% elongation. The 5% bronze has a tensile strength of about 75,000 
lbs. and about 8% elongation. More than 5% or 5V2% of silicon in cop- 
per makes a brittle alloy. In using silicon, either as a flux or for making 
silicon bronze, the rich alloy of silicon and copper which is now on the 
market should be used. It should be free from iron and other metals if 
the best results are to be obtained. Ferro-silicon is not suitable for use 
in copper or bronze mixtures. 

Copper and Vanadium Alloys. The Vanadium Sales Co. of America 
reports (1908) that the addition of vanadium to copper has given a tensile 
strength of 83,000 lbs. per sq. in.; with an elongation of over 60%. 

ALLOTS FOR CASTING UNDER PRESSURE IN METAL 
MOLDS. E. L. Lake, Am. Mach., Feb. 13, 1908. 



No. 


Tin. 


Copper. 


Alumi- 
num. 


Zinc. 


Lead. 


Anti- 
mony. 


Iron 


, 


14.75 
19 
12 
30.8 


5.25 

5 

10.6 
20.4 


6.25 
1. 

3.4 
2.6 


73.75 
72.7 
73.8 
46.2 








2 
3 


2 


0.3 


0.2." 


4 

















Nos. 1 and 2 suitable for ordinary work, such as could be performed by 
average brass castings. No. 3 and 4 are harder. 

ALUMINUM ALLOTS. 

The useful alloys of aluminum so far found have been chiefly in two 
groups, the one of aluminum with not more than 35% of other metals, and 
the other of metals containing not over 15% of aluminum; in the one case 
the metals impart hardness and other useful qualities to the aluminum, 
and in the other the aluminum gives useful qualities to the metal with 
which it is alloyed. 

Aluminum-Copper Alloys. — The useful aluminum-copper alloys can 
be divided into two classes, — the one containing less than 11% of 
aluminum, and the other containing less than 15% of copper. The first 
class is best known as Aluminum Bronze. 

Aluminum Bronze. (Cowles Electric Smelting and Al. Co.'s circular.) 
The standard A No. 2 grade of aluminum bronze, containing 10% of 
aluminum and 90% of copper, has many remarkable characteristics 
which distinguish it from all other metals. 



372 



The tenacity of castings of A No. 2 grade metal varies between 75,000 
and 90,000 lbs. to the square inch, with from 4% to 14% elongation. 

Increasing the proportion of aluminum in bronze beyond 11% pro- 
duces a brittle alloy; therefore nothing higher than the A No. 1, which 
contains 11%, is made. 

The B, C, D, and E grades, containing 71/2%, 5%, 21/2%, and ii/4% of 
aluminum, respectively, decrease in tenacity in the order named, that 
of the former being about 65,000 pounds, while the latter is 25,000 
pounds. While there is also a proportionate decrease in transverse and 
torsional strengths, elastic limit, and resistance to compression as the 
percentage of aluminum is lowered and that of copper raised, the ductil- 
ity on the other hand increases in the same proportion. The specific 
gravity of the A No. 1 grade is 7.56. 

Bell Bros., Newcastle, gave the specific gravity of the aluminum bronzes 
as follows: 

3%, 8.691; 4%, 8.621; 5%, 8.369; 10%, 7.689. 

The Thermit Process. — When finely divided aluminum is mixed 
with a metallic oxide and ignited the aluminum burns with great rapidity 
and intense heat, the chemical reaction being Al + Fe203 = AI2O3 + Fe. 
The heat thus generated may be used to fuse or weld iron and other metals, 
See the Thermit Process, under Welding of Steel, page 463. 

Tests of Aluminum Bronzes. 

(John H. J. Dagger, British Association, 1889.) 



Per cent 


Tensile Strength. 


Elonga- 
tion, 
per cent. 


Specific 
Gravity. 


of 
Aluminum. 


Tons per 
square inch. 


Pounds per 
square inch. 


It 


40 to 45 
33 " 40 
25 " 30 
15 " 18 
13 " 15 
11 " 13 


89,600 to 100,800 
73,920 " 89,600 
56,000 " 67,200 
33,600 " 40,320 
29,120 " 33,600 
24,640 " 29,120 


8 
14 
40 
40 
50 
55 


7 23 


10 


7.69 


71/2 

5-31/2 

21/-> 


8.00 
8.37 
8.69 


U/4 









Both physical and chemical tests made of samples cut from various 
sections of 21/2%, 5%, 71/2%, or 10% aluminized copper castings tend to 
prove that the aluminum unites itself with each particle of copper with 
uniform proportion in each case, so that we have a product that is free 
from liquation and highly homogeneous. (P. C. Cole, Iron Age, Jan. 16, 
1890.) 

Casting. — The melting point of aluminum bronze varies slightly with 
the amount of aluminum contained, the higher grades melting at a 
somewhat lower temperature than the lower grades. The A No. 1 grades 
melt at about 1700° F., a little higher than ordinary bronze or brass. 

Aluminum bronze shrinks more than ordinary brass. As the metal 
solidifies rapidly it is necessary to pour it quickly and to make the 
feeders amply large, so that there will be no " freezing " in them before 
the casting is properly fed. Baked-sand maids are preferable to green 
sand, except for small castings, and when fine skin colors are desired in 
the castings. (Thos. D. West, Trans. A. S. M. E., 1886, vol. viii.) 

All grades of aluminum bronze can be rolled, swedged, spun, or drawn 
cold except A 1 and A 2. They can all be worked at a bright red heat. 

In rolling, swedging, or spinning cold, it should be annealed very often, 
and at a brighter red heat than is used for annealing brass. 

Seamless Tubes. — Leonard Waldo, Trans. A. S. M. E. , vol. xviii, 
describes the manufacture of aluminum bronze seamless tubing. Many 
difficulties were met in all stages of the process. A cold drawn bar, 1.49 
ins. outside diameter, 0.05 in. thick, showed a yield point of 68,700, and a 
tensile strength of 96,000 lbs. per sq. in. with an elongation of 4.9% in 
10 in.; heated to bright red and plunged in water, the Y. P. reduced to 
24,200 and the T. S. to 47,600 lbs. per sq. in., and the elongation in 10 
ins. increased to 64.9%. 



ALUMINUM ALLOYS. 



373 



Brazing. — Aluminum bronze will braze as well as any other metal, 
using one-quarter brass solder (zinc 500, copper 500) and three-quarters 
borax, or, better, three-quarters cryolite. 

Soldering. — To solder aluminum bronze with ordinary soft (pewter) 
solder: Cleanse well the parts to be joined free from grease and dirt. 
Then place the parts to be soldered in a strong solution of sulphate of 
copper and place in the bath a rod of soft iron touching the parts to be 
joined. After a while a coppery-like surface will be seen on the metal. 
Remove from bath, rinse quite clean, and brighten the surfaces. These 
surfaces can then be tinned by using a fluid consisting of zinc dissolved 
in hydrochloric acid, in the ordinary way, with common soft solder. 

Mierzinski recommends ordinary hard solder, and says that Hulot uses 
an alloy of the usual half-and-half lead-tin solder, with 12.5%, 25% or 
50% of zinc amalgam. 

Aluminum Brass. (E. H. Cowles, Trans. A. I. M. E., vol. xviii.) — 
Cowles aluminum brass is made by fusing together equal weights of A 1 
aluminum bronze, copper, and zinc. The copper and bronze are first 
thoroughly melted and mixed, and the zinc is finally added. The 
material is left in the furnace until small test-bars are taken from it and 
broken. When these bars show a tensile strength of 80,000 pounds or 
over, with 2 or 3 per cent ductility, the metal is ready to be poured. 
Tests of this brass, on small bars, have at times shown as high as 100,000 
pounds tensile strength. 

The screw of the United States gunboat Petrel is cast from this brass 
mixed with a trifle less zinc in order to increase its ductility. 



Tests of Aluminum Brass. 

(Cowles E. S. & Al. Co.) 



Specimen (Castings) 


Diameter 

of Piece, 

Inch. 


Area, 
sq. in. 


Tensile 

Strength, 

lbs. per 

sq. in. 


Elastic 
Limit, 
lbs. per 
sq. in. 


Elonga 
tion, 
per ct. 


Remarks. 


15%A grade Bronze ) 
17% Zinc | 


0.465 
0.465 
0.460 


0.1698 
0.1698 
0.1661 


41,225 
78,327 
72,246 


17,668 


41 1/2 

21/2 

21/2 


S3 bC 


68% Copper ) 

1 part A Bronze . . . ) 




1 part Copper ) 

1 part A Bronze . . . ) 

I part Zinc j 

1 part Copper ) 





The first brass on the above list is an extremely tough metal with low 
elastic limit, made purposely so as to "upset" easily. The other, which 
is called Aluminum brass No. 2, is very hard. 

We have not in this country or in England any official standard by 
which to judge of the physical characteristics of cast metals. There are 
two conditions that are absolutely necessary to be known before we can 
make a fair comparison of different materials; namely, whether the 
casting was made in dry or green sand or in a chill, and whether it was 
attached to a larger casting or cast by itself. It has also been found that 
chill-castings give higher results than sand-castings, and that bars cast 
by themselves purposely for testing almost invariably run higher than 
test-bars attached to castings. It is also a fact that bars cut out from 
castings are generallv weaker than bars cast alone. (E. H. Cowles.) 

Caution as to Reported Strength of Alloys. — The same variation 
in strength which has been found in tests of gun-metal (copper and 
tin) noted above, must be expected in tests of aluminum bronze and in 
fact of all alloys. They are exceedingly subject to variation in density 
and in grain, caused by differences in method of moulding and casting, 
temperature of pouring, size and shape of casting, depth of "sinking 
head," etc. 



374 



Aluminum Hardened by Addition of Copper. 

Tests of rolled sheets 0.04 inch thick. (The Engineer, Jan. 2, 1891.) 



Al. 
Per cent. 


Cu. 
Per cent. 


Sp. Gr. 
Calculated. 


Sp. Gr. 
Determined. 


Tensile Strength 
lbs. per 
sq. in. 


100 






2.67 
2.71 
2.77 

2.82 
2.85 


26,535 
43,563 
44,130 
54,773 
50,374 


98 
96 
94 
92 


2 
4 
6 

8 


2.78 
2.90 
3.02 
3.14 



Tests of Aluminum Alloys. 

(Engineer Harris, U. S. N., Trans. A. I. M. E., vol. xviii.) 



Composition. 


Tensile 
Strength 
per sq. 
in., lbs. 


Elastic 
Limit, 
lbs. per 
sq. in. 


Elonga- 
tion, 
per ct. 


Reduc- 
tion of 
Area, 
per ct' 


Copper. 


Alumi- 
num. 


Silicon. 


Zinc. 


Iron. 


91.5G% 
88.50 
91.50 
90.00 


6.5G% 

9.33 

6.50 

9.00 

3.33 

3.33 

6.50 

6.50 

9.33 

6.50 


1.73% 

1.66 

1.75 

1.00 

0.33 

0.33 

1.75 

0.50 

1.66 

0.50 




0.25% 
0.50 

0.25 


60,700 
66,000 
67,600 
72,830 
82,200 
70,400 
59,100 
53,000 
69,930 
46,530 


18,000 
27,000 
24,000 
33,000 
60,000 
55,000 
19,000 
19,000 
33,000 
17,000 


23.2 
3.8 

13 

2.40 
2.33 
0.4 

15.1 
6.2 
1.33 
7.8 


30.7 
7.8 

21.62 
5.78 


63.00 
63.00 
91.50 
93.00 


33.33% 
33.33 


"6!25" 


9.88 
4.33 
23.59 
15.5 


88.50 
92.00 




0.50 


3.30 
19.19 











For comparison with the above 6 tests of " Navy Yard Bronze," 
Cu 88, Sn 10, Zn 2, are given in which the T. S. ranges from 18,000 to 
24,590, E. L. from 10,000 to 13,000, El. 2.5 to 5.8%, Red. 4.7 to 10.89. 



Alloys of Aluminum, Silicon and Iron. 

M. and E. Bernard have succeeded in obtaining through electrolysis, 
by treating directly and without previous purification, the aluminum 
earths (red and white bauxites), the following: 

Alloys such as ferro-aluminum, ferro-silicon-aluminum and silicon- 
aluminum, where the proportion of silicon may exceed 10%, which are 
employed in the metallurgy of iron for refining steel and cast-iron. 

Also silicon-aluminum, where the proportion of silicon does not exceed 
10%, which may be employed in mechanical constructions in a rolled or 
hammered condition, in place of steel, on account of their great resist- 
ance, especially where the lightness of the piece in construction consti- 
tutes one of the main conditions of success. 

The following analyses are given: 

1. Alloys applied to the metallurgy of iron, the refining of steel and 
cast iron: No. 1. Al, 70%; Fe, 25%: Si, 5%. No. 2. Al, 70; Fe, 20; 
Si, 10. No. 3. Al, 70; Fe, 15; Si, 15. No. 4. Al, 70; Fe, 10; Si, 20. 
No. 5. Al, 70; Fe, 10; Si, 10; Mn, 10. No. 6. Al, 70; Fe, trace; Si, 20; 
Mn, 10. 

2. Mechanical alloys: No. 1. Al, 92; Si, 6.75; Fe, 1.25. No. 2. 
Al, 90; Si, 9.25; Fe, 0.75. No. 3. Al, 90; Si, 10; Fe, trace. The best 
results were with alloys where the proportion of iron was very low, and 
the proportion of silicon in the neighborhood of 10%. Above that pro- 
portion the alloy becomes crystalline and can no longer be employed. 
The density of the allovs of silicon is approximately the same as that of 
aluminum. — La Melallurgie, 1892. 



ALUMINUM ALLOYS. 375 

Tungsten and Aluminum. — Mr. Leinhardt Mannesmann says that 
the addition of a little tungsten to pure aluminum or its alloys com- 
municates a remarkable resistance to the action of cold and hot Mater, 
salt water and other reagents. When the proportion of tungsten is 
sufficient the alloys offer great resistance to tensile strains. An alloy of 
aluminum and tungsten called partinium, from the name of its inventor, 
M. Partin, has been used in France since 1898 for motor-car bodies. Its 
properties are stated as follows: Cast, sp. gr., 2.86; T. S., 17,000 to 
24,000; elong., 12 to 6%. Rolled, sp. gr., 3.09; T. S., 45,500 to 53,600; 
elong., 8 to 6%. 

Aluminum, Copper, and Tin. — Prof. R. C. Carpenter, Trans. 
A. S. M. E., vol. xix., finds the following alloys of maximum strength iai 
a series in which two of the three metals are in equal proportions: 

Al, 85; Cu, 7.5; Sn, 7.5; tensile strength, 30,000 lbs. per sq. in.; 
elongation in 6 in., 4%; sp. gr., 3.02. Al, 6.25; Cu, 87.5; Sn, 6.25; 
T. S., 63,000; EL, 3.8; sp. gr., 7.35. Al, 5; Cu, 5; Sn, 90; T. S., 11,000; 
EL, 10.1; sp.gr., 6.82. 

From 85 to 95% Cu the bars have considerable strength, are close 
grained and of a golden color. Between 78 and 80% the color changes 
to silver white and the bars become brittle. From 78 to 20% Cu the 
alloys are very hard and brittle, and worthless for practical purposes. 
Aluminum is strengthened by the addition of equal parts of copper and 
tin up to 7.5% of each, beyond which the strength decreases. All the 
alloys that contain between 20 and 60% of either one of the three metals 
are very weak. 

Aluminum and Zinc. — Like the copper alloys, the zinc alloys can 
be divided into two classes, (1) those containing a relatively snail amount 
of aluminum, and (2) those containing less than 35% of zinc. The first 
class is used largely in galvanizing baths to produce greater fluidity, while 
the second class embraces the zinc casting alloys. Prof. Carpenter finds 
that the strongest alloy of these metals consists of two parts of alumi- 
num and one part of zinc. Its tensile strength is 24,000 to 26,000 lbs. 
per sq. in.; has but little ductility, is readily cut with machine-tools, and 
is a good substitute for hard cast brass. 

Aluminum and Tin. — M. Bourbouze has compounded an alloy of 
aluminum and tin, by fusing together 100 parts of the former vith 10 
parts of the latter. This alloy is paler than aluminum, and has a specific 
gravity of 2.85. The alloy is not as easily attacked by several reagents 
as aluminum is, and it can also be worked more readily. Another 
advantage is that it can be soldered as easily as bronze, without fuither 
preliminary preparations. Prof. Carpenter found that aluminum-tin 
alloys with from 2 to 10% Al are as a rule weaker than pure aluminum 
and of little practical value. 

Aluminum with Nickel, German Silver or Titanium. — J. W. 
Richards, Jour. Frank. Inst., 1895, says that an addition of 5% of nickel 
or German silver, or 2% of titanium to aluminum increases the tensile 
strength to 20,000-30,000 lbs. per sq. in. in castings and to 40,000-50,000 
lbs. in sheet. For purposes where the requirements are fine color, 
strength, hardness and springiness the German-silver alloy is recom- 
mended. 

Aluminum-Antimony Alloys. — Dr. C. R, Alder Wright describes 
some aluminum-antimony alloys in a communication read before the 
Society of Chemical Industry. The results of his researches do not dis- 
close the existence of a commercially useful alloy of these two metals, 
and have greater scientific than practical interest. A remarkable point 
is that the alloy with the chemical composition Al Sb has a higher melt- 
ing-point than either aluminum or antimony alone, and that when al urm - 
num is added to pure antimony the melting-point goes up from that of 
antimony (450° C.) to a certain temperature rather above that of silver 
(1000° C). 

Aluminum and Cast Iron. — Aluminum alloys readily with cast 
iron, up to 14 to 15% Al, but the metal decreases in strength as the Al 
is increased. Mixtures with greater percentages of Al are granular, 
and have practically no coherence. — Trans. A. I. M. E., vol. xviu., 
A. S. M. E., vol. xix. 

Other Aluminum Alloys. — Al 75.7, Cu 3, Zn 20, Mn 1.3 is an 
excellent casting metal, having a tensile strength of over 35,000 lbs. 
per sq. in., and a sp. gr. slightly above 3. It has very little ductility. 



376 



Al 96.5, Cu 2, and chromium 1.5 is a little heavier than pure alumi- 
num and has a tensile strength of 26,300 lbs. per sq. in. — A. S. M E., 
vol. xix. 

Aluminum and 31agnesium. — Magnalium. — An alloy containing 
90 to 98% of aluminum, the balance being mainly magnesium, has been 
patented under the trade name of "magnalium." Its specific gravity is 
only 2.5; it is whiter, harder and stronger than aluminum, and can be 
forged, rolled, drawn, machined and filed. It takes a high polish and 
resists oxidation better than any other light metals or alloys. The 
tensile strength of cast magnalium, class X, is reported at 18,400 to 
21,300 lbs. per sq. in., with a reduction of area of 3.75%; hard rolled 
plates, class Z, 52,200 lbs. per sq. in., with 3.7% reduction; annealed 
plates, 42,200 lbs. per sq. in., 17.8% reduction. Made by the Magna- 
lium Syndicate of Berlin. The price is said to be about twice that of 
aluminum. — (Mach'y, July, 1908.) 

Prof. Carpenter (A. S. M. E., vol. xix) found that additions of Mn 
increased the strength of Al up to 10% Mn. Larger additions made 
brittle alloys. 

Resistance of Aluminum Alloys to Corrosion. — J. W. Richards, 
Jour. Frank. Inst., 1895, gives the following table showing the relative j 
resistance to corrosion of aluminum (99% pure) and alloys of aluminum | 
with different metals, when immersed in the liquids named. The J 
figures are losses per day in milligrams per square centimeter of surface: 



3% 
Caustic 
potash 
Cold. 



3% 
Hydro- 
chloric 

Acid. 

Cold. 







Strong 
Nitric 
Acid. 
Cold. 



Strong 
Salt 
Solu- 
tion. 

150° F. 



Strong 
Acetic 
Acid. 
140° F. 



Car- 
bonic 
Acid. 
Water. 
77° F. 



3 per cent copper 

3 per cent German silver 

3 per cent nickel 

2 per cent titanium 

99 per cent aluminum . . . 



265.0 
1534.4 

580.3 
73.4 
34.6 



53.3 
130.6 
180.0 

4.3 
5.8 



36.1 
97.7 
83.0 
18.6 
9.6 



0.1 

0.05 

0.13 

0.06 

0.04 



0.4 
0.6 
0.75 
0.20 
0.15 



0.0 
0.01 
0.04 
0.0 
0.01 



Aluminum Alloys used in Automobile Construction {Am. Mach., 
Aug. 22, 1907.) 

(1) Al 2, Zn, 1, T.S. 35,000; Sp. gr. 3.1 

(2) Al 92, Cu, 8, T.S. 18,000; Sp. gr. 2.84 Ni, trace 

(3) Al 83, Zn, 15, Cu, 2, T.S. 23,000; Sp. gr. 3.1 

(1) Unsatisfactory on account of failures under repeated vibration. 
(2) Generally used. Resists vibrations well. (3) Used to some extent. 
Many motor-car makers decline to use it because of uncertainty of its| 
behavior under vibration. 

ALLOTS OF MANGANESE AND COPPER. 

Various Manganese Alloys. — E. H. Cowles, in Trans. A. I. M. E. 
vol. xviii, p. 495, states that as the result of numerous experiments on 
mixtures of the several metals, copper, zinc, tin, lead, aluminum, iron, 
and manganese, and the metalloid silicon, and experiments upon the; 
same in ascertaining tensile strength, ductility, color, etc., the most 
important determinations appear to be about as follows: 

1. That pure metallic manganese exerts a bleaching effect upon copper 
more radical in its action even than nickel. In other words, it was| 
found that 181/2% of manganese present in copper produces as white a 
color in the resulting alloy as 25% of nickel would do, this being the 
amount of each required to remove the last trace of red. 

2. That upwards of 20% or 25% of manganese may be added to cop- 
per without reducing its ductility, although doubling its tensile strength 
and changing its color. 

3. That manganese, copper, and zinc when melted together and 
poured into molds behave very much like the most "yeasty" German 



ALLOYS OF MANGANESE AND COPPER. 



377 



silver, producing an ingot which is a mass of blow-holes, and which 
swells up above the mold before cooling. 

4. That the ahoy of manganese and copper by itself is very easily 
oxidized. 

5. That the addition of 1.25% of aluminum to a manganese-copper 
alloy converts it from one of the most refractory of metals in the casting 
process into a metal of superior casting qualities, and the non-corrodi- 
bility of which is in many instances greater than that of either German 
or nickel silver. 

A "silver-bronze" alloy especially designed for rods, sheets, and wire 
has the following composition: Mn, 18; Al, 1.20; Si, 0.5; Zn, 13; and Cu, 
67.5%. It has a tensile strength of about 57,000 lbs. on small bars, and 
20% elongation. It has been rolled into thin plate and drawn into wire 
0.008 inch in diameter. A test of the electrical conductivity of this 
wire (of size No. 32) shows its resistance to be 41.44 times that of pure 
copper. This is far lower conductivity than that of German silver. 

Manganese Bronze. (F. L. Garrison, Jour. F. I., 1891.) — This 
alloy has been used extensively for casting propeller-blades. Tests of 
some made by B. H. Cramp & Co., of Philadelphia, gave an average 
elastic limit of 30,000 lbs. per sq, in., tensile strength of about 60,000 lbs. 
per sq. in. with an elongation of 8% to 10% in sand castings. When 
rolled, the E. L. is about 80,000 lbs. per sq. in., tensile strength 95,000 to 
106,000 lbs. per sq. in., with an elongation of 12% to 15%. 

Compression tests made at United States Navy Department from the 
metal in the pouring-gate of propeller-hub of U. S. S. Maine gave in 
two tests a crushing stress of 126,450 and 135,750 lb. per sq. in. The 
specimens were 1 inch high by 0.7 x 0.7 inch in cross-section = 0.49 
square inch. Both specimens gave way by shearing; on a plane making 
an angle of nearly 45° with the direction of stress. 

A test on a specimen 1 x 1 x 1 inch was made from a piece of the 
same pouring-gate. Under stress of 150,000 pounds it was flattened to 
0.72 inch high by about ll/4 x 11/4 inches, but without rupture or any 
sign of distress. 

One of the great objections to the use of manganese bronze, or in fact 
any alloy except iron or steel, for the propellers of iron ships is on 
account of the galvanic action set up between the propeller and the 
stern-posts. This difficulty has in great measure been overcome by 
putting strips of rolled zinc around the propeller apertures in the stern- 
frames. 

The following analysis of Parsons' manganese bronze No. 2 was made 
from a chip from the propeller of Mr. W. K. Vanderbilt's vacht Alva. 
Cu, 88.64; Zn, 1.57; Sn, 8.70; Fe, 0.72; Pb, 0.30; P, trace. 

It will be observed there is no manganese present and the amount of 
zinc is very small. 

E. H. Cowles, Trans. A. I. M. E., vol. xviii, says: Manganese bronze, 
so called, is in reality a manganese brass, for zinc instead of tin is the 
chief element added to the copper. Mr. P. M. Parsons, the proprietor of 
this brand of metal, has claimed for it a tensile strength of from 24 to 
28 tons per sq. in. in small bars when cast in sand. 

E. S. Sperry, Am. Mach., Feb. 1, 1906, gives the following analyses of 
manganese bronze: 





Cu. 


Zn. 


Fe. 


Sn. 


Al. 


Mn. 


Pb. 


No. 1.. .. 


60.27 
56.11 
60.00 
56.00 


37.52 
41.34 
38.00 
42.38 


1.41 
1.30 
1.25 
1.25 


0.75 
0.75 
0.65 
0.75 


0.47 

6;5o" 


0.01 
0.01 
0.10 
0.12 


O.Ui 


" 2 

" 3 


0.02 


" 4 





No. 1 is Parsons' alloy for sheet, No. 2 for sand casting. No. 3 is Mr. 
Sperry's formula for sheet, and No. 4 his formula for sand castings. 
The mixture for No. 3, allowing for volatilization of some zinc is: copper: 
60 lbs.; zinc, 39 lbs.; "steel alloy," 2 lbs. That for No. 4 is: copper. 
56 lbs.; zinc, 43 lbs.; "steel alloy," 2 lbs.; aluminum, 0.5 lb. The steel 
alloy is made by melting wrought iron, 18 lbs.; ferro-manganese 
(80 Fe, 20 Mn), 4 lbs.; tin, 10 lbs. The iron and ferro-manganese are 
first melted and then the tin is added. In making the bronzes about 
15 lbs. of the copper is first melted under charcoal, the steel alloy is 



378 



added, melted and stirred, then the aluminum is added, melted and 
stirred, then the rest of the copper is added, and finally the zinc. The 
only function of the manganese is to act as a carrier to the iron, which 
is difficult to alloy with copper without such carrier. The iron is 
needed to give a high elastic limit. Green sand castings of No. 4 fre- 
quently give results as high as the following: T. S., 70,000; E. L 
30,000 lbs. per sq. in.; elongation in 6 ins., 18%; reduction of area' 
26%. 

Magnetic Alloys of Non-Magnetic Metals. (El. World, April 15, 
1905; Electrot.-Zeit. Mar. 2, 1905.) — Dr. Heusler has discovered that 
alloys of manganese, aluminum, and copper are strongly magnetic. The 
best results have been obtained when the Mn and Al are in the proportions 
of their respective atomic weights, 55 and 27.1. Two such alloys are 
described (1) Mn, 26.8; Al, 13.2; Cu, 60. (2) Mn, 20.1; Al, 9.9; Cu, 70, 
with 1% Pb added. The first was too brittle to be workable. The 
second was machined without difficulty. These alloys have as yet no 
commercial importance, as they are far inferior magnetically (at most 
1 to 4) to iron. 

GERMAN-SILVER, AND OTHER NICKEL ALLOTS. 

German Silver. — The composition of German silver is a very un- 
certain thing and depends largely on the honesty of the manufacturer 
and the price the purchaser is willing to pay. It is composed of copper, 
zinc, and nickel in varying proportions. The best varieties contain 
from 18% to 25% of nickel and from 20% to 30% of zinc, the remainder 
being copper. The more expensive nickel silver contains from 25% to 
33% of nickel and from 75% to 66% of copper. The nickel is used as a 
whitening element; it also strengthens the alloy and renders it harder 
and more non-corrodible than the brass made without it, of copper and 
zinc. Of all troublesome alloys to handle in the foundry or rolling-mill, 
German silver is the worst. It is unmanageable and refractory at every 
step in its transition from the crude elements into rods, sheets, or wire. 
(E. H. Cowles, Trans. A.I.M.E., xviii, p. 494.) 

The following list of copper-nickel alloys is from various sources: 





Copper. 


Nickel. 


Tin. 


Zinc. 




51.6 
50.2 
51.1 
52 to 55 
75 to 66 
40.4 

8 

2 

8 

8 


25.8 

14.8 

13.8 

18 to 25 

25 to 33 

31.6 

3 

1 

2 

3 


22.6 
3.1 

3.2 






31.9 




31.9 


" " 


20 to 30 


Nickel " 










6.5 parts 
6.5 " 










1 






3.5 " 






3.5 " 









Nickel-copper Alloys. — (F. L. Sperry, A. I. M. E., 1895.) 



- 


Copper. 


Nickel. 


Zinc. 


Iron. 


Cobalt. 




52 to 63 

50 

65.4 

50 
50 to 60 
45.7 to 60 

52.5 

50 

88 

75 


22 to 6 
18.7 to 20 

16.8 

50 
25 to 20 
31.6 to 15 

17.7 

25 

12 

25 


26 to 31 

31.3 to 30 

13.4 














3.4 




Christofle 






25 to 20 
25.4 to 17 
28.8 
25 






English, Sheffield 


to 2.6 


to 3.4 































ALLOYS OF BISMUTH. 



379 



A refined copper-nickel alloy containing 50% copper and 49% nickel, 
with very small amounts of iron, silicon and carbon, is produced direct 
from Bessemer matte in the Sudbury (Canada) Nickel Works. German- 
silver manufacturers purchase a ready-made alloy, which melts at a 
low heat and requires only the addition of zinc, instead of buying the 
nickel and copper separately. This alloy, "50-50" as it is called, is 
almost indistinguishable from pure nickel. Its cost is less than nickel, 
its melting-point much lower, it can be cast solid in any form desired, 
and furnishes a casting which works easily in the lathe or planer, yield- 
ing a silvery- white surface unchanged by air or moisture. For bullet 
casings now used in various British and Continental rifles, a special alloy 
of 80% copper and 20% nickel is made. 

Monel Metal. — An alloy of about 72% Ni, 1.5 Fe, 26.5 Cu, made from 
the Canadian copper-nickel ores, is described in the Metal Worker, Oct. 10, 
1908. It has many valuable properties when rolled into sheets, making 
it especially suitable for roofing. It is ductile and flexible, is easily 
soldered, has a high resistance to corrosion, and a relatively small expan- 
sion and contraction under temperature changes. The tensile strength 
in castings is from 70,000 to 80,000 lbs. per sq. in., and in rolled sheets as 
high as 108,000 lbs. 

Constantan is an alloy containing about 60% copper and 40% nickel, 
which is much used for resistance wire in electrical instruments. Its 
electrical resistance is about twenty-eight to thirty times that of copper, 
and it possesses a very low temperature coefficient, — approximately 
.00003. This same material is also much used to form one element of 
base-metal thermo-couples. 



ALLOYS OF BISMUTH. 

By adding a small amount of bismuth to lead the latter may be 
hardened and toughened. An alloy consisting of three parts of lead 
and two of bismuth has ten times the hardness and twenty times the 
tenacity of lead. The alloys of bismuth with both tin and lead are 
extremely fusible, and take fine impressions of casts and molds. An 
alloy of one part Bi, two parts Sn, and one part Pb is used by pewter- 
workers as a soft solder, and by soap-makers for molds. An alloy of five 
parts Bi, two parts Sn, and three parts Pb imelts at 199° F., and is 
somewhat used for stereotyping, and for metallic writing-pencils. Thorpe 
gives the following proportions for the better-known fusible metals: 



Name of Alloy. 


Bis- 
muth. 


Lead. 


Tin. 


Cad- 
mium. 


Mer- 
cury. 


Melting- 
point. 




50 
50 
50 
50 
50 
50 
50 


31.25 
28.10 
25.00 
25.00 
25.00 
26.90 
20.55 


18.75 
24.10 
25.00 
25.00 
12.50 
12.78 
21.10 






202° F. 








203° " 








201° " 


D' Arcet's with mercury 
Wood's 


10.40 
' 14.03 


250.0 


113° " 
149° " 
149° " 


Guthrie's " Eutectic ". 


"Very low.'? 



The action of heat upon some of these alloys is remarkable. Thus, 
Lipowitz's alloy, which solidifies at 149° F., contracts very rapidly at 
first, as it cools from this point. As the cooling goes on the contrac- 
tion becomes slower and slower, until the temperature falls to 101.3° 
F. From this point the alloy expands as it cools, until the temperature 
falls to about 77° F., after which it again, contracts, so that at 32° F. 
a bar of the alloy has the same length as at 115° F. 

Alloys of bismuth have been used for making fusible plugs for boilers, 
but it is found that they are altered by the continued action of heat, 
so that one cannot rely upon them to melt at the proper temperature. 
Pure Banca tin is used "by the U. S. Government for fusible plugs. 



380 



FUSIBLE ALLOTS. 

(From various sources. Many of the figures are probably very 

inaccurate.) 

Sir Isaac Newton's, bismuth 5, lead 3, tin 2, melts at 212° F. 

Rose's, bismuth 2, lead 1, tin 1, melts at 200 " 

Wood's, cadmium 1, bismuth 4, lead 2, tin 1, melts at 165 " 

Guthrie's, cadmium 13.29, bismuth 47.38, lead 19.36, tin 19.97, 

melts at 160 " 

Lead 1, tin 1, bismuth 1, cadmium 1, melts at 155 " 

Lead 3, tin 5, bismuth 8, melts at 208 " 

Lead 1, tin 3, bismuth 5, melts at 212 " 

Lead 1, tin 4, bismuth 5, melts at 240 " 

Tin 1, bismuth 1, melts at 286 ' 

Lead 2, tin 3, melts at 334 to 367 ' 

Tin 2, bismuth 1, melts at 336 ' 

Lead 1, tin 2, melts at 340 to 360 ' 

Tin 8, bismuth 1, melts at 392 ' 

Lead 2, tin 1, melts at 440 to 475 ' 

Lead 1, tin 1, melts at 370 to 400 ' 

Lead 1, tin 3, melts at 356 to 383 ' 

Tin 3, bismuth 1, melts at 392 ' 

Lead 1 , bismuth 1 , melts at 257 ' 

Lead 1, tin 1, bismuth 4, melts at 201 ' 

Lead 5, tin 3, bismuth 8, melts at 202 ' 

Tin 3, bismuth 5, melts at 202 ' 



BEARING-METAL ALLOTS. 

(C. B. Dudley, Jour. F. I., Feb. and March, 1892.) 

Alloys are used as bearings in place of wrought iron, cast iron, or 
steel, partly because wear and friction are believed to be more rapid 
when two metals of the same kind work together, partly because the I 
soft metals are more easily worked and got into proper shape, and partly 
because it is desirable to use a soft metal which will take the wear j 
rather than a hard metal, which will wear the journal more rapidly. 

A good bearing-metal must have five characteristics: (1) It must be 
strong enough to carry the load without distortion. Pressures on car- 
journals are frequently as high as 350 to 400 lb! per square inch. 

(2) A good bearing-metal should not heat readily. The old copper- 
tin bearing, made of seven parts copper to one part tin, is more apt to 
heat than some other alloys. In general, research seems to show that 
the harder the bearing-metal, the more likely it is to heat. 

(3) Good bearing-metal should work well in the foundry. Oxidation 
while melting causes spongy castings. It can be prevented by a liberal 
use of powdered charcoal while melting. The addition of 1% to 2% of 
zinc or a small amount of phosphorus greatly aids in the production of I 
sound castings. This is a principal element of value in phosphor- 
bronze. 

(4) Good bearing-metals should show small friction. It is true that J 
friction is almost wholly a question of the lubricant used; but the metal j ( 
of the bearing has certainly some influence. 

(5) Other things being equal, the best bearing-metal is that which I 
wears slowest. 

The principal constituents of bearing-metal alloys are copper, tin, W 
lead, zinc, antimony, iron, and aluminum. The following table gives I 
the constituents of most of the prominent bearing-metals as analyzed at : 
the Pennsylvania Railroad laboratory at Altoona. 



BEARING-METAL ALLOYS. 



381 



Analyses of Bearing-metal Alloys. 



Metal. 


Copper. 


Tin. 


Lead. 


Zinc. 


Anti- 
mony. 


Iron. 




70.20 
1.60 


4.25 
98.13 


14.75 


10.20 




55 








87.92 
84.87 

1.15 
67.73 
80.69 
14.57 
12.40 

5.10 
83.55 

78.44 
0.31 
15.06 
12.52 


"85l57 


12.08 
15.10 








trace 
9.91 
14.38 






4.01 






16.73 

18.83 


? (1) 








75.47 
77.83 
92.39 
trace 


9.72 
9.60 
2.37 


• (2) 




trace 




trace(3) 
0.07 






trace 

0.98 
38.40 


16.45 
19.60 




American anti-friction 


65 




59.66 
75.80 
76.41 
90.52 
81.24 


2J6 
9.20 

10.60 
9.58 

10.98 


11 




















(5) 




7.27 
88.32 

"84 J3" 
94.40 
9.61 
15.00 






(6) 




"42!67' 
trace 


11.93 

"i4J8' 
6.03 




Harrington bronze 


55.73 


0.97 


0.68 
61 












79.17 

76.80 


10.22 
8.00 


...(7) 


Ex. B. metal 






(*\ 



Other constituents: 

(1) No graphite. 

(2) Possible trace of carbon. 

(3) Trace of phosphorus. 

(4) Possible trace of bismuth. 



(5) No manganese. 

(6) Phosphorus or arsenic, 0.37. 

(7) Phosphorus, 0.94. 

(8) Phosphorus, 0.20. 



* Dr. H. C. Torrey says this analysis is erroneous and that Magnolia 
metal always contains tin. 

As an example of the influence of minute changes in an alloy, the Har- 
rington bronze, which consists of a minute proportion of iron in a cop- 
per-zinc alloy, showed after rolling a tensile strength of 75,000 lb. and 
20% elongation in 2 inches. 

In experimenting on this subject on the Pennsylvania Railroad, a 
certain number of the bearings were made of a standard bearing-metal, 
and the same number were made of the metal to be tested. These 
bearings were placed on opposite ends of the same axle, one side of the 
car having the standard bearings, the other the experimental. Before 
going into service the bearings were carefully weighed, and after a 
sufficient time they were again weighed. The standard bearing-metal 
used is the "S bearing-metal" of the Phosphor-Bronze Smelting Co. 
It contains about 79.70% copper, 9.50% lead, 10% tin, and 0.80% phos- 
phorus. A large number of experiments have shown that the loss of 
weight of a bearing of this metal is 1 lb. to each 18,000 to 25,000 miles 
traveled. Besides the measurement of wear, observations were made 
on the frequency of "hot boxes" with the different metals. 

The results of the tests for wear, so far as given, are condensed into 
the following table: 

Composition. Rate 

Metal. , — A \ of 



Copper. 

Standard 79.70 

Copper-tin 87.50 

Same, second experiment , 

Same, third experiment 

Arsenic-bronze 89.20 

Arsenic-bronze 79.20 

Arsenic-bronze 79.70 

"K" bronze 77.00 

Same, second experiment , 

Alloy "B" 77.00 



Tin. 

10.00 

12.50 



Lead. 
9.50 



Phos. Arsenic. Wear. 



0.80 



10.00 
10.00 
10.00 
10.50 



7.00 
9.50 
12.50 



0.80 
0.80 
0.80 



100 
148 
153 
147 
142 
115 
101 
92 
92.7 
86.5 



382 ALLOYS. 

The old copper-tin alloy of 7 to 1 has repeatedly proved its inferiority 
to the phosphor-bronze metal. Many more of the copper-tin bearings 
heated than of the phosphor-bronze. The showing of these tests was so 
satisfactory that phosphor-bronze was adopted as the standard bearing- 
metal of the Pennsylvania R.R., and was used for a long time. 

The experiments, however, were continued. It was found that arsenic ii 
practically takes the place of phosphorus in a copper-tin alloy, and three 
tests were made with arsenic-bron2es as noted above. As the propor- i 
tion to lead is increased to correspond with the standard, the durability 
increases as well. In view of these results the "K" bronze was tried, in 
which neither phosphorus nor arsenic were used, and in which the lead 
was increased above the proportion in the standard phosphor-bronze. I 
The result was that the metal wore 7.30% slower than the phosphor-! 
bronze. No trouble from heating was experienced with the "K" bronze j 
more than with the standard. Dr. Dudley continues: 

At about this time we began to find evidences that wear of bearing- 
metal alloys varie 1 in accordance with the following law: "That alloy 
which has the greatest power of distortion without rupture (resilience), 
will best resist wear." It was now attempted to design an alloy in 
accordance with this law, taking first the proportions of copper and tin. j 
91/2 parts copper o 1 of in was settled on by experiment as the standard, 
although some evidence since that time tends to show that 12 or possi- 
bly 15 parts copper to 1 of tin might have been better. The influence of i 
lead on this copper-tin alloy seems to be much the same as a still further 
diminution of tin. However, the tendency of the metal to yield under 
pressure increases as the amount of tin is diminished, and the amount 
of the lead increased, so a limit is set to the use of lead. A certain 
amount of tin is also necessary to keep the lead alloyed with the copper. I 

Bearings were cast of the metal noted in the table as alloy "B/" and it i 
wore 13.5% slower tha.n the standard phosphor-bronze. This metal is i 
now the standarrl bearingr-metal of the Pennsylvania Railroad, being | 
slightly changed in composition to allow the use of phosphor-bronze 
scrap. The formula adopted is: Copper, 105 lbs.; phosphor-bronze, j 
60 lbs.; tin, 93/4 lbs.; lead, 251/4 lbs. By using ordinary care in the | 
foundry, keeping the metal well covered with charcoal during the melt- I 
ing, no trouble is found in casting good bearings with this metal. The { 
copper and the phosphor-bronze can be put in the pot before putting it 
in the melting-hole. The tin and lead should be added after the pot is j 
taken from the fire. 

It is not known whether the use of a little zinc, or possibly some other 1 
combination, might not give still better results. For the present, how- j 
ever, this alloy is considered to fulfill the various conditions required for i| 
good bearing-metal better than any other alloy. The phosphor-bronze 
had an ultimate tensile strength of 30,000 lb., with 6% elongation, 
whereas the alloy "B" had 24,000 lb. T. S. and 11% elongation. 

Bearing Metal Practice, 1907. (G. H. Clamer, Proc. A. S. T. M., vii, 
302, discusses the history of bearing metal practice since the date of 
Dr. Dudley's paper quoted above. It was found that tin could be dimin- 
ished and lead inceased far beyond the figures formerly used, and a satis- 1 ' 
factory bearing metal was made with 65% copper, 5% tin and 30% lead. ' 
This alloy is largely sold under the name of "plastic bronze." It has a , 
Compressive strength of about 15,000 lbs. per sq. in., and is found to 
operate without distortion in the bearings of the heaviest locomotives, 
not only for driving brasses, but also for rod brasses and bushings, and 
for bearings of cars of 100,000 lbs. capacity, the heaviest cars now in 
service. Specifications of different railroads cover bearing alloys with 
tin from 8 to 10% and lead from 10 to 15%. There is also used a vast 
quantity of bearings made from scrap. These contain copper, 65 to 75%, j 
tin, 2 to 8%, lead, 10 to 18%, zinc, 5 to 20%, and they constitute from 
50 to 75 per cent of the car bearings now in use. 

White Metal for Engine Bearings. (Report of a British Naval) 
Committee, Eng'g, July 18, 1902.) — For lining bearings, crankpin 
bushes, and other parts exclusive of cross-head bushes: Tin 12, copper 1, 
antimony 1. Melt 6 tin 1 copper, and 6 tin 1 antimony separately and 
mix the two together. For cross-head bushes a harder alloy, viz., 85% 
tin, 5% copper, 10% antimony, has given good results. 

(For other bearing-metals, see " Alloys containing Antimony," below.) 



ALLOYS CONTAINING ANTIMONY. 



383 



ALLOYS CONTAINING ANTIMONY. 



Various Analyses of 


Babbitt Metal and other 
ing Antimony. 


Alloys 


CONTAIN- 


Tin. 


Copper. 


Antimony. 


Zinc. 


Lead. 


Bismuth. 


Babbitt metal 1 


50 

= 89.3 
96 

= 88.9 
.85.7 
.81.9 
.81.0 
.70.5 
.22 
.45.5 
.89.3 
.85 


1 

1.8 
4 

3.7 
1.0 

"2" 

4 
10 
1.5 
1.8 
5 


5 parts 
8.9 per ct. 








for light duty ) 








Harder Babbitt ) 


8 parts 

7.4per ct. 
10.1 
16. 2 
16 

25.5 
62 
13 

7.1 
10 
















2.9 
1.9 
1 












«« 














6 






" Babbitt " 


40.0 




Plate pewter 

White metal 




1 8 


Bearings 


an Ger. locomotives. 



* It is mixed as follows: Twelve parts of copper are first melted and 
then 36 parts of tin are added; 24 parts of antimony are put in, and 
then 36 parts of tin, the temperature being lowered as soon as the 
copper is melted in order not to oxidize the tin and antimony, the sur- 
face of the bath being protected from contact with the air. The alloy 
thus made is subsequently remelted in the proportion of 50 parts of 
alloy to 100 tin. (Joshua Rose.) 

White-metal Alloys. — The following alloys are used as lining metals 
by the Eastern Railroad of France (1890): 



Number. 


Lead. 


Antimony. 


Tin. 


Copper. 


1.. 


65 

70 
80 


25 

11.12 
20 
8 




83.33' 
10 
12 


10 


2 


5.55 


3 





4 












No 1 is used for lining cross-head slides, rod-brasses and axle-bear- 
ings; No. 2 for lining axle-bearings and connecting-rod brasses of heavy 
engines; No. 3 for lining eccentric straps and for bronze slide-valves; 
and No. 4 for metallic rod-packing. 

Some of the best-known white-metal alloys are the following (Circular 
of Hoveler & Dieckhaus, London, 1893): 





Tin. 


Anti- 
mony. 


Lead. 


Copper. 


Zinc. 




86 
70 
55 
16 

71/2 
85 


1 
15 

18 



71/2 


2 

101/2 
231/2 



7 




2 . 
41/2 
31/2 

5 
7 

71/2 


27 


2. Richards' 

3. Babbitt's 






4. Fenton's 


79 

871/2 


6. German Navy 






"There are engineers who object to white metal containing lead or 
zinc. This is, however, a prejudice quite unfounded, inasmuch as lead 
and zinc often have properties of great use in white alloys. 

It is a further fact that an "easy liquid" alloy must not contain more 
than 18% of antimony, which is an invaluable ingredient of white metal 



384 ALLOYS. 

for improving its hardness; but in no case must it exceed that margin, 
as this would reduce the plasticity of the compound and make it 
brittle. 

Hardest tin-lead alloy: 6 tin, 4 lead. Hardest of all tin alloys (?) : 74 
tin, 18 antimony, 8 copper. 

Alloy for thin open-work, ornamental castings: Lead 2, antimony 1. 
White metal for patterns: Lead 10, bismuth 6, antimony 2, common 
brass 8, tin 10. 

Type-metal is made of various proportions of lead and antimony, 
from 17% to 20% antimony according to the hardness desired. 

Babbitt Metals. (C. R. Tompkins, Mechanical News, Jan., 1891.) 

The practice of lining journal-boxes with a metal that is sufficiently 
fusible to be melted in a common ladle is not always so much for the 
purpose of securing anti-friction properties as for the convenience and 
cheapness of forming a perfect bearing in line with the shaft without 
the necessity of boring them. Boxes that are bored, no matter how 
accurate, require great care in fitting and attaching them to the frame 
or other parts of a machine. 

It is not good practice, however, to use the shaft for the purpose of 
casting the bearings, especially if the shaft be steel, for the reason that 
the hot metal is apt to spring it; the better plan is to use a mandrel 
of the same size or a trifle larger for this purpose. For slow-running 
journals, where the load is moderate, almost any metal that may be 
conveniently melted and will run free will answer the purpose. For 
wearing properties, with a moderate speed, there is probably nothing 
superior to pure zinc, but when not combined with some other metal it 
shrinks so much in cooling that it cannot be held firmly in the recess, 
and soon works loose; and it lacks those anti-friction properties which 
are necessary in order to stand high speed. 

For line-shafting, and all work where the speed is not over 300 or 400 
r. p. m., an alloy of 8 parts zinc and 2 parts block-tin will not only wear 
longer than any composition of this class, but will successfully resist a 
heavy load. The tin counteracts the shrinkage, so that the metal, if not 
overheated, will firmly adhere to the box until it is worn out. But this 
mixture does not possess sufficient anti-friction properties to warrant its 
use in fast-running journals. 

Among all the soft metals in use there are none that possess greater 
anti-friction properties than pure lead; but lead alone is impracticable, 
for it is so soft that it cannot be retained in the recess. But when by 
any process lead can be sufficiently hardened to be retained in the boxes 
without materially injuring its anti-friction properties, there is no metal 
that will wear longer in light fast-running journals. With most of the 
best and most popular anti-friction metals in use and sold under the 
name of the Babbitt metal, the basis is lead. 

Lead and antimony have the property of combining with each other 
in all proportions without impairing the anti-friction properties of either. 
The antimony hardens the lead, and when mixed in the proportion of 80 
parts lead by weight with 20 parts antimony, no other known compo- 
sition of metals possesses greater anti-friction or wearing properties, or 
will stand a higher speed without heat or abrasion. It runs free in its 
melted state, has no shrinkage, and is better adapted to light high- 
speed machinery than any other known metal. Care, however, should be 
manifested in using it, and it should never be heated beyond a temper- 
ature that will scorch a dry pine stick. 

Many different compositions are sold under the name of Babbitt 
metal. Some are good, but more are worthless; while but very little 
genuine Babbitt metal is sold that is made strictly according to the 
original formula. Most of the metals sold under that name are the 
refuse of type-foundries and other smelting-works, melted and cast into 
fancy ingots with special brands, and sold under the name of Babbitt 
metal. 

It is difficult at the present time to determine the exact formulas 
used by the original Babbitt, the inventor of the recessed box, as a num- 
ber of different formulas are given for that composition. Tin, copper, 



SOLDERS. 385 

and antimony were the ingredients, and from the best sources of infor- 
mation the original proportions were as follows: 

Another writer gives: 

50 parts tin == 89.3% 83.3% 

2 parts copper = 3.6% 8.3% 

4 parts antimony = 7.1 % 8.3 % 

The copper was first melted, and the antimony added first and then 
about ten or fifteen pounds of tin, the whole kept at a dull-red heat and 
constantly stirred until the metals were thoroughly incorporated, after 
which the balance of the tin was added, and after being thoroughly 
stirred again it was then cast into ingots. When the copper is thoroughly 
melted, and before the antimony is added, a handful of powdered char- 
coal should be thrown into the crucible to form a flux, in order to exclude 
the air and prevent the antimony from vaporizing; otherwise much of it 
will escape in the form of a vapor and consequently be wasted. This 
metal, when carefully prepared, is probably one of the best metals in use 
for lining boxes that are subjected to a heavy weight and wear; but for 
light fast-running journals the copper renders it more susceptible to 
friction, and it is more liable to heat than the metal composed of lead and 
antimony in the proportions just given. 

SOLDERS. 

Common solders, equal parts tin and lead; fine solder, 2 tin to 1 lead; 
cheap solder, 2 lead, 1 tin. 

Fusing-point of tin-lead alloys (many figures probably inaccurate). 

Tin H/2 to lead 1 334° F. 

2 " " 1 340 

" 3 " " 1 356 

" 4 " " 1 365 

" 5 " " 1 378 

" 6 " " 1 381 



1 to lead 25 . . . 


. . . 558< 


1 " " 10... 


... 541 


1 " " 5... 


...511 


1 " " 3... 


...482 


1 " " 2... 


...441 


1 " " 1... 


...370 



The melting point of the tin-lead alloys decreases almost proportionately 
to the increase of tin, from 619°F, the melting point of pure lead, to 356°F 
when the alloy contains 68% of tin, and then increases to 44S°F., the melt- 
ing point of pure tin. Alloys on either side of the 68% mixture begin to 
sorten materially at 356°F, because at that temperature the eutectic alloy 
melts and permits the whole alloy to soften. (Dr. J. A. Mathews.) 

Common pewter contains 4 lead to 1 tin. 

The relative hardness of the various tin and lead solders has been 
determined by Brinell's method. The results are as follows: 



% Tin 
Hardness 



3.90 


10 
10.10 


20 
12.16 


30 
14.46 


40 
15.76 


50 
14.90 


60 
14.58 


% Tin 
Hardness 


66 
16.66 


67 
15.40 


68 
14.58 


70 
15.84 


80 
15.20 


90 
13.25 


100 
4.14 



The hardest solder is the one composed of 2 parts of tin and 1 part of 
lead. It is the eutectic alloy, or the one with the lowest melting point of 
all the mixtures. — Mechanical World. 

Gold solder: 14 parts gold, 6 silver, 4 copper. Gold solder for 14-carat 
gold; 25 parts gold, 25 silver, 12 1/2 brass, 1 zinc. 

Silver solder: Yellow brass 70 parts, zinc 7, tin 11 1/2. Another: Silver 
145 parts, brass (3 copper, 1 zinc) 73, zinc 4. 

German-silver solder: Copper 38, zinc 54, nickel 8. 

Novel's solders for aluminum: 



Tin 100 parts, 


lead 5; 


melts at 536° 


to 572° F 


100 " 


zinc 5; 


536 


to 612 


" 1000 " 


copper 10 to 15; 


662 


to 842 


" 1000 " 


nickel 10 to 15; 


" - 662 


to 842 



Novel's solder for aluminum bronze: Tin, 900 parts, copper 100, bis- 
muth 2 to 3. It is claimed that this solder is also suitable for joining 
aluminum to copper, brass, zinc, iron, or nickel. 



386 



ROPES AJJD CABLES. 



ROPES AND CABLES. 



STRENGTH OF ROPES. 



(A. S. Newell & Co., Birkenhead. Klein's Translation of Weisbach, 
vol. iii, part 1, sec. 2.) 



Hemp. 


Iron. 


Steel. 


Tensile 
Strength, 




Weight 




Weight 




Weight 


Girth. 


per 


Girth. 


per 


Girth. 


per 


Gross tona. 


Inches. 


Fathom. 
Pounds. 


Inches. 


Fathom. 
Pounds. 


Inches. 


Fathom. 
Pounds. 




23/4 


2 


1 

H/2 


1 
H/2 


1 


1 


2 
3 


3 3/ 4 


4 


15/8 


2 






4 






13/4 


21/2 


11/2 


H/2 


5 


41/2 


5 


17/8 


3 






6 






2 


31/2 


. 15/8 


2 


7 


51/2 


7 


21/8 
21/4 


4 

41/2 


13/ 4 


21/2 


8 
9 


6 


9 


23/ 8 
21/2 


5 
51/2 


17/8 


3 


10 
11 


61/2 


10 


25/8 


6 


2 


31/2 


12 






23/4 


61/2 


21/8 


4 


13 


7 


12 


27/8 
3 


7 
71/2 


21/4 


41/2 


14 
15 


71/2 


14 


31/8 
31/4 


8 
81/2 


23/8 


5 


16 
17 


8 


16 


33/8 


9 


21/2 


51/2 


18 






31/2 


10 


25/8 


6 


20 


81/2 


18 


35/ 8 
33/4 


11 
12 


23/4 


61/2 


22 
24 


91/2 


22 


37/s 


13 


31/4 


8 


26 


10 


26 


4 


14 






28 


11 


30 


41/4 
43/s 


15 
16 


33/s 


9 


30 
32 






41/2 


18 


31/2 


10 


36 


12 


34 


45/ 8 


20 


33/4 


12 


40 



Length Sufficient to Cause the Maximum Working Stress. 
(Weisbach.) 

Hempen rope, dry and untarred 2855 feet. 

Hempen rope, wet or tarred 1975 " 

Wire rope 4590 " 

Open-link chain 1360 " 

Stud chain 1660 " 

Sometimes, when the depths are very great, ropes are given approxi- 
mately the form of a body of uniform strength, by making them of separ- 
ate pieces, whose diameters diminish towards the iower end. It is evident 
that by this means the tensions in the fibres caused by the rope's own 
weight can be considerably diminished. 

Rope for Hoisting or Transmission. Manila Rope. (C. W. Hunt 
Company, New York.) — Rope used for hoisting or for transmission of 
power is subjected to a very severe test. Ordinary rope chafes and grinds 
to powder in the center, while the exterior may look as though it was little 
worn. 

In bending a rope over a sheave, the strands and the yarns of these 
strands slide a small distance upon each other, causing friction, and wear 
the rone internally. 



STRENGTH OF ROPES. 



387 



The "Stevedore "rope used by theC.W. Hunt Company is made by lubri- 
cating the fibres with plumbago, mixed with sufficient tallow to hold it in 
position. This lubricates the yarns of the rope, and prevents internal 
chafing and wear. After running a short time the exterior of the -rope 
gets compressed and coated with the lubricant. 

In manufacturing rope, the fibres are first spun into a yarn, this varn 
being twisted in a direction called "right hand." From 20 to 80 of these 
yarns, depending on the size of the rope, are then put together and 
twisted in the opposite direction, or "left hand," into a strand. Three of 
these strands, for a 3-strand, or four for a 4-strand rope, are then twisted 
together, the twist being again in the " right hand " direction. When the 
strand is twisted, it untwists each of the threads, and when the three 
strands are twisted together into rope, it untwists the strands, but again 
twists up the threads. It is this opposite twist that keeps the rope in its 
proper form. When a weight is hung on the end of a rope, the tendency 
is for the rope to untwist, and become longer. In untwisting the rope, it 
would twist the threads up, and the weight will revolve until the strain of 
the untwisting s;rands just equals the strain of the threads being twisted 
tighter. In making a rope it is impossible to make these strains exactly 
balance each other. It is this fact that makes it necessary to take out the 
"turns" in a new rope, that is, untwist it when it is put at work. The 
proper twist that should be put in the threads has been ascertained approx- 
imately by experience. 

The amount of work that the rope wall do varies greatly. It depends 
not only on the quality of the fibre and the method of laying up the rope, 
but also on the kind of weather when the rope is used, the blocks or 
sheaves over which it is run, and the strain in proportion to the strain put 
upon the rope. The principal wear comes in practice from defective or 
badly set sheaves, from excess of load and exposure to storms. 

The loads put upon the rope should not exceed those given in the 
tables, for the most economical wear. The indications of excessive load 
will be the twist coming out of the rope, or one of the strands slipping out 
of its proper position. A certain amount of twist comes out in using it 
the first day or two, but after that the rope should remain substantially 
the same. If it does not, the load is too great for the durability of the 
rope. If the rope wears on the outside, and is good on the inside, it 
shows that it has been chafed in running over the pulleys or sheaves. If 
the blocks are very small, it will increase the sliding of the strands and 
threads, and result in a more rapid internal wear. Rope made for hoist- 
ing and for rope transmission is usually made with four strands, as expe- 
rience has shown this to be the most serviceable. 

The strength and weight of "Stevedore" rope is estimated as follows: 
Breaking strength in pounds = 720 (circumference in inches) 2 ; 
Weight in pounds per foot = 0.032 (circumference in inches) 2 . 

Flat Ropes. (Weisbach.) 



Iron 




Steel. 




Iron 




Steel. 






u 








M 




u 


re 


O 




s 


ft8 
•-P ° 

§"5 


%S 
v a 03 

— a> 03 

03 £ O 

H 




-^ ° 






£■ a 
jj) a 03 


In. 


Lbs. 


In. 


Lbs. 




In. 


Lbs. 


In. 


Lbs. 




21/4X1/2 


11 






20 


3 3/4X11/, 6 


22 


21/2X1/2 


13 


40 


21/2X1/2 


13 






23 


4 X ll/i 6 


25 


23/4X3/8 


15 


45 


23/4X5/ 8 


15 






27 


41/4X3/4 


28 


3 x3/ 4 


16 


50 


3 x5/ 8 


16 


2 xl/ 2 


10 


28 


41/ 2 x3/4 


32 


31/ 4 x3/8 


18 


56 


31/4X5/8 


18 


21/4X1/2 


11 


32 


45/ 8 x3/ 4 


34 


31/2X3/8 


20 


60 


31/2X5/8 


20 


21/4X1/2 


12 


36 













OOO ROPES AND CABLES. 

The Technical Words relating to Cordage most frequently heard 

are: 

Yarn. — Fibres twisted together. 
Thread. —Two or more small yarns twisted together. 
String. — The same as a thread but a little larger yarns. 
Strand. — Two or more large yarns twisted together. 
• Cord. — Several threads twisted together. 
Rope. — • Several strands twisted together. 
Hawser. — A rope of three strands. 
Shroud-Laid. — A rope of four strands. 
Cable. — Three hawsers twisted together. 
Yarns are laid up left-handed into strands. 
Strands are laid up right-handed into rope. 
Ha wsers are laid up left-handed into a cable. 

A rope is: 

Laid by twisting strands together in making the rope. 

Spliced by joining to another rope by interweaving the strands. 

Whipped. — By winding a string around the end to prevent untwisting. 

Served. — When covered by winding a yarn continuously and tightly 
around it. 

Parceled. — By wrapping with canvas. 

Seized. — When two parts are bound together by a yarn, thread or 
string. 

Payed. — When painted, tarred or greased to resist wet. 

Haul. — To pull on a rope. 

Taut.*— Drawn tight or strained. 

Splicing of Ropes. — The splice in a transmission rope is not only the 
weakest part of the rope but is the first part to fail when the rope is worn 
out. If the rope is larger at the splice, the projecting part will wear on 
the pulleys and the rope fail from the cutting off of the strands. The fol- 
lowing directions are given for splicing a 4-strand rope. 

The engravings show each successive operation in splicing a 13/ 4 -inch 
manila rope. Each engraving was made from a full-size specimen. 

Tie a piece of twine, 9 and 10, around the rope to be spliced, about 
6 feet from each end. Then unlay the strands of each end back to the 
twine. 

Butt the ropes together and twist each corresponding pair of strands 
loosely, to keep them from being tangled, as shown in Fig. 80. 

The twine 10 is now cut, and the strand 8 unlaid and strand 7 carefully 
laid in its place for a distance of four and a half feet from the junction. 

The strand 6 is next unlaid about one and a half feet and strand 5 laid 
in its place. 

The ends of the cores are now cut off so they just meet. 

Unlay s.\rand 1 four and a half feet, laying strand 2 in its place. 

Unlay strand 3 one and a half feet, laying in strand 4. 

Cut all the s rands off to a length of about twenty inches for convenience 
in manipulation. 

The rope now assumes the form shown in Fig. 81 with the meeting 
points of the strands three feet apart. 

Each pair of strands is successively subjected to the following operation: 

From the point of meeting of the strands 8 and 7, unlay each one three 
turns; split both the strand 8 and the strand 7 in halves as far back as 
they are now unlaid and "whip" the end of each half strand with a small 
piece of twine. 

The half of the strand 7 is now laid in three turns and the half of 8 also 
laid in three turns. The half strands now meet and are tied in a simple 
knot, 11, Fig. 82, making the rope at this point its original size. 

The rope is now opened with a marlin spike and the half strand of 7 
worked around the half strand of 8 by passing the end of the half strand 7 
through the rope, as shown in the engraving, drawn taut, and again 
worked around this half strand until it reaches the half strand 13 that was 
not laid in. This half strand 13 is now split, and the half strand 7 drawn 
through the opening thus made, and then tucked under the two adjacent 
strands, as shown in Fig. 83. The other half of the strand 8 is now 
wound around the other half strand 7 in the same manner. After each 
pair of strands has been treated in this manner, the ends are cut off at 12, 
leaving them about four inches long. After a few days' wear they will 



STRENGTH OF ROPES. 389 




Fig. 83. 
Splicing of Ropes. 



390 



ROPES AND CABLES. 



draw into the body of the rope or wear off, so that the locality of the 
splice can scarcely be detected. 

Cargo Hoisting. (C. W. Hunt Company.) — The amount of coal that 
can be hoisted with a rope varies greatly. Under the ordinary conditions 
of use a rope hoists from 5000 to 8000 tons. Where the circumstances are 
more favorable, the amounts run up frequently to 12,000 or 15,000 tons, 
occasionally to 20,000 and in one case 32,400 tons to a single fall. 

When a hoisting rope is first put in use, it is likely from the strain put 
upon it to twist up when the block is loosened from the load. This occurs 
in the first day or two only. The rope should then be taken down and 
the "turns" taken out of the rope. When put up again the rope should 
give no further trouble until worn out. 

It is necessary that the rope should be much larger than is needed to 
bear the strain from the load. 

Practical experience for many years has substantially settled the most 
economical size of rope to be used which is given in the table below. 

Hoisting ropes are not spliced, as it is difficult to make a splice that will 
not pull out while running over the sheaves, and the increased wear to be 
obtained in this way is very small. 

Coal is usually hoisted with what is commonly called a "double whip; " 
that is, with a running block that is attached to the tub which reduces the 
strain on the rope to approximately one-half the weight of the load 
hoisted. 

Hoisting rope is ordered by circumference, transmission rope by 
diameter. 

Working Loads for Manila Rope (C. W. Hunt, Trans. A. S. M. E., 
xxiii, 125.) 



Diameter 
of Rope, 
Inches. 


Ultimate 
Strength, 
Pounds. 


Working Load in Pounds. 


Minimum Diameter of 
Sheaves in Inches. 


Rapid . 


Medium. 


Slow. 


Rapid. 


Medium. 


Slow. 


1 


7,100 


200 


400 


1000 


40 


12 


8 


H/8 


9,000 


250 


500 


1250 


45 


13 


9 


H/4 


11,000 


300 


600 


1500 


50 


14 


10 


13/8 


13,400 


380 


750 


1900 


55 


15 


11 


U/2 


15,800 


450 


900 


2200 


60 


16 


12 


15/8 


18,800 


530 


1100 


2600 


65 


17 


13 


13/ 4 


21,800 


620 


1250 


3000 


70 


18 14 



In this table the work required of the rope is, for convenience, divided 
into three classes — "rapid," "medium," and "slow," these terms being 
used in the following sense: "Slow" — Derrick, crane and quarry work; 
speed from 50 to 100 feet per minute. "Medium" —Wharf and cargo, 
hoisting 150 to 300 feet per minute. "Rapid" — 400 to 800 feet per 
minute. 

The ultimate strength given in the table is materially affected by the 
age and condition of a rope in active service, and also it is said to be 
weaker when it is wet. Trautwine states that a few months of exposed 
work weakens rope 20 to 50 per cent. The ultimate strength of a new 
rope given in the table is the result of tests of full sized specimens of 
manila rope, purchased in the open market, and made by three inde- 
pendent rope walks. 

The proper diameter of pulley-block sheaves for different classes of 
work given in the table is a compromise of the various factors affecting 
the case. An increase in the diameter of sheave will materially increase 
the life of a rope. The advantage, however, is gained by increased 
difficulty of installation, a clumsiness in handling, and an increase in 
first cost. The best size is one that considers the advantages and the 
drawbacks as they are found in practical use, and makes a fair balance 
between the conflicting elements of the problem. 

Records covering many years have been kept by various coal dealers, 
of the diameter and cost of their rope per ton of coal hoisted from ves- 
sels, using sheaves of from 12 to 16 inches in diameter. These records 
show conclusively that, in hoisting a bucket that produces 900 pounds 
stress upon the rope, a 11/4-inch diameter rope is too small and a 13/4- 
inch rope is too large for economy. The Pennsylvania Railroad Company 



STRENGTH OF ROPES. 391 

uses 11/2-inch rope, running over 14-inch diameter sheaves for hoisting 
freight on lighters in New York harbor, and handle on a single part of 
the rope loads up to 3,000 pounds as a maximum. Greater weights are 
handled on a 6-part tackle. 

Life of Hoisting and Transmission Rope. A rope 1 1/2-in. diam. usu- 
ally hoists from a vessel from 7000 to 10,000 tons of coal, running with a 
working stress of 850 to 950 lbs. over three sheaves, one 12 in., and two 
16-in. diam. In hoisting 10,000 tons it makes 20,000 trips, bending in 
that time from a straight line to the curve of the sheave 120,000 times, 
when it is worn out. A 1000 ft. transmission in a tin-plate mill, with H/2 
in. rope, sheaves 5 ft., 17 ft., and 36 ft. apart, center to center, runs 5000 
ft. per minute making 13,900 bends per hour, or more bends in 9 hours 
than the hoisting rope made in its entire life, yet the life of a transmission 
rope is measured in years, not hours. This enormous difference in the 
life of ropes of the same size and quality is wholly gained by reducing the 
stresses on the rope and increasing the diameter of the sheaves. 

Efficiency of Knots as a percentage of the full strength of the rope, 
and the factor of safety when used with the stresses given in the 5th col- 
umn of the table of working loads. 

Kind of Knot. Effy. Fact. S 

Eye splice over an iron thimble 90 6.3 

Short splice in the rope 80 5 ."6 

Timber hitch, round turn, half-hitch 65 4.5 

Bowline slip knot, clove hitch 60 4.2 

Square knot, weaver's knot sheet bend 50 3.5 

Flemish loop, overhand knot 45 3.1 

Full strength of dry rope, average of four tests 100 7 . 

Efficiency of Rope Tackles. Robert Grimshaw in 1893 tested a 33/ 4 -in., 
3-strand ordinary dry manila rope on a "cat and fish" tackle with a 
6-fold purchase. The sheaves were 8-in. diam., the three upper ones hav- 
ing roller bearings and the three lower ones solid bushings. The results 
were as below: 

Net load on tackle, weight raised, lbs 600 800 1000 1200 

Theoretical force required to raise the weight 100 1333.3 166.7 200 

Actual force required 158 198 243 288 

Percentage above the theoretical 58 48 45. 8 44 

Weight and Strength of Manila Rope. Spencer Miller (Eng'g News, 
Dec. 6, 1890) gives a table of breakMg strength of manila rope, which he 
considers more reliable than the strength computed by Mr. Hunt's formula: 
Breaking strength = 720 X (circumference in inches) . 2 Mr. Miller's formula 
is: Breaking weight lbs. = circumference 2 X a coefficient which varies 
from 900 for 1/2" to 700 for 2" diameter rope, as below: 

Circumference .-. H/ 2 2 2 1/2 23/ 4 3 3 1/2 33/ 4 41/4 4 1/2 5 5 1/2 6 
Coefficient ...... 900 845 820 790 780 765 760 745 735 725 712 700 

Knots. The principle of a knot is that no two parts, which would 
move in the same direction if the rope were to slip, should lay along side 
of and touching each other. (See illustrations on the next page.) 

The bowline is one of the most useful knots, it will not slip, and after 
being strained is easily untied. Commence by making a bight in the 
rope, then put the end through the bight and under the standing part as 
shown in G, then pass the end again through the bight, and haul tight. 

The square or reef knot must not be mistaken for the "granny" knot 
that slips under a strain. Knots H, K and M are easily untied after 
being under strain. The knot M is useful when the rope passes through 
an eye and is held by the knot, as it will not slip and is easily untied 
after being strained. 

The timber hitch £ looks as though it would give way, but it will not; 
the greater the strain the tighter it will hold. The wail knot looks com- 
plicated, but is easily made by proceeding as follows: Form a bight with 
strand 1 and pass the strand 2 around the end of it, and the strand 3 
round the end of 2 and then through the bight of 1 as shown in the cut Z. 
Haul the ends taut when the appearance is as shown in A A. The end of 
the strand 1 is now laid over the center of the knot, strand 2 laid over 1 
and 3 over 2, when the end of 3 is passed through the bight of 1 as shown 
in BB. Haul all the strands taut as shown in CC. 



392 



ROPES AND CABLES. 



"Varieties of Knots. — A great number of knots have been devised of 
which a tew only are illustrated, but those selected are the most frequently 
used. In the cut, Fig. 84, they are shown open, or before being drawn 
taut, in order to show the position of the parts. The names usually 
given to them are: 



A. Bight of a rope. 

B. Simple or Overhand knot. 

C. Figure 8 knot. 

D. Double knot. 

E. Boat knot. 

F. Bowline, first step. 

G. Bowline, second step. 
H. Bowline completed. 
I. Square or reef knot. 

J. Sheet bend or weaver's knot. 

K. Sheet bend with a toggle. 

L. Carrick bend. 

M. Stevedore knot completed. 

N. Stevedore knot commenced. 

/O. Slip knot. . 



P. Flemish loop. 

Q. Chain knot with toggle. 

R. Half-hitch. 

S. Timber-hitch. 

T. Clove-hitch. 

U. Rolling-hitch. 

V. Timber-hitch and half-hitch. 

W. Black wall-hitch. 

X. Fisherman's bend. 

Y. Round turn and half-hitch 

Z. Wall knot commenced. 

AA. Wall knot completed. 

BB. Wall knot crown commenced. 

CC. Wall knot crown completed. 




Fig. 84. — Knots. 



STRENGTH OF ROPES. 



393 



To Splice a Wire Rope. — The tools required will be a email marline 
spike, nipping cutters, and either clamps or a small hemp-rope sling with 
wnicn to wrap around and untwist the rope. If a bench-vise is acces- 
sible it will be found convenient. 

In splicing rope, a certain length is used up in making the splice. An 
allowance of not less than 16 feet for 1/2-inch rope, and proportionately 
longer for larger sizes, must be added to the length of an endless rope in 
ordering. 

Having measured, carefully, the length the rope should be after splicing, 
and marked the points M and M' , Fig. 85, unlay the strands from each 
end E and E' to M and M' and cut off the center at M and M', and then: 

(1). Interlock the six unlaid strands of each end alternately and draw 
them together so that the points M and M' meet, as in Fig. 86. 

(2). Unlay a strand from one end, and following the unlay closely, lay 
into the seam or groove it opens, the strand opposite it belonging to the 
other end of the rope, until within a length equal to three or four times 
the length of one lay of the rope, and cut the other strand to about the 
same length from the point of meeting as at A, Fig. 87. 

(3). Unlay the adjacent strand in the opposite direction, and following 
the unlay closely, lay in its place the corresponding opposite strand, cut- 
ting the ends as described before at B, Fig. 87. 

There are now four strands laid in place terminating at A and B, with 
the eight remaining at MM', as in Fig. 87. 

It will be well after laying each pair of strands to tie them temporarily 
at the points A and B. 




Fig. 88. Splicing Wire Rope. Fig. 89. 

Pursue the same course with the remaining four pairs of opposite 
strands, stopping each pair about eight or ten turns of the rope short of 
the preceding pair, and cutting the ends as before. 

We now have all the strands laid in their proper places with their re- 
spective ends passing each other, as in Fig. 88. 

All methods of rope-splicing are identical to this point: their variety 
consists in the method of tucking the ends. The one given below is the 
one most generally practiced'. 

Clamp the rope either in a vise at a point to the left of A, Fig. 88, and 
by a hand-clamp applied near A, open up the rope by untwisting suffi- 
cientlv to cut the core at A, and seizing it with the nippers, let an assis- 
tant draw it out slowly, you following it closely, crowding the strand in 
its place until it is all laid in. Cut the core where the strand ends, and 
push the end back into its place. Remove the clamps and let the rope 
close together around it. Draw out the core in the opposite direction 
and lay the other strand in the center of the rope, in the same manner. 
Repeat the operation at the five remaining points, and hammer the rope 
lightly at the points where the ends pass each other at A, A, B, B, etc., 
with small wooden mallets, and the splice is complete, as shown in Fig. 89. 

If a clamp and vise are not obtainable, two rope slings and short 
wooden levers may be used to untwist and open up the rope. 

A rope spliced as above will be nearlv as strong as the original rope 
and smooth everywhere. After running a few days, the splice, if well 
made, cannot be found except bv close examination. 

The above instructions have been adopted by the leading rope manu- 
facturers of America. 



394 



SPRINGS. 

Definitions. — A spiral spring is one which is wound around a fixed 
point or center, and continually receding from it, like a watch spring. A 
helical spring is one which is wound around an arbor, and at the same time 
advancing like the thread of a screw. An elliptical or laminated spring is 
made of flat bars, plates, or "leaves," of regularly varying lengths, super- 
posed one upon the other. 

Laminated Steel Springs. — Clark (Rules, Tables and Data) gives 
the following from his work on Railway Machinery, 1855: 

. _ 1.66 L\ _ Wn . _ 1.66 L 3 . 



U 3 n 11.3 L AW3 

A = elasticity, or deflection, in sixteenths of an inch per ton of load; 
• s = working strength, or load, in tons (2240 lbs.) ; 
L = span, when loaded in inches; 

6 = breadth of plates, in inches, taken as uniform; 

t = thickness of plates, in sixteenths of an inch; 
n = number of plates. 

Note. — 1. The span and the elasticity are those due to the spring 
when weighted. 

2. When extra thick back and short plates are used, they must be 
replaced by an equivalent number of plates of the ruling thickness, prior 
to the employment of the first two formulae. This is found by multiply- 
ing the number of extra thick plates by the cube of their thickness, and 
dividing by the cube of the ruling thickness. Conversely, the number 
of plates of the ruling thickness given by the third formula, required to 
be deducted and replaced by a given number of extra thick plates, are 
found by the same calculation. 

3. It is assumed that the plates are similarly and regularly formed, 
and that they are of uniform breadth, and but slightly taper at the ends. 

Reuleaux's Constructor gives for semi-elliptic springs: 

D Snbh* , ' 6 PI 3 . 

P = -GT and f = EnW 3 '' 

8 = max. direct fiber-strain in plate; b = width of plates; 

n = number of plates in spring; ft = thickness of plates; 

I = one-half length of spring; / = deflection of end of spring; 

P = load on one end of spring; E = modulus of direct elasticity 

The above formula for deflection can be relied upon where all the plates 
of the spring are regularly shortened; but in semi-elliptic springs, as 
used, there are generally several plates extending the full length of the 
spring, and the proportion of these long plates to the whole number is 

usually about one-fourth. In such cases/ = '^ ,,„ • (G. R. Henderson, 

Enbh 3 
Trans. A. S. M. E., vol. xvi.) 

In order to compare the formulae of Reuleaux and Clark we may make 
the following substitutions in the latter: s in tons = P in lbs. **- 1120; 
As = 16/; L = 21; t = 16ft; then 

Ao ,_. 1.66 X 8 Z-'XP . PI 3 ' 

AS = 16 /= 4096 X 1120 Xttftfts ' Whence ^ 5,527,133 ' 

which corresponds with Reuleaux's formula for deflection if in the latter 

we take E = 33,162,800. 

Also s 



which corresponds with Reuleaux's formula for working load when S in 
the latter is taken at 76,120. 



395 



The value of E is usually taken at 30,000,000 and S at 80,000, in which 
case Reuleaux's formulae become 



13,333 nbh" 1 



and / = 



PP 

),000,OOOw&7i 3 ' 



G. R. Henderson, in Trans. A. S. M. E., vol. xvii, gives a series of 
tables for use in designing both elliptical and helical springs. 

Helical Steel Springs. 

Notation. Let d = diam. of wire or rod of which the spring is made. 
D = outside diameter of coil, inches. 
R = mean radius of coil, = 1/2 (D — d). 
n = number of coils. 
P = load applied to the spring, lbs. 
G = modulus of torsional elasticity. 
S = stress on extreme fiber caused by load P. 
F = extension or compression of one coil, in., for load P. 
Fn= total extension or compression, for load P. 
W = safe carrying capacity of spring, lbs. 



64 PR* 
Gd* ' 



Fn 



64 PR 3 n . 
Gd* ' 



W 



0.1963 Sd s 
R 



Sd? 
I R' 



Values of G according to different authorities range from 10,000,000 to 
14,000,000. 

The safe working value commonly taken for S = 60,000 lbs. per sq. in. 
Taking G at 12,000,000 and S at 60,000 the above formulas become 



PR 3 
'' 187,500 d 4 ' 



W = 11,781 



If P = W, then F = 0.06285 



R* 



For square steel the values found for F and W are to be multiplied by 
0.59 and 1.2 respectively, d being the side of the square. 

The stress in a helical spring is almost wholly one of torsion. For 
method of deriving the formulas for springs from torsional formulas see 
paper by J. W. Cloud, Trans. A. S. M. E., vol. 173. Mr. Cloud takes 
S = 80,000 and G = 12,600,000. 

Taking from the Pennsylvania Railroad Specifications (1891) the 
capacity when closed, Wi, of the following springs, and the total com- 
pression when closed H — h, in which H = height when free and h 
when closed, and assuming n = h h- d, we have the following compari- 
son of the specified values of capacity and compression with those ob- 
tained from. the. formulas. 



No. 


d, in. 


D 


D-d 


W t 


W 


H 


h 


H-h 


Fn 


n 


T. 


1/4 


11/2 


11/4 


400 


295 


9 


6 


3 


3.20 


24 


S. 


1/9 


3 


21/9 


1900 


1178 


8 


5 


3 


3.16 


10 


K. 


3/4 


53/ 4 


5 


2100 


1988 


7 


41/4 


23/ 4 


3.15 


52/s 


D. 


1 


5 


4 


8100 


5890 


101/2 


8 


21/o 


2.76 


8 


I. 


U/4 


8 


6 3/4 


10000 


6788 


9 


53/4 


31/ 4 


3.86 


43/5 


C. 


IVs 


47/ 8 


3 3/ 4 


16000 


8946 


43/ 8 


3 3/ 8 


1 


1.05 


3 



The value of Fn in the table is calculated from the formula with P= W t 
Wilson Hartnell (Proc. Inst. M. E., 1882, p. 426), says: The size of a 
spiral spring may be calculated from the formula on page 304 of " Rank- 
ine's Useful Rules and Tables;" but the experience with Salter's springs 
has shown that the safe limit of stress is more than twice as great as there 
given, namely 60,000 to 70,000 lbs. per square inch of section with 3/ 8 -mch 
wire, and about 50,000 with 1/2-inch wire. Hence the work that can be 
done by springs of wire is four or five times as great as Rankine allows. 



396 

For 3/ 8 -inch wire and under, 



Maximum load in lbs. 



12,000 X (diam. of wire) 3 . 

Mean radius of springs 

-..-...' n . 180,000 X (diam.) 4 

Weight in lbs. to deflect spring 1 in. = = r- 1 — -. — -. — w . , .„ • 

Number of coils X (rad.) 3 



The work in foot-pounds that can be stored up in a spiral spring would 
lift it above 50 ft. 

In a few rough experiments made with Salter's springs the coefficient of 
rigidity was noticed to be 12,600,000 to 13,700,000 with 1/4-inch wire; 
11,000,000 for n/32 inch; and 10,600,000 to 10,900,000 for 3/ 8 _inch wire. 

Helical Springs. — J. Begtrup, in the American Machinist of Aug. 
18, 1892, gives formulas for the deflection and carrying capacity of helical 
springs of round and square steel, as follow: 

W = 0.3927 2J^?V F = 8 P ^Ed*^ 3 ' f ° r r0Und SteeL 

,Sf73 P (D — d)3 

W = 0.471 ~^- d , F = 4.712 K mi a) , for square steel. 

W = carrying capacity in pounds, 

8 = greatest shearing stress per square inch of material, 
d = diameter of steel, 
D = outside diameter of coil, 
F = deflection of one coil, 
E = torsional modulus of elasticity, 
P = load in pounds. 

From these formulas the following table has been calculated by Mr. 
Begtrup. A spring being made of an elastic material, and of such shape 
as to allow a great amount of deflection, will not be affected by sudden 
shocks or blows to the same extent as a rigid body, and a factor of safety 
very much less than for rigid constructions may be used. 

HOW TO USE THE TABLE. 

When designing a spring for continuous work, as a car spring, use a 
greater factor of safety than in the table; for intermittent working, as in 
a steam-engine governor or safety valve, use figures given in table; for 
square steel multiply line W by 1.2 and line F by 0.59. 

Example 1. — How much will a spring of 3/ 8 " round steel and 3" outside 
diameter carry with safety? In the line headed D we find 3, and right 
underneath 473, which is the weight it will carry with safety. How many 
coils must this spring have so as to deflect 3" with a load of 400 pounds? 
Assuming a modulus of elasticity of 12 millions we find in the line headed 
F the figure 0.0610; this is deflection of one coil for a load of 100 pounds; 
therefore 0.061 X 4 = 0.244" is deflection of one coil for 400 pounds load, 
and 3 -s- 0.244 = 121/2 is the number of coils wanted. This spring will 
therefore be 43/ 4 " long when closed, counting working coils only, and 
stretch to 73/ 4 ". 

Example 2. — A spring 31/4" outside diameter of 7/ 16 " steel is wound close; 
how much can it be extended without exceeding the limit of safety? We 
find maximum safe load for this spring to be 702 pounds, and deflection of 
one coil for 100 pounds load 0.0405 inches; therefore 7.02 X 0.0405 = 0.284" 
is the greatest admissible opening between coils. We may thus, without 
knowing the load, ascertain whether a spring is overloaded or not. 

Carrying Capacity and Deflection of Helical Springs of 
Round Steel. 

d — diameter of steel. D — outside diameter of coil. TF= safe work- 
ing load in pounds — tensile stress not exceeding 60,000 pounds per 
square inch. F = deflection by a load of 100 pounds of one coil, with a 
modulus of elasticity of 12 millions. The ultimate carrying capacity 
will be about twice the safe load. (The original table gives three values 



397 



of F, corresponding respectively to a modulus of elasticity of 10, 12 and 
14 millions. To find values of F for 10 million modulus increase the fig- 
ures here given by one-sixth; for 14 million subtract one-sixth.) 



d 

in. 
.065 


D 

w 

F 


0.25 

35 

0.0236 


0.50 
15 

0.3075 


0.75 
9 

1.228 


1.00 

7 

3.053 


1.25 

5 

6.214 


1.50 

4.5 

11.04 


1.75 

3.8 
17.87 


2.00 
3.3 

27.06 








.120 


D 
W 

F 


0.50 
107 
0.0176 


0.75 
65 

0.0804 


1.00 

46 

0.2191 


1.25 
36 

0.4639 


1.50 

29 
0.8448 


1.75 

25 

1.392 


2.00 

22 

2.136 


2.25 

19 

3.107 


2.50 

17 

4.334 






.180 


D 
W 

F 


0.75 

241 
0.0118 


1.00 
167 
0.0350 


1.25 

128 
0.0778 


1.50 

104 
0.1460 


1.75 

88 
0.2457 


2.00 
75 

0.3828 


2.25 

66 

0.5632 


2.50 

59 

0.7928 


2.75 

53 
1.077 


3.00 

49 

1.423 




V4 


D 
W 

F 


1.25 

368 
0.0171 


1.50 

294 
0.0333 


1.75 
245 
0.0576 


2.00 
210 
0.0914 


2.25 

184 
0.1365 


2.50 
164 
0.1944 


2.75 

147 
0.2665 


3.00 
134 
0.3548 


3.25 
123 

0.4607 


3.50 
113 

0.5859 




5/16 


D 
W 

F 


1.50 
605 
0.0117 


1.75 
500 
0.0207 


2.00 
426 
0.0336 


2.25 
371 
0.0508 


2.50 
329 
0.0732 


2.75 
295 
0.1012 


3.00 
267 
0.1357 


3.25 
245 
0.1771 


3.50 
226 
0.2263 


3.75 

209 
0.2839 


4.00 
195 

0.3503 


3/8 


D 
W 

F 


2.00 
765 
0.0145 


2.25 
663 
0.0222 


2.50 

589 
0.0323 


2.75 
523 
0.0452 


3.00 

473 
0.0610 


3.25 
433 
0.0801 


3.50 

398 
0.1029 


3.75 

368 
0.1297 


4.00 
343 
0.1606 


4.25 
321 
0.1963 


4.50 
301 
0.2363 


7/16 


D 
W 

F 


2.00 
1263 
0.0069 


2.25 

1089 
0.0108 


2.50 
957 
0.0160 


2.75 
853 
0.0225 


3.00 
770 
0.0306 


3.25 

702 
0.0405 


3.50 
644 
0.0529 


3.75 

596 
0.0661 


4.00 

544 
0.0823 


4.50 
486 
0.1220 


5.00 
432 
0.1728 


1/2 


D. 
W 
F 


2.00 
1963 
0.0036 


2.25 
1683 
0.0057 


2.50 

1472 
0.0085 


2.75 

1309 
0.0121 


3.00 
1178 
0.0167 


3.25 

1071 
0.0222 


3.50 
982 
0.0288 


3.75 

906 
0.0366 


4.00 
841 
0.0457 


4.50 
736 
0.0683 


5.00 

654 
0.0972 


9/16 


D 
W 

F 


2.50 
2163 
0.0048 


2.75 
1916 
0.0070 


3.00 
1720 
0.0096 


3.25 

1560 
0.0129 


3.50 
1427 
0.0169 


3.75 
1315 
0.0216 


4.00 

1220 

0.0271 


4.25 

1137 
0.0334 


4.50 
1065 
0.0406 


5.00 
945 
0.0582 


5.50 
849 
0.0801 


5/8 


D 
W 

F 


2.50 
3068 
0.0029 


2.75 
2707 
0.0042 


3.00 

2422 
0.0058 


3.25 
2191 
0.0079 


3.50 

2001 
0.0104 


3.75 

1841 
0.0133 


4.00 
1704 
0.0168 


4.25 

1587 
0.0208 


4.50 

1484 
0.0254 


5.00 

1315 

0.0366 


5.50 
1180 
0.0506 


11/16 


D 
W 

F 


3.00 
3311 
0.0037 


3.25 
2988 
0.0050 


3.50 

2723 
0.0066 


3.75 

2500 
0.0086 


4.00 
2311 
0.0108 


4.25 
2151 
0.0135 


4.50 
2009 
0.0165 


4.75 
1885 
0.0200 


5.00 

1776 
0.0239 


5.50 

1591 

0.0333 


6.00 
1441 

0.0447 


3/4 


D 
W 

F 


3.00 
4418 
0.0024 


3.25 
3976 
0.0033 


3.50 
3615 
0.0044 


3.75 
3313 
0.0057 


4.00 
3058 
0.0072 


4.25 
2840 
0.0090 


4.50 
2651 
0.0111 


4.75 
2485 
0.0135 


5.00 

2339 
0.0162 


5.50 
2093 
0.0226 


6.003 

1893 

0.005 


7/8 


D 
W 

F 


3.50 
6013 
0.0018 


3.75 

5490 
0.0024 


4.00 
5051 
0.0030 


4.25 
4676 
0.0038 


4.50 
4354 
0.0047 


4.75 
4073 
0.0058 


5.00 
3826 
0.0070 


5.25 
3607 
0.0083 


5.50 
3413 
0.0098 


6.00 
3080 
0.0134 


6.50 
2806 
0.0177 


1 


D 
W 

F 


3.50 
9425 
0.0010 


3.75 

8568 
0.0014 


4.00 
7854 
0.0018 


4.25 

7250 
0.0023 


4.50 
6732 
0.0028 


4.75 
6283 
0.0035 


5.00 
5890 
0.0043 


5.25 
5544 
0.0051 


5.50 

5236 
0.0061 


6.0Q 
4712 
0.0083 


6.50 
4284 
0.0111 



F. D. Howe, Am. Mach, Dec. 20, 1906, using Begtrup's formulae, com- 
putes a table for springs made from wire of Roebling's or Washburn and 
Moen gauges, Nos. 28 to 000. It is here given somewhat abridged, 
values of F corresponding to a torsional modulus of elasticity of 12,000,000 
only being used. 



398 



No. 28 
0.016" 


D 
W 
F 


0.20 
0.524 
6.32 


0.25 
0.41 
13.02 


0.3125 
0.31 
30.2 


0.375 
0.27 
47.0 


0.4375 
0.23 
76.0 


0.500 
0.20 
115 


0.5625 
0.175 
166 


0.625 
0.16 
230 


0.75 
0.13 
402 


0.875 
0.11 
695 


No. 24 
0.0225" 


D 
W 
F 


0.25 

1.18 
2.78 


0.3125 
0.92 
6.31 


0.375 
0.76 
11.35 


0.4375 
0.45 
18.57 


0.500 
0.56 
28.2 


0.5625 
0.50 
40.8 


0.625 
0.45 
56.9 


0.75 
0.37 
97.5 


0.875 
0.31 
166 


0.100 
0.28 
242 


No. 22 
0.028" 


D 
W 
F 


0.25 
2.35 
1.19 


0.3125 

1.84 

2.50 


0.375 
1.49 
4.53 


0.4375 
1.26 
7.42 


0.50 
1.095 
11.40 


0.5625 
0.96 
16.5 


0.625 
0.865 
23.1 


0.75 

0.715 

40.8 


0.875 
0.61 
66.0 


1.00 
0.53 
99.5 


No. 20 
0.035" 


D 
W 

F 


0.25 

4.7 

0.451 


0.3125 
3.64 
0.952 


0.375 
2.97 
1.75 


0.4375 
2.5 
2.90 


0.50 

2.18 
4.47 


0.5625 
1.92 
6.51 


0.625 
1.72 
9.14 


0.75 
1.42 
16.3 


0.875 
1.20 
26.4 


1.00 
1.05 
40.0 


No. 18 
0.047" 


D 

W 
F 


0.25 
12.05 
0.1158 


3125 

9.2 
0.294 


0.375 

74.5 
0.488 


0.4375 
6.57 
0.824 


0.50 
5.40 
1.320 


0.625 
4.23 
1.870 


0.75 
3.48 
3.96 


0.875 
2.95 
7.85 


1.00 

2.85 
12.60 


1.125 
2.27 
17.5 


No. 14 
0.08" 


D 
W 
F 


0.375 

41 
0.0418 


0.5 
28.8 
0.128 


0.625 
22.2 
0.342 


0.75 
18.1 
0.572 


0.875 

15.2 

0.82 


1.00 
13.15 
1.27 


1.125 
11.6 
1.86 


1.25 
10.35 
2.60 


1.50 

8.52 
5.48 


1.75 
7.25 
7.57 


No. 12 
0.105" 


D 
W 

F 


0.625 
52.5 
0.069 


0.75 
42.25 
0.1480 


0.875 
35.4 
0.262 


1.00 
30.4 
0.395 


1.25 
2.38 
0.830 


1.50 
19.5 
1.49 


1.75 
16.6 
2.45 


2.00 

14.4 

3.74 


2.25 
12.7 
5.45 


2.50 
11.4 
7.34 


No. 10 
0.135" 


D 
W 
F 


0.875 

77 

0.081 


1.00 

67 

0.135 


1.25 
52 
0.276 


1.50 
42.5 
0.5)2 


1.75 

36 

0.846 


2.00 

31 

1.295 


2.25 

27 

1.910 


2.50 

24 

2.660 


2.75 
22 
3.58 


3.00 
20 

4.75 


No. 8 
0.162" 


D 

W 
F 


1.00 

120 

0.0570 


1.25 
98.5 
0.124 


1.50 
76 
0.199 


1.75 

64 
0.554 


2.00 
55.5 
0.597 


2.25 
48.8 
0.880 


2.50 

43.5 
1.26 


2.75 

39 

1.68 


3.00 
36 
2.20 


3.25 

33 

2.85 


No. 7 
0.177" 


D 

W 

F 


1.00 

159 

0.0382 


1.25 

122 

0.0828 


1.50 
99 
0.156 


1.75 
83.5 
0.265 


2.00 

72 

0.416 


2.25 

63 

0.603 


2.50 

56.4 
0.830 


2.75 

51 

1.15 


3.00 

46.5 
1.54 


3.25 
42.5 
1.96 


No. 6 
0.192" 


D 
W 
F 


1.25 

158 

0.0572 


1.50 

128 

0.108 


1.75 
107 
0.185 


2.00 
92.5 
0.284 


2.25 

81 

0.420 


2.50 

72 

0.590 


2.75 

65 

0.802 


3.00 
59.5 
1.07 


3.25 
55 5 
1.38 


3.50 

50 

1.74 


No. 5 
0.205" 


D 
W 

F 


1.50 

155 

0.0820 


1.75 

131 

0.139 


2.00 
113 
0.218 


2.25 

99 

0.321 


2.50 
88.5 
0.412 


2.75 

80 

0.6175 


3.00 

70 

0.82 


3.25 

67 

1.60 


3.50 
61.5 
1.34 


4.00 
53.5 

2.22 


No. 4 
0.225" 


D 
W 

F 


1.50 

210 
0.0536 


1.75 

175 

0.093 


2.00 
150 
0.147 


2.25 

132 

0.220 


2.50 

118 

0.303 


2.75 

106 

0.412 


3.00 

97 

0.652 


3.25 

89 

0.715 


3.50 
82 
0.91 


4.00 

71 

1.30 


No. 2 
0.263" 


D 

W 
F 


1.50 

345 
0.0264 


1.75 

290 

0.0458 


2.00 

250 

0.0730 


2.25 
215 
0.109 


2.50 

192 

0.154 


2.75 

175 

0.214 


3.00 
156 

0.274 


3.25 

146 

0.371 


3.50 

134 
0.469 


4.00 
115 

0.720 


No.l 
0.283" ' 


D 

W 
F 


1.75 

360 

0.0328 


2.00 

310 

0.0550 


2.25 

270 

0.0778 


2.50 
240 
0.112 


2.75 

215 

0.155 


3.00 

195 

0.208 


3.25 

180 
0.270 


3.50 

165 

0.344 


4.00 
145 
0.530 


4.50 

127 

0.775 


No. 
0.307" 


D 
W 

F 


1.75 

470 

0.0308 


2.00 

400 

0.0380 


2.25 

350 

0.0548 


2.50 
310 
0.0788 


2.75 

280 

0.109 


3.00 

250 
0.149 


3.25 

230 

0.199 


3.50 

212 
0.244 


4.00 
185 
0.327 


4.50 

162 

0.550 


No. 00 
0.331" 


D 
W 
F 


2.00 
510 

0.0289 


2.25 

445 
0.0388 


2.50 

390 

0.0564 


2.75 
350 
0.0780 


3.00 

320 

0.105 


3.25 

290 

0.137 


3.50 

270 
0.176 


4.00 
230 

0.273 


4.50 
205 
0.414 


5.00 
183 

0.562 



To find deflection of one coil by one pound, divide the values of F by 100. 



SPRINGS TO RESIST TORSIONAL FORCE. 



399 



ELLIPTICAL SPRINGS, SIZES, AND PROOF TESTS. 

Pennsylvania Railroad Specifications, 1896. 



c 




CD 




m ■ 




* -i 


ri 


"S c 










> 


— 5 

r a, 


8-8 


^ 


£~ 


40 


113/4 


40 


151/9 


36 


113/4 


40 




40 




42 




35 


?13/ 4 


32 


nh 


36 


91/2 


40 


151/2 


40 


151/2 


34 


151/9, 


30 


91/2 


40 


91/?, 


36 


151/9, 


30 


151/9, 


36 


91/9 


42 




22 


101/9 


22 


101/2 


24 


101/2 


24 


101/9, 


36 


10 


36 


10 



Plates, 
No. Size, In 



Ins. high. lbs. 
(a) (6) 



Ins. lbs. 

(a) 



aS 



E I, Triple 

E 2, Quadruple . 

E 3, Triple 

E 4, Singlet-... 
E 5, " t-... 
E6. " t .-. 

E 7, Triple 

E 8, Double 

E 9, ' 

E 10, Quadruple 

E 11, 

E 12, 

E 13, Double.... 

E 14, " .... 

E 15, Quadruple 

E 16, 

E 17, Double.... 

E 18, Singlet--. 

E 19, Double.... 

E 20, " 

E 21, " .... 

E 22, " 

E 23, " .... 

E 24, " .... 



3 X 11/32 
3x3/ 8 
' 3x11/32 
3x11/32 
3 x3/ 8 

• 31/ 2 x3/ 8 

• 3 X ll/3 2 

3 x3/ 8 

4 X 11/32 



33/4 
33/4 



15/16* 



93/s 
93/4 
95/ 8 



21/ 2 91/ 2 11,f 



4,800 
6,650 
6,000 
free 
3,000 
4,375 



3x3/ 8 
3x3/8 
4X3/8 
• 4 X U/39 
, 3X11/32 
3 'X 11/32 
4x3/ 8 
31/ 2 x3/8 
4I/9XH/39 
4I/2XH/32 
41/2X3.8 
41/ 2 x3/8 
4x3/8 
4x3/ 8 



31/2 



33/4 
33/4 



8,000 
87/ 16 5,400 
8,000 



93/4 
93/4 



93/4 11,820 



3 3/ 8 
37/16 

41/2 101/8 8, 
23/ 4 
I* 
13/16 

13/16 



10,600 
13,100 
5,600 
6,840 



1 
1 

21/4 
21/4 



000 
,070 
.... 5,250 
67/i 6 13,800 
71/g 15,600 
71/4 15,750 
8I/2 18,000 
8 8,750 

8 7,500 



5,500 
8,000 
8,000 
2,350 
4,970 
6,350 



6,000 
10,000 
12,200 
15,780 
10,600 
8,600 
21/2 14,370 
23/ 4 15,500 
2 9,540 
7,300 



28,800 
32,930 
U/4 10,750 
11/4 9,500 



(a) Between bands; (b) overall; a.p.t., auxiliary plates touching. 
* Between bottom of eye and top of leaf, t Semi-elliptical. 
Tracings are furnished for each class of spring. 



SPRINGS TO RESIST TORSIONAL FORCE. 

(Reuleaux's Constructor.) 



Flat spiral or helical spring P ■- 

Round helical spring . .P ■■ 

Round bar, in torsion P ■■ 

Flat bar, in torsion P -- 



Sbh\ 
6 R ' 




' = **= 12 JW 


SxdK 
32 R' 




f ~ R * ~ K Ed*' 


Snd*. 
16R' 






S b% 2 . 
3R \Zb°-+ h 2 ' 


f ~ R * ~ ~~g~ ~~m? 



P = force applied at end of radius or lever-arm R; ■& = angular motion 
at end of radius R; S = permissible maximum stress, = 4 /s of permissible 
stress in flexure: E = modulus of elasticity in tension; G = torsional 
modulus, = 2/5 E; I = developed length of spiral, or length of bar; d == 
diameter of wire; b = breadth of flat bar; h = thickness. 

Compare Elastic Resistance to Torsion, p. 311. 



400 



HELICAL SPRINGS — SIZES AND CAPACITIES. 

(Selected from Specifications of Penna. R. R. Co., 1899.) 















Test. Height and 


"So 




c 


u 




^ 







Loads. 


a 




oS 

PQ 


oS 

pq 


.5 



0J 


'53 


a 

oS 






m 


d 
O 


a 


a 


A 






«| 


03 


&0 H3 

fl PI 


a 

oS 


I 




Jjo 

30 


f 


12 

"0 




*2 

OS 
O 




PM 


Q 


h3 


H 


fc 





Eh 


GQ 




k! 










lbs. oz. 








' 






H 26 


9/64 


571/2 


59 


4 


1 


53/4 


3 


31/ 4 


110 


130 


H 18 


H/64 


75 


761/4 


8 


1 


8 


5 


6 


170 


270 


H 55 


3/16 


451/g 


465/ 16 


55/8 


1 


41/2 


35/i 6 


4 


103 


245 


H 73 


3/16 


426 


4273/ 4 


3 51/2 


15/16 


39 


221/2 


35 


45 


185 


H 29 


7/32 


201/ 2 


227/ 16 


31/ 2 


1 15/32 


HI/16 


19/64 


13/8 


110 


200 


H 1 


1/4 


451/2 


47 


10 


11/4 


51/8 


35/ 8 


43/s 


250 


500 


H 5 


1/4 


251/ 4 


281/4 


6 


21/4 


21/4 


U/8 


11/2 


164 


240 


H 58 


5/16 


2531/2 


2561/2 


5 7 


21/4 


23 


13 


18 


248 


495 


H 74 


5/16 


180 


1821/s 


3 I4l/ 2 


1 U/16 


191/s 


13 


141/8 


587 


700 


H 68!* 


3/8 


991/2 


1031/4 


3 11/2 


23/4 


9 


5 


7 


350 


700 


H 79 


3/8 


88 


903/4 


2 12 


21/8 


85/ 8 


6 


63/4 


676 


946 


H 80 2 


13/32 


1923/s 


1953/4 


7 H/2 


29/16 


18 


119/16 


151/2 


380 


975 


H 43 


7/16 


96 


l025/i 6 


4 1 


47/i 6 


815/16 


33/s 


51/8 


450 


660 


H 64 


7/16 


755/ 8 


781/2 


3 3 


29/32 


75/s 


55/8 


53/4 


1350 


1440 


H 53 2 


15/32 


1695^ 


I729/i 6 


8 4 


217/32 


16 1/2 


121/4 


151/2 


330 


1410 


H 27 2 


1/2 


903/4 


951/ 8 


5 


31/4 


8 1/2 


51/4 


63/4 


810 


1500 


H 61 


1/2 


151/2 


213/s 


133/4 


41/4 


13/8 


05/ 8 


1 


532 


1050 


H 19 


17/32 


81 1/2 


851/ 2 


5 2 


31/32 


8 


59/16 


67/ie 


1200 


1900 


H 86 3 


17/32 


I535/ 8 


159 


9 10 


4 


133/4 


71/2 


87/ie 


1156 


1360 


H 63 


9/16 


98 


103 


6 15 


33/4 


91/8 


51/2 


7 


1050 


1800 


H 33 3 


9/16 


80 1/4 


847/g 


5 10l/ 9 


31/4 


8 


53/s 


613/ie 


1000 


2200 


H 59 2 


5/8 


741/4 


773/4 


6 7 


27/s 


81/4 


69/16 


71/4 


2100 


3500 . 


H 8O1 


5/8 


1921/9 


1973/4 


16 11 


315/16 


18 


119/16 


151/2 


900 


2315 


H 72 2 


21/32 


601/s 


631/2 


5 117/g 


23/4 


75/16 


6 


63/g 


3260 


4240 


H 15 2 


H/16 


557/8 


593/4 


5 14 


31/2 


53/4 


45/16 


53/16 


1400 


3500 


H 41 


11/16 


1171/2 


1231/2 


12 10 


41/2 


07/s 


63/4 


85/8 
87/£ 


1500 


2720 


H 40 


3/4 


1771/2 


1865/ 8 


22 21/2 


6 1/2 


6 


73/s 


1900 


2300 


H 70 


3/4 


62 


66 


7 12 


3 3/s 


7 


55/s 


61/4 


2750 


5050 


H 17 2 


13/16 


100 


1063/4 


14 12 


51/8 


91/8 


6 


75/8 


1700 3700 


H 66 2 


13/16 


1051/4 


1103/s 


15 7 


45/32 


07/s 


81/8 


87/s 


3670 5040 


H 37 


27/32 


77 


817/s 


12 21/2 


315/16 


8 1/2 


6H/16 


71/2 


3300 


6250 


H 87 2 


27/32 


13013/ 16 


13715/ 16 


20 9 


5 3/8 


21/4 


73/4 


87/ie 


3540 


4165 


H 12 2 


7/8 


85 


9H/2 


14 7 


5 


8 1/2 


53/4 


73/s 


2000 


5200 


H 33 2 


7/8 


82 


8811/i 6 


13 15 


51/8 


8 


53/s 


613/ie 


2250 


5000 


H 2 


15/16 


46 


523/s 


8 151/4 


5 


45/ 8 


33/s 


4 


3250 


7000 


H 16 


15/16 


85 


927/ 8 


16 10 


6 


8 


5 


6 


3600 


5100 


H 10 


1 


85 


92 


18 14 


51/2 


8 1/2 


6 


7 


4500 


7000 


H 42 x 


1 


36 


427/g 


8 


5 3/8 


35/8 


25/s 


33/ 8 


1795 


7180 


H 4 


U/16 


987/s 


105 


24 12 


5 


07/s 


8 1/2 


93/ 8 


6000 


9570 


H 861 


U/16 


1535/8 


1641/2 


38 9 


8 


33/4 


71/2 


87/i 6 


4624 


5440 


H 3 


11/8 


353/ 8 


4II/4 


9 15 


47/s 


41/8 


33/s 


33/4 


6000 


12000 


H 14i 


U/8 


51 


587/s 


14 4 


61/8 


51/8 


3H/16 


43/16 


5000 


8950 


H 6! 


13/16 


991/g 


1093/ 4 


31 1 


8 


91/8 


51/2 


7 


4550 


7750 


H 47 


13/16 


731/ 2 


791/2 


23 


5 7/16 


8I/4 


69/16 


71/4 


7400 


12500 


H 9 


11/4 


971/2 


108 


33 12 


8 


9 


53/4 


71/2 


4000 


9100 


H 72i 


11/4 


621/s 


683/4 


21 8I/2 


53/s 


75/i 6 


6 


63/ 8 


10700 


14875 


H 8 


15/16 


96 


106 1/2 


36 12 


8 


91/8 


6 


71/4 


6350 


10600 


H 62 


1 5/16 


70 


771/16 


26 12 


513/16 


8 


6 1/2 


71/4 


7900 


15800 


H 12i 


13/8 


87 


973/s 


36 7 


8 


8 1/2 


53/4 


73/s 


5000 


12200 


H 39i 


13/s 


755/ 8 


831/2 


31 11 


63/g 


83/s 


65/ 8 


71/2 


8150 


16300 


H 28i 


1 13/32 


8411/ie 


95 


37 3 


8 


81/4 


53/4 


67/s 


7325 


13250 



* The subscript 1 means the outside coil of a concentric group or 
cluster; 2 and 3 are inner coils. 



RIVETED JOINTS. 401 

Phosphor-Bronze Springs. Wilfred Lewis (Engs'. Club, Phila., 1887) 
made some tests of a helical spring of phosphor-bronze wire, 0.12 in. 
diameter, 1V4 in. diameter from center to center, making 52 coils. 

Such a spring of steel, according to the practice of the P. R. R., might 
be used for 40 lbs. A load of 30 lbs. gradually applied gave a permanent 
set. With a load of 21 lbs. in 30 hours the spring lengthened from 20 Vs 
inches to 21 1/8 inches, and in 200 hours to 21 1/4 inches. It was concluded 
that 21 lbs. was too great for durability. For a given load the extension 
of the bronze spring was just double the extension of a similar steel 
spring, that is, for the same extension the steel spring is twice as strong. 
Chromium- Vanadium Spring Steel. (Proc. Inst. M. E., 1904, pp 
1263, 1305.) —A spring steel containing C, 0.44; Si, 0.173; Mn, 0.837; Cr, 
1.044; Va, 0.188 was made into a spring with dimensions as follows: length 
unstretched 9.6 in., mean diam. of coils (D) 5.22; No. of coils (n) 4; diam. 
of wire, (d) 0.561. It was tempered in the usual way. When stretched 
it showed signs of permanent set at about 1900 lbs. Compared with two 
springs of ordinary steels the following formulae are obtained: 

Load at which Permanent Set begins. Extension for a load W. 

Chrome-Vanadium Spring. . .56,300 d 3 /D lbs. WnD 3 -*- 1,468,000 d* 

West Bromwich Spring 28,400 d 3 /D " WnD 3 -s- 1,575,000 d* 

Turton & Piatt Spring 44,200 d s /D " WnD 3 -i- 1,331,600 d* 

Test of a Vanadium-steel Spring. (Circular of the American Vana- 
dium Co., 1908). — Comparative tests of an ordinary carbon-steel loco- 
motive flat spring and of a vanadium-steel spring, made by the American 
Locomotive Co., showed the following: The vanadium spring, on 36-in. 
centers tested to 94,000 lbs., reached its elastic limit at 85,000 lbs., or 
234,000 lbs. per sq. in. fiber stress, and a permanent set of 0.48 in. The 
test was repeated three times without change in the deflection. The 
carbon spring was tested to 89,280 lbs. and reached an elastic limit at 
65,000 lbs., or 180,000 lbs. fiber stress, with a permanent set of 1.12 in. 
On repeating the test it took an additional set of 0.25 in., and on the next 
test several of the plates failed. 

RIVETED JOINTS. 

Fairbairn's Experiments. — The earliest published experiments on 
riveted joints are contained in the memoir by Sir W. Fairbairn in the 
Transactions of the Royal Society. Making certain empirical allow- 
ances, he adopted the following ratios as expressing the relative strength 

of riveted joints: Solid plate 100 

Double-riveted joint 70 

Single-riveted joint 56 

These celebrated ratios appear to rest on a very unsatisfactory analysis 
of the experiments on which they were based. 

Loss of Strength in Punched Plates. (Proc: Inst. M. E., 1881.) — 
A report by Mr. W. Parker and Mr. John, made in 1878 to Lloyd's Com- 
mittee, on the effect of punching and drilling, showed that thin steel 
plates lost comparatively little from punching, but that in thick plates 
the loss was very considerable. The following table gives the results for 
plates punched and not annealed or reamed: 

Thickness of plates V\ 3 /s V2 3 /4 

Loss of tenacity, per cent 8 18 26 33 

When 7/8-in. punched holes were reamed out to lVsin. diameter, the loss 
of tenacity disappeared, and the plates carried as high a stress as drilled 
plates. Annealing also restores to punched plates their original tenacity. 

The Report of the Research Committee of the Institution of Mechanical 
Engineers, on Riveted Joints (1881), and records of investigations by Prof. 
A. B. W. Kennedy (1881, 1882, and 1885), summarize the existing in- 
formation regarding the comparative effects of punching and drilling 
upon iron and steel plates. An examination of the voluminous tables 
given in Professor Unwin's Report, of the experiments made on iron and 
steel plates, leads to the general conclusion that, while thin plates, even 
of steel, do not suffer very much from punching, yet in those of 1/2 inch 
thickness and upwards the loss of tenacity due to punching ranges from 
10% to 23% in iron plates, and from 11% to 33% in the case of mild 
steel. In drilled plates there is no appreciable loss of strength. It is 



402 



RIVETED JOINTS. 



possible to remove the bad effects of punching by subsequent reaming or 
annealing. The introduction of a practicable method of drilling the 
plating of ships and other structures, after it has been bent and shaped, 
is a matter of great importance. In the modern English practice (1887) 
of the construction of steam-boilers with steel plates punching is almost 
entirely abolished, and all rivet-holes are drilled after the plates have 
been bent to the desired form. 

Strength of Perforated Plates. (P. D. Bennett, Eng'g, Feb. 12, 
1886. p. 155.) — Tests were made to determine the relative effect pro- 
duced upon tensile strength of a flat bar of iron or steel: 1. By a 3/4-inch 
hole drilled to the required size; 2. By a hole punched Vs inch smaller 
and then drilled to the size of the first hole; and, 3. By a hole punched in 
the bar to the size of the drilled hole. The relative results in strength 
per square inch of original area were as follows: 





1. 


2. 


3. 


4. 




Iron. 
1.000 
1.029 
1.030 
0.795 


Iron. 
1.000 
1.012 
1.008 
0.894 


Steel. 
1.000 
1.068 
1.059 
0.935 


Steel. 
1.000 




1.103 


Perforated by punching and drilling- 
Perforated by punching only 


1.110 
0.927 



In tests 2 and 4 the holes were filled with rivets driven by hydraulic 
pressure. The increase of strength per square inch caused by drilling is 
a phenomenon of similar nature to that of the increased strength of a 
grooved bar over that of a straight bar of sectional area equal to the 
smallest section of the grooved bar. Mr. Bennett's tests on an iron bar 
0.84 in. diameter, 10 in. long, and a similar bar turned to 0.84 in. diam- 
eter at one point only, showed that the relative strength of the latter to 
the former was 1.323 to 1.000. 

Comparative Efficiency of Riveting done by Different Methods. 

The Reports Of Professors Unwin and Kennedy to the Institution of 
Mechanical Engineers (Proc. 1881, 1882, and 1885) tend to establish the 
four following points: 

1. That the shearing resistance of rivets is not highest in joints riveted 
by means of the greatest pressure; 

2. That the ultimate strength of joints is not affected to an appre- 
ciable extent by the mode of riveting; and, therefore, 

3. That very great pressure upon the rivets in riveting is not the in- 
dispensable requirement that it has been sometimes supposed to be; 

4. That the most serious defect of hand-riveted as compared with 
machine-riveted work consists in the fact that in hand-riveted joints 
visible slip commences at a comparatively small load, thus giving such 
joints a low value as regards tightness, and possibly also rendering them 
liable to failure under sudden strains after slip has once commenced. 

The following figures of mean results give a comparative view of hand 
and hydraulic riveting, as regards their ultimate strengths in joints, and 
the periods at which in both cases visible slip commenced. 



Total breaking load. Tons 
Load at which visible slip began 



Hand. . . . . 
Hydraulic 

Hand 

Hydraulic 



86.01 


82.16 


149.2 


85.75 


82.70 


145.5 


21.7 


25.0 


31.7 


47.5 


53.7 


49:7 



193.6 
183.1 
25.0 
56.0 



Some of the Conclusions of the Committee of Research on Riveted 
Joints. 

(Proc. Inst. M. E., April, 1885.) 
The conclusions refer to joints made in soft steel plate with steel rivets, 
the holes drilled, and the plates in their natural state (unannealed). 
The rivet or shearing area has been assumed to be that of the holes, not 
the area of the rivets themselves. The strength of the metal in the joint 
has been compared with that of strips cut from the same plates. 



RIVETED JOINTS. 



403 



The metal between the rivet-holes has a considerably greater tensile 
resistance per square inch than the imperforated metal. This excess 
tenacity amounted to more than 20%, both in 3/ 8 -inch and 3/4-inch plates, 
when the pitch of the rivet was about 1.9 diameters. In other cases 3/g-inch 
plate gave an excess of 15% at fracture with a pitch of 2 diameters, of 
10% with a pitch of 3.6 diameters, and of 6.6%, with a pitch of 3.9 
diameters; and 3/ 4 -in C h plate gave 7.8% excess with a pitch of 2.8 
diameters. 

In single-riveted joints it may be taken that about 22 tons per square 
inch is the shearing resistance of rivet steel, when the pressure on the 
rivets does not exceed about 40 tons per square inch. In double-riveted 
joints, with rivets of about 3/4-inch diameter, most of the experiments 
gave about 24 tons per square inch as the shearing resistance, but the 
joints in one series went at 22 tons. [Tons of 2240 lbs.] 

The ratio of shearing resistance to tenacity is not constant, but dimin- 
ishes very markedly and not very irregularly as the tenacity increases. 

The size of the rivet heads and ends plays a most important part in the 
strength of the joints — at any rate in the case of single-riveted joints. 
An increase of about one-third in the weight of the rivets (all this increase, 
of course, going to the heads and ends) was found to add about 8V2% to 
the resistance of the joint, the plates remaining unbroken at the full 
shearing resistance of 22 tons per square inch, instead of tearing at a 
shearing stress of only a little over 20 tons. The additional strength is 
probably due to the prevention of the distortion of the plates by the 
great tensile stress in the rivets. 

The intensity of bearing pressure on the rivet exercises, with joints 
proportioned in the ordinary way, a very important influence on their 
strength. So long as it does not exceed 40 tons per square inch (meas- 
ured on the projected area of the rivets), it does not seem to affect their 
strength; but pressures of 50 to 55 tons per square inch seem to cause 
the rivets to shear in most cases at stresses varying from 16 to 18 tons 
per square inch. For ordinary joints, which are to be made equally 
strong in plate and in rivets, the bearing pressure should therefore prob- 
ably not exceed 42 or 43 tons per square inch. For double-riveted butt- 
joints perhaps, as will be noted later, a higher pressure may be allowed, 
as the shearing stress may probably not be more than 16 or 18 tons per 
square inch when the plate tears. 

A margin (or net distance from outside of holes to edge of plate) equal 
to the diameter of the drilled hole has been found sufficient in all cases 
hitherto tried. 

To attain the maximum strength of a joint, the breadth of lap must be 
such' as to prevent it from breaking zigzag. It has been found that the 
net metal measured zigzag should be from 30% to 35% in excess of that 
measured straight across, in order to insure a straight fracture. This 
corresponds to a diagonal pitch of 2/3 p-\- rf/3, if p be the straight pitch 
and d the diameter of the rivet-hole. 

Visible slip or "give" occurs always in a riveted joint at a point very 
much below its breaking load, and by no means proportional to that load. 
A collation of the results obtained in measuring the slip indicates that it 
depends upon the number and size of the rivets in the joint, rather than 
upon anything else; and that it is tolerably constant for a given size of 
rivet in- a given type of joint. The loads per rivet at which a joint will 
commence to slip visibly are approximately as follows: 



Diameter of Rivet. 


Type of Joint. 


Riveting. 


Slipping Load per 
Rivet. 


3/4 inch 
3/ 4 " 
3/4 " 
1 inch 
1 " 
1 " 


Single- riveted 
Double- riveted 
Double- riveted 
Single-riveted 
Double- riveted 
Double- riveted 


Hand/ 

Hand 

Machine 

Hand 

Hand 

Machine 


2.5 tons 

3.0 to 3.5 tons 

7 tons 

3.2 tons 

4.3 tons 

8 to 10 tons 



404 



RIVETED JOINTS. 



To find the probable load at which a joint of any breadth will commence 
to slip, multiply the number of rivets in the given breadth by the proper 
figure taken from the last column of the table above. The above figures 
are not given as exact ; but they represent the results of the experiments. 

The experiments point to simple rules for the proportioning of joints of 
maximum strength. Assuming that a bearing pressure of 43 tons per 
square inch may be allowed on the rivet, and that the excess tenacity of 
the plate is 10% of its original strength, the following table gives the 
values of the ratios of diameter d of hole to thickness t of plate (d -4- t), 
and of pitch p to diameter of hole (p -s- d) in joints of maximum strength 
in 3/s-inch plate. 

For Single-riveted Plates. 



Original Tenacity of 
Plate. 


Shearing Resistance 
of Rivets. 


Ratio. 
d+t 


Ratio. 
p + d 


Ratio. 
Plate Area 
Rivet Area 


Tons per 
Sq. In. 


Lbs. per 
Sq. In. 


Tons per 
Sq. In. 


Lbs. per 
Sq. In. 


30 

28 
30 
28 


67,200 
62,720 
67,200 
62,720 


22 
22 
24 
24 


49,200 
49,200 
53,760 
53,760 


2.48 
2.48 
2.28 
2.28 


2.30 
2.40 
2.27 
2.36 


0.667 
0.785 
0.713 
0.690 



This table shows that the diameter of the hole should be 2V3 times the 
thickness of the plate, and the pitch of the rivets 23/s times the diameter 
of the hole. Also, it makes the mean plate area 71 % of the rivet area. 
If a smaller rivet be used than that here specified, the joint will not be of 
uniform, and therefore not of maximum, strength; but with any other 
size of rivet the best result will be got by use of the pitch obtained from the 
simple formula p = ad 2 /t + d, where, as before, d is the diameter of the 
hole. 

The value of the constant a in this equation is as follows: 

For 30-ton plate and 22-ton rivets, a = 0.524 

" 28 " " " 22 " " " 0.558 

" 30 " " " 24 " " " 0.570 

" 28 " " " .24 " " " 0.606 

d 2 
Or, in the mean, the pitch p = 0.56 -r + d. With too small rivets this 

gives pitches often considerably smaller in proportion than 23/g times the 
diameter. 

For double-riveted lap-joints a similar calculation to that given 
above, but with a somewhat smaller allowance for excess tenacity, on 
account of the large distance between the rivet-holes, shows that for joints 
of maximum strength the ratio of diameter to thickness should remain 
precisely as in single-riveted joints; while the ratio of pitch to diameter 
of hole should be 3.64 for 30-ton plates and 22 or 24 ton rivets, and 3.82 
for 28-ton plates with the same rivets. 

Here, still more than in the former case, it is likely that the prescribed 
size of rivet may often be inconveniently large. In this case the diameter 
of rivet should be taken as large as possible; and the strongest joint for 
a given thickness of plate and diameter of hole can then be obtained by 
using the pitch given by the equation p = ad 2 /t + d, where the values of 
the constant a for different strengths of plates and rivets may be taken 
as follows, for any thickness of plate from 3/ 8 to 3/ 4 -inch: 

For 30-ton plate and 24-ton rivets \ __ _ , 1rt & , j. 
" 28 " " " 22 " " j ' t 

(12 

" 30 ' 22 " " p = 1.06 - + d°, 

d? 
" 28 24 " " p = 1.24y+a\ 



RIVETED JOINTS. 



4D5 



In double-riveted butt-joints it is impossible to develop the full 
shearing resistance of the joint without getting excessive bearing pressure, 
because the shearing area is doubled without increasing the area on which 
the pressure acts. Considering only the plate resistance and the bearing 
pressure, and taking this latter as 45 tons per square inch, the best pitch 
would be about 4 times the diameter of the hole. We may probably say 
with some certainty that a pressure of from 45 to 50 tons per square inch on 
the rivets will cause shearing to take place at from 16 to 18 tons per square 
inch. Working out the equations as before, but allowing excess strength 
of only 5% on account of the large pitch, we find that the proportions of 
double-riveted butt-joints of maximum strength, under given conditions, 
are those of the following table: 

Double-riveted Butt-joints. 



Original Ten- 
acity of Plate, 
Tons per Sq. 
In. 


Shearing Re- 
sistance of 

Rivets, Tons 
per Sq. In. 


Bearing Pres- 
sure, Tons per 
Sq. In. 


Ratio 
d 

t 


Ratio 
P 
d 


30 


16 


45 


1.80 


3.85 


•28 


16 


45 


. 1.80 


4.06 


30 


18 


48 • 


1.70 


4.03 


28 


18 


48 


1.70 


4.27 


30 


16 


50 


2.00 


4.20 


28 


* 16 


50 


2.00 


4.42 



Practically, therefore, it may be said that we get a double-riveted butt- 
joint of maximum strength by making the diameter of hole about 1.8 
times the thickness of the plate, and making the pitch 4.1 times the 
diameter of the hole. 

The proportions just given belong to joints of maximum strength. 
But in a boiler the one part of the joint, the plate, is much more affected 
by time than the other part, the rivets. It is therefore not unreasonable 
to estimate the percentage by which the tplates might be weakened by 
corrosion, etc., before the boiler would be unfit for use at its proper 
steam-pressure, and to add correspondingly to the plate area. Probably 
the best thing to do in this case is to proportion the joint, not for the 
actual thickness of plate, but for a nominal thickness less than the actual 
by the assumed percentage. In this case the joint will be approximately 
one of uniform strength by the time it has reached its final workable 
condition; up to which time the joint as a whole will not really have been 
weakened, the corrosion only gradually bringing the strength of the plates 
down to that of rivets. 

Efficiencies of Joints. 

The average results of experiments by the committee gave: For double- 
riveted lap-joints in 3 8 -inch plates, efficiencies ranging from 67.1% to 
81.2%. For double-riveted butt-joints (in double shear) 61.4% to 71.3%. 
These low results were probably due to the use of very soft steel in the 
rivets. For single-riveted lap-joints of various dimensions the efficiencies 
varied from 54.8% to 60.8%. The shearing resistance of steel did not in- 
crease nearly so fast as its tensile resistance. With very soft steel, for 
instance, of only 26 tons tenacity, the shearing resistance was about 80% 
of the tensile resistance, whereas with very hard steel of 52 tons tenacity 
the shearing resistance was only somewhere about 65% of the tensile 
resistance. 

Proportions of Pitch and Overlap of Plates to Diameter of Rivet- 
Hole and Thickness of Plate. 

(Prof. A. B. W. Kennedy, Proc. Inst. M. E., April, 1885.) 

t = thickness of plate: 

d = diameter of rivet (actual) in parallel hole; 

p = pitch of rivets, center to center- 

s = space between lines of rivets; 

I = overlap of plate. 



406 



RIVETED JOINTS. 



The pitch is as wide as is allowable without impairing the tightness ot 
the joint under steam. 

For single-riveted lap-joints in the circular seams of boilers which have 
double-riveted longitudinal lap-joints, 

d = t X 2.25; v = dX 2.25 = tX 5 (nearly) ; I = 1X6. 

For double-riveted lap-joints: 

d = 2.25t; p = Si; s = 4.5* ; I = 10.5L 



Single- riveted Joints. 


Double-riveted Joints. 


t 


d 


V 


I 


t 


d 


V 


s 


I 


3/16 


7/16 


15/16 


U/8 


3/16 


7/16 


U/2 


7/8 


2 


V4 


0/16 


U/4 


U/2 


1/4 


9/16 


2 


13/16 


23/4 


6/16 


11/16 


1 9/16 


17/8 


5/16 


11/16 


21/2 


U/2 


33/a 


3/8 


13/16 


1 7/ 8 


21/4 


3/8 


13/16 


3 


13/ 4 


4 


7/16 


1 


2 3/ 16 


25/8 


7/16 


1 


31/2 


2 


45/8 


1/2 


11.8 


2 1/2 


3 


1/2 


U/8 


4 


21/4 


51/4 


9/16 


11/4 


213/i 6 


3 3/8 


9/16 


H/4 


41/2 


21/2 


57/a 



With these proportions and good workmanship there need be no fear of 
leakage of steam through the riveted joint. 

The net diagonal area, or area of plate, along a zigzag line of fracture 
should not be less than 30% in excess of the net area straight across the 
joint, and 35% is better. 

Mr. Theodore Cooper (R. R. Gazette, Aug. 22, 1890), referring to Prof. 
Kennedy's statement quoted above, gives as a sufficiently approximate 
rule for the proper pitch between the rows in staggered riveting, one-half 
of the pitch of the rivets in a row plus one-quarter the diameter of a 
rivet-hole. 

Test of Double-riveted Lap and Butt Joints. 

{Proc. Inst. M. E., October, 1888.) 
Steel plates of 25 to 26 tons per square inch T. S., steel rivets of 24.6 
tons shearing strength per square inch. 



Kind of Joint. 


Thickness of 
Plate. 


Diameter of 
Rivet-holes. 


Ratio of 
Pitch to 
Diameter. 


Comparative 

Efficiency of 

Joint. 


Lap 


3/8" 
3/8 
3/4 
3/4 
3/4 
3/4 

1 

1 

1 


0.8" 

0.7 

1.1 

1.6 

1.1 

1.6 

1.3 

1.75 

1.3 


3.62 
3.93 
2.82 
3.41 
4.00 
3.94 
2.42 
3.00 
3.92 


75.2 


Butt 

Lap 

Lap 

Butt 

Butt 


76.5 
68.0 
73.6 
72.4 
76.1 


Lap 

Lap 

Butt 


63.0 
70.2 
76.1 



Diameter of Rivets for Different Thicknesses of Plates. 



Thickness 
of Plate. 


5/16 


3/8 


7/16 


1/2 

3/4 
13/16 

3/4 
...... 

15/16 
H/16 


9/16 

3/4 
13/16 

7/8 
3/4 


5/8 

3/4 
7/8 
7/8 


H/16 

3/8 

7/8 
7/8 
13/16 


3/4 

7/8 

15/16 
1 
7/8 


13/16 

7/8 
1 
1 


7/8 

I 

1 1/8 
Us 
1 


15/16 

1 

13/16 

U/8 


1 


Diam. (1). 
Diam. (2). 
Diam. (3). 
Diam. (4). 


• 5/ 8 
. 5/ 8 

. 1/2 


5/8 
5/8 
5/8 
5/8 
7/8 
3/4 
1/2 


5/8 
3/ 4 
3/4 
5/8 
15/16 
7/8 
9/16 


1 

U/4 
U/8 
11/16 


Diam. (5). 


. 3/ 4 
. H/16 

. 3/ 8 




1 

3/4 


1 

13/16 














Diam. (7). 















RIVETED JOINTS. 



407 



(1) Lloyd's Rules. (2) Liverpool Rules. (3) English Dock-yards. 
(4) French Veritas. (5) Hartford Steam Boiler Inspection and Insur- 
ance Co., double-riveted lap-joints. (6) Ditto, triple-riveted butt-joints. 
(7) F. E. Cardullo. (Vie less than diam. of hole.) 

Calculated Efficiencies — Steel Plates and Steel Rivets.— The 
following table has been calculated by the author on the assumptions that 
the excess strength of the perforated plate is 10%, and that the shearing 
strength of the rivets per square inch is four-fifths of the tensile strength 
of the plate (or, if no allowance is made for excess strength of the perfo- 
rated plate that the shearing strength is 72.7% of the tensile strength). 
If t = thickness of plate, d = diameter of rivet-hole, p = pitch, and T = 
tensile strength per square inch, then for single-riveted plates 

w A d 2 

(p - d)t X I.IQT = - c/ 2 X | T, whence p = 0.571 ~ + d. 



The coefficients 0.571 and 1.142 agree closely with the averages of those 
given in the report of the committee of the Institution of Mechanical En- 
gineers, quoted on page 404, ante. » 





> 


Pitch. 


Efficiency. 




0> 
> 


Pitch. 


Efficiency. 


























bi> 




bi) 


ti) 






bi) 


M 


bi) 


bi 






c 


a 










a 


E 


c 




PI 










a>'$ 


a 






o>'£ 




0>+3 






"So > 

as 


3£ 


■52 






flJS 

c3 O 

Q^ 5 


o> "2 

bfi> 


11 


"bb> 

■S£ 


11 

Q 


in. 


in. 


in. 


in. 


% 


% 


in 


in. 


in. 


in. 


% 


% 


3/16 


7/16 


1.020 


1.603 


57.1 


72.7 


V2' 


3/4 


1.392 


2.035 


46.1 


63.1 


3/16 


1/2 


1.261 


2.023 


60.5 


75.3 


1/2 


7/8 


1.749 


2.624 


50.0 


66.6 


1/4 


1/2 


1.071 


1.642 


53.3 


69.6 


1/2 


1 


2.142 


3.284 


53.3 


70.0 


1/4 


9 /l6 


1.285 


2.008 


56.2 


72.0 


1/2 


11/8 


2.570 


4.016 


56.2 


72.0 


5/16 


9/16 


1.137 


1.712 


50.5 


67.1 


9/16 


3/4 


1.321 


1.892 


43.2 


60.3 


5/16 


5/8 


1.339 


2.053 


53.3 


69.5 


9/16 


7/8 


1.652 


2.429 


47.0 


64.0 


5/16 


11/16 


1.551 


2.415 


55.7 


71.5 


9/16 


1 


2.015 


3.030 


50.4 


67.0 


3/8 


5/8 


1.218 


1.810 


48.7 


65.5 


9/16 


1V8 


2.410 


3.694 


53.3 


69.5 


3/8 


3/4 


1.607 


2.463 


53.3 


69.5 


9/16 


11/4 


2.836 


4.422 


55.9 


71.5 


3/8 


7/8 


2.041 


3.206 


5" 1 


72.7 


5/8 


3/4 


1.264 


1.778 


40.7 


57.8 


7/16 


5/8 


1.136 


1.647 


45.') 


62.0 


5/8 


7/8 


1.575 


2.274 


44.4 


61.5 


7/16 


3/ 4 


1.484 


2.218 


49. i 


66.2 


5/8 


1 


1.914 


2.827 


47.7 


64.6 


7/16 


7/8 


1.869 


2.864 


53.2 


69.4 


5/8 


11/8 


2.281 


3.438 


50.7 


67.3 


7/16 


1 


2.305 


3.610 


56.6 


72.3 


5/8 


11/4 


2.678 


4.105 


53.3 


69.5 



Apparent Shearing Resistance of Rivet Iron and Steel. 

(Proc. Inst. M. E., 1879, Engineering, Feb. 20, 1880.) 

The true shearing resistance of the rivets cannot be ascertained from 
experiments on riveted joints (1) because the uniform distribution of the 
load to all the rivets cannot be insured; (2) because of the friction of the 
plates, which has the effect of increasing the apparent resistance to shear- 
ing in an element uncertain in amount. Probably in the case of single- 
riveted joints the shearing resistance is not much affected by the friction. 

Fairbairn's experiments show that a rivet is 6 1/7% weaker in a drilled 
t^an in a punched hole. By rounding the edge of the rivet-hole, the 
apparent shearing: resistance is increased 12%. Messrs. Greig and Eyth's 
experiments indicate a greater resistance of the rivets in punched holes 
than in drilled holes. 

If the apparent shearing resistance is less for double than for single 
shear, it is probably due to unequal distribution of the stress on the two- 
rivet sections. 



408 



RIVETED JOINTS. 



Shearing, 16.5 


Ratio, 0.62 


20.2 


0.79 


19.0 


0.85 


22.1 


" 0.77 



The shearing resistance of a bar, when sheared in circumstances which 
prevent friction, is usualiy less than the tenacity of the bar. The ioi« 
lowing results show the decrease: 

Harkort, iron Tenacity, 26.4 

Lavalley, iron. " 25.4 

Greig and Eyth, iron. " 22.2 
Greig and Eyth, steel " 28.8 

In Wohler's researches (in 1870) the shearing strength of iron was found 
to be four-fifths of the tenacity. Later researches of Bauschinger con- 
firm this result generally, but they siiow that for iron the ratio of the 
shearing resistance and tenacity aepends on the direction of the stress 
relatively to the direction of rolling. The above ratio is valid only if the 
shear is in a plane perpendicular to the direction of rolling, and if the 
tension is applied parallel to the direction of rolling. If the plane of shear 
is parallel to the breadth of the bar, the resistance is only half as great 
as in a plane perpendicular to the fibers. 

THE STRENGTH OF RIVETED JOINTS. 

Joint of Maximum Efficiency. — (F. E. CardulkO If a riveted joint 
is made with sufficient lap, and a proper distance between the rows of 
rivets, it will break in one of the three following ways: 

1. By tearing the plate along a line, through the outer row of rivets, 

2. By shearing the rivets, 

3. By crushing the plate or the rivets. 
Let t = the thickness of the main plates. 

d = the diameter of the rivet-holes. 

/ = the tensile strength of the plate in pounds per sq. in. 

s = the shearing strength of the rivets in pounds per sq. in. when 
in single shear. 

p = the distance between the centers of rivets of the outer row 
(see Figs. 90 and 91)= the pitch in single and double lap riveting = twice 



(p"""@ w 



© © © © © 



MM 1 



&._©_©_ 




Fig. 90. 
Triple Riveting. 



Fig. 91. 
Quadruple Riveting. 



the pitch of the inner rows in triple butt strap riveting, in which alter- 
nate rivets in the outer row are omitted, = four times the pitch in quad- 
ruple butt strap riveting, in which the outer row has one-fourth of the 
number of rivets of the two inner rows. 

c = the crushing strength of the rivets or plates in pounds per 
sq. in. 

n = the number of rivets in each grouD in single shear. (A group 
is the number of rivets on one side of a joint corresponding to the dis- 
tance p; = 1 rivet in single riveting, 2 in double riveting, 5 in triple 
butt strap riveting, and 11 in quadruple butt strap riveting.) 

m = the number of rivets in each group in double shear. 

s" = the shearing strength of rivets in double shear, in pounds per 
sq. in., the rivet section being counted once. 

T = the strength of the plate at the weakest section. = ft (p — d). 

S = the strength of the rivets against shearing, = 0.7854 d 2 (ns + 
ms") . 

C = the strength of the rivets or the plates against crushing, = 
dtc (n + m). 



THE STRENGTH OF RIVETED JOINTS. 409 

In order that the joint shall have the greatest strength possible, the 
tearing, snearing, and crushing strength must all be equal. In order to 
make it so, 

1. Substitute the known numerical values, equate the expressions for 
shearing and crushing strength, and find the value of d, taking it to the 
nearest Vi6in. 

2. Next find the value of S in the second equation, and substitute it 
for T in the first equation. Substitute numerical values for the other 
factors in the first equation, and solve for p. 

The efficiency of a riveted joint in tearing, shearing and crushing, is 
equal to the tearing, shearing or crushing strength, divided by the quan- 
tity ftp, or the strength of the solid plate. 

The efficiency in tearing is also equal to (p — d) -s- p. 

The maximum possible efficiency for a well-designed joint is 



m + n + (/ -*- c) 



Empirical formula for the diameter of the rivet-hole when the crush- 
ing strength is unknown. Assuming that c = 1.4/, and s"= 1.75 s, we have 
by equating C and S, and substituting, 



s{n+ 1.75 m) 



Margin. The distance from the center of any rivet-hole to the edge of 
the plate should be not less than 1 1/2(1 The distance between two adja- 
cent rivet centers should be not less than 2d. It is better to increase 
each of these dimensions by 1/8 in. 

The distance between the rows of rivets should be such that the net 
section of plate material along any broken diagonal through the rivet- 
holes should be not less than 30 per cent greater than the plate section 
along the outer line of rivets. 

The thickness of the inner cover strap of a butt joint should be 3/ 4 of 
the thickness of the main plate or more. The thickness of the outer strap 
should be 5/8 of the thickness of the main plate or more. 

Steam Tightness. It is of great importance in boiler riveting that 
the joint be steam tight. It is therefore necessary that the pitch of the 
rivets nearest to the calked edge be limited to a certain function of the 
thickness of the plate. The Board of Trade rule for steam tightness is 

p= Ct + 15/ 8 in. 

where p = the maximum allowable pitch in inches. 
t = the thickness of main plate in inches. 
C = a constant from the following table. 

No. of Rivets per Group.. 

Lap Joints 

Double-strapped Joints.... C= 1.75 3.50 4.63 5.52 6.00 

The pitch should not exceed ten inches under any circumstances. 

When the joint has been designed for strength, it should be checked by 
the above formula. Should the pitch for strength exceed the pitch for 
steam tightness, take the latter, substitute it in the formula 

ft (p -d) =0.7854 d 2 (ns + ms"), 

and solve for d. If the value of d so obtained is not the diameter of some 
standard size rivet, take the next larger Vi6in. 

Calculation of Triple-riveted Butt and Strap Joints. — Formulae: 
T = ft (p-d), S = -0.7854 d 2 (ns + ms"), C = dtc (m + n) (notation on 
preceding page), n = 1, m .= 4. 

Take / = 55,000; * = 0.8/, = 44,000; s" = 1.75s = 77,000, c = 1.4 / 
= 77,000. 

Then T = 55,000 1 (p-d), S = 276,460 rf 2 , C = 385,000 dt. 





1 


2 


3 


4 


(]=] 


1 31 


2.62 


3.47 


4.14 


c= 


1.75 


3.50 


4.63 


5.52 



410 RIVETED JOINTS. 

For maximum strength, T = S = C; dividing by 55,000 1, (p- d) = 
5.027 d 2 = 7dt; whence d = 1.3925$; p = 3d. 

Thickness of plate, < =5/ie 3 /8 7 /i6 V2 9 /i6 5 /s 

Diam. rivet hole, 

d= 1.3925$. .... 0.4353 0.5222 0.6092 0.6962 0.7833 0.8703 
Pitch of outer row, 

p = 8d. ....... 3.4816 A 1776 4.8736 5.5696 6.2664 6.9624 

T= 55,000 t(p-d) 52,360 75,390 102,610 134,020 169,630 209,420 
5= 276,460 d 2 . . . 52,330 75,360 102,570 133,970 169,560 209,330 
C = 385,000 dt . . 52,350 75,390 102,620 134,030 169,630 209,420 

Calculations by logarithms, to nearest 10 pounds. 

Efficiency of all joints (p — d)+p = 87.5 per cent. 

Maximum efficiency by Cardullo's formula, — ■ —77- = _ , ' , 

n + m + f/c 5+1/1.4 
= 87.5 per cent. 
Diameter of rivet-hole, next largest 16th, 7/ 16 9/ 16 5/ 8 3/4 13/ 16 7/ 8 

For the same thickness of plates the Hartford Steam Boiler Inspection 
and Insurance Co. gives the following proportions: 
Thickness, t, 5/ 16 3/ 8 7/ 16 i/ 2 9/ 16 5/ 8 

Diam. rivet-hole, d, 3/ 4 13/ 16 15/ 16 1 n/ 16 n/ 16 

Pitch of outer row, p, 6 1/4 6 1/2 63/ 4 71/2 73/ 4 72/4 

Using the same values for /, s, s" and c, we obtain: 

T= 94,530 117,300 139,860 178,750 207,850 229,880 

S = 155,400 168,400 194,300 207,300 220,200 220,200 

C= 90,030 117,300 157,900 192,500 230,000 255,500 

Strength of solid 

plate, fvt = 107,360 134,060 162,420 206,250 239,770 266,400 

Efficiency T, S or 

C, lowest -h fpt, 

per cent 83.9 87.5 86.1 86.7 86.7 82.6 

The 5 /i6 in. plate fails by crushing, the 5/ 8 by shearing, the others by 
tearing. 

Calculation of Quadruple Riveting. — In this case there are 11 rivets 
in the group. If the upper strap plate contains all the rivets except the 
outer row, then n = 1, m = 10. Using the same values for/, s, s" and 
c as above, we have ns + ms" = 814,000; T = 55,000$ (p - d); S = 
639,315 d 2 ; C = 847,000 dt. 

For maximum strength, t (p — d) = 11.624d 2 = 15.4 dt; whence d = 
1.32485$, p = 16.4 d. Efficiency (p - d)+p = 93.9 per cent. Check by 

Cardullo's formula — ; -—rr = 71 — , in/ ■ = 93.9 per cent. 

n+ m + f/c 11+ 10 /ii 
British Board of Trade and Lloyd's Rules for Riveted Joints. — 

Board of Trade. — Tensile strength of rivet bars between 26 and 30 tons, 
el. in 10" not less than 25%, and contr. of area not less than 50%. 

The shearing resistance of the rivet steel to be taken at 23 tons per 
square inch, 5 to be used for the factor of safety independently of any 
addition to this factor for the plating. Rivets in double shear to have 
only 1.75 times the single section taken in the calculation instead of 2. 
The diameter must not be less than the thickness of the plate, and the 
pitch never greater than 8 1/2". The thickness of double butt-straps 
(each) not to be less than 5/ 8 the thickness of the plate; single butt-straps 
not less than 9/ 8 . 

Distance from center of rivet to edge of hole = diameter of rivet X IV2. 

Distance between rows of rivets 

= 2 X diam. of rivet or = [(diam. X 4) + 1] -*- 2, if chain, and 

V[(pitch X 11) + (diam. X 4)1 X (pitch + diam. X 4)' . 
= — ^ i j~ — if zigzag. 

Diagonal pitch = (pitch X 6 + diam. X 4) -f 10. 

Lloyd's. — T. S. of rivet bars, 26 to 30 tons; el. not less than 20% in 8". 
The material must stand bending to a curve, the inner radius of which is 



THE STRENGTH OF RIVETED JOINTS 



411 



not greater than 11/2 times the thickness of the plate, after having been 
uniformly heated to a low cherry-red, and quenched in water at 82° F. 

Rivets in double shear to have only 1.75 times the single section taken 
in the calculation instead of 2. The shearing strength of rivet steel to 
be taken at 85% of the T. S. of the material of shell plates. In any case 
where the strength of the longitudinal joint is satisfactorily shown by 
experiment to be greater than given by the formula, the actual strength 
may be taken in the calculation. 



Proportions of Riveted Joints. (Hartford S. B. Insp. and Ins. Co.) 

Single-riveted Girth Seams of Boilers. 



Thickness. 


1/4 


5 /l6 


3/8 


7/16 


1/2 


Diam. rivet-hole. 
Pitch 


3/4 H/I6 
2Vl6 21/16 
U/8 H/32 


13/16 3/4 
21/8 21/8 
17/32 U/8 


15/16 13/16 
23/ 8 21/8 
113/32 17/3 2 


1 15/16 
27/ie 23/s 
U/2 U3/32 


I 1/16 I 

21/2 21/2 
19/32 U/2 


Center to edge . . 



Double-riveted Lap Joints. 










1/4 


5/16 


3/8 


7/16 


1/2 








3/ 4 
27/8 
1 15/16 
U/8 
0.74 


13/16 
27/8 
1 15/16 
17/32 
0.72 


15 /l6 
31/ 4 
2 3/, 6 
1 13/32 
0.70 


1 

31/4 

23/16 

U/2 

0.70 


U/l6 


Pitch 


3.32 


Dist. bet. rows 


2.2 
1 19/32 
0.68 









Triple-riveted Lap Joints. 



Thickness 

Diam. rivet-hole. . 

Pitch 

Dist. bet. rows. . . . 
Inner row to edge 
Efficiency 



1/4 


5/16 


3/8 


7/16 


H/16 


3/ 4 


13/16 


15/16 


3 


31/8 


31/4 


33/4 


2 


2Vi6 


23/18 


21/2 


U/32 


U/8 


17/32 


1 13/32 


7/ 


0.76 


0.75 


0.75 



1 

315/ie 
25/s 
U/2 
0.75 



Triple-riveted Butl-slrap Joints. 



Thickness 

Diam. rivet-hole 

Pitch, inner rows. . . . 
Dist. bet. inner rows. 
Dist. outer to 2d row 
Edge to nearest row. 
Efficiency % 



5/16 


3/8 


7/16 


1/2 


9 /l6 


3/ 4 


13/16 


15/16 


1 


11/16 


31/8 


31/4 


3 3/8 


33/4 


37/s 


21/8 


2 3/ 16 


21/4 


23/8 


2 5/8 


23/s 


21/2 


23/4 


3 


3 3/! 6 


U/4 


17/32 


1 13/32 


U/2 


1 19/32 


88 (?) 


87.5 


86 


86.6 


85.4 



U/16 
37/ 8 
25/ 8 
3 3/16 
1 19/32 
84(?j 



The distance to the edge of the plate is from the center of rivet-holes. 



4.12 



RIVETED JOINTS. 



Pressure Required to Drive Hot Rivets. 

Philadelphia, give the following table (1897): 



-R. D. Wood & Co. 



Power to Dkive Rivets Hot. 



Size. 


Girder- 


Tank- 


Boiler- 


Size. 


Girder- 


Tank- 


Boiler- 


work. 


work. 


work. 


work. 


work. 


work. 


in. 


tons. 


tons. 


tons. 


in. 


tons. 


tons. 


tons. 


1/2 


9 


15 


20 


H/8 


38 


60 


75 


5/8 


12 


18 


25 


H/4 


45 


70 


100 


3/4 


15 


22 


33 


U/2 


60 


85 


125 


7/8 
1 


22 
30 


30 

45 


45 
60 


13/4 


75 


100 


150 



The above is based on the rivet passing through only two thicknesses of 
plate which together exceed the diameter of the rivet but little, if any. 

As the plate thickness increases the power required increases approxi- 
mately in proportion to the square root of the increase of thickness. Thus, 
if the total thickness of plate is four times the diameter of the rivet, we 
should require twice the power given above in order to thoroughly fill the 
rivet-holes and do good work. Double the thickness of plate would 
increase the necessary power about 40%. 

It takes about four or five times as much power to drive rivets cold as 
to drive them hot. Thus, a machine that will drive 3/ 4 -in. rivets hot will 
usually drive 3/ 8 -in. rivets cold (steel). Baldwin Locomotive Worka 
drive 1/2 -in. soft-iron rivets cold with 15 tons. 

Riveting Pressure Required for Bridge and Boiler Work. 

(Wilfred Lewis, Engineers' Club of Philadelphia, Nov., 1893.) 

A number of 3/ 8 _inch rivets were subjected to pressures between 10,000 
and 60,000 lbs. At 10,000 lbs. the rivet swelled and filled the hole with- 
out forming a head. At 20,000 lbs. the head was formed and the plates 
were slightly pinched. At 30,000 lbs. the rivet was well set. At 40,000 
lbs. the metal in the plate surrounding the rivet began to stretch, and the 
stretching became more and more apparent as the pressure was increased 
to 50,000 and 60,000 lbs. From these experiments the conclusion might 
be drawn that the pressure required for cold riveting was about 300,000 
lbs. per square inch of rivet section. In hot riveting, until recently there 
was never any call for a pressure exceeding 60,000 lbs., but now pressures 
as high as 150,000 lbs. are not uncommon, and even 300,000 lbs. have been 
contemplated as desirable. 

Pressure Required for Heading Cold Rivets. — Experiments made 
by the author in 1906 on 1/2 and 5/ 8 in. soft steel rivets showed that the 
pressure required to head a rivet cold, with a hemispherical heading die, 
was a function of the final or maximum diameter of the head. The 
metal began to flow and fill the hole at about 50,000 lbs. per sq. in. press- 
ure, but it hardened and increased its resistance as it flowed until it reached 
a maximum of about 100,000 lbs. per sq. in. of the maximum area of the 
head. 

Chemical and Physical Tests of Soft Steel Rivets. — Ten rivet 
bars and ten rivets selected from stock of the Champion Rivet Co., Cleve- 
land, O., were analyzed bv Oscar Textor, with results as follows: 

P. 0.008 to 0.027, av. 6.015; Mn, 0.31 to 0.69, av. 0.46; S, 0.023 to 
0.044, av. 0.033; Si, 0.001 to 0.008, av. 0.005: C, 0.06 to 0.19, av. 0.11. 
Only four of the 20 samples were over 0.14 C, and these were made for 
high strength. Ten bars and two rivets gave tensile strength, 46,735 to 
55,380, av. 52,195 lbs. per sq. in.; elastic limit, 31,350 to 43,150, av. 
35,954: elongation, bars only, 28 to 35, av. 31.9% in 8 ins.; reduction of 
area. 65.6%. Eight bars in single shear gave shearing strength 35,660 
to 50 190 av. 44,478 lbs. per sq. in.; seven bars in double shear gave 
39,170 to 53,900, av. 45,720 lbs. The shearing strength averaged 86.3% 
of the tensile strength. 



IRON AND STEEL. 



413 











5? L"^ 










o ^ 








« 








s 


cX! 


g o3^ 






-B 


H 


-3 mS 






S 


2 






s 


^ 


o 


ined 
ct p: 
shea 

ed st 




>> 






03 £ ~3 










3^ §12 

°.SSa 




3 -S 




oo 




tocS 


















Is 






S "S 2 § oi — 




S ° 


s 


O 


'btained by dir 
is from ores, as C 
Chenot, and ot] 
is irons. 

btained by indir 
is from cast iron, 
■hearth and pudd 




o 


1 

e 
1 


S 

o 
p 
o 

03 








' £ 






K^ 


^ 


° £ .SO « >>» 








C^ 


eala^lco 


£ 








a"3 & &«•- 








,n 


c 










g 






j 


. - c3 

.2 3 2« 








H 








a 








w 


) Cruci 
)Bessei 
and 
) Open 
stei 
) Mitis 




$ 


« 




CS C S 




03 










s 


§ 








03 O ^ 
_2^5 3 <» 












12 
'3 

33 


l 






03 






_q 03 c3 <U 

"3 c ^"3 




§ O 






:p£'§ ■ 




^£ 






o3^ ~ 






fc 


§°-.S 








O 


^0°M 








^Q 










o 




<! 








i^ 


o 


o 




O 


e 




o3 


a 


T3 
4) 


bJO 






g 


'-S • 








'3 


.2 >> 


.2 


.2 




O 


M"^ 


o 


.2 


CD 

B 

ct 


o 

w 


5 


cc 


> 



w 3 ft ,H^3 

CD OJ £ "^ M .So 

1 1 ! °m 

1 i i §t§i 

m » ■£ £-.3 >>> 

T3P, . CI Og^a 

O +^ pTI CD 



lp 

2^- 
"2^ 



P O £ a, 



.2o£ o ST!®-* 



III f S||l 



_ a 



60 2|, § i'3 

0) > g" . C CD' 

t 1- T 



S|5l 



cdx: oj _ 

S "^ '> ^ ~ ' «3 ^ to i^ 
'>co3^'a — "eS & ° 
5 3^^S SIS® 



! cud" 

c5-S 



- r- 

o S 3 a 3 



■c-3 o — 



t«H as 3 

fio,„§c 



bj^ 



££ 



= 12 > 2 






Tx.-cPcd'O >d°^ 

(^ o3 o3 • p O rj 



o.>^.2.E; = 
• w .-a-2-2 ^ Sf,a M 

«5o3C»o3'3^£J-ro- t; ' OT 

m .2 5 ££3,3 



414 



IRON AND STEEL. 



CAST IRON. 

The Manufacture of Cast Iron. — Pig iron is the name given to the 
crude form of iron as it is produced in the blast furnace. This furnace 
is a tall shaft, lined with fire brick, often as large as 100 ft. high and 20 ft. 
in diameter at its widest part, called the "bosh." The furnace is kept 
filled with alternate layers of fuel (coke, anthracite or charcoal), while a 
melting temperature is maintained at the bottom by a strong blast. 
The iron ore as it travels down the furnace is decarbonized by the carbon 
• monoxide gas produced by the incomplete combustion of the fuel, and as 
it travels farther, into a zone of higher temperature, it absorbs carbon 
and silicon. The phosphorus originally in the ore remains in the iron. 
The sulphur present in the ore and in the fuel may go into combination 
with the lime in the slag, or into the iron, depending on the constitution 
of the slag and on the temperature. The silica and alumina in the ore 
unite with the lime to form a fusible slag, which rests on the melted iron 
in the hearth. The iron is tapped from the furnace several times a day, 
while in large furnaces the slag is usually run off continuously. 

Grading of Pig Iron. — Pig iron is approximately giaded according 
to its fracture, the number of grades varying in different districts. In 
Eastern Pennsylvania the principal grades recognized are known as No. 
1 and 2 foundry, gray forge or No. 3, mottled or No. 4, and white or No. 
5. Intermediate grades are sometimes made, as No. 2 X, between No. 1 
and No. 2, and special names are given to irons more highly silicized than 
No. 1, as No. 1 X, silver-gray, and soft. Charcoal foundry pig iron is 
graded by numbers 1 to 5, but the quality is very different from the 
corresponding numbers in anthracite and coke pig. Southern coke pig 
iron is graded into ten or more grades. Grading by fracture is a fairly 
satisfactory method of grading irons made from uniform ore mixtures 
and fuel, but is unreliable as a means of determining quality of irons 
produced in different sections or from different ores. Grading by chemi- 
cal analysis, in the latter case, is the only satisfactory method. The 
following analyses of the five standard grades of northern foundry and 
mill pig irons are given by J. M. Hartman {Bull. I. & S. A., Feb., 1892): 





No. 1. 


No. 2. 


No. 3. 


No. 4. 


No.4B. 


No. 5. 




92.37 
3.52 
0.13 
2.44 
1.25 
0.02 
0.28 


92.31 
2.99 
0.37 
2.52 
1.08 
0.02 
0.72 


94.66 
2.50 
1.52 
0.72 
0.26 

trace 
0.34 


94.48 
2.02 
1.98 
0.56 
0.19 
0.08 
0.67 


94.08 
2.02 
1.43 
0.92 
0.04 
0.04 
2.02 


94.68 


Graphitic carbon 

Combined carbon 


0.41 




0.04 




0.02 




0.98 







Characteristics of These Irons. 

No. 1. Gray. — A large, dark, open-grain iron, softest of all the num- 
bers and used exclusively in the foundry. Tensile strength low. Elastic 
limit low. Fracture rough. Turns soft and tough. 

No. 2. Gray. — A mixed large and small dark grain, harder than No. 
1 iron, and used exclusively in the foundry. Tensile strength and elastic 
limit higher than No. 1. Fracture less rough than No. 1. Turns harder, 
less tough, and more brittle than No. 1. 

No. 3. Gray. — Small, gray, close grain, harder than No. 2 iron, used 
either in the rolling-mill or foundry. Tensile strength and elastic limit 
higher than No. 2. Turns hard, less tough, and more brittle than No. 2. 

No. 4. Mottled. — White background, dotted closely with small black 
spots of graphitic carbon; little or no grain. Used exclusively in the 
rolling-mill. Tensile strength and elastic limit lower than No. 3. Turns 
with difficulty; less tough and more brittle than No. 3. The manganese 
in the B pig iron replaces part of the combined carbon, making the iron 
harder and closing the grain, notwithstanding the lower combined carbon. 



CAST IRON. 415 

No. 5. White. — Smooth, white fracture, no grain, used exclusively in 
the rolling mill. Tensile strength and elastic limit much lower than No. 4. 
Too hard to turn and more brittle than No. 4. 

Southern pig irons are graded as follows, beginning with the highest in 
silicon: Nos. 1 and 2 silvery, Nos. 1 and 2 soft, all containing over 3% 
of silicon; Nos. 1, 2, and 3 foundry, respectively about 2.75%, 2.5% and 
2% silicon; No. 1 mill, or " foundry forge;" No. 2 mill, or gray forge; 
mottled; white. 

Chemistry of Cast Iron. — Abbreviations, TC, total carbon; GC, 
graphitic carbon; CC, combined carbon. Numerous researches have been 
made and many papers written, especially between the years 1895 and 
1908, on the relation of the physical properties to the chemical constitu- 
tion of cast iron. Much remains to be learned on the subject, but the 
following is a brief summary of prevailing opinions. 

Carbon. — Carbon exists in three states in cast iron: 1, Combined 
carbon, which has the property of making iron white and hard; 2, Graphi- 
tic carbon or graphite, which is not alloyed with the iron, but exists in it 
as a separate body, since it may be removed from the fractured surface 
of pig iron by a brush; 3, a third form, called by Ledebur "tempering 
graphite carbon," into which combined carbon may be changed by pro- 
longed heating. The relative percentages in which GC and CC may 
be found in cast iron differ with the rate of cooling from the liquid 
state, so that in a large casting, cooled slowly, nearly all the C may 
be GC, while in a small casting from the same ladle cooled quickly, 
it may be nearly all CC. The total C in cast iron usually is between 
3 and 4%. 

Combined Carbon. — CC increases hardness, brittleness and shrink- 
age. Up to about 1% it increases strength, then decreases it. The 
presence of S tends to increase the CC in a casting, while Si tends to 
change CC to GC. 

Graphite. — GC in a casting causes softness and weakness when 
above 3%; softness and strength when added to irons low in GC and over 
1% in CC. It increases with the size of the casting, with slow cooling, 
or rather with holding a long time in the mold at a high temperature. 

Silicon. — Si acts as a softener by counteracting the hardening effect 
of S, and by changing CC into GC, changes white iron to gray, increases 
fluidity and lessens shrinkage. When added to hard brittle iron, high in 
CC, it may increase strength by removing hard brittleness, but when it 
reduces the CC to 1% and less it weakens the iron. Above 3.5 or 4% it 
changes the fracture to silvery gray, and the iron becomes brittle and 
weak. The softening effect of Si is modified by S and Mn. 

Sulphur. — S causes the C to take the form of CC, increases hardness, 
brittleness, and shrinkage, and also has a weakening effect of its own. 
Above about 0.1% it makes iron very weak and brittle. When Si is 
below 1%, even 0.06 S makes the iron dangerously brittle. 

Manganese. — Mnin small amount, less than 0.5%, counteracts the 
hardening influence of S; in larger amounts it changes GC into CC, and 
acts as a hardener. Above 2% it makes the iron very hard. Mn com- 
bines with iron in almost all proportions. When it is from 10 to 30% 
the alloy is called spiegeleisen, from the German word for mirror, and has 
large, bright crystalline faces. Above 50% it is known as ferro-man- 
ganese. Mn has the property of increasing the solubility of iron for 
carbon; ordinary pig iron containing rarely over 4.2% C, while spiegel- 
eisen may have 5%, and ferro-manganese as high as 6%,. Cast iron with 
1% Mn is used in making chilled rolls, in which a hard chill is desired. 
When softness is required in castings, Mn over 0.4% has to be avoided. 
Mn increases shrinkage. It also decreases the magnetism of iron. Iron 
with 25% Mn loses all its magnetism. It therefore has to be avoided in 
castings for dynamo fields and other pieces of electrical machinery. 

Phosphorus. — P increases fluidity, and is therefore valuable for thin 
and ornamental castings in which strength is not needed. It increases 
softness and decreases shrinkage. Below 0.7% it does not appear to 
decrease strength, but above 1% it is a weakener. 

Copper. — Cu is found in pig irons made from ores containing Cu. 
From 0.1 to 1% it closes the grain of cast iron, but does not appreciably 
cause brittleness. 



416 IRON AND STEEL. 

Aluminum. — Al from 0.2 to 1.0% (added to the ladle in the form of 
a FeAl alloy) increases the softness and strength of white iron; added to 
gray iron it softens and weakens it. 

Titanium. — An addition of 2 to 3% of a TiFe alloy containing 10% 
Ti caused an increase of 20 to 30% in strength of cast iron. A. J. Rossi, 
A.I.M.E., xxxiii, 194. Ti reacts with any O or N present in the metal 
and thus purifies it, and does not remain in the metal. After enough 
Ti for deoxidation has been added, further additions have no effect. 
R. Moldenke, A.I.M.E., xxxv, 153. 

Vanadium. — Va to the extent of 0.15% added to the ladle in the form 
of a ground FeVa alloy greatly increases the strength of cast iron. It 
acts as a deoxidizer and also by alloying. 

Oxide of Ikon. — The cause of the difference in strength of charcoal 
and coke irons of identical composition is believed by Dr. Moldenke 
(A.I.M.E., xxxi, 988) to be the degree of oxidation to which they have 
been subjected in making or remelting. Since Mn, Ti, and Va all act as 
deoxidizers, it should be possible by additions to the ladle of alloys of 
FeMn, FeVa, or FeTi, to make the two irons of equal strength. 

Temper Carbon. The main part of the C in white cast iron is the carbide 
Fe 3 C. This breaks down under annealing to what Ledebur calls "temper 
carbon," and in annealing in oxides, as in making malleable iron, it is 
oxidized to CO. The C remaining in the casting at the end of the process 
is nearly all GC, since the latter is very slowly oxidized. 

Influence of Various Elements on Cast Iron. — W. S. Anderson, 
Castings, Sept., 1908, gives the following: 

Fluidity, increased by Si, P, G.C. Reduced by S, C.C. 

Shrinkage, increased by S, Mn, C.C. Reduced by Si, P, G.C. 

Strength, increased by Mn, C.C. Reduced by Si, S, P, G.C. 

Hardness, increased by S, Mn, C.C. Reduced by Si, G.C. 

Chill, increased by S, Mn, C.C. Reduced by Si, P, G.C. 

Microscopic Constituents. (See also Metallography, under Steel.) 

Ferrite, iron free from carbon. It is found in miid steel in small amounts 
in gray cast iron, and in malleable cast iron. 

Cementite, Fe 3 C. Fe with 6.67% C. Harder than hardened steel. 
Hardness U on the mineralogical scale. Found in high C steel, and in 
white and mottled pig. 

Pearlite, a compound made up of alternate laminee of ferrite and cemen- 
tite, in the ratio of 7 ferrite to 1 cementite, and containing therefore 
0.83% C. Found in iron and steel cooled very slowly from a high temper- 
ature. In steel of 0.83 C it composes the entire mass. Steels lower or 
higher than 0.83 C contain pearlite mixed with ferrite or with cementite 
respectively. 

Martensite, the hardening component of steel. Found in iron and 
steel quenched above the recalescence point, and in tempered steel. It 
forms the entire structure of 0.83 C steel quenched. 

Analyses of Cast Iron. (Notes of the table on page 417.) 

1 to 7. R. Moldenke, Pittsbg. F'drymen's Assn., 1898; 1 to 5, pig irons; 
6, white iron cast in chills; 7, gray iron cast in sand from the same ladle. 
The temperatures were taken with a Le Chatelier pyrometer. For 
comparison, steel, 1.18 C, melted at 2450° F.; silico-spiegel, 12.30 Si, 
16.98 Mn, at 2190°; ferro-silicon, 12.01 Si, 2.17 CC, at 2040°; ferro- 
tungsten, 39.02 W, at 2280°; ferro-manganese, 81.4- Mn, at 2255°; ferro- 
chrome, 62.7 Cr, at 2400°; ditto, 5.4 Cr., at 2180°. 

8. Gray foundry Swedish pig, very strong. 9. Pig to be used in mix- 
tures of gray pig and scrap, for castings requiring a hard close grain, 
machining to a fine surface, and resisting wear. 8 to 15, from paper by 
F. M. Thomas, Castings, July, 1908. 

16. Specification by J. E. Johnston, Jr., Am. Mack., Oct. 15, 1903. 
The results were excellent. Si might have been 0.75 to 1.25 if S had 
been kept below 0.035. 

17 to 22. G. R. Henderson, Trans. A.S.M.E., vol. xx. The chill is to 
be measured in a test bar 2 X 2 X 24 in., the chill piece being so placed 
as to form part of one side of the mold. The actual depth of white iron 
will -be measured. 



CAST IRON. 



417 



Analyses of Cast Iron. 

(Abbreviations, TC, total carbon; GC, graphitic carbon; CC, combined 
carbon.) 



No. 


TC 


GC 


CC 


Silicon. 


Man- 
ganese. 


Phos- 
phorus . 


Sul- 
phur. 




1 


3.98 


0.39 


3.59 


0.38 


0.13 


0.20 


0.038 


Melts at 2048° F. 


2 


3 78 


1.76 


2.01 


0.69 


0.44 


0.53 


0.031 


Melts at 2156° F. 


3 


3.88 


2.60 


1.28 


1.52 


0.49 


0.45 


0.035 


Melts at 221 l°F. 


4 


4.03 


3.47 


0.56 


2.01 


0.49 


0.39 


0.034 


Melts at 2248° F. 


5 


3.56 


3.43 


0.13 


2.40 


0.90 


0.08 


0.032 


Melts at 2280° F. 


6 


4.39 


0.13 


4.26 


0.65 


0.40 


0.25 


0.038 


Melts at 2000° F. 


7 


4 45 


2 99 


1.46 


0.67 


0.41 


0.26 


0.039 


Melts at 2237° F. 


8 


3 . 30 


2.80 


0.50 


2.00 


0.60 


0.08 


0.03 


Swedish char- 
coal pig. 


9 




2.25-2.5 


0.6-0.8 


0.8-1.2 


0.4-0.8 


0.15-0.4 




For engine cylin- 
ders. 


10 


3 . 40 


3.40 


trace 


2.90 


0.50 


1.65 


0.04 


English, high P. 

No. 1. 
English, high P. 

No. 3. 
For thin orna- 


11 


3.40 


3.20 


0.20 


2.60 


0.50 


1.58 


0.04 


12 




3.2-3.6 


0.1-0.15 


2.5-2.8 


up to 


1.3-1.5 


.03-. 04 












1.0 






mental work. 


13 




Y. 0-3. 2 


0.4-0.5 


2-2.3 


up to 
1.0 


1-1.3 


.06-. 08 


For medium size 
castings. 


14 




2.8-3.0 


0.4-0.6 


1.2-1.5 


0.6-0.9 


0.4-0.6 


.06-. 08 


Heavy machin- 
ery castings. 


15 




2.5-2.8 


0.6-0.8 


1.0-1.3 


0.5-0.7 


0.4-0.7 


.08-. 12 


Cylinders and 
hydraulic work. 


16 








1.2-1.8 


0.4-1.0 


0.4-0.7 


to .06 


For' hydraulic 










cylinders. 


17 




2.7-3.0 


0.5-0.8 


0.5-0.7 


0.3-0.5 


0.3-0.5 


.05-. 07 


For car wheels. 


18 




2.6-3.1 


0.6-1.0 


0.6-0.7 


0.1-0.3 


0.3-0.5 


.05-. 08 


For car wheels. 


19 




2.5-3.0 


0.4-0.9 


1.3-1.7 


0.5-1.0 


0.3-0.4 


.03 max 


Charcoal pig. 1/4 
in. chill. 


20 




2.3-2.7 


0.5-1.0 


1.0-1.5 


0.5-1.0 


0.3 0.4 


.03 " 


Ditto 1/2 in. chill. 


21 




2.0-2.5 


0.8-1.2 


0.8-1.2 


0.5-1.0 


0.3-0.4 


.035 " 


Ditto 3/4 in. chill. 


22 




1.8-2.2 


0.9-1.4 


0.5-1.0 


0.3-0.7 


0.3-0.4 


.035 " 


Ditto 1 in. chill. 


23 


3! 87 


3.44 


0.43 


1.67 


0.29 


0.095 


0.032 


Series A. Am. 
F' dm en's Assn. 


24 


3.82 


3.23 


0.59 


1.95 


0.39 


0.405 


0.042 


Series B. ditto. 


25 


3.84 


3.52 


0.32 


2.04 


0.39 


0.578 


0.044 


Series C. ditto. 


26 




2.8-3.2 


0.5-0.7 


1.3-1.5 


0.3-0.6 


0.5-0.8 


.06-. 10 


For locomotive 
cylinders. 


27 




2.3-2.4 


0.8-1.0 


1.8-2.0 


0.8-1.0 


0.6-0.8 


.06-. 10 


" Semi-steel." 


28 




2.4-2.6 


0.8-1.0 


0.9-1.0 


0.6-0.7 


0.1-0.3 


.04-. 06 


li Semi-steel." 


29 


4J3 


3.08 


1.25 


0.73 


0.44 


0.43 


0.08 


A strong car 
wheel, Cu, 0.03. 


30 


3.17 


2.72 


0.45 


1.99 


0.39 


0.65 


0.13' 


Automobile cyl- 
inders. 


31 


3.34 


2.57 


0.77 


1.89 


0.39 


0.70 


0.09 


Ditto. 


32 


3.5 


2.9 


0.6 


0.7 


0.4 


5 


0.08 


Good car wheel. 


33 


3.55 


3.0 


0.55 


2.75 


2.39 


0.86 


0.014 


Scotch irons. 


34 








3.10 


1.80 


0.90 




" Am. Scotch " 










Ohio irons. 


35 








0.75-1.5 


to 0.6 


to 0:22 


to 0.04 


Pig for malle- 










able castings. 


36 








2-25 
1.2-1.5 


to 0.7 
0.5-0.8 


to 0.7 
0.35-0.6 


to 0.15 
to 0.09 


Brake-shoes. 


37 








Hard iron for 


















heavy work. 


38 








1.5-2 


0.5-0.8 


J. 35-0. 6 


to 0.08 


Medium iron for 










general work. 


39 








2.2-2.8 


to 0.7 


to 0.7 


to 0.085 


Soft iron cast'gs 











418 IRON AND STEEL. 

23 to 25. Series of bars tested by a committee of the association. 
See results of tests on page 419. Series A, soft Bessemer mixture; B, 
dynamo-frame iron; C, light machinery iron. Samples for analysis were 
taken from the 1-in. square dry sand bars. 

26. Specifications by a committee of the Am. Ry. Mast. Mechs. Assn., 
1906. T.S., 25,000; transverse test, 3000 lb. on 11/4-in. round bar, 12 in. 
between supports; deflection, 0.1 in. minimum; stirinkage, 1/8 in. max. 
27, soft "semi-steel;" 28, harder do. They approach air-furnace iron 
in most respects, and excel it in strength; test bars 2 XI X 24 in. of the 
low Si semi-steel showing 2800 to 3000 lb. transverse strength, with 
7/i 6 in. deflection. M. B. Smith, Eng. Digest, Aug., 1908. 29. J. M. 
Hartman, Bull. I. & S. Assn., Feb., 1892. The chill was very hard, 1/4 in. 
deep at root of flange, 1/2 in. deep on tread. 30, 31. Strong and shock- 
resisting. T.S., 38,000. Castings, June, 1908. 32. Com. of A.S.T.M., 
1905, Proc, v. 65. Successful wheels varying quite considerably from 
these figures may be made. 33, 34. C. A. Meissner, Iron Age, 1890. 
Average of several. 35. R. Moldenke, A.S.M.E., 1908. 36-39. J. W. 
Keep, A.S.M.E., 1907. 

A Chilling Iron is one which when cooled slowly has a gray fracture, 
but when cast in a mold one side of which is a thick mass of cast-iron, 
called a chill, the fractured surface shows white iron for some depth on 
the side that was rapidly cooled by the chill. See Table Nos. 19-22. 

Specifications for Castings, recommended by a committee of the 
A.S.T.M., 1908. S in gray iron (-listings, light, not over 0.08; medium, 
not over 0.10; heavy, not over 0.12. Alight casting is one having no 
section over 1/2 in. thick, a heavy casting one having no section less than 
2 in. thick, and a medium casting one not included in the classification of 
light or heavv. The transverse strength of the arbitration bar shall not 
be under 2500 lb. for light, 2900 lb. for medium, and 3300 lb. for heavy 
castings; in no case shall the deflection be under 0.10 in. When a ten- 
sile test is specified this shall run not less than 18,000 lb. per sq. in. for 
light, 21,000 lb. for medium, and 24,000 lb. for heavy castings. 

The " arbitration bar" is 1 1/4 in. diam., 15 in. long, cast in a thoroughly 
dried and cold sand mold. The transverse test is made with supports 
12 in. apart. The moduli of rupture corresponding to the figures for 
transverse strength are respectively 39115, 45373, and 51632, being the 
product of the figures given and the constant 15.646, the factor for R/P 
for a 11/4-in. round bar 12 in. between supports.* The standard form of 
tensile test piece is 0.8 in. diam., 1 in. long between shoulders, with a 
fillet 7/32 in. radius, and ends 1 in. long, 11/4 in. diam., cut with standard 
thread, to fit the holders of the testing machine. 

Specifications by J. W. Keep, A.S.M.E., 1907. See Table of Analyses, 
Nos. 37-39, page 417. Transverse test, lxl x 12-in. bar, hard iron castings. 
No. 37, 2400 to 2600 lb.; tensile test of same bar, 22,000 to 25,000 lb. 
No. 38, medium, transverse, 2200 to 2400; tensile, 20,000 to 23,000. 
No. 39, soft, transverse, 2000 to 2200; tensile, 18,000 to 20,000. 

Standard Specifications for Foundry Pig Iron. 

(American Foundrymen's Association, May, 1909.) 

Analysis. — It is recommended that found-y pig be bought by analysis. 

Sampling. — Each carload or its equivalent shall be considered as a 
Jinit. One pig of machine-cast, or one-half pig of sand-cast iron shall be 
iaken to every four tons in the car, and shall be so chosen from different 
parts of the car as to represent as nearly as possible the average quality 
of the iron. Drillings shall be taken so as to fairly represent the composi- 
tion of the pig as cast. An equal quantity of the drillings from each pig 
shall be thoroughly mixed to make up the sample for analysis. 

Percentage of Elements. — When the elements are specified the fol- 
lowing percentages and variations shall be used. Opposite each percent- 
age of the different elements a syllable has been affixed so that buyers, 
by combining these syllables, can form a code word to be used in 
telegraphing. 

* Formula, ViPl = RI/c; see page 283. 7=1/64 n-0 4 ; c=l/2tZ; d = H/4in.; 
1 = 12 in. 







CAST IRON. 






419 


Silicon 


Sulphur 
(max.) Code 


Total Carbon 
(min J Code 


Manganese 
% Code ' 


Phosp 


HORUS 




% 


Code 


% Code 


0.04 Sa 


3.00 Ca 


0.20 Ma 


0.20 


Pa 


1 . 00 La 


0.05 Se 


3.20 Ce 


0.40 Me 


0.40 


Pe 


1 . 50 Le 


0.06 Si 


3.40 Ci 


0.60 Mi 


0.60 


Pi 


2.00 Li 


0.07 So 


3.60 Co 


0.80 Mo 


0.80 


Po 


2.50 Lo 


. 08 Su 


3.80 Cu 


1.00 Mu 


1.00 


Pu 


3.00 Lu 


0.09 Sy 
0.10 Sh 




1 . 25 My 
1 . 50 Mh 


1.25 


a 






1.50 



Percentages of any element specified one-half way between the above 
shall be designated by the addition of the letter x to the next lower symbol, 
thus Lex means 1.75 Si. 

Allowed variation: Si, 0.25; P, 0.20; Mn, 0.20. The percentages of P 
and Mn may be used as maximum or minimum figures when so specified. 

Example: — Le-sa-pi-me represents 1.50 Si, 0.04 S, 0.60 P, 0.40 Mn. 

Base or Quoting Price.— For market quotations an iron of 2.00 Si 
(with variation 0.25 either way) and S 0.05 (,max.) shall be taken as the 
base. The following table may be filled out, and become a part of a con- 
tract; "B," or Base, represents the price agreed upon for a p g of 2.00 Si 
and under 0.05 S. "C" is a constant differential to be determined at 
the time the contract is made. 

Sul-, Silicon * 

phur 3.25 3.00 2.75 2.50 2.25 2.00 1.75 1.50 1.25 1.00 
0.04 B + 6C B + 5C B + 4C B + 3C B + 2C B + C B B-1C B-2C B-3C 

0.05 B + 5C B + 4C B + 3C B + 2C B + 1C B B-1C B-2C B-3C B-4C 

0.03 B + 4C B + 3C B + 2C B + 1C B B-1C B-2C B-3C B-4C B-5C 

0.07 B + 3C B + 2C B + 1C B B-1C B-2C B-3C B-4C B-5C B-6C 

0.08 B + 2C B + 1C B B-1C B-2C B-3C B-4C B-5C B-6C B-7C 

0.09 B + 1C B B-1C B-2C B-3C B-4C B-5C B-6C B-7C B-8C 

0.10 B B-1C B-2C B-3C B-4C B-5C B-6C B-7C B-8C B-9C 

Specifications for Metal for Cast-iron Pipe.— Proc. A.S.T.M ., 1905, 
A.I.M.E., xxxv, 166. Specimen bars 2 in. wide x 1 in. thick x 24 in. 
between supports, loaded in the center, for pipes 12 in. or less in diam. 
shall support 1900 lb. and show a deflection of not less than 0.30 in, 
before breaking. For pipes larger than 12 in., 2000 lb. and 0.32 in. 
The corresponding moduli of rupture are respectivelv 34,200 and 36,000 
Vo. Four grades of pig are specified: No. 1, Si, 2.75; S, 0.035. No 2. 
Si, 2.25; S, 0.045. No. 3, Si, 1.75; S, 0.055. No. 4, Si, 1.25; S, 0.065. A 
variation of 10% of the Si either way, and of 0.01 in the S above the 
standard, is allowed. 



Tensile Tests of Cast-iron Bars. 

(American Foundrymen's Association, 1899.) 



Square Bars. 



Round Bars. 



Size, in... 
(A)g,c. 
' g. m. 
" d. s.. 
" d. m. 
(B)g.c. 
g. m. 
" d. c 
d. m. 



(C) i 



d. c. . 
d. m. 



0.5x0.5 
15,900 



14,600 
'17,100 



16,300 
17*766 



13,600 
15,800 
14,700 



1x1 
13,900 
15,400 
12,900 
13,800 
15,200 
17,600 
15,100 
18,400 
16,000 
18,500 
16,000 
17,100 
16,100 
15,500 
14,800 
16,800 



1.5x1.5 
12,100 
12,900 
12,300 
13,400 
12,900 
15,000 
13,300 
15,000 
12,500 
15,100 
12,200 
14,100 
13,400 
13,400 
12,500 
14,200 



2x2 
10,600 
10,900 

9,800 
12,100 
11,500 
11,800 
11,100 
12,100 
11,100 
11,700 
11,300 

9,800 
11,300 
11,000 
10,900 
11,400 



0.56 
16,000 



14,300 
'l 6,566 ' 



16,700 
17,800 



13,400 
15,800 
16,300 



1.13 
13,800 
13,800 
13,700 
13,600 
15,900 
19,000 
16,200 
16,900 
15,900 
17,400 
15,900 
17,700 
16,000 
15,700 
15,200 
16,400 



1.69 
12,000 
13,500 
11,700 
13,200 
13,100 
15,400 
13,200 
15,100 
14,200 
15,000 
14,000 
15,900 
13,900 
13,800 
13,000 
14,600 



2.15 
11,000 
12,200 
10,500 
10,600 
1 1 ,400 
12,500 
11,000 
13,100 
12,000 
11,600 
11,600 
10,400 
11,600 
11,200 
11,200 
11,700 



420 



IRON AND STEEL. 



Transverse Tests of 


Dast-Iron Bars. Modulus of Rupture. 


Size * 


0.5x0.5 


1x1 


1.5x1.5 


2x2 


2.5x2.5 


3x3 


3.5x3.5 


4x4 


Diam. f 


0.56 


1.13 


1.69 


2.15 


2.82 


3.38 


3.95 


4.51 


(A) r.d.c 


31,100 


33,400 


33,900 


31,700 


27,000 


26,600 


23,400 


22,600 


" r. d.m. . . 




27,800 


38,000 


32,300 


28,000 


28,600 


22,400 


22,900 


(B) s.g.c... 


44,400 


39,100 


39,500 


33,900 


31,900 


29,700 


27,200 


27,600 


" s.g.m... 




37,400 


40,300 


34,700 


35,800 


33,500 


30,100 


27,100 


" s.d.c... 


35,500 


38,300 


34,000 


32,900 


31,900 


30,200 


29,300 


25,900 


" s.d.m. .. 




30,200 


36,200 


33,300 


35,200 


30,900 


28,100 


25,800 


" r.g.c. . .. 


36,400 


46,200 


41,200 


41,400 


41,300 


36,300 


34,800 


31,000 


' r.g.m... 




40,000 


44,800 


38,800 


37,100 


32,900 


32,700 


32,300 


" r d. c. . . . 


37,800 


49,000 


44,300 


39,200 


40,700 


31,800 


35,300 


31,100 


r. d.m. 




39,100 


37,800 


37,700 


33,900 


32,800 


32,000 


31,200 


(C) s.g.c... 


51,800 


39,200 


33,600 


37,900 


32,200 


31,100 


31,300 


29,200 


" s.g. m. .. 






40,200 


37,000 


33,700 


33,300 


32,300 


27,900 


" s. d. c. ... 


48,000 


39,100 


38,800 


35,100 


31,200 


29,300 


29,300 


27,800 


" s. d. m. 






38,900 


35,400 


33,500 


32,700 


29,100 


25,500 


" r. g. c. . . . 


62,800 


48,500 


39,000 


44,500 


41,400 


41,200 


35,000 


32,300 


" r. g. m. . . 




55,700 


49,200 


42,900 


41,500 


36,500 


34,100 


36,000 


" r. d. c. . . . 


53,000 


50,400 


44,000 


40,200 


39,500 


37,800 


35,200 


32,100 


" r. d.m. . . 




47,900 


51,300 


38,000 


38,900 


36,300 


32,200 


33,500 


Av. (B)s. ... 


39,900 


36,200 


37,500 


33,700 


33,700 


31,100 


28,700 


26,600 


" r. . . . 


37,100 


43,600 


42,000 


39,300 


38,200 


33,400 


33,700 


31,400 


" (C)s 


49,900 


39,100 


37,900 


36,300 


32,600 


31,600 


30,500 


27,600 


" r 


57,900 


50,600 


45,900 


41,400 


40,400 


37,900 


34,100 


33,200 


"(B)&(C)g. 


48,800 


43,100 


41,000 


38,800 


36,800 


33,900 


32,200 


30,400 


' d. 


43,300 


41,600 


40,700 


36,500 


35,600 


32,700 


31,300 


30,400 


Gen'l av 


46,100 


42,400 


40,800 


37,700 


36,200 


33,400 


31,700 


29,900 


Equiv. load. . 


320 


2356 


7650 


16,756 


31,424- 


50,100 


75,516 


106,311 



* Size of square bars as cast, in. t Diam. of round bars as cast, in. 
Compression Tests of Cast-iron Bars. 



Size, in.. . 

(A) (1)... 

(2>... 


0.5x0.5 
29,570 


1x1 
20,010 
21,990 


1.5x1.5 
17,180 
17,920 
17,180 


2x2 
13,810 
13,750 
13,880 


2.5x2.5 
10,950 
12,040 
11,430 
10,950 
15,060 
18,270 
15,940 

'17,840 
19,800 
18,050 


3x3 
9,830 
11,200 
10,270 
10,430 
13,790 
17,000 
14,410 
13,900 
15,950 
18,170 
16,850 
16,040 


3.5x3.5 
9,350 
10,770 
9,830 
9,540 
13,160 
15,970 
15,200 
13,560 
15,880 
17,100 
16,510 
16,080 


4x4 
9,100 
10,340 


" (3)... 




9,950 


" (4). 






9,570 


(B) (I)... 

" (2)... 

(3)... 


. 38,360 


23,000 
12,440 


20,980 
24,820 
20,980 


18,130 
21,640 
18,740 
15,060 
18,010 
21,750 
19,340 
17,840 


12,430 
16,140 
13,950 


" (4)... 






13,760 


(C) (0... 
" (2)... 


38,360 


24,890 
27,900 


20,750 
22,060 
20,750 


14,220 
16,410 


" (3)... 




15 250 


'* (4)... 






14,880 



Notes on the Tables of Tests. — The machined bars were cut to 
the next size smaller than the size they were cast. The transverse bars 
were 12in. long between supports. (A), (B), (C), three qualities of iron; 
for analyses see page 417; r, round bars; s, square bars; <7, cast in dry sand; 
g, cast in green sand; r, bar tested as cast; m, bar machined to size. The 
general average (next to last line of the first table) is the average of the six 
lines preceding. The equivalent load (last line) is the calculated total 
load that would break a square bar whose modulus of rupture is that 
of the general average. 

Compression Tests. —The figures given are the crushing strengths, in 
pounds, of i in. cubes cut from the bars. Multiply by 4 to obtain lbs. 
per sq. in. (1) Cube cut from the middle of the bar; (2) first J in. from 
edge; (3) second § in. from edge; (4) third \ in from edge- 
Some Tests of Cast Iron. (G. Lanza, Trans. A.S.M.E., x, 187.) — 
The chemical analyses were as follows: Gun iron: TC, 3.51; GC, 2.80; 
S, 0.133; P, 0.155; Si, 1.140. Common iron: S, 0.173; P, 0.413; Si, 1.89. 
The test specimens were 26 in. long; those tested with the skin on being 
very nearly 1 in. square, and those tested with the skin removed being 
cast nearly 11/4 in. square, and afterwards planed down to 1 in. square. 



CAST IKON. 421 

Tensile Elastic Modulus 
Strength. Limit. of 

Elasticity. 
Unplaned common. .20,200 to 23,000 T.S. Av. = 22,066 6,500 13,194.233 

Planed common 20,300 to 20,800 " " =20,520 5,833 11,943,953 

Unplaned gun 27,000 to 28,775 " " =28,175 11,000 16,130,300 

Planed gun 29,500 to 31,000 " " =30,500 8,500 15,932,880 

The elastic limit is not clearly defined in cast iron, the elongations increas- 
ing faster than the increase of the loads from the beginning of the test. 
The modulus of elasticity is therefore variable, decreasing as the loads 
increase. 

The Strength of Cast Iron depends on many other things besides 
its chemical composition. Among them are the size and shape of the 
casting, the temperature at which the metal is poured, and the rapidity of 
cooling. Internal stresses are apt to be induced by rapid cooling, and 
slow cooling tends to cause segregation of the chemical constituents and 
opening of the grain of the metal, making it weak. The author recom- 
mends that in making experiments on the strength of cast iron, bars of 
several different sizes, such as 1/2, 1, IV2, and 2 in. square (or round), 
should be taken, and the results compared. Tests of bars of one size 
only do not furnish a satisfactory criterion of the quality of the iron of 
which they are made. Trans. A.I.M.E., xxvi, 1017. 

Theory of the Relation of Strength to Chemical Constitution. — 
J. E. Johnston, Jr. (Am. Mach., April 5 and 12, 1900), and H. M. Howe 
(Trans. A.I.M.E., 1901) have presented a theory to explain the variation 
in strength of cast iron with the variation in combined carbon. It is 
that cast iron is steel of CC ranging from to 4%, with particles of graph- 
ite, which have no strength, enmeshed with it. The strength of the cast 
iron therefore is that of the steel or graphiteless iron containing the same 
percentage of CC, weakened in some proportion to the percentage of GC. 
The tensile strength of steel ranges approximately from 40,000 lb. per 
sq. in. withO C to 125,0001b. with 1.20 C. With higher C it rapidlv becomes 
weak and brittle. White cast iron with 3% CC is about 30,000 T.S., 
and with 4% about 18,000. The amount of weakening due to GC is not 
known, but by making a few assumptions we may construct a table of 
hypothetical strengths of different compositions, with which results of 
actual tests may be compared. Suppose the strength of the steel-white 
cast-iron series is as given below for different percentages of CC, that 
6.25% GC entirely destroys the strength, and that the weakening effect 
of other percentages is proportional to the ratio of the square root of that 
percentage to the square root of 6.25, that the TC. in two irons is respec- 
tively 3% and 4%, then we have the following: 
Per cent CC. 0.2 0.4 0.6 0.8 1.0 1.2 1.5 2.0 2.5 3 3.5 4 

Steel, T.S 40 60 80 100 110 120 125 110 60 40 30 22 18 

Cast iron, 4% 

TC 8 13.2 19.2 26 31.2 37 41.5 40.5 26 20.7 18 15.8 18 

Cast iron, 3% 

TC 15.4 19.9 28.5 38 42.9 52.1 58 56.1 36 28.7 30 

The figures for strength are in thousands of pounds per sq. in. The 
table is calculated as follows: Take 0.6 CC; with 4% TC, this leaves 
3.4 GC, and with 3% TC, 2.4 GC The sq. root of 3.4 is 1.9, and of 2.4 is 
1.55. The ratio of these to V6.25 is respectively 74 and 62%, which 
subtracted from 100 leave 26 and 38% as the percentage of strength of 
the 0.6 C steel remaining after the effect of the GC is deducted. The 
table indicates that strength is increased as total C is diminished, and this 
agrees with general experience. 

Relation of Strength to Size of Bar as Cast. — If it is desired that a 
test bar shall fairly represent a casting made from the same iron, then 
the dimensions of the bar as cast should correspond to the dimensions of 
the casting, so as to have about the same ratio of cooling surface to 
volume that the casting has. If the test bar is to represent the strength 
of a plate, it should be cut from the plate itself if possible or else cut 
from a cylindrical shell made of considerable diameter and of a thickness 
equal to that of the casting. If the test is for distinguishing the quality 
of the iron, then at least two test bars should be cast, one say 1/2 or 5/ 8 in. 
and one say 2 or 21/2 in. diameter, in order to show the effect of rapid 
and slow cooling. 



422 



IRON AND STEEL. 



In 1904 the author made some tests of four bars of " semi-steel " adver- 
tised to have a strength of over 30,000 lb. per sq. in. The bars were cast 
1/2, 1, 2, and 3 in. diam., and turned to 0.46, 0.69, 1.6, and 1.85 in. respec- 
tively. The results of transverse and tensile tests were: 

Mod. of rupture. . 1/2 in., 100.000; 1 in., 61,613; 2 in., 67,619; 3 in., 58,543 
T.S. per sq. in... " 38,510; " 37,005; " 25,685; " 20,375 

The 1/2-in. piece was so hard that it could not be turned in a lathe and 
had to be ground. 

Influence of Length of Bar upon the Modulus of Rupture. — 

(R. Moldenke, Jour. Am. Foundry men's Assn., Sept., 1899.) Seven 
sets, each of five 2-in. square bars, made of a heavy machinery mixture, 
and cast on end, were broken transversely, the distance between sup- 
ports ranging from 6 to 16 ins. The average results were: 
Dist. bet. supports, ins.... 6 8 10 12 14 16 

Modulus of rupture 40,000 39,000 35,600 37,000 36,000 34,400 

The 10-in. bar in six out of seven cases gave a lower result than the 
12-in. It appears that the ordinary formulas used in calculating the 
cross breaking strength of beams are not only incorrect for cast iron, on 
account of the chemical differences in the iron itself when in different 
cross sections, but that with the cross sections identical the distance 
between the supports must be specially provided for by suitable con- 
stants in whatever formulae may be developed. As seen from the above 
results, the doubling of the distance between supports means a drop in 
the modulus of rupture in the same sized bar of nearly 10 per cent. 

Strength in Relation to Silicon and Cross-section. — In castings 
one half-inch square in section the strength increases as silicon increases 
from 1.00 to 3.50; in castings 1 in. square in section the strength is practi- 
cally independent of silicon, while in larger castings the strength decreases 
as silicon increases. 

The following table shows values taken from Mr. Keep's curves of the 
approximate transverse strength of cast bars of different sizes reduced to 
the equivalent strength of a 1/2-in. x 12-in. bar. 





Size of Square Cast Bars. 




Size of Square Cast Bars. 


If 

73 U 


1/2 in. 


1 in. 


2 in. 


3 in. 


4 in. 


1/2 in. 


1 in. 


2 in. 


3 in. 


4 in. 


*ft 


Strength of a 1/2-in. x 12-in. 
Section, lb. 


Strength of a 1/2-in. X 12-in. 
Section, lb. 


1.00 

1.50 
2.00 


290 

324 
358 


260 

272 
278 


232 
228 
220 


222 
212 
202 


220 

208 
196 


2.50 
3.00 
3.50 


392 
426 
446 


278 
276 
264 


212 

202 
192 


190 
180 
168 


184 
172 
160 





















350 




! 
















\ 














(U 250 




^ 


^ 


























__ 












*••>- 


--. 


__ 





- I nches S quare 
Fig. 92. 
Fig. 92 shows the relation of the strength to the size of the cast-iron bar 
and to Si, according to the figures in the above table. Comparing the 
2-in. bars with the 1/2-in. bars, we find 

Si, per cent 1 1.5 2 2.5 3 3.5 

2-in, weaker than 1/2-in. .percent. . 20 30 35 46 53 57 



CAST IRON. 



423 



The fact that with the 1-in. bar the strength is nearly independent of 
Si, shows that it is the worst size of bar to use to distinguish the quality 
of the metal. If two bars were used, say 1/2-in. and 2-in., the drop in 
strength would be a better index to the quality than the test of any 
single bar could be. 

Shrinkage of Cast Iron. — W. J. Keep (^4. S. M. E. xvi., 1082) gives a 
series of curves showing that shrinkage depends on silicon and on the 
cross-section of the casting, decreasing as the silicon and the section 
increase. The following figures are obtained by inspection of the curves: 





Size of Square Bars. 


0^ 
Ah 


Size of Square Bars. 


a c 

g8 


V2 in. 


1 in. 


2 in. 


3 in. 


4 in. 


1/2 in. 


1 in. 


2 in. 


3 in. 


4 in. 


"£ 


Shrinkage, In. per Foot. 


Shrinkage, In. per Foot. 


1.00 
1.50 
2.00 


0.178 
.166 
.154 


0.158 
.145 
.133 


0.129 
.116 
.104 


0.112 
.099 
.086 


0.102 
.088 
.074 


2.50 
3.00 
3.50 


0.142 
.130 
.118 


0.121 
.109 
.097 


0.091 
.078 
.065 


0.072 
.058 
.045 


0.060 
.046 
.032 



Mr. Keep says: "The measure of shrinkage is practically equivalent to 
a chemical analysis of silicon. It tells whether more or less silicon is 
needed to bring the quality of the casting to an accepted standard of 
excellence." 

A shrinkage of l/s in. per ft. is commonly allowed by pattern makers. 
According to the table, this shrinkage will be obtained by varying the Si 
in relation to the size of the bar as follows: 1/2 in., 3.25 Si; 1 in., 2.4 Si; 
2 in., 1.1 Si; 3 and 4, less than 1.0 Si. 

Shrinkage and Expansion of Cast Iron in Cooling. (T. Turner, 
Proc. L & S. I., 1906.) — Some irons show the phenomenon of expanding 
immediately after pouring, and then contracting. Four irons were 
tested, analyzing as follows: (1) " Washed " white iron, CC 2.73; Si, 
0.01; P, 0.01; Mn and S, traces. (2) Gray hematite, GC, 2.53; CC, 0.86; 
Si, 3.47; Mn, 0.55; P, 0.04; S, 0.03. (3) Northampton, GC, 2.60; CC, 
0.15; Si, 3.98; Mn, 0.50; P, 1.25; S, 0.03. (4) Cast iron, GC, 2.73; CC, 
0.79; Si, 1.41; Mn, 0.43; P, 0.96; S, 0.07. No. 1 was stationary for 5 sec- 
onds after pouring, shrunk 125 sec, stationary 10 sec, then shrunk till 
cold. No. 2 expanded 15 sec, shrunk 20 sec. to original size, continued 
shrinking 90 sec. longer, stationary 10 sec, expanded 30 sec, then shrunk 
till cold. No. 3 expanded irregularly with three expansions and two 
shrinkages, until 125 sec. after pouring the total expansion was 0.019 in. 
in 12 in., then shrunk till cold. No. 4 expanded 0.08 in. in 50 sec, then 
shrunk till cold. 

Shrinkage Strains Relieved hy Uniform Cooling. (F. Schumann, 
A.S.M.E., xvii, 433.) — Mr. Jackson in 1873 cast a flywheel with a very 
large rim and extremely small straight arms. Cast in the ordinary way, 
the arms broke either at the rim or at the hub. Then the same pattern 
was molded so that large chunks of iron were cast between the arms, a 
thickness of sand separating them. Cast in this way, all the arms re- 
mained unbroken. 

Deformation of Castings from Unequal Shrinkage. — (F. Schu- 
mann, A. S. M. E., vol. xvii.) A prism cast in a sand mold will main- 
tain its alignment, after cooling in the mold, provided all parts around 
its center of gravity of cross section cool at the same rate as to time and 
temperature. Deformation is due to unequal contraction, and this is 
due chiefly to unequal cooling. 

Modifying causes that effect contraction are: Imperfect alloying of 
two or more different irons having different rates of contraction; varia- 
tions in the thickness of sand forming the mold; unequal dissipation of 
heat, the upper surface dissipating the greater amount of heat; position 
and form of cores, which tend to resist the action of contraction, also 
the difference in conducting power between moist sand and dry-baked 
cores; differences in the degree of moisture of the sand; unequal expos- 



424 IRON AND STEEL. 

ure by the removal of the sand while yet in the act of contracting; 
Manges, ribs, or gussets that project from the side of the prism, of suffi- 
cient area to cause the sand to act as a buttress, and thus prevent the 
natural longitudinal adjustment due to contraction; in light castings of 
sufficient length the unyielding sand between the flanges, etc., may 
cause rupture. 

Irregular Distribution of Silicon in Pig Iron. — J. W. Thomas 
{Iron Age, Nov. 12, 1891) finds in analyzing samples taken from every 
other bed of a cast of pig iron that the silicon varies considerably, the iron 
coming first from the furnace having generally the highest percentage. In 
one series of tests the silicon decreased from 2.040 to 1.713 from the first 
bed to the eleventh. In another case the third bed had 1.260 Si, the 
seventh 1.718, and the eleventh 1.101. He also finds that the silicon 
varies in each pig, being higher at the point than at the butt. Some of 
his figures are: Point of pig, 2.328 Si; butt of same, 2.157; point of pig, 
1.834; butt of same, 1.787. 

White Iron Converted into Gray by Heating. (A. E. Outerbridge, 
Jr., Proc. Am. Socy. for Testing Mat'ls, 1902, p. 229.) — When white chilled 
iron containing a considerable amount of Si and low in GC is heated to 
about 1850° F. from 31/2 to 10 hours the CC is changed into C, which 
differs materially from graphite, and a metal is formed which has prop- 
erties midway between those of steel and cast iron. The specific gravity 
is raised from 7.2 to about 7.8; the fracture is of finer grain than normal 
gray iron; and the metal is capable of being forged, hardened, and taking 
a sharp cutting edge, so that it may be used for axes, hatchets, etc. It 
differs from malleable cast iron, since the latter has its carbon removed 
by oxidation, while the converted cast iron retains its original total 
carbon, although in a changed form. The tensile strength of the new 
metal is high, 40,000 to 50,000 lb. per sq. in., with very small elongation. 
The peculiar change from white to gray iron does not take place if Si 
is low. The analysis of the original castings should be about TC, 3.4 to 
3.8; Si, 0.9 to 1.2; Mn, 0.35 to 0.20; S, 0.05 to 0.04; P, 0.04 to 0.03. The 
following shows the change effected by the heat treatment: 

Before annealing, GC, 0.72; CC, 2.60; Si, 0.71; Mn, 0.11; S, 0.045; P, 0.04 
After annealing, GC, 2.75; CC, 0.82; Si, 0.73; Mn, 0.11; S, 0.040; P, 0.04 

The GC after annealing is, however, not ordinary graphite, but an 
allotropic form, evidently identical with what Ledebur calls " tempering 
graphite carbon." 

Change of Combined to Graphitic Carbon by Heating. — (H. M. 
Howe, Trans. A.l.M. E., 1908, p. 483.) On heating white cast iron to dif- 
ferent temperatures for some hours, the carbon changes from the com- 
bined to the graphitic state to a degree which increases in general with 
the temperature and with the silicon-content. With 0.05 Si, a little 
graphite formed at 1832° F.; with 0.13 Si, at 1652° F.; with 2.12 Si, graphite 
formed at a moderate rate at 1112°, and with 3.15 Si, it formed rapidly 
at 1112° F. In iron free from Si, with 4.271 comb. C. and 0.255 graphitic, 
none of the C. was changed to graphite on long heating to from 1680° to 
2J40°F., but in iron with 0.75 Si the graphite, originally 0.938%, rose 
to 1.69% on heating to 1787°, and to 2.795% on heating to 2057° F. On 
the other hand, when carbon enters iron, as in the cementation process 
in making blister-steel, it appears chiefly as cementite (combined carbon). 
Also on heating iron containing graphite to high temperatures and cooling 
quickly, some of the graphite is changed to cementite. 

Mobility of Molecules of Cast Iron. (A. E. Outerbridge, Jr., 
A.l.M. E., xxvi, 176; xxxv, 223.) — Within limits, cast iron is materially 
strengthened by being subjected to repeated shocks or blows. Six bars 
1 in. sq., 15 in. long, subjected for about 4 hours to incessant blows in a 
tumbling barrel, were 10 to 15% stronger than companion bars not 
thus treated. Six bars were struck 1000 blows on one end only with a 
hand hammer, and they showed a like gain in strength. The increase is 
greater in hard mixtures, or strong iron, than in soft mixtures, or weak 
iron; greater in 1-in. bars than in 1/2-in., and somewhat greater in 2-in. 
than in 1-in. bars. Bars were treated in a machine by dropping a 14-lb. 
weight on the middle of a 1-in, bar, supports 12 in. apart. Six bars 



CAST IRON. 425 

were first broken by having the weight fall a sufficient distance to break 
them at the first blow, then six companion bars were subjected to from 
10 to 50 blows of the same weight falling one-half the former distance, 
and then the weight was allowed to fall from the height at which the first 
bars broke. Not one of the bars broke at the first blow; and from 2 to 
10, and in one case 15 blows from the extreme height were required to 
break them. Mr. Outerbridge believes that every casting when first 
made is under a condition of strain, due to the difference in the rate of 
cooling at the surface and near the center, and that it is practicable to 
relieve these strains by repeatedly tapping the casting, allowing the parti- 
cles to rearrange themselves and assume a new condition of molecular 
equilibrium. The results, first reported in 1896, were corroborated by 
other experimenters. A report in Jour. Frank. Inst., 1898, gave tests of 
82 bars, in which the maximum gain in strength compared with untreated 
bars was 40%, and the maximum increase in deflection was 41%. 

In his second paper, 1904, Mr. Outerbridge describes another series of 
tests which showed that 1-in. sq. bars 15 in. long subjected to repeated 
heating and cooling grew longer and thicker with each successive oper- 
ation. One bar heated about an hour each day to about 1450° F. in a 
gas furnace for 27 times increased its length HVi6in. and its cross-section 
1/8 in. Soft iron expands more rapidly than hard iron. White iron does 
not expand sufficiently to cover the original shrinkage. Wrought iron and 
steel bars similarly treated in a closed tube all contracted slightly, the 
average contraction after 60 heatings being Vsin. per foot. The strength 
and deflection of the cast-iron bars was greatly decreased by the treatment, 
1250 as compared with 2150 lb., and 0.1 in. deflection as compared with 
0.15 in. The specific gravity of the expanded bars was 5.49 to 6.01, as 
compared with 7.13 for the untreated bars. 

Grate-bars of boiler furnaces grow longer in use, as do also cast-iron 
pipes in ovens for heating air. 

Castings from Blast Furnace Metal. Castings are frequently made 
from iron run directly from the blast furnace, or from a ladle filled with 
furnace metal. Such metal, if high in Si, is more apt to throw out " kish " 
or loose particles of graphite than cupola metal. With the same percen- 
tage of Si,, it is softer than cupola metal, which is due to two causes: 1, • 
lower S; 2, higher temperature. T. D. West, A.I.M.E., xxxv, 211, 
reports an example of furnace metal containing Si, 0.51; S, 0.045; Mn, 
0.75; P, 0.094; which was easily planed, whereas if it had been cupola 
metal it would have been quite hard. J. E. Johnson, Jr., ibid., p. 213, 
says that furnace metal with S, 0.03, and Si, 0.7, makes good castings, not 
too hard to be machined. Should the metal contain over 0.9 Si, diffi- 
culty is experienced in preventing holes and soft places in the castings, 
caused by the deposition of kish or graphite during or after pouring. 
The best way to prevent this is to pour the iron very hot when making 
castings of small or moderate size. 

Effect of Cupola Melting. (G. R. Henderson, A.S.M.E., xx, 621.) — 
27 car-wheels were analyzed in the pig and also after remelting. The 
P remains constant, as does Si when under 1%. Some of the Mn always 
disappears. The total C remains the same, but the GC and CC vary in 
an erratic manner. The metal charged into the cupola should contain 
more GC, Si and Mn than are desired in the castings. Fairbairn (Manu- 
facture of Iron, 1865) found that remelting up to 12 times increased the 
strength and the deflection, but after 18 remeltings the strength was only 
5/8 and the deflection 1/3 of the original. The increase of strength in the 
first remeltings was probably due to the change of GC into CC, and the 
subsequent weakening to the increase of S absorbed from the fuel. 

Hard Castings from Soft Pig. (B. F. Fackenthal, Jr., A.I.M.E., 

xxxv, 993.) — Samples from a car load of pig gave Si, 2.61 ; S, 0.023. Cast- 
ings from the. same iron gave 2.33 and 2.26 Si, and 0.26 and 0.25 S, or 
12 times the S in the original pis; probably due to fuel too high in S, but 
more probably to the use of too little fuel in remelting. 

The loss of Si in remelting, and the consequent hardening, is affected 
by the amount of Mn, as shown below: 

Mn, per cent 0.04 0.20 0.43 0.53 

Si lost in remelting, per cent 34 23 12 4 



426 



IRON AND STEEL. 



Difficult Drilling due to LowMn.-H. Souther, A.S.T.M., v, 219, 
reports a case where thin castings drilled easily while thick parts on the 
same castings rapidly dulled 1/2 and 3/ 4 -in. drills. The chemical constitu- 
tion was normal except Mn; Si, 2.5; P, 0.7; S about 0.08; C, 3.5; Mn, 0.16. 
When the Mn was raised to 0.5 the trouble disappeared. 

Addition of Ferro-silicon in the Ladle. (A. E. Outerbridge, Proc. 
A.S.T.M., vi, 263.)— Half a pound of FeSi, containing 50% Si, added to a 
200-lb. ladle of soft cast iron used for making pulleys with rims 1/4 in. 
thick, prevented the chilling of the surface of the casting, and enabled 
the pulleys to be turned more rapidly. Analysis showed that the actual 
increase of the Si in the casting was less than the calculated increase. 
Tests of the metal treated with FeSi as compared with untreated metal 
showed a gain in strength of from 2 to 26%, and a gain in deflection of 2 
to 3%. The reason assigned for the increase of strength with increase of 
softness is that cupola iron contains a small amount of iron oxide, which 
reacts with the Si added in the ladle, forming Si02, which goes into the 
slag. 

Experiments with Titanium added to cast iron in the ladle are 
reported by R. Moldenke, Proc. Am. Fdrymen's Assn., 1908. Two 
irons were used: gray, with 2.58 Si, 0.042 S, 0.54 P, 0.74 Mn; and white, 
with 0.85 Si, 0.07 S, 0.42 P, 0.6 Mn. Two Fe Ti alloys with 10 % Ti 
were used, one containing no C, and the other 5% C. The latter has the 
lower melting point. The results were as below: 



White Iron. Lbs. 



Original iron 

Plus0.05Ti... 
PlusO.lOTi... 
Plus 0.05 Ti and C 
PlusO.lOTiandC 
Plus0.15TiandC 



9 tests 
4 tests 

3 tests 
6 tests 
6 tests 

4 tests 



1720-2260 av. 2020 



2750-3140 
2880-3150 
2850-3230 
2850-3150 
3030-3270 



Average of treated iron . 
Increase over original. . . 



3100 
3030 
3070 
2990 
3190 

. 3070 

. 52% 



8 tests 
1 1 tests 



1920-2110 av. 2050 
2210-2660 " 2400 



9 tests 
10 tests 
10 tests 



2230-2720 " 2420 
2320-2460 " 2400 
2280-2620 " 2520 

2430 
18% 



Modulus of rupture, treated iron, 48,030 



The test bars were H/4 in. diam. 12 in. between supports. The im- 
provement is as marked whether 0.05, 0.10, or 0.15% Ti is used, which 
indicates that if sufficient Ti is used for deoxidation of the iron, any 
additional Ti is practically wasted. 

Ti lessens the chilling action, yet whatever chill remains shows much 
harder iron. Test pieces made with iron which chilled H/2 in. deep 
gave but 1 in. chill when the iron was treated in the ladle. The original 
iron crushed at 173,000 lbs. per sq. in. and stood 445 in Brinel's test 
for hardness, soft steel running about 105. The treated piece ran 
298,000 lbs. per sq. in. and showed a hardness of 557. Testing the soft 
metal below the chilled portion for hardness gave 332 for the original 
and 322 for the treated piece. 

Additions of Vanadium and Manganese. — R. Moldenke, Am. 
Fdrymen's Assn., 1908, Am. Mach., Feb. 20, '08. Experiments were 
made by adding to melted cast iron in the ladle a ground alloy of ferro- 
vanadium, containing 14.67 Va, 6.36 C, and 0.1S Si. In other experi- 
ments ferro-manganese (80% Mn) was added, together with the vana- 
dium. Four kinds of iron were used: burnt gray iron (gratebars, stove 
iron, etc.), burnt white iron, gray machinery iron (Si, 2.72, S, 0.065, 
P, 0.068, Mn, 0.54) and remelted car wheels (white, two samples anal- 
yzed: Si, 0.60 and 0.53, S, 0.122, 0.138; P, 0.399, 0.374; Mn, 0.38, 
0.44). The following are average results: 



CAST IRON. 



427 



Gray Machinery Iron. 


Remelted Car Wheels. 


Added Per cent. 


Breaking 

Strength, 
lbs. 


Deflec- 
tion, In. 


Added Per cent. 


Breaking 

Strength, 

lbs. 


Deflec- 
tion, In. 


Va. 


Mn. 


Va. 


Mn. 


0.0 
0.0 
0.05 


0.0 
0.50 


1980 
1970 
1980 
2130 
2372 
2530 
2360 


0.105 
0.100 
0.100 
0.100 
0.090 
0.120 
0.100 


0.0 

0^05' 
0.05 
0.10 
0.10 
0.15 
0.15 


0.0 
0.50 

0^50 

0.50 

"o!50 


1470 
2790 
3020 
2970 
2800 
3030 
2950 
3920 

3069 


0.050 
0.070 
0.060 


0.05 
0.10 


0.50 


0.090 
0.055 


0.10 
0.15 


0.50 


0.090 
0.070 




Viar>5 


095 


Average treated 


2224 




Mod. of ri 


ipture 


. 35,800 








48,020 





The bars were 11/4 in. diam. 12 in. between supports. 

The burnt gray iron was increased in breaking strength from 1310 to 
2220 lbs. by the addition of 0.05% Va, and the burnt white iron from 
1440 to 1910 lbs. by the addition of 0.05 Va and 0.50 Mn. 

Strength of Cast-iron Beams. — C. H. Benjamin, MacWy, May, 
1906. Numerous tests were made of beams of different sections, includ- 
ing hollow rectangles and cylinders, I and T-shapes, etc. All the sec- 
tions were made approximately the same area, about 4.4 sq. in., and all 
were tested by transverse loading, with supports 18 in. apart. The 
results, when reduced by the ordinary formula for stress on the extreme 
fiber, 'S = My /I, showed an extraordinary variation, some of the values 
beins: as follows: Square bar, 23,300; Round bar, 25,000. Hollow round, 
3.4 in. outside and .2.5 in. inside diam., 26,450, and 35,800. Hollow 
ellipse, 3 in. wide, 3.9 in. high, 0.9 in. thick, 36,000. /-beam, 4 in. high, 
web 0.44 in. thick, 17,700. The hollow cylindrical and elliptical sec- 
tions are much stronger than the solid sections. This is due to the 
thinner metal, the greater surface of hard skin, and freedom from 
shrinkage strains. Professor Benjamin's conclusions from these tests 
are: 

(1) The commonly accepted formulas for the strength and stiffness 
of beams do not apply well to cored and ribbed sections of cast iron. 

(2) Neither the strength nor the stiffness of a section increases in pro- 
portion to the increase in the section modulus or the moment of inertia. 

(3) The best way to determine these qualities for a cast-iron beam is 
by experiment with the particular section desired and not by reasoning 
from any other section. 

Bursting Strength of Cast-iron Cylinders. — C. H. Benjamin, 
A. S. M. E., XIX, 597; Mach'y, Nov., 1905. Four cylinders. 20 in. long, 
10 1/8 in. int. diam., 3/ 4 in. thick, with flanged ends and bolted covers, 
burst at 1350, 1400, 1350, and 1200 lbs. per sq. in. hydraulic pressure, 
the corresponding fiber stress, from the formula S = pd/2 t, being 9040, 
10,200, 9735 and 9080. Pieces cut from the shell had an average tensile 
strength of 14,000 lbs. per sq. in., and a modulus of rupture in trans- 
verse tests of 30,000. 

Transverse Strength of Cast-iron Water-pipe. (Technology Quar- 
terly, Sept., 1897.) — ■ Tests of 31 cast-iron pipes by transverse stress gave 
a maximum outside fibre stress, calculated from maximum load, assuming 
each half of pipe as a beam fixed at the ends, ranging from 12,800 lbs. to 
23,303 lbs. per sq. in. 

Bars 2 in. wide cut from the pipes gave moduli of rupture ranging from 
28,400 to 51,400 lbs. per sq. in. Four of the tests, bars and pipes : 



Moduli of rupture of bar 28,400 

Fiber stress of pipe 18,300 



34,400 
12,800 



40,000 
14,500 



51,400 
26,300 



428 



IRON AND STEEL. 



These figures show a great variation in the strength of both bars and 
pipes, and also that the strength of the bar does not bear any definite 
relation to the strength of the pipe. 

Bursting Strength of Flanged Fittings. — Power, Feb. 4, 1908. 
The Crane Company, Chicago, published in the Valve World records of 
tests of tees and ells, standard and extra heavy, which show that the 
bursting strength of such fittings is far less than is given by the standard 
formulae for thick cylinders. As a result of the tests they give the 
following empirical formula: B = TS/D, in which B = bursting pres- 
sures, lbs. per sq. in., T = thickness of metal, D = inside diam., and 
S = 65% of the tensile strength of the metal for pipes up to 12 in. diam., 
for larger sizes use 60%. The pipes were made of " ferro-steel " of 
33,000 lbs. T. S., and of cast iron of 22,000 lbs. as tested in bars. The 
following are the principal results of tests of extra heavy tees and ells 
compared with results of calculation by the Crane Company's formula: 
Bursting Strength of Pipe-Fittings. Pounds per Square Inch. 



Inside Diam. 
Thickness. 


6 

3/4 


8 
13/16 


10 
15/16 


12 

1 


14 

H/8 


16 
13/16 


18 
11/4 


20 
« 5 /l6 


24 
11/2 


B, Ferro-steel 

calculated 

B, Cast iron 

calculated 


2733 

2680 
1687 
1790 
3266 
2275 


2250 
2180 
1350 
1450 
2725 
1625 


2160 
2010 
1306 
1340 
2350 
1541 


2033 
1870 
1380 
1190 
2133 
1275 


1825 
1570 
1100 
1060 


1700 
1450 
1025 
980 


1450 
1350 
600 
920 


1275 
1280 
750 
870 


1300 
1220 
700 
820 




1075 


1250 

















Specific Gravity and Strength. (Major Wade, 1856.) 

Third-class guns: Sp. Gr. 7.087, T. S. 20,148. Another lot: least Sp. 
Gr. 7.163, T. S. 22,402. 

Second-class guns: Sp. Gr. 7.154, T. S. 24,767. Another lot: mean 
Sp. Gr. 7.302, T. S. 27,232. 

First-class guns: Sp. Gr. 7.204, T. S. 28,805. Another lot: greatest 
Sp. Gr. 7.402, T. S. 31,027. 

Strength of Charcoal Pig Iron. — Pig iron made from Salisbury 
ores, in furnaces at Wassaic and Millerton, N. Y., has shown over 40,000 
lbs. T. S. per square inch, one sample giving 42,281 lbs. Muirkirk, Md., 
iron tested at the Washington Navy Yard showed: average for No. 2 
iron, 21,601 lbs.; No. 3, 23,959 lbs.; No. 4, 41,329 lbs.; average den- 
sity of No. 4, 7.336 (J. C. I. W., v. p. 44). 

Nos. 3 and 4 charcoal pig iron from Chapinville, Conn., showed a 
tensile strength per square inch of from 34,761 lbs. to 41,882 lbs. Char- 
coal pig iron from Shelby, Ala. (tests made in August, 1891), showed a 
strength of 34,800 lbs. for No. 3; No. 4, 39,675 lbs.; No. 5, 46,450 lbs.; 
and a mixture of equal parts of Nos. 2, 3, 4, and 5, 41,470 lbs. (Bull. 
I. & S. A.) 

Variation of Density and Tenacity of Gun-Irons. — An increase of 
density invariably follows the rapid cooling of cast iron, and as a general 
rule the tenacity is increased by the same means. The tenacity gener- 
ally increases quite uniformly with the density, until the latter ascends 
to some given point; after which an increased density is accompanied 
by a diminished tenacity. 

The turning-point of density at which the best qualities of gun-iron 
attain their maximum tenacity appears to be about 7.30. At this point 
of density, or near it, whether in proof-bars or gun-heads, the tenacity is 
greatest. 

As the density of iron is increased its liquidity when melted is dimin- 
ished. This causes it to congeal quickly, and to form cavities in the 
interior of the casting. (Pamphlet of Builders' Iron Foundry, 1893.) 

" Semi-steel " is a trade name given by some founders to castings made 
from pig iron melted in the cupola with additions of from 20 to 30 per 
cent of steel scrap. Ferro-manganese is also added either in the cupola or 
in the ladle. The addition of the steel dilutes the Si of the pig iron, and 
changes some of the C from GC to CC, but the TC is unchanged, for any 
reduction made by the steel is balanced by absorption of C from the fuel. 



MALLEABLE CAST IRON. 429 

Semi-steel therefore is nothing more than a strong cast iron, low in Si 
and containing some Mn, and the name given it is a misnomer. 

Mixture of Cast Iron with Steel. — Car wheels are sometimes made 
from a mixture of charcoal iron, anthracite iron, and Bessemer steel. 
The following shows the tensile strength of a number of tests of wheel 
mixtures, the average tensile strength of the charcoal iron used being 
22,000 lbs. {Jour. C. I. W., iii, p. 184): 

lbs. per sq. in. 

Charcoal iron with 2V2% steel 22,467 

" 33/4% steel 26,733 

" 61/4% steel and 6 1/4% anthracite 24,400 

" 7V 3 % steel and 71/2% anthracite 28,150 

" 21/2% steel, 21/2% wro't iron, and 61/4% anth. 25,550 
" 5 % steel, 5% wro't iron, and 10% anth 26,500 

Cast Iron Partially Bessemerized. — Car wheels made of partially 
Bessemerized iron (blown in a Bessemer converter for 31/2 minutes), 
chilled in a chill test mold over an inch deep, just as a test of cold blast 
charcoal iron for car wheels would chill. Car wheels made of this blown 
iron have run 250,000 miles. (Jour. C. I. W., vi, p. 77.) 

Bad Cast Iron. — On October 15, 1891, the cast-iron fly-wheel of a 
large pair of Corliss engines belonging to the Amoskeag Mfg. Co., of Man- 
chester, N.H., exploded from centrifugal force. The fly-wheel was 30 
feet diameter and 110 inches face, with one set of 12 arms, and weighed 
116,000 lbs. After the accident, the rim castings, as well as the ends of 
the arms, were found to be full of flaws, caused chiefly by the drawing 
and shrinking of the metal. Specimens of the metal were tested for 
tensile strength, and varied from 15,000 lbs. per square inch in sound 
pieces to 1000 lbs. in spongy ones. None of these flaws showed on the 
surface, and a rigid examination of the parts before they were erected 
failed to give any cause to suspect their true nature. Experiments were 
carried on for some time after the accident in the Amoskeag Company's 
foundry in attempting to duplicate the flaws, but with no success in 
approaching the badness of these castings. 

Permanent Expansion of Cast Iron by Heating. (Valve World, 
Sept., 1908.) — Cast iron subjected to continued temperatures of approx- 
imately 500° to 600° took a permanent expansion and did not return to 
its original volume when cooled. 

As steam is being superheated quite commonly to temperatures above 
575°, this fact is of great interest inasmuch as it modifies our ideas about 
the proper material to be used in the construction of valves and fittings 
for service under high temperatures. A permanent volumetric expan- 
sion is followed by a loss of strength, the loss in cast iron being fully 40 
per cent in four years. 

Crane Co. made an attempt to determine whether cast steel was affected 
in the same manner as cast iron. Three flanges were taken, one of cast 
iron, one of ferrosteel, and the third of cast steel. These flanges were 
exposed for a total period of 130 hours to temperatures ranging as follows: 

Less than 500°, 18 hours; 500° to 700°, 97 hours; 710° to 800°, 12 hours; 
over 800°, 3 hours. Average temp., 583°. 

The outside diameter in each case was 121/2 in. and the bore 629/ 64 j n . 

The results were: Cast-steel flange, no change. Cast-iron flange, 
outside diam. increased 0.019 in., inside diam. increased 0.007 in. Ferro- 
steel flange, outside diam. increased 0.033 in., inside diam. increased 0.017 
in. 

If the permanent expansion of cast iron stopped at the figures given 
above, it would not be a serious matter; but all evidence points toward a 
steady increase as time goes on, as was shown by one of Crane Co.'s 
14-in. valves, which originally was 221/2 in. face to face, and increased 
5 /i6 in. in length in four years under an average temperature of about 
590°. 

MALLEABLE CAST IRON.* 

There are four great classes of work for whose requirements malleable 
cast iron (commonly called "malleable iron" in America) is especially 

* References. — R. Moldenke, Cass. Mag., 1907, and Iron Trade 
Review, 1908; E. C. Wheeler, Iron Age, Nov. 9, 1899; C. H. Gale, Indust. 
World, April 13, 1908; W. H. Hatfield, ibid. G. A. Akerlund, Iron Tr. 
Rev., Aug. 23, 1906; C. H. Day, Am. Mach., April 5, 1906. 



430 IRON AND STEEL. 

adapted. These are agricultural implements, railway supplies, carriage 
and harness castings and pipe fittings. Besides these main classes there 
are innumerable other unclassified uses. The malleable casting is seldom 
over 175 lbs. in weight, or 3 ft. in length, or 3/ 4 in. in thickness. The 
great majority of even the heavier castings do not exceed 10 lbs. 

When properly made, malleable cast iron should have a tensile strength 
of 42,000 to 48,000 lbs. per sq. in., with an elongation of 5% in 2 in. 
Bars 1 in. square and on supports 12 in. apart should show a transverse 
strength of 2500 to 3500 lbs., with a deflection of at least 1/2 in. 

While the strength of malleable iron should be as stated, much of it 
will fall as low as 35,000 lbs. per sq. in., and this will still be good for such 
work as pipe fittings, hardware castings and the like. On the other hand, 
even 63,000 lbs. per sq. in. has been reached, with a load of 5000 lbs. and 
a deflection of 21/2 in. in the transverse test. This high strength is not 
desirable, as the softness of the casting is sacrificed, and its resistance to 
continued shock is lessened. For the repeated stresses of severe service 
the malleable casting ranks ahead of steel, and only where a high tensile 
strength is essential must it be replaced by that material. 

The process of making malleable iron may be summarized as follows: 
The proper cast irons are melted in either the crucible, the air furnace, 
the open-hearth furnace or the cupola. The metal when cast into the 
sand molds must chill white or not more than just a little mottled. After 
removing the sand from the hard castings they are packed in iron scale, 
or other materials containing iron oxide, and subjected to a red heat 
(1250 to 1350° F.) for over 60 hours. They are then cooled slowly, 
cleaned from scale, chipped or ground, and straightened. 

When hard, or just from the sand, the composition of the iron should 
be about as follows: Si, from 0.35 up to 1.00, depending upon the thick- 
ness and the purpose the casting ia to be used for; P not over 0.225, Mn 
not over 0.20, S not over 0.05. The total carbon can be from 2.75 upward, 
4.15 being about the highest that can be carried. The lower the carbon 
the stronger the casting subsequently. Below 2.75 there is apt to be 
trouble in the anneal, the black-heart structure may not appear, and the 
castings remain weak. A casting 1 in. thick would necessitate silicon at 
0.35, and the use of chills in the mold in addition, to get the iron white. 
For a casting 1/2 in. thick, Si about 0.60 is the proper limit, except where 
great strength is desired, when it can be dropped to 0.45. Above 0.60 
there is danger of getting heavily-mottled if not gray iron from the sand 
molds, and this material, when annealed the long time required for the 
white castings, would be ruined. For very thin castings, Si can run up to 
1 .00 and still leave the metal white in fracture. 

Pig Iron for 31alleable Castings. — The specifications run as follows: 

Si, 0.75, 1.00, 1.25, 1.50, 1.75, 2.00%, as required; Mn, not over 0.60; 
P, not over 0.225; S, not over 0.05. 

Works making heavy castings almost exclusively, specify Si to include 
0.75 up to 1.50%. Makers of very light work take 1.25 to 2.00%. 

The Melting Furnace. — Malleable iron is melted in the reverbera- 
tory furnace, the open-hearth furnace and the cupola; the reverberatory 
being the most extensively used, about 85 per cent of the entire output 
of the United States being melted by this process. Prior to about 1885, 
the standard furnace was one of 5 tons capacity. At present (1908) we 
have furnaces of 25 and 30 tons capacity, though furnaces of from 10 to 
15 tons are the most popular and give more uniform results than those 
of larger capacity. 

The adoption of the open-hearth furnace for malleable iron dates 
back to about 1893. It is used largely in the Pittsburg district. 

Cupola melted iron does not possess the tensile strength nor ductility 
of iron melted in the reverberatory or open-hearth furnace, due partly to 
the higher carbon and sulphur caused by the metal being in contact 
with the fuel. This feature is rather an advantage than otherwise, as 
most of the product of cupola melted iron consists of pipe fittings; cast- 
ings that are not subjected to any great stress or shock. The castings 
are threaded, and a strong, tough malleable iron does not cut a clean, 
smooth thread, but rather will rough up under the cutting tool. 

In the reverberatory and open-hearth furnaces the metal may be partly 
desiliconized at will, by an oxidizing flame or by additions of scrap or 
other low-silicon material, Manganese is also oxidized in the furnace. 



MALLEABLE CAST tRON. 



431 



The composition of good castings in American practice is: Si, from 0.45 
to 1.00%; Mn, up to 0.30%; P, up to 0.225%; S, up to 0.07%; total 
carbon in the hard casting, above 2.75%. 

In special cases, especially for very small castings, the silicon may go 
up as high as 1.25%, while for very heavy work it may drop down to 
0.35% with very good results. In the case of charcoal iron this figure 
gives the strongest castings. With coke irons, however, especially when 
steel scrap additions are the rule, 0.45 should be the lower limit, and 0.65 
is the best silicon for all-around medium and heavy work, such as rail- 
road castings. 

In American practice phosphorus is required not to exceed 0.225%, 
and is preferred lower. In European practice it is required as low as 
0.10%, but castings have been made successfully with P as high as 
0.40%. 

The heat treatment of metal during melting has an important bearing 
upon its tensile strength, elongation, etc. Excessive temperatures pro- 
mote the chances of burning. Iron is burnt mainly through the genera- 
tion in melting furnaces of higher temperatures than those prevailing 
during the initial casting at blast furnaces and an excess of air in the 
flame. The choicest irons may thus turn out poor material. 

Shrinkage of the Casting. — The shrinkage of the hard casting is 
about 1/4 in. to the foot, or double that of gray iron. In annealing about 
half of this is recovered, and hence the net result is the same as in ordi- 
nary foundry pattern practice. The effect of this great shrinkage is to 
cause shrinkage cracks or sponginess in the interior of the casting. As 
soon as the liquid metal sets against the surface of the mold and the 
source of supply is cut off, the contraction of the metal in the interior 
as it cools causes the particles to be torn apart and to form minute 
cracks or cavities. " Every test bar, and for that matter every casting 
may be regarded as a shell of fairly continuous metal with an interior of 
slight planes of separation at right angles to the surface. This charac- 
teristic of malleable iron forms the basis of many a mysterious failure." 
(Moldenke.) 

Packing for Annealing. — After the castings have been chipped and 
sorted they are packed in iron annealing pots, holding about 800 pounds 
of iron, together with a packing composed of iron ore, hammer and 
rolling mill scale, turnings, borings, etc. The turnings, etc., were form- 
erly treated with a solution of salammoniac or muriatic acid to form a 
heavy coating of oxide, but such treatment is now considered unnec- 
essary. Blast furnace slag, coke, sand, and fire clay have also been used 
for packing. The changes in chemical composition of the castings when 
annealed in slag and in coke are given as follows by C. H. Gale: 





Si. 


S. 


P. 


Mn. 


C. C. 


G. C. 




0.63 
0.61 
0.61 


0.043 
0.049 
0.065 


0.147 
0.145 
0.150 


0.21 
0.21 
0.21 


2.54 
0.24 
0.25 


Trace 




1 65 


Annealed in coke 


2.00 



The Annealing Process. — The effect of the annealing is to oxidize 
and remove the carbon from the surface of the casting, to remove it 
to a greater or less degree below the surface, and to convert the remain- 
ing carbon from the combined form into the amorphous form called a 
"temper carbon" by Professor Ledebur, the German metallurgist. It 
differs from the graphite found in pig iron, but is usually reported as 
graphitic carbon by the chemists. In the original malleable process, 
invented by Reaumur, in 1722, the castings were packed in iron ore and 
annealed thoroughly, so that most of the carbon was probably oxidized, 
but in American practice the annealing process is rather a heat treat- 
ment than an oxidizing process, and its effect is to precipitate the carbon 
rather than to eliminate it. According to the analysis quoted above, the 
metal annealed in slag lost 0.65% of its total C, while that annealed in 
coke lost only 0.29%. In the former, S increased 0.006% and in the 
latter '0.022%. The Si decreased 0.02% in both cases, while the P and 
Mn remained constant. 



432 IRON AND STEEL. 



As to the distribution of carbon in an annealed casting, Dr. Moldenke 
says: "Take a flat piece of malleable and plane off the skin, say Vie in. 
deep and gather the chips for analysis. The carbon will be found, say, 
0.1o% perhaps even less. Cut in another 1/16 in. and the total C will be 
nearer 0.60%. Now go down successively by sixteenths and the total 
C will range from, say, 1.70 to 3.65% and will then remain constant until 
the center is reached." "The malleable casting is for practical purposes 
a poor steel casting with a lot of graphite, not crystallized, between the 
crystals or groups of crystals of the steel." 

The heat in the annealing process must be maintained for from two to 
four days, depending upon the thickness of sections of the castings and 
the compactness with which the castings or annealing boxes are placed 
in the furnace. An annealing temperature 1550° to 1600° Fahr. is often 
used, but it is not essential, as the annealing can be accomplished at 
1300°, but the time required will be longer than that at the higher tem- 
perature. Burnt iron in the anneal is no uncommon feature, and, gen- 
erally speaking, it is the result of carelessness. The most carefully pre- 
pared metal from melting furnaces can here be turned into worthless 
castings by some slight inattention of detail. The highest temperature 
for annealing should be registered in each foundry, and kept there by the 
daily and frequent use of a thermometer constructed for that sole pur- 
pose. Steady, continued heat insures soft castings, while unequal tem- 
peratures destroy all chances for successful work, although the initial 
metal was of the most excellent quality. 

After annealing, the castings are cleaned by tumblers or the sand 
blast; they are carefully examined for cracks or other defects, and if 
sprung out of shape are hammered or forced by hydraulic power to the 
correct shape. Such parts as are produced in great quantities are placed 
in a drop hammer and one or two blows will insure a correct form. They 
may be drop-forged or even welded when the iron has been made for that 
purpose. Castings are sometimes dipped into asphaltum diluted with 
benzine to give them a better finish. 

Malleable castings must never be straightened hot, especially when 
thick. In the case of very thin castings there is some latitude, as the 
material is so decarbonized that it is nearer a steel than genuine mal- 
leable cast iron. In heating portions of castings that were badly warped, 
it seems that the amorphous carbon in them was combined again, and 
while the balance of the casting remained black and sound, the heated 
parts became white and brittle, as in the original hard casting. Hence 
the advice to straighten the castings cold, preferably with a drop ham- 
mer and suitable dies, or still better in the hydraulic press. (R. Moldenke. 
Proc. A.S. T.M., vi, 244.) 

Physical Characteristics. — The characteristic that gives malleable 
iron its greatest value as compared with gray iron is its ability to resist 
shocks. Malleability in a light casting 1/4 in. thick and Jess means a 
soft, pliable condition and the ability to withstand considerable distor- 
tion without fracture, while in the heavy sections, 1/2 in. and over, it 
means the ability to resist shocks without bending or breaking. 

For general purposes it is not altogether desirable to have a metal 
very high in tensile strength, but rather one which has a high transverse 
strength, and especially a good deflection. It is not always that a strong 
and at the same time soft material can be produced in a foundry operat- 
ing on the lighter grades of castings. The purchaser, therefore, unless he 
requires very stiff material, should rather look upon the deflection of 
the metal coupled with the weight it took to do this bending before 
failure, than for a high tensile strength. 

The ductility of the malleable casting permits the driving of rivets, 
which cannot so readily be done with gray cast iron; and for certain 
parts of cars, like the journal boxes, malleable cast iron may be con- 
sidered supreme, leaving cast iron and "semi-steel " far behind. 

It was formerly the general belief that the strength of malleable iron- 
was largely in the white skin always found on this material, but it has 
been demonstrated that the removal of the skin does not proportionately 
lessen the strength of the casting. 

Test Bars. — The rectangular shape is used for test bars in preference 
to the round section, because the latter is more apt to have serious cracks 
in the center, due to shrinkage, especially if the diameter is large. A 
round section, unless in very light hardware, is to be avoided, as the 



MALLEABLE CAST IRON. 433 

shrinkage crack in the center may have an outlet to the skin, and cause 
failure in service. 

It is customary to provide for two sizes of test bars, the heavy and 
the light. Thus the 1-in. square bar represents work 1/2 an inch thick 
and over, and a 1 X V2-in. section bar cares for the lighter castings. 
Both are 14 inches long. They should be cast at the beginning and at 
the end of each heat. 

Design of 31alleable Castings. — As white cast iron shrinks a great 
deal more than gray iron, and as the sections of malleable castings are 
lighter than those of similar castings of gray iron, fractures are very 
common. It is therefore the designer's aim to distribute the metal so 
as to meet these conditions. In long pieces the stiffening ribs should 
extend lengthways so as to produce as little resistance as possible to the 
contraction of the metal at the time of solidification. If this be not 
possible, the molder provides a "crush core" whose interior is filled with 
crushed coke. When the metal solidifies in the flask the core is crushed 
by the casting and thus prevents shrinkage cracks. At other times a 
certain corner or juncture of ribs in the casting will be found cracked. 
In order to prevent this a small piece of cast iron (chill) is embedded in 
the sand at this critical point, and the metal will cool here more quickly 
than elsewhere, and thus fortify this point, although it may happen that 
some other part of the casting will be found fractured instead, and in 
many cases the locations and the shape of strengthening ribs in the 
casting must be altered until a casting is procured free from shrinkage 
cracks. In designing of malleable cast-iron details the following rules 
should be observed: 

(1) Endeavor to keep the metal in different parts of the casting at a 
uniform thickness. In a small casting, of, say, 10 lbs. weight. 1/4-in. 
metal is about the practical thickness. -Via in. for a casting of 15 to 20 
lbs., and 3/ 8 to 1/2 in. for castings of 40 lbs. and over. (2) Endeavor to 
avoid sharp junctions of ribs or parts, and if the casting is long, say 24 
inches or more, the ends should be made of such shape as to offer as 
little resistance as possible to the contraction of metal when cooling in 
the mold. 

Specifications for Malleable Iron. — The tensile strength of malle- 
able iron varies with the thickness of the metal, the lighter sections hav- 
ing a greater strength per square inch than the heavier sections. An 
Eastern railroad designates the tensile strength desired as follows: Sec- 
tions 3/ 8 in. thick or less should have a tensile strength of not less than 
40,000 lbs. per sq. in.; 3/ 8 to 3/ 4 in. thick, not less than 3S,000: and over 
3/4 in., not less than 36,000 lbs. per sq. in. Test bars 5/s and 7/ 8 in. diam. 
were made in the same mold and poured from the same ladle, and an- 
nealed together. The average tensile strength of five pairs of bars so 
treated, representing five heats, was, 5/s-in. bars, 45,095; 7/8-m. bars, 
41,316 lbs. per sq. in. Average elongation in 6 in.: 5/ 8 -in. bars 5.3^; 
7/ 8 -in. bars 4.2%. 

A very high tensile strength can be obtained approaching that of 
cast steel but at the expense of the malleability of the product. Malle- 
able test bars have been made with a tensile strength of between 60,000 
and 70,000 lbs. per sq. in., but the ductility and ability to resist shocks 
of these bars was not equal to that of bars breaking at 40,000 to 45,000 
pounds per sq. in. 

The British Admiralty specification is IS tons (40,320 lbs.) per square 
inch, a minimum elongation of 4i/2 c o in three inches and a bending angle 
of at least 90° over a 1-in. radius, the bar being 1 X 3 / 8 in. in section. 

The specifications of the American Society for Testing Materials 
include the following: 

Cupola iron is not recommended for heavy or important castings. 

Castings for which physical requirements are specified shall not con- 
tain over 0.06 sulphur or over 0.225 phosphorus. 

The Standard Test Bar is 1 in. square and 14 in. long, cast without 
chills and left perfectly free in the mold. Three bars shall be cast in one 
mold, heavy risers insuring sound bars. "Where the full heat goes into 
castings which are subject to specification, one mold shall be poured 
two minutes after tapping into the first ladle, and another mold from 
the last iron of the heat. 

The tensile strength of a standard test bar shall not be less than 40,000 
lbs. per sq. in. The elongation in 2 in. shall not be less than 21/2%. 



434 



IRON AND STEEL. 



The transverse strength of a standard test bar on supports 12 inches 
apart shall not be less than 3000 lbs., deflection being at least 1/2 in. 

Improvement in Quality of Castings. (Moldenke.) — -The history 
of improvement in the malleable casting is admirably reflected in the 
test records of any works that has them. Going back to the early 90's~, 
the average tensile strength of malleable cast iron was about 35,000 lbs. 
per sq. in., with an elongation of about 2% in 2 in. The transverse 
strength was perhaps 2800 lbs., with a deflection of 1/2 in. Toward the 
close of the 90's a fair average of the castings then made would run 
about 44,000 lbs. per sq. in., with an elongation of 5% in 2 in., and the 
transverse strength, about 3500 lbs., with a deflection of 1/2 inch. These 
average figures were greatly exceeded in establishments where special 
attention was given to the niceties of the process. The tensile strength 
here would run 52,000 lbs. per sq. in. regularly, with 7% elongation in 
2 in., and the transverse strength, 5000 and over, with 1 1/2 in. deflection. 

Further Progress Desirable. (Moldenke.) — We do not know at 
the present time why cupola malleables require an annealing heat sev- 
eral hundred degrees higher than air or open-hearth furnace iron. The 
underlying principles of the oxidation of the bath, which is a frequent 
cause of defective iron, is practically unknown to the majority of those 
engaged in this industry. Heats are frequently made that will not 
pour nor anneal properly, but the causes are still being sought. To 
produce castings from successive heats, so that with the same composi- 
tion they will have the same physical strength regardless of how they 
are tested, is a problem partially solved for steel, but not yet approached 
for malleable cast iron. 

Sufficient progress in the study of iron with the microscope has been 
made to warrant the belief that in the not distant future we may be 
able to distinguish the constituents of the material by means of etching 
with various chemicals. "When the sulphides and phosphides of iron, 
or the manganese-sulphur compounds, can be seen directly under the 
microscope, it is probable that a method may be found by which the 
dangerous ingredients may be so scattered or arranged that they will 
do the least harm. 

The high sulphur in European malleable accounts to some extent for 
the comparatively low strength when contrasted with our product. 
Their castings being all very light, so long as they bend and twist prop- 
erly, the purpose is served, and hence until heavier castings become the 
rule instead of the exception, "white heart" and steely-looking frac- 
tures will remain the characteristic feature of European work. 

Strength of Malleable Cast Iron. 

Bars cast by Buhl Malleable Co., Detroit, Mich. Reported by Chas. H. 
Day, Am. Mach., April 5, 1906. The castings were all made at the same 
time. The figures here given are the maximum and minimum results 
from three bars of each section. 





Tensile Tests. 




Compression Tests. 


Section. 


Area, 


Tensile 
St'gth, 
lbs. per 
sq. in. 


Elong. 
in 8 in., 


Red. of 
Area, 


Area, 


L'gth, 


Comp. 
Str., 


Final 




sq. in. 


%. 


%. 


sq. in. 


in. 


lbs. per 
sq. in. 


sq. in. 


Round 


0.817 


43,000 


5.87 


4.76 


0.847 


15 


31,700 


0.901 




0.801 


43,400 


6.21 


3.98 


0.801 


. 15 


33,240 


0.886 




0.219 


41,130 


7.70 


3.40 


0.209 


7.5 


32,600 


0.221 




0.202 


44,700 


13.00 


3.63 


0.204 


7.5 


34,600 


0.215 


Square 


0.277 


36,700 


4.70 


2.20 


0.263 


7.5 


33,200 


0.272 




0.277 


38,100 


3.72 


3.00 


0.254 


7.5 


31,870 


0.278 


" 


1.040 


38,460 


4.10 


3.30 


1.051 


15 


29,650 


1.070 


" 


1.050 


37,860 


2.38 


2.94 


1.040 


15 


30,450 


1.066 


Rect. 


0.239 


31,200* 


5.19 


1.50 


0.436 


15 


32,200 


0.448 




0.244 


37,600 


3.87 


3.80 


0.457 


15 


30,400 


0.467 


Star 


0.584 
0.575 


34,600 
37,200 


4.20 

4.80 


3.10 
3.50 











Broke in flaw. 



WROUGHT IRON. 



435 



The rectangular sections were approximately 1/4 X 3 /4 in. The star 
sections were square crosses, 1 inch wide, with arms about 1/4 in. thick. 

Tests of Rectangular Cast Bars, made by a committee of the Mas- 
'ter Car-builders' Assn. in 1891 and 1892, gave the following results 
(selected to show range of variation) : 



Size of 
Section, 



0.25x1.52 
0.5 xl.53 

0.78x2 

0.88x1.54 

1.52x1.54 



Tensile 


Elastic 


St'gth, 


Limit, 


lbs. per 


lbs. per 


sq. m. 


sq. m. 


34,700 


21,100 


32,800 


17,000 


25,100 


15,400 


33,600 


19,300 


28,200 





Elonga- 
tion, % 
in 4 in. 



Size of 
Section, 



0.29x2.78 
0.39x2.82 
0.53x2.76 
0.8 X2.76 
1.03x2.82 



Tensile 
St'gth, 
lbs. per 
sq. in. 



28,160 
32,060 
27,875 
25,120 
28,720 



Elastic 
Limit, 
lbs. per 



22,650 
20,595 
19,520 
18,390 
18,220 



Elong. 
in 8 in., 

%• 



0.6 
1.5 
1.1 



Tests of Square Bars, 1/2 in. and 1 in., by tension, compression and 
transverse stress, by M. H. Miner and F. E. Blake (Railway Age, Jan. 25, 
1901). 

Tension. Six 1/2-in. and six 1-in. round bars, also two 1-in. bars 
turned to remove the skin, from each of four makers. Average results: 

T. S., l/2-in. bars, 37,470-42,950, av. 40,960; E. L., 16,500-21,100, av. 
19,176. 

T. S., 1-in. bars, 35,750-40,530, av. 38,300; E. L., 14,860-19,900, av. 
17,181. 

Tensile strength, turned bars. av. 35,090; Elastic limit, av. 15,660. 

Elong. in 8 in., 1/2-in. bars, 4.75%; 1-in. bars, 4.32%; turned bars, 
3 73%. 
' Modulus of elasticity, 1/2-in. bars, 22,289,000; 1-in. bars, 21,677,000. 

Compression. 16 short blocks, 2 in. long, 1 in. and 1/2 in. square 
respectively. 

8 long columns, 15 in. long, 1 in. sq., and 7.5 in. long, 1/2 in. sq. respec- 
tively. 

Averages of blocks from each of four makers: 

Short blocks, 1/2-in. sq., 93,000 to 114,500 lbs. per sq. in. Mean, 
101,900 lbs. per sq. in. 

Short blocks, 1 in. sq., 137,600 to 165,300 lbs. per sq. in. Mean, 
152,800 lbs. per sq. in. 

Ratio of final to original length, l/2in., 61.7%; 1 in., 52.6%. A small 
part of the shortening was due to sliding on the 45° plane of fracture. 

Long columns: 1/2 in. X 7.5 in. Mean, 29,400 lbs. per sq. in.: 1 in. 
X 15 in., 27,500 lbs. per sq. in. Ratio of final to original length, 1/2 in., 
98.5%; 1 in., 98.8%. The long columns did not rupture, but reached 
the maximum stress after bending into a permanent curve. 

Transverse Tests. Maximum fiber stress, mean of 8 tests, 1/2-in. 
bars, 34,163 lbs. per sq. in. 1-in. bars, 36,125 lbs. persq. in. Length 
between supports, 20 in. The bars did not break, but failed by bending. 
The 1/2-in. bars could be bent nearly double. 



WROUGHT IRON. 

The Manufacture of Wrought Iron. — When iron ore, which is an 
oxide of iron, Fe203 or Fe30 4 , containing silica, phosphorus, sulphur, 
etc., as impurities, is heated to a yellow heat in contact with charcoal or 
other fuel, the oxygen of the ore combines with the carbon of the fuel, 
part of the iron combines with silica to form a fusible cinder or slag, and 
the remainder of the iron agglutinates into a pasty mass which is inter- 
mingled with the cinder. Depending upon the time and the tempera- 
ture of the operation, and on the kind and quality of the impurities 
present in the ore and the fuel, more or less of the sulphur and phos- 
phorus may remain in the iron or may pass into the slag; a small amount 
of carbon -may also be absorbed by the iron. By squeezing, hammering, 
or rolling the lump of iron while It is highly heated, the cinder may be 



436 



IRON AND STEEL. 



nearly all expelled from it, but generally enough remains to give a bar 
after being rolled, cooled and broken across, the appearance of a fibrous 
structure. The quality of the finished bar depends upon the extent to 
which the chemical impurities and the intermingled slag have been' 
removed from the iron. 

The process above described is known as the direct process. It is 
now but little used, having been replaced by the indirect process known 
as puddling or boiling. In this process pig iron which has been melted 
ia a reverb eratory furnace is desiiiconized and decarbonized by the 
oxygen derived from iron ore or iron scale in the bottom of the furnace, 
and fro n the oxidizing flame of the furnace. The temperature being too 
lov to maintain the iron, when low in carbon, in a melted condition, it 
gradually " comes to nature" by the formation of pasty particles in the 
bath, which adhere to each other, until at length all the iron is decarbon- 
ized and becomes of a pasty condition, and the lumps so formed when 
gathered together make the "puddle-ball" which is consolidated into a 
bloom by the squeezer and then rolled into "muck-bar." By cutting 
the muck -bar into short lengths and making a "pile" of them, heating 
the pile to a welding heat and rerolling, a bar is made which is freer 
from cinder and more homogeneous than the original bar, and it may 
be further "refined" by another piling and rerolling. The quality of 
the iron depends on the quality of the pig-iron, on the extent of the 
decarbonization, on the extent of dephosphorization which has been 
effected in the furnace, on the greater or less contamination of the iron 
by sulphur derived from the fuel, and on the amount of work done on 
the piles to free the iron from slag. Iron insufficiently decarbonized is 
irregular, and hard or "steely." Iron thoroughly freed from impurities 
is soft an I of low tensile strength. Iron high in sulphur is "hot-short," 
liable to break when being forged. Iron high in phosphorus is "cold- 
short," of low ductility when cold, and breaking with an apparently 
crystalline fracture. 

See papers on Manufacture and Characteristics of Wrought Iron, by 
J. P. Roe, Trans. A. I. M. E., xxxiii, p. 551; xxxvi, pp. 203, 807. 

Influence of Chemical Composition on the Properties of Wrought 
Iron. (Beardslee on Wrought Iron and Chain Cables. Abridgment by 
W. Kent. Wiley & Sons, 1879.) — A series of 2000 tests of specimens 
from 14 brands of wrought iron, most of them of high repute, was made 
in 1877 by Capt. L. A. Beardslee, U.S.N. , of the United States Testing 
Board. Forty-two chemical analyses were made of these irons, with a 
view to determine what influence the chemical composition had upon the 
strength, ductility, and welding power. From the report of these tests 
by A. L. Holley the following figures are taken: 



Brand. 


Average 
Tensile 
Strength. 


Chemical Composition. 


S. 


P. 


Si. 


C. 


Mn. 


Slag. 


L 

P 
B 
J 
O 
C 


66,598 
54,363 
52,764 
51,754 

51,134 
50,765 


trace 
(0.009 
{0.001 

0.008 
(0.003 
{0.005 
(0.004 
{ . 005 

0.007 


(0.065 
{0.084 
0.250 
0.095 
0.231 
0.140 
0.291 
0.067 
0.078 
0.169 


0.080 
0.105 
0.182 
0.028 
0.156 
0.182 
0.321 
0.065 
0.073 
0.154 


0.212 
0.512 
0.033 
0.066 
0.015 
0.027 
0.051 
0.045 
0.042 
0.042 


0.005 
0.029 
0.033 
0.009 
0.017 
trace 
0.053 
0.007 
0.005 
0.021 


0.192 
0.452 
0.848 
1.214 

' 6.678' 
1.724 
1.168 
0.974 



Where two analyses are given, they are the extremes of two or more 
analyses of the brand. Where one is given, it is the only analysis. Brand 
L should be classed as a puddled steel. 



WROUGHT IRON. 



437 



Order of Qualities Graded from No. 1 to No. 19. 



Brand. 


Tensile 
Strength. 


Reduction of 
Area. 


Elongation. 


Welding Power. 


L 
P 
B 
J 

O 

c 


1 

6 
12 
16 
18 
19 


18 
6 
16 
19 

1 
12 


19 
3 

15 

18 
4 

16 


most imperfect. 

badly. 

best. 

rather badly. 

very good. 



The reduction of area varied from 54.2 to 25.9 per cent, and the elonga- 
tion from 29.9 to 8.3 per cent. 

Brand O, the purest iron of the series, ranked No. 18 in tensile strength, 
but was one of the most ductile; brand B, quite impure, was below the 
average both in strength and ductility, but was the best in welding 
power; P, also quite impure, was one of the best in every respect except 
welding, while L, the highest in strength, was not the most pure, it had 
the least ductility, and its welding power was most imperfect. The 
evidence of the influence of chemical composition upon quality, there- 
fore, is quite contradictory and confusing. The irons differing remark- 
ably in their mechanical properties, it was found that a much more 
marked influence upon their qualities was caused by different treatment 
in rolling than by differences in composition. 

In regard to slag Mr. Holley says: "It appears that the smallest and 
most worked iron often has the most slag. It is hence reasonable to 
conclude that an iron may be dirty and yet thoroughly condensed." 

In his summary of "What is learned from chemical analysis," he says: 
" So far, it may appear that little of use to the makers or users of wrought 
iron has been learned. ... The character of steel can be surely pred- 
icated on the analyses of the materials; that of wrought iron is altered by 
subtle and unobserved causes." 

Influence of Reduction in Rolling from Pile to Bar on the 
Strength of Wrought Iron. — The tensile strength of the irons used 
in Beardslee's tests ranged from 46,000 to 62,700 lbs. per sq. in., brand 
L, which was really a steel, not being considered. Some specimens of L 
gave figures as high as 70,000 lbs. The amount of reduction of sectional 
area in rolling the bars has a notable influence on the strength and elastic 
limit ; the greater the reduction from pile to bar, the higher the strength. 

The following are a few figures from tests of one of the brands: 



Size of bar, in. diam.: 
Area of pile, sq. in.: 
Bar per cent of pile: 
Tensile strength, lb.: 
Elastic limit, lb.: 



2 


1 


1/2 


1'4 


72 


25 


9 


3 


4.36 


3.14 


2.17 


1.6 


48,280 


51,128 


52,275 


59,585 


31,892 


36,467 


39,126 






3 

80 80 

15.7 8.83 

46,322 47,761 

23.430 26,400 

Specifications for Wrought Iron. (F. H. Lewis, Engineers' Club oi 
Philadelphia, 1891.) — 1. All wrought iron must be tough, ductile, 
fibrous, and of uniform quality for each class, straight, smooth, free from 
cinder-pockets, flaws, buckles, blisters, and injurious cracks aiong the 
edges, and must have a workmanlike finish. No specific process or 
provision of manufacture will be demanded, provided the material fulfills 
the requirements of these specifications. 

2. The tensile strength, limit of elasticity, and ductility shall be deter- 
mined from a standard test-piece not less than 1/4 inch thick, cut from 
the full-sized bar, and planed or turned parallel. The area of cross- 
section shall not be less than 1/2 square inch. The elongation shall be 
measured after breaking on an original length of 8 inches. 

3. The tests shall show not less than the following results: 



For bar iron in tension 

For shape iron in tension. . . 
For plates under 36 in. wide 
For plates over 36 in. wide . 



T. S. 













in 8 in. 


= 50,000; 


E 


L. 


= 26,000; 


E 


L. 


18% 
15% 


= 48,000; 






= 26,000, 






= 48,000; 






= 26,000; 




** 


12% 


= 46,000; 






= 25,000; 






10% 



438 IRON AND STEEL. 

4. When full-sized tension members are tested to prove the strength of 
their connections, a reduction in their ultimate strength of (500 X width 
of bar) pounds per square inch will be allowed. 

5. All iron shall bend, cold, 180 degrees around a curve whose diameter 
is twice the thickness of piece for bar iron, and three times the thickness 
for plates and shapes. 

6. Iron which is to be worked hot in the manufacture must be capable 
of bending sharply to a right angle at a working heat without sign of 
fracture. 

7. Specimens of tensile iron upon being nicked on one side and bent 
shall show a fracture nearly all fibrous. 

8. All rivet iron must be tough and soft, and be capable of bending 
cold until the sides are in close contact without sign of fracture on the 
convex side of the curve. 

Penna. R. It. Co.'s Specifications for Merchant-bar Iron (1904). — 
One bar will be selected for test from each 100 bars in a pile. 

All the iron of one size in the shipment will be rejected if the average 
tensile strength of the specimens tested full size as rolled falls below 
47,000 lbs. or exceeds 53,000 lbs. per sq. in., or if a single specimen falls 
below 45,000 lbs. per sq. in.; or when the test specimen has been reduced 
by machining if the average tensile strength exceeds 53,000 or falls below 
46,000, or if a single specimen falls below 44,000 lbs. per sq. in. 

All the iron of one size in the shipment will be rejected if the average 
elongation in 8 in. falls below the following limits: Flats and rounds, 
tested as rolled, 1/2 in. and over, 20%; less than 1/2 in., 16%. Flats and 
rounds reduced by machining 16%. 

Nicking and Bending Tests. — When necessary to make nicking and 
bending tests, the iron will be nicked lightly on one side and then broken 
by holding one end in a vise, or steam hammer, and breaking the iron by 
successive blows. It must when thus broken show a generally fibrous 
structure, not more than 25% crystalline, and must be free from admix- 
ture of steel. 

Stay-bolt Iron. (Penna. R. R. Co.'s specifications, 1902). — Sample 
bars must show a tensile strength of not less than 48,000 lbs. per sq. in. 
and an elongation of not less than 25% in 8 in. One piece from each lot 
will be threaded in dies with a sharp V thread, 12 to 1 in. and firmly 
screwed through two holders having a clear space between them of 5 in. 
One holder will be rigidly secured to the bed of a suitable machine, and the 
other vibrated at right "angles to the axis over a space of 1/4 in. or 1/8 in. 
each side of the center line. Acceptable iron should stand 2800 double 
vibrations before breakage. 

Mr. Vauclain, of the Baldwin Locomotive Works, at a meeting of the 
American Railway Master Mechanics' Association, in 1892, says: Many 
advocate the softest iron in the market as the best for stay-bolts. He 
believed in an iron as hard as was consistent with heading the bolt nicely. 
The higher the tensile strength of the iron, the more vibrations it will 
stand, for it is not so easily strained beyond the yield-point. The Baldwin 
specifications for stay-bolt iron call for a tensile strength of 50,000 to 
52,000 lbs. per square inch, the upper figure being preferred, and the 
lower being insisted upon as the minimum. 

Specifications for Wrought Iron for the World's Fair Buildings. 
(Eng'g News, March 26, 1892.) — All iron to be used in the tensile mem- 
bers of open trusses, laterals, pins and bolts, except plate iron over 
8 inches wide, and shaped iron, must show by the standard test-pieces 
a tensile strength in lbs. per square inch of: 

_ 9 „ _ 7000 X area of original bar in sq. in. 
circumference of original bar in inches' 
with an elastic limit not less than half the strength given by this formula, 
and an elongation of 20% in 8 in. 

Plate iron 8 to 24 inches wide, T. S. 48,000, E. L. 26,000 lbs. per sq. in., 
elong. 12%. Plates over 24 inches wide, T. S. 46,000, E. L. 26,000 lbs. 
per sq. in. Plates 24 to 36 in. wide, elong. 10%; 36 to 48 in., 8%; over 
48 in., 5%. 

All shaped iron, flanges of beams and channels, and other iron not 
hereinbefore specified, must show a T. S. in lbs. per sq. in. of: 
_ 7000 X area of original bar 
circumference of original bar ' 



METALS AT VARIOUS TEMPERATURES. 439 

with an elastic limit of not less than half the strength given by this formula, 
and an elongation of 15% for bars 5/8 inch and less in thickness, and of 
12% for bars of greater thickness. For webs of beams and channels, 
specifications for plates will apply. 

All rivet iron must be tough and soft, and pieces of the full diameter of 
the rivet must be capable of bending cold, until the sides are in close con- 
tact, without sign of fracture on the convex side of the curve. 

TENACITY OF METALS AT VARIOUS TEMPERATURES. 

The British Admiralty made a series of experiments to ascertain what 
loss of strength and ductility takes place in gun-metal compositions when 
raised to high temperatures. It was found that all the varieties of gun 
metal suffer a gradual but not serious loss of strength and ductility up to 
a certain temperature, at which, within a few degrees, a great change 
takes place, the strength falls to about one-half the original, and the 
ductility is wholly gone. At temperatures above tins point, up to 500° F., 
there is little, if any, further loss of strength; the temperature at which 
this great change and loss of strength takes place, although uniform in 
the specimens cast from the same pot, varies about 100° in the same 
composition cast at different temperatures, or with some varying condi- 
tions in the foundry 'process. The temperature at which the change took 
place in No. 1 series was ascertained to be about 370°, and in that of 
No. 2, at a little over 250°. Rolled Muntz metal and copper are satis- 
factory up to 500°, and may be used as securing-bolts with safety. 
Wrought iron increases in strength up' to 500°, but loses slightly in duc- 
tility up to 300°, where an increase begins and continues up to 500°, 
where it is still less than at the ordinary temperature of the atmosphere. 
The strength of Landore steel is not affected by temperature up to 500°, 
but its ductility is reduced more than one-half. (Iron, Oct. 6, 1877.) 

Tensile Strength of Iron and Steel at High Temperatures. — 
James E. Howard's tests (Iron Age, April 10, 1S90) show that the tensile 
strength of steel diminishes as the temperature increases from 0° until a 
minimum is reached between 200° and 300° F., the total decrease being 
about 4000 lbs. per square inch in the softer steels, and from 6000 to 
8000 lbs. in steels of over 80,000 lbs. tensile strength. From this mini- 
mum point the strength increases up to a temperature of 400° to 650° F., 
the maximum being reached earlier in the harder steels, the increase 
amounting to from 10,000 to 20,000 lbs. per square inch above the mini- 
mum strength at from 200° to 300°. From this maximum, the strength 
of all the steel decreases steadily af a rate approximating 10,000 lbs. 
decrease per 100° increase of temperature. A strength of 20,000 lbs. 
per square inch is still shown by 0.10 C. steel at about 1000° F., and by 
0.60 to 1.00 C. steel at about 1600° F. 

The strength of wrought iron increases with temperature from 0° up 
to a maximum at from 400 to 600° F., the increase being from 8000 to 
10,000 lbs. per square inch, and then decreases steadily till a strength of 
only 6000 lbs. per square inch is shown at 1500° F. 

Cast iron appears to maintain its strength, with a tendency to in- 
crease, until 900° is reached, beyond which temperature the strength 
gradually diminishes. Under the highest temperatures, 1500° to 1600° F., 
numerous cracks on the cylindrical surface of the specimen were devel- 
oped prior to rupture. It is remarkable that cast iron, so much inferior 
in strength to the steels at atmospheric temperature, under the highest 
temperatures has nearly the same strength the high-temper steels then 
have. 

Strength of Iron and Steel Boiler-plate at High Temperatures. 
(Chas. Huston, Jour. F. I., 1877.) 

Average of Three Tests of Each. 
Temperature F. 68° 575° 925° 

Charcoal iron plate, tensile strength, lbs 55,366 63,080 65,343 

contr. of area % 26 23 21 

Soft open-hearth steel, tensile strength, lbs 54,600 66,083 64,350 

" contr. % 47 38 33 

" Crucible steel, tensile strength, lbs 64,000 69,266 68,600 

contr. % 36 30 21 

Strength of Wrought Iron and Steel at High Temperatures. 
(Jour. F. I., cxii, 1881, p. 241.) — Kollmann's experiments at Oberhausen 



440 



IRON AND STEEL. 



included tests of the tensile strength of iron and steel at temperatures 
ranging between 7U° and 2000° F. Three kinds of metal were tested, 
viz., fibrous iron of 52,464 lbs. T. S., 38,280 lbs. E. L., and 17.5% 
elong.; fine-grained iron of 56,s«j2 lbs. T. S., 39,113 lbs. E. L., and 20% 
elong.; and Bessemer steei of 84,826 lbs. T. S., 55,029 lbs. E. L., and 
14.5% elong. The mean ultimate tensile strength of each material 
expressed in per cent of that at ordinary atmospheric temperature is 
given in the following table, the fifth column of which exhibits, for pur- 
poses of comparison, the results of experiments by a committee of the 
Franklin Institute in the years 1832-36. 



Temperature 


Fibrous 


Fine-grained 


Bessemer 


Franklin In- 


Degrees F. 


Iron, %. 


Iron, %. 


Steel, %. 


stitute, %. 





100.0 


100.0 


100.0 


96.0 


100 


100.0 


100.0 


100.0 


102.0 


200 


100.0 


100.0 


100.0 


105.0 


300 


97.0 


100.0 


100.0 


106.0 


400 


95.5 


100.0 


100.0 


106.0 


500 


92.5 


98.5 


98.5 


104.0 


600 


88.5 


95.5 


92.0 


99.5 


700 


81.5 


90.0 


68.0 


92.5 


800 


67.5 


77.5 


44.0 


75.5 


900 


44.5 


51.5 


36.5 


53.5 


1000 


26.0 


36.0 


31.0 


36.0 


1100 


20.0 
18.0 
13.5 
7.0 
4.5 
3.5 


30.5 
28.0 
19.0 
12.5 
8.5 
5.0 


26.5 
22.0 
15.0 
10.0 
7.5 
5.0 




1200 




1400 




1600 




1800 




2000 









Effect of Cold on the Strength of Iron and Steel. — ■ The following 
conclusions were arrived at by Mr. Styffe in 1865: 

(1) The absolute strength of iron and steel is not diminished by cold, 
even at the lowest temperature which ever occurs in Sweden. 

(2) Neither in steel nor in iron is the extensibility less in severe cold 
than at the ordinary temperature. 

(3) The limit of elasticity in both steel and iron lies higher in severe 
cold. 

(4) The modulus of elasticity in both steel and iron is increased on 
reduction of temperature, and diminished on elevation of temperature; 
but that these variations never exceed 0.05% for a change of 1.8° F. 

W. H. Barlow (Proc. Inst. C. E.) made experiments on bars of wrought 
iron, cast iron, malleable cast iron, Bessemer steel, and tool steel. The 
bars were tested with tensile and transverse strains, and also by im- 
pact; one-half of them at a temperature of 50° F., and the other half at 
5°F. 

The results of the experiments were summarized as follows: 

1. When bars of wrought iron or steel were submitted to a tensile 
strain and broken, their strength was not affected by severe cold (5° F.), I 
but their ductility was increased about 1% in iron and 3% in steel. 

2. When bars of cast iron were submitted to a transverse strain at a 
low temperature, their strength was diminished about 3% and their 
flexibility about 16%. 

3. When bars of wrought iron, malleable cast iron, steel, and ordinary 
cast iron were subjected to impact at 5° F., the force required to break 
them, and their flexibility, were reduced as follows: 





Reduction of 
Force of Im- 
pact, %. 


Reduction of 

Flexibility, 

%. 




3 

31/2 
41/2 
21 


18 




17 




15 


(Sast iron, about 


not taken 



DURABILITY OF IRON, CORROSION, ETC. 



441 



The experience of railways in Russia, Canada, and other countries 
where the winter is severe, is that the breakages of rails and tires are far 
more numerous in the cold weather than in the summer. On this 
account a softer class of steel is employed in Russia for rails than is usual 
in more temperate climates. 

The evidence extant in relation to this matter leaves no doubt that the 
capability of wrought iron or steel to resist impact is reduced by cold. On 
the other hand, its static strength is not impaired by low temperatures. 

Increased Strength of Steel at very Low Temperature. — Steel of 
72,300 lb. T. S. and 62,800 lb. elastic limit when tested at 76° F. gave 
97,600 T. S. and 80,000 E. L. when tested at the temperature of liquid 
air. — Watertown Arsenal Tests, Eng. Rec, July 21, 1906. 

Prof. R. C. Carpenter (Proc. A. A. A. S. 1897) found that the strength 
of wrought iron at — 70° F. was 20% greater than at 70° F. 

Effect of Low Temperatures on Strength of Railroad Axles. 
(Thos. Andrews, Proc. hist. C. E., 1891.) — Axles 6 ft. 6 in. long be- 
tween centers of journals, total length 7 ft. 3V2 in., diameter at middle 
4V2 in., at wheel-sets 51/8 in., journals 33/4 x 7 in., were tested by impact 
at temperatures of 0° and 100° F. Between the blows each axle was 
half turned over, and was also replaced for 15 minutes in the water-bath. 

The mean force of concussion resulting from each impact was ascer- 
tained as follows: 

Let h = height of free fall in feet, w = weight of test ball, hw = W = 
"energy," or work in foot-tons, re = extent of deflections between bearings 

then F (mean force) = W/x = liw/x . 

The results of these experiments show that whereas at 0° F. a total 
average Vnean force of 179 tons was sufficient to cause the breaking of the 
axles, at 100° F. a total average mean force of 428 tons was required. 
In other words, the resistance to concussion of the axles at 0° F. was only 
about 42% of what it was at 100° F. 

The average total deflection at 0° F. was 6.48 in., as against 15.06 in. 
with the axles at 100° F. under the conditions stated; this represents an 
ultimate reduction of flexibility, under the test of impact, of about 57% 
for the cold axles at 0° F., compared with the warm axles at 100° F. 



EXPANSION OF IRON AND STEEL BY HEAT. 

James E. Howard, engineer in charge of the IT. S. testing-machine at 
Watertown, Mass., gives the following results of tests made on bars 35 
inches long (Iron Age, April 10, 1890): 





C. 


Mn. 


Si. 


Coeffi. of 

Expansion 

per degree 

F. 




c. 


Mn. 


Si. 

.07 
.08 
.17 
.19 

.28 


Coeffi. of 

Expansion 

per degree 

F. 










0.0000067302 
.0000067561 
.0000066259 
.0000065149 
.0000066597 
.0000066202 


Steel 


0.57 
.71 
.81 

.89 
.97 


0.93 

.58 
.56 
.57 
.SO 


0.G00C063891 


Steel 


0.C9 
.20 
.31 
.37 
.51 


0.11 
.45 
.57 
.70 
.58 


m 




.0000064716 






0000062167 






.0000062335 






.C000061700 




Cast (gun) 
iron 






.0000059261 



DURABILITY OF IRON, CORROSION, ETC. 

Crystallization of Iron by Fatigue. — Wrought iron of the best 
quality is very tough, and breaks, on being pulled in a testing machine or 
bent after nicking, with a fibrous fracture. Cold-short iron, however, is 
more brittle, and breaks square across the fibers with a fracture which is 
commonly called crystalline although no real crystals are present. Iron 
which has been repeatedly overstrained, and especially iron subjected 
to repeated vibrations and shocks, also becomes brittle, and breaks with 
an apparentlv crystalline fracture. See " Resistance of Metals to Repeated 
Shocks," p. 262. 



442 IRON AND STEEL. 



Walter H. Finley (Am. Mack., April 27, 1905) relates a case of fail- 
ures of H/8-in. wrougnt-iron coupling pins on a train of 1-ton mine cars, 
apparently due to crystallization. After two pins were broken after a 
year's hard service, " several hitchings were laid on an anvil and the pin 
broken by a single blow from a sledge. Pieces of the broken pins were 
then heated to a bright red, and, after cooling slowly, were again put 
under the hammer, which failed entirely to break them. After cutting 
with a cleaver, the pins were broken, and the fracture showed a complete 
restoration of the fibrous structure. This annealing process was then 
applied to the whole supply of hitchings. Piles of twenty-five or thirty 
were covered by a hot wood fire, which was allowed to die down and go 
out, leaving the hitchings in a bed of ashes to cool off slowly. By 
repeating this every six months the danger from brittle pins was entirely 
avoided." 

Durability of Cast Iron. — Frederick Graff, in an article on the 
Philadelphia water-supply, says that the first cast-iron pipe used there 
was laid in 1820. These pipes were made of charcoal iron, and were in 
constant use for 53 years. They were uncoated, and the inside was well 
filled with tubercles. In salt water good cast iron, even uncoated, will 
last for a century at least ; but it often becomes soft enough to be cut by 
a knife, as is shown in iron cannon taken up from the bottom of harbors 
after long submersion. Close-grained, hard white metal lasts the longest 
in sea water. (Eng'g News, April 23, 1887, and March 26, 1892.) 

Tests of Iron after Forty Years' Service. — A square link 12 inches 
broad, 1 inch thick and about 12 feet long was taken from the Kieff 
bridge, then 40 years old. and tested in comparison with a similar link 
which had been preserved in the stock-house since the bridge was built. 
The following is the record of a mean of four longitudinal test-pieces, 
1 X WsX 8 inches, taken from each link (Stah? und Eisen, 1890): 

Old Link T. S., 21.8 tons; E. L., 11.1 tons; Elong., 14.05% 

New Link " 22.2 " " 11.9 " " 13.42% 

Durability of Iron in Bridges. (G. Lindenthal, Eng'g, May 2, 1884, 
p. 139.) — The Old Monongahela suspension bridge in Pittsburg, built 
in 1845, was taken down in 1882. The wires of the cables were frequently 
strained to half of their ultimate strength, yet on testing them after 37 
years' use they showed a tensile strength of from 72,700 to 100,000 lbs. 
per sq. in. The elastic limit was from 67,100 to 78,600 lbs. per sq in. 
Reduction at point of fracture, 35% to 75%. Their diameter was 0.13 in. 

A new ordinary telegraph wire of same gauge tested for comparison 
showed: T. S., of 100.000 lbs.; E. L., 81,550 lbs.; reduction, 57%. Iron 
rods used as stays or suspenders showed: T. S., 43,770 to 49,720 lbs. E. 
L., 26,380 to 29,200. Mr. Lindenthal draws these conclusions: 

" The above tests indicate that iron highly strained for a long number 
of years, but still within the elastic limit, and exposed to slight vibration, 
will not deteriorate in quality. 

"That if subjected to only one kind of strain it will not change its 
texture, even if strained beyond its elastic limit, for many years. It will 
stretch and behave much as in a testing-machine during a long test. 

"That iron will change its texture only when exposed to alternate 
severe straining, as in bending in different directions. If the bending is 
slight but very rapid, as in violent vibrations, the effect is the same." 

Durability of Iron in Concrete. — In Paris a sewer of reinforced con- 
crete 40 years old was removed and the metal was found in a perfect state 
of preservation. In excavating for the foundations of the new General 
Post Office in London some old Roman brickwork had to be removed, 
and the hoop-iron bonds were still perfectly bright and good. (Eng'g, 
Aug. 16, 1907, p. 227.) 

Corrosion of Iron Bolts. — On bridges over the Thames in London, 
bolts exposed to the action of the atmosphere and rain-water were eaten 
away in 25 years from a diameter of 7/g in. to 1/2 in., and from 5/g in. diam- 
eter to 5/i6 inch. 

Wire ropes exposed to drip in colliery shafts are very liable to corrosion. 

Corrosive Agents in the Atmosphere. — The experiments of F. 
Crace Calvert (Chemical News, March 3, 1871) show that carbonic acid, 
in the presence of moisture, is the agent which determines the oxidation 
of iron in the atmosphere. He subjected perfectly cleaned blades of iron 



DURABILITY OF IRON, CORROSION, ETC. 443 

and steel to the action of different gases for a period of four months, with 
results as follows: 

Dry oxygen, dry carbonic acid, a mixture of both gases, dry and damp 
oxygen and ammonia: no oxidation. Damp oxygen: in three experi- 
ments one blade only was slightly oxidized. 

Damp carbonic acid: slight appearance of a white precipitate upon the 
iron, found to be carbonate of iron. Damp carbonic acid and oxygen: 
oxidation very rapid. Iron immersed in water containing carbonic acid 
oxidized rapidly. 

Iron immersed in distilled water deprived of its gases by boiling rusted 
the iron in spots that were found to contain impurities. 

Sulphurous acid (the product of the combustion of the sulphur in coal) 
is an exceedingly active corrosive agent, especially when the exposed iron 
is coated with soot. Tins accounts for the rapid corrosion of iron in 
railway bridges exposed to the smoke from locomotives. (See account of 
experiments by the author, on action of sulphurous acid in Jour. Frank, 
hist., June, 1875, p. 437.) An analysis of sooty iron rust from a railway 
bridge showed the presence of sulphurous, sulphuric, and carbonic acids, 
chlorine, and ammonia. Bloxam states that ammonia is formed from 
the nitrogen of the air during the process of rusting. 

Galvanic Action is a most active agent of corrosion. It takes place 
when two metals, one electro-negative to the other, are placed in contact 
and exposed to dampness. 

Corrosion in Steam-boilers. ■ — Internal corrosion may be due either 
to the use of water containing free acid, or water containing sulphate 
or chloride of magnesium, which decompose when heated, liberating the 
acid, or to water containing air or carbonic acid in solution. External 
corrosion rarely takes place when a boiler is kept hot, but when cold it 
is apt to corrode rapidly in those portions where it adjoins the brick- 
work or where it may be covered by dust or ashes, or wherever damp- 
ness may lodge. (See Impurities of Water, p. 691, and Incrustation and 
Corrosion, p. 897.) 

Corrosion of Iron and Steel. — Experiments made at the Riverside 
Iron Works, Wheeling, W. Va., on the comparative liability to rust of 
iron and soft Bessemer steel: A piece of iron plate and a similar piece of 
steel, both clean and bright, were placed in a mixture of yellow loam and 
sand, with which had been thoroughly incorporated some carbonate of 
soda, nitrate of soda, ammonium chloride, and chloride of magnesium. 
The earth as prepared was kept moist. At the end of 33 days the pieces 
of metal were taken out, cleaned, and weighed, when the iron was found 
to have lost 0.84% of its weight and the steel 0.72%. The pieces were 
replaced and after 28 days weighed again, when the iron was found to 
have lost 2.06% of its original weight and the steel 1.79%. (Eng'g, June 
26, 1891.) 

Internal Corrosion of Iron and Steel Pipes by Warm Water. 
(T. N. Thomson, Proc. A. S. H. V. E., 1908.) —Three short pieces of iron 
and three of steel pipes, 2 in. diam., were connected together by nipples 
and made part of a pipe line conveving water at a temperature varving 
from 160° to 212° F. In one year 913/32 lbs. of wrought iron lost 203/4 oz., 
and 913/32 lbs. of steel 247/§ oz. The pipes were sawed in two lengthwise, 
and the deepest pittings were measured by a micrometer. Assuming that 
the pitting would have continued at a uniform rate the wrought-iron pipes 
would have been corroded through in from 686 to 780 days, and the steel 
pipes from 760 to 850 days, the average being 742 days for iron and 797 
days for steel. Two samples each of galvanized iron and steel pipe were 
also included in the pipe line, and their calculated life was: iron 770 and 
1163 days; steel 619 and 1163 days. Of numerous samples of corroded 
pipe received from heating engineers ten had given out within four years 
of service, and of these six were steel and four were iron. 

To ascertain whether Pipe is made of Wrought Iron or Steel, cut 
off a short piece of the pipe and suspend it in a solution of 9 parts of water, 
3 of sulphuric acid, and 1 of hydrochloric acid in a porcelain or glass dish 
in such a way that the end will not touch the bottom of the dish. After 
2 to 3 hours' immersion remove the pipe and wash off the acid. If the 
pipe is steel the end will present a bright, solid, unbroken surface, while 
if made of iron it will show faint ridges or rings, like the year rings in a 
tree, showing the different layers of iron and streaks of cinder. In order 
that the scratches made by the cutting-off tool may not be mistaken for 



444 IRON AND STEEL. 

the cinder marks, file the end of the pipe straight across or grind on an 
emery wheel until the marks of the cutting-off tool have disappeared 
before putting it in the acid. 

Relative Corrosion of Wrought Iron and Steel. (H. M. Howe, 
Proc. A. S. T. M., 1906.) — On one hand we have the very general 
opinion that steel corrodes very much faster than wrought iron, an opinion 
held so widely and so strongly that it cannot be ignored. On the other 
hand we have the results of direct experiments by a great many observers, 
in different countries and under widely differing conditions; and these 
results tend to show that there is no very great difference between the 
corrosion of steel and wrought iron. Under certain conditions steel seems 
to rust a little faster than wrought iron, and under others wrought iron 
seems to rust a little faster than steel. Taking the tests in unconfmed 
sea water as a whole wrought iron does constantly a little better than 
steel, and its advantage seems to be still greater in the case of boiling sea 
water. In the few tests in alkaline water wrought iron seems to have the 
advantage over steel, whereas in acidulated water steel seems to rust more 
slowly than wrought iron. 

Steel which in the first few months may rust faster than wrought iron 
may, on greatly prolonging the experiments, or pushing them to destruc- 
tion, actually rust more slowly, and vice versa. 

Carelessly made steel, containing blowholes, may rust faster than 
wrought iron, yet carefully made steel, free from blowholes, may rust 
more slowly. Any difference between the two may be due not to the 
inherent and intrinsic nature of the material, but to defects to which it 
is subject if carelessly made. Care in manufacture, and special steps to 
lessen the tendency to rust, might well make steel less corrodible than 
wrought iron, even if steel carelessly made should really prove more 
corrodible than wrought iron. 

For extensive discussions on this subject see Trans. A. I. M. E., 1905, 
and Proc. A. S. T. M., 1906. 

Corrosion of Fence Wire. (A. S. Cushman, Farmers' Bulletin, No. 
239, U. S. Dept. of Agriculture, 1905.) — "A large number of letters were 
received from all over the country in response to official inquiry, and 
all pointed in the same direction. As far as human testimony is capable 
of establishing a fact, there need be not the slightest question that modern 
steel does not serve the purpose as well as the older metal manufactured 
twenty or more years ago." 

Electrolytic Theory, and Prevention of Corrosion. (A. S. Cush- 
man, Bulletin No. 30, U. S. Dept. of Agriculture, Office of Public Roads, 
1907. The Corrosion of Iron.) — The various kinds of merchantable iron 
and steel differ, within wide limits, in their resistance, not only to the 
ordinary processes of oxidation known as rusting, but also in other corro- 
sive inliuences. Different specimens of one and the same kind of iron or 
steel will show great variability in resistance to corrosion under the con- 
ditions of use and service. The causes of this variability are numerous 
and complex, and the subject is not nearly so well understood at the 
present time as it should be. All investigators are agreed that iron can- 
not rust in air or oxygen unless water is present, and on the other hand 
it cannot rust in water unless oxygen is present. 

From the standpoint of the modern theory of solutions, all reactions 
which take place in the wet way are attended with certain readjustments 
of the electrical states of the reacting ions. The electrolytic theory of 
rusting assumes that before iron can oxidize in the wet way it must first 
pass into solution as a ferrous ion. 

Dr. Cushman then gives an account of his experiments which he con- 
siders demonstrate that iron goes into solution up to a certain maximum 
concentration in pure water, without the aid of oxygen, carbonic acid or 
other reacting substances. It is apparent that the rusting of iron is 
primarily due, not to attack by oxygen, but by hydrogen ions. 

Solutions of chromic acid and potassium bichromate inhibit the rusting 
of iron. If a rod or strip of bright iron or steel is immersed for a few 
hours in a 5 to 10 per cent solution of potassium bichromate, and is then 
removed and thoroughly washed, a certain change has been produced 
on the surface of the metal. The surface may be thoroughly washed 
and wiped with a clean cloth without disturbing this new surface condi- 
tion. No visible change has been effected, for the polished surfaces 



DURABILITY OF IRON, CORROSION, ETC. 445 

examined under the microscope appear to be untouched. If, however, 
the polished strips are immersed in water it will be found that rusting is 
inhibited. An ordinary untreated polished specimen of steel will show 
rusting in a few minutes when immersed in the ordinary distilled water of 
the laboratory. Chromatid specimens will stand immersion for varying 
lengths of time before rust appears. In some cases it is a matter of 
hours, in others of days or even weeks before the inhibiting effect is over- 
come. 

It would follow from the electrolytic theory that in order to have the 
highest resistance to corrosion a metal should either be as free as possible 
from certain impurities, such as manganese, or should be so homogene- 
ous as not to retain localized positive and negative nodes for a long time 
without change. Under the first condition iron would seem to have the 
advantage over steel, but under the second much would depend upon 
care exercised in manufacture, whatever process was used. 

There are two lines of advance by which we may hope to meet the 
difficulties attendant upon rapid corrosion. One is by the manufacture 
of better metal, and the other is by the use of inhibitors and protective 
coverings. Although it is true that laboratory tests are frequently 
unsuccessful in imitating the conditions in service, it nevertheless appears 
that chromic acid and its salts should under certain circumstances come 
into use to inhibit extremelv rapid corrosion bv electrolysis. 

Chrome Paints. — G. B. Heckel (Jour. F. I., Eng. Dig., Sept., 1908) 
quotes a letter from Mr. Cushman as follows: "My observation that 
chromic acid and certain of its compounds act as inhibitives has led to 
many experiments by other workers along the same line. I have found 
that the chrome compounds on the market vary very much in their action. 
Some of them show up as strong inhibitors, while others go to the op- 
posite extreme and stimulate corrosion. Referring only to the labeled 
names of the pigments, I find among the good ones, in the order cited: 
Zinc chromate, American vermilion, chrome yellow orange, chrome 
yellow dd. Among the bad ones, also in the order given, I find: Chrome 
yellow medium, chrome green, chrome red. Much the worst of all is 
chrome yellow lemon. I presume that the difference is due to impurities 
that are present in the bad pigments." 

Mr. Heckel suggests the following formula for a protective paint: 40 
lbs. American vermilion, 10 lbs. red lead, 5 lbs. Venetian red. Zinc 
oxide and lamp-black to produce the required tint or shade. Grind in 
1 1/3 gal. of raw linseed oil — increasing the quantity as required for added 
zinc oxide or lamp-black — and 1/8 gal. crusher's drier. For use, thin 
with raw oil and very little turpentine or benzine. 

He states that the substitution of zinc chrome for the American ver- 
milion; of any high-grade finely ground iron oxide for the Venetian red; 
and of American vermilion for the red lead, would probably improve the 
protective value of the formula; that the addition of a very little kauri 
gum varnish, if zinc oxide' is used, might be found advantageous; and 
that the substitution of a certain proportion of China wood oil for some 
of the linseed oil might improve the wearing qualities of the paint. 

Dr. Cushman points out two dangers confronting us when we attempt 
to base an inhibitive formula on commercial products. The first is that 
all carbon pigments, excepting pure graphite, may contain sulphur com- 
pounds easily oxidizable to sulphuric acid when spread out as in a paint 
film. The second is the probability of variation in the composition of 
basic lead chromate or American vermilion. Because of these facts, it 
is necessary, before selecting any particular pigment for its inhibitive 
quality, to ascertain that it is free from acids or acid-forming impurities. 
As a result of his experiments he recommends the substitution of Prus- 
sian blue for the lamp-black in Mr. Heckel's formula, and lays down as a 
safe rule in the formulation of inhibitive paints, a careful avoidance of 
all potential stimulators of the hydrogen ions and consequently of any 
substance which might develop acid ; preference being given to chromate 
pigments which are to some extent soluble in water, and to other pig- 
ments which in undergoing change tend to develop an alkaline rather 
than an acid reaction. Calcium sulphate, for example, in any form (as 
a constituent of Venetian red, for example), he deems dangerous to use 
because of the possibility of its developing acid. Barium sulphate, on 
the other hand, he regards as practically safe, because of its well-known 
chemical stability. 



446 IRON AND STEEL. 

Corrosion caused by Stray Electric Currents. (W. W. Churchill, 
Science, Sept. 28, 1906). — Surface condensers in electric lighting and 
other plants were abandoned on account of electrolytic corrosion. The 
voltage of the rails in the freight yard of the Long Island railroad at the 
peak of the load was 9 volts above the potential of the river, decreasing 
to 2 volts or less at light loads. This caused a destruction of water pipes 
and other things in the railroad yards. Experiments with various metal 
plates immersed in samples of East River water showed that it gave a 
more violent action than ordinary sea water. It was further observed 
that there was a local galvanic action going on, and that the amount of 
stray currents had something to do with the polarization of the surfaces, 
making the galvanic action exceedingly violent and destroying thin cop- 
per tubes at a very rapid rate. There was a violent local action between 
the zinc and the copper of the brass tubes which were in contact with the 
electrolyte, and this increased in the reaction as it progressed in stagnant 
conditions. By interposing a counter electromotive force against the 
galvanic couple which should exceed in pressure the voltage of the couple, 
the actions of the electrolytic corrosion ceased. When unconnected, or 
electrically separated, plates were placed in the electrolyte, if they were 
of composite construction and had sharp projections into the fluid, raised 
by cutting and prying up with a knife, they would have these projections 
promptly destroyed, and if an electric battery having a pressure exceed- 
ing that of the couple in the East River water was caused to act to pro- 
duce a counter current, and having a pressure exceeding that of the 
galvanic couple (0.42 volt), the capacity of this electrolyte to drive off 
atoms of the mechanically combined metals in the alloys used was over- 
come and corrosion was arrested. 

It, therefore, became desirable not only to carefully provide the bal- 
ancing quantity of current to equal the stray traction currents arising 
from the ground returns of railway and other service, but to add to this 
the necessary voltage through a cathode placed in the circulating water 
in such a way as to bring to bear electrolytic action which would pre- 
vent the galvanic action due to this current coming into contact with 
alloys of mechanically combined metals such as the brass tubes (60% 
copper, 40% zinc). 

In order to accomplish these two things, it was first necessary to so 
install the condensers as to prevent undue amounts of stray currents 
flowing through them, thus tending to reduce the amount of power 
required to prevent injurious action of these currents and otherwise to 
neutralize them. This was done by insulating the joints in the piping 
and from ground connections, and even lining the large water connec- 
tions with glass melted on to the surface. 

To furnish electromotive force, a 3-K.W. motor generator was pro- 
vided. By means of a system of wiring, with ammeters and voltmeters, 
and a connection to an outlying anode in the condensing supply intake 
at its harbor end, this generator was planned to provide current to neu- 
tralize the stray currents in the condenser structure to any extent that 
they had passed the insulated joints in the supports and connections, as 
well as through the columns of water in the pipe connections, and then 
to adjust the. additional voltage needed to counteract and prevent the 
galvanic action. All connections were made in a manner to insure a 
uniform voltage of the various parts of the condenser to prevent local 
action, each connection being so made and provided with such measuring 
instruments as to insure ready adjustment to effect this. The apparatus 
was designed in accordance with the above statements. Its operation 
has extended over fourteen months (to date, 1906), and with the excep- 
tion of about ten tubes which have become pitted, the results have been 
satisfactory. The efficiency of the apparatus amply justifies the ex- 
pense of its installation, while its operation is not expensive, and the 
plant described will be followed by other protecting plants of the same 
character. 

Electrolytic Corrosion due to Overstrain. (C. F. Burgess, El. Rev., 
Sept. 19, 1908.) — Mild steel bars overstrained in their middle portion 
were subjected to corrosion by suspension in dilute hydrochloric acid 
solutions, and others by making them the anode in neutral solutions of 
ammonium chloride and causing current to flow under low current den- 
sity. In all cases a marked difference was noted in the rate at which the 
strained portions corroded as compared with the unstrained. 



PRESERVATIVE COATINGS. 447 

Differences of potential of from five to nine millivolts were noted 
between two electrodes, one of which constituted the strained portion 
and one the unstrained. 

The more rapid electrolytic corrosion of the strained portion appears 
to be due to the fact that the strained metal is electropositive to the 
unstrained, the current finding the easier path through the surface of 
the electropositive metal. That the strained metal is the more electro- 
positive is also shown by a liberation of hydrogen bubbles on the un- 
strained portion. 

PRESERVATIVE COATINGS. 

The following notes have been furnished to the author by Prof. A. H. 
Sabin. (Revised, 1908.) 

Cement. — Iron-work is often bedded in concrete; if free from cracks 
and voids it is an efficient protection. The metal should be cleaned and 
then washed with neat cement before embedding. 

Asphaltum. — This is applied either by dipping (as water-pipe) or 
by pouring it on (as bridge floors). The asphalt should be slightly elastic 
when cold, with a high melting-point, not softening much at 100° F., 
applied at 300° to 400°; the surface must be dry and should be hot; the 
coating should be of considerable thickness. 

Paint. — Composed of a vehicle or binder, usually linseed oil or some 
inferior substitute, or varnish (enamel paints); and a pigment, which is a 
more or less inert solid in the form of a powder, either mixed or ground 
together. Nearly all paint contains paint drier or japan, which is a lead 
or (and) manganese compound soluble in oil, and acts as a carrier of 
oxygen; as little should be used as possible. Boiled oil contains drier; 
no'additional drier is needed. None should be used with varnish paints, 
nor with " ready-mixed paints " in general. 

The principal pigments are white lead (carbonate or oxy-sulphate) and 
white zinc (oxide), red lead (peroxide), oxides of iron, hydrated and 
anhydrous, graphite, lampblack, bone black, chrome yellow, chrome 
green, ultramarine and Prussian blue, and various tinting colors. White 
lead has the greatest body or opacity of white pigments; three coats of it 
equal five of white zinc; zinc is more brilliant and permanent, but it is 
liable to peel, and it is customary to mix the two. These are the standard 
white paints for all uses, and the basis of all light-colored paints. Anhy- 
drous iron oxides are brown and purplish brown, hydrated oxides are 
yellowish red to reddish yellow, with more or less brown; most iron 
oxides are mixtures of both sorts, and often contain a little manganese 
and much clay. They are cheap, and are serviceable paints on wood and 
are often used on iron, but for the latter use are falling into disrepute. 
Graphite used for painting iron contains from 10 to 90% foreign matter, 
usually silicates. It is very opaque, hence has great covering power and 
may be applied in a very thin coat, which is to be avoided. The best 
graphite paints give very good results. There are many grades of lamp- 
black; the cheaper sorts contain oily matter and are especially hard to 
dry; all lampblack is slow to dry in oil. In a less degree this is true of all 
paints containing carbon, including graphite. Lampblack is used with 
advantage with red lead; it is also an ingredient of many "carbon" 
paints, the base of which is either bone black or artificial graphite. Red 
lead dries by uniting chemically with the oil to form a cement; it is heavy, 
and makes an expensive paint, and is often highly adulterated. Pure red 
lead has long had a high reputation as a paint for iron and steel, and is 
still used extensively, especially as a first coat; but of late years some of 
the new paints and varnish-like preparations have displaced it to a con- 
siderable extent even, on the most important work. 

Varnishes. — These are made by melting fossil resin, to which is then 
added from half its weight to three times its weight of refined linseed oil, 
and the compound is thinned with turpentine; they usually contain a 
little drier. They are chiefly used on wood, being more durable and 
more brilliant than oil, and are often used over paint to preserve it. 
Asphaltum is sometimes substituted in part or in whole for the fossil 
resin, and in this way are made black varnishes which have been used on 
iron and steel with good results. Asphaltum and substances like it have 



448 IRON AND STEEL. 



also been simply dissolved in solvents, as benzine or carbon disulphide, 
and used for the same purpose. 

All these preservative coatings are supposed to form impervious films, 
keeping out air and moisture; but in fact all are somewhat porous. On 
this account it is necessary to have a film of appreciable thickness, best 
formed by successive coats, so that the pores of one will be closed by the 
next. The pigment is used to give an agreeable color, to help fill the 
pores of the oil film, to make the paint harder, so that it will resist abra- 
sion, and to make a thicker film. In varnishes these results are sought to 
be attained by the resin which is dissolved in the oil. There is no sort of 
agreement among practical men as to which coating is best for any par- 
ticular case; this is probably because so much depends on the preparation 
of the surface and the care with which the coating is applied, and also 
because the conditions of exposure vary so greatly. 

Methods of Application. — From the surface of the metal mud and 
dirt must be first removed, then any rusty spots must be cleaned thor- 
oughly; loose scale may be removed with wire brushes, but thick and 
closely adherent rust must be removed with steel scrapers, or with hammer 
and chisel if necessary. The sand-blast is used largely and increasingly 
to clean before painting, and is the best method known. Pickling is 
usually done with 10% sulphuric acid; the solution is made more active 
by heating. All traces of acid must be removed by washing, and the 
metal must be immediately dried and painted. Less than two coats of 
paint should never be used, and three or four are better. The first paint- 
ing of metal is the most important. Paint is always thin on angles and 
edges, also on bolt and rivet heads; after the first full coat apply a partial 
or striping coat, covering the angles and edges for at least an inch back 
from the edge, also all bolt and rivet heads. After this is dry apply the 
second full coat. At least a week should elapse between coats. 

Cast-iron water pipes are usually coated by dipping in a hot mixture of 
coal-tar and coal-tar pitch; riveted steel pipes by dipping in hot asphalt 
or by a japan enamel which is baked on at about 400° F. Ships' bottoms 
are coated with a varnish paint to prevent rusting, over which is a similar 
paint containing a poison, as mercury chloride, or a copper compound, 
or else for this second coat a greasy copper soap is applied hot; this 
prevents the accumulation of marine growths. Galvanized iron and tin 
surfaces should be thoroughly cleaned with benzine and scrubbed before 
painting. When new they are partly covered with grease and chemicals 
used in coating the plates, and these must be removed or the paint will 
not adhere. 

Quantity of Paint for a Given Surface. — One gallon of paint will 
cover 250 to 400 sq. ft. as a first coat, depending on the character of the 
surface, and from 350 to 500 sq. ft. as a second coat. 

Qualities of Paints. — The Railroad and Engineering Journal, vols, 
liv. and lv., 1890 and 1891, has a series of articles on paint as applied to 
wooden structures, its chemical nature, application, adulteration, etc., by 
Dr. C. B. Dudley, chemist, and F. N. Pease, assistant chemist, of the 
Penna. R. R. They give the results of a long series of experiments on 
paints as applied to railway purposes. 

Inoxydation Processes. (Contributed by Alfred Sang, Pittsburg, 
Pa., 1908.) — The black oxide of iron (Fe30 4 ) as a continuous coating 
affords excellent protection against corrosion. Lavoisier (1781) noted its 
artificial production and its stable qualities. Faraday (1858) observed 
the protective properties of the coating formed by the action of steam 
in superheating tubes. Berthier discovered its formation by the action 
of highly heated air. 

Bower-Barff Process. — Dr. Barff's method was to heat articles to be 
coated to about 1800° F. and inject steam heated to 1000° F. into the 
muffle. George and A. S. Bower used air instead of steam, then carbon 
monoxide (producer gas) to reduce the red oxide. In the combined 
process, the articles are heated to 1600° F. in a closed retort; super- 
heated steam is injected for 20 min., then producer gas for 15 to 25 min.; 
the treatment can be repeated to increase the depth of oxidation. Less 
heat is required for wrought than for cast iron or steel. By a later 
improvement, steam heated above the temperature of the articles was 
injected during the last 1 to 2 hours. Bv a further improvement known 
as the "Wells Process," the work is finished in one operation, the steam 



PRESERVATIVE COATINGS. 449 

and producer-gas being injected together. Articles are slightly in- 
creased in size by the treatment. The surface is gray, changing to 
black when oiled; it will chip off if too thin; it will take paint or enamel 
and may be polished, but cannot be either bent or machined; the coating 
itself is incorrodible and resists sea- water, mine-water and acid fumes; 
the strength of the metal is slightly reduced. The process is exten- 
sively used for small hardware. (See F. S. Barff, Jour. I. & S. Inst., 1877, 
p. 356; A. S. Bower, Trans. A. I. M. E. 18S2, p. 329; B. H. Thwaite, Proc. 
Inst. C. E. 1883, p. 255; George W. Maynard, Trans. A. S. M. E. iv, 
351.) 

Gesner Process. — Dr. George W. Gesner's process is in commercial 
operation since 1890. The coating retort is kept at 1200° F. for 20 
minutes after charging, then steam, partially decomposed by passing 
through a red-hot pipe, is allowed to act at intervals during' 35 min.; 
finally, a small quantity of naphtha, or other hydrocarbon, is intro- 
duced and allowed to act for 15 min. The work is withdrawn when the 
heat has fallen to 800° F. The articles are neither increased in size nor 
distorted; the loss of strength and reduction of elongation are only slight. 
Large pieces can be treated. (See Jour. I. & S. Inst., 1890 (ii), p. 850; 
Iron Age, 1890, p. 544.) 

Hydraesfer Process. — An improvement of the Gesner process pat- 
ented by J. J. Bradley and in commercial operation. As its name implies, 
the coating is thought to be an alloy of hydrogen, copper and iron. 
The sulphides and phosphides are claimed to be burned out of the sur- 
face of the metal by the action of hydrogen at a high temperature, 
giving additional rust-proof qualities. The appearance of the finished 
work is that of genuine Bower Barffing. 

Russia and Planished Iron. — Russia iron is made by cementation 
and slight oxidation. W. Dewees Wood (U. S. Pat. No. 252,166 of 
1882) treated planished sheets with hydrocarbon vapors or gas and 
superheated steam within an air-tight and heated chamber. 

Niter Process. — An old process improved by Col. A. R. Buffington in 
1884. The articles are stirred about in a mixture of fused potassium 
nitrate (saltpeter) and manganese dioxide, then suspended in the vapors 
and finally dipped and washed in boiling water. Pure chemicals are 
essential. Used for small arms and pieces which cannot stand the high 
heat of other processes. {Trans. A. S. M. E., vol. vi, p. 628.) 

Electric Process. — A. de Meritens connected polished articles as 
anodes in a bath of warm distilled water and used a current as weak as 
would be conducted. A black film of oxide was formed; too strong a 
current produced rust. It being essential that hydrogen be occluded in 
the surface of the metal, it was found necessary, as a rule, to connect 
the articles as cathodes for a short time previous to inoxidation. (Bull. 
Soc. Intle. des Electr., 1886, p. 230.) 

Aluminum Coatings. — Aluminum can be deposited electrically, the 
main difficulties being the high voltage required and the readiness of the 
coating to redissolve. The metal-work of the tower of City Hall, Phila- 
delphia, was coated by the Tacony Iron & Metal Co., Tacony, Pa., with 
14 oz. per sq. ft. of copper on which was deposited 21/2 oz. of an alloy of 
tin and aluminum. The Reeves Mfg. Co., Canal Dover, Ohio, makes 
aluminum-coated conductor pipes, etc., said to be as durable as copper 
and as rust-proof as aluminum. The Aluminum Co. of America makes 
" bi-metallic " tubing composed of aluminum and other metal tubes 
placed one inside the other and drawn down together to the required 
size. 

Galvanizing is a method of coating articles, usually of iron or steel, 
with zinc. Galvanized iron resists ordinary corroding agencies, the 
zinc becoming covered with a film of zinc carbonate, which protects the 
metal from further chemical action. The coating is, however, quickly 
destroyed by mine-water, tunnel gases, sea water and conditions that 
commonly exist in tropical countries. If the work is badly done and the 
coating does not adhere properly, and if any acid from the pickle or any 
chloride from the flux remains on the iron, corrosion takes place under 
the zinc coating. (See M. P. Wood: Trans. A. S. M. E. xvi. 350. Alfred 
Sans: Trans. Am. Foundn/mcn's Assoc, 1907. Iron Age, May 23d and 
30th, 1907, and Proc. Eng. Soc. of W. Penna., Nov., 1907.) 

The Penna. R. R. Specifications for galvanized sheets for car roofs 



450 IRON AND STEEL. 

(1907) prescribe that the black sheets before galvanizing should weigh 
16 oz. per sq. ft., the galvanized sheet 18 oz. Sheets will not be accepted 
if a chemical determination shows less than 1.5 oz. of zinc per sq. ft. 

Hot Galvanizing. — The articles to be galvanized are first cleaned by 
pickling and then dipped in a solution of hydrochloric acid and immersed 
in a bath of molten zinc at a temperature of from 800 to 900° F.; when 
tney have reached the temperature of the bath, they are withdrawn and 
the coating is set in water; sal-ammoniac is used on the pot as a flux, 
either alone or as an emulsion with glycerine or some other fatty medium. 
Wire, bands and similar articles are drawn continuously through the 
bath, and may be passed through asbestos wipers to remove the surplus 
metal; in this case it is advisable to use a very soft spelter free from iron. 
If wire is treated slowly and passed through charcoal dust instead of 
wipers the product is known as "double-galvanized. " Tin can be added 
to the bath to help bring out the spangles, but it gives a less durable 
coating. Aluminum is added as a Zn-Al alloy, with about 20% Al, to 
give fluidity. Sheets are galvanized continuously, and except in the 
case of so-called "flux sheets," are put through rolls as they emerge 
from the bath, to squeeze off the excess of zinc and improve the adherence. 

Test for Galvanized Wire.— Sir W. Preece devised the following 
standard test for the British Post Office: dip for one minute in a saturated 
neutral solution of sulphate of copper, wash and wipe; to pass, the 
material must stand 3 dips. 

The American standard test is as follows: prepare a neutral solution of 
sulphate of copper of sp. gr. 1.185, dip for one minute, wash and wipe dry; 
the wire must stand 4 dips without a permanent coating of copper show- 
ing on any part of the wire. 

Galvanizing by Cementation; Sherardizing. — The alloying of metals 
at temperatures below their melting points has been known since 1820 
or earlier. Berry (1838) invented a process of depositing zinc, in which 
the objects to be coated were placed in a closed retort and covered with 
a mixture of charcoal and powder of zinc; the retort was heated to cherry- 
red for a longer or shorter period, according to the bulk of the article and 
to the desired thickness of the coating. Dumas gave iron articles a slight 
coating of copper by dipping them in a solution of sulphate of copper and 
then heated them in a closed retort with oxide of zinc and charcoal dust. 
Sheet steel cowbells are coated with brass by placing them in a mixture 
of finely divided brass and charcoal dust and heating them to redness in 
an air-tight crucible. 

S. Cowper-Coles's process, known as Sherardizing, patented in 1902, 
consists in packing the objects which are to be coated in zinc dust or 
pulverized zinc to which zinc oxide with a small percentage of charcoal 
dust is added, and heating in a closed retort to a temperature below the 
melting point of zinc. A large proportion of sand can be used to reduce 
the amount of zinc dust carried in the retort, to prevent caking and give 
a brighter finish; motion of the retort is in most cases necessary to obtain 
an even coating. The operation lasts from 30 minutes to several hours, 
depending on the size of the drum. Tempered steel is not affected by 
the process, but surfaces are hardened, there being a zinc-iron alloy 
formed to a depth varying with the time of treatment. This process is 
suitable for small work, giving a superior quality of zinc coating. (See 
Cowper-Coles, " Preservation and Ornamentation of Iron and Steel Sur- 
faces," Trans. Soc. Engrs. 1905, p. 183; "Sherardizing," Iron Age, 
1904, p. 12. Alfred Sang, "Theory and Practice of Sherardizing," 
El. Chem. and Metall. Ind., May, 1907.) 

Lead Coatings. — ■ Lead is a good protection for iron and steel pro- 
vided it is perfectly gas-tight. Electrically deposited lead does not 
bond well and the coating is porous. Sheets having a light coating of 
lead, produced by dipping in the molten metal, are known as terne 
plates; they have no lasting qualities. Lead-lined wrought pipe, fittings 
and valves are made for conveying acids and other corroding liquids. 



STEEL. 451 



• STEEL. 

The Manufacture of Steel. (See Classification of Iron and Steel, 
p. 413.) Cast steel is a malleable alloy of iron, cast from a fluid mass. 
It is distinguished from cast iron, which is not malleable, by being much 
lower in carbon, and from wrought iron, which is welded from a pasty 
mass, by being free from intermingled slag. Blister steel is a highly 
carbonized wrought iron, made by the "cementation" process, which 
consists in keeping wrought-iron bars at a red heat for some days in 
contact with charcoal. Not over 2% of C is usually absorbed. The 
surface of the iron is covered with small blisters, supposedly due to the 
action of carbon on slag. Other wrought steels were formerly made by 
direct processes from iron ore, and by the puddling process from wrought 
iron, but these steels are now replaced by cast steels. Blister steel is, 
however, still used as a raw material in the manufacture of crucible steel. 
Case-hardening is a process of surface cementation. 

Crucible Steel is commonly made in pots or crucibles holding about 
80 pounds of metal. The raw material may be steel scrap; blister steel 
bars; wrought iron with charcoal; cast iron with wrought iron or with 
iron ore; or any mixture that will produce a metal having the desired 
chemical constitution. Manganese in some form is usually added to 
prevent oxidation of the iron. Some silicon is usually absorbed from the 
crucible, and carbon also if the crucible is made of graphite and clay. 
The crucible being covered, the steel is not affected by the oxygen or 
sulphur in the flame. The quality of crucible steel depends on the free- 
dom from objectionable elements, such as phosphorus, in the mixture, 
on the complete removal of oxide, slag and blowholes by "dead-melting" 
or "killing" before pouring, and on the kind and quantity of different 
elements which are added in the mixture, or after melting, to give par- 
ticular qualities to the steel, such as carbon, manganese, chromium, 
tungsten and vanadium. 

Bessemer Steel is made by blowing air through a bath of melted pig 
iron. The oxygen of the air first burns away the silicon, then the carbon, 
and before the carbon is entirely burned away, begins to burn the iron. 
Spiegeleisen or ferro-manganese is then added to deoxidize the metal 
and to give it the amount of carbon desired in the finished steel. In the 
ordinary or "acid" Bessemer process the lining of the converter is a 
silicious material, which has no effect on phosphorus, and all the phos- 
phorus in the pig iron remains in the steel. In the "basic" or Thomas 
and Gilchrist process the lining is of magnesian limestone, and limestone 
additions are made to the bath, so as to keep the slag basic, and the phos- 
phorus enters the slag. By this process ores that were formerly unsuited 
to the manufacture of steel have been made available. 

Open-hearth Steel. — Any mixture that may be used for making 
steel in a crucible may also be melted on the open hearth of a Siemens 
regenerative furnace, and may be desiliconized and decarbonized by the 
action of the flame and by additions of iron ore, deoxidized by the addi- 
tion of spiegeleisen or ferro-manganese, and recarbonized by the same 
additions or by pig iron. In the most common form of the process pig 
iron and scrap steel are melted together on the hearth, and after the 
manganese has been added to the bath it is tapped into the ladle. In the 
Talbot process a large bath of melted material is kept in the furnace, 
melted pig iron, taken from a blast furnace, is added to it, and iron ore 
is added which contributes its iron to the melted metal while its oxygen 
decarbonizes the pig iron. When the decarbonization has proceeded far 
enough, ferro-manganese is added to destroy iron oxide, and a portion 
of the metal is tapped out, leaving the remainder to receive another 
charge of pig iron, and thus the process is continued indefinitely. In 
the Duplex Process melted cast iron is desiliconized in a Bessemer con- 
verter, and then run into an open hearth, where the steel-making opera- 
tion is finished. 

The open-hearth process, like the Bessemer, may be either acid or 
basic, according to the character of the lining. The basic process is a 
dephosphorizing one, and is the one most generally available, as it can 
use pig irons that are either low or high in phosphorus. 



452 



STEEL. 



Relation between the Chemical Composition and Physical 
Character of Steel. 

W. R. Webster {Trans. A.I. M. E., vols, xxi and xxii, 1893-4) gives re- 
sults of several hundred analyses and tensile tests of basic Bessemer steel 
plates, and from a study of them draws conclusions as to the relation of 
chemical composition to strength, the chief of which are condensed as 
follows: 

The indications are that a pure iron, without carbon, phosphorus, man- 
ganese, silicon, or sulphur, if it could be obtained, would have a tensile 
strength of 34,750 lbs. per sq. in., if tested in a 3/ 8 -in. plate. With this as a 
base, a table is constructed by adding the following hardening effects, as 
shown by increase of tensile strength, for the several elements named. 

Carbon, a constant effect of 800 lbs. for each 0.01%. 

Sulphur, " " 500 " " " 0.01%, 

Phosphorus, the effect is higher in high-carbon than in low-carbon steels. 
With carbon hun- 



dredths % 9 10 

Each 0.01% Phas 
an effect of lbs .. 900 1000 1100 
Manganese, the effect decreases ai 
.00 .15 .20 .25 



12 13 



14 



15 



16 



17 



Mn bein 
cent . . 



per 



to 



to 



to 



1200 1300 1400 1500 1500 1500 

the per cent of manganese increases. 

.30 .35 .40 .45 .50 .55 



to 



to 



to to 



to 



to 
.65 



. .15 .20 .25 .30 .35 .40 .45 .50 .55 
Strength incr. 

for 0.01%... 240 240 220 200 180 160 140 120 100 100 lbs. 
Total increase 

fromO Mn... 3600 4800 5900 6900 7800 8600 9300 9900 10,400 11,400 

Silicon is so low in this steel that its hardening effect has not been con- 
sidered. 

With the above additions for carbon and phosphorus the following table 
has been constructed (abridged from the original by Mr. Webster). To 
the figures given the additions for sulphur and manganese should be made 
as above. 

Estimated Ultimate Strengths of Basic Bessemer-steel Plates. 

For Carbon, 0.06 to 0.24; Phosphorus, .00 to .10; Manganese and Sulphur, 
.00 in all cases. 



Carbon. 


0.06 


.08 


.10 


.12 


.14 


.16 


.18 


.20 


.22 


.24 


Phos. .005 


39,950 


41,550 


43,250 


44,953 


46,650 


48,300 


49,900 


51,500 


53,100 


54,700 


" .01 


40,350 


41,950 


43,750 


5,550 


47,350 


49,050 


50,650 


52,250 


53,850 


55,450 


" .02 


41,150 


42,750 


44,750 


46,750 


48,750 


50,550 


52,150 


53,750 


55,350 


56,950 


" .03 


41,950 


43,550 


45,750 


47,950 


50,150 


52,050 


53,650 


55,250 


56,850 


58,450 


" .04 


42,750 


41,350 


46,750 


49,150 


51,550 


53,550 


55,150 


56,750 


58,350 


59,950 


" .05 


43,550 


45,150 


47,750 


50,350 


52,950 


55,050 


56,650 


58,250 


59,850 


61,450 


" .06 


44,350 


45,950 


48,750 


51,550 


54,350 


56,550 


58,159 


59,750 


61,350 


62,950 


" .07 


45,150 


46,750 


49,750 


52,750 


55,750 


58,050 


59,650 


61,250 


62,850 


64,450 


" .08 


45,950 


47,550 


50,750 


53,950 


57,150 


59,550 


61,150 


62,750 


64,350 


65,950 


" .09 


46,750 


48,350 


51,750 


55,150 


58,550 


61,050 


62,650 


64,250 


65,850 


67,450 


" .10 


47,550 


49,150 


52,750 


56,359 


59,950 


62,550 


64,150 


65,750 


57,350 


68,950 


0.001 P.= 


80 lbs. 


80 lbs. 


100 1b. 


1201b. 


1401b. 


1501b. 


150 lb. 


1501b. 


1501b. 


1501b. 



In all rolled steel the quality depends on the size of the bloom or ingot 
from which it is rolled, the work put on it, and the temperature at which 
it is finished, as well as the chemical composition. 

The above table is based on tests of plates 3/ 8 inch thick and under 70 
inches wide; for other plates Mr. Webster gives the following corrections 
for thickness and width. They are made necessary only by the effect of 
thickness and width on the finishing temperature in ordinary practice. 
Steel is frequently spoiled by being finished at too high a temperature. 



STEEL. 



453 



Thickness, in 


3/ 4 * 

-2000 
-1000 


U/16 

-17I>0 
- 750 


5/8 9 /l6 
-1500-1250 

- 500 - 25C 


1/2 
-1UO0 




7/16 

-500 
±500 


3/8 

+ 1000 


5/16 

+ 3000 




+ 5000 







* And over. (1) Plates up to 70 in. wide. (2) Over 70 in. wide. 

Comparing the actual result of tests of 408 plates with the calculated 
results, Mr. Webster found the variation to range as below. 

Within lbs. 1000 2000 3000 4000 5000 

Per cent. . .28 4 55.1 74.7 89.9 94.9 

The last figure would indicate that if specifications were drawn calling 
for steel plates not to vary more than 5000 lbs. T. S. from a specified 
figure (equal to a total range of 10,000 lbs.), there would be a probability 
of the rejection of 5% of the blooms rolled, even if the whole lot was made 
from steel of identical chemical analysis. 

Campbell's Formulae. (H. H. Campbell, The Manufacture and Prop- 
erties of Iron and Steel, p. 387.) — 



Acid steel, 40,000 
Basic steel, 41,500 



1000 C 
770 C ■ 



1000 P + xMn = Ultimate strength. 
1000 P + yMn = Ultimate strength. 



The values of xMn and yMn are given by Mr. Campbell in a table, 
but they may be found from the formulse xMn = 8 CMn - 320 C and 
yMn = 90 Mn + 4 CMn - 2700 - 120 C, or, combining the formulse 
we have: 



Ult. strength, acid steel, 40,000 
basic " 38,800 - 



680 C - 
650 C • 



1000 P +8 CMn. 

1000 P + 90 Mn+4CMn 



In these formulse the unit of each chemical element is 0.01%. 

Examples. Required the tensile strength of two steels containing 
respectively C, 0.10, P, 0.10, Mn, 0.30, and C, 0.20, P, 0.10, Mn, 0.65. 

Answers, by Webster, 59,650 and 77,150; by Campbell, 57,700 and 72,850. 

Low Tensile Strength of Very Pure Steel. — Swedish nail-rod 
open-hearth steel, tested by the author in 1881, showed a tensile strength of 
only 42,591 lbs. per sq. in. A piece of American nail-rod steel showed 
45,021 lbs. per sq. in. Both steels contained about 0.10 C and 0.015 P, 
and were very low in S, Mn, and Si. The pieces tested were bars about 
2 x 3/ 8 in. section. 

R. A. Hadfield (Jour. Iron and Steel Inst., 1894) gives the strength of 
very pure Swedish iron, remelted and tested as cast, 45,024 lbs. per sq. 
in.; remelted and forged, 47,040 lbs. The analvsis of the cast bar was: 
C, 0.08; Si, 0.04; S, 0.02; P, 0.02; Mn, 0.01; Fe, 99.82. 

Effect of Oxygen upon Strength of Steel. — A. Lantz, of the 
Peine works, Germany, in a letter to Mr. Webster, says that oxygen plays 
an important role — such that, given a like content of C, P, and Mn, a 
blow with greater oxygen content gives a greater hardness and less ductility 
than a blow with less oxygen content. The method used for determin- 
ing oxygen is that of Prof. Ledebur, given in Stahl und Eisen, May, 1892, 
p. 193. The variation in O may make a difference in strength of nearly 
1/2 ton per sq. in. (Jour. I. and^S. I., 1894.) 

Electric Conductivity of Steel. — Louis Campredon reports in Le 
Genie Civil [prior to 1895] the results of experiments on the electric resist- 
ance of steel wires of different composition, ranging from 0.09 to 0.14 C; 
0.21 to 0.54 Mn; Si,.S, and P low. The figures show that the purer and 
softer the steel the better is its electric conductivity, and, furthermore, that 
manganese is the element which most influences' the conductivity. The 
results may be expressed by the formula R = 5.2 + 6.2*S ± 0.3; in which 
R = relative resistance, copper being taken as 1, and S = the sum of the 
percentages of C, P, S, Si, and Mn. The conclusions are confirmed by 
J. A. Capp, in 1903, Trans. A. I. M. E., vol. xxxiv, who made forty-five 
experiments on steel of a wide range of composition. His results may be 
expressed by the formula R = 5.5 + 43 ± 1. High manganese increases 
the resistance at an increasing rate. Mr. Capp proposes the following 
specification for steel to make a satisfactory third rail, having a resistance 
eight times that of copper: C, 0.15; Mn, 0.30; P, 0.06; S, 0.06; Si, 0.05; 
none of these figures to be exceeded. 



454 



STEEL. 



Range of Variation in Strength of Bessemer and Open-Hearth 
Steels. 

The Carnegie Steel Co. in 1888 published a list of 1057 tests of Bessemer 
and open-hearth steel, from which the following figures are selected: 



Kind of Steel. 


H 
'o 

6 


Elastic Limit. 


Ultimate 
Strength. 


Elongation 

per cent 
in 8 Inches. 




High't. 


Lowest. 


High't. 


Lowest. 


High't. 


Lowest. 


(a) Bess, structural. 
(6) " 

(c) Bess, angles 

(d) 0. H. fire-box... 


100 
170 
72 
25 
20 


46,570 
47,690 
41,890 


39,230 
39,970 
32,630 


71,300 
73,540 
63,450 
62,790 
69,940 


61,450 
65,200 
56,130 
50,350 
63,970 


33.00 
30.25 
34.30 
36.00 
30.00 


23.75 
23.15 
26.25 
25.62 


(e) 0. H. bridge 






22.75 











Requirements of Specifications. 

(a) E. L., 35,000; T. S., 62,000 to 70,000; elong., 22% in 8 in. 

(b) E. L., 40,000; T. 8., 67,000 to 75,000. 

(c) E. L., 30,000; T. S., 56,000 to 64,000; elong., 20% in 8 in. 

(d) T. S., 50,000 to 62,000; elong., 26% in 4 in. 

(e) T. S., 64,000 to 70,000; elong., 20% in 8 in. 

Bending Tests of Steel. (Pencoyd Iron Works.) — Steel below 0.10 C 
should be capable of doubling flat without fracture, after being chilled 
from a red heat in cold water. Steel of 0.15 C will occasionally submit 
to the same treatment, but will usually bend around a curve whose radius 
is equal to the thickness of the specimen; about 90% of specimens stand 
the latter bending test without fracture. As the steel becomes harder its 
ability to endure this bending test becomes more exceptional, and when 
the carbon becomes 0.20 little over 25% of specimens will stand the last- 
described bending test. Steel having about 0.40% C will usually harden 
sufficiently to cut soft iron and maintain an edge. 

EFFECT OF HEAT TREATMENT AND OF WORK ON STEEL. 

Low Strength Due to Insufficient Work. (A. E. Hunt, Trans. 
A. I. M. E., 1886.) — Soft steel ingots, made in the ordinary way for 
boiler plates, have only from 10,000 to 20,000 lbs. tensile strength per sq. 
in., an elongation of only about 10% in 8 in., and a reduction of area of 
less than 20%. Such ingots, properly heated and rolled down from 10 in. 
to 1/2 in. thickness, will give from 55,000 to 65,000 lbs. tensile strength, an 
elongation in 8 in. of from 23% to 33%, and a reduction of area of from 
55% to 70%. Any work stopping short of the above reduction in thick- 
ness ordinarily yields intermediate results in tensile tests. 

Effect of Finishing Temperature in Rolling. — The strength and 
ductility of steel depend to a high degree upon fineness of grain, and 
this may be obtained by having the temperature of the steel rather low, 
say at a dull red heat, 1300° to 1400° F., during the finishing stage of 
rolling. In the manufacture of steel rails a great improvement in quality 
has been obtained by finishing at a low temperature. An indication of 
the finishing temperature is the amount of shrinkage by cooling after 
leaving the rolls. The Phila. & Reading Railway Co.'s specification for 
rails (1902) says, "The temperature of the ingot or bloom shall be such 
that with rapid rolling and without holding before or in the finishing 
passes or subsequently, and without artificial cooling after leaving the 
last pass, the distance between the hot saws shall not exceed 30 ft. 6 in. 
for a 30-ft. rail." 

Fining the Grain by Annealing. — Steel which is coarse-grained 
on account of leaving the rolls at too high a temperature may be made 
fine-grained and have its ductility greatly increased without lowering its 
tensile strength by reheating to a cherry-red and cooling at once in air. 
(See paper on "Steel Rails," by Robert Job, Trans. A. I. M. E., 1902.) 



EFFECT OF HEAT TREATMENT ON STEEL. 



455 



Effect of Cold Rolling. — Cold rolling of iron and steel increases the 
elastic limit and the ultimate strength, and decreases the ductility. 
Major Wade's experiments on bars rolled and polished cold by Lauth's 
process showed an average increase of load required to give a slight per- 
manent set as follows: Transverse, 162%; torsion, 130%; compression, 
161% on short columns 1 1/2 hi* long, and 64% on columns 8 in. long; 
tension, 95%. The hardness, as measured by the weight required to 
produce equal indentations, was increased 50%; and it was found that 
the hardness was as great in the center of the bars as elsewhere. Sir 
W. Fairbairn's experiments showed an increase in ultimate tensile 
strength of 50%, and a reduct on in the elongation in 10 in. from 2 in. 
or 20% to 0.79 in. or 7.9%. 

Hardening of Soft Steel. — A. E. Hunt (Trans. A. I. M. E., 1883, vol. 
xii) says that soft steel, no matter how low in carbon, will harden to a cer- 
tain extent upon being heated red-hot and plunged into water, and that it 
hardens more when plunged into brine and less when quenched in oil. 

A heat of open-hearth steel of 0.15% C and 0.29% Mn gave the follow- 
ing results upon test-pieces from the same 1/4 in. thick plate. 

Unhardened T. S. 55,000 El. in 8 in. 27% Red. of Area 62% 

Hardened in water " 74,000 " 25% " 50% 

Hardened in brine " 84,000 " 22% " 43%) 

Hardened in oil " 67,000 " 26% " 49% 

The greatly increased tenacity after hardening indicates that there must 
be a considerable molecular change in the steel thus hardened, and that 
if such a hardening should be created locally in a steel plate, there must 
be very dangerous internal strains caused thereby. 

Comparative Tests of Full-sized Eye-bars and Small Samples. 
(G. G. S. Morison, A. S. C. E., 1893.) — 17 full-sized eye-bars, of the steel 
used in the Memphis bridge, sections 10 in. wide X 1 to 23/ig in. thick, and 
sample bars from the same melts. Average results: 

Eye-bars: E. L., 32,350; T. S., 63,330; El. in full length, 13.7%; Red. 
of area, 36.3 %. 

Small bars: E. L., 40,650; T. S„ 71,640; El. in 8 ins., 26.2%; Red. 
of area, 46.7%. 

Effect of Annealing on Rolled Bars. (Campbell, Mfr. of Iron and 
Steel, p. 275.) — 



Ultimate 


Elastic 


Elong. in 


Red. Area, 


Elaa. 


Strength. 


Limit. 


8 in., %. 


%• 


Ratio. 


Natural. 


An- 


Nat- 


An- 


Nat- 


An- 


Nat- 


An- 


Nat- 


An- 


nealed. 


ural. 


nealed. 


ural. 


nealed. 


ural. 


nealed. 


ural. 


nealed. 


•-§(58,568 


54,098 


40,300 


31,823 


29.7 


28.8 


60.8 


62.7 


68.8 


58.8 


.£ cj62,187 


58,364 


42,606 


35,120 


28.0 


28.6 


62.2 


63.5 


68.5 


60.2 


*g 170,530 


65,500 


49,000 


37,685 


26.9 


23.4 


61.1 


55.3 


69.5 


57.5 


w ^ 176,616 


69,402 


51,108 


40,505 


24.5 


23.0 


53.7 


56.5 


66.7 


58.4 


w[ 58, 130 


51,418 


40,400 


30,393 


30.1 


31.1 


61.8 


60.5 


69.5 


59.1 


4» ta J 62,089 


55,021 


42,441 


31,576 


30.1 


30.4 


60.9 


60.0 


68.4 


57.4 


"5=169,420 
<n d 175,865 


60,850 


45,090 


34,000 


25.6 


26.5 


59.3 


52.1 


65.0 


55.9 


67,618 


49,691 


39,403 


24.7 


26.3 


54.4 


51.4 


65.5 


58.3 



The bars were rolled from 4X 4-in. billets of open-hearth steel. The 
figures are averages of from 2 to 12 tests of each heat. In annealing the 
bars were heated in a muffle and withdrawn when they had reached a 
dull yellow heat. 

*' Recalescence " of Steel. — If we heat a bar of copper by a flame 
of constant strength, and note carefully the interval of time occupied in 
passing from each degree to the next higher degree, we find that these in- 
tervals increase regularly, i.e., that the bar heats more and more slowly, 
as its temperature approaches that of the flame. If we substitute a bar of 
steel for one of copper, we find that these intervals increase regularly up 
to a certain point, when the rise of temperature is suddenly and in most 



456 STEEL. 

cases greatly retarded or even completely arrested. After this the regular 
rise of temperature is resumed, though other like retardations may recur 
as the temperature rises farther. So if we cool a bar of steel slowly the 
fall of temperature is greatly retarded when it reaches a certain point in 
dull redness. If the steel contains much carbon, and if certain favoring 
conditions be maintained, the temperature, after descending regularly, 
suddenly rises spontaneously very abruptly, remains stationary a while 
and then redescends. This spontaneous reheating is known as "recales- 
cence." 

These retardations indicate that some change which absorbs or evolves 
heat occurs within the metal. A retardation while the temperature is 
rising points to a change which absorbs heat; a retardation during cooling 
points to some change which evolves heat. (Henry M. Howe, on "Heat 
Treatment of Steel," Trans. A. I. M. E., vol. xxii.) 

Critical Point. (Campbell, p. 287.) — If a piece of steel containing over 
0.50 C be allowed to cool slowly from a high temperature the cooling at 
first proceeds at a uniformly retarded rate, but when about 700° C. is 
reached there is an interruption of this regularity. In some cases the 
rate of cooling may be very slow, in other cases the bar may not decrease 
in temperature at all, while in still other cases the bar may actually grow 
hotter for a moment. When this " critical point " is passed, the bar cools 
as before until it reaches the temperature of the atmosphere. 

In metallography such a critical point is denoted by the letter A, and 
the particular one just described is known as Ar. In heating a piece of 
steel an opposite phenomenon is observed, there being an absorption of 
heat by internal molecular action, with a consequent retardation in the 
rise of temperature, and this point, which is some 30° C. higher than Ar, 
is called Ac. 

In soft steels, below 0.30 C, three critical points are found in cooling a 
bar from a high temperature, called Ar 3 , Ar 2 , Ari, A^ being the lowest, 
and in heating the bar there are also three points, Aci, Ac 2 , Ac 3 , the first 
named being the lowest. At each of the points there is a change in the 
micro-structure of the steel. 

Metallography. — This is a name given to a study of the micro-structure 
of metals. The steel metallographist designates the different structures 
that are found in a polished and etched section by the names austenite, 
martensite, pearlite, cementite, ferrite, troostite, and sorbite. Austenite 
is produced by quenching steel of over 1.40 C in ice water from above 
1050° C. Martensite is produced by quenching this steel from tempera- 
tures between 1050° C. and Ari. It is also found together with cementite 
or ferrite in carbon steels below 1.30 C quenched at any point above Ar x . 
It is the constituent which confers hardness on steel. In steels cooled 
slowly to below Ar t the structure is composed entirely of ferrite, or 
entirely of pearlite, or of pearlite mixed with ferrite or cementite. Ferrite 
is iron free from carbon and forms almost the whole of a low-carbon steel, 
while cementite is considered to be a compound of iron and carbon, Fe3C, 
the C of this form being known as cement carbon. Pearlite is an inti- 
mate mixture of definite proportions of ferrite and cementite, corre- 
sponding to a pure steel of about 0.80 C, which, unhardened, consists of 
pearlite alone. Steels lower in C contain pearlite with ferrite, and steels 
higher in C contain pearlite and cementite. Troostite is a structure found 
when steel is quenched while cooling through the critical range, and 
sorbite when it is quenched at the end of the critical range. Quenching 
in lead or reheating quenched steel to a purple tint may also produce 
sorbite. (Campbell, p. 296.) 

Effect of Work on the Structure of Soft and Medium Steel. — Steel 
as usually cast, cooling slowly, forms in crystals or grains. Rolling tends 
to break-up this grain, but immediately after the cessation of work the 
formation of grains begins and continues until the metal has cooled to 
the lower critical point. Hence the lower the temperature to which the 
steel is worked, the more broken up the structure will be, but on the 
other hand if the rolling be continued below the critical point, the effect 
of cold work will be shown and strains will be set up which will make the 
piece unfit for use without annealing. 

Effect of Heat Treatment. — In heating steel through the lowest 
critical point the crystalline structure is obliterated, the metal assuming the 
finest condition of which it is capable. Above this point the size of grain 
increases with the temperature. 



EFFECT OF HEAT TREATMENT ON STEEL. 



457 



Effect of Heating on Crucible Steel. (W. Campbell, Proc. A.S.T. M., 
vi, 213.) — Six steels, containing carbon as follows: (1) 2.04, (2) 1.94, (3) 
1.72, (4) 1.61, (5) 1.04, and (6) 0.70, were heated in a small gas furnace 
to the temperatures given in the table and allowed to cool slowly in the 
furnace, and were then tested, with results as below. 





As 
Rolled. 


650° C 


715° C 


760° C 


800° C 


855° C 


905° C 


950° C 


1070° 
C 


1200° 
C 


(1) T.S... 


144000 


1 15400 


114500 


98800 


95650 


93800 


95250 


95200 


99000 


57400 


E.L 


104200 


84600 


83900 


57700 


57800 


55500 


55350 


49350 


49600 


56000 


El. in 2 in. 


4.0 


6.0 


7.0 


11.5 


12.5 


12.0 


11.5 


6.0 


4.5 


1.0 


(2) T.S... 


146400 


115200 


104100 


95000 


92000 


89000 


95350 


91800 


97000 


61350 


E.L 


91000 


91500 


72600 


68650 


50500 


51000 


49450 


49800 


41750 


47000 


El. in 2 in. 


6.3 


8.0 


9.5 


15.0 


17.0 


12.5 


7.0 


9.5 


8.5 


2.0 


(3) T.S... 


153100 


126000 


114100 


1 00300 


98000 


94000 


94350 


95000 


92350 


65300 


E.L 


98100 


78300 


75700 


50500 


48750 


47900 


48600 


45200 


43100 


50600 


EI. in 2 in. 


7.2 


8.0 


11.5 


16.5 


10.0 


13.5 


11. 


7.5 


6.0 


2.0 


(4) T. S. . . 


157700 


128100 


1 1 7000 


98650 


97700 


95000 


97350 


96350 


94400 


69800 


E.L 


105200 


85300 


81300 


52300 


53350 


51350 


51350 


48500 


51400 




El. in 2 in. 


6.5 




14.5 




18.5 


15.0 


11.5 


7.5 


3.5 


3.0 


(5) T.S... 


141100 


105400 


97800 


86800 


96600 


111800 


115900 


111500 


106100 


112600 


E.L 


75800 


57700 


55200 


44850 


46600 


47200 


50600 


46800 


56500 


89600 


El. in 2 in. 


12.8 


18.0 


22.0 


26.5 


19.0 


13.0 


13.0 


10.5 


11.0 


11.5 


(6) T.S... 


117000 


95200 


88700 


85600 


94300 


91350 


90300 


90500 


89500 


90000 


E.L 


64700 


53250 


49700 


40200 


42150 


42100 


41400 


39700 


57350 


58500 


El. in 2 in. 


17.0 


23.0 


27.5 


27.0 


19.0 


18.5 


18.0 


16.5 


18.0 


16.0 



The critical points Ar x and Ac x were determined, and the six steels gave 
practically identical results; thus Ar x ranged from 696 to 708, averaging 
704° C, and Ac! ranged from 730 to 737, averaging 733° C. 

The temperatures at which the finest-grained and a very coarse-grained 
fracture were found are as follows: 



Steel No 


1 

800 
1070 


2 

760 
1070 


3 

715-760 

1070 


4 

760 
1070 


5 
715 

855 


6 




715° C 


Very coarse fracture 


800° C 



Mr. Campbell's paper gives a list of fourteen papers by different authori- 
ties on the micro-structure and the heat treatment of steel. 

Burning, Overheating, and Restoring Steel. (G. B. Waterhouse, 
A.S. T.M., vi, 247.) — Burnt metal is defined as coarsely crystalline and 
exceedingly brittle iron or steel, in consequence of excessive heating, 
often with some layers of oxide of iron. It cannot be effectively restored 
by heat treatment or mechanical work. Overheated metal is coarsely 
crystalline from excessive heating, but with no inter-crystalline spaces. 
It can be restored by heat treatment or mechanical work. Seven lots of 
nickel steel bars, containing 3.8% Ni, and C as in the table, were heated 
to various temperatures in a muffle furnace, with results as below. 



%c. 




IOOJt 

90246 

26.0 

99109 

21.0 

115421 

16.5 

135194 

14.0 

156827 

7.5 

168697 

3.5 

145642 

10.5 


1000b 
71800 

26.0 
78600 

25.0 
89000 

20.5 
108960 

15.0 
130336 

97510 
15.0 

63950 
23.6 


1100b 

71700 

25.5 

78800 

24.0 

89400 

19.0 

111840 

14.0 

138112 

3.5 

98183 

1.0 

66640 

25.0 


120ub 
74000 

11.0 
84900 

11.5 
99600 

7.0 
109600 

3.0 
83117 

0.5 
90729 

0.5 
97894 

8.0 


13C0b 
71320 

7.0 
79600 

5.0 
85200 

2.0 
66800 

0.5 
46648 

0.0 
60600 

0.0 
35480 

1.0 


1200c 
71487 

10.5 
81487 

15.5 
96040 

10.0 
102705 

6.0 
114107 

5.5 

95103 

1.5 

89045 

17.5 


1200d 


0.41 


T. S 


74989 




El. % in 2 in 


25.0 


0.51 


T.S 


80795 




El. % in 2 in 


22.5 


0.63 


T.S 


89842 




El. % in 2 in 


21.0 


0.79 


T.S 


90214 




El. % in 2 in 


21.0 


0.97 


T.S 


103476 




El. % in 2 in 


18.0 


1.24 


T.S 


106304 




El. in 2 in 


3.5 


1.48 


T. S 


74592 




El. in 2 in 


24.0 



458 STEEL. 

a. Heated to 1000 C, which took 1 hr. 25 min., held there 25 min. and 
cooled in air. b. The time required to heat to the temperatures named 
was respectively 1 h. 10 m., 1 h. 45 m., 2 h. 35 m., and 2 h. 35 m. The 
bars were kept at the desired temperature for an hour and then cooled 
slowly in place, c. Reheated to 700 C. d. Reheated to 775 C. 

In the steels below 1% C heating to 1200° is accompanied by an increase 
in ultimate strength and a drop in ductility. Heating above 1200° pro- 
duces a very coarse crystallization and a great loss in strength and 
ductility. Reheating the overheated bars to 700° does not materially 
affect their structure, but reheating to 775° restores the structure nearly 
to that found before overheating, and completely restores the ductility. 
Similar results are found with carbon steel. 

Working Steel at a Blue Heat. — Not only are wrought iron and 
steel much more brittle at a blue heat (i.e., the heat that would produce an 
oxide coating ranging from light straw to blue on bright steel, 430° to 
600° F.), but while they are probably not seriously affected by simple 
exposure to blueness, even if prolonged, yet if they be worked in this range 
of temperature they remain extremely brittle after cooling, and may 
indeed be more brittle than when at blueness; this last point, however, 
is not certain. (Howe, Metallurgy of Steel, p. 534.) 

Tests by Prof. Krohn, for the German State Railways, show that work- 
ing at blue heat has a decided influence on all materials tested, the injury 
done being greater on wrought iron and harder steel than on the softer 
steel. The fact that wrought iron is injured by working at a blue heat 
was reported by Stromeyer. (Engineering News, Jan. 9, 1892.) 

A practice among boiler-makers for guarding against failures due to 
working at a blue heat consists in the cessation of work as soon as a plate 
which had been red-hot becomes so cool that the mark produced by 
rubbing a hammer-handle or other piece of wood will not glow. A plate 
which is not hot enough to produce this effect, yet too hot to be touched 
by the hand, is most probably blue hot, and should under no circumstances 
be hammered or bent. (C. E. Stromeyer, Proc. Inst. C. E., 1886.) 

Oil-tempering and Annealing of Steel Forgings. — H. F. J. Porter 
says (1897) that all steel forgings above 0.1% carbon should be annealed, 
to relieve them of forging and annealing strains, and that the process 
of annealing reduces the elastic limit to 47% of the ultimate strength. 
Oil-tempering should only be practiced on thin sections, and large forgings 
should be hollow for the purpose. This process raises the elastic limit 
above 50% of the ultimate tensile strength, and in some alloys of steel, 
notably nickel steel, will bring it up to 60'% of the ultimate. 

Heat Treatment of Armor Plates. (Hadfield Process, Iron Tr. 
Rev., Dec. 7, 1905.) — A cast armor plate of nickel-chromium steel is 
heated to from 950° C. to 1100° C, then cooled, preferably in air, then 
reheated to about 700° and cooled slowly, preferably in the furnace in 
which the heating was previously effected., again heated to about 700° 
and allowed to cool slowly to 640° C, whereupon it is suddenly cooled by 
spraying with water or by an air blast, but preferably in water. It is 
then reheated to about 600° and again suddenly cooled, preferably by 
quenching in water. Steel treated as described is suitable for armor 
plates and other articles, including parts of safes. Satisfactory results 
have been obtained by thus treating cast 6-in. armor plates containing 
about 0.3 to 0.4 C, 0.25 Mn, 1.8 Cr, and 3.3 Ni cast in a sand mold. 
Such a 6-in. plate attacked by armor-piercing projectiles of 4.7-in. and 
6-in. calibers, stood over 15,000 foot-tons of energy without showing a 
crack. Also a 4-in. plate treated as described and having a carbonized 
or cemented face has withstood the attack of a 5.7-in. armor-piercing shell. 

Brittleness Due to Long-continued Heating. If low-carbon steel, 
(say under 0.15%) is held for a very long time at temperatures between 
500 and 750° C. (930 and 1380° F.), the crystals become enormous and 
the steel loses a large part of its strength and ductility. It takes a long time, 
in fact days, to produce this effect to any alarming degree, so that it is 
not liable to occur during manufacture or mechanical treatment, but 
steel is sometimes placed in positions where it may suffer this injury, for 
example, in the case of the tie-rods of furnaces, supports of boilers, etc., 
so that the danger should be borne in mind by all engineers and users of 
steel. A wrought-iron chain that supported one side of a 50-ton open- 
hearth ladle, which was heated many times to a temperature above 500° O, 
finally reached a condition of coarse crystallization, so that it was unable 



TREATMENT OF STRUCTURAL STEEL. 459 

to bear the strain upon it. This phenomenon of coarse crystallization in 
low-carbon steel is known as "Stead's Brittleness," after J. E. Stead, who 
has explained its cause. The effect seems to begin at a temperature of 
about 500° C. and proceeds more rapidly with an increase in temperature 
until we reach 750° C. The damage may be repaired completely by heat- 
ing the steel to a temperature between 800 and 900° C. The remedy is 
the same as that for coarse crystallization, due to overheating, and all 
steel which is placed in positions where it is liable to reach these tempera- 
tures frequently should be restored at intervals of a week or a month, or 
as often as may be necessary. (Stoughton.) 

Influence of Annealing upon Magnetic Capacity. 

Prof. D. E. Hughes (Eng'g, Feb. 8, 1884, p. 130) has invented a "Mag- 
netic Balance," for testing the condition of iron and steel, which consists 
chiefly of a delicate magnetic needle suspended over a graduated circular 
index, and a magnet coil for magnetizing the bar to be tested. He finds 
that the following laws hold with every variety of iron and steel: 

1. The magnetic capacity is directly proportional to the softness, or 
molecular freedom. 

2. The resistance to a feeble external magnetizing force is directly as 
the hardness, or molecular rigidity. 

The magnetic balance shows that annealing not only produces softness 
in iron, and consequent molecular freedom, but it entirely frees it from 
all strains previously introduced by drawing or hammering. Thus a bar 
of iron drawn or hammered has a peculiar structure, say a fibrous one, 
which gives a greater mechanical strength in one direction than another. 
This bar, if thoroughly annealed at high temperatures, becomes homo- 
geneous in all directions, and has no longer even traces of its previous 
strains, provided that there has been no actual separation into a distinct 
series of fibers. 

TREATMENT OF STRUCTURAL STEEL. 

(James Christie, Trans. A. S. C. E., 1893.) 

Effect of Punching and Shearing. — The physical effects of punching 
and shearing as. denoted by tensile test are for iron or steel: 

Reduction of ductility; elevation of tensile strength at elastic limit; 
reduction of ultimate tensile strength. 

In very thin material the disturbance described is less than in thick; 
in fact, a degree of thinness is reached where this disturbance practi- 
cally ceases. On the contrary, as thickness is increased the injury becomes 
more evident. 

The effects described do not invariably ensue; for unknown reasons there 
are sometimes marked deviations from what seems to be a general result. 

By thoroughly annealing sheared or punched steels the ductility is to a 
large extent restored and the exaggerated elastic limit reduced, the change 
being modified by the temperature of reheating and the method of cooling. 

It is probable that the best results combined with least expenditure can 
be obtained by punching all holes where vital strains are not transferred by 
the rivets, and by reaming for important joints where strains on riveted 
joints are vital, or wherever perforation may reduce sections to a mini- 
mum. The reaming should be sufficient to thoroughly remove the mate- 
rial disturbed by punching; to accomplish this it is best to enlarge punched 
holes at least i/s in. diameter with the reamer. 

Riveting. — It is the current practice to perforate holes Vie in. larger 
than the rivet diameter. For work to be reamed it is also a usual require- 
ment to punch the holes from l/s to 3/ 16 in. less than the finished diameter, 
the holes being reamed to the proper size after the various parts are 
assembled. 

It is also excellent practice to remove the sharp corner at both ends of 
the reamed holes, so that a fillet will be formed at the junction of the body 
and head of the finished rivets. 

The rivets of either iron or mild steel should be heated to a bright red or 
yellow heat and subjected to a pressure of not less than 50 tons per square 
inch of sectional area. 

For rivets of ordinary length this pressure has been found sufficient to 
completely fill the hole. If, however, the holes and the rivets are excep- 



460 STEEL. 

tionally long, a greater pressure and a slower movement of the closing tool 
than is used for shorter rivets has been found advantageous. 

Welding. — No welding should be allowed on any steel that enters into 
structures. [See page 463.] 

Upsetting. — Enlarged ends on tension bars for screw-threads, eye- 
bars, etc., are formed by upsetting the material. With proper treatment 
and a sufficient increment of enlarged sectional area over the body of 
the bar the result is entirely satisfactory. The upsetting process should 
be performed so that the properly heated metal is compelled to flow 
without folding or lapping. 

Annealing. — The object of annealing structural steel is for the pur- 
pose of securing homogeneity of structure that is supposed to be impaired 
by unequal heating, or by the manipulation necessarily attendant on 
certain processes. The objects to be annealed should be heated through- 
out to a uniform temperature and uniformly cooled. 

The physical effects of annealing, as indicated by tensile tests, depend 
on the grade of steel, or the amount of hardening elements associated with 
it; also on the temperature to which the steel is raised, and the method 
or rate of cooling the heated material. 

The physical effects of annealing medium-grade steel, as indicated by 
tensile test, are reported very differently by different observers, some 
claiming directly opposite results from others. It is evident, when all the 
attendant conditions are considered, that the obtained results must vary 
both in kind and degree. 

The temperatures employed will vary from 1000° to 1500° F. In 
some cases the heated steel is withdrawn at full temperature from the 
furnace and allowed to cool in the atmosphere; in others the mass is 
removed from the furnace, but covered under a muffle, to lessen the free 
radiation; or, again, the charge is retained in the furnace, and the whole 
mass cooled with the furnace, and more slowly than by either of the other 
methods. 

The best general results from annealing will probably be obtained by 
introducing the material into a uniformly heated oven in which the tem- 
perature is not so high as to cause a possibility of cracking by sudden and 
unequal changing of temperature, then gradually raising the temperature 
of the material until it is uniformly about 1200° F., then withdrawing the 
material after the temperature is somewhat reduced and cooling under 
shelter of a muffle sufficiently to prevent too free and unequal cooling on 
the one hand or excessively slow cooling on the other. 

G. G. Mehrtens, Trans. A. S. C. E., 1893, says: "Annealing is of advan- 
tage to all steel above 64,000 lbs. strength per square inch, but it is ques- 
tionable whether it is necessary in softer steels. The distortions due to 
heating cause trouble in subsequent straightening, especially of thin plates. 

" In a general way all unannealed mild steel for a strength of 56,000 to 
64,000 lbs. may be worked in the same way as wrought iron. Rough 
treatment or working at a blue heat must, however, be prohibited. Shear- 
ing is to be avoided, except to prepare rough plates, which should after- 
wards be smoothed by machine tools or files before using. Drifting is also 
to be avoided, because the edges of the holes are thereby strained beyond 
the yield-point. Reaming drilled holes is not necessary, particularly 
when sharp drills are used and neat work is done. A slight counter- 
sinking of the edges of drilled holes is all that is necessary. Working the 
material while heated should be avoided as far as possible, and the 
engineer should bear this in mind when designing structures. Upsetting, 
cranking, and bending ought to be avoided, but when necessary the 
material should be annealed after completion. 

"The riveting of a mild-steel rivet should be finished as quickly as pos- 
sible, before it cools to the dangerous heat. For this reason machine work 
is the best. There is a special advantage in machine work from the fact 
that the pressure can be retained upon the rivet until it has cooled suffi- 
ciently to prevent elongation and the consequent loosening of the rivet." 

Punching and Drilling of Steel Plates. (Proc. Inst. M. E., Aug., 
1887, p. 326.) — In Prof. TJnwin's report the results of the greater number 
of the experiments made on iron and steel plates lead to the general con- 
clusion that while thin plates, even of steel, do not suffer very much from 
punching, yet in those of 1/2 in. thickness and upwards the loss of tenacity 
due to punching ranges from 10% to 23% in iron plates and from 11% to 
33% in the case of mild steel. 



MISCELLANEOUS NOTES ON STEEL. 461 

MISCELLANEOUS NOTES ON STEEL. 

May Carbon be Burned Out of Steel ? — Experiments made at the 
Laboratory of the Penna. Railroad Co. (Specifications for Springs, 1888) 
with the steel of spiral springs, show that the place from which the borings 
are taken for analysis has a very important influence on the amount of 
carbon found. Ifithe sample is a piece of the round bar, and the borings 
are taken from the end of this piece, the carbon is always higher than if the 
borings are taken from the side of the piece. It is common to find a 
difference of 0.10% between the center and side of the bar, and in some 
cases the difference is as high as 0.23%. Apparently during the process 
of reducing the metal from the ingots to the round bar, with successive 
heatings, the carbon in the outside of the bar is burned out. 

Effect of Nicking a Steel Bar. — The statement is sometimes made 
that, owing to the homogeneity of steel, a bar with a surface crack or nick 
in one of its edges is liable to fail by the gradual spreading of the nick, and 
thus break under a very much smaller load than a sound bar. With iron 
it is contended this does not occur, as this metal has a fibrous structure. 
Sir Benjamin Baker has, however, shown that this theory, at least so far 
as statical stress is concerned, is opposed to the facts, as he purposely 
made nicks in specimens of the mild steel used at the Forth Bridge, but 
found that the tensile strength of the whole was thus reduced by only 
about one ton per square inch of section. In an experiment by the Union 
Bridge Company a full-sized steel counter-bar, with a screw-turned 
buckle connection, was tested under a heavy statical stress, and at the 
same time a weight weighing 1040 lbs. was allowed to drop on it from 
various heights. The bar was first broken by ordinary statical strain, 
and showed a breaking stress of 66,800 lbs. per square inch. The longer 
of the broken parts was then placed in the machine and put under the 
following loads, whilst a weight, as already mentioned, was dropped on it 
from various heights at a distance of .five feet from the sleeve-nut of the 
turn-buckle, as shown below: 

Stress in pounds per sq. in 50,000 55,000 60,000 63,000 65,000 

ft. in. ft. in. ft. in. ft. in. ft. in. 
Height of fall 21 26 30 40 50 

The weight was then shifted so as to fall directly on the sleeve-nut, and 
the test proceeded as follows: 

Stress on specimen in lbs. per square inch 65,350 65,350 68,800 

Height of fall, feet 3 6 6 

It will be seen that under this trial the bar carried more than when 
originally tested statically, showing that the nicking of the bar by screw- 
ing had not appreciably weakened its power of resisting shocks. — Eng'g 
News. 

Specific Gravity of Soft Steel. (W. Kent, Trans. A. I.M.E., xiv, 
585.) — Five specimens of boiler-plate of C 0.14, P 0.03 gave an average 
sp. gr. of 7.932, maximum variation 0.008. The pieces were first planed 
to remove all possible scale indentations, then filed smooth, then cleaned 
in dilute sulphuric acid, and then boiled in distilled water, to remove all 
traces of air from the surface. 

The figures of specific gravity thus obtained by careful experiment on 
bright, smooth pieces of steel are, however, too high for use in determining 
the weights of rolled plates for commercial purposes. The actual average 
thickness of these plates is always a little less than is shown by the calipers, 
on account of the oxide of iron on the surface, and because the surface is 
not perfectly smooth and regular. A number of experiments on com- 
mercial plates, and comparison of other authorities, led to the figure 
7.854 as the average specific gravity of open-hearth boiler-plate steel. 
This figure is easily remembered as being the same figure with change of 
position of the decimal point (.7854) which expresses the relation of the 
area of a circle to that of its circumscribed square. Taking the weight 
of a cubic foot of water at 62° F. as 62.36 lbs. (average of several authori- 
ties), this figure gives 489.775 lbs. ns the weight of a cubic foot of steel, 
or the even figure, 490 lbs., may bo taken as a convenient figure, and 
accurate within the limits of the error of observation. 

A common method of approximating the weight of iron plates is to con- 
sider them to weigh 40 lbs. per square foot one inch thick. Taking this 



462 



weight and adding 2% gives almost exactly the weight of steel boiler- 
plate given above (40 X 12 X 1.02 = 489.6 lbs. per cubic foot). 

Occasional Failures of Bessemer Steel. — G. H. Clapp and A. 
E. Hunt, in their paper on "The Inspection of Materials of Construction'in 
the United States " (Trans. A.I.M. E., vol. xix), say: Numerous instances 
could be cited to show the unreliability of Bessemer steel for structural 
purposes. One of the most marked, however, was the following: A 
12-in. I-beam weighing 30 lbs. to the foot, 20 feet long, on being unloaded 
from a car broke in two about 6 feet from one end. 

The analyses and tensile tests made do not show any cause for the failure. 

The cold and quench bending tests of both the original 3/4-in. round test- 
pieces, and of pieces cut from the finished material, gave satisfactory re- 
sults; the cold-bending tests closing down on themselves without sign of 
fracture. 

Numerous other cases of angles and plates that were so hard in places as 
to break off short in punching, or, what was worse, to break the punches, 
have come under our observation, and although makers of Bessemer steel 
claim that this is just as likely to occur in open-hearth as in Bessemer steel, 
we have as yet never seen an instance of failure of this kind in open- 
hearth steel having a composition such as C 0.25%, Mn 0.70%, P 0.08%. 

J. W. Wailes, in a paper read before the Chemical Section of the British 
Association for the Advancement of Science, in speaking of mysterious 
failures of steel, states that investigation shows that "these failures occur 
in steel of one class, viz., soft steel made by the Bessemer process." 

Segregation in Steel Ingots. (A. Pourcel, Trans. A.I. M. E., 1893.) 
— H. M. Howe.in his " Metallurgy of Steel," gives a resume of observations, 
with the results of numerous analyses, bearing upon the phenomena of 
segregation. 

A test-piece taken 24 inches from the head of an ingot 7.5 feet in length 
gave by analysis very different results from those of a test-piece taken 
30 inches from the bottom. 





C. 


Mn. 


Si. 


S. 


P. 


Top 


0.92 
0.37 


0.535 

0.498 


0.043 
0.006 


0.161 
0.025 


0.261 




0.096 







Segregation is less marked in ingots of extra-soft metal cast in cast-iron 
molds of considerable thickness. It is, however, still important, and ex- 
plains the difference often shown by the results of tests on pieces taken 
from different portions of a plate. Two samples, taken from the sound 
part of a flat ingot, one on the outside and the other in the center, 7.9 
inches from the upper edge, gave: 





c. 


s. 


P. 


Mn. 




0.14 
0.11 


0.053 
0.036 


0.072 
0.027 


0.576 




0.610 







Manganese is the element most uniformly disseminated in hard or soft 
steel. 

For cannon of large caliber, if we reject, in addition to the part cast in 
sand and called the masselotte (sinking-head), one-third of the upper part 
of the ingot, we can obtain a tube practically homogeneous in composition, 
because the central part is naturally removed by the boring of the tube. 
With extra-soft steels, destined for ship- or boiler-plates, the solution for 
practically perfect homogeneity lies in the obtaining of a metal more 
closely deserving its name of extra-soft metal. 

The injurious consequences of segregation must be suppressed by redu- 
cing, as far as possible, the elements subject to liquation. 

Segregation in Steel Plates. (C. L. Huston, Proc. A. S. T. M., vi, 182.) 

A plate 370 X 76 X 5 /i6 in. was rolled from a 16 X 18-in. ingot, weighing 



MISCELLANEOUS NOTES ON STEEL. 



463 



2800 lbs., the ladle test of which showed 0.18 C. Test pieces from the 

plate gave the following: 

Top of Ingot: 

Tensile Strength 56,730 67,420 67,050 66,980 56,440 

Carbon 0.13 0.25 0.27 0.25 0.13 

Bottom of Ingot: 

Tensile Strength 56,120 57,720 58,400 58,140 56,900 

Carbon 0.13 0.13 0.16 0.16 0.14 

1 2 3 4 5 

Columns 1 and 5, edge of plate; 3, middle; 2 and 4, half way between 
middle and edge. 

Other tests of low-carbon steel showed a lower degree of segregation. 
A plate from an ingot of 0.23 C gave minimum 0.18 C T. S., 64,580: 
maximum 0.38 C, T. S., 70,340. One from an ingot of 0.26 C gave 
maximum 0.20 C, T. S., 59,600; maximum 0.50 C, T. S., 78,600. (See 
also paper on this subject by H. M. Howe in vol. vii, p. 75.) 

Endurance of Steel under Repeated Alternate Stresses. (J. E. 
Howard, A. S. T M., 1907, p. 252.) — Small bars were rapidly rotated in a 
machine while being subjected to a transverse strain. Two steels gave 
results as follows: (1) 0.55 C, T. S., 111,200; E. L., 59,000; Elong., 12%; 
Red. of area, 33.5%. (2) 0.82 C, T. S., 142,000; E. L., 64,000; Elong., 
7%; Red. of area, 11.8%. 



Fiber stress 

No. of rotations be- 
fore rupture. 



60,000 
f(l) 12,490 
\(2) 37,250 


50,000 
33,160 
213,150 


45,000 
166,240 
605,640 



40,000 

455,000 

202,000,000 



35,000 30,000 

900,720 |76,326,240 
Not broken. 



Welding of Steel. — H. H. Campbell {Manuf. of Iron and Steel, 
p. 402) had numerous bars of steel welded by different skilled blacksmiths. 
The record of results, he says, "is extremely unsatisfactory." The 
worst weld by each of four workmen showed respectively 70, 54, 58, and 
44% of the strength of the original bar. Forging steel showed one weld 
with only 48%, common soft steel 44%, and pure basic steel 59%. In 
a series of tests by the Royal Prussian Testing Institute, the average 
strength of welded bars of medium steel was 58% of the natural, the 
poorest bar showing only 23%. In softer steel the average was 71%, 
and the poorest 33%, while in puddled iron the average was 81% and the 
poorest 62%. Mr. Campbell concludes: "A weld as performed by 
ordinary blacksmiths, whether on iron or steel, is not nearly as good as 
the rest of the bar; and it is still more certain that welds of large rods of 
common forging steel are unreliable and should not be employed in 
structural work. Electric methods do not offer a solution of the problem, 
for the metal is heated beyond the critical temperature of crystallization, 
and only by heavy reductions under the hammer' or press can much be 
done towards restoring the ductilitv of the piece." 

Welding of Steel.— A. E. Hunt (A. I. M. E., 1892) says: "I have never 
seen so-called 'welded ' pieces of steel pulled apart in a testing-machine 
or otherwise broken at the joint which have not shown a smooth cleavage 
plane, as it were, such as in iron would be condemned as an imperfect 
weld. My experience in this matter leads me to agree with the position 
taken by Mr. William Metcalf in his paper upon Steel in the Trans. A. S. 
C. E., vol. xvi, p. 301. Mr. Metcalf says. 'I do not believe steel can be 
welded.' " 

The Thermit Welding Process. (Goldschmidt Thermit Co., New 
York.)— When powdered or finelv divided aluminum is mixed with a 
metallic oxide and ignited, the aluminum burns with great rapidity and 
intense heat, reducing the oxide to a metal and fusing it. It is said that 
iron oxide and aluminum will make a temperature of 5400° F., producing 
fused iron which will melt any iron or steel with which it comes in con- 
tact. The process is largely used for repairing breaks of large castings 
or forcings, such as the stern post of a steamship, a locomotive frame, 
etc. In the operation of welding a large fractured piece, the fracture 
is drilled out with a series of 3/ 4 -in. holes close together, making a clear 
opening. A mold of fire-clay and sand is then made to fit all around 
the fracture, leaving a collar' or ring surrounding it, baked in a furnace 



464 



and then placed in position. The fractured section is then heated by a 
blow-torch inserted in the riser of the mold. A conical sheet iron cru- 
cible, lined with magnesia tar, is then inserted in the riser, and thermit 
(the mixture of aluminum and oxide of iron) poured into it. An ignition 
powder is placed on top of the thermit, and lighted with a storm match. 
The mixture begins to burn with great agitation; when this ceases the 
crucible is tapped, and white-hot fused iron or steel runs into the mold 
and thoroughly fuses with the pieces to be joined. 

Oxy-acetylene Welding and Cutting of Metals. — Autogenous 
Welding. — By means of acetylene gas and oxygen, stored in tanks 
under pressure, and a properly constructed nozzle or torch in which the 
two gases are united and fired, an intense temperature said to be 6000° F., 
is generated, and it may be used to weld or fuse together iron, steel, alumi- 
num, brass, copper, or other metals. The process of uniting metals by heat 
without using either flux or compression is called autogenous welding. 
The oxy-acetylene torch may also be used for cutting metals, such as 
steel plates, beams and large forgings, and for repairing flaws or defects, 
or filling cavities by melting a strip of metal and flowing it into place. 
The apparatus, with instruction in its use, is furnished by the Davis- 
Bournonville Co., Jersey City, N. J. 

Electric Welding. — For description see Electrical Engineering. 

Hydraulic Forging. — In the production of heavy forgings from 
cast ingots of mild steel it is essential that the mass of metal should be 
operated on as equally as possible throughout its entire thickness. When 
employing a steam-hammer for this purpose it has been found that the ex- 
ternal surface of the ingot absorbs a large proportion of the sudden impact 
of the blow, and that a comparatively small effect only is produced on the 
central portions of the ingot, owing to the resistance offered by the inertia 
of the mass to the rapid motion of the falling hammer — a disadvantage 
that is entirely overcome by the slow, though powerful, compression of the 
hydraulic forging-press, which appears destined to supersede the steam- 
hammer for the production of massive steel forgings. 

Fluid-compressed Steel by the " Whitworth Process." (Proc. 
Inst. M. E., May, 1887, p. 167.) — In this system a gradually increasing 
pressure up to 6 or 8 tons per square inch is applied to the fluid ingot, and 
within half an hour or less after the application of the pressure the column 
of fluid steel is shortened 1 1/2 inches per foot or one-eighth of its length; the 
pressure is then kept on for several hours, the result being that the metal 
is compressed into a perfectly solid and homogeneous material, free from 
blow-holes. 

In large gun-ring ingots during cooling the^carbon is driven to the center, 
the center containing 0.8 carbon and the outer ring 0.3. The center is 
bored out until a test shows that the inside of the ring contains the same 
percentage of carbon as the outside. 

Fluid-compressed steel is made by the Bethlehem Steel Co. for gun and 
other heavy forgings. 

Putting sufficient pressure upon the outside of the ingot when the walls 
are solid but the interior is still liquid will prevent the formation of a 
pipe. In Whitworth's system the ingot is raised and compressed length- 
wise against a solid ram situated above it, during and shortly after solidifi- 
cation. In Harmet's method the ingot is forced upward during solidifi- 
cation into its tapered mold. This causes a large radial pressure on its 
sides. In Lilienberg's method the ingots are stripped and then run on 
their cars between a solid and movable wall. The movable wall is then 
pressed against one side of the ingots. (Stoughton's Metallurgy of Iron 
and Steel.) 

For other methods of compressing ingots see paper by A. J. Capron in 
Jour. I. & S. I., 1906, Iron Tr. Rev., May 24, 1906. 

STEEL CASTINGS. 

(E. S. Cramp, Proc. Eng'g Congress, Dept. of Marine Eng'g, Chicago, 1893.) 
In 1891 American steel-founders had successfully produced a consider- 
able variety of heavy and difficult castings, of which the following are the 
most noteworthy speeimens: 

Bed-plates up to 24,000 lbs.; stern-posts up to 54,000 lbs.; stems up to 
21,000 lbs.; hydraulic cylinders up to 11,000 lbs.; shaft-struts up to 32,000 
lbs.; hawse-pipes up to 7500 lbs.; stern-pipes up to 8000 lbs. 



STEEL CASTINGS. 



465 



The percentage of success in these classes of castings since 1890 has 
ranged from 65% in the more difficult forms to 90% in the simpler ones; 
the tensile strength has been from 62,000 to 78,000 lbs., elongation from 
15% to 25%. 

The first steel castings of which anything is generally known were 
crossing-frogs made for the Philadelphia & Reading R. R. in July, 1867, by 
the William Butcher Steel Works, now the Midvale Steel Co. The molds 
were made of a mixture of ground fire-brick, black-lead crucible-pots 
ground fine, and fire-clay, and washed with a black-lead wash. The steel 
was melted in crucibles, and was about as hard as tool steel. The surface 
of these castings was very smooth, but the interior was very much honey- 
combed. This was before the days when the use of silicon was known for 
solidifying steel. The sponginess, which was almost universal, was a great 
obstacle to their general adoption. 

The next step was to leave the ground pots out of the molding mixture 
and to wash the mold with finely ground fire-brick. This was a great im- 
provement, especially in very heavy castings; but this mixture still clung so 
strongly to the casting that only Comparatively simple shapes could be 
made with certainty. A mold made of such a mixture became almost as 
hard as fire-brick, and was such an obstacle to the proper shrinkage of 
castings that, when at all complicated in shape, they had so great a 
tendency to crack as to make their successful manufacture almost impos- 
sible. By this time the use of silicon had been discovered, and the only 
obstacle in the way of making good castings was a suitable molding 
mixture. This was ultimately found in mixtures having the various kinds 
of silica sand as the principal constituent. 

One of the most fertile sources of defects in castings is a bad design. 
"Very intricate shapes can be cast successfully if they are so designed as to 
cool uniformly. Mr. Cramp says while he is not yet prepared to state that 
anything that can be cast successfully in iron can be cast in steel, indica- 
tions seem to point that way in all cases where it is possible to put on suit- 
able sinking-heads for feeding the casting. 

H. L. Gantt {Trans. A. S. M. E.,xii, 710) says: Steel castings not only 
shrink much more than iron ones, but with less regularity. The amount of 
shrinkage varies with the composition and the heat of the metal; the hotter 
the metal the greater the shrinkage; and, as we get smoother castings from 
hot metal, it is better to make allowance for large shrinkage and pour the 
metal as hot as possible. Allow 3/ 16 or 1/4 in. per ft. in length for shrinkage, 
and 1/4 in. for finish on machined surfaces, except such as are cast "up." 
Cope surfaces which are to be machined should, in large or hard castings, 
have an allowance of from 3/ 8 to 1/2 in. for finish, as a large mass of metal 
slowly rising in a mold is apt to become crusty on the surface, and such a 
crust is sure to be full of imperfections. On small, soft castings 1/8 in. on 
drag side and 1/4 in. on cope side will be sufficient. No core should have 
less than 1/4 in. finish on aside and very large ones should have as much as 
1/2 in. on a side. Blow-holes can be entirely prevented in castings by the 
addition of manganese and silicon in sufficient quantities; but both of 
these cause brittleness, and it is the object of the conscientious steel- 
maker to put no more manganese and silicon in his steel than is just suffi- 
cient to make it solid. The best results are arrived at when all portions of 
the castings are of a uniform thickness, or very nearly so. 

The following table will illustrate the effect of annealing on tensile 
strength and elongation of steel castings: 



Carbon. 


Tensile Strength. 


Elongation. 


Unannealed. 


Annealed. 


Unannealed. 


Annealed. 


0.23% 

0.37 

0.53 


68,738 
85,540 
90,121 


67,210 
82,228 
106,415 


22.40% 
8.20 
2.35 


31.40% 
21.80 
9.80 



The proper annealing of large castings takes nearly a week. 

The proper steel for roll pinions, hammer dies, etc., seems to be that con- 
taining about 0.60% of carbon. Such castings, properly annealed, have 
worn well and seldom broken. Miscellaneous gearing should contain 



466 STEEL. 

carbon 0.40% to 0.60%, gears larger in diameter being softest. General 
machinery castings should, as a rule, contain less than 0.40% of carbon, 
those exposed to great shocks containing as low as 0.20% of carbon. Such 
castings will give a tensile strength of from 60,000 to 80,000 lbs. per sq. 
in. and at least 15% extension in 2 in. Machinery and hull castings for 
war-vessels for the United States Navy, as well as carriages for naval 
guns, contain from 0.20% to 0.30% of carbon. 

For description of methods of manufacture of steel castings by the Besse- 
mer, open-hearth, and crucible processes, see paper by P. G. Salom, Trans. 
A. I. M. E., xiv. 118. 

CRUCIBLE STEEL. 

Selection of Grades by the Eye, and Effect of Heat Treatment. 

(J. W. Langley, Amer, Chemist, Nov., 1876.) — In the early days of steel 
making the grades were determined by inspection of the fractured surfaces 
of the cast ingots. The method of selection is described as follows: 

The steel when thoroughly fluid is poured into cast-iron molds, and 
when cold the top of the ingot is broken off, exposing a freshly fractured 
surface. The appearance presented is that of confused groups of crystals, 
all appearing to have started from the outside and to have met in the 
center; this general form is common to all ingots of whatever composition, 
but to the trained eye, and only to one long and critically exercised, a 
minute but indescribable difference is perceived between varying samples 
of steel, and this difference is now known to be owing almost wholly to 
variations in the amount of combined carbon, as the following table will 
show. Twelve samples selected by the eye alone, and analyses of drillings 
taken direct from the ingot before it had been heated or hammered, gave 
results as below: 

Ingot Nos. 1 2 3456789 10 11 12 

O 0.302 .490 .529 .649 .801 .841 .867 .871 .955 1.005 1.058 1.079 

Diff. of C 0.188 .039 .120 .152 .040 .026 .004 .084 .050 .053 .021 

The C is seen to increase in quantity in the order of the numbers. The 
other elements, with the exception of total iron, bear no relation to the 
number on the samples. The mean difference of C is 0.071. 

In mild steels the discrimination is less perfect. 

The appearance of the fracture by which the above twelve selections 
were made can only be seen in the cold ingot before any operation, except 
the original one of casting, has been performed upon it. As soon as it is 
hammered, the structure changes, so that all trace of the primitive con- 
dition appears to be lost. 

The specific gravity of steel is influenced not only by its chemical analy- 
sis but by the heat to which it is subjected. 

The sp. gr. of the ingots in the above list ranged from 7.855 for No. 1 
down to 7.803 for No. 12. Rolling into bars produced a very slight dif- 
ference, — 0.005 in Nos. 5 and 6 and +0.020 in No. 12, but overheating 
reduced the sp. gr. of the bar 0.023 in No. 3 to 0.135 in No. 12, the sp. gr. of 
the burnt sample of No. 12 being only 7.690. 

Effect of Heat on the Grain of Steel. (W. Metcalf, — Jeans on 
Steel, p. 642.) — A simple experiment will show the alteration produced 
in a high-carbon steel by different methods of hardening. If a bar of such 
steel be nicked at about 9 or 10 places, and about half an inch apart, a 
suitable specimen is obtained for the experiment. Place one end of the 
bar in a good fire, so that the first nicked piece is heated to whiteness, 
while the rest of the bar, being out of the fire, is heated up less and less 
as we approach the other end. As soon as the first piece is at a good 
white heat, which of course burns a high-carbon steel, and the temperature 
of the rest of the bar gradually passes down to a very dull red, the metal 
should be taken out of the fire and suddenly plunged in cold water, in 
which it should be left till quite cold. It should then be taken out and 
carefully dried. An examination with a file will show that the first piece 
has the greatest hardness, while the last piece is the softest, the inter- 
mediate pieces gradually passing from one condition to the other. On 
now breaking off the pieces at each nick it will be seen that very consider- 
able and characteristic changes have been produced in the appearance of 
the metal. The first burnt piece is very open or crystalline in fracture; 
the succeeding pieces become closer and closer in the grain until one piece 
is found to possess that perfectly even grain and velvet-like appearance 



CRUCIBLE STEEL. 467 

which is so much prized by experienced steel users. The first pieces also, 
which have been too much hardened, will probably be cracked; those at 
the other end will not be hardened through. Hence if it be desired to 
make the steel hard and strong, the temperature used must be high 
enough to harden the metal through, but not sufficient to open the grain. 

Heating Tool Steel. (Crescent Steel Co., Pittsburg, Pa.) — There are 
three distinct stages or times of heating: First, for forging; second, for 
hardening; third, for tempering. 

The first requisite for a good heat for forging is a clean fire and plenty of 
fuel, so that jets of hot air will not strike the corners of the piece; next, 
the fire should be regular, and give a good uniform heat to the whole part 
to be forged. It should be keen enough to heat the piece as rapidly as 
may be, and allow it to be thoroughly heated through, without being 
so fierce as to overheat the corners. 

Steel should not be left in the fire any longer than is necessary to heat it 
clear through, as "soaking " in fire is very injurious; and, on the other 
hand, it is necessary that it should be hot through, to prevent surface 
cracks. 

By observing these precautions a piece of steel may always be heated 
safely, up to even a bright yellow heat, when there is much forging to be 
done on it. 

The best and most economical of welding fluxes is clean, crude borax, 
which should be first thoroughly melted and then ground to fine powder. 

After the steel is properly heated, it should be forged to shape as quickly 
as possible; and just as the red heat is leaving the parts intended for cutting 
edges, these parts should be refined by rapid, light blows, continued until 
the red disappears. 

For the second stage of heating, for hardening, great care should be used: 
first, to protect the cutting edges and working parts from heating more 
rapidly than the body of the piece; next, that the whole part to be hardened 
be heated uniformly through, without any part becoming visibly hotter 
than the other. A uniform heat, as low as will give the required hardness, 
is the best for hardening. 

For every variation of heat which is great enough to be seen there will 
result a variation in grain, which may be seen by breaking the piece; and 
for every such variation in temperature there is a very good chance for a 
crack to be seen. Many a costly tool is ruined by inattention to this point. 

The effect of too high heat is to open the grain; to make the steel coarse. 
The effect of an irregular heat is to cause irregular grain, irregular strains, 
and cracks. 

As soon as the piece is properly heated for hardening, it should be 
promptly and thoroughly quenched in plenty of the cooling medium, water, 
brine, or oil, as the case may be. 

An abundance of the cooling bath, to do the work quickly and uniformly 
all over, is very necessary to good and safe work. 

To harden a large piece safely a running stream should be used. 

Much uneven hardening is caused by the use of too small baths. 

For the third stage of heating, to temper, the first important requisite is 
again uniformity. The next is time; the more slowly a piece is brought 
down to its temper, the better and safer is the operation. 

When expensive tools are to be made it is a wise precaution to try small 
pieces of the steel at different temperatures, so as to find out how low a 
heat will give the necessary hardness. The lowest heat is the best for any 
steel. [This is true of carbon steel but not of " high speed " alloy steels.] 

Heating in a Lead Bath. — A good method of heating steel to a 
uniform temperature is by means of a bath of lead kept at a red heat by 
a gas furnace. See Heat Treatment by the Taylor-White Process, under 
Machine Shop. 

Heating Steel in Melted Salts by Electric Current. — L. M. Cohn 
(Elertrot. Z., Aug., 1906, Mach'y, Dec, 1906) describes a furnace pat- 
ented by Gebr. Korting, Berlin, in which steel may be heated uniformly 
to any desired temperature up to 1300° C. (2372° F.) without danger of 
oxidizing. 

The furnace consists mainly of a cast-iron box, lined inside with fire- 
clay, a second lining of fire-bricks, lined again with asbestos, and 
inclosing the crucible made of one piece of fireproof material. Two 
electrodes lead into the crucible, through which alternating current is 
sent. The crucible is filled with metal salts. For temperatures above 



468 STEEL. 

1000° C. pure chloride of barium is used, the melting-point of which is 
at about 950° C. (1742 F.); for lower temperatures a mixture of chloride 
of barium and chloride of potassium, 2 to 1, is used, melting at about 
670° C. (1238 F.). Any other suitable salts may be used. A special 
regulating transformer serves to regulate the current, and thus also the 
temperature. 

A test was made with a furnace, the bath of which was 6 1/2 X 6 1/2 X 7 
in. A 50-period alternating current of 190-volt primary tension was 
used. This tension had to be reduced to from 50 to 55 volts by the 
regulating transformer for starting the furnace, and lowered later on. 
The heating lasted about half an hour. For temperatures from 750 to 
1300° C, the secondary tension amounted to from 13 to 18 volts. The 
consumption of energy was as follows: 880° C, 5.4 Kw.; 1140° C, 8.5 Kw.; 
1300° C, 12.25 Kw. 

A milling cutter 5 in. diameter, H/4 in. bore, 1 in. thick, was heated in 
62 seconds to 1300° C. A bushing of tool steel 23/ 4 in. diam., 23/ 4 in. 
long, 5/ 8 in. bore, was heated in 243 seconds to 850° C. 

Heating to Forge. (Crescent Steel Co.) — The trouble in the forge 
fire is usually uneven heat, and not too high heat. Suppose the piece to 
be forged has been put into a very hot fire, and forced as quickly as possible 
to a high yellow heat, so that it is almost up to the scintillating point. If 
this be done, in a few minutes the outside will be quite soft and in a nice 
condition for forging, while the middle parts will not be more than red-hot. 
Now let the piece be placed under the hammer and forged, and the soft 
outside will yield so much more readily than the hard inside, that the 
outer particles will be torn asunder, while the inside will remain sound. 

Suppose the case to be reversed and the inside to be much hotter than the 
outside; that is, that the inside shall be in a state of semi-fusion, while the 
outside is hard and firm. Now let the piece be forged, and the outside will 
be all sound and the whole piece will appear perfectly good until it is 
cropped, and then it is found to be hollow inside. 

In either case, if the piece had been heated soft all through, or if it had 
been only red-hot all through, it would have forged perfectly sound. 

In some cases a high heat is more desirable to save heavy labor, but in 
every case where a fine steel is to be used for cutting purposes it must be 
borne in mind that very heavy forging refines the bars as they slowly cool, 
and if the smith heats such refined bars until they are soft, he raises the 
grain, makes them coarse, and he cannot get them fine again unless he has 
a very heavy steam-hammer at command and knows how to use it well. 

Annealing. (Crescent Steel Co.) — Annealing or softening is accom- 
plished by heating steel to a red heat and then cooling it very slowly, 
to prevent it from getting hard again. 

The higher the degree of heat, the more will steel be softened, until the 
limit of softness is reached, when the steel is melted. 

It does not follow that the higher a piece of steel is heated the softer it 
will be when cooled, no matter how slowly it may be cooled; this is proved 
by the fact that an ingot is always harder than a rolled or hammered bar 
made from it. 

Therefore there is nothing gained by heating a piece of steel hotter than 
a good, bright, cherry-red; on the contrary, a higher heat has several dis- 
advantages: First. If carried too far.it may leave the steel actually 
harder than a good red heat would leave it. Second. If a scale is raised 
on the steel, this scale will be harsh, granular oxide of iron, and will spoil 
the tools used to cut it. Third. A high scaling heat continued for a little 
time changes the structure of the steel, makes it brittle, liable to crack in 
hardening, and impossible to refine. 

To anneal any piece of steel, heat it red-hot; heat it uniformly and heat it 
through, taking care not to let the ends and corners get too hot. 

As soon as it is hot, take it out of the fire, the sooner the better, and cool 
it as slowly as possible. A good rule for heating is to heat it at so low a 
red that when the piece is cold it will still show the blue gloss of the oxide 
that was put there by the hammer or the rolls. • 

Steel annealed in this way will cut very soft: it will harden very hard, 
without cracking; and when tempered it will be very strong, nicely 
refined, and will hold a keen, strong edge. 

Tempering. — Tempering steel is the act of giving it, after it has been 
shaped, the hardness necessary for the work it has to do. This is done by 



CRUCIBLE STEEL. 469 

first hardening the piece, generally a good deal harder than is necessary, 
and then toughening it by slow heating and gradual softening until it is 
just right for work. 

A piece of steel properly tempered should always be finer in grain than 
the bar from which it is made. If it is necessary, in order to make the 
piece as hard as is required, to heat it so hot that after being hardened the 
grain will be as coarse as or coarser than the grain in the original bar, then 
the steel itself is of too low carbon for the desired work. 

If a great degree of hardness is not desired, as in the case of taps and 
most tools of complicated form, and it is found that at a moderate heat the 
tools are too hard and are liable to crack, the smith should first use a lower 
heat in order to save the tools already made, and then notify the steel- 
maker that his steel is too high, so as to prevent a recurrence of the 
trouble. 

For descriptions of various methods of tempering steel, see "Tempering 
of Metals," by Joshua Rose, in App. Cyc. Mech., vol. ii, p. 863; also, 
"Wrinkles and Recipes," from the Scientific American. In both of these 
works Mr. Rose gives a "color scale," lithographed in colors, by which the 
following is a list of the tools in their order on the color scale, together 
with the approximate color and the temperature at which the color 
appears on brightened steel when heated in the air: 

Scrapers for brass; very pale yellow, Hand-plane irons. 

430° F. Twist-drills. 

Steel-engraving tools. Flat drills for brass. 

Slight turning tools. Wood-boring cutters. 

Hammer faces. Drifts. 

Planer tools for steel. Coopers' tools. 

Ivory-cutting tools. Edging cutters; light purple, 530° F. 

Planer tools for iron. Augers. 

Paper-cutters. Dental and surgical instruments. 

Wood-engraving tools. Cold chisels for steel. 

Bone-cutting tools. Axes; dark purple, 550° F. 
Milling-cutters; straw yellow, 460° F. Gimlets. 

Wire-drawing dies. Cold chisels for cast iron. 

Boring-cutters. Saws for bone and ivory. 

Leather-cutting dies. Needles. 

Screw-cutting dies. Firmer-chisels. 

Inserted saw-teeth. Hack-saws. 

Taps. Framing-chisels. 

Rock-drills. Cold chisels for wrought iron. 

Chasers. Molding and planing cutters to be 
Punches and dies. filed. 

Penknives. Circular saws for metal. 

Reamers. Screw-drivers. 

Half-round bits. Springs. 

Planing and molding cutters. Saws for wood. 
Stone-cutting tools; brown yellow, Dark blue, 570° F. 

500° F. Pale blue, 610°. 

Gouges. Blue tinged with green, 630°. 

Uses of Crucible Steel of Different Carbons. (Metcalf on Steel.) — 
0.50 to 0.60 C, for hot work and for battering tools. 
0.60 to 0.70 C, ditto, and for tools of dull edge. 
0.70 to 0.80 C, battering tools, cold-sets, and some forms of reamers and 

taps. 
0.80 to 0.90 C, cold-sets, hand-chisels, drills, taps, reamers and dies. 
0.90 to 1.00 C, chisels, drills, dies, axes, knives, etc. 
1.00 to 1.10 C, axes, hatchets, knives, large lathe-tools, and many kinds 

of dies and drills if care be used in tempering them. 
1.10 to 1.50 C, lathe-tools, graving tools, scribers, scrapers, little drills, 

and many similar purposes. 

The best all-around tool steel is found between 0.90 and 1.10 C; steel 
that can be adapted safely and successfully to more uses than any 
other. 

High-speed Tool Steel. (A. L. Valentine. Am. Mach., July 2, 1908.) — 
Eight brands of high-speed steel were analyzed with the following 
results; 



470 



Steel. 


C. 


W. 


Cr. 


Mn. 


Si. 


Mo. 


P. 


s. 




0.70 
0.25 
0.75 
0.49 
0.65 
0.60 
0.55 
0.66 


14.91 
17.27 
14.83 
17.60 


2.95 
2.69 
2.90 
5.11 


0.01 
Trace 
0.08 






0.013 

0.035 

0.02 

0.01 

0.016 

0.019 


0.008 


b 
c 

d 


0.179 


"b.\k" 


Trace 
0.01 
0.007 




0.19 


0.039 


9.60 


0.005 


f 


13.00 
17.81 
19.03 


2.88 
2.48 


0.0! 


I 


0.11 


0.090 
0.036 








0.015 






1 





W, Wolfram, symbol for tungsten. 

Where blanks appear in the table, the steel was not analyzed for these 
ingredients. 

Many different brands of high-speed steel are being made. Some that 
have been marketed are almost worthless. From some of these steels a 
tool can be made from one end of a bar that is easily forged, machined 
and hardened, while the other end of the bar would resist almost any 
cutting tool and would invariably crack in hardening. Different bars of 
the same make also give very different results. These faults are some- 
times caused by non-uniform annealing in the steels which are sent out as 
thoroughly annealed, and in many cases they are caused by the use of 
impure ingredients. A good high-speed steel will stand a temperature 
as high as 1200° F., or over double that of carbon steel, without losing its 
hardness, and experience has proven that the higher the temperature is 
raised over the white-heat point, the higher a temperature caused by 
friction the tool will withstand, before losing its intense hardness. The 
higher the percentage of carbon is, the more brittle and hard to work the 
steel will be, especially to forge. The steel which has given the best all- 
around results has contained about 0.40 C. The analysis of this same 
steel showed nearly 3% of chromium. The higher the percentage of 
'tungsten in the steel, the better has been its cutting qualities. (See Best 
High-Speed Tool Steel, and description of the Taylor-White process of 
heat treatment, under "The Machine-Shop. " 

MANGANESE, NICKEL, AND OTHER "ALLOT" STEELS. 

Manganese Steel. (H. M. Howe, Trans. A. S. M. E., vol. xii.) — 
Manganese steel is an alloy of iron and manganese, incidentally, and 
probably unavoidably, containing a considerable proportion of carbon. 

The effect of small proportions of manganese on the hardness, strength, 
and ductility of iron is probably slight. The point at which manganese 
begins to have a predominant effect is not known; it may be somewhere 
about 2.5%. 

Manganese steel is very free from blow-holes; it welds with great diffi- 
culty; its toughness is increased by quenching from a yellow heat; its elec- 
tric resistance is enormous, and very constant with changing temperature; 
it is low in thermal conductivity. Its remarkable combination of great 
hardness, which cannot be materially lessened by annealing, and great 
tensile strength, with astonishing toughness and ductility, at once creates 
and limits its usefulness. 

The hardness of manganese steel seems to be of an anomalous kind. 
The alloy is hard, but under some conditions not rigid. It is very hard in 
its resistance to abrasion; it is not always hard in its resistance to impact. 

Manganese steel forges readily at a yellow heat, though at a bright white 
heat it crumbles under the hammer. But it offers greater resistance to 
deformation, i.e., it is harder when hot, than carbon steel. 

The most important single use for manganese steel is for the pins which 
hold the buckets of elevator dredges. Here abrasion chiefly is to be 
resisted. Another important use is for the links of common chain- 
elevators. As a material for stamp-shoes, for horse-shoes, for the knuckles 
of an automatic car-coupler, it has not met expectations. 

Manganese steel has been regularly adopted for the blades of the Cyclone 
pulverizer. Some manganese-steel wheels are reported to have run over 
300,000 miles each without turning, on a New England railroad. 



"alloy" steels. 471 

Manganese Steel and its Uses. (E. F. Lake, Am. Mach., May 16, 
1907.) — When more than 2% and less than 6% of Mn is added, with C 
less than 0.5%, it makes steel very brittle, so that it can be powdered 
under a hand hammer. From 6% Mn up, this brittleness gradually dis- 
appears until 12% is reached, when the former strength returns and 
reaches its maximum at 15%. After this, a decrease in toughness, but 
not in transverse strength, takes place until 20% is reached, after which 
a rapid decrease in strength again takes place. 

Steel with from 12 to 15% Mn and less than 0.5% of C is very hard and 
cannot be machined or drilled in the ordinary way; yet it is so tough that 
it can be twisted and bent into peculiar shapes without breaking. It is 
malleable enough to be used for rivets that are to be headed cold. 

This hardness, toughness and malleability make manganese steel the 
most durable metal known, in its ability to resist wear, for such parts 
as the teeth on steam-shovel dippers, where they will outwear about three 
teeth made of the best tool steel; for plow points on road-building work; 
for frogs, switches and crossings in railroad construction; for fluted or 
toothed crushing rolls used on ore, coal and stone crushers; for screen 
shells to screen these crushings; gears, sprockets, link belts, etc., when 
used in the vicinity of ore, stone and coal crushers or other places where 
they are subjected to the hard, grinding wear of the gritty particles of 
dust with which they are usually covered. 

The higher the percentage of C in the steel, the less percentage of Mn 
will be required to produce brittleness. Si, however, neutralizes the 
injurious tendencies of Mn, and in Europe the Si-Mn alloy is used for 
automobile springs and gears. This steel is not high in Mn and can be 
rolled, while the peculiar properties given to steel by the addition of from 
12 to 15% of manganese make such steel impossible to roll; therefore all 
parts made of this steel have to be cast, after which it can be forged and 
rendered tougher by quenching from a white heat. 

One of its peculiarities is that it is softened by rapid cooling and can be 
restored to its former hardness by heating to a bright red. 

• It is more difficult to mold in the foundry than the ordinary cast steel, 
as it must be poured at a very high temperature, and in cooling it shrinks 
nearly twice as much. The shrinkage allowed for patterns to be cast of 
the ordinary cast steel is 3/ 16 in. per foot, and for manganese-steel castings 
5/i6 in. per foot. 

This enormous shrinkage makes it impossible to cast in any intricate or 
delicate shapes, and as it is too hard to machine or drill successfully, all 
holes must be cored in the casting. If a close fit is desired in these 
they must be ground out with an emery wheel. These properties limit 
its use to a large extent. 

The composition that seems to give the best results is: 

Mn, from 12 to 15%; C, not over 0.5%-; P, not over 0.04%; S, not over 
0.04%. 

Manganese-steel castings should be annealed in order to remove any 
internal strains which may be caused by its high shrinkage and the fact 
that the outer surface cools so much quicker than the core, which leaves 
the center of the casting strained. This can be done by heating to 1500° 
F. and quenching in water, after which it can be hardened by heating to 
900° and allowed to cool slowly. 

Manganese-steel castings, when tested in a 7/ 8 -inch round bar, should 
show: 

T. S. per sq. in., not less than 140,000 lbs.; E. L., not less than 90,000 
lbs.; Red. of area, not less than 50%; Elong. in 2 in., not less than 20%. 

Chrome Steel. (F. L. Garrison, Jour. F. I., Sept., 1891.) — Chromium 
increases the hardness of iron, perhaps also the tensile strength and elastic 
limit, but it lessens its weldability. 

Chromium does not appear to give steel the power of becoming harder 
when quenched or chilled. Howe states that chrome steels forge more 
readily than tungsten steels, and when not containing over 0.5 of chro- 
mium nearly as well as ordinary carbon steels of like percentage of carbon. 
On the whole the status of chrome steel is not satisfactory. There are 
other steel alloys coming into use, which are so much better, that it would 
seem to be only a question of time when it will drop entirely out of the 
race. Howe states that many experienced chemists have found no 
chromium, or but the merest traces, in chrome steel sold in the markets. 

J. W. Langley) Trans. A. S. C. E., 1892) says: Chromium, like manganese. 



472 STEEL. 

is a true hardener of iron even in the absence of carbon. The addition of 
1% or 2% of chromium to a carbon steel will make a metal which gets 
excessively hard. Hitherto its principal employment has been in the 
production of chilled shot and shell. Powerful molecular stresses result 
during cooling, and the shells frequently break spontaneously months after 
they are made. 

Tungsten Steel — Mushet Steel. (J. B. Nau, Iron Age, Feb. 11, 1892.) 
— By incorporating simultaneously carbon and tungsten in iron, it is 
possible to obtain a much harder steel than with carbon alone, without 
danger of an extraordinary brittleness in the cold metal or an increased 
difficulty in the working of the heated metal. 

When a special grade of hardness is required, it is frequently the custom 
to use a high tungsten steel, known in England as special steel. A speci- 
men from Sheffield, used for chisels, contained 9.3% of tungsten, 0.7% of 
silver, and 0,6% of carbon. This steel, though used with advantage in its 
untempered state to turn chilled rolls, was not brittle; nevertheless it was 
hard enough to scratch glass. 

A sample of Mushet's special steel contained 8.3% of tungsten and 
1.73% of manganese. 

According to analyses made by the Due de Luynes of ten specimens of 
the celebrated Oriental damasked steel, eight contained tungsten, two 
of them in notable quantities (0.518% to 1%), while in all of the sam- 
ples analyzed nickel was discovered ranging from traces to nearly 4%. 

Stein & Schwartz, of Philadelphia, in a circular say: It is stated that 
tungsten steel is suitable for the manufacture of steel magnets, since it re- 
tains its magnetism longer than ordinary steel. Cast steel to which 
tungsten has been added needs a higher temperature for tempering than 
ordinary steel, and should be hardened only between yellow, red, and white. 
Chisels made of tungsten steel should be drawn between cherry-red and 
blue, and stand well on iron and steel. Tempering is best done in a 
mixture of 5 parts of yellow rosin, 3 parts of tar, and 2 parts of tallow, 
and then the article is once more heated and then tempered as usual in 
water of about 15° C. 

Aluminum Steel. — R. A. Hadfield (Trans. A. I. M. E., 1890) says: 
Aluminum appears to be of service as an addition to baths of molten iron or 
steel unduly saturated with oxides, and these in properly regulated steel 
manufacture should not often occur. Speaking generally, its role appears 
to be similar to that of silicon. The statement that aluminum lowers the 
melting-point of iron seems to have no foundation in fact. If any increase 
of heat or fluidity takes place by the addition of small amounts of alumi- 
num, it may be due to evolution of heat from oxidation of the aluminum, 
as the calorific value of this metal is very high — in fact, higher than 
silicon. According to Berthollet, the conversion of aluminum to A1 2 3 
equals 7900 cal.; silicon to Si0 2 is stated as 7800. 

The action of aluminum may be classed along with that of silicon, 
sulphur, phosphorus, arsenic, and copper, as giving no increase of hardness 
to iron, in contradistinction to carbon, manganese, chromium, tungsten, 
and nickel. Its special advantage seems to be that it combines in itself 
the advantages of both silicon and manganese; but so long as alloys con- 
taining these metals are so cheap and aluminum dear, its extensive use 
seems hardly probable. 

J. E. Stead, in discussion of Mr. Hadfield's paper, said: Every one of our 
trials has indicated that aluminum can kill the most fiery steel, providing, 
of course, that it is added in sufficient quantity to combine with all the 
oxygen which the steel contains. The metal will then be absolutely 
dead, and will pour like dead-melted silicon steel. If the aluminum is 
added as metallic aluminum, and not as a compound, and if the addition 
is made just before the steel is cast, 0.1% is ample to obtain perfect solidity 
in the steel. 

Nickel Steel. — The remarkable tensile strength and ductility of nickel 
steel, as shown by the test-bars and the behavior of nickel-steel armor- 
plate under shot tests, are witness of the valuable qualities conferred upon 
steel by the addition of a few per cent of nickel. 

Nickel steel has shown itself to be possessed of some exceedingly valuable 
properties; these are, resistance to cracking, high elastic limit, and homo- 
geneity. Resistance to cracking, a property to which the name of non-fissi- 
bility has been given, is shown more remarkably as the percentage of nickel 
increases. Bars of 27% nickel illustrate this property. A H/4-in. square 



473 



bar was nicked 1/4 in. deep and bent double on itself without further fracture 
than the splintering off, as it were, of the nicked portion. Sudden failure 
or rupture of this steel would be impossible; it seems to possess the tough- 
ness of rawhide with the strength of steel. With this percentage of nickel 
the steel is practically non-corrodible and non-magnetic. The resistance 
to cracking shown by the lower percentages of nickel is best illustrated in 
the many trials of nickel-steel armor. 

In such places (shafts, axles, etc.) where failure is the result of the fatigue 
of the metal this higher elastic limit of nickel steel will tend to prolong in- 
definitely the life of the piece, and at the same time, through its superior 
toughness, offer greater resistance to the sudden strains of shock. 

Howe states that the hardness of nickel steel depends on the proportion 
of nickel and carbon jointly, nickel up to a certain percentage increasing 
the hardness, beyond this lessening it. Thus while steel with 2% of nickel 
and 0.90% of carbon cannot be machined, with less than 5% nickel it can 
be worked cold readily, provided the proportion of carbon be low. As the 
proportion of nickel rises higher, cold-working becomes less easy. It forges 
easily whether it contain much or little nickel. 

The presence of manganese in nickel steel is most important, as it 
appears that without the aid of manganese in proper proportions the 
conditions of treatment would not be successful. 

Properties of Nickel Steel. — D. H. Browne, in Proc. A. I. M. E., 
1899, gives a paper of 79 pages, entitled "Nickel Steel: a synopsis of 
experiment and opinion," including a bibliography containing 50 titles. 
Some extracts from this paper are here given. 

Commercially pure nickel, containing 98.13 Ni, 1.15 Co, 0.43 Fe, 
0.08 Si, 0.11 Mn, showed the following physical properties: 





L. P.* 


E. L. 


T.S. 


M.E.f 


El., % 
in 2 in. 




5,119 
9,243 
17,064 


12,557 
21,045 
18,059 
16,921 


40,669 
72,522 
72,806 
71,860 


23,989,140 
29,506,500 
26,870,800 


18.2 


^ (Raw 


43.9 




48.6 




45.0 











* Limit of Proportionality. t Modulus of Elasticity. 

Annealed Cast Bars of Nickel Steel with C 0.15 to 0.20. (Hadfield.) 
— The proportion of Ni used in soft steels for armor and for engine- 
forgings is from 3 to 3.5%. With 0.25 C this produces an E. L. and T. S. 
equal to open-hearth steel of 0.45 C without Ni, with a ductility equal to 
that of the lower-carbon steel. 

Nickel Steel, 3.25 Ni, and Simple Steel Forging s" Compared. 
(Bethlehem Steel Co.) 



c. 


Ni. 


T.S. 


E L. 


El., 

%• 


Red. 
Area, 

%• 


C. 


Ni. 


T.S. 


E. L. 


El., 

%• 


Red. 
Area, 

%. 


0.20 





55000 


28000 


34 


60 


0.20 


3.5 


85000 


48000 


26 


55 


0.30 





75000 


37000 


30 


50 


0.30 


3.5 


95000 


60000 


22 


48 


0.40 





85000 


43000 


25 


45 


0.40 


3.5 


110000 


72000 


18 


40 


0.50 





95000 


48000 


21 


40 


0.50 


3.5 


125000 


85000 


13 


32 



As compared with simple steels of the same tensile strength, a 3% 
nickel steel will have from 10 to 20% higher E. L. and from 20 to 30% 
greater elongation, while as compared with simple steels of the same 
carbon, the nickel steel, up to 5% Ni, will have about 40% greater tensile 
strength, with practically the same elongation and reduction of area. 

Cholat and Harmet found with 0.30 C and 15% Ni a T. S. of 213,400 lbs. 
per sq. in.; when oil-tempered a T. S. of 277,290 and an E. L. of 166,300. 

Riley states that steel of 25% Ni and 0.27 C gave a T. S. of 102,600 
and elong. 29%, while steel of 25% Ni gave 94,300 T. S. and 40% elong. 
Steels high in Ni are entirely different in physical properties from low- 
nickel steels, 



474 



Effect of Ni on Hardness. — Gun barrels with 4.5% Ni and 0.30 C are 
soft and very ductile; T. S. 80,000, elong. 25%, red. of area 45%. Rolls 
with 5% Ni and 1% C turned easier than simple steel of 1% C. If a steel 
contains less than 6% Ni the influence of the C present on the hardness 
produced by water quenching is strongly marked. Above 8% Ni the effect 
of the C seems to be masked by the Ni; steel with 18% Ni is as hard and 
elastic with 0.30 as with 0.75 C. If steel with 18% Ni and 0.60 C be heated 
and plunged in water it will be perceptibly softened, and if the Ni is 
raised to 25% this softening is very noticeable. 

Compression Tests of Low-Carbon Nickel Steels. (Hadfield.) 



Carbon 

Nickel 

E. L., tons 

Shortening* .. . 



0.17 
7.65 



0.16 
9.51 
70 
3 



0.18 
11.39 
100 



0.23 
13. 



0.19 
19.64 
80 



0.16 
24.51 
50 



0.14 
29.07 
24 



* Shortening by 100-ton load, %. 

Specific Gravity. — The sp. gr. of low-carbon nickel steels containing 
up to 15% Ni is about the same as that of carbon steel, from 7.86 to 7.90- 
from 19 to 39% Ni it is from 7.91 to 8.08; one sample of wire of 29% Ni, 
however, being reported at 8.4. A 44% Ni steel, according to Guillaume, 
has a sp: gr. of 8.12. 

The Resistance of Corrosion of nickel steel increases with the per- 
centage of Ni up to 18. "This alloy is practically non-corrodible." 
"Tico " resistance wire, 27.5% Ni, was very slightly rusted after a year's 
exposure in a wet cellar; iron wire under the same conditions was entirely 
changed to oxide. With the ordinary nickel steels, 3 to 3.5% Ni, corrosion 
is slightly less than in simple steels. 

Electrical Resistance. — All nickel steels have a high electrical resist- 
ance which does not seem to vary much with the percentage of Ni. The 
resistance wires, "Tico," "Superior," and "Climax," containing from 25 
to 30% Ni, have about 48 times, while German silver has about 18 times 
the resistance of copper. 

Magnetic Properties. — According to Guillaume all nickel steels below 
25.7% Ni can be, at the same temperature, either magnetic or non- 
magnetic, according to their previous heat-treatment, and they show 
different properties at ascending and at descending temperatures. The 
low-nickel steels, 3 to 5% Ni, possess a magnetic permeability greater than 
that of wrought iron. 

Nickel Steel for Bridges. — J. A. L. Waddell, Trans. A. S. C. E., 1908, 
presents at length an argument in favor of the use of nickel steel in long- 
span bridges. 

Some Uses of Nickel Steel. (F. L. Sperry, A. I. M. E., xxv, 51.) — The 
propeller shaft of the U. S. cruiser Brooklyn was made of hollow-forged,, 
oil-tempered nickel steel, 17in. outside, 11 in. inside diam., length 38 ft. 11" 
in., weight per foot, 449 lbs. Test bars cut from the tube gave T. S., 90,350 
to 94,245; E. L., 56,470 to 60,770; El. in 2 in., 25.5 to 28.0%; Red. of area, 
59.8 to 61.3%. A solid shaft of the same elastic strength of simple steel, 
having anE.L.of 3/5 of that of the nickel steel, would be 18.9 in. diam., and 
would have weighed 920 lbs. per foot. 

The rotating field of the 5000 H.P. electric generators of the Niagara 
Falls Power Co. is inclosed in a ring of forged nickel steel, outside diam. 
1393/8 in.; inside, 130 in.; width, 503/4 in.; weight, 28,840 lbs. It travels 
at the rate of nearly two miles per minute. 

Nickel steel wire with 27.7% Ni and 0.40 C used for torpedo defense 
netting, 0.116 in. diam., gave a T. S. of 198,700; El. in 2 in., 6.25%; Red. 
of area, 16.5%. 

Flange plate of soft nickel steel, Ni, 2.69; C, 0.08; Mn, 0.36; P, 0.045; S, 
0.038, gave, average of 6 tests, T. S., 65,760; E. L., 47,080; El. in 8 in., 
24.8%; Red. of area, 52.0%. For comparison: Soft carbon steel, C, 
0.10; Mn, 0.27; P, 0.048; S, 0.039; T. S., 54,450; E. L., 35.240; El., 27.4%; 
Red. of area, 55.3%. 

Coefficients of Expansion of Nickel Steel. (D. H. Browne, 
A. I. M. E\, 1899.) — Per degree C. (Prefix 0.0000 to the figures here given.) 
% Ni. 26. 28. 28.7 30.4 31.4 34.6 35.6 37.3 39.4 44.4 
Coeff. 1312 1131 1041 0458 0340 0137 0087 0356 0537 0856 



"alloy" steels. 475 

Tor comparison: Brass, 1878; Hard steel, 1239; Soft steel, 1078- 
Platinum, 0884; Glass, 0861; Nickel, 1252. Ordinary commercial nickel 
steels, containing 3 to 4% Ni, have coefficients about the same as carbon 
steel. See also page 540. 

Invar is a nickel-iron alloy, which is characterized by an extraordinarily 
low coefficient of expansion at ordinary temperatures. The analysis is 
about as follows: — carbon, 0.18; nickel, 35.5%; manganese, 0.42, — the 
other elements being low. Guillaume gives the mean coefficient of 
expansion for an alloy containing 35.6% nickel as (0.877 + 0.00117 i) 10-6 
between temperatures 0° C. and t° C. where t does not exceed 200° C. 
This material is used in measuring instruments and for standards of 
length, chronometers, etc. Its expansion as compared with ordinary 
steel is about as 1:11.5; with brass, as 1:17.2; with glass, as 1 : 8.5. Alloys 
either richer or poorer in nickel show much greater expansion, and the 
alloy containing 47.5% nickel, known as "Platinite," has the same 
coefficient of expansion as platinum and glass. See also page 540. 

Copper Steels. — Pierre Breuil (Jour. Land S. I., 1907) gives an account 
of experiments on four series of copper steels containing respectively 0.15, 
0.40, 0.65, and 1% of C with Cu in each ranging from to 34%. An ab- 
stract of his principal conclusions is as follows: 

Copper steel does not yield a metal capable of being rolled in practice, 
if Cu exceeds 4%. 

When in the ingot state copper hardens steel in proportion as there is 
less C present. 

Copper steels as rolled appear to be stronger in proportion as they con- 
tain more Cu. This difference is the more manifest in •proportion as the 
C is lower. 

Annealing leaves the steels with the same characteristics, but greatly 
reduces the differences observed in the case of the untreated steels. 
Quenching restores the differences encountered in the case of the steels 
as cast. 

Copper steels equal nickel steels in tensile strength and would be less 
costly than the latter. They are no more brittle than nickel steels con- 
taining equivalent percentages of Ni. The steel containing 0.16% C and 
4% Cu is remarkable in this respect. 

The presence of copper makes the constituents of the steel finer, 
approximating them to classes containing higher percentages of C. 
While hardening the steel the presence of Cu does not render it brittle. 
It confers upon it a very fair degree of elasticity, while leaving the elon- 
gation good, thus conducing to the production of a most valuable metal. 

Cutting tests were carried on with steels containing C about 1 % and 
Cu 0%, 1%, and 3% respectively. The presence of Cu in no wise altered 
the cutting properties. . 

The presence of Cu was found to increase the electrical resistance, 
and a well-defined maximum was shown, coinciding with 2% Cu in 0.15 C, 
with 1.7% in 0.35% C, and with 0.5% Cu in 0.7 to 1% carbon steels. 

Nickel- Vanadium Steels. (Eng. Mag., April, 1906.) — M. Leon Guillet 
has investigated the influence of Ni and Va when used jointly. 

In steels containing 0.20 C and from 2 to 12% of Ni, the tensile strength 
and the elastic limit are both materially increased by the addition of 
small percentages of Va. In no case should the Va exceed 1%, the best 
results being secured by the use of 0.7 to 1%. A steel containing 0.20 C, 
2% of Ni, and 0.7% Va showed a tensile strength of 91,000 lbs., an 
elastic limit of 70,000 lbs., and an elongation of 23.5%. With 1% Va, 
the T. S. increased to 119,500 lbs., and the E. L. to 91,000 lbs., the elong. 
falling to 22%. A nickel steel of 0.20% C and 12% Ni gave, with 
0.7 Va, a T. S. of over 200,000 lbs. and an E. L. of 172,000 lbs. per sq. in., 
the elong. being 6%, while with 1% Va the T. S. rose to 220,000 lbs. 
and the E. L. to 176,000 lbs., the elongation remaining unchanged. 
When the Va is increased above 1 % the tensile strength falls off, and the 
material begins to show evidence of brittleness. 

Similar effects are produced for steels of the higher carbon, but in a 
lesser c n 



When the nickel-vanadium steels are subjected to a tempering process 
the beneficial effects of the Va are still further emphasized. The temper- 
ing experiments of M. Guillet were conducted by heating the steel to a 
temperature of 850° O, and cooling in water at 20° C. The T. S. and 



476 



the E. L. were increased, being nearly doubled for the low nickel con- 
tent. Thus while the 0.20 C steel with 2% of Ni, untempered, and 
containing 0.7% of Va, gave a T. S. of 91,000 lbs., with an E. L. of 70,000 
lbs., the same steel, tempered from 850° C, showed a T. S. of 168,000 lbs. 
and an E. L. of 150,000 lbs., the resistance to shock and the hardness 
being also increased. 

Static and Dynamic Properties of Steels. (W. L. Turner, Iron Age, 
July 2, 1908.) — The term "crystallization" is a name given to designate 
phenomena due to the influences of shock and alternating stresses, 
whether pure or combined. The name has been advantageously altered 
to "intermolecular disintegration," but, whatever we choose to call it, 
there remains the evidence that some modification takes place in the 
structure of steel when the above-named forces are to be dealt with. 

Resistance to fatigue is not a function of static strength. 

An example of our knowledge of the "life" properties of ordinary steel 
is the case of the staying of a locomotive fire-box. Something is re- 
quired which will possess considerable strength combined with the 
power to withstand a moderate degree of flexure in all directions. Expe- 
rience has shown that the use of anything but the mildest steel for this 
work is prohibitive, and that wrought iron, or even copper, is still more 
satisfactory. 

The writer has completed a preliminary investigation into the relative 
dynamic properties of iron and the various ordinary and alloy steels, 
the results being given in the accompanying table. The conditions of 
the "dynamic" tests were as follows: 

A cylindrical test-piece, 6 in. long, 3/ 8 in. diam., finished with emery to 
remove all tool marks, is clamped at one end in a vise. A tool-steel 
head, in which there is cut a slot, is placed over the other end, the dis- 
tance from the striking center of this head to the vise line being 4 in. 
A crank and connecting rod furnished the reciprocating motion for this 
head, thereby causing the test-piece to be deflected'3/ 8 in. each side of 
the neutral position. In addition to this alternating flexure, the test- 
piece is also subjected, at each reversal, to an impact, due to the slot on 
the reciprocating head. The sample undergoes 650 alternations per 
minute. A deflection of 3/g in. on each side has the effect of imparting a 
permanent set to the test-piece. 

On each class of steel a large number of dynamic tests were made, an 
average being taken of the results after elimination of those figures which 
were apparently abnormal. 

It is apparent that the action of nickel is twofold: 1. It statically 
intensifies. 2. It dynamically "poisons." As an instance of this, take 
tests Nos. 13 and 15, the former being a 3.7% nickel steel and the latter a 
chrome-vanadium steel. In the annealed condition, the elastic limits of 
the two are almost identical, but at the same time the alternations of 
stress endured by the latter are 2V4 times the number sustained by the 
nickel steel. Take again Nos. 17 and 18. The dynamic figures are more 
than three to one in favor of the chrome-vanadium product, whereas the 
difference in elastic limit is only about 3%. 

It is manifest that the static action of vanadium is similar to that of 
nickel, but that its dynamic effects are the exact converse. The differ- 
ences are markedly brought out in the quality figures, which invite 
attention as to comparison with those of ordinary carbon steel. Taking 
the latter as standard, the chrome-vanadium steels are as much above it 
as the nickel steels are below it. 

Chromium, per se, does not appear to exert appreciable influence other 
than statically, but it is possible that the effect of this metal in a ternary 
steel might be very marked. 

The dynamic attributes of plain carbon steel reach a maximum with 
about 0.25% C, falling away on both sides of this amount. 

The quality figure in the case of the chrome-vanadium steel does not 
appear to undergo much alteration in the process of oil tempering, but 
there are considerable variations in other cases. The dynamic test may 
eventually act as a reliable guide to the correct methods for the heat 
treatment of individual steels. 

Strength for strength, the chrome-vanadium steels also have the 
advantage over all others as regards machining properties. Chrome- 
vanadium steel may be forged with the same ease as ordinary steel of simi- 
lar contents, no special precaution being necessary as to temperatures. 



' ALLOY STEELS. 



477 



Hi 



-<N — NNtA-X 



Dsoooaooo 



-Ols-OtsTTa 






-^r>00*moiriO>0>in inrAMNMnooooo — en cs oo o \o u 

3 rn C>1 ■* m in O 00 "*■ ■* O C-l in t~% in — OO •'T O^ m '0»0*'*tOOP 

0m\OvOvO'C>o>ot , tN so vo in — \© vo ■•© T >•© -mifivommu 






momooooooomo 
nj-rmmmToomcNioomvO 



OOOmOmOOO mOOOOOu 

OinifM»vOooir-N OvO*»Ntu 
m CN CM cn rs tN cn cn _ _ _ , 



oooooooooooo 
o^t'o'o"©"— "tCu-T— oo'o'tN 



88g§||8 

vo oo '— T" o** r-s o 






O — — t (A O N IN m * m «■ 



ooooooooo ooooooo 

^•^MONt^mOO OOOOOOO 

— »— o^ oo in •— • cn — o Of^^oo^cA^fi 

— n — cfiiso^o^mo — in — o^ cn en "^ 

O N vO ^O vO O N O^ OO OO^"Nm00cA 



oo § 



«s 1 



O 1 - \0 in QO O 



in — tN o O oo oo in -"Tin o oo "£ 
oooooooooooo F5 



iflinOONrNNNf m ONONISN'* 
1 1 in lAts N is N m is mMAisNtNtn 

O © O © © O © © © P5 O © © © O © © 



n — ■«■ oo oo vo vo m vo co a^ rs — 



> O T r~> r-s o o o ■* o o vO 

pun rN w ^f fMS in f^ O "*?" rn CN m "*T rn 

OOO— OOOOO — OOOOOO 



03 g "5 






^o^^^h ddddddrH 



.9° >•£>£;>££ 



b> M "^ U LZ2 O O (rf t-r+3 03 S-i •— • -* £_< Q, t-t t-4"-* E-i £-t 



C L n 03 oj-i o3 — 

•5^t>>£>£ 
a fc< &-.A i ^ i 



— N m ■>r in * r> oo o> o - n 



1*in*N00O>O- 



^m-*m>ONoo 



a g 

03 o3 


of 

1 




OQ 


© ° 


0) 


- So 


43 






few •!• 


2 


?nt< 


o 


3^X 




Si* 

^■5x 




s 






llTs 


*1>£; 


o,-gft 


p^ 


c © aS 




ong. 
of: E 

; T, 


2 in. 
duct 
tigue- 
pered 


xs^a 


d m-2 



cn£3n j 



rt CJO 8 - 1 

J£r8 

© o3 r 

mi 

■■5 3 o S © 

w. c$S h 

1 2 K § a 

n-^ © W.3 

2- ft « 

S © -d 

• Si- •** 



478 



STEEL. 



Comparative Effects of Cr and Va. 

Inst. M. E., 1904. 



Sankey and J. Kent Smith, Proc. 



Cr. Va. 


T.S.* 


E.L.* 


El. in 
2 in. 


Red. A. 


Cr. Va. 


T.S.* 


E.L.* 


El. in 
2 in. 


Red. A. 


0.5 


34.0 


22.9 


33% 


60.6% 


1.0 0.15 


48.6 


36.2 


24. 


56.6 


1.0 


38.2 


25.0 


30 


57.3 


1.0 0.15 


+52.6 


34.4 


25.0 


55.5 


... 0.1 


34.8 


28.5 


31 


60.0 


1.0 0.25 60.4 


49.4 


18.5 


46.3 


... 0.15 


36.5 


30.4 


26 


59.0 


C-Mn | 27.0 


16.0 


35. 


60.0 


... 0.25 


39.3 


34.1 


24 


59.0 


C-Mn 


+32.2 


17.7 


34. 


52.6 



* Tons, of 2240 lbs., per sq. in. + Open-hearth steels; all the others 
are crucible. The last two steels in the table are ordinary carbon 
steels. 

Effect of Heat Treatment on Cr-Va Steel. (H. R. Sankey and 
J. Kent Smith, Proc. Inst. M. E., 1904, p. 1235.) — Various kinds of 
heat treatment were given to several Cr-Va steels, the results of which 
are recorded at length. The following is selected as a sample of the 
results obtained. Steel with C, 0.297; Si, 0.086; Mn, 0.29; Cr, 1.02; Va, 
0.17, gave: 



As rolled 

Annealed l/ 2 hr. at 800° C 

Soaked 12 hours at 800° C 

Water quenched at 800° C 

Oil quenched at 800° C 

Oil quenched at 800°, reheated to 

350° 

Water quenched at 1200° C 

Oil quenched at 1200° C 



Tens. 


Yield 


El. in 


Red. 


Im- 


Str. 


Point. 


2 in. 


Area. 


pact. 


121,200 


82,650 


24.0% 


44.9% 


3.1 


87,360 


47,260 


34.5 


53.1 


15.6 


86,020 


68,100 


33.7 


51.5 


11.2 


167,100 


135,070 


7.5 


16.6 


1.2 


122,080 


82,880 


22.0 


35.2 


2.4 


132,830 


111,550 


23.0 


50.8 


9.0 


209,440 


191,520 


1.2 


1.5 


* 


140,220 


118,500 


8.5 


21.5 


3.0 



1906 
2237 



174 
296 



* Too hard to machine. 

The impact tests were made on a machine described in Eng'g, Sept. 25, 
1903, p. 431. The test-piece was 3/ 4 in. broad, notched so that 0.137 in. in 
depth remained to be broken through. The figures represent ft.-lbs. of 
energy absorbed. The piece was broken in one blow. The alternations- 
of-stress tests were made on Prof. Arnold's machine, described in The 
Engineer, Sept. 2, 1904, p. 227. The pieces were 3/ 8 in. square, one end 
was gripped in the machine and the free end, 4 in. long, was bent forwards, 
and backwards about 710 times a minute, the motion of the free end being 
3/4 in. on each side of the center line. 

Tests by torsion of the same steel were made. The test-piece was 6 in. 
long, 3/ 4 in. diam. The results were: 





Shearing Stress. 


Twist 
Angle. 






Elastic. 


Ulti- 
mate. 


No. of 

Twists. 




45,700 
38,528 


99,900 
90,272 


1410° 
1628° 


3.92 


Annealed l/ 2 hr. at 800° C. 


4.52 







"alloy" steels. 479 

Heat-treatment of Alloy Steels. (E. F. Lake, Am. Mach., Aug. 1, 
1907.) — In working the high-grade alloy steels it is very important that 
they be properly heat treated, as poor workmanship in this regard will 
produce working parts that are no better than ordinary steel, although 
the stock used be the highest grade procurable. By improperly heat- 
treating them it is possible to make these high-grade steels more brittle 
than ordinary carbon steels. 

The theory of heat treatment rests upon the influence of the rate of 
cooling on certain molecular changes in structure occurring at different 
temperatures. These changes are of two classes, critical and progres- 
sive; the former occur periodically between certain narrow temperature 
limits, while the latter proceed gradually with the rise in temperature, 
each, change producing alterations in the physical characteristics. By 
controlling the rate of cooling, these changes can be given a permanent 
set, and the characteristics can thus be made different from those in the 
metal in its normal state. 

The results obtained are influenced by certain factors: 1. The original 
chemical and physical properties of the metal; 2. The composition of 
the gases and other substances which come in contact with the metal in 
heating and cooling. 3. The time in which the temperature is raised 
between certain degrees. 4. The highest temperature attained. 5. The 
length of time the metal is maintained at the highest temperature. 
6. The time consumed in allowing the temperature to fall to atmos- 
pheric. 

The highest temperature that it is safe to submit a steel to for heat- 
treating is governed by the chemical composition of the steel. Thus 
pure carbon steel should be raised to about 1300° F., while some of the 
high-grade alloy steels may safely be raised to 1750°. The alloy steels 
must be handled very carefully in the processes of annealing, hardening, 
and tempering; for this reason special apparatus has been installed to 
aid in performing these operations with definite results. 

The baths for quenching are composed of a large variety of materials. 
Some of the more commonly used are as follows, being arranged accord- 
ing to their intensity on 0.85% carbon steel: Mercury; water with sulphuric 
acid added; nitrate of potassium; sal ammoniac; common salt; carbonate 
of lime; carbonate of magnesia; pure water; water containing soap, 
sugar, dextrine or alcohol; sweet milk; various oils; beef suet; tallow; 
wax. 

"With many of these alloy steels a dual quenching gives the best results, 
that is, the metal is quenched to a certain temperature in one bath and 
then immersed in the second one until completely cooled, or it may 
be cooled in the air after being quenched in the first bath. For this a 
lead bath, heated to the proper temperature, is sometimes used for the 
first quenching. 

With the exception of the oils and some of the greases, the quenching 
effect increases as the temperature of the bath lowers. Sperm and lin- 
seed oils, however, at all temperatures between 32° and 250°, act about 
the same as distilled water at 160°. 

The more common materials used for annealing are powdered char- 
coal, charred bone, charred leather, fire clay, magnesia or refractory 
earth. The piece to be annealed is usually packed in a cast-iron box 
in some of these materials or combinations of them, the whole heated 
to the proper temperature and then set aside, with the cover left on, to 
cool gradually to the atmospheric temperature. For certain grades of 
steel these materials give good results; but for all kinds of steels and for 
all grades of annealing, the slow-cooling furnace no doubt gives the 
best satisfaction, as the temperature can be easily raised to the right 
point, kept there as long as necessary, and then regulated to cool down 
as slowly as is desired. The gas furnace is the easiest to handle and 
regulate. 

A high-grade alloy steel should be annealed after every process in man- 
ufacturing which tends to throw it out of its equilibrium, such as forging, 
rolling and rough machining, so as to return it to its natural state of 
repose. It should also be annealed before quenching, case-hardening 
or carbonizing. 

The wide range of strength given to some of the alloy steels by heat 



480 



treatment is shown by the table below. The composition of the alloy 
was: Ni, 2.43; Cr, 0.42; Si, 0.26; C, 0.23; Mn, 0.43; P, 0.025; S, 0.022. 









1* 


|l 
ft? 


OHM 

ao 


a— 


H 03 


Tensile Strength . 
E. L 


227,000 

208,000 

4 


219,000 

203,500 

6 


195,500 

150,000 

8 


172,000 

148,500 

11 


156,500 

125,000 

13 


141,000 

102,000 

15 


109,500 
70,500 


Elong.,% in 2 in. 


22 



VARIOUS SPECIFICATIONS FOR STEEL. 

Structural Steel. — There has been a change during the ten years from 
1880 to 1890, in the opinions of engineers, as to the requirements in speci- 
fications for structural steel, in the direction of a preference for metal of 
low tensile strength and great ductility. The following specifications for 
tension members at different dates are given by A. E. Hunt and G. H. 
Clapp, Trans. A. I. M. E., xix, 926: 

1879. 1881. 1882. 1885. 1887. 1888. 

Elastic limit,. . . 50,000 40 @ 45,000 40,000 40,000 40,000 38,000 

Tensile strength 80,000 70 @ 80,000 70,000 70,000 67@75,000 63 @ 70,000 
Elongation in 8 in. 12% 18% 18% 18% 20% 22% 

Reduction of area 20% 30% 45% 42% 42% 45% 

F. H. Lewis (IronAae, Nov. 3, 1892) says: Regarding steel to be used 
under the same conditions as wrought iron, that is, to be punched without 
reaming, there seems to be a decided opinion (and a growing one) among 
engineers, that it is not safe to use steel in this way, when the ultimate 
tensile strength is above 65,000 lbs. The reason for this is not so much 
because there is any marked change in the material of this grade, but 
because all steel,. especially Bessemer steel, has a tendency to segrt gations 
of carbon and phosphorus, producing places in the metal which are harder 
than they normally should be. As long as the percentages of carbon and 

Ehosphorus are kept low, the effect of these segregations is inconsiderable; 
ut when these percentages are increased, the existence of these hard 
spots in the metal becomes more marked, and it is therefore less adapted 
to the treatment to which wrought iron is subjected. 

There is a wide consensus of opinion that at an ultimate of 64,000 to 
65,000 lbs. the percentages of carbon and phosphorus reach a point where 
the steel has a tendency to crack when subjected to rough treatment. 

A grade of steel, therefore, running in ultimate strength from 54,000 to 
62,000 lbs., or in some cases to 64,000 lbs., is now generally considered a 
proper material for this class of work. 

A. E. Hunt, Trans. A.I.M.E., 1892, says: Why should the tests for steel 
be so much more rigid than for iron destined for the same purpose? Some 
of the reasons are as follows: Experience shows that the acceptable quali- 
ties of one melt of steel offer no absolute guarantee that the next melt to It, 
even though made of the same stock, will be equally satisfactory. 

It is now almost universally recognized that soft steel, if properly made 
and of good quality, is for many purposes a safe and satisfactory substitute 
for wrought iron, being capable of standing the same shop-treatment as 
wrought iron. But the conviction is equally general, that poor steel, or an 
unsuitable grade of steel, is a very dangerous substitute for wrought iron 
even under the same unit strains. 

For this reason it is advisable to make more rigid requirements in select- 
ing material which may range between the brittleness of glass and a duc- 
tility greater than that of wrought iron. 

Specifications for Structural Steel for Bridges. (Proc. A. S. T. M., 
1905.) — Steel shall be made by the open-hearth process. The chemi- 
cal and physical properties shall conform to the following limits: 



VABIOUS SPECIFICATIONS FOR STEEL. 



481 



Elements Considered. 



Phosphorus, f Basic . . 

Max \ Acid. . . , 

Sulphur, Max 

Tensile strength, lbs. 

per sq. in 

Elong.: Min. % in 8 in. 
Elong.:Min. % in 2 in. 
Fracture 

Cold bend without 
fracture 



Structural Steel 



0.04% 
0.08% 
0.05% 

Desired 

60,000 

1,500,000* 

tens. str. 

22 

Silky 



0.04% 
0.04% 
0.04% 

Desired 

50,000 

1,500,000 

tens. str. 



Silky 



180° flat* 



Steel Castings. 



0.05% 
0.08% 
0.05% 

Not less than 
65,000 



18 

Silky or fine 

granular 



* The following modifications will be allowed in the requirements for 
elongation for structural steel: For each Vi6 inch in thickness below 
5/i6 inch, a deduction of 2 1/2 will be allowed from the specified percent- 
age. For each Vs inch in thickness above 3/ 4 inch, a deduction of 1 will 
be allowed from tne specified percentage. 

t Plates,. shapes and bars less than 1 in. thick shall bend as called for. 
Full-sized material for eye-bars and other steel 1 in. thick and over, tested 
as rolled, shall bend cold 180° around a pin of a diameter twice the thick- 
ness of the bar, without fracture on the outside of bend. When required 
by the inspector, angles 3/ 4 in. and less in thickness shall open flat, and 
angles 1/2 in. and less in thickness shall bend shut, cold, under blows of 
a hammer, without sign of fracture. 

t Rivet steel, when nicked and bent around a bar of the same diam- 
eter as the rivet rod, shall give a gradual break and a fine, silky, uniform 
fracture. 

If the ultimate strength varies more than 4000 lbs. from that desired, 
a retest may be made, at the discretion of the inspector, on the same 
gauge, which, to be acceptable, shall be within 5000 lbs. of the desired 
strength. 

Chemical determinations of C, P, S, and Mn shall be made from a 
test ingot taken at the time of the pouring of each melt of steel. Check 
analyses shall be made from finished material, if called for by the pur- 
chaser, in which case an excess of 25% above the required limits will be 
allowed. 

Specimens for tensile and bending tests for plates, shapes and bars 
shall be made by cutting coupons from the finished product, which shall 
have both faces rolled and both edges milled with edges parallel for at 
least 9 in.; or they may be turned 3/ 4 in. diam. for a length of at least 
9 in., with enlarged ends. Rivet rods shall be tested as rolled. Speci- 
mens shall be cut from the finished rolled or forged bar in such manner 
that the center of the specimen shall be 1 in. from the surface of the bar. 
The specimen for tensile test shall be turned with a uniform section 2 in. 
long, with enlarged ends. The specimen for bending test shall be 1 X 1/2 
in. in section. 

Specifications for Steel for the Manhattan Bridge. (Eng. News, 
Aug. 3, 1905.) — 

Material for Cables. Suspenders and Hand Ropes. Open- 
hearth steel. (The wire for serving the cables shall be made of Norway 
iron of approved quality.) The ladle tests of the steel shall contain not 
more than : C, 0.85; Mn, 0.55; Si, 0.20; P, 0.04; S, 0.04; Cu, 0.02% . 
The wire shall have an ultimate strength of not less than 215,000 lbs. 
per sq. in. before galvanizing, and an elongation of not less than 2% in 
12 in. The bright wire shall be capable of bending cold around a rod 
11/2 times its own diam. without sign of fracture. The cable wire before 
galvanizing shall be 0.192 in. ± 0.003 in. in diam.; after galvanizing, the 
wire shall have an ultimate strength of not less than 200,000 lbs. per sq. 
in. of gross section. 



482 



Caebon Steel. The ladle tests as usually taken shall contain not 
more than: P, 0.04; S, 0.04; Mn, 0.60; Si, 0.10%. The ladle tests of 
the carbon rivet steel shall contain not more than: P, 0.035; S, 0.03. 
Rivet steel shall be used for all bolts and threaded rods. 

Nickel. Steel. The ladle test shall contain not less than 3.25 Ni, 
and not more than: P, 0.04; S, 0.04; Mn, 0.60; Si, 0.10; nickel rivet steel 
not more than: P, 0.035; S, 0.03%. 

Nickel steel for plates and shapes in the finished material must show: 
T. S., 85,000 to 95,000 lbs. per sq. in.; E. L., 55,000 lbs. min.; elong. in 
8 ins., min., = 1,600,000 -i- T. S.; min. red. of area, 40%. 

Specimens . cut from the finished material shall show the following 
physical properties: 



T. S., lbs. per sq. 



Min.E.L. 
lbs. per 
sq. in. 



Min. 
Elong., 
% in 8 in. 



Min. Red. 
of Area, 

%• 



Shapes and universal mill 
plates 

Eye-bars, pins and rollers 

Sheared plates 

Rivet rods 

High-carbon steel for 
trusses 



60,000 to 68,000 
64,000 to 72,000 
60,000 to 68,000 
50,000 to 58,000 

85,000 to 95,000 



33,0001 
35,000 
33,000 
30,000 

45,000 J 



44 
50 



Nickel rivet steel: T. S., 70,000 to 80,000; E. L., min., 45,000; elong., 
min., 1,600,000 -e- T. S., % in 8 ins. 

Steel Castings. The ladle test of steel for castings shall contain 
not more than: P, 0.05; S, 0.05; Mn, 0.80; Si, 0.35%. Test-pieces taken 
from coupons on the annealed castings shall show T. S., 65,000; E. L., 
35,000; elong. 20% in 8 ins. They shall bend without cracking around a 
rod three times the thickness of the test-piece. 



Specifications for Steel. (Proc. A. S. T. M., 1905.) 



Steel Forgings. 



Solid or hollow forgings, no diam. 
or thickness of section to exceed 
10 in. 

Solid or hollow forgings, diam. 
not to exceed 20 in. or thickness 
of section 15 in. 

Solid forgings, over 20 in 

Solid forgings 

Solid or hollow forgings, diam. or 
thickness not over 3 in. 

Solid rectangular sections, thick- 
ness not over 6 in., or hollow 
with walls not over 6 in. thick. 

Solid rect. sections, thickness not 
over 10 in., or hollow with walls 
not over 10 in. thick. 

Locomotive forgings 



Kind of 
Steel. 


Tensile 
Strength. 


Elast. 
Limit. 


El. in 
2 in., 

%. 


Red 
Area, 


IS: 

fC.A. 

Jn.a. 


58,000 
75,000 
80,000 
80,000 


29,000* 
37,500* 
40,000 
50,000 


28 
18 
22 
25 


35(a) 
30(c) 
35(b) 
45(a) 


(C.A. 
JN.A. 


75 000 
80,000 


37,500 
45,000 


23 
25 


35(b) 
45(a) 


C.A. 

N.A. 
)C.O. 
JN.O. 


70,000 
80,000 
90,000 
95,000 


35,000 
45,000 
55,000 
65,000 


24 
24 
20 
21 


30(c) 
40(a) 
45(b) 
50(b) 


(c.o. 

jN.O. 


85,000 
90,000 


50,000 
60,000 


22 
22 


45(b) 
50(b) 


)c.o. 

jN.O. 


80,000 
85,000 


45,000 
55,000 


23 
24 


40(b) 
45(b) 




80,000 


40,000 


20 


25(d) 



* The yield point, instead of the elastic limit, is specified for soft steel 
and carbon steel not annealed. It is determined by the drop of the 
beam or halt in the gauge of the testing machine. The elastic limit, 
specified for all other steels, is determined by an extensometer, and is 
defined as that point where the proportionality changes. The standard 
test specimen is 1/2 in. turned diam. with a gauged length of 2 inches. 



VARIOUS SPECIFICATIONS FOR STEEL. 



483 



Kind of steel: S., soft or low carbon. C, carbon steel, not annealed. 
C. A., carbon steel, annealed. C. O., carbon steel, oil tempered. N. A., 
nickel steel, annealed. N. O., nickel steel, oil tempered. Bending 
tests: A specimen 1 X V2 in. shall bend cold 1S0° without fracture on 
outside of bent portion, as follows: (a) around a diam. of 1/2 in.; (b) 
around a diam. of 1 in.; (c) around a diam. of 1/2 in.; (d) no bending 
test required. 

Chemical composition: P and S not to exceed 0.10 in low-carbon steel, 
0.06 in carbon steel not annealed, 0.04 in carbon or nickel steel oil tem 
pered or annealed, 0.05 in locomotive forgings. Mn not to exceed 0.60 
in locomotive forgings. Ni 3 to 4% in nickel steel. 

Specifications for Steel Ship Material. (Amer. Bureau of Shipping, 
1900. Proc. A. S. T. M., 1906, p. 175.) — 



For Hull. Construction. 


Tens. Strength. 


E. L. 


El. in 
8 in., %. 




58,000 to 60,000 
60,000 to 75,000 
55,000 to 65,000 


1/2 T. S. 


22* I8t 




\5 






20 









In plates 18 lbs. per sq. ft. and over. 



f In plates under 18 lbs. 



For Marine Boilers: Open-hearth steel; Shell: P and S, each not over 
0.04%. Fire-box, not over 0.035%. Tensile Strength: Rivet steel, 
45,000 to 55,000; Fire-box, 52,000 to 62,000; Shell, 55,000 to 73,000; 
Braces and stays, 55,000 to 65,000; Tubes and all other steel, 52,000 to 
62,000 lbs. per sq. in. 

Elongation in 8 in.: Rivet steel, 28%; Plates 3/ 8 in. and under, 20%; 
3/ 8 to 3/4 in., 22%; 3/ 4 in. and over, 25%. 

Cold Bending and Quenching Tests. Rivet steel and all steel of 
52,000 to 62,000 lbs. T. S., 1/2 in. thick and under, must bend 180° flat on 
itself without fracture on outside of bent portion; over 1/2 in. thick, 180° 
around a mandrel IV2 times the thickness of the test-piece. For hull 
construction a specimen must stand bending on a radius of half its thick- 
ness, without fracture on the convex side, either cold or after being 
heated to cherry-red and quenched in water at 80° F. 

High-strength Steel for Shipbuilding. (Eng'g, Aug. 2, 1907, p. 137.)— 
The average tensile strength of the material selected for the Lusitania 
was 82,432 lbs. per sq. in. for normal high-tensile steel, and 81,984 lbs. 
for the same annealed, as compared with 66,304 lbs. for ordinary mild 
steel. The metal was subjected to tup tests as well as to other severe 
punishments, including the explosion of heavy charges of dynamite 
against the plates, and in every instance the results were satisfactory. 
It was not deemed prudent to adopt the high-tensile steel for the rivets, 
a point upon which there seems some difference of opinion.' 



Penna. R. R. Specifications for Steel. 








c3 

3 


C. 


Mn. 


Si. 


P. 


s. 


Cu. 




(1) 


1899 
1901 
1899 
1904 
1902 
1906 
1906 


0.12 
1.00 
0.40 
0.45 
0.45 
0.18 
0.18 


0.35 

0.25 

0.50 

0.60- 

0.50 

0.40- 

0.40- 


0.05 

0.15- 

0.05 

0.05- 

0.05 

0.05- 

0.02- 


0.04- 
0.03- 
0.05- 
0.03- 
0.03- 
0.04- 
0.03- 


0.03- 
0.03- 
0.04- 
0.04- 
0.02- 
0.03- 
0.02- 






0.03- 




(2) 
(3) 
(4) 
(5) 
(6) 








Billets or blooms for forging 


0.05- 
0.03- 


Fire-box sheets 


0.03- 



484 STEEL. 

The minus sign after a figure means "or less." The figures without 
the minus sign represent the composition desired. 

Steel castings. Desired T. S., 70,000 lbs. per sq. in.; elong. in 2 in., 
15%. Will be rejected if T. S. is below 60,000, or elong. below 12%, or if 
the castings show blow-holes or shrinkage cracks on machining. 

Notes. (1) Tensile strength, 52,000 lbs. per sq. in.; elong. in 8 ins. 
= 1,500,000 -*- T. S. (2) Axles are also subjected to a drop test, similar 
to that of the A. S. T. M. specifications. Axles will be rejected if they 
contain C below 0.35 or above 0.50, Mn above 0.60, P above 0.07%. 
(3) T. S. desired, 85,000 lbs. per sq. in.; elong. in 8 ins. 18%. Pins will 
be rejected if the T. S. is below 80,000 or above 95,000, if the elongation 
is less than 12%, or if the P is above 0.05%. (4) The steel will be re- 
jected if the C is below 0.35 or above 0.50, Si above 0.25, S above 0.05, 
P above 0.05, or Mn above 0.60%. (5) T. S. desired, 60,000; elong. in 
8 ins. 26%. Sheets will be rejected if the T. S. is less than 55,000 or 
over 65,000, or if the elongation is less than the quotient of 1,400,000 
divided by the T. S., or if P is over 0.05%. (6) T. S. desired, 60,000, 
with elong. of 2S*% in 8 in. Sheets will be rejected if the T. S. is les^ 
than 55,000 or above 65,000 (but if the elong. is 30% or over plates will 
not be rejected for, high T. S.),if the elongation is less than 1,450,000 -*- 
T. S., if a single seam or cavity more than 1/4 in. long is shown in either 
one of the three fractures obtained in the test for homogeneity, describe I 
below, or if on analysis C is found below 0.15 or over 0.25, P over 0.035, 
Mn over 0.45, Si over 0.03, S over 0.045, or Cu over 0.05%. 

Homogeneity Test for Fire-box Steel. — This test is made on one of the 
broken tensile-test specimens, as follows: 

A portion of the test-piece is nicked with a chisel, or grooved on a ma- 
chine, transversely about a sixteenth of an inch deep, in three places 
about 2 in. apart. The first groove should be made on one side, 2 in. from 
the square end of the piece; the second, 2 in. from it on the opposite side; 
and the third, 2 in. from the last, and on the opposite side from it. The 
test-piece is then put in a vise, with the first groove about 1/4 in. above 
the jaws, care being taken to hold it firmly. The projecting end of the 
test-piece is then broken off by means of a hammer, a number of light 
blows being used, and the bending being away from the groove. The 
piece is broken at the other two grooves in the same way. The object 
of this treatment is to open and render visible to the eye any seams due 
to failure to weld up, or to foreign interposed matter, or cavities due 
to gas bubbles in the ingot. After rupture, one side of each fracture is 
examined, a pocket lens being used if necessary, and the length of the 
seams and cavities is determined. The sample shall not show any single 
seam or cavity more than 1/4 in. long in either of the three fractures. 

Dr. Chas. B. Dudley, chemist of the P. R. R. (Trans. A. I. M. E., 1892), 
referring to tests of crank-pins, says: In testing a recent shipment, the 
piece from one side of the pin showed 88,000 lbs. strength and 22% elon- 
gation, and the piece from the opposite side showed 106,000 lbs. strength 
and 14% elongation. Each piece was above the specified strength and 
ductility, but the lack of uniformity between the two sides of the pin was 
so marked that it was finally determined not to put the lot of 50 pins in 
use. To guard against trouble of this sort in future, the specifications 
are to be amended to require that the difference in ultimate strength of 
the two specimens shall not be more than 3000 lbs. 

Specifications for Steel Rails. (Adopted by the manufacturers of the 
U. S. and Canada. In effect Jan. 1, 1909.)— Bessemer rails: 
Wt. per yard, lbs. 50 to 60 61 to 70 71 to 80 81 to 90 91 to 100 

Carbon, % 0.35-0.45 0.35-0.45 0.40-0.50 0.43-0.53 0.45-0.55 

Manganese, %... .0.70-1 .00 0.70-1.00 0.75-1.05 0.80-1.10 0.84-1.14 

Phosphorus not over 0.10%; silicon not over 0.20%. Drop Test: A 
piece of rail 4 to 6 ft. long, selected from each blow, is placed head up- 
wards on supports 3 ft. apart. The anvil weighs at least 20,000 lbs., 
and the tup, or falling weight, 2000 lbs. The rail should not break when 
the drop is as follows: 

Weight per yard, lbs 71 to 80 81 to 90 91 to 100 

Height of drop, feet 16 17 18 

If any rail breaks when subjected to the drop test, two additional tests 
will be made of other rails from the same blow of steel, and if either of 



VARIOUS SPECIFICATIONS FOR STEEL. 



485 



these latter tests fail, all the rails of the blow which they represent will 
be rejected; but if both of these additional test-pieces meet the require- 
ments, all the rails of the blow which they represent will be accepted. 

Shrinkage: The number of passes and the speed of the roll train shall 
be so regulated that for sections 75 lbs. per yard and heavier the temper- 
ature on leaving the rolls will not exceed that which requires a shrinkage 
allowance at the hot saws of 6U/16 inches for a 33-ft. 75-lb. rail, with an 
increase of Vie in. for each increase of 5 lbs. in the weight of the section. 

Open-hearth rails; chemical specifications: 

Weight per yard, lbs. . . 50 to 60 61 to 70 71 to 80 81 to 90 90 to 100 
Carbon, % 0.46-0.59 0.46-0.59 0.52-0.65 0.59-0.72 0.62-0.75 

Manganese, 0.60 to 0.90; Phosphorus, not over 0.04; Silicon, not over 
0.20. Drop Tests : 50 to 60-lb„ 15 ft.; 61 to 70-lb., 16 ft.; heavier sec- 
tions same as Bessemer. 

Specifications for Steel Axles. (Proc. A. S. T. M., 1905 p. 56.) — 





P.& 


Tens. 

Str. 


Yield 
Pt. 


El. in 
2 in. 


Red. 
Area. 




0.06 
0.06 
0.04 










Driving and engine truck, C. S.* 

Driving and engine truck, N. S.f 


80,000 
80,000 


40,000 
50,000 


20% 
25% 


25% 
45% 



* Carbon steel. 

t Nickel steel, 3 to 4 % Ni. 

% Each not to exceed. Mn in carbon steel not over 0.60 %. 

Drop Tests. — One drop test to be made from each melt. The axle 
rests on supports 3 ft. apart, the tup weighs 1640 lbs., the anvil supported 
on springs, 17,500 lbs.; the radius of the striking face of the tup is 5 in. 
The axle is turned over after the first, third and fifth blows. It must 
stand the number of blows named below without rupture and without 
exceeding, as the result of the first blow, the deflection given. 



Diam. axle at center, 

Number of blows 

Height of drop, ft.... 
Deflection, in 



41/4" 

24 
8I/4, 



43/8 

26 
8I/4 



4 5 7/16 

281/2 
81/4 



45/ 8 

31 



43/4 
34 



53/8 

43 

7 



57/8 

43 
51/2 



Specifications for Tires. (A. S. T. M., 1901.) — Physical require- 
ments of test-piece 1/2 in. diam. Tires for passenger engines: T. S., 100,000; 
El. in 2 in., 12%. Tires for freight engines and car wheels: T. S., 119,000; 
El., 10%. Tires for switching engines: T. S., 120,000; EL, 8%. 

Drop Test. — If a drop test is called for, a selected tire shall be placed 
vertically under the drop on a foundation at least 10 tons in weight and 
subjected to successive blows from a tup weighing 2240 lbs. falling from 
increasing heights until the required deflection is obtained, without break- 
ing or cracking. The minimum deflection must equal D 2 -*■ (40 T 2 -f 
2D), D being internal diameter and T thickness of tire at center of 
tread. 

Splice-bars. (A. S. T. M., 1901.) — Tensile strength of a specimen 
cut from the head of the bar, 54,000 to 64,000 lbs.; yield point, 32,000 
lbs. Elongation in 8 in., not less than 25 per cent. A test specimen 
cut from the head of the bar shall bend 180° flat on itself without fracture 
on the outside of the bent portion. If preferred, the bending test may 
be made on an unpunched splice-bar, which shall be first flattened and 
then bent. One tensile test and one bending test to be made from each 
blow or melt of steel. 



486 



STEEL. 



Specifications for Steel Used in Automobile Construction. 

(E. F. Lake, Am: Mach., March 14, 1907.) — 





C. 


Mn. 


Cr. 


Ni. 


P. 


S. 


T. S. 


E. L. 


El. in 
2 in. 


R. of 
A. 


(1) 

(2) 
(3) 

(4) 


0.40-0.55 

0.20-O.35 

0.25 

0.25-0.35 

0.45-0.55 
0.28-0.36 
0.85-1.00 
0.50 


0.40- 

0.40- 

0.40 

0.60 

1.1-1.3 

0.3-0.6 

0.25-0.5 

1.50- 


0.80+ 
0.80 + 
1.50 


1.50+ 

1.50 + 
3.50 
1.50 + 


0.04- 

0.04- 

0.015 

0.03 

0.065- 
0.05- 
0.03- 
0.04- 


0.04- 

0.04- 

0.025 

0.04 

0.06- 

0.06- 

0.03- 

0.06- 


f 90000 + 
i 180000 + 
/ 85000 + 
1130000 + 

120000 

f 85000 + 

1100000 + 

85000 + 

75000 + 


65000 + 
140000 + 
65000 + 
100000 + 
105000 
60000 + 
70000 + 
55000 + 
40000 + 


18 + 
8+ 
20 + 
12+ 
20 
25 + 
20+ 
15 + 
25 + 


35+a 
20 +b 
50 + a 
30+b 
58c 
50+a 
50+b 
45 + c 








ft 










30.0 





















The plus sign means "or over"; the minus sign "or less." 
a, fully annealed; b, heat-treated, that is oil-quenched and partly 
annealed; c, as rolled. 

(1) 45% carbon chrome-nickel steel, for gears of high-grade cars. 
When annealed this steel can be machined with a high-speed tool at the 
rate of 35 ft. per min., with a l/i6-in. feed and a 3/ 16 -in. cut. It is annealed 
at 1400° F. 4 or 5 hours, and cooled slowly. In heat-treating it is heated 
to 1500°, quenched in oil or water and drawn at 500° F. 

(2) 25% carbon chrome-nickel steel, for shafts, axles, pivots, etc. 
This steel may be machined at the same rate as (1), and it forges more 
easily. 

(3) A foreign steel used for forgings that have to withstand severe 
alternating shocks, such as differential shafts, transmission parts, universal 
joints, axles, etc. 

(4) Nickel steel, used instead of (1) in medium and low-priced cars. 

(5) " Gun-barrel " steel, used extensively for rifle barrels, also in low- 
priced automobiles, for shafts, axles, etc. It is used as it comes from 
the maker, without heat-treating. 

(6) Machine steel. Used for parts that do not require any special 
strength. 

(7) Spring steel used in automobiles. 

(8) Nickel steel for valves. Used for its heat-resisting qualities in 
valves of internal-combustion engines. 

Carbonizing or Case-hardening. — Some makers carbonize the surface 
of gears made from steel (1) above. They are packed in cast-iron boxes 
with a mixture of bone and powdered charcoal and heated four hour* 
at nearly the melting-point of the boxes, then cooled slowly in the boxes. 
They are then taken out, heated to 1400° F. for four hours to break up the 
coarse grain produced by the carbonizing temperature. After this the 
work is heat-treated as above described. 

The machine stee! (6) case-hardens well by the use of this process. 

Specifications for Steel Castings. (Proc. A. S. T. M., 1905, p. 53.) — 
Open-hearth, Bessemer, or crucible. Castings to be annealed unless 
otherwise specified. Ordinary castings, in which no physical require- 
ments are specified, shall contain not over 0.04 C and not over 0.08 P. 
Castings subject to physical test shall contain not over 0.05 P and not 
over 0.05 S. The minimum requirements are: 





T. S. 

85,000 
70,000 
60,000 


Y. P. 


El. in 2 
in. 


Red. 
Area. 




38,250 
31,500 
27,000 


15% 
18 % 
22% 


20% 




25% 




30% 







FORCE, STATICAL MOMENT, EQUILIBRIUM, ETC. 487 

For small or unimportant castings a test to destruction may be sub- 
stituted. Three samples are selected from each melt or blow, annealed 
in the same furnace charge, and shall show the material to be ductile 
and free from injurious defects, and suitable for the purpose intended. 
Large castings are to be suspended and hammered all over. No cracks, 
flaws, defects nor weakness shall appear after such treatment. A speci- 
men 1 X 1/2 in. shall bend cold around a diam. of 1 in. without fracture 
on outside of bent portion, through an angle of 120° for soft and 90° for 
medium castings. 

Specifications for steel castings issued by the U. S. Navy Department, 
1889 (abridged): Steel for castings must be made by either the open-' 
hearth or the crucible process, and must not show more than 0.06% of 
phosphorus. All castings must be annealed, unless otherwise directed. 
The tensile strength of steel castings shall be at least 60,000 lbs., with an 
elongation of at least 15% in 8 in. for all castings for moving parts of 
machinery, and at least 10% in 8 in. for other castings. Bars 1 in. sq. 
shall be capable of bending cold, without fracture, through an angle of 
90°, over a radius not greater than 11/2 in. All castings must be sound, 
free from injurious roughness, sponginess, pitting, shrinkage, or other 
cracks, cavities, etc. 

Pennsylvania Railroad specifications, 1888: Steel castings should have a 
tensile strength of 70,000 lbs. per sq. in. and an elongation of 15% in 
section originally 2 in. long. Steel castings will not be accepted if tensile 
strength falls below 60,000 lbs., nor if the elongation is less than 12%, nor 
if castings have blow-holes and shrinkage cracks. Castings weighing 80 
lbs. or more must have cast with them a strip to be used as a test-piece. 
The dimensions of this strip must be 3/ 4 in. sq. by 12 in. long. 



MECHANICS. 

FORCE, STATICAL MOMENT, EQUILIBRIUM, ETC. 

Mechanics is the science that treats of the action of force upon bodies. 
Statics is the mechanics of bodies at rest relatively to the earth's surface. 
Dynamics is the mechanics of bodies in motion. Hydrostatics and hydro- 
dynamics are the mechanics of liquids, and Pneumatics the mechanics 
of air and other gases. These are treated in other chapters. 

There are four elementary quantities considered in Mechanics: Matter, 
Force, Space, Time. 

Matter. — Any substance or material that can be weighed or measured. 
It exists in three forms: solid, liquid, and gaseous. A definite portion 
of matter is called a body. 

The Quantity of Matter in a body may be determined either by 
measuring its bulk or by weighing it, but as the bulk varies with temper- 
ature, with porosity, with size, shape and method of piling its particles, 
etc., weighing is generally the more accurate method of determining its 
quantity. 

Weight. Mass. — The word "weight" is commonly used in two 
senses: 1. As the measure of quantity of matter in a body, as deter- 
mined by weighing it in an even balance scale or on a lever or platform 
scale, and thus comparing its quantity with that of certain pieces of metal 
called standard w r eights, such as the pound avoirdupois. 2. As the 
measure of the force which the attraction of gravitation of the earth 
exerts on the body, as determined by measuring that force with a spring 
balance. As the force of gravity varies with the latitude and elevation 
above sea level of different parts of the earth's surface, the weight deter- 
mined in this second method is a variable, while that determined by 
the first method is a constant. For this reason, and also because spring 
balances are generally not as accurate instruments as even balances, or 
lever or platform scales, the word "weight," in engineering, unless other- 
wise specified, means the quantity of matter as determined by weigh- 
ing it by the first method. The standard unit of weight, is the pound. 

The word "mass" is used in three senses by writers on physics and 
engineering: 1. As a general expression of an indefinite quantity, syn- 
onymous with lump, piece, portion, etc., as in the expression "a mass 
whose weight is one pound." 2. As the quotient of the weight, as 



488 MECHANICS. 

determined by the first method of weighing given above, by 32.2, the 
value of g, the acceleration due to gravity, at London, expressed by 
the formula M = Wig. This value is merely the arithmetical ratio of 
the weight in pounds to the acceleration in feet per second per second, 
and it has no unit. 3. As a measure of the quantity of matter, exactly 
synonymous with the first meaning of the word " weight," given above. 
In this sense the word is used in many books on physics and theoretical 
mechanics, but it is not so used by engineers. The statement in such 
books that the engineers' unit of mass is 32.2 lbs. is an error. There is 
no such unit. Whenever the term " mass " is represented by M in engi- 
neering calculations it is equivalent to Wig, in which W is the quantity 
of matter in pounds, and g = 32.2. 

A Force is anything that tends to change the state of a body with 
respect to rest or motion. If a body is at rest, anything that tends to 
put it in motion is a force; if a body is in motion, anything that tends to 
change either its direction or its rate of motion is a force. 

A force should always mean the pull, pressure, rub, attraction (or repul- 
sion) of one body upon another, and always implies the existence of a 
simultaneous equal and opposite force exerted by that other body on the 
first body, i.e., the reaction. In no case should we call anything a force 
unless we can conceive of it as capable of measurement by a spring 
balance, and are able to say from what other body it comes. (I. P. 
Church.) 

Forces may be divided into two classes, extraneous and molecular: 
extraneous forces act on bodies from without; molecular forces are exerted 
between the neighboring particles of bodies. 

Extraneous forces are of two kinds, pressures and moving forces: pres- 
sures simply tend to produce motion; moving forces actually produce 
motion. Thus, if gravity act on a fixed body, it creates pressure; if on a 
free body, it produces motion. 

Molecular forces are of two kinds, attractive and repellent: ..attractive 
forces tend to bind the particles of a body together; repellent forces tend 
to thrust them asunder. Both kinds of molecular forces are continu- 
ally exerted between the molecules of bodies, and on the predominance of 
one or the other depends the physical state of a body, as solid, liquid, or 
gaseous. 

The Unit of Force used in engineering, by English writers, is the 
pound avoirdupois. For some scientific purposes, as in electro-dynamics, 
forces are sometimes expressed in "absolute units." The absolute unit of 
force is that force which acting on a unit of mass during a unit of time pro- 
duces a unit of velocity. In the French C. G. S., or centimeter-gram- 
second system, it is the force which acting on the mass whose weight is one 
gram at Paris will produce in one second a velocity of one centimeter per 
second. This unit is called a "dyne " = 1/981 gram at Paris. 

An attempt has been made by some writers on physics to introduce the 
so-called " absolute system " into English weights and measures, and to 
define the "absolute unit " of force as that force which acting on the 
mass whose weight is one pound at London will in one second produce a 
velocity of one foot per second, and they have given this unit the name 
"poundal." The use of this unit only makes confusion for students, 
and it is to be hoped that it will soon be abandoned in high-school text- 
books. Professor Perry in his "Calculus for Engineers," p. 26, says, 
" One might as well talk Choctaw in the shops as to speak about ... so 
many poundals of force and so many foot-poundals of work." * 

Inertia is that property of a body by virtue of which 'it tends to con- 
tinue in the state of rest or motion in which it may be placed, until acted 
on by some force. 

Newton's Laws of Motion. — 1st Law. If a body be at rest, it will 
remain at rest ; or if in motion, it will move uniformly in a straight line till 
acted on by some force. 

* Professor Perry himself, however, makes a slip on the same page In 
saying: " Force in pounds is the space-rate at which work in foot-pounds 
is done; it is also the time-rate at which momentum is produced or de- 
stroyed." He gets this idea, no doubt, from the equations FT = M V, 
F = MVIT, F = i/ 2 IF 2 v S. Force is not these things; it is merely 
numerically equivalent, when certain units are chosen, to these last two 
quotients. We might as well say, since T = MV/F, that time is the 
force-rate of momentum, 



FORCE, STATICAL MOMENT, EQUILIBRIUM, ETC. 489 



2d Law. If a body be acted on by several forces, it will obey each as 
though the others did not exist, and this whether the body be at rest or in 
motion. 

3d Law. If a force act to change the state of a body with respect to rest 
or motion, the body will offer a resistance equal and directly opposed to the 
force. Or, to every action there is opposed an equal and opposite reaction. 

Graphic Representation of a Force. — Forces may be represented 
geometrically by straight lines, proportional to the forces. A force is 
given when we know its intensity, its point of application, and the direc- 
tion in which it acts. When a force is represented by a Mne, the length of 
the line represents its intensity; one extremity represents the point of 
application; and an arrow-head at the other extremity shows the direc- 
tion of the force. 

Composition of Forces is the operation of finding a single force whose 
effect is the same as that of two or more given forces. The required 
force is called the resultant of the given forces. 

Resolution of Forces is the operation of finding two or more forces 
whose combined effect is equivalent to that of a given force. The required 
forces are called components of the given force. 

The resultant of two forces applied at a point, and acting in the same di- 
rection, is equal to the sum of the forces. If two forces act in opposite 
directions, their resultant is equal to their difference, and it acts in the 
direction of the greater. 

If any number of forces be applied at a point, some in one direction and 
others in a contrary direction, their resultant is equal to the sum of those 
that act in one direction, diminished by the sum of those that act in the 
opposite direction; or, the resultant is equal to the algebraic sum of the 
components. 

Parallelogram of Forces. — If two forces acting on a point be rep- 
resented in direction and intensity by adjacent sides of a parallelogram, 
their resultant will be represented by that diagonal of the parallelogram 
which passes through the point. Thus OR, Fig. 93, is the resultant of OQ 
and OP. 





Polygon of Forces. — If several forces are applied at a point and act 
in a single plane, their resultant is found as follows: 

Through the point draw a line representing the first force; through the 
extremity of this draw a line representing the second force; and so on, 
throughout the system; finally, draw a line from the starting-point to the 
extremity of the last line drawn, and this will be the resultant required. 

Suppose the body A, Fig. 94, to be urged in the directions Al, A 2, A3, 
A4, and A5 by forces which are to each other as the lengths of those lines. 
Suppose these forces to act successively and the body to first move from A 
to 1 ; the second force A 2 then acts and finding the body at 1 would take it 
to 2' ; the third force would then carry it to 3', the fourth to 4', and the fifth 
to 5'. The line Ah' represents in magnitude and direction the resultant of 
all the forces considered. If there had been an additional force, Ax, in 
the group, the body would be returned bv that force to its original position, 
supposing the forces to act successively, but if they had acted simul- 
taneously the body would never have moved at all; the tendencies to 
motion balancing each other. 

It follows, therefore, that if the several forces which tend to move a 
body can be represented in magnitude and direction by the sides of a 
closed polygon taken in order, the body will remain at rest; but if the 
forces are represented by the sides of an open polygon, the body will move 



490 



MECHANICS. 



and the direction will be represented by the straight line which closes the 
polygon. 

Twisted Polygon. — The rule of the polygon of forces holds true even 
when the forces are not in one plane. In this case the lines Al, 1-2', 2 / -3', 
etc.. form a twisted polygon, that is, one whose sides are not in one plane. 

Parallelopipedon of Forces. — If three forces acting on a point be 
represented by three edges of a parallelopipedon which meet in a common 
point, their resultant will be represented by the diagonal of the parallelo- 
pipedon that passes through their common point. 

Thus OR, Fig. 95, is the resultant of OQ, OS and OP. OM is the result- 
ant of OP and OQ, and OR is the resultant of OM and OS. 

^d 





Fig. 96. 



Moment of a Force. — The moment of a force (sometimes called 
statical moment), with respect to a point, is the product of the force by 
the perpendicular distance from the point to the direction of the force. 
The fixed point is called the center of moments; the perpendicular distance 
is the lever-arm of the force; and the moment itself measures the tendency 
of the force to produce rotation about the center of moments. 

If the force is expressed in pounds and the distance in feet, the moment 
is expressed in foot-pounds. It is necessary to observe the distinction be- 
tween foot-pounds of statical moment and foot-pounds of work or energy. 
(See Work.) 

In the bent lever, Fig. 96 (from Trautwine), if the weights n and m 
represent forces, their moments about the point / are respectively nX af 
and m X fc. If instead of the weight m a pulling force to balance the 
weight n is applied in the direction bs, or by or bd, s, y, and d being the 
amounts of these forces, their respective moments are sXft, yX fb, 
dXfh. 

If the forces acting on the lever are in equilibrium it remains at rest, and 
the moments on each side of / are equal, that is, n X af = m X fc, or s X 
ft, or yX fb, or d X hf. 

The moment of the resultant of any number of forces acting together in 
the same plane is equal to the algebraic sum of the moments of the forces 
taken separately. 

Statical Moment. Stability. — The statical moment of a body is 
the product of its weight by the distance of its line of gravity from some, 
assumed line of rotation. The line of gravity is a vertical line drawn from 
its center of gravity through the body. The stability of a body is that 
resistance which its weight alone enables it to oppose against forces tend- 
ing to overturn it or to slide it along its foundation. 

To be safe against turning on an edge the moment of the forces tending 
to overturn it, taken with reference to that edge, must be less than the 
statical moment. When a body rests on an inclined plane, the line of 
gravity, being vertical, falls toward the lower edge of the body, and the 
condition of its not being overturned by its own weight is that the line of 
gravity must fall within this edge. In the case of an inclined tower 
resting on a plane the same condition holds — the line of gravity must 
fall within the base. The condition of stability against sliding along a 
horizontal plane is that the horizontal component of the force exerted 
tending to cause it to slide shall be less than the product of the weight of 






FORCE, STATICAL MOMENT, EQUILIBRIUM, ETC. 491 

the body into the coefficient of friction between the base of the body and 
its supporting piane. This coefficient of friction is the tangent of the 
angle of repose, or the maximum angle at which the supporting plane, 
might be raised from the horizontal before the body would begin to slide. 
(See Friction.) 

The Stability of a Dam against overturning about its lower edge 
is calculated by comparing its statical moment referred to that edge with 
the resultant pressure of the water against its upper side. The horizontal 
pressure on a square foot at the bottom of the dam is equal to the weight of 
a column of water of one square foot in section, and of a height equal to the 
distance of the bottom below water-level; or, if // is the height, the pressure 
at the bottom per square foot = 62.4 X H lbs. At the water-level the 
pressure is zero, and it increases uniformly to the bottom, so that the sum 
of the pressures on a vertical strip one foot in breadth may be represented 
by the area of a triangle whose base is 62.4 X H and whose altitude is H, 
or 62.4 H 2 -s- 2. The center of gravity of a triangle being 1/3 of its altitude, 
the resultant of all the horizontal pressures may be taken as equivalent 
to the sum of the pressures acting at 1/3 H, and the moment of; the sum of 
the pressures is therefore 62.4 X H 3 ■* 6. 

Parallel Forces. — [If two forces are parallel and act in the same direc- 
tion, their resultant is parallel to both, and lies between them, and the 
intensity of the resultant is equal to the sum of the intensities of the two 
forces. Thus in Fig. 96 the resultant of the forces n and m acts vertically 
downward at /, and is equal to n + m. 

If two parallel forces act at the extremities of a straight line and in the 
same direction, the resultant divides the line joining the points of appli- 

N 



£*4 


Fig 


>Q 

97. 


>R 


W*z -v 

m/ i: 






S6 £- 

Fig. 98. 


-^-R 





cation of the components, inversely as the components. Thus in Fig. 96, 
m: n:: af:fc; and in Fig. 97, P: Q:: SN: SM. 

The resultant of two parallel forces acting in opposite directions is 
parallel to both, lies without both, on the side and in the direction of the 
greater, and its intensity is equal to the differe- 1 R 

nee of the intensities of the two forces. 

Thus the resultant of the two forces Q and P, 
Fig. 98, is equal to Q - P = R. Of any two par- 
allel forces and their resultant each is propor- 
tional to the distance between the other two; 
thus in both Figs. 97 and 98, P:Q:R:: SN: 
SM: MN. 

Couples. — If P and Q be equal and act in 
opposite directions, #=0; that is, they have no 
resultant. Two such forces constitute what is 



m 



called a couple. , rg 

The tendency of a couple is to produce rota- ' -p. Qq 

tion; the measure of this tendency, called the ya ' 

moment of the couple, is the product of one of the forces by the distance 
between the two. 

Since a couple has no single resultant, no single force can balance a 
couple. To prevent the rotation of a body acted on by a couple the applica- 
tion of two other forces is required, forming a second couple. Thus in 
Fig. 99, P and Q, forming a couple, may be balanced by a second couple 
formed by R and S. The point of application of either R or S may be a 
fixed pivot or axis. 

Moment of the couple PQ = P (c + b + a) = moment of RS = Rb. 
Also, P + R = Q + S. 

The forces R and 5 need not be parallel to P and Q, but if not, then their 
components parallel to PQ are to be taken instead of the forces themselves. 



492 Mechanics. 



Equilibrium of Forces. — A system of forces applied at points of a 
solid body will be in equilibrium when they have no tendency to produce 
motion, either of translation or of rotation. 

The conditions of equilibrium are: 1. The algebraic sum of the compo- 
nents of the forces in the direction of any three rectangular axes must be 
separately equal to 0. 

2. The algebraic sum of the moments of the forces, with respect to any 
three rectangular axes, must be separately equal to 0. 

If the forces lie in a plane: 1. The algebraic sum of the components of 
the forces, in the direction of any two rectangular axes, must be separately 
equal to 0. 

2. The algebraic sum of the moments of the forces, with respect to any 
point in the plane, must be equal to 0. 

If a body is restrained by a fixed axis, as in case of a pulley, or wheel and 
axle, the forces will be in equilibrium when the algebraic sum of the mo- 
ments of the forces with respect to the axis is equal to 0. 

CENTER OF GRAVITY. 

The center of gravity of a body, or of a system of bodies rigidly connected 
together, is that point about which, if suspended, .all the parts will be in 
equilibrium, that is, there will be no tendency to rotation. It is the point 
through which passes the resultant of the efforts of gravitation on each of 
the elementary particles of a body. In bodies of equal heaviness through- 
out, the center of gravity is the center of magnitude. 

(The center of magnitude of a figure is a point such that if the figure be 
divided into equal parts the distance of the center of magnitude of the 
whole figure from any given plane is the mean of the distances of the 
centers of magnitude of the several equal parts from that plane.) 

If a body be suspended at its center of gravity, it will be in equilibrium 
in all positions. If it be suspended at a point out of its center of gravity, it 
will swing into a position such that its center of gravity, is vertically 
beneath its point of suspension. 

To find the center of gravity of any plane figure mechanically, suspend 
the figure by any point near its edge, and mark on it the direction of a 
plumb-line hung from that point; then suspend it from some other point, 
and again mark the direction of the plumb-line in like manner. Then the 
center of gravity of the surface will be at the point of intersection of the 
two marks of the plumb-line. 

The Center of Gravity of Regular Figures, whether plane or solid, 
is the same as their geometrical center; for instance, a straight line, 
parallelogram, regular polygon, circle, circular ring, prism, cylinder, 
sphere, spheroid, middle frustums of spheroid, etc. 

Of a triangle: On a line drawn from any angle to the middle of the op- 
posite side, at a distance of one-third of the line from the side; or at the 
intersection of such lines drawn from any two angles. 

Of a trapezium or trapezoid: Draw a diagonal, dividing it into two tri- 
angles. Draw a line joining their centers of gravity. Draw the other 
diagonal, making two other triangles, and a line joining their centers 
of gravity. The intersection of the two lines is the center of gravity 
required. 

Of a sector of a circle: On the radius which bisects the arc, 2 cr-e-3 I from 
the center, c being the chord, r the radius, and I the arc. 

Of a semicircle: On the middle radius, 0.4244 r from the center. 

Of a quadrant: On the middle radius, 0.6002 r from the center. 

Of a segment of a circle: c 3 -f- 12 a from the center, c = chord, a = area. 

Of a parabolic surface: In the axis, 3/ 5 of its length from the vertex. 

Of a semi-parabola (surface): 3/ 5 length of the axis from the vertex, and 
3/8 of the semi-base from the axis. 

Of a cone or pyramid: In the axis, 1/4 of its length from the base. 

Of a paraboloid: In the axis, 2/ 3 of its length from the vertex. 

Of a cylinder, or regular prism: In the middle point of the axis. 

Of a frustum of a cone or pyramid- Let a = length of a line drawn from 
the vertex of the cone when complete to the center of gravity of the base, 
and a' that portion of it between the vertex and the top of the frustum; 
then distance of center of gravity of the frustum from center of gravity of 

its base = - — ■ . 9 , ' — -. — ■ — 75-.- 
4 4 (a 2 + aa' + a' 2 ) 



MOMENT OF INERTIA. 493 

For two bodies, fixed one at each end of a straight bar, the common 
center of gravity is in the bar, at that point which divides the distance 
between their respective centers of gravity in the inverse ratio of the 
weights. In this solution the weight of the bar is neglected. But it may 
be taken as. a third body, and allowed for as in the following directions: 

For more than two bodies connected in one system: Find the common 
center of gravity of two of them: and find the common center of these two 
jointly with a third body, and so on to the last body of the group. 

Another method, by the principle of moments: To find the center of 
gravity of a system of bodies, or a body consisting of several parts, whose 
several centers are known. If the bodies are in a plane, refer their several 
centers to two rectangular coordinate axes. Multiply each weight by its 
distance from one of the axes, add the products, and divide the sum by the 
sum of the weights; the result is the distance of the center of gravity from 
that axis. Do the same with regard to the other axis. If the bodies are 
not in a plane, refer them to three planes at right angles to each other, and 
determine the mean distance of the sum of the weights from each of the 
three planes. 

MOMENT OF INERTIA. 

The moment of inertia of the weight of a body with respect to an axis la 
the algebraic sum of the products obtained by multiplying the weight of 
each elementary particle by the square of its distance from the axis. If 
the moment of inertia with respect to any axis = /, the weight of any 
element of the body = w, and its distance from the axis = r, we have 
1 = 2 (vrr 2 ). 

The moment of inertia varies, in the same body, according to the 
position of the axis. It is the least possible when the axis passes through 
the center of gravity. To find the moment of inertia of a body, referred 
to a given axis, divide the body into small parts of regular figure. Multi- 
ply the weight of each part by the square of the distance of its center of 
gravity from the axis. The sum of the products is the moment of inertia. 
The value of the moment of inertia thus obtained will be more nearly 
exact, the smaller and more numerous the parts into which the body is 
divided. 

Moments of Inertia of Regular Solids. — Rod, or bar, of uniform 
thickness, with respect to an axis perpendicular to the length of the rod, 

/= w (| +d*) (1) 

W == weight of rod, 21 = length, d = distance of center of gravity from 

axis. 

Thin circular plate, axis in its ) r _ w ( r 2_ , ^ \ fo \ 

own plane, J l ~ w U ) ( ; 

r = radius of plate. 

Circular plate, axis perpendicular to ) j = w M + rf2 \ ,^ 

ttl© pi£LLC, ) \2 * / 

Circular ring, axis perpendicular to) T _ w (r^+r^ . ^ 2 \ (a\ 

its own plane, I ' \ 2 /.' ' ' ' " K } 

r and r' are the exterior and interior radii of the ring. 
Cylinder, axis perpendicular to the) i ^-n? ( r2 ,V , ^\ /n 

axis of the cylinder. ) ~ 1 4 + 3 + / ' ' ' * { } 

r = radius of base. 2 1 = length of the cylinder. 

By making d = in any of the above formulae, we find the moment of 
inertia for a parallel axis through the center of gravity. 

The moment of inertia, 2wr 2 , numerically equals the weight of a body 
which, if concentrated at the distance unity from the axis of rotation, 
would require the same work to produce a given increase of angular 
velocity that the actual body requires. It bears the same relation to 
angular acceleration which weight does to linear acceleration (Rankine). 
The term moment of inertia is also used in regard to areas, as the cross- 
sections of beams under strain. In this case / = 2ar 2 , in which a is any 
elementary area, and r its distance from the center. (See under Strength 
of Materials, p. 279.) Some writers call 2mr 2 =2w 2 -*- g the moment of 
inertia. 



494 MECHANICS. 



CENTERS OF OSCILLATION AND OF PERCUSSION. 

Center of Oscillation. — If a body oscillate about a fixed horizontal 
axis, not passing through its center of gravity, there is a point in the line 
drawn from the center of gravity perpendicular to the axis whose motion 
is the same as it would be if the whole mass were collected at that point 
and allowed to vibrate as a pendulum about the fixed axis. This point is 
called the center of oscillation. 

The Radius of Oscillation, or distance of the center of oscillation 
from the point of suspension = the square of the radius of gyration -s- dis- 
tance of the center of gravity from the point of suspension or axis. The 
centers of oscillation and suspension are convertible. 

If a straight line, or uniform thin bar or cylinder, be suspended at one 
end, oscillating about it as an axis, the center of oscillation is at 2/3 the 
length of the rod from the axis. If the point of suspension is at 1/3 the 
length from the end, the center of oscillation is also at 2/3 the length from 
the axis, that is, it is at the other end. In both cases the oscillation will 
be performed in the same time. If the point of suspension is at the 
center of gravity, the length of the equivalent simple pendulum is infinite, 
and therefore the time of vibration is infinite. 

For a sphere suspended by a cord, r = radius, h = distance of axis of 
motion from the center of the sphere, h' = distance of center of oscillation 

2r_ 2 
" 5h' 



from center of the sphere, I = radius of oscillation = h+ h' = h + ~ 

If the sphere vibrate about an axis tangent to its surface, h = r, and 
Z = r+2/ 5 r. If h = 10 r, I = 10 r+ ■£=• 

Lengths of the radius of oscillation of a few regular plane figures or thin 
plates, suspended by the vertex or uppermost point. 

1st. When the vibrations are flatwise, or perpendicular to the plane of 
the figure: 

In an isosceles triangle the radius of oscillation is equal to 3/ 4 of the 
height of the triangle. 

In a circle, 5/8 of the diameter. 

In a parabola, 5/ 7 of the height. 

2d. When the vibrations are edgewise, or in the plane of the figure: 

In a circle the radius of oscillation is 3/ 4 of the diameter. 

In a rectangle suspended by one angle, 2/3 of the diagonal. 

In a parabola, suspended by the vertex, 5/ 7 of the height plus 1/3 of 
the parameter. 

In a parabola, suspended by the middle of the base, 4/ 7 of the height plus 
1/2 the parameter. 

Center of Percussion. — The center of percussion of a body oscillat- 
ing about a fixed axis is the point at which, if a blow is struck by the body, 
the percussive action is the same as if the whole mass of the body were 
concentrated at the point. This point is identical with the center of 
oscillation. 

CENTER AND RADIUS OF GYRATION. 

The center of gyration, with reference to an axis, is a point at which, if 
the entire weight of a body be concentrated, its moment of inertia will re- 
main unchanged; or, in a revolving body, the point in which the whole 
weight of the body may be conceived to be concentrated, as if a pound of 
platinum were substituted for a pound of revolving feathers, the angular 
velocity and the accumulated work remaining the same. The distance of 
this point from the axis is the radius of gyration. If W = the weight of a 
body, / = 2w 2 = its moment of inertia, and k = its radius of gyration, 

/ =Wk* = 2w 2 ; k = \^7p' 

The moment of inertia = the weight X the square of the radius of gyration. 
To find the radius of gyration divide the body into a considerable 
number of equal small parts, — the more numerous the more nearly exact 
is the result, — then take the mean of all the squares of the distances of the 
parts from the axis of revolution, and find the square root of the mean 
square. Or, if the moment of inertia is known, divide it by the weight 
and extract the square root. For radius of gyration of an area, as a cross- 
section of a beam, divide the moment of inertia of the area by the area 
and extract the square root. 



CENTER AND RADIUS OF GYRATION. 



495 



The radius of gyration is the least possible when the axis passes through 
the center of gravity. This minimum radius is called the principal radius 
of gyration. If we denote it by k and any other radius of gyration by k' , 
we have for the five cases given under the head of moment of inertia above 
the following values: 



(1) Rod, axis perpen. to > i. _ 7 4 A. h , _ ./l* 
length, )k-L \-, k - y- 



(2) Circular plate, axis in 
its plane, 



(3) Circular plate, axis per- ) fr 
pen. to plane, J 



(4) Circular ring, axis per- 
pen. to plane, 



(5) Cylinder, axis 
pen. to length, 






Principal Radii of Gyration and Squares of Radii of Gyration. 

(For radii of gyration of sections of columns, see page 281.) 



Surface or Solid. 



Parallelogram: ) axis at its base 

height 7i ) " mid-height 

Straight rod: ) „_• . „, ■, 

i „-i 7 „i, .t; ■ ( axis at end 

iss&i&n •■ *^ 

Rectangular prism: 

axes 2 a, 2 b, 2 c, referred to axis 2 a... . 
Parallelopiped: length I, base b, axis at ) 

one end, at mid-breadth ) 

Hollow square tube: 

out. side h, inner h', axis mid-length . . . 

very thin, side = h, axis mid-length . . . 
Thin rectangular tube: sides &, h, axis ) 

mid-length J 

Thin circ. plate: rad. r, diam. h, ax. diam. 
Flat circ. ring: diams. h, h', axis diam.. . 
Solid circular cylinder: length I, axis di- ) 

ameter at mid-length ) 

Circular plate: solid wheel of uniform j 

thickness, or cylinder of any length, > 

referred to axis of cyl ) 

Hollow circ. cylinder, or flat ring: 

I, length; R, r, outer and inner radii. 

Axis, 1, longitudinal axis; 2, diam. at 

mid-length ! 

Same: very thin, axis its diameter 

" radius r; axis, longitudinal axis . . 

Circumf . of circle, axis its center 

" " " " diam 

Sphere: radius r, axis its diam 

Spheroid: equatorial radius r, revolving) 

polar axis a J 

Paraboloid: r = rad. of base, rev. on axis 
Ellipsoid: semi-axes a,b,c; revolving on ) 

axis 2 a J 

Spherical shell: radii R, r, revolving on ) 

its diam J 

Same: very thin, radius r 

Solid cone: r = rad. of base, rev. on axis. . 



Rad. of Gyration. %%%$% 



0.5773/* 
0.2886 h 
0.5773 1 

0.2886 I 



0.577 V&2 . 



0.289 V4Z 2 + 62 



0.289 V^ +h'2 
.403 h 



0.289A %/ h -r^ 
1/4 V h? + h' 2 



0.289 Vp + 3r 2 

0.7071 r 
0.7071 iVF 



289\//2 + 3 (iJ2 +r 2) 



1/3 ft 2 
1/12 h 2 

Vl2 1 2 

(b 2 + c 2 ) + 3 

4P + b 2 

12 

(h 2 +h' 2 ) + \2 

h 2 + 6 

¥ h + 3b 

12' h + b 

l/ 4 r 2 = ft 2 + 16 

(h 2 + h' 2 ) -h 16 

P. -J* 

12 + 4 

1/2 r 2 

(R 2 + r 2 ) +2 
I 2 , R 2 - ' 



0.289 Vp + 6ft2 

r 

r 
0.7071 r 
0.6325 r 
0.6325 r 
0.5773 r 

0.4472V&2 + C 2 

l R 5 - r 5 



^ 



0.8165r 

0.5477r 




496 MECHANICS. 

THE PENDULUM. 

A body of any form suspended from a fixed axis about which it oscillates 
by the force of gravity is called a compound pendulum. The ideal body 
concentrated at the center of oscillation, suspended from the center of sus- 
pension by a string without weight, is called a simple pendulum. This 
equivalent simple pendulum has the same weight as the given body, and 
also the same moment of inertia, referred to an axis passing through the 
point of suspension, and it oscillates in the same time. 

The ordinary pendulum of a given length vibrates in equal times when 
the angle of the vibrations does not exceed 4 or 5 degrees, that is, 2° or 
21/2° each side of the vertical. This property of a pendulum is called its 
isochronism. 

The time of vibration of a pendulum varies directly as the square root 
of the length, and inversely as the square root of the acceleration due to 
gravity at the given latitude and elevation above the earth's surface. 

If T = the time of vibration, I = length of the simple pendulum, g = 

acceleration = 32.16, T = n \ — ; since it is constant, Too — =.• At a given 

* 9 _ Vg 

location g is constant and T oo vz. if I be constant, then for any location 

T oo —j=.- If T be constant, gT 2 = ir 2 l; I oo g; g = ?—■ From this equation 

v g 
the force of gravity at any place may be determined if the length of the 
simple pendulum, vibrating seconds, at that place is known. At New 
York this length is 39.1017 inches = 3.2585 ft., whence g = 32.16 ft. At \ 
London the length is 39.1393 inches. At the equator 39.0152 or 39.0168 
inches, according to different authorities. 

Time of vibration of a pendulum of a given length at New York 

-t- i/ ~ T ~ = -^L, 

▼ 39.1017 6.253 

t being in seconds and I in inches. Length of a pendulum having a given 
time of vibration, I = t 2 X 39.1017 inches. 

The time of vibration of a pendulum may be varied by the addition of a 
weight at a point above the center of suspension, which counteracts the 
lower weight, and lengthens the period of vibration. By varying the 
height of the upper weight the time is varied. 

To find the weight of the upper bob of a compound pendulum, vibrating 
seconds, when the weight of the lower bob and the distances of the 
weights from the point of suspension are given: 

(39.1XP)-J>». 
(39.1 X d) + d 2 

W = the weight of the lower bob, w = the weight of the upper bob; 
D = the distance of the lower bob and d = the distance of the upper bob 
from the point of suspension, in inches. 

Thus, by means of a second bob, short pendulums may be constructed to 
vibrate as slowly as longer pendulums. 

By increasing w or d unti< the lower weight is entirely counterbalanced, 
the time of vibration may be made infinite. 

Conical Pendulum. — A weight suspended by a cord and revolving 
at a uniform speed in the circumference of a circular horizontal plane 
whose radius is r, the distance of the plane below the point of suspension be- 
ing h, is held in equilibrium by three forces — the tension in the cord, the 
centrifugal force, which tends to increase the radius r, and the force of 
gravity acting downward. If v= the velocity in feet per second of the 
center of gravity of the weight, as it describes the circumference, g = 32.16, 
and r and h are taken in feet, the time in seconds of performing one 
revolution is 



-Vl 



V^; /*=|^= 0.8146 £ 2 . 



If t = 1 second, h = 0.8146 foot = 9.775 inches. 

The principle of the conical pendulum is used in the ordinary fly-ball 
governor for steam-engines. (See Governors.) 



VELOCITY, ACCELERATION; FALLING BODIES. 497 



CENTRIFUGAL FORCE. 

A body revolving in a curved path of radius = R in feet exerts a force, 
called centrifugal force, F, upon the arm or cord which restrains it from 
moving in a straight line, or " hying off at a tangent." If W = weight of 
the body in pounds, N = number of revolutions per minute, v = linear 
velocity of the center of gravity of the body, in feet per second, g = 32.16, 
then 

2nRN „ Wv 2 Wv 2 W4ir 2 RN 2 WRN 2 nnno „ nWDW ,u 
V - -60- ; F - 1R = 32-16^ = -36007- = ^93T = - 000341 ° WRN ^' 

If n = number of revolutions per second, F = 1.2276 WRn 2 . 
(For centrifugal force in fly-wheels, see Fly-wheels.) 

VELOCITY, ACCELERATION, FALLING BODIES. 

Velocity is the rate of motion, or the speed of a body at any instant. 
If s = space in feet passed over in t seconds, and v = velocity in feet per 
second, if the velocity is uniform, 

S xx S 

v = r ; s = vt; t = — 

i v 

If the velocity varies uniformly, the mean velocity v m =1/2 (v x + v 2 ), in which 
Vi is the velocity at the beginning and v 2 the velocity at the end of the time t. 

S = l/ 2 (^ +V 2 )t (1) 

If vi = 0, then s = 1/2 v 2 t. v 2 = 2 s/t . 

If the velocity varies, but not uniformly, v for an exceedingly short 
interval of time = s/t, or in calculus v = ds/dt. 

Acceleration is the change in velocity which takes place in a unit of 
time. Unit of acceleration = a = 1 foot per second in one second. For 
uniformly varying velocity, the acceleration is a constant quantity, and 

a= Vll^l . V2 = Vl + at; Vt = v 2 -at\t= V2 ~ Vi ■ . . . (2) 

If the body start from rest, v x = 0; then if v TO = mean velocity 

v n = I 2 ; v 2 = 2v m ; a= j; v 2 = at; v 2 -at = 0; t=\ 

Combining (1) and (2), we have 

v 2 2 -v t 2 . , at 2 . at 2 

s = 2a ; s = Vit+—; s = v 2 t — -• 

If Vi = 0, s=y 2 v 2 t. 

Retarded Motion. ■ — If the body start with a velocity Vi and come to 
rest, v 2 = 0; then s=V2Vit. 

In any case, if the change in velocity is v, 

v . v 2 a ... 

s = -t; s = — ; s = -t-. 
2 2a 2 

For a body starting from or ending at rest, we have the equations 

. v , at 2 , 

v = at; s = -t; s = — ; v 2 = 2 as. 

Falling Bodies. — In the case of falling bodies the acceleration due 
to gravity, at 40° latitude, is 32.16 feet per second in one second. = g. 
Then if v = velocity acquired at the end of t seconds, or final velocity, 
and h = height or space in feet passed over in the same time, 

v=gt = S2.1Qt = ^2~gh = 8.02 ^h = ^j ; 
&-J# 2 _i«ns*2_ v * v * - £■ 



498 



MECHANICS. 



: V 9 4.01 



g 32.16 

u = space fallen through in the jPth second = g (T - 1/2). 

From the above formulae for falling bodies we obtain the following: 
During the first second the body starting from a state of rest (resistance 
of the air neglected) falls g -j- 2 = 16.08 feet; the acquired velocity is g = 

32.16 ft. per sec; the distance fallen in two seconds is h = g — = 16.08 X 4 

= 64.32 ft.; and the acquired velocity is v = gt = 64.32 ft. The acceler- 
ation, or increase of velocity in each second, is constant, and is 32.16 ft: 
per second. Solving the equations for different times, we find for 

Seconds, t 12 3 4 5 6 

Acceleration, g 32.16X111 1 1 1 

Velocity acquired at end of time, v 32.16 x 12 3 4.5 6 

Height of fall in each second, u — - — x 1 3 5 7 9 11 



Total height of fall, 



9 16 25 36 



Value of g. — The value of g increases with the latitude, and decreases 
with the elevation. At the latitude of Philadelphia, 40°, its value is 32.16. 
At the sea-level, Everett gives g = 32.173 - .082 cos 2 lat. - .000003 
height in feet. _At Paris, lat. 48° 50' N., g = 980.87 cm. = 32.181 ft. 

Values of *^2g, calculated by an equation given by C. S. Pierce, are 
given in a table in Smith's Hydraulics, from which we take the following: 

Latitude 0° 10° 20° 30° 40° 50° 60° 

Value of VJ^.. 8.0112 8.0118 8.0137 8.0165 8.0199 8.0235 8.0269 
Valueofp 32.090 32.094 32.105' 32.132 32.160 32.189 32.216 

The value of ^2g decreases about .0004 for every 1000 feet increase in 
elevation above the sea-level. 

For all ordinary calculations for the United States, _£_is generally taken 
at 32.16. and V2g at 8.02. In England g = 32.2. \/2g = 8.025. Practi- 
cal limiting values of g for the United States, according to Pierce, are: 

Latitude 49° at sea-level g = 32. 186 

25° 10,000 feet above the sea = 32.089 

Fig. 100 represents graphically the velocity, space, etc., of a body falling 
for six seconds. The vertical line at the left is the time in seconds, the 
horizontal lines represent the acquired 
velocities at the end of each second = 
32.16 1. The area of the small triangle 
at the top represents the height fallen 
through in the first second = 1/2 9= 16.08 
feet, and each of the other triangles is an 
equal space. The number of triangles 
between each pair of horizontal lines rep- 
resents the height of fall in each second, 
and the number of triangles between any 
horizontal line and the top is the total 
height fallen during the time. The figures 
under h, u and v adjoining the cut are to 
be multiplied by 16.08 to obtain the actual 
velocities and heights for the given times 

Angular and Linear Velocity of a 
Turning Body. — Let r — radius of a 
turning body in feet, n = number of revo- 25 9 10 5" 
lutions per minute, i>= linear velocity of 
a point on the circumference in feet per 
second, and 60 v = velocity in feet per 36 11 12 6- 
minute. 

v = 2 -IgZL 60v = 2»rrn 
bO 



t 



3 4 2" 



I 

\3\ 



16 



K 



Fig. 100. 



PARALLELOGRAM OF VELOCITIES. 



499 



Angular velocity is a term used to denote the angle through which any 
radius of a body turns in a second, or the rate at which any point in it 
having a radius equal to unity is moving, expressed in feet per second. 
The unit of angular velocity is the angle which at a distance = radius 
from the center is subtended by an arc equal to the radius. This unit 

angle = — degrees = 57.3°. 2wX 57.3° = 360°, or the circumference. 
If A = angular velocity, v = Ar, A = ■ 

r DU 

called a radian. 

Height Corresponding to a Given Acquired Velocity. 



>> 




>> 




>> 




>> 




>> 




£> 






























^3 




m 








A 




A 




-a 


ja 


.SP 


JO 


_M 


_o 


.£? 


^o 


_M 


_o 


.SP 


o 


.SP 


"a5 

> 


'53 

w 


"a 

> 


w 


"53 

> 


'53 

w 


"53 
> 


& 


"53 

> 


'53 


i> 


& 


feet 




feet 




feet 




feet 




feet 




feet 




per 


feet. 


per 


feet. 


per 


feet. 


per 


feet. 


per 


feet. 


per 


feet. 


sec. 




sec. 




sec. 




sec. 




sec. 




sec 




.25 


0.0010 


13 


2.62 


34 


17.9 


55 


47.0 


76 


89.8 


97 


146 


.50 


0.0039 


14 


3.04 


35 


19.0 


56 


48.8 


77 


92.2 


98 


149 


.75 


0.0087 


15 


3.49 


36 


20.1 


57 


50.5 


78 


94.6 


99 


152 


1.00 


0.016 


16 


3.98 


37 


21.3 


58 


52.3 


79 


97.0 


100 


155 


1.25 


0.024 


17 


4.49 


38 


22.4 


59 


54.1 


80 


99.5 


105 


171 


1.50 


0.035 


18 


5.03 


39 


23.6 


60 


56.0 


81 


102.0 


110 


188 


1.75 


0.048 


19 


5.61 


40 


24.9 


61 


57.9 


82 


104.5 


115 


205 


2 


0.062 


20 


6.22 


41 


26.1 


62 


59.8 


83 


107.1 


120 


224 


2.5 


0.097 


21 


6.85 


42 


27.4 


63 


61.7 


84 


109.7 


130 


263 


3 


0.140 


22 


7.52 


43 


28.7 


64 


63.7 


85 


112.3 


140 


304 


3.5 


0.190 


23 


8.21 


44 


30.1 


65 


65.7 


86 


115.0 


150 


350 


4 


0.248 


24 


8.94 


45 


31.4 


66 


67.7 


87 


117.7 


175 


476 


4.5 


0.314 


25 


9.71 


•46 


32.9 


67 


69.8 


88 


120.4 


200 


622 


5 


0.388 


26 


10.5 


47 


34.3 


68 


71.9 


89 


123.2 


300 


1399 


6 


0.559 


27 


11.3 


48 


35.8 


69 


74.0 


90 


125.9 


400 


2488 


7 


0.761 


28 


12.2 


49 


37.3 


70 


76.2 


91 


128.7 


500 


3887 


8 


0.994 


29 


13.1 


50 


38.9 


71 


78.4 


92 


131.6 


600 


5597 


9 


1.26 


30 


14.0 


51 


40.4 


72 


80.6 


93 


134.5 


700 


7618 


10 


1.55 


31 


14.9 


52 


42.0 


73 


82.9 


94 


137.4 


800 


9952 


11 


1.88 


32 


15.9 


53 


43.7 


74 


85.1 


95 


140.3 


900 


12,593 


12 


2.24 


33 


16.9 


54 


45.3 


75 


87.5 


96 


143.3 


1000 


15,547 



Parallelogram of Velocities. — The principle of the composition 
and resolution of forces may also be applied to velocities or to distances 
moved in given intervals of time. Referring 
to Fig. 93, page 489, if a body at O has a 
force applied to it which acting alone would a ri 
give it a velocity represented by OQ per 
second, and at the same time it is acted on 
by another force which acting alone would 
give it a velocity OP per second, the result 
of the two forces acting, together for one sec- 
ond will carry it to R, OR being the diagonal 
of the parallelogram of OQ and OP, and the 
resultant velocitv. If the two component 
velocities are uniform, the resultant will be 
uniform and the line OR will be a straight 
line: but if either velocity is a varying one, 
the line will be a curve. Fig. 101 shows the 

resultant velocities, also the path traversed „„<f„ rm 

by a body acted on by two forces, one of which would carry it at a uniform 
velocitv over the intervals 1. 2. 3, B and the other of vvhich would carry it 
by an accelerated motion over the i ntervals a,b,c,Dm the same times. At 




Fig. 101. 



500 



MECHANICS. 



Falling Bodies: Velocity Acquired by a Body Falling a Given 
Height. 





>> 




>> 




>> 




>> 




£ 




>> 






























-Q 








J3 




,c 








a 


o 


M 


o 


_M 


o 


_bJ) 


o 


M 


o 


,M 


_o 






'S 








'3 




'3 








K 


> 


w 


> 


K 


> 


K 


f> 


K 


> 


w 


> 


feet. 


feet 


feet. 


feet 


feet. 


feet 


feet. 


feet 


feet. 


feet 


feet. 


feet 




p. sec. 




p. sec. 




p. sec. 




p. sec. 




p. sec. 




p. sec. 


0.005 


.57 


0.39 


5.01 


1.20 


8.79 


5. 


17.9 


23. 


38.5 


72 


68.1 


0.010 


.80 


0.40 


5.07 


1.22 


8.87 


.2 


18.3 


.5 


38.9 


73 


68.5 


0.015 


.98 


0.41 


5.14 


1.24 


8.94 


.4 


18.7 


24. 


39.3 


74 


69.0 


0.020 


1.13 


0.42 


5.20 


1.26 


9.01 


.6 


19.0 


.5 


39.7 


75 


69.5 


0.025 


1.27 


0.43 


5.26 


1.28 


9.08 


.8 


19.3 


25 


40.1 


76 


69.9 


0.030 


1.39 


0.44 


5.32 


1.30 


9.15 


6. 


19.7 


26 


40.9 


77 


70.4 


0.035 


1.50 


0.45 


5.38 


1.32 


9.21 


.2 


20.0 


27 


41.7 


78 


70.9 


0.040 


1.60 


0.46 


5.44 


1.34 


9.29 


.4 


20.3 


28 


42.5 


79 


71.3 


0.045 


1.70 


0.47 


5.50 


1.36 


9.36 


.6 


20.6 


29 


43.2 


80 


71.8 


0.050 


1.79 


0.48 


5.56 


1.38 


9.43 


.8 


20.9 


30 


43.9 


81 


72.2 


0.055 


1.88 


0.49 


5.61 


1.40 


9.49 


7. 


21.2 


31 


44.7 


82 


72.6 


0.060 


1.97 


0.50 


5.67 


1.42 


9.57 


.2 


21.5 


32 


45.4 


83 


73.1 


0.065 


2.04 


0.51 


5.73 


1.44 


9.62 


.4 


21.8 


33 


46.1 


84 


73.5 


0.070 


2.12 


0.52 


5.78 


1.46 


9.70 


.6 


22.1 


34 


46.8 


85 


74.0 


0.075 


2.20 


0.53 


5.84 


1.48 


9.77 


.8 


22.4 


35 


47.4 


86 


74.4 


0.080 


2.27 


0.54 


5.90 


1.50 


9.82 


8. 


22.7 


36 


48.1 


87 


74.8 


0.085 


2.34 


0.55 


5.95 


1.52 


9.90 


.2 


23.0 


37 


48.8 


88 


75.3 


0.090 


2.41 


0.56 


6.00 


1.54 


9.96 


.4 


23.3 


38 


49.4 


89 


75.7 


0.095 


2.47 


0.57 


6.06 


1.56 


10.0 


.6 


23.5 


39 


50.1 


90 


76.1 


0.100 


2.54 


0.58 


6.11 


1.58 


10.1 


.8 


23.8 


40 


50.7 


91 


76.5 


0.105 


2.60 


0.59 


6.16 


1.60 


10.2 


9. 


24.1 


41 


51.4 


92 


76.9 


0.110 


2.66 


0.60 


6.21 


1.65 


10.3 


.2 


24.3 


42 


52.0 


93 


77.4 


0.115 


2.72 


0.62 


6.32 


1.70 


10.5 


.4 


24.6 


43 


52.6 


94 


77.8 


0.120 


2.78 


0.64 


6.42 


1.75 


10.6 


.6 


24.8 


44 


53.2 


95 


78.2 


0.125 


2.84 


0.66 


6.52 


1.80 


10.8 


.8 


25.1 


45 


53.8 


96 


78.6 


0.130 


2.89 


0.68 


6.61 


1.90 


11.1 


10. 


25.4 


46 


54.4 


97 


79.0 


0.14 


3.00 


0.70 


6.71 


2. 


11.4 


.5 


26.0 


47 


55.0 


98 


79.4 


0.15 


3.11 


0.72 


6.81 


2.1 


11.7 


11. 


26.6 


48 


55.6 


99 


79.8 


0.16 


3.21 


0.74 


6.90 


2.2 


11.9 


.5 


27.2 


49 


56.1 


100 


80.2 


0.17 


3.31 


0.76 


6.99 


2.3 


12.2 


12. 


27.8 


50 


56.7 


125 


89.7 


0.18 


3.40 


0.78 


7.09 


2.4 


12.4 


.5 


28.4 


51 


57.3 


150 


98.3 


0.19 


3.50 


0.80 


7.18 


2.5 


12.6 


13. 


28.9 


52 


57.8 


175 


106 


0.20 


3.59 


0.82 


7.26 


2.6 


12.0 


.5 


29.5 


53 


58.4 


200 


114 


0.21 


3.68 


0.84 


7.35 


2.7 


13.2 


14. 


30.0 


54 


59.0 


225 


120 


0.22 


3.76 


0.86 


7.44 


2.8 


13.4 


.5 


30.5 


55 


59.5 


250 


126 


0.23 


3.85 


0.88 


7.53 


2.9 


13.7 


15. 


31.1 


56 


60.0 


275 


133 


0.24 


3.93 


0.90 


7.61 


3. 


13.9 


.5 


31.6 


57 


60.6 


300 


139 


0.25 


4.01 


0.92 


7.69 


3.1 


14.1 


16. 


32.1 


58 


61.1 


350 


150 


0.26 


4.09 


0.94 


7.78 


3.2 


14.3 


.5 


32.6 


59 


61.6 


400 


160 


0.27 


4.17 


0.96 


7.86 


3.3 


14.5 


17. 


33.1 


60 


62.1 


450 


170 


0.28 


4.25 


0.98 


7.94 


3.4 


14.8 


.5 


33.6 


61 


62.7 


500 


179 


0.29 


4.32 


1.00 


8.02 


3.5 


15.0 


18. 


34.0 


62 


63.2 


550 


188 


0.30 


4.39 


1.02 


8.10 


3.6 


15.2 


.5 


34.5 


63 


63.7 


600 


197 


0.31 


4.47 


1.04 


8.18 


3.7 


15.4 


19. 


35.0 


64 


64.2 


700 


212 


0.32 


4.54 


1.06 


8.26 


3.8 


15.6 


.5 


35.4 


65 


64.7 


800 


227 


0.33 


4.61 


1.08 


8.34 


3.9 


15.8 


20. 


35.9 


66 


65.2 


900 


241 


0.34 


4.68 


1.10 


8.41 


4. 


16.0 


.5 


36.3 


67 


65.7 


1000 


254 


0.35 


4.74 


1.12 


8.49 


.2 


16.4 


21. 


36.8 


68 


66.1 


2000 


359 


0.36 


4.81 


1.14 


8.57 


.4 


16.8 


.5 


37.2 


69 


66.6 


3000 


439 


0.37 


4.88 


1.16 


8.64 


.6 


17.2 


22. 


37.6 


70 


67.1 


4000 


507 


0.38 


4.94 


1.18 


8.72 


.8 


17.6 


.5 


38.1 


71 


67.6 


5000 


567 



FORCE OP ACCELERATION. 501 

the end of the respective intervals the body will be found at C lt C 2 , C3, C, 
and the mean velocity during each intervals is represented by the distances 
between these points. Such a curved path is traversed by a shot, the 
impelling force from the gun giving it a uniform velocity in the direction 
the gun is aimed, and gravity giving it an accelerated velocity downward. 
The path of a projectile is a parabola. The distance it will travel is 
greatest when its initial direction is at an angle 45° above the horizontal. 
Mass — Force of Acceleration. — The mass of a body, m = w/g, is a 
constant quantity. If g = the acceleration due to gravity, and w = 

weight, then the mass m = — ; w = mg. If the weight w is taken to be the 

resultant of the force of gravity on the particles of a body such as may 
be measured by a spring balance, or by the extension or deflection of a 
rod of metal loaded with the given weight, then the weight varies accord- 
ing to the variation in the force of gravity at different places, and the value 
of g is that at the place where the body is weighed ; but if w is the weight 
as weighed on a platform scale, then g = 32.2, the English value. In either 
case m = w/g is a constant. 

Force has been defined as that which causes, or tends to cause, or to 
destroy, motion. It may also be defined as the cause of acceleration; 
and the unit of force, the pound, as the force required to produce an 
acceleration of 32.2 ft. per second per second in a pound of free mass. 

Force equals the product of the mass by the acceleration, or / = ma. 

Also, if v = the velocity acquired in the time t,ft = mv;f = mv -*- t; the 
acceleration being uniform. 

The force required to produce an acceleration of g (that is, 32.16 ft. per 

sec. in one second) is / = mg = — g = w, or the weight of the body. Also, 
/ = ma = m -^—. — - . in which v 2 is the velocity at the end, and vi the 
velocity at the beginning of the time t, and / = mg = — 2 ■■ . — -f a; 



weight of the body as that acceleration is to the acceleration produced by 
gravity. (The weight w is the weight where g is measured.) 

Example. — Tension in a cord lifting a weight. A weight of 100 lbs. is 
lifted vertically by a cord a distance of 80 feet in 4 seconds, the velocity 
uniformly increasing from to the end of the time. What tension must 
be maintained in the cord? Mean velocity = v m =20 ft. per sec; final 

velocity = v 2 = 2 v m = 40; acceleration a = y = — = 10. Force / = 

ma = — = — X 10 = 31.1 lbs. This is the force required to pro- 
duce the acceleration only; to it must be added the force required to lift 
the weight without acceleration, or 100 lbs., making a total of 131.1 lbs. 

The Resistance to Acceleration is the same as the force required to pro- 
duce the acceleration = — V<2 ~ ■♦ 
g t 

Formulae for Accelerated Motion. — For cases of uniformly accel- 
erated motion other than those of falling bodies, we have the formulae 

already given, / = — a, = — V2 ~ — • If the body starts from rest, Vi = 0. 

IV v vt 

Vi = v, and/ = - j ; fgt = wv. We also have s = -■ Transforming and 

substituting for g its value 32.16, we obtain 

32.16.ft _ 64.32 /g. 



/ = 



64.32 s 32.16 4 16.08 1 2 ' 

wv 2 = 16.08 .ft 2 = vt m= _ Rn9 k /fs = 32.16.ft 
'64.32/ w 2* 



32.16/ 4. 



.01 V / 



y « 



502 MECHANICS. 

For any change in velocity, f=w r 2 ' ~ ^ *" ■ ) • 

(See also Work of Acceleration, under Work.) 

Motion on Inclined Planes. — The velocity acquired by a body 
descending an inclined plane by the force of gravity (friction neglected) is 
equal to that acquired by a body falling freely from the height of the plane. 

The times of descent down different inclined planes of the same height 
vary as the length of the planes. 

The rules for uniformly accelerated motion apply to inclined planes. 
If a is the angle of the plane with the horizontal, sin a = the ratio of the 

height to the length = j , and the constant accelerating force is g sin a. 

The final velocity at the end of t seconds is. v = gt sin a. The distance 
passed over in t seconds is I = 1/2 gt 2 sin a. The time of descent is 

V g sin a 4.01 Vh 

FUNDAMENTAL EQUATIONS IN DYNAMICS. 

(1) FS = 1/2 MV 2 = WH. Force into space equals energy, or work. 

(2) FT = MV. Force into time equals momentum, 

(3) F = M A = M V/T. Force equals mass into acceleration. 

(4) 7 = V2 gH. Falling bodies. 

The sign = here means "numerically equivalent to," the proper units 
of each elementary quantity being chosen. 

M = mass = Wig; W = weight in pounds, g = 32.2; F = force in 
pounds, exerted on a mass free to move; S = space, or distance in feet 
through which F is exerted; T = time in seconds; H = height in feet 
through which a body falls, or in eq. (1) is lifted; A = acceleration in feet 
per second per second, = V/T; V = velocity in feet per second acquired at 
the end of the time T, the space S, or the height of fall H. 

By these four equations and their algebraic transformations practically 
all problems in dynamics (except those relating to impact) may be solved. 

MOMENTUM, VIS-VITA. 

Momentum, in many books erroneously defined as the quantity of 
motion in a body, is the product of the mass by the velocity at any instant, 

w 
..= mv = — v. 

Since the moving force = product of mass by acceleration, / = ma; 

v mv 

and if the velocity acquired in t seconds = v, or a = j, f = — — ; ft = 

mv; that is, the product of a constant force into the time in which it acts 
equals numerically the momentum. 

Since ft = mv, if t = 1 second mv = f, whence momentum might be de- 
fined as numerically equivalent to the number of pounds of force that will 
stop a moving body in 1 second, or the number of pounds of force which 
acting during 1 second will give it the given velocity. 

Vis- viva, or living force, is a term used by early writers on Mechanics 
to denote the energy stored in a moving body. Some defined it as the 

product of the mass into the square of the velocity, mv 2 , =— v 2 ; others as 

one-half of this quantity, or lfomv 2 , or the same as what is now known as 
energy. The term is now obsolete, its place being taken by the word 
energy. 

WORK, ENERGY, POWER. 

Work is the overcoming of resistance through a certain distance. _ It is 
measured by the product of the resistance into the space through which it 
is overcome. It is also, measured by the product of the moving force into 
the distance through which the force acts in overcoming the resistance. 
Thus in lifting a body from the earth against the attraction of gravity, 



WORK, ENERGY, POWER. 503 

the resistance is the weight of the body, and the product of this weight 
into the height the body is lifted is the work done. 

The Unit of Work, in British measures, is the foot-pound, or the 
amount of work done in overcoming a pressure or weight equal to one 
pound through one foot of space. 

The work performed by a piston in driving a fluid before it, or by a fluid 
in driving a piston before it, may be expressed in either of the following 
ways: 

Resistance X distance traversed 
= intensity of pressure X area X distance traversed; 
= intensity of pressure X volume traversed. 

By intensity of pressure is meant pressure per unit of area, as lbs. per sq. in. 

The work performed in lifting a body is the product of the weight ot the 
body into the height through which its center of gravity is lifted. 

If a machine lifts the centers of gravity of several bodies at once to 
heights either the same or different, the whole quantity of work performed 
in so doing is the sum of the several products of the weights and heights; 
but that quantity can also be computed by multiplying the sum of all the 
weights into the height through which their common center of gravity is 
lifted. (Rankine.) 

Power is the rate at which work is done, and is expressed by the quo- 
tient of the work divided by the time in which it is done, or by units of 
work per second, per minute, etc., as foot-pounds per second. The most 
common unit of power is the horse-power, established by James Watt as 
the power of a strong London draught-horse to do work during a short 
interval, and used by him to measure the power of his steam-engines. 
This unit is 33,000 foot-pounds per minute = 550 foot-pounds per second 
= 1,980,000 foot-pounds per hour. 

Expressions for Force, Work, Power, etc. 

The fundamental conceptions in Dynamics are: 

Mass, Force, Time, Space, represented by the letters M, F, T, S. 

Mass = weight -*■ g. If the weight of a body is determined by a spring 
balance standardized at London it will vary with the latitude, and the 
value of g to be taken in order to find the mass is that of the latitude 
where the weighing is done. If the weight is determined by a balance 
or by a platform scale, as is customary in engineering and in commerce, 
the London value of g, = 32.2, is to be taken. 

Velocity = space divided by time, V = S -s- T, if V be uniform. 
V = 2S -s- T if V be uniformly accelerated. 

Work = force multiplied by space = FS = i/ 2 MV 2 = FVT (V uniform). 

Power = rate of work = work divided by time = FS •*■ T = P = 
product of force into uniform velocity == FV. 

Power exerted for a certain time produces work; PT = FS = FVT. 

Effort is a force which acts on a body in the direction of its motion. 

Resistance is that which is opposed to an acting force. It is equal 
and opposite to the force. 

Horse-power Hours, an expression for work measured as the product 
of a power into the time during which it acts, = PT. Sometimes it 
is the summation of a variable power for a given time, or the average power 
multiplied by the time. 

Energy, or stored work, is the capacity for performing work. It is 
measured by the same unit as work, that is, in foot-pounds. It may be 
either potential, as in the case of a body of water stored in a reservoir, 
capable of doing work by means of a water-wheel, or actual, sometimes 
called kinetic, which is the energy of a moving body. Potential energy is 
measured by the product of the weight of the stored body into the distance 
through which it is capable of acting, or by the product of the pressure it 
exerts into the distance through which that pressure is capable of acting. 
Potential energy may also exist as stored heat, or as stored chemical 
energy, as in fuel, gunpowder, etc., or as electrical energy, the measure of 
these energies being the amount of work that they are capable of perform- 
ing. Actual energy of a moving body is the work which it is capable of 
performing against a retarding resistance before being brought to rest, 
and is equal to the work which must be done upon it to bring it from a 
state of rest to its actual velocity. 



504 MECHANICS. 

The measure of actual energy is the product of the weight of the body 
into the height from which it must fall to acquire its actual velocity. If 
v = the velocity in feet per second, according to the principle of falling 

v 2 
bodies, h, the height due to the velocity, = — ; and if w = the weight, the 

energy = 1/2 fnv 2 = wv 2 -4- 2g = wh. Since energy is the capacity for perform- 
ing work, the units of work and energy are equivalent, or FS = i/2 mv 2 = wh. 
Energy exerted = work done. 

The actual energy of a rotating body whose angular velocity is A and 
A 2 1 
moment of inertia 2w 2 = /is — , that is, the product of the moment of 

inertia into the height due to the velocity, A, of a point whose distance 

from the axis of rotation is unity; or it is equal to — , in which w is the 

weight of the body and v is the velocity of the center of gyration. 

Work of Acceleration. — The work done in giving acceleration to a 
body is equal to the product of the force producing the acceleration, or of 
the resistance to acceleration, into the distance moved in a given time. 
This force, as already stated, equals product of the mass into the accelera- 
tion, or / = ma = — — • . If the distance traversed in the time t = s, 

then work = fs = -t— s. 

9 t 

Example. — What work is required to move a body weighing 100 lbs. 
horizontally a distance of 80 ft. in 4 seconds, the velocity uniformly 
increasing, friction neglected? 

Mean velocity v m = 20 ft. per second; final velocity = V2 = 2v m = 40; 

initial velocity vi = 0; acceleration, a = — — - = — = 10; force = 

-a= ^L X 10 = 31.1 lbs.; distance 80 ft.; work = fs = 31.1 X SO = 

2488 foot-pounds. 

The energy stored in the body moving at the final velocity of 40. ft. 
per second is 

1/2 mv 2 = I %2 = ^x^Te = 2488 f00t -P° urKls ' 
which equals the work of acceleration, 

. W V2 10 Vo V2 . 1 w „ 

If a body of the weight W falls from a height H, the work of acceleration 
is simply WH, or the same as the work required to raise the body to the 
same height. 

Work of Accelerated Rotation. — Let A = angular velocity of a 
solid body rotating about an axis, that is, the velocity of a particle whose 
radius is unity. Then the velocity of a particle whose radius is r is v = Ar. 
If the angular velocity is accelerated from A t to A 2 , the increase of the 
velocity of the particle is vi — Vi=r (Ai — At), and the work of accelerat- 
ing it is 

w v£ — -t>i 2 _ wr 2 A2 2 — Ai 2 
9 2 ~ g 2 

in which w is the weight of the particle. A is measured in radians. 
The work of acceleration of the whole body is 

The term 2w 2 is the moment of inertia of the body. 

" Force of the Blow " of a Steam Hammer or Other Falling 
Weight. — The question is often asked: "With what force does a falling 
hammer strike? " The question cannot be answered directly, and it 
is based upon a misconception or ignorance of fundamental mechanical 



IMPACT. 505 

laws. The energy, or capacity of doing work, of a body raised to a given 
height and let fall cannot be expressed in pounds, simply, but only in foot- 
pounds, which is the product of the weight into the height through which 
it falls, or the product of its weight -*- 64.32 into the square of the velocity, 
in feet per second, which it acquires after falling through the given height. 
If F = weight of the body, M its mass, g the acceleration due to gravity, 
*S the height of fall, and v the velocity at the end of the fall, the energy in 
the body just before striking is FS = 1/2 Mv 2 =Wv 2 -i-2ji= Wv 2 -*- 64.32, 
which is the general equation of energy of a moving body. Just as the 
energy of the body is a product of a force into a distance, so the work it 
does when it strikes is not the manifestation of a force, which can be ex- 
pressed simply in pounds, but it is the overcoming of a resistance through 
a certain distance, which is expressed as the product of the average resist- 
ance into the distance through which it is exerted. If a hammer weighing 
100 lbs. falls 10 ft., its energy is 1000 foot-pounds. Before being brought 
to rest it must do 1000 foot-pounds of work against one or more resistances. 
These are of various kinds, such as that due to motion imparted to the 
body struck, penetration against friction, or against resistance to shearing 
or other deformation, and crushing and heating of both the falling body 
and the body struck. The distance through which these resisting forces 
act is generally indeterminate, and therefore the average of the resisting 
forces, which themselves generally vary with the distance, is also indeter- 
minate. 

Impact of Bodies. — If two inelastic bodies collide, they will move on 
together as one mass, with a common velocity. The momentum of the 
combined mass is equal to the sum of the momenta of the two bodies 
before impact. If m 3 and m 2 are the masses of the two bodies and v x and v 2 
their respective velocities before impact, and v their common velocity 
after impact, (mi + m 2 )v = niiVi + m 2 v 2 , 

_ m x v x + m 2 V2 



rrti + m 2 



m,\V\ — m 2 v 2 



If the bodies move in opposite directions, v= ; — — , or the velocity 

mi + tn 2 
of two inelastic bodies after impact is equal to the algebraic sum of their 
momenta before impact, divided by the sum of their masses. 

If two inelastic bodies of equal momenta impinge directly upon one an- 
other from opposite directions they will be brought to rest. 

Impact of Inelastic Bodies Causes a Loss of Energy, and this loss 
is equal to the sum of the energies due to the velocities lost and gained 
by the bodies, respectively. 

y2miVi 1 + l/2m 2 t> 2 2 — V2 (m x + m 2 ) v 2 =1/2 mi (vi — v) 2 + 1/2 mi (vi — v) 2 ; 
in which vi — v is the velocity lost by mi and v — vi the velocity gained 
by mi. 

Example. — Let mi = 10, mi = 8, v x = 12, vi = 15. 

10 X 12 8X15 

If the bodies collide they will come to rest, for v= " = 0. 

The energy loss is 
1/2 10 X 144+ I/28 X 225 -1/2 18 X = 1/2 10(12 - 0)2+1/28(15- 0) 2 = 
1620 ft.-lbs. 

What becomes of the energy lost? Ans. It is used doing internal work 
on the bodies themselves, changing their shape and heating them. 

For imperfectly elastic bodies, let e = the elasticity, that is, the ratio 
which the force of restitution, or the internal force tending to restore the 
shape of a body after it has been compressed, bears to the force of com- 
pression; and let mi and m 2 be the masses, Vi and v 2 their velocities before 
impact, and Vi, v 2 their velocities after impact; then 



f 


m-iVi + mivi m 2 e (v t — v 2 ) 


Ul 


mi + mi mi + m 2 


Vi 


mivi + mivi m\e (v t — vi) 
pi\ + mi mi + mi 



506 MECHANICS. 



If the bodies are perfectly elastic, their relative velocities before and 
after impact are the same. That is, vi' — vi' = v 2 — vi. 

In the impact of bodies, the sum of their momenta after impact is the 
same as the sum of their momenta before impact. 

mxVi + m 2 v 2 = m 1 v 1 + m 2 v 2 . 

For demonstration of these and other laws of impact, see Smith's Me- 
chanics; also, Weisbach's Mechanics. 

Energy of Recoil of Guns. {Eng'g, Jan. 25, 1884, p. 72.) — 

Let W = the weight of the gun and carriage; 
V = the maximum velocity of recoil; 
w = the weight of the projectile; 
v = the muzzle velocity of the projectile. 

Then, since the momentum of the gun and carriage is equal to the 
momentum of the projectile (because both are acted on by equal force, 
the pressure of the gases in the gun, for equal time), we have WV = wv, 
or V = wv -5- W. 

Taking the case of a 10-inch gun firing a 400-lb. projectile with a muzzle 
velocity of 2000 feet per second, the weight of the gun and carriage being 
22 tons = 50,000 lbs., we find the velocity of recoil = 

, 7 2000 X 400 n . , , , 

V = — t- n nhn — =16 feet per second. 

Now the energy of a body in motion is WV 2 -*■ 2 g. 

Therefore the energy of recoil = 5 °'°°°* 162 = 198,800 foot-pounds. 

Ji X O — .— 

400 X 2000 2 
The energy of the projectile is - QO = 24,844,000 foot-pounds. 

Z X oZ.JL 

Conservation of Energy. — No form of energy can ever be pro- 
duced except by the expenditure of some other form, nor annihilated ex- 
cept by being reproduced in another form. Consequently the sum total of 
energy in the universe, like the sum total of matter, must always remain 
the same. (S. Newcomb.) Energy can never be destroyed or lost; it can 
be transformed, can be transferred from one body to another, but no 
matter what transformations are undergone, when the total effects of the 
exertion of a given amount of energy are summed up the result will be 
exactly equal to the amount originally expended from the source. This 
law is called the Conservation of Energy. (Cotterill and Slade.) 

A heavy body sustained at an elevated position has potential energy. 
When it falls, just before it reaches the earth's surface it has actual or 
kinetic energy, due to its velocity. When it strikes, it may penetrate the 
earth a certain distance or may be crushed. In either case friction results 
by which the energy is converted into heat, which is gradually radiated 
into the earth or into the atmosphere, or both. Mechanical energy and 
heat are mutually convertible. Electric energy is also convertible into 
heat or mechanical energy, and either kind of energy may be converted 
into the other. 

Sources of Energy. — The principal sources of energy on the earth's 
surface are the muscular energy of men and animals, the energy of the 
wind, of flowing water, and of fuel. These sources derive their energy 
from the rays of the sun. Under the influence of the sun's rays vegetation 
grows and wood is formed. The wood may be used as fuel under a steam- 
boiler, its carbon being burned to carbon dioxide. Three-tenths of its heat 
energy escapes in the chimney and by radiation, and seven-tenths appears 
as potential energy in the steam. In the steam-engine, of this seven-tenths 
six parts are dissipated in heating the condensing water and are wasted; 
the remaining one-tenth of the original heat energy of the wood is con- 
verted into mechanical work in the steam-engine, which may be used to 
drive machinery. This work is finally, by friction of various kinds, or pos- 
sibly after transformation into electric currents, transformed into heat 
which is radiated into the atmosphere, increasing its temperature. Thus 



ANIMAL POWER. 



507 



all the potential heat energy of the wood is, after various transformations, 
converted into heat, which, mingling with the store of heat in the atmos- 
phere, apparently is lost. But the carbon dioxide generated by the com- 
bustion of the wood is, again, under the influence of the sun's rays, 
absorbed by vegetation, and more wood may thus be formed having poten- 
tial energy equal to the original. 

Perpetual Motion. — The law of the conservation of energy, than 
which no law of mechanics is more firmly established, is an absolute barrier 
to all schemes for obtaining by mechanical means what is called " perpetual 
motion," or a machine which will do an amount of work greater than the 
equivalent of the energy, whether of heat, of chemical combination, of elec- 
tricity, or mechanical energy, that is put into it. Such a result would be 
the creation of an additional store of energy in the universe, which is not 
possible by any human agency. 

The Efficiency of a Machine is a fraction expressing the ratio of 
the useful work to the whole work performed, which is equal to the energy 
expended. The limit to the efficiency of a machine is unity, denoting the 
efficiency of a perfect machine in which no work is lost. The difference 
between the energy expended and the useful work done, or the loss, is 
usually expended either in overcoming friction or in doing work on bodies 
surrounding the machine from which no useful work is received. Thus 
in an engine propelling a vessel part of the energy exerted in the cylinder 
does the useful work of giving motion to the vessel, and the remainder is 
spent in overcoming the friction of the machinery and in making currents 
and eddies in the surrounding water. 

A common and useful definition of efficiency is " output divided by 
input." 



ANIMAL POWER. 

Work of a Man against Known Resistances. 



(Rankine.) 



Kind of Exertion. 


lbs. 


V, 

ft. per 

sec. 


T" 
3600 

(hours 
per 
day). 


RV, 
ft.-lbs. 
per sec. 


RVT, 

ft.-lbs. 
per day. 


1. Raising his own weight up 


143 

40 

44 

143 
6 

132 

26.5 
(12.5 
^ 18.0 
(20.0 

13.2 

15 


0.5 

0.75 
0.55 

0.13 

1.3 

0.075 

2.0 
5.0 
2.5 
14.4 
2.5 
? 


8 

6 
6 

6 

10 

10 

8 
? 

8 

2 min. 

10 

8? 


71.5 

30 

24.2 

18.5 
7.8 

9.9 

53 
62.5 

45 
288 
33 

? 


2,059,200 

648,000 
522,720 

399,600 

280,800 


2. Hauling up weights with rope, 
and lowering the rope un- 


3. Lifting weights by hand 

4. Carrying weights up-stairs 

and returning unloaded 

5. Shoveling up earth to a 


6. Wheeling earth in barrow up 
slope of 1 in 12, 1/2 horiz. 
veloc. 0.9 ft. per sec, and re- 


356,400 


7. Pushing or pulling horizon- 
tally (capstan or oar) 


1,526,400 


8. Turning a crank or winch 


1,296,000 




1,188,000 




480,000 







Explanation. — R, resistance; V, effective velocity = distance 
through which R is overcome -h total time occupied, including the time 
of moving unloaded, if any; T", time of working, in seconds per day; 
T" -*- 3600, same time, in hours per day; RV, effective power, in foot- 
pounds per second; RVT, daily work. 



508 



MECHANICS. 



Performance of a Man in Transporting Loads Horizontally. 

(Rankine.) 



Kind of Exertion. 







T" 


LV, 


L, 


V, 


3600 


lbs. 


lbs. 


ft.-sec. 


(hours 
per 


con- 
veyed 






day). 


1 foot. 


140 


5 


10 


700 


224 


12/3 


10 


373 


132 


12/3 


10 


220 


90 


21/2 


7 


225 


140 


12/3 


6 


233 


( 252 










\ 126 


11.7 




1474.2 


I o 


23.1 








LVT, 
lbs. con- 
veyed 
1 foot. 



11. Walking unloaded, viana- 

porting his own weight 

12. Wheeling load L in 2-whld. 

barrow, return unloaded . . 

13. Ditto in 1-wh. barrow, ditto. . 

14. Traveling with burden. ..... . 

15. Carrying burden, returning 

unloaded 

16. Carrying burden, for 30 sec- 

onds only 



13,428,000 
7,920,000 
5,670,000 



Explanation. — L, load; V, effective velocity, computed as before; 
T", time of working, in seconds per day; T" -*- 3600, same time in hours 
per day; LV, transport per second, in lbs. conveyed one foot; LVT, 
daily transport. 

In the first line only of each of the two tables above is the weight of 
the man taken into account in computing the work done. 

Clark says that the average net 
daily work of an ordinary laborer 
at a pump, a winch, or a crane may 
be taken at 3300 foot-pounds per 
minute, or one-tenth of a horse- 
power, for 8 hours a day; but for 
shorter periods from four to five 
times this rate may be exerted. 

Mr. Glynn says that a man may 
exert a force of 25 lbs. at the 
handle of a crane for short periods; 
but that for continuous work a 
force of 15 lbs. is all that should 
be assumed, moving through 220 
feet per minute. 

Man-wheel. — Fig.102 is a sketeh 
of a very efficient man-power hoist- 
ing-machine which the author saw 
Fig. 102. in Berne, Switzerland, in 1889. 

The face of the wheel was wide 
enough for three men to walk abreast, so that nine men could work in it 
at one time. 

Work of a Horse against a Known Resistance. (Rankine.) 




Kind of Exertion. 



1. Cantering and trotting, draw- 

ing a light railway carriage 
(thoroughbred) 

2. Horse drawing cart or boat, 

walking (draught-horse) . . . 

3. Horse drawing a gin or mill, 

walking 

4. Ditto, trotting 



min. 221/2 
mean 301/2 
max. 50 



100 
66 



V. 


T" 

3600 


RV. 


J H2/3 


4 


4471/2 


3.6 


8 


432 


3.0 
6.5 


8 
41/2 


300 
429 



8,640,000 
6,950,000 



ANIMAL POWER. 



509 



Explanation. — R, resistance, in lbs.; V, velocity, in feet per second; 
T" ■*■ 3600, hours work per day; RV, work per second; RVT, work per 
day. 

The average power of a draught-horse, as given in line 2 of the above 
table, being 432 foot-pounds per second, is 4 32/55o = 0.785 of the con- 
ventional value assigned by Watt to the ordinary unit of the rate of 
work of prime movers. It is the mean of several results of experiments, 
and may be considered the average of ordinary performance under favor- 
able circumstances. 

Performance of a Horse in Transporting Loads Horizontally. 

(Rankine.) 



Kind of Exertion. 


L. 


V. 


T. 


LV. 


LVT. 


5. Walking with cart, always 


T500 

750 

1500 
270 
180 


3.6 

. 7.2 

2.0 
3.6 
7.2 


10 
41/2 

10 
10 
7 


5400 
5400 

3000 
972 
1296 


194,400,000 




87,480,000 


7. Walking with cart, going 

loaded, returning empty; 
V, mean velocity 

8. Carrying burden, walking . . 


108,000,000 
34,992,000 
32,659,200 







Explanation. — L, load in lbs. ; V, velocity in feet per second ; T, work- 
ing hours per day; LV, transport per second; LVT, transport per day. 

This table has reference to conveyance on common roads only, and 
those evidently in bad order as respects the resistance to traction upon 
them. 

Horse-Gin. — In this machine a horse works less advantageously 
than in drawing a carriage along a straight track. In order that the best 
possible results may be realized with a horse-gin, the diameter of the cir- 
cular track in which the horse walks should not be less than about forty 
feet. 

Oxen, 31ules, Asses. — Authorities differ considerably as to the power 
of these animals. The following may be taken as an approximative com- 
parison between them and draught-horses (Rankine): 

Ox. — Load, the same as that of average draught-horse; best velocity 
and work, two-thirds of horse. 

Mule. — Load, one-half of that of average draught-horse; best velocity, 
the same as horse; work, one-half. 

Ass. — Load, one-quarter that of average draught-horse; best velocity, 
the same; work, one-quarter. 

Reduction of Draught of Horses by Increase of Grade of Roads. 
(Engineering Record, Prize Essays on Roads, 1892.) — Experiments on 
English roads by Gay frier & Parnell: 

Calling load that can be drawn on a level 100: 

On a rise of 1 in 100. 1 in 50. 1 in 40. 1 in 30. 1 in 26. 1 in 20. 1 in 10. 

A horse can draw only 90 81 72 64 54 40 25 

The Resistance of Carriages on Roads is (according to Gen. Morin) 
given approximately by the following empirical formula: 

W 

r = IL [a + b (u - 3.28)]. 



In this formula R — total resistance; r = radius of wheel in inches; 
W = gross load; u = velocity in feet per second; while a and b are 
constants, whose values are: For good broken-stone road, a = 0.4to0.55, 
b = 0.024 to 0.026; for paved roads, a = 0.27, b = 0.0684. 

Rankine states that on gravel the resistance is about double, and on 
sand five times, the resistance on good broken-stone roads. 



510 MECHANICS. 



ELEMENTS OF MACHINES. 

The object of a machine is usually to transform the work or mechanical 
energy exerted at the point where the machine receives its motion into 
work at the point where the final resistance A r. d 

is overcome. The specific result may be to 
change the character or direction of mo- 
tion, as from circular to rectilinear, or vice 



\ 6* 



6w 



a 

Ow 



versa, to change the velocity, or to overcome L (\w 

a great resistance by the application of a W 
moderate force. In all cases the total energy p 1n „ 

exerted equals the total work done, the latter G - IUd ' 

including the overcoming of all the frictional 
resistances of the machine as well as the use- 
ful work performed. No increase of power 
can be obtained from any machine, since this 

is impossible according to the law of conser- _] B 

vationof energy. In a frictionless machine the 
product of the force exerted at the driving- 
point into the velocity of the driving-point, 
cr the distance it moves in a given interval 
of time, equals the product of the resistance 
into the distance through which the resist- Fl 104 

ance is overcome in the same time. 

The most simple machines, or elementary 
machines, are reducible to three classes, viz., 
the Lever, the Cord, and the Inclined Plane. 

The first class includes every machine con- 
sisting of a solid body capable of revolving B 
on an axis, as the Wheel and Axle. 

The second class includes every machine in 
which force is transmitted by means of flexi- 
ble threads, ropes, etc., as the Pulley. vJW 

The third class includes every machine in jr IG jq5 

which a hard surface inclined to the direc- 
tion of motion is introduced, as the Wedge and the Screw. 

A Lever is an inflexible rod capable of motion about a fixed point, 
called a fulcrum. The rod may be straight or bent at any angle, or 
curved. 

It is generally regarded, at first, as without weight, but its weight may 
be considered as another force applied in a vertical direction at its center 
of gravity. 

The arms of a lever are the portions of it intercepted between the force, 
P, and fulcrum, C, and between the weight or load, W, and fulcrum. 

Levers are divided into three kinds or orders, according to the relative 
positions of the applied force, load, and fulcrum. 

In a lever of the first order, the fulcrum lies between the points at which 
the force and load act. (Fig. 103 ) 

In a lever of the second order, the load acts at a point between the 
fulcrum and the point of action of the force. (Fig. 104.) 

In a lever of the third order, the point of action of the force is between 
that of the load and the fulcrum. (Fig. 105.) 

In all cases of levers the relation between the force exerted or the pull, 
P, and the load lifted, or resistance overcome, W, is expressed by the 
equation P X AC = W X BC, in which AC is the lever-arm of P, and 
BC is the lever-arm of W, or moment of the force = the moment of the 
resistance. (See Moment.) 

In cases in which the direction of the force (or of the resistance) is not 
at right angles to the arm of the lever on which it acts, the "lever-arm" 
is the length of a perpendicular from the fulcrum to the line of direction 
of the force (or of the resistance). W : P : : AC : BC, or, the ratio of 
the resistance to the applied force is the inverse ratio of their lever-arms. 
Also, if Vwis the velocity of W, and Vp is the velocity of P, W : P : : Vp: 
Vw, and P X Vp = W X Vw. 

If Sp is the distance through which the applied force acts, and Sw is 
the distance the load is lifted or through which the resistance is over- 
come, W : P : : Sp : Sw : W X Sw = P X Sp, or the load into the dis- 



ELEMENTS OF MACHINES. 



511 



tance it is lifted equals the force into the distance through which it is 
exerted. 

These equations are general for all classes of machines as well as for 
levers, it being understood that friction, which in actual machines in- 
creases the resistance, is not at present considered. 

The Bent Lever. — In the bent lever (see Fig. 96, p. 490), the lever- 
arm of the weight m is cf instead of bf. The lever is in equilibrium when 
n X af — m X cf, but it is to be observed that the action of a bent lever 
may be very different from that of a straight lever. In the latter, so 
long as the force and the resistance act in lines parallel to each other, the 
ratio of the lever-arms' remains constant, although the lever itself changes 
its inclination with the horizontal. In the bent lever, however, this 
ratio changes: thus, in the cut, if the arm bf is depressed to a horizontal 
direction, the distance cf lengthens while the horizontal projection of 
af shortens, the latter becoming zero when the direction of af becomes 
vertical. As the arm af approaches the vertical, the weight m which 
may be lifted with a given force s is very great, but the distance through 
which it may be lifted is very small. In all cases the ratio of the weight 
m to the weight n is the inverse ratio of the horizontal projection of their 
respective lever-arms. 

The Moving Strut (Fig. 106) is similar to the bent lever, except that 
one of the arms is missing, and that the force and the resistance to be 
overcome act at the same end of the 
single arm. The resistance in the 
case shown in the cut is not the load 
W, but its resistance to being 
moved, R, which may be simply 
that due to its friction on the hori- 
zontal plane, or some other oppos- 
ing force. When the angle between 
the strut and the horizontal plane 
changes, the ratio of the resistance 
to the applied force changes. When 
the angle becomes very small, a 
moderate force will overcome a 
very great resistance, which tends 
to become infinite as the angle ap- 
proaches zero. If a =the angle, P X cos a = R X sin a. 
cos a = 0.99619, sin a = 0.08716, R = 11.44 P. 

The stone-crusher (Fig. 107) shows a practical example of the use of 
two moving struts. 

The Toggle-joint is an elbow or knee-joint consisting of two bars so 
connected that they may be brought into a straight line and made to 
produce great endwise pressure when a force is applied to bring them 
into this position. It is a case of two moving struts placed end to end, 




Fig. 106. 



If a = 5 degrees, 





Fig. 107. 



Fig. 108. 



the moving force being applied at their point of junction, in a direction 
at right angles to the direction of the resistance, the other end of one of 
the struts resting against a fixed abutment, and that of the other against 
the body to be moved. If a=the angle each strut makes with the straight 
line joining the points about which their outer ends rotate, the ratio of 
the resistance to the applied force is R : P ' : : cos a : 2 sin a ; 2 R sin a 
= P cos a. The ratio varies when the angle varies, becoming infinite 
when the angle becomes zero. 



512 



MECHANICS. 




Fig. 109. 



The toggle-joint is used where great resistances are to be overcome 
through very small distances, as in stone-crushers (Fig. 108). 

The Inclined Plane, as a mechanical element, is supposed perfectly 
hard and smooth, unless friction be considered. It assists in sustaining 
a heavy body by its reaction. This reaction, however, being normal to 
the plane, cannot entirely counteract the weight of the body, which acts 
vertically downward. Some other force must 
therefore be made to act upon the body, in order 
that it may be sustained. 

If the sustaining force act parallel to the plane 
(Fig. 109), the force is to the weight as the height 
of the plane is to its length, measured on the 
incline. 

If the force act parallel to the base of the 
plane, the force is to the weight as the height is 
to the base. 

If the force act at any other angle, let i = the 
angle of the plane with the horizon, and e= the 
angle of the direction of the applied force with the angle of the plane. 
P : W : : sin i : cos e; PX cos e = W sin i. 

Problems of the inclined plane may be solved by£the parallelogram of 
forces thus: 

Let the weight W be kept at rest on the incline by the force P, acting 
in the line bP' , parallel to the plane. Draw the vertical line ba to repre- 
sent the weight; also bb' perpendicular to the plane, and complete the 
parallelogram b'c. Then the vertical weight bais the resultant of bb' , the 
measure of support given by the plane to the weight, and be, the force of 
gravity tending to draw the weight down the plane. The force required 
to maintain the weight in equilibrium is represented by this force be. 
Thus the force and the weight are in the ratio of be to ba. Since the 
triangle of forces abc is similar to the triangle of the incline ABC, the 
latter may be substituted for the former in determining the relative 
magnitude of the forces, and 

P : W : : be : ab : : BC : AB. 
The Wedge is a pair of inclined planes united by their bases. In the 
application of pressure to the head or butt end of the wedge, to cause it to 
penetrate a resisting body, the applied force is to the resistance as the 
thickness of the wedge is to its length. Let t be the thickness, I the length, 
IF the resistance, and Pthe applied force or pressure on the head of the 

wedge. Then, friction neglected, P; W : : t : I; P = -— ; W = -r- 

The Screw is an inclined plane wrapped around a cylinder in such a 
way that the height of the plane is parallel to the axis of the cylinder. If 
the screw is formed upon the internal surface of a hollow cylinder, it is 
usually called a nut. When force is applied to raise a weight or overcome 
a resistance by means of a screw and nut, either the screw or the nut may 
be fixed, the other being movable. The force is generally applied at the 
end of a wrench or lever-arm, or at the circumference of a wheel. If r = 
radius of the wheel or lever-arm, and p = pitch 
of the screw, or distance between threads, that 
is, the height of the inclined plane for one revo- 
lution of the screw, P = the applied force, and 
W = the resistance overcome, then, neglecting 
resistance due to friction, 2 irr X P = Wp; W 
= 6.283 Pr -*- p. The ratio of P to W is thus 
independent of the diameter of the screw. In 
. actual screws, much of 
the power transmitted is 
lost through friction. 

The Cam is a revolv- 
ing inclined plane. It 
may be either an in- 
clined plane wrapped 
around a cylinder in such 
a way that the height of jr IG ] 

the plane is radial to the 
cylinder, such as the ordinary lifting-cam, used in stamp-mills (Fig. 110), 





ELEMENTS OF MACHINES. 



513 



or it may be an inclined plane curved edgewise, and rotating in a plane 
parallel to its base (Fig. 111). The relation of the weight to the applied 
force is calculated in the same manner as in the case of the screw. 

Pulleys or Blocks. — P = force applied, or pull; W = load lifted, 
or resistance. In the simple pulley A (Fig. 112) the point P on the 
pulling rope descends the same amount that the load is lifted, therefore 
P = W. In B and C the point P moves twice as far as the load is lifted, 
therefore W = 2 P. In B and C there is one movable block, and two 
plies of the rope engage with it. In D there are three sheaves in the 
movable block, each with two plies engaged, or six in all. Six plies of 
the rope are therefore shortened by the same amount that the load is 
lifted, and the point P moves six times as far as the load, consequently 




W — 6 P. In general, the ratio of W to P is equal to the number of plies 
of the rope that are shortened, and also is equal to the number of plies that 
engage the lower block. If the lower block has 2 sheaves and the upper 
3, the end of the rope is fastened to a hook in the top of the lower block, 
and then there are 5 plies shortened instead of 6, and W= 5 P. If 7 = 
velocity of W, and v = velocity of P, then in all cases VW = vP, whatever 
the number of sheaves or their arrangement. If the hauling rope, at the 
pulling end, passes first around a sheave in the upper or stationary block, 
it makes no difference in what direction the rope is led 
from this block to the point at which the pull on the 
rope is applied ; but if it first passes around the movable 
block, it is necessary that the pull be exerted in a direc- 
tion parallel to the line of action of the resistance, or a 
line joining the centers of the two blocks, in order to 
obtain the maximum effect. If the rope pulls on the 
lower block at an angle, the block will be pulled out of 
the line drawn between the load and the upper block, 
and the effective pull will be less than the actual pull 
on the rope in the ratio of the cosine of the angle the 
pulling rope makes with the vertical, or line of action of 
the resistance, to unity. 

Differential Pulley. (Fig. 113.)— Two pulleys, B 
and C, of different radii, rotate as one piece about a 
fixed axis, A. An endless chain, BDECLKH, passes 
over both pulleys. The rims of the pulleys are shaped 
so as to hold the chain and prevent it from slipping. 
One of the bights or loops in which the chain hangs, DE, 
passes under and supports the running block F. The 
other loop or bight, HKL, hangs freely, and is called the 
hauling part. It is evident that the velocity of the haul- 
ing part is equal to that of the pitch-circle of the pulley B. 

In order that the velocity-ratio may be exactly 
uniform, the radius of the sheave F should be an exact 
mean between the radii of B and C. 

Consider that the point B of the cord BD moves through an arc whose 
length = AB, during the same time the point C or the cord CE will 




514 



MECHANICS. 



threads wind the same way. 

Si s 2 r 



Fig. 115. 




Fig. 114. 



move downward a distance = AC. The length of the bight or loop 
BDEC will be shortened by AB — AC, which will cause the pulley F to 
be raised half of this amount. If P = the pulling force on the cord HK, 
and W the weight lifted at F, then P X AB = W X 1/2 (AB -AC). 

To calculate the length of chain required for a differential pulley, take 
the following sum: Half the circumference of A + half the circumference 
of B + half the circumference of F + twice the greatest distance of F 
from A + the least length of loop HKL. The last quantity is fixed 
according to convenience. 

The Differential Windlass (Fig. 114) is identical in principle with the 
differential pulley, the difference in construction being that in the dif- 
ferential windlass the running block hangs in the 
bight of a rope whose two parts are wound round, 
and have their ends respectively made fast to two 
barrels of different radii, which rotate as one piece 
about the axis A. The differential windlass is 
little used in practice, because of the great length 
of rope which it requires. 

The Differential Screw (Fig. 115) is a com- 
pound screw of different pitches, in which the 
. JVi and N2 are the 

two nuts; S1S1, 

the longer-pitched 

thread; S 2 Sn. the 

short er-pi t ch ed 

thread: in the figure 

both these threads 

are left-handed. At 
each turn of the screw the nut N 2 advances relatively to Ni through a 
distance equal to the difference of the pitches. The use of the differential 
screw is to combine the slowness of advance due to a fine pitch with 
the strength of thread which can be obtained by means of a coarse 
pitch only. 

A Wheel and Axle, or Windlass, resembles two pulleys on one axis, 
having different diameters. If a weight be lifted by means of a rope 
wound over the axle, the force being applied at the rim of the wheel, 
the action is like that of a lever of which the shorter arm is equal to the 
radius of the axle plus half the thickness of the rope, and the longer 
arm is equal to the radius of the wheel. A wheel and axle is therefore 
sometimes classed as a perpetual lever. If P = the applied force, D — 
diameter of the wheel, 17 = the weight lifted, and d the diameter of the 
axle + the diameter of the rope, PD = Wd. 

Toothed-wheel Gearing is a combination of. two or more wheels and 
axles (Fig. 116). If a series of wheels and pinions gear into each other, 
as in the cut, friction neglected, the weight lifted, or resistance over- 
come, is to the force applied inversely as the distances through which 
they act in a given time. If R, Ri, Ri be the radii of the successive wheels, 
measured to the pitch-line of the teeth, and r, r t , r 2 the radii of the cor- 
responding pinions, P the applied force, and W the weight lifted, f X 
R X Ri X R2 = W X r X n X ri, or the applied force is to the weight 
as the product of the radii of the pinions is to the product of the radii of 
the wheels; or, as the product of the numbers expressing the teeth in 
each pinion is to the product of the numbers expressing the teeth in each 
wheel. 

Endless Screw, or Worm-gear. (Fig. 117.) — This gear is com- 
monly used to convert motion at high speed into motion at very slow 
speed. When the handle P describes a complete circumference, the pitch- 
line of the cog-wheel moves through a distance equal to the pitch of the 
screw, and the weight W is lifted a distance equal to the pitch of the screw 
multiplied by the ratio of the diameter of the axle to the diameter of the 

J)itch-circle of the wheel. The ratio of the applied force to the weight 
ifted is inversely as their velocities, friction not being considered; but the 
friction in the worm-gear is usually very great, amounting sometimes to 
three or four times the useful work done. 

If v = the distance through which the force P acts in a given time, say 
1 second, and V = distance the weight W is lifted in the same time, r = 
radius of the crank or wheel through which P acts, t = pitch of the screw, 



STRESSES IN FRAMED STRUCTURES. 



515 



and also of the teeth on the cog-wheel, d = diameter of the axle, and 

6 283 v D 
D = diameter of the pitch-line of the cog-wheel, v = - L -r — -r X V; 

V= vXtd -T- 6.283 rD. Pv = WV+ friction. 





STRESSES IN FRAMED STRUCTURES. 

Framed structures in general consist of one or more triangles, for the 
reason that the triangle is the one polygonal form whose shape cannot be 
changed without distorting one of its sides. Problems in stresses of 
simple framed structures may generally be solved either by the applica- 
tion of the triangle, parallellogram, or polygon of forces, by the principle 
of the lever, or by the method of moments. We shall give a few ex- 
amples, referring the student to the works of Burr, Dubois, Johnson, and 
others for more elaborate treatment of the subject. 

1. A Simple Crane. (Figs. 118 and 119.) — A is a fixed mast, B a 
brace or boom, T a tie, and P the load. Required the strains in B and T. 
The weight P, considered as acting at the end of the boom, is held in 
equilibrium by three forces: first, gravity acting downwards; second, the 
tension in T; and third, the thrust of B. Let the length of the line p 
represent the magnitude of the downward force exerted by the load, and 
draw a parallelogram with sides bt parallel, respectively, to B and T, 
such that p is the diagonal of the parallelogram. Then b and t are the 
components drawn to the same scale as p, p being the resultant. Then 
if the length p represents the load, t is the tension in the tie, and b is the 
compression in the brace. 

Or, more simply, T, B, and that portion of the mast included between 
them or A' may represent a triangle of forces, and the forces are propor- 
tional to the length of the sides of the triangle; that is, if the height of the 




J 


t 


rl 


T/ // 
// 


-^ 


— \ 


*- % 



© 



Fig. 118. 



Fig. 120 



triangle A' — the load, then B = the compression in the brace, and T = 
the tension in the tie; or if P = the load in pounds, the tension in T *= 

P X -77 » and the compression in B = P X -ry Also, if a = the angle 

the inclined member makes with the mast, the other member being 



516 



MECHANICS. 



horizontal, and the triangle being right-angled, then the length of the 
inclined member = height of the triangle X secant a, and the strain in the 
inclined member = P secant a. Also, the strain in the horizontal 
member = P tan a. 

The solution by the triangle or parallelogram of forces, and the equa- 
tions Tension in T=PX T/A', and Compression in B = PX B/A', hold true 
even if the triangle is not right-angled, as in Fig. 120; but the trigono- 
metrical relations above given do not hold, except in the case of a right- 
angled triangle. It is evident that as A' decreases, the strain in both T 
and B increases, tending to become infinite as A' approaches zero. If 
the tie T is not attached to the mast, but is extended to the ground, as 
shown in the -dotted line, the tension in it remains the same. 

2. A Guyed Crane or Derrick. (Fig. 121.) — The strain in B is, as 
before, P X B/A', A' being that portion of the vertical included between 
B and T, wherever T may be attached to A. If, however, the tie T is 
attached to B beneath its extremity, there may be in addition a bending 
strain in B due to a tendency to turn about the point of attachment of T 
as a fulcrum. 

The strain in T may be calculated by the principle of moments. The 
moment of P is Pc, that is, its weight X its perpendicular distance from 
the point of rotation of B on the mast. The moment of the strain on T 
is the product of the strain into the perpendicular distance from the line 
«*. — ?L_ 

T 




Fig. 121. 

of its direction to the same point of rotation of B, or Td. The strain in 
T therefore = Pc •*■ d. As d decreases, the strain on T increases, tending 
to infinity as d approaches zero. 

The strain on the guy-rope is also calculated by the method of moments. 
The moment of the load about the bottom of the mast O is, as before, Pc. 
If the guy is horizontal, the strain in it is F and its moment is Ff, and F = 
Pc -r- /. If it is inclined, the moment is the strain G X the perpendicular 
distance of the line of its direction from O, or Gg, and G = Pc ■*■ g. 

The guy-rope having the least strain is the horizontal one F, and the 
strain in G.= the strain in F X the secant of the angle between F and 
G. As G is made more nearly vertical g decreases, and the strain increases, 
becoming infinite when g = 0. 

3. Shear-poles with Guys. 
(Fig. 122.) — First assume that 
the two masts act as one placed 
at BD, and the two guys as 
one at AB. Calculate the strain 
in BD and AB as in Fig. 120. 
Multiply half the strain in BD 
(or AB) by the secant of half 
the angle the two masts (or 
guys) make with each other to 
find the strain in each mast (or 
guy). 

Two Diagonal Braces and 
a Tie-rod. (Fig. 123.) — Sup- 
pose the braces are used to 
Compressive stress on AD = 1/2 P X AD 
AB. This is true only if CB and BD 




Fig. 122. 



sustain a single load P. 
v i5; on Ci = 1/2 PX CA 



STRESSES IN FRAMED STRUCTURES. 



517 



are of equal length, in which case 1/2 of P is supported by each abutment 
C and D. If they are unequal in length (Fig. 124), then, by the principle 
of the lever, find the reactions of the abutments Pi and R 2 . If P is the 
load applied at the point B on the lever CD, the fulcrum being D, 
then Bi X CD = P X BD and Ri X CD = P X BC; Ri = PX BD + CD; 
P 2 = PX BC + CD. 

The strain on AC = Ri X AC -*> AS, and on AD = #2 X AD -*- AS. 

The strain on the tie = RiX CB + AB = R2X BD + AB. 

When CP = BD, Ri — R2. The strain on CB and BD is the same, 
whether the braces are of equal length or not, and is equal to 1/2 P X 
1/2 CD •*■ AB. 






Fig. 125. 



Fig. 124. 

If the braces support a uniform load, as a pair of rafters, the strains 
caused by such a load are equivalent to that caused by one-half of the 
load applied at the center. The horizontal thrust of the braces against 
each other at the apex equals the tensile strain in the tie. 

King-post Truss or Bridge. (Fig. 125.) — If the load is distributed 
over the whole length of the truss, the effect is the same as if half the 
load were placed at the center, the other 
half being carried by the abutments. Let 
P = one-half the load on the truss, then 
tension in the vertical tie A B = P. Com- 
pression in each of the inclined braces 
= l/ 2 P X AD -4- AB. Tension in the tie 
CD = 1/2 P X BD + AB. Horizontal 
thrust of inclined brace AD at D = the 
tension in the tie. If W = the total 
load on one truss uniformly distributed, 
I = its length and d = its depth, then 
the tension on the horizontal tie = Wl ■*■ 8 d. 

Inverted King-post Truss. (Fig. 126.) — If P = a load applied at B, 
or one-half of a uniformly distributed load, then compression on AB = P 
(the floor-beam CD not being considered 
to have any resistance to a slight bend- 
ing). Tension on AC or AD = V2 P 
X AD h- AB. Compression on CD = 
1/2 P X BD + AB. 

Queen-post Truss. (Fig. 127.) — If 
uniformly loaded, and the queen-posts 
divide the length into three equal bays, 
the load may be considered to be divided 
into three equal parts, two parts of 
which, Pi and P2, are concentrated at the panel joints and the remainder 
is equally divided between the 
abutments and supported by them 
directly. The two parts Pi and P2 
only are considered to affect the 
members of the truss. Strain in 
the vertical ties BE and CF each 
equals Pi or P2. Strain on AB and 
CD each = Pi X CD +- CF. Strain 
on the tie AE or EF or PD = Pi X 
t-, , 07 FD-i- CF. Thrust on BC = tension 

Fig. 127. on EF ^ 

For stability to resist heavy unequal loads the queen-post truss should 
have diagonal braces from B to F and from C to E. 




Fig. 126. 




518 



MECHANICS. 



Inverted Queen-post Truss. (Fig. 128.) — Compression on EB and 
FC each = Pi or P 2 . Compression on AB or BC or CD = Pi X AP -*-#P. 
Tension on A E or FD = Pi X AP -*- 
PP. Tension on EF = compression 
on BC. For stability to resist 
unequal loads, ties rhouid be run 
from C to E and from B to P. 

Burr Truss of Five Panels. 
(Fig. 129.) — Four-fifths of the load 
may be taken as concentrated at the 
points P, K, L and P, the other fifth 
being supported directly by the two 
abutments. For the strains in BA 
and CD the truss may be considered as a queen-post truss, with the loads 
Pi, P2 concentrated at E, and the loads P 3 , P 4 concentrated at P Then 
compressive strain on AB = {Pi + P 2 ) x AB -=- BE. The strain on 
CD is the same if the loads and panel lengths are equal. The tensile 




Fig. 128. 




Fig. 129. 

strain on BE or CF = Pi + P 2 . That portion of the truss between E 
and P may be considered as a smaller queen-post truss, supporting the 
loads P 2 , Pz at K and L. The strain on EG or HF = P 2 X EG + GK. 
The diagonals GL and KH receive no strain unless the truss is unequally 
loaded. The verticals GK and HL each receive a tensile strain equal to 
P2 or P 3 . 

For the strain in the horizontal members: BG and CH receive a thrust 
equal to the horizontal component of the thrust in AB or CD, = (Pi + P 2 ) 
X tan angle ABE, or (Pi + P 2 ) x AE ^ BE. GH receives this thrust, 
and also, in addition, a thrust equal to the horizontal component of the 
thrust in EG or HF, or, in all, (Pi 4- P 2 + P 3 ) X AE + BE. 

The tension in AE or FD equals the thrust in BG or HC, and the ten- 
sion in EK, KL, and LF equals the thrust in GH. 

Pratt or Whipple Truss. (Fig. 130.) — In this truss the diagonals are 
ties, and the verticals are struts or columns. 

Calculation by the method of distribution of strains: Consider first the 
load Pi. The truss having six bays or panels, 5/6 of the load is trans- 
mitted to the abutment H, and l/e to the abutment 0, on the principle 
of the lever. As the five-sixths must be transmitted through J A and 
AH, write on these members the figure 5. The one-sixth is transmitted 
successively through JC, CK, KD, DL, etc., passing alternately through 
a tie and a strut. Write on these members, up to the strut GO inclusive, 
the figure 1. Then consider the load P 2 , of which 4/ 6 goes to AH and 
2/6 to GO. Write on KB, BJ, J A, and AH the figure 4, and on KD, 
DL, LE, etc., the figure 2. The load P 2 transmits 3/ 6 in each direction; 
write 3 on each of the members through which this stress passes, and so 
on for all the loads, when the figures on the several members will appear 
as on the cut. Adding them up, we have the following totals: 

Tension on diagonals \ AJ BH BK CJ CL DK DM EL EN FM F0 GN 
.tension on aiagonaisj 15 10 x 6 3 3 6 1 10 ,0 15 

Compression on verticals {*$ f Q J C f D Q L E f ™ <*> 

Each of the figures in the first line is to be multiplied by Ve P X secant 
of angle HAJ, or l/e P X AJ •*■ AH, to obtain the tension, and each 



STRESSES IN FRAMED STRUCTURES. 



519 



figure in the lower line is to be multiplied by l/ 6 P to obtain the com- 
pression. The diagonals HB and FO receive no -strain. 

It is common to build this truss with a diagonal strut at HB instead 
of the post HA and the diagonal AJ; in which case 5/ 6 f the load P is 
carried through JB and the strut BH, which latter then receives a strain 
= 15 /6 P X secant of HBJ. 




OOO 

fi f 2 P 3 P 4 h 

Fig. 130. 

The strains in the upper and lower horizontal members or chords in- 
crease from the ends to the center, as shown in the case of the Burr 
truss. AB receives a thrust equal to the horizontal component of the 
tension in AJ, or 15/6 P X tan A JB. BC receives the same thrust + 
the horizontal component of the tension in BK, and so on. The tension 
in the lower chord of each panel is the same as the thrust in the upper 
chord of the same panel. (For calculation of the chord strains by the 
method of moments, see below.) 

The maximum thrust or tension is at the center of the chords and is 
WL 
equal to ^j-> in which W is the total load supported by the truss, L is 

the length, and D the depth. This is the formula for maximum stress in 
the chords of a truss of any form whatever. 

The above calculation is based on the assumption that all the loads 
Pi, P2, etc., are equal. If they are unequal, the value of each has to be 
taken into account in distributing the strains. Thus the tension in AJ, 
with unequal loads, instead of being 15 X V6P secant would be seed 
X (5/e Pi + 4/e P2 + 3/ 6 P 3 + 2/ 6 P 4 + 1/6 P 5 ). Each panel load, Pi, etc., 
includes its fraction of the weight of the truss. 

General Formula for Strains in Diagonals and Verticals. — Let 
n = total number of panels, x = number of any vertical considered from 
the nearest end, counting the end as 1, r = rolling load for each panel, 
P = total load for each panel, 

_. [(n-x) + (n-x) 2 -(x-l) + (x-l)*] P r(x-l) + (x-l)* 



Strain on verticals = 



2ft 



For a uniformly distributed load, leave out the last term, 
[r (x - 1) + (x - 1) 2 J v2ji. 

Strain on principal diagonals (AJ, GN, etc.) = strain on verticals 
X secant 0, that is secant of the angle the diagonal makes with the 
vertical. 

Strain on the counterbraces (BH, CJ, FO, etc.): The strain on the 
counterbrace in the first panel is 0, if the load is uniform. On the 2d, 

3d, 4th, etc., it is P secant X ^ » 1 -~ < 1+ ^ +3 , etc., P being the total 
load in one panel. 

Strain in the Chords — Method of 31oments. — Let the truss be 
uniformly loaded, the total load acting on it = W. Weight supported at 
each end, or reaction of the abutment = W/2. Length of the truss = L. 
Weight on a unit of length = W/L. Horizontal distance from the nearest 
abutment to the point (say M in Fig. 130) in the chord where the strain 
is to be determined = x. Horizontal strain at that point (tension on the 
lower chord, compression in the upper) = H. Depth of the truss = D. 



520 



MECHANICS. 



By the method of moments we take the difference of the moments, about 
the point M, of the reaction of the abutment and of the load between 
M and the abutments, and equate that difference with the moment of 
the resistance, or of the strain in the horizontal chord, considered with 
reference to a point in the opposite chord, about which the truss would 
turn if the first chord were severed at M . 

The moment of the reaction of the abutment is Wx/2. The moment of 

the load from the abutment to M is (W/Lx) X the distance of its center of 

gravity from M , which is x/2, or moment = Wx 2 -5- 2 L. Moment of the 

Wx Wx 2 W / x 2 \ 

stress in the chord = HD = — — — -5-^- - whence H — — I x - -=-!• 



If x = or L, H ■■ 



Itx 



2 
■ L/2, 



II 



WL 
8D' 



which is the horizontal 



strain at the middle of the chords, as before given. 




Fig. 131. 

The Howe Truss. (Fig. 131.) — In the Howe truss the diagonals are 
struts, and the verticals are ties. The calculation of strains may be made 
in the same method as described above for the Pratt truss. 

The Warren Girder. (Fig. 132.) — In the Warren girder, or triangu- 
lar truss, there are no vertical struts, and the diagonals may transmit either 
tension or compression. The strains in the diagonals may be calculated by 
the method of distribution of strains as in the case of the rectangular truss. 




Fig. 132. 

On the principle of the lever, the load Pi being 1/10 of the length of the 
span from the line of the nearest support a, transmits 9/io of its weight to 
a and 1/10 to g. Write 9 on the right hand of the strut la, to represent the 
compression, and 1 on the right hand of 16, 2c, 3d, etc., to represent com- 
pression, and on the left hand of b2, c3, etc., to represent tension. The 
load Pi transmits T/\.o of its weight to a and 3/i to g. Write 7 on each 
member from 2 to a, and 3 on each member from 2 to g, placing the figures 
representing compression on the right hand of the member, and those 
representing tension on the left. Proceed in the same manner with all 
the loads, then sum up the figures on each side of each diagonal, and 
write the difference of each sum beneath, and on the side of the greater 
sum, to show whether the difference represents tension or compression. 
The results are as follows: Compression, la, 25; 2b, 15; 3c, 5; 3d, 5; 4e, 15; 
5a, 25. Tension, lb, 15; 2c, 5; 4d, 5;5e, 15. Each of these figures is to 



STRESSES IN FRAMED STRUCTURES. 



521 



be multiplied by 1/10 of one of the loads as Pi, and by the secant of the 
angle the diagonals make with a vertical line. 

The strains in the horizontal chords may be determined by the method 
of moments as in the case of rectangular trusses. 

Roof-truss. — Solution by Method of Moments. — The calculation of 
strains in structures by the method of statical moments consists in taking 
a cross-section of the structure at a point where there are not more than 
three members (struts, braces, or chords). 

To find the strain in either one of these members take the moment about 
the intersection of the other two as an axis of rotation. The sum of the 
moments of these members must be if the structure is in equilibrium. 
But the moments of the two members that pass through the point of ref- 
erence or axis are both 0, hence one equation containing one unknown 
quantity can be found for each cross-section. 




Fig. 133. 



In the truss shown in Fig. 133 take a cross-section at ts, and determine 
the strain in the three members cut by it, viz., CE, ED, and DF. Let 
X = force exerted in direction CE, Y = force exerted in direction DE, 
Z = force exerted in direction FD. 

For X take its moment about the intersection of Y and Z at D = Xx. 
For Y take its moment about the intersection of X and Z at A = Yy. 
For Z take its moment about the intersection of X and Y at E = Zz. 
Let z = 15, x = 18.6, y = 38.4, AD = 50, CD = 20 ft. Let P a , P 2 , 
P 3 , Pa be equal loads, as shown, and 3 1/2 P the reaction of the abutment A. 

The sum of all the moments taken about D or A or E will be when the 
structure is at rest. Then - Xx + 3.5 P X 50 - P 3 X 12.5 - P 2 X 25 

- Pi X 37.5 = 0. 

The +■ signs are for moments in the direction of the hands of a watch or 
" clockwise " and — signs for the reverse direction or anti-clockwise. Since , 
P = Pi = P2 = P 3 , - 18.6 X + 175 P - 75 P = 0; - 18.6 X = - 100 P; 
X = 100 P-5- 18.6 = 5.376 P. 

- Yy + P 3 X 37.5 + P 2 X 25 + Pi X 12.5 = 0; 38.4 Y = 75 ,; Y = 

75 P h- 38.4 = 1.953 P. 

- Zz + 3.5 PX 37.5 - PiX 25 - P 2 X 12.5 - P 3 X = 0; 15 Z = 

93.75 P;Z = 6.25 P. 
In the same manner the forces exerted in the other members have been 
found as follows: EG = 6.73 P;G J = 8.07 P; J A = 9A2P;JH = 1.35 P; 
GF = 1.59 P; AH = 8.75 P; HF = 7.50 P. 

The Fink Roof-truss. (Fig. 134.) — An analysis by Prof. P. H. 
hilbrick {Van N„ Mag., Aug., 1880) gives the following results: 
W= total load on roof; 
JV== No. of panels on both rafters; 
W/N= P = load at each joint b, d, f, etc.; 
V= reaction at A = 1/2 W = 1/2 NP = 4P; 
AD= S; AC = L; CD = D; 
ti,h,tz= tension on De, eg, gA, respectively; 
ci, C2, c 3 , c 4 = compression on Cb, bd, df, and fA. 



522 



MECHANICS. 



Strains in 

1, orDe = h= 2PS + D; 

2, " eg = k = 3 PS -s- Z>; 

3, " gA = t s =7frPS -*- D; 

4, "A/ = c 4 =7/ 2 PL + D; 

5, " /d = c 3 = 7/ 2 PL/D-PD/L; 

6, " eft = c 2 \=y2PL/D-2PD/L; 



7, or &C = c t = 7/ 2 PL/D - 3 PD/L; 

8, " bcoxfg= PS -h L; 
9," de =2PSh- L; 

10, " cd or dg= 1/2 PS -^ D; 
11," ec =PS -v- D; 

12," cC =3/2 PS •*• Z>. 




Exampm:. — Given a Fink roof-truss of span 64 ft., depth 16 ft., with 
four panels on each side, as in hecut; total load 32 tons, or 4 tons 
each at the points /, d, 6, C, etc. (and 2 tons each at A and B, which trans- 
mit no strain to the truss me mbers). Here W = 32tons, P = 4 tons, 
S= 32 ft., D = 16 ft., L = ^S 2 + Z> 2 = 2.236 X D. L + D = 2.236, 
D -*- L = 0.4472, £-i-D = 2, S -i- L = 0.8944. The strains on the 
numbered members then are as follows: 



1, 2X4X2 =16 tons; 

2, 3X4X2 =24 

3, 7/ 2 X4X2 =28 

4, 7/2X4X2.236=31.3 " 

5, 31.3-4X0.447 = 29.52 " 

6, 31.3-8X0.447 = 27.72 " 



7,31.3-12X0.447 =25.94 tons. 

8, 4X0.8944= 3.58 " 

9, 8X0.8944= 7.16 " 

10, 2X2 =4 

11, 4X2 =8 " 

12, 6X2 =12 " 



The Economical Angle. — A structure of tri- 
angular form, Fig. 135, is supported at a and b. It 
sustains any load L, the elements cc being in com- 
pression and t in tension. Required the angle 9 so 
that the total weight of the structure shall be a 
minimum. F. R. Honey (Sci. Am. Supp., Jan. 17, 
1891) gives a solution of this problem, with the 



result tan 9 



=v/H- r ' 



in which C and T represent 




Fig. 135. 



the crushing and the tensile strength respectively of 

the material employed. It is applicable to any 

material. For C = T, 9 = 543/ 4 °. For C = 0.4 T (yellow pine), 9 = 

49 3/4 . For Cj= 0.8 T (soft steel), 9 = 531/4°. For C = 6 T (cast iron), 

0= 691/4°. 



PYROMETRY. 523 

HEAT. 

THERM031ETERS. 

The Fahrenheit thermometer is generally used in English-speaking 
countries, and the Centigrade, or Celsius, thermometer in countries that 
use the metric system. In many scientific treatises in English, however, 
the Centigrade temperatures are also used, either with or without their 
Fahrenheit equivalents. The Reaumur thermometer is used to some 
extent on the Continent of Europe. 

In the Fahrenheit thermometer the freezing-point of water is taken at 
32°, and the boiling-point of water at mean atmospheric pressure at the 
sea-level, 14.7 lbs. per sq. in., is taken at 212°, the distance between these 
two points being divided into 180°. In the Centigrade and Reaumur 
thermometers the freezing-point is taken at 0°. The boiling-point is 
100° in the Centigrade scale, and 80° in the Reaumur. 

1 Fahrenheit degree = 5/9 deg. Centigrade =4/9 deg. Reaumur. 

1 Centigrade degree = 9/5 deg. Fahrenheit =4/5 deg. Reaumur. 

1 Rdaumur degree = 9/4 deg. Fahrenheit =5/4 deg. Centigrade. 

Temperature Fahrenheit = 9/ 5 x temp. C. + 32° =9/ 4 R. + 32°. 
Temperature Centigrade = 5/ 9 (temp. F. — 32°) =5/4 R. 
Temperature Reaumur = 4/ 5 temp. C. =4/ 9 (F. _ 32 ). 

Handy Rule for Converting Centigrade Temperature to Fah- 
renheit. — Multiply by 2, subtract a tenth, add 32. 

Example. — 100° C.X2 = 200, - 20 = 180, +32= 212° F. 

Mercurial Thermometer. (Rankine, S. E., p. 234.) — The rate of 
expansion of mercury with rise of temperature increases as the temperature 
becomes higher; from which it follows, that if a thermometer showing the 
dilatation of mercury simply were made to agree with an air thermometer 
at 32° and 212°, the mercurial thermometer would show lower temperatures 
than the air thermometer between those standard points, and higher tem- 
peratures beyond them. 

For example, according to Regnault, when the air thermometer marked 
350° C. (= 662° F.), the mercurial thermometer would mark 362.16° C. 
(= 683.89° F.), the error of the latter being in excess 12.16° C. (= 21.89° 
F.). 

Actual mercurial thermometers indicate intervals of temperature pro- 
portional to the difference between the expansion of mercury and that of 
' glass. 

The inequalities in the rate of expansion of the glass (which are very 
different for different kinds of glass) correct, to a greater or less extent, the 
errors arising from the inequalities in the rate of expansion of the mercury. 

For practical purposes connected with heat engines, the mercurial ther- 
mometer made of common glass may be considered as sensibly coinciding 
with the air-thermometer at all temperatures not exceeding 500° F. 

If the mercury is not throughout its whole length at the same tempera- 
ture as that being measured, a correction, k, must be added to the tem- 
perature t in Fahrenheit degrees; k = 95 D (t-f) 4- 1,000,000, where D is 
the length of the mercury column exposed, measured in Fahrenheit 
degrees, and t is the temperature of the exposed part of the thermometer. 
When long thermometers are used in shallow wells in high-pressure steam 
pipes this correction is often 5° to 10° F. (Moyer on Steam Turbines.) j 

PYROMETRY. 

Principles Used in Various Pyrometers. 

Pyrometers may be classified according to the principles upon which 
they operate, as follows: 

1. Expansion of mercury in a glass tube. When the space above the 
mercury is filled with compressed nitrogen, and a specially hard glass is 
used for the tube, mercury thermometers may be made to indicate tem- 
peratures as high as 1000° F. 





TEMPERATURES, 


CENTIGRADE AND FAHRENHEIT 




c. 


F. 


C. 


F. 


C. 


F. 


C. 


F. 


C. 


F. 


C. 


F. 


€. 


F. 


-40 


-40. 


26 


78.8 


92 


197.6 


158 


316.4 


224 


435.2 


290 


554 


950 


1742 


-39 


-38.2 


27 


80.6 


93 


199.4 


159 


318.2 


225 


437. 


300 


572 


960 


1760 


-38 


-36.4 


28 


82.4 


94 


201.2 


160 


320. 


226 


438.8 


310 


590 


970 


1778 


-37 


-34.6 


29 


84.2 


95 


203. 


161 


321.8 


227 


440.6 


320 


608 


980 


1796 


-36 


-32.8 


30 


86. 


96 


204.8 


162 


323.6 


228 


442.4 


330 


626 


990 


1814 


-35 


-31. 


31 


87.8 


97 


206.6 


163 


325.4 


229 


444.2 


340 


644 


1000 


1832 


-34 


-29.2 


32 


89.6 


98 


208.4 


164 


327.2 


230 


446. 


350 


662 


1010 


1850 


-33 


-27.4 


33 


91.4 


99 


210.2 


165 


329. 


231 


447.8 


360 


680 


1020 


1868 


-32 


-25.6 


34 


93.2 


100 


212. 


166 


330.8 


232 


449.6 


370 


698 


1030 


1886 


-31 


-23.8 


35 


95. 


101 


213.8 


167 


332.6 


233 


451.4 


380 


716 


1040 


1904 


-30 


-22. 


36 


96.8 


102 


215.6 


168 


334.4 


234 


453.2 


390 


734 


1050 


1922 


-29 


-20.2 


37 


98.6 


103 


217.4 


169 


336.2 


235 


455. 


400 


752 


1060 


1940 


-28 


-18.4 


38 


100.4 


104 


219.2 


170 


338. 


236 


456.8 


410 


770 


1070 


1958 


-27 


-16.6 


39 


102.2 


105 


221. 


171 


339.8 


237 


458.6 


420 


788 


1080 


1976 


-26 


-14.8 


40 


104. 


106 


222.8 


172 


341.6 


238 


460.4 


430 


806 


1090 


1994 


-25 


-13. 


41 


105.8 


107 


224.6 


173 


343.4 


239 


462.2 


440 


824 


1100 


2012 


-24 


-11.2 


42 


107.6 


108 


226.4 


174 


345.2 


240 


464. 


450 


842 


1110 


2030 


-23 


- 9.4 


43 


109.4 


109 


228.2 


175 


347. 


241 


465.8 


460 


i 860 


1120 


2048 


-22 


- 7.6 


44 


111.2 


110 


230. 


176 


348.8 


242 


467.6 


470 


878 


1130 


2066 


-21 


- 5.8 


45 


113. 


111 


231.8 


177 


350.6 


243 


469.4 


480 


896 


1140 


2084 


-20 


- 4. 


46 


114.8 


112 


233.6 


178 


352.4 


244 


471.2 


490 


914 


1150 


2102 


-19 


- 2.2 


47 


116.6 


113 


235.4 


179 


354.2 


245 


473. 


500 


932 


1160 


2120 


-18 


- 0.4 


48 


118.4 


114 


237.2 


180 


356. 


246 


474.8 


510 


950 


1170 


2138 


-17 


4- 1.4 


49 


120.2 


115 


239. 


181 


357.8 


247 


476.6 


520 


968 


1180 


2156 


-16 


3.2 


50 


122. 


116 


240.8 


182 


359.6 


248 


478.4 


530 


986 


1190 


2174 


-15 


5. 


51 


123.8 


117 


242.6 


183 


361.4 


249 


480.2 


540 


1004 


1200 


2192 


-14 


6.8 


52 


125.6 


118 


244.4 


184 


363.2 


250 


482. 


550 


1022 


1210 


2210 


-13 


8.6 


53 


127.4 


119 


246.2 


185 


365. 


251 


483.8 


560 


1040 


1220 


2228 


-12 


10.4 


54 


129.2 


120 


248. 


186 


366.8 


252 


485.6 


570 


1058 


1230 


2246 


-11 


12.2 


55 


131. 


121 


249.8 


187 


368.6 


253 


487.4 


580 


1076 


1240 


2264 


-10 


14. 


56 


132.8 


122 


251.6 


188 


370.4 


254 


489.2 


590 


1094 


1250 


2282 


- 9 


15.8 


57 


134.6 


123 


253.4 


189 


372.2 


255 


491. 


600 


1112 


1260 


2300 


- 8 


17.6 


58 


136.4 


124 


255.2 


190 


374. 


256 


492.8 


610 


1130 


1270 


2318 


- 7 


19.4 


59 


138.2 


125 


257. 


191 


375.8 


257 


494.6 


620 


1148 


1280 


2336 


- 6 


21.2 


60 


140. 


126 


258.8 


192 


377.6 


258 


496.4 


630 


1166 


1290 


2354 


- 5 


23. 


61 


141.8 


127 


260.6 


193 


379.4 


259 


498.2 


640 


1184 


1300 


2372 


- 4 


24.8 


62 


143.6 


128 


262.4 


194 


381.2 


260 


500. 


650 


1202 


1310 


2390 


- 3 


26.6 


63 


145.4 


129 


264.2 


195 


383. 


261 


501.8 


660 


1220 


1320 


2408 


- 2 


28.4 


64 


147.2 


130 


266. 


196 


384.8 


262 


503.6 


670 


1238 


1330 


2426 


- 1 


■ 30.2 


65 


149. 


131 


267.F 


197 


386.6 


263 


505.4 


680 


1256 


1340 


2444 





32. 


66 


150.8 


132 


269.6 


198 


388.4 


264 


507.2 


690 


1274 


1350 


2462 


+ 1 


33.8 


67 


152.6 


133 


271.4 


199 


390.2 


265 


509. 


700 


1292 


1360 


2480 


2 


35.6 


68 


154.4 


134 


273.2 


200 


392. 


266 


510.8 


710 


1310 


1370 


2498 


3 


37.4 


69 


156.2 


135 


275. 


201 


393.8 


267 


512.6 


720 


1328 


1380 


2516 


4 


39.2 


70 


158. 


136 


276.8 


202 


395.6 


268 


514.4 


730 


1346 


1390 


2534 


5 


41. 


71 


159.8 


137 


278.6 


203 


397.4 


26*9 


516.2 


740 


1364 


1400 


2552 


6 


42.8 


72 


161.6 


138 


280.4 


204 


399.2 


270 


518. 


750 


1382 


1410 


2570 


7 


44.6 


73 


163.4 


139 


282.2 


205 


401. 


271 


519.8 


760 


1400 


1420 


2588 


8 


46.4 


74 


165.2 


140 


284. 


206 


402.8 


272 


521.6 


770 


1418 


1430 


2606 


9 


48.2 


75 


167. 


141 


285.8 


207 


404.6 


273 


523.4 


780 


1:436 


1440 


2624 


10 


50. 


76 


168.8 


142 


287.6 


208 


406.4 


274 


525.2 


790 


1454 


1450 


2642 


11 


51.8 


77 


170.6 


143 


289.4 


209 


408.2 


275 


527. 


800 


1472 


1460 


2660 


12 


53.6 


78 


172.4 


144 


291.2 


210 


410. 


276 


528.8 


310 


1490 


1470 


2678 


13 


55.4 


79 


174.2 


145 


293. 


211 


411.8 


277 


530.6 


320 


1508 


1480 


2696 


14 


57.2 


80 


176. 


146 


294.8 


212 


413.6 


278 


532.4 


830 


1526 


1490 


2714 


15 


59. 


81 


177.8 


147 


296.6 


213 


415.4 


279 


534.2 


840 


1544 


1500 


2732 


16 


60.8 


82 


179.6 


148 


298.4 


214 


417.2 


280 


536. 


850 


1562 


1510 


2750 


"7 


62.6 


83 


181.4 


149 


300.2 


215 


419. 


281 


537.8 


360 


1580 


1520 


2768 


18 


64.4 


84 


183.2 


150 


302. 


216 


420.8 


282 


539.6 


370 


1598 


1530 


2786 


19 


66.2 


85 


185. 


151 


303.8 


217 


422.6 


283 


541.4 


380 


1616 


1540 


2804 


20 


68. 


86 


186.8 


152 


305.6 


218 


424.4 


284 


543.2 


890 


1634 


1550 


2822 


21 


69.8 


87 


188.6 


153 


307.4 


219 


426.2 


285 


545. 


900 


1652 


1600 


2912 


22 


71.6 


88 


190.4 


154 


309.2 


220 


428. 


286 


546.8 


910 


1670 


1650 


3002 


23 


73.4 


89 


192.2 


155 


311. 


221 


429.8 


287 


548.6 


920 


1688 


1700 


3092 


24 


75.2 


90 


194. 


156 


312.8 


222 


431.6 


288 


550.4 


930 


1706 


1750 


3182 


25 


77. 


91 


195.8 


157 


314.6 


223 


433.4 


289 


552.2 


940 


1724 


1800 


3272 





TEMPERATURES 


, FAHRENHEIT AND CENTIGRADE 


• 


F. 


C. 


F. 
26 


C. 
-3.3 


F. 


C. 
33.3 


F. 


C. 


F. 


C. 


F. 


C. 
143.3 


F. 


C. 


-40 


-40. 


92 


158 


70. 


224 


106.7 


290 


360 


182.2 


-39 


-39.4 


27 


-2.8 


93 


33.9 


159 


70.6 


225 


107.2 


291 


143.9 


370 


187.8 


-38 


-38.9 


28 


-2.2 


94 


34.4 


160 


71.1 


226 


107.8 


292 


144.4 


380 


193.3 


-37 


-38.3 


29 


-1.7 


95 


35. 


161 


71.7 


227 


108.3 


293 


145. 


390 


198.9 


-36 


-37.8 


30 


-1.1 


96 


35.6 


162 


72.2 


228 


108.9 


294 


145.6 


400 


204.4 


-35 


-37.2 


31 


-0.6 


97 


36.1 


163 


72.8 


229 


109.4 


295 


146.1 


410 


210. 


-34 


-36.7 


32 0. 


98 


36.7 


164 


73.3 


230 


110. 


296 


146.7 


420 


215.6 


-33 


-36.1 


33 


+0.6 


99 


37.2 


165 


73.9 


231 


I 10.6 


297 


147.2 


430 


221.1 


-32 


-35.6 


34 


1.1 


100 


37.8 


166 


74.4 


232 


111.1 


298 


147.8 


440 


226.7 


-31 


-35. 


35 


].7 


101 


38.3 


167 


75. 


233 


111.7 


299 


148.3 


450 


232.2 


-30 


-34.4 


36 


2.2 


102 


38.9 


168 


75.6 


234 


112.2 


300 


148.9 


460 


237.8 


-29 


-33.9 


37 


2.8 


103 


39.4 


169 


76.1 


235 


112.8 


301 


149.4 


470 


243.3 


-28 


-33.3 


38 


3.3 


104 


40. 


170 


76.7 


236 


113.3 


302 


150. 


480 


248.9 


-27 


-32.8 


39 


3.9 


105 


40.6 


171 


77.2 


237 


113.9 


303 


150.6 


490 


254.4 


-26 


-32.2 


40 


4.4 


106 


41.1 


172 


77.8 


238 


114.4 


304 


151.1 


500 


260. 


-25 


-31.7 


41 


5. 


107 


41.7 


173 


78.3 


239 


115. 


305 


151.7 


510 


265.6 


-24 


-31.1 


42 


5.6 


108 


42.2 


174 


78.9 


240 


115.6 


306 


152.2 


520 


271.1 


-23 


-30.6 


43 


6.1 


109 


42.8 


175 


79.4 


241 


116.1 


307 


152.8 


530 


276.7 


-22 


-30. 


44 


6.7 


110 


43.3 


176 


80. 


242 


116.7 


308 


153.3 


540 


282.2 


-21 


-29.4 


45 


7.2 


111 


43.9 


177 


80.6 


243 


117.2 


309 


153.9 


550 


287.8 


-20 


-28.9 


46 


7.8 


112 


:■: : 


178 


81.1 


244 


117.8 


310 


154.4 


560 


293.3 


-19 


-28.3 


47 


8.3 


113 


45. 


179 


81.7 


245 


118.3 


311 


155. 


570 


298.9 


-18 


-27.8 


48 


8.9 


114 


45.6 


180 


82.2 


246 


118.9 


312 


155.6 


580 


304.4 


-17 


-27.2 


49 


9.4 


115 


46.1 


181 


82.8 


247 


119.4 


313 


156.1 


590 


310. 


-16 


-26.7 


50 


10. 


116 


46.7 


182 


83.3 


248 


120. 


314 


156.7 


600 


315.6 


-15 


-26.1 


51 


10.6 


117 


47.2 


183 


83.9 


249 


120.6 


315 


157.2 


610 


321.1 


-14 


-25.6 


52 


11.1 


118 


47.8 


184 


84.4 


250 


121.1 


316 


157.8 


620 


326.7 


-13 


-25. 


53 


11.7 


119 


48.3 


185 


85. 


251 


121.7 


317 


158.3 


630 


332.2 


-12 


-24.4 


54 


12.2 


120 


48.9 


186 


85.6 


252 


122.2 


318 


158.9 


640 


337.8 


-11 


-23.9 


55 


12.8 


121 


49.4 


187 


86.1 


253 


122.8 


319 


159.4 


650 


343.3 


-10 


-23.3 


56 


13.3 


122 


50. 


188 


86.7 


254 


123.3 


320 


160. 


660 


348.9 


- 9 


-22.8 


57 


13.9 


123 


50.6 


189 


87.2 


255 


123.9 


321 


160.6 


670 


354.4 


- 8 


-22.2 


58 


14.4 


124 


51.1 


190 


87.8 


256 


124.4 


322 


161.1 


680 


360. 


- 7 


-21.7 


59 


15. 


125 


51.7 


191 


83.3 


257 


125. 


323 


161.7 


690 


365.6 


- 6 


-21.1 


60 


15.6 


126 


52.2 


192 


88.9 


258 


125.6 


324 


162.2 


700 


371.1 


- 5 


-20.6 


61 


16.1 


127 


52.8 


193 


89.4 


259 


126.1 


325 


162.8 


710 


376.7 


- 4 


-20. 


62 


16.7 


128 


53.3 


194 


90. 


260 


126.7 


326 


163.3 


720 


382.2 


- 3 


-19.4 


63 


17.2 


129 


53.9 


195 


90.6 


261 


127.2 


327 


163.9 


730 


387.8 


- 2 


-18.9 


64 


17.8 


130 


54.4 


196 


91.1 


262 


127.8 


328 


164.4 


740 


393.3 


- 1 


-18.3 


65 


18.3 


131 


55. 


197 


91.7 


263 


128.3 


329 


165. 


750 


398.9 





-17.8 


66 


18.9 


132 


55.6 


198 


92.2 


264 


128.9 


330 


165.6 


760 


404.4 


+ 1 


-17.2 


67 


19.4 


133 


56.1 


199 


92.8 


265 


129.4 


331 


166.1 


770 


410. 


2 


-16.7 


68 


20. 


134 


56.7 


200 


93.3 


266 


130. 


332 


166.7 


780 


415.6 


3 


-16.1 


69 


20.6 


135 


57.2 


201 


93.9 


267 


130.6 


333 


67.2 


790 


421.1 


4 


-15.6 


70 


21.1 


136 


57.8 


202 


94.4 


268 


131.1 


334 


67.8 


800 


426.7 


5 


-15. 


71 


21.7 


137 


58.3 


203 


95. 


269 


131.7 


335 


68.3 


810 


432.2 


6 


-14.4 


72 


22.2 


138 


58.9 


204 


95.6 


270 


132.2 


336 


68.9 


820 


437.8 


7 


-13.9 


73 


22.8 


139 


59.4 


205 


96.1 


271 


132.8 


337 


69.4 


830 


443.3 


8 


-13.3 


74 


23.3 


140 


50. 


206 


96.7 


272 


133.3 


338 


70. 


840 


448.9 


9 


-12.8 


75 


23.9 


141 


50.6 


207 


97.2 


273 


133.9 


339 


70.6 


850 


454.4 


10 


-12.2 


76 


24.4 


142 


51.1 


208 


97.8 


274 


134.4 


340 


71.1 


860 


460. 


11 


-11.7 


77 


25. 


143 


51.7 


209 


98.3 


275 


135. 


341 


71.7 


870 


465.6 


12 


-11.1 


78 


25.6 


144 


52.2 


210 


98.9 


276 


135.6 


342 


72.2 


880 


471.1 


13 


-10.6 


79 


26.1 


145 


52.8 


211 


99.4 


277 


136.1 


343 


72.8 


890 


476.7 


14 


-10. 


80 


26.7 


146 


53.3 


212 


100. 


278 


136.7 


344 


73.3 


900 


482.2 


15 


- 9.4 


81 


27.2 


147 


53.9 


213 


100.6 


279 


137.2 


345 


73.9 


910 


487.8 


16 


- 8.9 


82 


27.8 


148 


54 4 


214 


101.1 


280 


137.8 


346 


74.4 


920 


493.3 


17 


- 8.3 


83 


28.3 


149 


55. 


215 


101.7 


281 


138.3 


347 


75. 


930 


498.9 


18 


- 7.8 


84 


28.9 


150 


55.6 


216 


102.2 


282 


138.9 


348 


75.6 


940 


504.4 


19 


- 7.2 


85 


29.4 


151 


56.1 


217 


102.8 


283 


139.4 


349 


76.1 


950 


510. 


20 


- 6.7 


86 


30. 


152 


56.7 


218 


103.3 


284 


140. 


350 


76.7 


960 


515.6 


21 


- 6.1 


87 


30.6 


153 


57.2 


219 


103.9 


285 


140.6 


351 


77.2 


970 


521.1 


22 


- 5.6 


88 


31.1 


154 


57.8 


220 


104.4 


286 


141.1 


352 


77.8 


980 


526.7 


23 


- 5. 


89 


31.7 


155 


38.3 


221 


105. 


287 


141.7 


353 


78.3 


990 


532.2 


24 


- 4.4 


90 


32.2 


156 


58.9 


222 


105.6 


288 


142.2 


354 


78.9 


1000 


537.8 


25 


- 3.9 


91 


32.8 


157 


39.4 


223 


106.1 


289 


142.8 


355 


179.4 


1010 


543.3 



526 



2. Contraction of clay, as in the old Wedgwood pyrometer, at one time 
used by potters. This instrument was very inaccurate, as the contraction 
of clay varied with its nature. 

3. Expansion of air, as in the air-thermometer, Wiborgh's pyrometer, 
Uehling and Steinbart's pyrometer, etc. 

4. Pressure of vapors, as in some forms of Bristol's recording pyrometer. 

5. Relative expansion of two metals or other substances, as in Brown's, 
Bulkley's and other metallic pyrometers, consisting of a copper rod or 
tube inside of an iron tube, or vice versa, with the difference of expansion 
multiplied by gearing and indicated on a dial. 

6. Specific heat of solids, as in the copper-ball and platinum-ball 
pyrometers. 

7. Melting-points of metals, alloys, or other substances, as in approxi- 
mate determination of temperature by melting pieces of zinc, lead, etc., 
or as in Seger's fire-clay pyrometer. 

8. Time required to heat a weighed quantity of water inclosed in a 
vessel, as in one form of water pyrometer. 

9. Increase in temperature of a stream of water or other liquid flow- 
ing at a given rate through a tube inserted into the heated chamber. 

10. Changes in the electric resistance of platinum or other metal, as 
in the Siemens pyrometer. 

11. Measurement of an electric current produced by heating the 
junction of two metals, as in the Le Chatelier pyrometer. 

12. Dilution by cold air of a stream of hot air or gas flowing from a 
heated chamber and determination of the temperature of the mixture by 
a mercury thermometer, as in Hobson's hot-blast pyrometer. 

13. Polarization and refraction by prisms and plates of light radiated 
from heated surfaces, as in Mesure" and Nouel's pyrometric telescope or 
optical pyrometer, and Wanner's pyrometer. 

14. Heating the filament of an electric lamp to the same color as that 
of an incandescent body, so that when the latter is observed through a 
telescope containing the lamp the filament becomes invisible, as in Hol- 
born and Kurlbaum's and Morse's optical pyrometers. The current 
required to heat the filament is a measure of the temperature. 

15. The radiation pyrometer. The radiation from an incandescent 
surface is received in a telescope containing a thermo-couple, and the 
electric current generated therein is measured, as in Fury's radiation 
pyrometer. 

(See "Optical Pyrometry " by C. W. W. Waidner and G. K. Burgess, 
Bulletin No. 2, Bureau of Standards, Department of Commerce and 
Labor; also Eng'g, Mar. 1, 1907.) 

Platinum or Copper Ball Pyrometer. — A weighed piece of platinum, 
copper, or iron is allowed to remain in the furnace or heated chamber till 
it has attained the temperature of its surroundings. It is then suddenly 
taken out and dropped into a vessel containing water of a known weight 
and temperature. The water is stirred rapidly., and its maximum tem- 
perature taken. Let W = weight of the water, w the weight of the ball, 
t = the original and T the final heat of the water, and S the specific heat of 
the metal; then the temperature of fire may be found from the formula 
' W(T - t) , _ 



wS 

The mean specific heat of platinum between 32° and 446° F. is 0.03333 or 
1/30 that of water, and it increases with the temperature about 0.000305 
for each 100° F. For a fuller description, by J. C. Hoadley, see Trans. 
A. S. M. E., vi, 702. Compare also Henry M. Howe, Trans. A. I. M. E., 
xviii, 728. 

For accuracy corrections are required for variations in the specific heat 
of the water and of the metal at different temperatures, for loss of heat by 
radiation from the metal during the transfer from the furnace to the water, 
and from the apparatus during the heating of the water; also for the heat- 
absorbing capacity of the vessel containing the water. 

Fire-clay or fire-brick may be used instead of the metal ball. 

Le Chatelier's Thermo-electric Pyrometer. — For a very full 
description, see paper by Joseph Struthers, School of Mines Quarterly, 
vol. xii, 1891; also, paper read by Prof. Roberts-Austen before the Iron 
and Steel Institute, May 7, 1891. 



PYROMETRY. 



527 



The principle upon which this pyrometer is constructed is the measure- 
ment of a current of electricity produced by heating a couple composed of 
two wires, one platinum and the other platinum with 10% rhodium — 
the current produced being measured by a galvanometer. 

The composition of the gas winch surrounds the couple has no influence 
on the indications. 

When temperatures above 2500° F. are to be studied, the wires must 
have an isolating support and must be of good length, so that all parts 
of a furnace can be reached. The wires are supported in an iron tube 1/2 
inch interior diameter and held in place by a cylinder of refractory clay 
having two holes bored through, in which the wires are placed. The 
shortness of time (five seconds) allows the temperature to be taken with- 
out deteriorating the tube. 

Tests made by this pyrometer in measuring furnace temperatures under 
a great variety of conditions show that the readings of the scale uncorrected 
are always within 45° F. of the correct temperature, and in the majority 
of industrial measurements this is sufficiently accurate. 

Graduation of Le Chatelier's Pyrometer. — W. C. Roberts-Austen 
in his Researches on the Properties of Alloys, Proc. Inst. M. E., 1892, 
says: The electromotive force produced by heating the thermo-junction 
to any given temperature is'measured by the movement of the spot of light 
on the scale graduated in millimeters. The scale is calibrated by heating 
the thermo-junction to temperatures which have been carefully deter- 
mined by the aid of the air-thermometer, and plotting the curve from 
the data so obtained. Many fusion and boiling-points have been estab- 
lished by concurrent evidence of various kinds, and are now generally 
accepted. The following table contains certain of these: 



Deg. F. 


Deg. 


C. 


Deg. F 


Deg. C. 


212 


100 


Water boils. 


1733 


945 


Silver melts. 


618 


326 


Lead melts. 


1859 


1015 


Potassium sulphate 


676 


358 


Mercury boils. 






melts. 


779 


415 


Zinc melts. 


1913 


1045 


Gold melts. 


838 


448 


Sulphur boils. 


1929 


1054 


Copper melts. 
Palladium melts. 


1157 


625 


Aluminum melts. 


2732 


1500 


1229 


665 


Selenium boils. 


3227 


1775 


Platinum melts. 



The Temperatures Developed in Industrial Furnaces. — M. Le 

Chatelier states that by means of his pyrometer he has discovered that 
the temperatures which occur in melting steel and in other industrial 
operations have been hitherto overestimated. He finds the melting 
heat of white cast iron 1135° (2075° F.), and that of gray cast iron 1220° 
(2228° F.). Mild steel melts at 1475° (2687° F.), and hard steel at 1410° 
(2570° F.). The furnace for hard porcelain at the end of the baking has a 
heat of 1370° (2498° F.). The heat of a normal incandescent lamp is 
1800° (3272° F.), but it may be pushed to beyond 2100° (3812° F.). 

Prof. Boberts- Austen (Recent Advances in Pyrometry, Trans. A.T.M.E., 
Chicago Meeting, 1893) gives an excellent description of modern forms of 
pyrometers. The following are some of his temperature determinations. 

Ten-ton Open-hearth Furnace, Woolwich Arsenal. 

Degrees Degrees 
Centigrade. Fahr. 
Temperature of steel, 0.3% carbon, pouring into ladle. . . 1645 2993 

Steel, 0.3% carbon, pouring into large mold 1580 2876 

Reheating furnace, interior . 930 1706 

Cupola furnace, No. 2 cast iron, pouring into ladle 1600 2912 

The following determinations have been effected by M. Le Chatelier: 
Bessemer Process. Six-ton Converter. 

A. Bath of slag 1580 2876 

B. Metal in ladle 1640 2984 

C. Metal in ingot mold 1580 2876 

D. Ingot in reheating furnace 1200 2192 

E. Ingot under the hammer , . . 1080 1976 



528 



HEAT. 



Open-hearth Furnace (Semi-mild Steel). Deg. C. Deg. F. 

A. Fuel gas near gas generator 720 1328 

B. Fuel gas entering into bottom of regenerator chamber. . 400 752 

C. Fuel gas issuing from regenerator chamber 1200 2192 

Air issuing from regenerator chamber 1000 1832 

Chimney gases. Furnace in perfect condition 300 590 

End of the melting of pig charge 1420 2588 

Completion of conversion . 1500 2732 

Molten steel. In the ladle — Commencement of casting. . . 1580 2876 

End of casting 1490 2714 

In the molds 1520 2768 

For very mild (soft) steel the temperatures are higher by 50° C. 

Blast-furnace (Gray-Bessemer Pig). 

Opening in face of tuyere 1930 3506 

Molten metal — Commencement of fusion 1400 2552 

End, or prior to tapping 1570 2858 

Hoffman Red-brick Kiln. 
Burning temperatures 1100 2012 

R. Moldenke (The Foundry, Nov., 1898) determined with a Le Chatelier 
pyrometer the melting-point of 42 samples of pig iron of different grades. 
The range was from 2030° F. for pig containing 3.98% combined carbon 
to 2280 for pig containing 0.13 combined carbon and 3.43% graphite. 
The results of the whole series may be expressed within 30° F. by the 
formula Temp. =2300° — 70 X % of combined carbon. 

Hobson's Hot-blast Pyrometer consists of a brass chamber having 
three hollow arms and a handle. The hot blast enters one of the arms 
and induces a current of atmospheric air to flow into the second arm. 
The two currents mix in the chamber and flow out through the third arm, 
in which the temperature of the mixture is taken by a mercury thermom- 
eter. The openings in the arms are adjusted so that the proportion of hot 
blast to the atmospheric air remains the same. 

The Wiborgh Air-pyrometer. (E. Trotz, Trans. A.I.M.E., 1892.) — 
The inventor using the expansion-coefficient of air, as determined by 
Gay-Lussac, Dulon, Rudberg, and Regnault, bases his construction on 
the following theory: If an air-volume, V, inclosed in a porcelain globe 
and connected through a capillary pipe with the outside air, be heated to 
the temperature T (which is to be determined) and thereupon the con- 
nection be discontinued, and there be then forced into the globe contain- 
ing V another volume of air V of known temperature t, which was 
previously under atmospheric pressure H, the additional pressure h, due 
to the addition of the air-volume V to the air-volume V, can be measured 
by a manometer. But this pressure is of course a function of the tem- 
perature T. Before the introduction of V , we have the two separate 
air-volumes, V at the temperature T, and V at the temperature t, both 
under the atmospheric pressure H. After the forcing in of V into the 
globe, we have, on the contrary, only the volume V of the temperature 
T, but under the pressure H + h. 

Seger Cones. (Catalog, Stowe-Fuller Co., 1907.) — Seger cones were 
developed in Germany by Dr. Herman A. Seger. They comprise a series 
of triangular pyramids about 3 in. high and 5/ 8 in. wide at the base, each a 
trifle less fusible than the next. When the series is placed in a furnace 
whose temperature is gradually raised, one cone after another will bend 
as its temperature of plasticity is reached. The temperature at which 
it bends so far that its apex touches the surface supporting it, determines 
a point on Seger's scale. Seger used as his standard, Zettlitz kaolin 
and Rackonitz shale clay of the following analyses: 



Zettlitz kaolin. . 
Rackonitz clay. . 



46.87 
52.50 



Alu- 



38.56 
45.22 



Iron 
Oxide. 



0.83 
0.81 



Mag- 
nesia. 



/ Potash) 
I Soda. J 



1.06 

trace 



Loss 
on Ig- 
nition. 

12.73 
0.78 



PYROMETRY. 



Rackomtz shale clay consists of 99.27% clay substance and 0.73% 
sand. The melting-point of a cone depends on the ratio of alumina to 
silica and the amount of fluxes contained. The following table shows the 
chemical formulae, mixtures and melting-points of Seger cones from 1 to 
36. The temperatures corresponding to the melting-points of cones 
21 to 26 are attained in the iron and steel industries. Cones 26 to 36 
serve to determine the refractoriness of clays. 





Chemical Composition. 


Mixture. 


Melting- 
Point. 




G 
O 

o 


6 




6 
fa 


6 
< 


d 


1 

a 

fa 


o3 


3 


So 


.2.S 


fa 


"I 
O 


1 

2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
78 


0.3 
0.3 
0.3 
0.3 
0.3 
0.3 
0.3 
0.3 
0.3 
0.3 
0.3 
0.3 
0.3 
0.3 
0.3 
0.3 
0.3 
0.3 
0.3 
0.3 
0.3 
0.3 
0.3 
0.3 
0.3 
0.3 
0.3 


0.7 
0.7 
0.7 
0.7 
0.7 
0.7 
0.7 
0.7 
0.7 
0.7 
0.7 
0.7 
0.7 
0.7 
0.7 
0.7 
0.7 
0.7 
0.7 
0.7 
0.7 
0.7 
0,7 
0.7 
0.7 
0.7 
0.7 


0.2 
0.1 
0.05 


0.3 
0.4 
0.45 
0.5 
0.5 
0.6 
0.7 
0.8 
0.9 
1.0 
1.2 
1.4 
1.6 
1.8 
2.1 
2.4 
2.7 
3.1 
3.5 
3.9 
4.4 
4.9 
5.4 
6.0 
6.6 
7.2 
20.0 
1.0 
1.0 
1.0 
1.0 
1.0 
1.0 
1.0 
1.0 


4 

4 

4 

4 

5 

6 

7 

8 

9 
10 
12 
14 
16 
18 
21 
24 
27 
31 
35 
39 
44 
49 
54 
60 
66 
72 
200 
10 

8 

6 

5 

4 

3 

2.5 

2 


83.55 
83.55 
83.55 
83.55 
83.55 
83.55 
83.55 
83.55 
83.55 
83.55 
83.55 
83.55 
83.55 
83.55 
83.55 
83.55 
83.55 
83.55 
83.55 
83.55 
83.55 
83.55 
83.55 
83.55 
83.55 
83.55 
83.55 


35 
35 
35 
35 
35 
35 
35 
35 
35 
35 
35 
35 
35 
35 
35 
35 
35 
35 
35^ 
35 
35 
35 
35 
35 
35 
35 
35 


66 

60 

57 

54 

84 

108 

132 

156 

180 

204 

252 

300 

348 

396 

468 

540 

612 

708 

804 

900 

1020 

1140 

1260 

1404 

1548 

1692 

4764 

240 

180 

120 

90 

60 

30 

15 


16.0 
8.0 
4.0 


"n'M 

19.43 
25.90 
25.90 
38.85 
51.80 
64.75 
77.70 
90.65 
116.55 
142.45 
168.35 
194.25 
233.10 
271.95 
310.80 
362.60 
414.40 
466.20 
530.95 
595.70 
660.45 
738.15 
815.85 
893.55 
2551.13 
129.50 
129.5 
129.5 
129.5 
129.5 
129.5 
129.5 


2102 
2138 
2174 
2210 
2246 
2282 
2318 
2354 
2390 
2426 
2462 
2498 
2534 
2570 
2606 
2642 
2678 
2714 
2750 
2786 
2822 
2858 
2894 
2930 
2966 
3002 
3038 
3074 
3110 
3146 
3182 
3218 
3254 
3290 
3326 
3362 


1150 
1170 
1190 
1210 
1230 
1250 
1270 
1290 
1310 
1330 
1350 
1370 
1390 
1410 
1430 
1450 
1470 
1490 
1510 
1530 
1550 
1570 
1590 
1610 
1630 
1650 
1670 
1690 


?q 












1710 


30 












1730 


31 












1750 


M 












1770 


33 












1790 


34 












1810 


35 








Zettlitz 




1830 


36 










1850 























Mesure and IVouel's Pyrometric Telescope. (H. M. Howe, E. and 
M. J., June 7, 1890.) — Mesure and Nouel's telescope gives an immediate 
determination of the temperature of incandescent bodies, and is therefore 
better adapted to cases where a great number of observations are to be 
made, and at short intervals, than Seger's. The little telescope, carried 
in the pocket or hung from the neek, can be used by foreman or heater 
at anv moment. 

It is based on the fact that a plate of quartz, cut at right angles to the 
axis, rotates the plane of polarization of polarized light to a degree nearly 
inversely proportional to the square of the length of the waves; and, 
further, on the fact that while a body at dull redness merely emits red 



530 



light, as the temperature rises, the orange, yellow, green, and blue waves 
successively appear. 

If, now, such a plate of quartz is placed between two Nicol prisms at 
right angles, "a ray of monochromatic light which passes the first, or 
polarizer, and is watched through the second, or analyzer, is not extin- 
guished as it was before interposing the quartz. Part of the light passes 
the analyzer, and, to again extinguish it, we must turn one of the Nicols a 
certain angle," depending on the length of the waves of light, and hence on 
the temperature of the incandescent object which emits this light. Hence 
the angle through which we must turn the analyzer to extinguish the light 
is a measure of the temperature of the object observed. 

The Uehling and Steinbart Pyrometer. (For illustrated descrip- 
tion see Engineering, Aug. 24, 1894.) — The action of the pyrometer is 
based on a principle which involves the law of the flow of gas through 
minute apertures in the following manner: If a closed tube or chamber be 
supplied with a minute inlet and a minute outlet aperture, and air be 
caused by a constant suction to flow in through one and out through the 
other of these apertures, the tension in the chamber between the apertures 
will vary with the difference of temperature between the inflowing and 
outflowing air. If the inflowing air be made to vary with the tem- 
perature to be measured, and the outflowing air be kept at a certain con- 
stant temperature, then the tension in the space or chamber between the 
two apertures will be an exact measure of the temperature of the inflow- 
ing air, and hence of the temperature to be measured. 

In operation it is necessary that the air be sucked into it through the 
first minute aperture at the temperature to be measured, through the 
second aperture at a lower but constant temperature, and that the suc- 
tion be of a constant tension. The first aperture is therefore located 
in the end of a platinum tube in the bulb of a porcelain tube over which 
the hot blast sweeps, or inserted into the pipe or chamber containing 
the gas whose temperature is to be ascertained. 

The second aperture is located in a coupling, surrounded by boiling 
water, and the suction is obtained by an aspirator and regulated by a 
column of water of constant height. 

The tension in the chamber between the apertures is indicated by a 
manometer. 

The Air-thermometer. (Prof. R. C. Carpenter, Eng'g News, Jan. 5, 
1893.) — Air is a perfect thermometric substance, and if a given mass of 
air be considered, the product of its pressure and volume divided by its 
absolute temperature is in every case constant. If the volume of air 
remain constant, the temperature will vary with the pressure; if the 
pressure remain constant, the temperature will vary with the volume. As 
the former condition is more easily attained, air-thermometers are usually 
constructed of constant volume, in which case the absolute temperature 
will vary with the pressure. 

If we denote pressures by p and p f , and the corresponding absolute 
temperatures by T and T', we should have 

T 
p \ p' \: T : T' and T' = p' - • 

The absolute temperature T is to be considered in every case 460 higher 
than the thermometer-reading expressed in Fahrenheit degrees. From 
the form of the above equation, if the pressure p corresponding to a 
known absolute temperature T be known, T' can be found. The quotient 
T/p is a constant which may be used in all determinations with the 
instrument. The pressure on the instrument can be expressed in inches 
of mercury, and is evidently the atmospheric pressure b as shown by a 
barometer, plus or minus an additional amount h shown by a manometer 
attached to the air-thermometer. That is, in general, p = b ± h. 

The temperature of 32° F. is fixed as the point of melting ice, in which 
case T = 460 + 32 == 492° F. This temperature can be produced by sur- 
rounding the bulb in melting ice and leaving it several minutes, so that the 
temperature of the confined air shall acquire that of the surrounding ice. 
When the air is at that temperature, note the reading of the attached 
manometer h, and that of a barometer; the sum will be the value of p 
corresponding to the absolute temperature of 492° F. The constant of 
the instrument, K = 492 -*■ p, once obtained, can be used in all future 
determinations. 



PYROMETRY. 



531 



High Temperatures judged by Color. — The temperature of a body 
can be approximately judged by the experienced eye unaided. M. 
Pouillet in 1836 constructed a table, which has been generally quoted in 
the text-books, giving the colors and their corresponding temperature, 
but which is now replaced by the tables of H. M. Howe and of Maunsel 



White and F. W. Taylor (Trans. 
below. 



A. S. M. E., 1899), which are given 



Howe. 
Lowest red vis- 
ible in dark . . 
Lowest red vis- 
ible in day- 
light 

Dull red 550 to 625 

Full cherry .... 700 

Light red 850 

Tull 



470 



475 



3 F. White and Taylor. ° C. °F. 
Dark blood-red, black- 

878 red 990 

Dark red, blood-red, low 

red 556 1050 

887 Dark cherry-red 635 1175 

1022 to 1157 Medium cherry- red 1250 

1292 Cherry, full red 746 1375 

1562 Light cherry, light red*. 843 1550 

Full yellow 950 to 1000 1742 to 1832 Orange, free scaling heat 899 1650 

Light yellow. . . 1050 1922 Light orange 941 1725 

White 1150 2102 Yellow 996 1825 

Light yellow 1079 1975 

White 1205 2200 

* Heat at which scale forms and adheres on iron and steel, i.e., does 
not fall away from the piece when allowed to cool in air. 

Skilled observers may vary 100° F. or more in their estimation of 
relatively low temperatures by color, and beyond 2200° F. it is practically 
impossible to make estimations with any certainty whatever. (Bulletin 
No. 2, Bureau of Standards, 1905.) 

. In confirmation of the above paragraph we have the following, in a 
booklet published by the Halcomb Steel Co., 1908. 



°C 
1000 
1100 
1200 
1300 
1400 
1500 



F. Colors. 

1832 Bright cherry-red. 

2012 Orange-red. 

2192 Orange-yellow. 

2372 Yellow-white. 

2552 White welding heat. 

2732 Brilliant white. 

1600 2912 Dazzling white (bluish 
white). 



°C. °F. Colors. 

400 752 Red, visible in the dark. 
474 885 Red, visible in the twilight. 
525 975 Red, visible in the day- 
light. 
581 1077 Red, visible in the sun- 
light. 
700 1292 Dark red. 
800 1472 Dull cherry- red. 
900 1652 Cherry-red. 

Different substances heated to the same temperature give out the 
same color tints. Objects which emit the same tint and intensity of light 
cannot be distinguished from each other, no matter how different their 
texture, surface, or shape may be. When the temperature at all parts of 
a furnace at a low yellow heat is the same, different objects inside the 
furnace (firebrick, sand, platinum, iron) become absolutely invisible. 
(H. M. Howe.) 

A bright bar of iron, slowly heated in contact with air, assumes the fol- 
lowing tints at annexed temperatures (Claudel): 



Cent. 

Yellow at 225 

Orange at 243 

Red at 265 

Violet at 277 

The Halcomb Steel Co. 
colors of steel: 

Colors. 



Fahr. 
437 
473 
509 
531 



Indigo at 

Blue at 

Green at 

"Oxide-gray" . 



Cent. 
288 
293 
332 
400 



Fahr. 
550 
559 
630 
752 



(1908) gives the following heats and temper 



221.1 


430 


226.7 


440 


232.2 


450 


237.8 


460 


243.3 


470 


248.9 


480 


254.4 


490 


260.0 


500 



430 Very pale yellow. 
Light yellow. 
Pale straw-yellow. 
Straw-yellow. 
Deep straw-yellow. 
Dark yellow. 
Yellow-b rown . 
Brown-yellow. 



Cent. Fahr. 
265.6 510 
271.1 
276.7 
282.2 
287.8 
293.3 



315.6 



Colors. 
Spotted red-brown. 
Brown-purple. 
Light purple. 
Full purple. 
Dark purple. 
Full blue. 
Dark blue. 
Very dark blue. 



532 HEAT. 

BOILING-POINTS AT ATMOSPHERIC PRESSURE. 

14.7 lbs. per square inch. 

Ether, sulphuric 100° F. Saturated brine 226° F. 

Carbon bisulphide 118 Nitric acid 248 

Ammonia 140 Oil of turpentine 315 

Chloroform 140 Aniline 363 

Bromine 145 Naphthaline 428 

Wood spirit 150 Phosphorus 554 

Alcohol 173 Sulphur 833 

Benzine 176 Sulphuric acid 590 

Water 212 Linseed oil 597 

Average sea-water 213.2 Mercury 676 

The boiling-points of liquids increase as the pressure increases. 

MELTING-POINTS OF VARIOUS SUBSTANCES. 

The following figures are given by Clark (on the authority of Pouillet. 
Claudel, and Wilson), except those marked *, which are given by Prof. 
Roberts-Austen, and those marked t, which are given by Dr. J. A. Harker. 
These latter are probably the most reliable figures. 

Sulphurous acid - 148° F. Cadmium 442° F. 

Carbonic acid - 108 Bismuth 504 to 507 

Mercury - 39, - 38f Lead 618*, 620t 

Bromine + 9.5 Zinc 779*, 786f 

Turpentine 14 Antimony 1150, 1169f 

Hyponitric acid 16 Aluminum 1157*, 1214f 

Ice 32 Magnesium 1200 

Nitro-glycerine 45 NaCl, common salt 1472f 

Tallow 92 Calcium Full red heat. 

Phosphorus 112 Bronze 1692 

Acetic acid 113 Silver 1733*, 1751f 

Stearine 109 to 120 Potassium sulphate.. 1859*, 1958 - 

Spermaceti 120 Gold 1913*, 1947" 

Margaric acid 131 to 140 Copper 1929*, 1943 - 

Potassium 136 to 144 Nickel 2600" 

Wax 142 to 154 Cast iron, white 1922, 2075- ■ 

Stearic acid 158 " gray 2012 to 2786, 2228* 

Sodium 194 to 208 Steel 2372 to 2532* 

Iodine 225 ". hard... 2570*; mild, 2687 

Sulphur 239 Wrought iron 2732 to 2912, 2737* 

Alloy, 1 1/2 tin, 1 lead 334, 367f Palladium 2732* 

Tin 446, 449f Platinum 3227*, 3110f 

Cobalt and manganese, fusible in highest heat of a forge. Tungsten 
and chromium, not fusible in forge, but soften and' agglomerate. Plati- 
num and iridium, fusible only before the oxyhydrogen blowpipe, or in an 
electrical furnace. For melting-point of fusible alloys see Alloys. For 
boiling and freezing points of air and other gases see p. 580. 

QUANTITATIVE MEASURE3IENT OF HEAT. 

Unit of Heat. — The British thermal unit, or heat unit (B.T.U.), is the 
quantity of heat required to raise the temperature of 1 lb. of pure water 
from 62° to 63° F. (Peabody), or i/iso of the heat required to raise the 
temperature of 1 lb. of water from 32° to 212° F. (Marks and Davis, see 
Steam, p. 840). 

The French thermal unit, or calorie, is the quantity of heat required to 
raise the temperature of 1 kilogram of pure water from 15° to 16° C. 

1 French calorie = 3.968 British thermal units; 1 B.T.U. = 0.252 
calorie. The "pound calorie" is sometimes used by English writers; 
it is the quantity of heat required to raise the temperature of 1 lb. of 
water 1° C. 1 lb. calorie = o/ 5 B.T.U. = 0.4536 calorie. The heat of 
combustion of carbon, to CO2, is said to be 8080 calories. This figure is 
used either for French calories or for pound calories, as it is the number of 
pounds of water that can be raised 1° C. by the complete combustion of 
1 lb. of carbon, or the number of kilograms of water that can be raised 
1° C. by the combustion of 1 kilo, of carbon; assuming in each case that 
all the heat generated is transferred to the water. 

The Mechanical Equivalent of Heat is the number of foot-pounds 
of mechanical energy equivalent to one British thermal unit, heat and 



HEAT OF COMBUSTION. 



533 



mechanical energy being mutually convertible. Joule's experiments, 
1843-50, gave the figure 772, which is known as Joule's equivalent. 
More recent experiments by Prof. Rowland (Proc. Am. Acad. Arts and 
Sciences, 1880; see also Wood's Thermodynamics) give higher figures, and 
the most probable average is now considered to be 778. 

1 heat-unit is equivalent to 778 ft. -lbs. of energy. 1 ft.-lb. = 1/778 = 
0.0012852 heat-unit. 1 horse-power = 33,000 ft.-lbs. per minute = 
2545 heat-units per hour = 42.416+ per minute = 0.70694 per second. 
1 lb. carbon burned to C0 2 = 14,600 heat-units. 1 lb. C per H.P. per 
hour = 2545 -*- 14,600 = 17.43% efficiency. 

Heat of Combustion of Various Substances in Oxygen. 





Heat-units. 


Authority. 




Cent. 


Fahr. 


Hydrogen to liquid water at 0® C. . 

" to steam at 100° C 

Carbon (wood charcoal) to car- 
bonic acid, CO2; ordinary tem- 


I 34,462 

\ 33,808 

( 34,342 

28,732 

( 8,080 

\ 7,900 

( 8,137 

7,859 

7,861 

7,901 

2,473 

( 2,403 

1 2,431 

( 2,385 

5,607 

(13,120 

\ 13,108 

( 13,063 

(11,858 

{ 11,942 

(11,957 

( 10,102 

X 9,915 


62,032 
60,854 
61,816 
51,717 
14,544 
14,220 
14,647 
14,146 
14,150 
14,222 
4,451 
4,325 
4,376 
4,293 
10,093 
23,616 
23,594 
23,513 
21,344 
21,496 
21,523 
18,184 
17,847 


Favre and Silbermann. 

Andrews. 

Thomsen. 

Favre and Silbermann. 

Andrews. 






black diamond to CO2 .... 




Carbon to carbonic oxide, CO 

Carbonic oxide to CO2 per unit of 
CO 


Favre and Silbermann. 

Andrews. 

Thomsen. 

Favre and Silbermann. 

Thomsen. 

Andrews. 

Favre and Silbermann. 

Andrews. 
Thomsen. 

Favre and Silbermann. 


CO to CO2 per unit of C=21/ 3 x2403 

Marsh-gas, Methane, CH 4 ,to water 

and CO2 


Olefiant gas, Ethylene, C2H4, to 


Benzole gas,C6H6,to water and CO2 



In calculations of the heating value of mixed fuels the value for carbon 
is commonly taken at 14,600 B.T.U., and that of hydrogen at 62,000. 
Taking the heating value of C burned to CO2 at 14,000, and that of C to 
CO at 4450, the difference, 10,150 B.T.U., is the heat lost by the imperfect 
combustion of each lb. of C burned to CO instead of to CO2. If the CO 
formed by this imperfect combustion is afterwards burned to CO2 the lost 
heat is regained. 

In burning 1 pound of hydrogen, with 8 pounds of oxygen to form 9 
pounds of water, the units of heat evolved are 62,000; but if the resulting 
product is not cooled to the initial temperature of the gases, part of the 
heat is rendered latent in the steam. The total heat of 1 lb. of steam at 
212° F. is 1150.0 heat-units above that of water at 32°, and 9 X 1150 = 
10,350 heat-units, which deducted from 62,000 gives 51,650 as the heat 
evolved by the combustion of 1 lb. of hydrogen and 8 lbs. of oxygen at 
32° F. to form steam at 212° F. 

Some writers subtract from the total heating value of hydrogen only 
the latent heat of the 9 lbs. of steam, or 9 X 969.7 = 8727 B.T.U., leaving 
as the "low" heating value 53,273 B.T.U. 

The use of heating values of hydrogen "burned to steam," in compu- 
tations relating to combustion of fuel, is. inconvenient, since it necessi- 
tates a statement of the conditions upon which the figures are based ; and 
it is, moreover, misleading, if not inaccurate, since hydrogen in fuel is not 
often burned in pure oxygen, but in air; the temperature of the gases 
before burning is not often the assumed standard temperature, and the 
products of combustion are not often discharged at 212°. In steam- 



534 HEAT. 

boiler practice the chimney gases are usually discharged above 300° ; but 
if economizers are used, and the water supplied to them is cold, the gases 
may be cooled to below 212°, in which case the steam in the gases is con- 
densed and its latent heat of evaporation is utilized. If there is any need 
at all of using figures of the "available" heating value of hydrogen, or its 
heating value when "burned to steam," the fact that the gas is burned in 
air and not in pure oxygen should be taken into consideration. The 
resulting figures will then be much lower than those above given, and they 
will vary with different conditions. (Kent, " Steam Boiler Economy," 
p. 23.) 

Suppose that 1 lb. of H is burned in twice the quantity of air required 
for complete combustion, or 2 X (8 O + 26.56 N) = 69.12 lbs. air 
supplied at 62° F., and that the products of combustion escape at 562° F. 
The heat lost in the products of combustion will be 

9 lbs. water heated fromJ62° to 212° 1352 B.T.U. 

Latent heat of 9 lbs. H 2 at 212°, 9 X 969.7 8727 

Superheated steam, 9 lbs. X (562° - 212°) X 0.48 (sp. ht.) 1512 

Nitrogen, 26.56 X (562° - 62°) X 0.2438 3238 " 

Excess air, 34.56 X (562° - 62°) X 0.2375 4104 " 

Total 18,933 " 

which subtracted from 62,000 gives 43,067 B.T.U. as the net available 
heating value under the conditions named. 

Heating Value of Compound or Mixed Fuels. — The heating value 
of a solid compound or mixed fuel is the sum of its elementary constituents, 
and is calculated as follows by Dulong's formula: 

B.T.U.- £^f 14,600 C + 62,000 (h - ^ + 4500 s] ; 

in which C, H, O, and S are respectively the percentages of the several 
elements. The term H — Vs O is called the "available" or "disposable" 
hydrogen, or that which is not combined with oxygen in the fuel. For 
all the common varieties of coal, cannel coal and some lignites excepted, 
the formula is accurate within the limits of error of chemical analyses and 
calorimetric determinations. 

Heat Absorbed by Decomposition. — By the decomposition of a 
chemical compound as much heat is absorbed or rendered latent as was 
evolved when the compound was formed. If 1 lb. of carbon is burned to 
CO2, generating 14,600 B.T.U., and the CO2 thus formed is immediately 
reduced to CO in the presence of glowing carbon, by the reaction CO2 + 
C = 2 CO, the result is the same as if the 2 lbs. C had been burned directly 
to 2 CO, generating 2 X 4450 = 8900 B.T.U. The 2 lbs. C burned to CO2 
would generate 2 X 14,600 = 29,200 B.T.U., the difference, 29,200 - 
8900 = 20,300 B.T.U., being absorbed or rendered latent in the 2 CO, or 
10,150 B.T.U. for each pound of carbon. 

In like manner if 9 lbs. of water be injected into a large bed of glowing 
coal, it will be decomposed into 1 lb. H and 8 lbs. O. The decomposition 
will absorb 62,000 B.T.U., cooling the bed of coal this amount, and the 
same quantity of heat will again be evolved if the H is subsequently 
burned with a fresh supply of O. The 8 lbs. of O will combine with 6 lbs. 
C, forming 14 lbs. CO (since CO is composed of 12 parts C to 16 parts O), 
generating 6 X 4450 = 26,700 B.T.U., and 6 X 10,150 = 60,900 B.T.U. 
will be latent in this 14 lbs. CO, to be evolved later if it is burned to CO2 
with an additional supply of 8 lbs. O. 

SPECIFIC HEAT. 

Thermal Capacity. — The thermal capacity of a body between two 
temperatures 7'o and T\ is the quantity of heat required to raise the tem- 
perature from 7 1 o to T\. The ratio of the heat required to raise the temper- 
ature of a certain weight of a given substance one degree to that required 
to raise the temperature of the same weight of water from 62° to 63° F. 
is commonly called the specific heat of the substance. Some writers 
object to the term as being an inaccurate use of the words " specific "■ 
and "heat." A more correct name would be "coefficient of thermal 
capacity." 

Determination of Specific Heat.— Method by Mixture.— The body 
whose specific heat is to be determined is raised to a known temperature, 
and is then immersed in a mass of liquid of which the weight, specific 



SPECIFIC HEAT. 



535 



heat, and temperature are known. When both the body and the liquid 
have attained the same temperature, this is carefully ascertained. 

Now the quantity of heat lost by the body is the same as the quantity of 
heat absorbed by the liquid. 

Let c, w, and t be the specific heat, weight, and temperature of the hot 
body, and d, w', and t' of the liquid. Let T be the temperature the mix- 
ture assumes. 

Then, by the definition of specific heat, c X w X (t — T) = heat-units 
lost by the hot body, and d X vf X (T — V) = heat-units gained by the 
cold liquid. If there is no heat lost by radiation or conduction, these 
must be equal, and 

cw (t - T) = did (T-f) or c = C ^ a (r _~[ ) - 

, Electrical Method. This method is believed to be more accurate in 
many cases than the method by mixture. It consists in measuring the 
quantity of current in watts required to heat a unit weight of a substance 
one degree in one minute, and translating the result into heat-units. 
1 Watt = 0.0569 B.T.U. per minute. 

Specific Heats of Various Substances. 

The specific heats of substances, as given by different authorities show 
considerable lack of agreement, especially in the case of gases. 

The following tables give the mean specific heats of the substances 
named according to Regnault. (From Rontgen's Thermodynamics, p. 
134.) These specific heats are average values, taken at temperatures 
which usually come under observation in technical application. The 
actual specific heats of all substances, in the solid or liquid state, increase 
slowly as the body expands or as the temperature rises. It is probable 
that the specific heat of a body when liquid is greater than when solid. 
For many bodies this has been verified by experiment. 



Solids. 



Antimony . 0508 

Copper 0.0951 

Gold 0.0324 

Wrought iron . 1138 

Glass 0.1937 

Cast iron 0.1298 

Lead 0.0314 

Platinum 0.0324 

Silver 0.0570 

Tin 0.0582 



Steel (soft) 0.1165 

Steel (hard) 0.1175 

Zinc . 0956 

Brass 0.0939 

Ice . 5040 

Sulphur 0.2026 

Charcoal . 2410 

Alumina 0.1970 

Phosphorus . 1887 



Water 1.0000 



Lead (melted). 
Sulphur " 

Bismuth " 

Tin " . . 

Sulphuric acid. 



. 0402 
. 2340 
. 0308 
0.0637 
. 3350 



Mercury 0.0333 

Alcohol (absolute) . 7000 

Fusel oil . 5640 

Benzine 0.4500 

Ether 0.5034 



Gases. 
Constant Pressure. 

Air.... 0.23751 

Oxygen . 21751 

Hydrogen 3 . 40900 

Nitrogen . 24380 

Superheated steam* 0. 4805 

Carbonic acid . . 217 

defiant gas (CH 2 ) 0. 404 

Carbonic oxide . 2479 

Ammonia . 508 

Ether 0.4797 

Alcohol 0.4534 

Acetic acid . 4125 

Chloroform . 1567 

* See Superheated Steam, page 833. 



Constant Volume. 
0.16847 
0.15507 
2.41226 
0.17273 
0.346 
0.1535 
0.173 
0.1758 
0.299 
0.3411 
0.3200 



536 



In addition to the above, the following are given by other authorities. 
(Selected from various sources.) 

Metals. 
Platinum, 32° to 446° F.. . . 0.0333 
(increased .000305 for each 100° F.) 
Cadmium 0.0567 



Wrought iron (Petit & Dulong). 

32° to 212°.. 0.109S 
32° to 392°.. 0.115 
32° to 572°. . 0.1218 
32° to 662°. . 0.1255 
Iron at high temperatures. 
(Pionchon, Comptes Rendus, 1887.) 

1382' to 1832° F 0.213 

1749' to 1843° F , 0.218 

1922 D to 2192° F 0.199 



Brass 0.0939 

Copper, 32° to 212° F 0.094 

32° to 572° F 0.1013 

Zinc, 32° to 212° F 0.0927 

32° to 572° F 0.1015 

Nickel 0.1086 

Aluminum, 0° F. to melting- 
point (A. E. Hunt) 0.2185 

Dr.-Ing. P. Oberhoffer, in Zeit. des Vereines Deutscher Ingenieure (Eng. 
Digest, Sept., 1908), describes some experiments on the specific heat of 
nearly pure iron. The following mean specific heats were obtained: 
Temp. F. 500 600 800 1000 1200 1300 

Sp. Ht. 0.1228 0.1266 0.1324 0.1388 0.1462 0.1601 

Temp. F. 1500 1800 2100 2400 2700 

Sp. Ht. 0.1698 0.1682 0.1667 0.1662 0.1666 

The specific heat increases steadily between 500 and 1200 F. Then it 
increases rapidly to 1400, after which it remains nearly constant. 

Otheb Solids. 



Brickwork and masonry, about . 20 

Marble 0.210 

Chalk 0.215 

Quicklime 0. 217 

Magnesian limestone 0. 217 

Silica 0.191 

Corundum . 198 

Stones generally 0. 2 to 0. 22 



Coal 0.20 to 0.241 

Coke . 203 

Graphite 0. 202 

Sulphate of lime 0. 197 

Magnesia . 222 

Soda 0.231 

Quartz 0.188 

River sand 0. 195 



Woods. 

Pine (turpentine). 0.467 I Oak. . 

Fir 0.650 | Pear. 



0.570 
0.500 



Liquids. 



Alcohol, density 0.793 

Sulphuric acid, density 1.87. 

1.30. 

Hydrochloric acid 



0.622 
0.335 
0.661 
0.600 



Olive oil 

Benzine 

Turpentine, density 0.872. . 
Bromine 



0.310 
0.393 
0.472 
1.111 



Gases. 

At Constant At Constant 

Pressure. Volume. 

Sulphurous acid 0. 1553 0. 1246 

Light carbureted hydrogen, marsh gas (CH 4 ) . . 5929 . 4683 

Blast-furnace gases > . 2277 

Specific Heat of Water. (Peabody's Steam Tables, from Barnes and 
Regnault.) 



,°c. 


°F. 


Sp. Ht. 


°.c. 


°F. 


Sp. Ht, 


°C. 


°F. 


Sp. Ht. 


°C. 


°F. 
248 


Sp. Ht. 





V. 


1.0G94 


35 


95 


0.99735 


70 


158 


1.00150 


17.0 


1.01620 


5 


41 


1.00530 


40 


(04 


0.99735 


75 


167 


1.00275 


140 


284 


1 .02230 


10 


50 


1 . 00^30 


45 


113 


0.90760 


80 


176 


1.00415 


160 


320 


1.02850 


15 


59 


1.00030 


50 


122 


0. 99800 


85 


188 


1.00557 


180 


356 


1.03475 


7.0 


68 


0.99895 


55 


131 


0.99850 


90 


194 


1.00705 


700 


392 


1.04100 


7.5 


77 


0.99806 


60 


140 


0.99940 


95 


203 


1.00855 


220 


428 


1.04760 


30 


86 


0.99759 


65 


149 


1.00040 


'00 


212 


1.01010 









SPECIFIC HEAT. 



537 



Specific Heat of Salt Solution. (Schuller.) 



Per cent salt in solution ... 5 

Specific heat 0.9306 



10 
0.S909 



15 20 
0.8606 0.S490 



25 
O.S073 



Specific Heat of Air.- 

pressure 

Between - 30° C. and 



Regnault gives for the mean value at constant 

10° C 0.23771 

100° C 0.23741 

200° C. 0.23751 



Hanssen uses 0.1686 for the specific heat of air at constant volume. 
The value of this constant has never been found to any degree of accuracy 
by direct experiment. Prof. Wood gives 0.2375 h- 1.406 = 0.16S9. The 
ratio of the specific heat of a fixed gas at constant pressure to the sp. ht. 
at constant volume is given as follows by different, writers (Eng'g, July 12 
1889): Regnault, 1.3953; Moll and Beck, 1.4085; Szathmari, 1.4027; J. 
Macfarlane Gray, 1.4. The first three are obtained from the velocity of 
sound in air. The fourth is derived from theory. Prof. Wood says: 
The value of the ratio for air, as found in the days of La Place, was 1.41, 
and we have 0.2377 h- 1.41 = 0.1686, the value used by Clausius, Hanssen, 
and many others. But this ratio is not definitely known. Rankine in 
his later writings used 1.408, and Tait in a recent work gives 1.404, while 
some experiments give less than 1.4, and others more than 1.41. Prof. 
Wood uses 1.406. 

Specific Heat of Gases. — Experiments by Mallard and Le Chatelier 

indicate a continuous increase in the specific heat at constant volume of 
steam, CO2, and even of the perfect gases, with rise of temperature. The 
variation is inappreciable at 100° C, but increases rapidly at the high tem- 
peratures of the gas-engine cylinder. (Robinson's Gas and Petroleum 
Engines.) 

Thermal Capacity and Specific Heat of Gases. (From Damour's 
" Industrial Furnaces.") — The specific heat of a gas at any temperature is 
the first derivative of the function expressing the thermal capacity. It 
is not possible to derive from the specific heat of a gas at a given temper- 
ature, or even from the mean specific heat between 0° and 100° C., the 
thermal capacity at a temperature above 100° C. The specific heats of 
gases under constant pressure between 0° and 100° C, given by Regnault, 
are not sufficient to calculate the quantity of heat absorbed by a gas in 
heating or radiated in cooling, hence all calculations based on these 
figures are subject to a more or less grave error. 

The thermal capacities of a molecular volume (22.32 liters) of gases 
from absolute 0° (— 273° C.) to a temperature T (= 273° + t) may be 
expressed by the formula Q = 0.001 aT + 0.000,001 bT*, in which a is a 
constant, 6.5, for all gases, and b has the following values for different 
gases: 2 , N 2 , H 2 , CO, 0.6; H2O vapor, 2.9; C0 2 , 3.7; CH4, 6.0. 



Specific Heats of Gases per Kilogram. 



Under Constant 
Pressure. 



Under Constant 
Volume. 



Oxygen 

Nitrogen and Carbon Monoxid< 

Hydrogen 

Water Vapor 

Carbon Dioxide 

Methane 



0.213+ 38x10-6* 
0.243+ 42xl0~6£ 
3. 400 + 600 x 10- *t 
0.447 + 324x10-6* 
0.193+168x10-6^ 
0.608 + 748x10-6* 



0.150+ 38x10-6£ 
0.171+ 42X10-H 
2. 400+600x!0-6£ 
0.335 + 324x10-6* 
0.150+168x10-6* 
0.491 + 748x10-6* 



538 



Thermal Capacities of Gases per Kilogram in Centigrade Degrees. 



Under Constant 
Pressure. 



Under Constant 
Volume. 



Oxygen 

Nitrogen and Carbon Monoxide 

Hydrogen 

Water Vapor 

Carbon Dioxide 

Methane or Marsh Gas 



0.213 t + 19x10~6{2 
0.243 * + 21x10-6*2 
3.400 £+300x10-0 P 
0.447 £ + 162x10-6^2 
0.193£+ 84x10-6*2 
0.608 £+374x10-6*2 



0.150 * + 19xl0-6£2 
0.243 * + 21x10-6*2 
2.400 £+300x10-6*2 
0.335 £ + 162x10-6*2 
0.150*+ 84x10-6*2 
0.491 £+3,4x10-6*2 



Thermal Capacities op Gases per Kilogram. 



Temperatures. 


o 2 


N 2 , CO 


H 2 


H 2 


C0 2 


CH 4 


Degrees Centigrade. 
200 




47.3 
88.0 
134.0 
181.0 
232.0 
284.0 
334.0 
391.0 
444.0 
503.0 
558.0 
6 0.0 
681.0 
735.0 
810.0 

i 




50 
100 
154 
207 
264 
325 
383 
445 
508 
575 
637 
708 
777 
850 
921 



700 
1400 
2150 
2900 
3700 
4550 
5350 
6250 
7100 
8050 
8950 
9900 
10900 
11900 
12950 




100 
203 
326 
461 
609 
770 
943 
1130 
1330 
154'. 
1751 
1985 
2241 
2520 
2799 




43.1 
91.0 
145.0 
208.0 
277.0 
354.0 
435.0 
523.0 
618.0 
728.0 
840.0 
950.0 
1070.0 
1200.0 
1355.0 



136.6 


400 

600 


303.0 
499.0 


800 


726.0 


1000 


982.0 


1200.... 


1269.0 


1400 


1584.0 


1600 


1931.0 


1800 

2000 


2307.0 
712.0 


2200 


3148.0 


>400 


3614.0 


2600 


4109.0 


2800 


4635.0 


3000 


5190.0 







EXPANSION BY HEAT. 

In the centigrade scale the coefficient of expansion of air per degree is 
0.003665 = 1/273; that is, the pressure being constant, the volume of a 
perfect gas increases 1 /273 of its volume at 0° C. for every increase in 
temperature of 1° C. In Fahrenheit units it increases 1/491.2= 0.003620 
of its volume at 32° F. for every increase of 1° F. 

Expansion of Gases by Heat from 32° to 212° F. (Regnault.) 





Increase in Volume, 

Pressure Constant. 

Volume at 32° Fahr. 

= 1.0, for 


Increase in Pressure, 

Volume Constant. 

Pressure at 32° 

Fahr. = 1.0, for 




100° c. 


1°F. 


100° C. 


1°F. 




0.3661 
0.3670 
0.3670 
0.3669 
0.3710 
0.3903 


0.002034 
0.002039 
0.002039 
0.002038 
0.002061 
0.002168 


0.3667 
0.3665 
0.3668 
0.3667 
0.3688 
0.3845 


0.002037 




0.002036 




0.002039 




0.002037 




0.002039 




0.002136 







If the volume is kept constant, the pressure varies directly as the abso- 
lute temperature. 



EXPANSION BY HEAT. 



539 



Lineal Expansion of Solids at Ordinary Temperatures. 

(Mostly British Board of Trade; from Clark.) 



For 
l°Fahr. 
Length 

= 1. 



For 
1°Cent. 
Length 



Expan- 
sion 
from 
32° to 
212° F. 



Accord- 
ing to 
Other 

Author- 
ties. 



Aluminum (cast) 

Antimony (cryst.) 

Brass, cast 

Brass, plate 

Brick 

Brick (fire) 

Bronze (Copper, 17; Tin, 2l/ 2 ; Zinc, 1) . . 

Bismuth 

Cement, Portland (mixed), pure 

Concrete: cement-mortar and pebbles. . 

Copper 

Ebonite 

Glass, English flint 

Glass, thermometer 

Glass, hard 

Granite, gray, dry 

Granite, red, dry 

Gold, pure 

Iridium, pure 

Iron, wrought 

Iron, cast 

Lead 

Magnesium 

Marbles, various { ^° m 

Masonry, brick { *™ m 

Mercury (cubic expansion) 

Nickel 

Pewter 

Plaster, white 

Platinum 

Platinum, 85 %, Iridium, 15 % 

Porcelain 

Quartz, parallel to maj. axis, 0° to 40° C 
Quartz, perpend, to maj. axis, 0° to 40°C 

Silver, pure 

Slate 

Steel, cast 

Steel, tempered 

Stone (sandstone), dry 

Stone (sandstone), Rauville 

Tin 

Wedgwood ware 

Wood, pine 

Zinc 

Zinc, 8, Tin, 1 



0.00001234 
0.00000627 
0.00000957 
0.00001052 
0.00000306 
0.00000300 
0.00000986 
0.00000975 
0.00000594 
0.00000795 
0.00000887 
0.00004278 
0.00000451 
0.00000499 
0.00000397 
00000438 
0.00000498 
0.00000786 
0.00000356 
0.00000648 
0.00000556 
0.00001571 



0.00002221 
0.00001129 
0.00001722 
0.00001894 
0.O0OOO55O 
0.00000540 
J. 0000 1774 
3.00001755 
3.00001070 
3.00001430 
0.00001596 
3 . 00007700 
3.00000812 
. 00000897 
00000714 
.00000789 
0.0000089^ 
0.00001415 
0.0000064 
0.00001166 
0.00001001 
0.00002828 



0.002221 

0.001129 

0.001722 

0.001894 

0.000550 

0.005400 

0.001774 

0.001755 

0.001070 

0.001430 

0.001596 

0.007700 

0.000812 

0.000897 

0.00071 

0.000789 

0. 000897 

0.001415 

0.000641 

0.001166 

0.001001 

0.002828 



0.001083 
0.001868 



0.001235 
0.001110 



0.00000308 
0.00000786 
0.00000256 
0.00000494 
0.00009984 
0.00000695 
0.00001129 
0.00000922 
0.00000479 
0.00000453 
0.00000200 
0.00000434 
0.00000788 
0.00001079 
0.00000577 
0.00000636 
0.00000689 
0.00000652 
0.00000417 
0.00001163 
0.00000489 
0.00000276 
0.00001407 
0.00001496 



0.00000554 
0.00001415 
0.00000460 

00000890 
0.00017971 
0.00001251 

.00002033 
0.00001660 
0.00000863 
0.00000815 
0.00000360 
0.00000781 
0.00001419 
0.00001943 
0.00001038 
0.00001144 
0.00001240 
0.00001174 
0.00000750 
0.00002094 
0.00000881 
0.00000496 
0.00002532 
0.00002692 



0.000554 
0.001415 
0.000460 
0.000890 
0.017971 
0.001251 
0.002033 
0.001660 
0.000863 
0.000815 
0.000360 
0.00078! 
0.001419 
0.001943 
0.001038 
0.001144 
0.001240 
0.001174 
0.000750 
0.002094 

0.000496 
0.002532 
0.002692 



0.018018 
0.001279 



Invar (see next page), .000,000,374 to 0.000,000,44 for 1° C. 

Cubical expansion, or expansion of volume = linear expansion X 3. 

Expansion of Steel at Hiffh Temperatures. (Charpy and Grenet, 
Comptes Rendus, 1902.) — Coefficients of expansion (for 1° C.) of annealed 
carbon and nickel steels at temperatures at which there is no transforma- 



540 



tion of the steel. The results seein to show that iron and carbide of iron 
have appreciably the same coefficient of expansion. [See also p. 474.] 



Composition 
of Steels. 


Mean Coefficients of Expansion 
from 


Coeffs. between 


f! 


\l.i 


Si 


P 


1.5° to 200 


3 200° to 500° 500° to 650° 






o 03 


) 01 


n rn 


013 


11.8X10""" 


14.3X10" 


> 17.0X10 " 6 


24.5X10- 6 


880° & 950° 


2,5 


) 04 


05 


010 


11.5 


14.5 


17.5 


23.3 


800° & 950° 


64 


) 12 


14 


009 


12.1 


14.1 


16.5 


23.3 


720° & 950° 


93 


) 10 


05 


005 


11.6 


14.9 


16.0 


27.5 




1 23 


) 10 


08 


005 


11.9 


14.3 


16.5 


33.8 




1 50 


) 04 


09 


0<G 


11.5 


14.9 


16.5 


36.7 




3.50 


3.03 


0.07 


0.005 


11.2 


14.2 


18.0 


33.3 




Nickel Steels. 


Mean Coefficients of Expansion from 


Ni 





Mr, 


15° to 100° 


00° to 200° 


200° to 400° 


400° to 600° 


600° to 900° 


26 9 


0.35 


30 


11.0x10-6 


18.0x10-6 


18.7x10-6 


22.0x10-6 


23.0X10- 6 


28,9 


0.35 


36 


10.0 


21.5 


19.0 


20.0 


22.7 


30 1 


0.35 


0.34 


9.5 


14.0 


19.5 


19.0 


21.3 


34 7 


0.36 


36 


2.0 


2.5 


11.75 


19.5 


;o.7 


36 1 


0.39 


39 


1.5 


1.5 


11.75 


17.0 


20.3 


32. e 


0.29 


0.66 


8.0 


14.0 


18.0 


21.5 


22.3 


35 f> 


0.31 


0,69 


2.5 


2.5 


12.5 


13.75 


1\3 


37 < 


0.30 


69 


2.5 


1.5 


8.5 


19.75 


18.3 


25 A 


1.01 


79 


12.5 


18.5 


19.75 


21.0 


35.0 


29 4 


0.99 


89 


11.0 


12 5 


19.0 


20.5 


31.7 


34.5 


0.97 


0.84 


3.0 


3.5 


13.0 


18.75 


26.7 



Invar, an alloy of iron with 36 per cent of nickel, has a smaller coeffi- 
cient of expansion with the ordinary atmospheric changes of temperature 
than any other metal or alloy known. This alloy is sold under the name 
of "Invar," and is used for scientific instruments, pendulums of clocks, 
steel tape-measures for accurate survey work, etc. The Bureau of Stand- 
ards found its coefficient of expansion to range from 0.000,000,374 to 
0.000,000,44 for 1° C, or about V28 of that of steel. For all surveys except 
in the most precise geodetic work a tape of invar may be used without 
correction for temperature. (Eng. News, Aug. 13, 1908.) 

Platinite, an alloy of iron with 42 per cent of nickel, has the same 
coefficient of expansion and contraction at atmospheric temperatures as 
has glass. It can, therefore, be used for the manufacture of armored 
glass, that is, a plate of glass into which a network of steel wire has been 
rolled, and which is used for fire-proofing, etc. It can also be used instead 
of platinum for the electric connections passing through the glass plugs in 
the base of incandescent electric lights. (Stoughton's " Metallurgy of 



Expansion of Liquids from 33° to 212° F. — Apparent expansion 
in glass (Clark). Volume at 212°, volume at 32° being 1: 



Water 1.0466 

Water saturated with salt . 1.05 

Mercury 1.0182 

Alcohol 1.11 



Nitric acid 1.11 

Olive and linseed oils 1 . 08 

Turpentine and ether 1 .07 

Hydrochloric and sulphuric 
acids 1.06 

For water at various temperatures, see Water. 

For air at various temperatures, see Air. 

ABSOLUTE TEMPERATURE — ABSOLUTE ZERO. 

The absolute zero of a gas is a theoretical consequence of the law of 
expansion by heat, assuming that it is possible to continue the cooling of 
a perfect gas until its volume is diminished to nothing. 



LATENT HEATS OF FUSION. 541 

If the volume of a perfect gas increases V273 of its volume at 0° C. for 
every increase of temperature of 1° C.,and decreases V273 of its volume 
for every decrease of temperature of 1° C„ then at -273° C. the volume 
of the imaginary gas would be reduced to nothing. This point -273° C , 
or 491.2° F. below the melting-point of ice on the air-thermometer, or 
492.66° F. below on a perfect gas-thermometer = -459.2° F. (or 
— 460.66°), is called the absolute zero; and absolute temperatures are 
temperatures measured, on either the Fahrenheit or Centigrade scale, 
from this zero. The freezing-point, 32° F., corresponds to 491.2° F. 
absolute. If p be the pressure and v the volume of a gas at the tem- 
perature of 32° F. = 491.2° on the absolute scale = T , and p the pressure, 
and v the volume of the same quantity of gas at any other absolute tem- 
perature T, then 

pv _ T_ = t + 459 . 2 . pv = p v 
p Vo T 491.2 ' T ~ T ' 

The value of p v ■*■ T for air is 53.37, and pv = 53.37 T, calculated as 
follows by Prof. Wood: 

A cubic foot of dry air at 32° F. at the sea-level weighs 0.080728 lb. 

The volume of one pound is v = nori _ 00 = 12.387 cubic feet. The 
pressure per square foot is 2116.2 lbs. 

Wo = 2116.2 X 12.387 26214 ro 
To 491.13 491.13 °° 

The figure 491.13 is the number of degrees that the absolute zero is below 
the melting-point of ice, by the air-thermometer. On the absolute scale, 
whose divisions would be indicated by a perfect gas-thermometer, the 
calculated value approximately is -192.66, which would make pv = 53.21 T. 
Prof. Thomson considers that — 273.1° C, = — 459.4° F., is the most 
probable value of the absolute zero. See Heat in Ency. Brit. 

LATENT HEATS OF FUSION AND EVAPORATION. 

Latent Heat means a quantity of heat which has disappeared, having 
been employed to produce some change other than elevation of tempera- 
ture. By exactly reversing that change, the quantity of heat which 
has disappeared is reproduced. Maxwell defines it as the quantity of 
heat which must be communicated to a body in a given state in order to 
convert it into another state without changing its temperature. 

Latent Heat of Fusion. — When a body passes from the solid to the 
liquid state, its temperature remains stationary, or nearly stationary, at 
a certain melting-point during the whole operation of melting; and in 
order to make that operation go on, a quantity of heat must be transferred 
to the substance melted, being a certain amount for each unit of weight 
of the substance. This quantity is called the latent heat of fusion. 

When a body passes from the liquid to the solid state, its temperature 
remains stationary or nearly stationary during the whole operation of 
freezing; a quantity of heat equal to the latent heat of fusion is produced 
in the body and rejected into the atmosphere or other surrounding bodies. 

The following are examples in British thermal units per pound, as 
given in Landolt and Bornstein's Phi/sikalische-Chemische Tabellen (Berlin, 
1894). 

Snhqtanrps Latent Heat s,,bstanrpq Latent Heat 

bubstances. of Fusion bubstances. of Fusion> 

Bismuth 22.75 Silver 37.93 

Cast iron, gray ... 41 . 4 Beeswax 76 . 14 

Cast iron, white . . 59 . 4 Paraffine 63 . 27 

Lead 9 . 66 Spermaceti 66 . 56 

Tin 25.65 Phosphorus 9.06 

Zinc 50.63 Sulphur 16.86 

Prof. Wood considers 144 heat-units as the most reliable value for the 
latent heat of fusion of ice. Person gives 142.65. 



542 HEAT. 



Latent Heat of Evaporation. — When a body passes from the 
solid or liquid to the gaseous state, its temperature during the operation 
remains stationary at a certain boiling-point, depending on the pressure of 
the vapor produced; and in order to make the evaporation go on, a 
quantity of heat must be transferred to the substance evaporated, whose 
amount for each unit of weight of the substance evaporated depends on 
the temperature. That heat does not raise the temperature of the sub- 
stance, but disappears in causing it to assume the gaseous state, and it is 
called the latent heat of evaporation. 

When a body passes from the gaseous state to the liquid or solid state, 
its temperature remains stationary, during that operation, at the boiling- 
point corresponding to the pressure of the vapor: a quantity of heat 
equal to the latent, heat of evaporation at that temperature is produced 
in the body; and in order that the operation of condensation may go on, 
that heat must be transferred from the body condensed to some other 
body. 

The following are examples of the latent heat of evaporation in British 
thermal units, of one pound of certain substances, when the pressure of 
the vapor is one atmosphere of 14.7 lbs. on the square inch: 

(,„!,„,„,... Boiling-point under Latent Heat in 

toUDSiance. one atm Fahr _ British units. 

Water 212.0 965.7 (Regnault). 

Alcohol 172.2 364.3 (Andrews). 

Ether 95.0 162.8 

Bisulphide of carbon 114.8 156.0 

The latent heat of evaporation of water at a series of boiling-points ex- 
tending from a few degrees below its freezing-point up to about 375 
degrees Fahrenheit has been determined experimentally by M. Regnault. 
The results of those experiments are represented approximately by the 
formula, in British thermal units per pound, 

I nearly = 1091.7 - 0.7 (t - 32°) = 965.7 - 0.7 (t - 212°). 

Henning (Ann. der Physik, 1906) gives for t from 0° to 100° C. 

Fori kg.,Z = 94.210 (365 - 1° C.) 0.31249. 

Fori lb., £ = 141.124 (689 -£° F.) 0.31249. 

The last formula gives for the latent heat at 212° F., 969.7 B.T.U. 

The Total Heat of Evaporation is the sum of the heat which dis- 
appears in evaporating one pound of a given substance at a given tem- 
perature (or latent heat of evaporation) and of the heat required to raise its 
temperature, before evaporation, from some fixed temperature up to the 
temperature of evaporation. The latter part of the total heat is called the 
sensible heat. 

In the case of water, the experiments of M. Regnault show that the 
total heat of steam from the temperature of melting ice increases at a 
uniform rate as the temperature of evaporation rises. The following is 
the formula in British thermal units per pound: 

h = 1091.7 + 0.305 (t - 32°). 

H. N. Davis (Trans. A. S. M. E„ 1908) gives, in British units, 
ft = 1150 + 0.3745 (t- 21-2) -0.000550 (f-212) 2 . 

For the total heat, latent heat, etc., of steam at different pressures, see 
table of the Properties of Saturated Steam. For tables of total heat, 
latent heat, and other properties of steams of ether, alcohol, acetone, 
chloroform, chloride of carbon, and bisulphide of carbon, see Rontgen's 
Thermodynamics (Dubois's translation). For ammonia and sulphur 
dioxide, see Wood's Thermodynamics; also, tables under Refrigerating 
Machinery, in this book. 

EVAPORATION AND DRYING. 

In evaporation, the formation of vapor takes place on the surface; in 
boiling, within the liquid: the former is a slow, the latter a quick, method 
of evaporation. 

If we bring an open vessel with water under the receiver of an air-pump 
and exhaust the air, the water in the vessel will commence to boil, and if we 
keep up the vacuum the water will actually boil near its freezing-point. 
The formation of steam in this case is due to the heat which the water 
takes out of the surroundings. 



EVAPORATION AND DRYING. 543 

Steam formed under pressure has the same temperature as the liquid in 
which it was formed, provided the steam is kept under the same pressure. 

By properly cooling the rising steam from boiling water, as in the mul- 
tiple-effect evaporating systems, we can regulate the pressure so that the 
water boils at low temperatures. 

Evaporation of Water in Reservoirs. — Experiments at the Mount 
Hope Reservoir, Rochester, N. Y., in 1891, gave the following results: 

July. Aug. Sept. Oct. 

Mean temperature of air in shade 70.5 70.3 68.7 53.3 

" water in reservoir. . . 68.2 70.2 66.1 54.4 

" humidity of air, per cent 67.0 74.6 75.2 74.7 

Evaporation in inches during month 5 . 59 4 . 93 4 . 05 3 . 23 

Rainfall in inches during month 3 . 44 2 . 95 1 . 44 2.16 

Evaporation of Water from Open Channels. (Flynn's Irrigation 
Canals and Flow of Water.) — Experiments from 1881 to 1885 in Tulare 
County, California, showed an evaporation from a pan in the river equal 
to an average depth of l/s in. per day throughout the year. 

When the pan was in the air the average evaporation was less than 3/ 16 
in. per day. The average for the month of August was 1/3 in. per day, 
and for March and April 1/12 in. per day. Experiments in Colorado show 
that evaporation ranges from 0.0S8 to 0.16 in. per day during the irriga- 
ting season. 

In Northern Italy the evaporation was from 1/12 to 1/9 inch per day, 
while in the south, under the influence of hot winds, it was from l/e to 1/5 
inch per day. 

In the hot season in Northern India, with a decidedly hot wind blow- 
ing, the average evaporation was 1/2 inch per day. The evaporation 
increases with the temperature of the water. 

Evaporation by the Multiple System. — A multiple effect is a series 
of evaporating vessels each having a steam chamber, so connected that 
the heat of the steam or vapor produced in the first vessel heats the 
second, the vapor or steam produced in the second heats the third, and so 
on. The vapor from the last vessel is condensed in a condenser. Three 
vessels are generally used, in which case the apparatus is called a Triple 
Effect. In evaporating in a triple effect the vacuum is graduated so that 
the liquid is boiled at a constant and low temperature. 

A series distilling apparatus of high efficiency is described by W. P. M, 
Goss in Trans, A. S. M. E., 1903. It has seven chambers in series, and 
is designed to distill 500 gallons of water per hour with an efficiency of 
approximately 60 lbs. of water per pound of coal. 

Tests of Yaryan six-effect machines have shown as high as 44 lbs. of 
water evaporated per pound of fuel consumed. — Mach'y, April, 1905. 
A description of a large distilling apparatus, using three 125-H.P. boilers 
and a Lillie triple effect, with record of tests, is given in Eng. News, 
Mar. 29, 1900, and in Jour. Am. Soc'y of Naval Engineers, Feb., 1900. 

Resistance to Boiling. — Brine. (Rankine.) — The presence in a 
liquid of a substance dissolved in it (as salt in water) resists ebullition, and 
raises the temperature at which the liquid boils, under a given pressure; but 
unless the dissolved substance enters into the composition of the vapor, 
the relation between the temperature and pressure of saturation of the 
vapor remains unchanged. A resistance to ebullition is also offered by a 
vessel of a material which attracts the liquid (as when water boils in a 
glass vessel), and the boiling take place by starts. To avoid the errors 
which causes of this kind produce in the measurement of boiling-points, 
it is advisable to place the thermometer, not in the liquid, but in the 
vapor, which shows the true boiling-point, freed from the disturbing 
effect of the attractive nature of the vessel. The boiling-point of saturated 
brine under one atmosphere is 226° F., and that of weaker brine is higher 
than the boiling-point of pure water by 1.2° F., for each V32 of salt that 
the water contains. Average sea-water contains 1/32; and the brine in 
marine boilers is not suffered to contain more than from 2/ 32 to 3/32. 

Methods of Evaporation Employed in the Manufacture of Salt. 
(F. E. Engelhardt, Chemist Onondaga Salt Springs; Report for 1889.) — 
1. Solar heat — solar evaporation. 2. Direct fire, applied to the heat- 
ing surface of the vessels containing brine — kettle and pan methods. 
3. The steam-grainer system — steam-pans, steam-kettles, etc. 4. Use 



544 



of steam and a reduction of the atmospheric pressure over the boiling 
brine — vacuum system. 

When a saturated salt solution boils, it is immaterial whether it is done 
under ordinary atmospheric pressure at 228° F., or under four atmospheres 
with a temperature of 320° F., or in a vacuum under Vio atmosphere, the 
result will always be a fine-grained salt. 

The fuel consumption is stated to be as follows: By the kettle method, 
40 to 45 bu. of salt evaporated per ton of fuel, anthracite dust burned on 
perforated grates; evaporation, 5.53 lbs. of water per pound of coal. By 
the pan method, 70 to 75 bu. per ton of fuel. By vacuum pans, single 
effect, 86 bu. per ton of anthracite dust (2000 lbs.). With a double 
effect nearly double that amount can be produced. 

Solubility of Common Salt in Pure Water. (Andrese.) 



32 50 86 104 140 176 

35.63 35.69 36.03 36.32 37.06 38.00 
26.27 26.30 26.49 26.64 27.04 27.54 



Temp, of brine, F 

100 parts water dissolve parts. 
100 parts brine contain salt . . . 

According to Poggial, 100 parts of water dissolve at 229.66° F., 40.35 
parts of salt, or in per cent of brine, 28.749. Gay-Lussac found that at 
229.72° F., 100 parts of pure water would dissolve 40.38 parts of salt, in 
per cent of brine, 28.764'parts. 

The solubility of salt at 229° F. is only 2.5% greater than at 32°. Hence 
we cannot, as in the case of alum, separate the salt from the water by 
allowing a saturated solution at the boiling-point to cool to a lower 
temperature. 

Strength of Salt Brines. — The following table is condensed from 
one given in U. S. Mineral Resources for 1888, on the authority of Dr. 
Engelhardt. 

Relations between Salinometer Strength, Specific Gravity, Solid 
Contents, etc., of Brines of Different Strengths. 



1 

o> 

a 

o 


03 
O) 

g> 
SB 


bfl 


"o3 
4) 


Mo 
ft 

*.£ 


.2 3 

o3_ 

°£ . 


'3 . 

® cm 

O «3 


0> 0) 

3 OS 

eg 3O 


of coal required to 
duce a bushel of 
;, 1 lb. coal evapo- 
ing 6 lbs. of water. 


§"3 

03.^ ft 

-■85 
■si's 


"c3 


o3 
ffl 


ft 


0) 


ga 


!-s 


O 1 " 


£o>03 


3 all 




1 


0.26 


1.002 


0.265 


8.347 


0.022 


2,531 


21,076 


3,513 


0.569 


2 


0.52 


1.003 


0.530 


8.356 


0.044 


1,264 


10,510 


1,752 


1.141 


4 


1.04 


1.007 


1.060 


8.389 


0.088 


629.7 


5,227 


871.2 


2.295 


6..... 


1.56 


1.010 


1.590 


8.414 


0.133 


418.6 


3,466 


577.7 


3.462 


8 


2.08 


1.014 


2.120 


8.447 


0.179 


312.7 


2,585 


430.9 


4.641 


10 


2.60 


1.017 


2.650 


8.472 


0.224 


249.4 


2,057 


342.9 


5.833 


12 


3.12 


1.021 


3.180 


8.506 


0.270 


207.0 


1,705 


284.2 


7.038 


14 


3.64 


1.025 


3.710 


8.539 


0.316 


176.8 


1,453 


242.2 


8.256 


16 


4.16 


1.028 


4.240 


8.564 


0.364 


154.2 


1,265 


210.8 


9.488 


18 


4.68 


1.032 


4.770 


8.597 


0.410 


136.5 


1,118 


186.3 


10.73 


20 


5.20 


1.035 


5.300 


8.622 


0.457 


122.5 


1,001 


176.8 


11.99 


30 


7.80 


1.054 


7.950 


8.781 


0.698 


80.21 


648.4 


108.1 


18.51 


40 


10.40 


1.073 


10.600 


8.939 


0.947 


59.09 


472.3 


78.71 


25.41 


50 


13.00 


1.093 


13.250 


9.105 


1.206 


46.41 


366.6 


61.10 


32.73 


60 


15.60 


1.114 


15.900 


9.280 


1.475 


37.94 


296.2 


49.36 


40.51 


70 


18.20 


1.136 


18.550 


9.454 


1.755 


31.89 


245.9 


40.98 


48.80 


80 


20.80 


1.158 


21.200 


9.647 


2.045 


27.38 


208.1 


34.69 


57.65 


90 


23.40 


1.182 


23.850 


9.847 


2.348 


23.84 


178.8 


29.80 


67.11 


109 


26.00 


1.205 


26.500 


10.039 


2.660 


21.04 


155.3 


25.88 


77.26 



EVAPORATION AND DRYING. 545 



Solubility of Sulphate of Lime in Pure Water. (Marignac.) 
Temperature F. degrees.. 32 64.5 89.6 100.4 105.8 127.4 186.8 212 
P \ rt parltvpsim diSSOlVe ) i15 386 371 368 370 375 417 452 
P ^^Z^t^!}^ «* 470 466 468 474 528 572 

In salt brine sulphate of lime is much more soluble than in pure water. 
In the evaporation of salt brine the accumulation of sulphate of lime tends 
to stop the operation, and it must be removed from the pans to avoid 
waste of fuel. 

The average strength of brine in the New York salt districts in 18S9 was 
69.38 degrees of the saliuometer. 

Concentration of Sugar Solutions.* (From " Heating and Con- 
centrating Liquids by Steam," by John G.Hudson; The Engineer, June 13, 
1890.) — In the early stages of the process, when the liquor is of low 
density, the evaporative duty will be high, say two to three (British) 
gallons per square foot of heating surface with 10 lbs. steam pressure, 
but will gradually fall to an almost nominal amount as the final stage is 
approached. As a generally safe basis for designing, Mr. Hudson takes 
an evaporation of one gallon per hour for each square foot of gross heating 
surface, with steam of the pressure of about 10 lbs. 

As examples of the evaporative duty of a vacuum pan when performing 
the earlier stages of concentration, during which all the heating surface 
can be employed, he gives the following: 

Coil Vacuum Pan. — 43/4 in. copper coils, 528 square feet of surface; 
steam in coils, 15 lbs.; temperature in pan, 141° to 148°; density of feed, 
25° Baumd, and concentrated to 31° Baume. 

First Trial. — Evaporation at the rate of 2000 gallons per hour = 3.8 
gallons per square foot; transmission, 376 units per degree of difference of 
temperature. 

Second Trial. — Evaporation at the rate of 1503 gallons per hour — 
2.8 gallons per square foot ; transmission, 265 units per degree. 
• As regards the total time needed to work up a charge of massecuite from 
liquor of a given density, the following figures, obtained by plotting the 
results from a large number of pans, form a guide to practical working. 
The pans were all of the coil type, some with and some without jackets, 
the gross heating surface probably averaging, and not greatly differing 
from, 0.25 square foot per gallon capacity, and the steam pressure 10 lbs. 
per square inch. Both plantation and refining pans are included, making 
various grades of sugar: 

Density of feed (degs. Baume) 10° 15° 20° 25° 30° 

Evaporation required per gallon masse- 
cuite discharged 6.123 3.6 2.26 1.5 .97 

Average working hours required per charge . 12. 9. 6.5 5. 4. 

Equivalent average evaporation per hour 
per square foot of gross surface, assum- 
ing 0.25 sq. ft. per gallon capacity. .. . 2.04 1.6 1.39 1.2 0.97 

Fastest working hours required per charge . 8.5 5.53.8 2 , 75 2.0 

Equivalent average evaporation per hour 

per square foot 2.88 2.6 2.38 2.18 1.9 

The quantity of heating steam needed is practically the same in vacuum 
as in open pans. The advantages proper to the vacuum system are pri- 
marily the reduced temperature of boiling, and incidentally the possibility 
of using heating steam of low pressure. 

In a solution of sugar in water, each pound of sugar adds to the volume 
of the water to the extent of 0.061 gallon at a low density to 0.0638 gallon 
at high densities. 

A Method of Evaporating by Exhaust Steam is described by 
Albert Stearns in Trans. A. S. M. E., vol. viii. A pan 17' 6" X 11' X 1' 6", 

* For other sugar data, see Bagasse as Fuel, under Fuel. 



546 HEAT. 

fitted with cast-iron condensing pipes of about 250 sq. ft. of surface, 
evaporated 120 gallons per hour from clear water, condensing only about 
one-half of the steam supplied by a plain slide-valve engine of 14" X 32" 
cylinder, making 65 revs, per min., cutting off about two-thirds stroke, 
with steam at 75 lbs. boiler pressure. 

It was found that keeping the pan-room warm and letting only sufficient 
air in to carry the vapor up out of a ventilator adds to its efficiency, as 
the average temperature of the water in the pan was only about 165° F. 

Experiments were made with coils of pipe in a small pan, first with no 
agitator, then with one having straight blades, and lastly with troughed 
blades; the evaporative results being about the proportions of one, two, 
and three respectively. 

In evaporating liquors whose boiling-point is 220° F., or much above 
that of water, it is found that exhaust steam can do but little more than 
bring them up to saturation strength, but on weak liquors, sirups, glues, 
etc., it should be very useful. 

Drying in Vacuum. — An apparatus for drying grain and other sub- 
stances in vacuum is described by Mr. Emil Passburg in Proc. Inst. Mech. 
Engrs., 18S9. The three essential requirements for a successful and eco- 
nomical process of drying are: 1. Cheap evaporation of the moisture; 
2. Quick drying at a low temperature; 3. Large capacity of the apparatus. 

The removal of the moisture can be effected in either of two ways: either 
by slow evaporation, or by quick evaporation — that is, by boiling. 

Slow Evaporation. — The principal idea carried into practice in machines 
acting by slow evaporation is to bring the wet substance repeatedly into 
contact with the inner surfaces of the apparatus, which are heated by 
steam, while at the same time a current of hot air is also passing through 
the substances for carrying off the moisture. This method requires much 
heat, because the hot-air current has to move at a considerable speed in 
order to shorten the drying process as much as possible; consequently a 
great quantity of heated air passes through and escapes unused. As a 
carrier of moisture hot air cannot in practice be charged beyond half its full 
saturation; and it is in fact considered a satisfactory result if even this 
proportion be attained. A great amount of heat is here produced which is 
not used; while, with scarcely half the cost for fuel, a much quicker 
removal of the water is obtained by heating it to the boiling-point. 

Quick Evaporation by Boiling. — This does not take place until the 
water is brought up to the boiling-point and kept there, namely, 212° F., 
under atmospheiic pressure. The vapor generated then escapes freely. 
Liquids are easily evaporated in this way, because by their motion conse- 
quent on boiling the heat is continuously conveyed from the heating sur- 
faces through the liquid, but it is different with solid substances, and 
many more difficulties have to be overcome, because convection of the 
heat ceases entirely in solids. The substance remains motionless, and 
consequently a much greater quantity of heat is required than with 
liquids for obtaining the same results. 

Evaporation in Vacuum. — All the foregoing disadvantages are avoided 
if the boiling-point of water is lowered, that is, if the evaporation is carried 
out under vacuum. 

This plan has been successfully applied in Mr. Passburg's vacuum drying 
apparatus, which is designed to evaporate large quantities of water con- 
tained in solid substances. 

The drying apparatus consists of a top horizontal cylinder, surmounted 
bv a charging vessel at one end, and a bottom horizontal cylinder with a 
discharging vessel beneath it at the same end. Both cylinders are 
incased in steam-jackets heated by exhaust steam. In the top cylinder 
works a revolving cast-iron screw with hollow blades, which is also heated 
by exhaust steam. The bottom cylinder contains a revolving drum of 
tubes, consisting of one large central tube surrounded by 24 smaller ones, 
all fixed in tube-plates at both ends; this drum is heated by live steam 
direct from the boiler. The substance to be dried is fed into the charg- 
ing vessel through two manholes, and is carried along the top cylinder 
by the screw creeper to the back end, where it drops through a valve 
into the bottom cylinder, in which it is lifted by blades attached to the 
drum and travels forward in the reverse direction; from the front end of 
the bottom cylinder it falls into a discharging vessel through another 



EVAPORATION AND DRYING. 547 

valve, having by this time become dried. The vapor arising during the 
process is carried off by an air-pump, through a dome and air-valve on 
the top of the upper cylinder, and also through a throttle-valve on 
the top of the lower cylinder; both of these valves are supplied with 
strainers. 

As soon as the discharging vessel is filled with dried material the valve 
connecting it with the bottom cylinder is shut, and the dried charge taken 
out without impairing the vacuum in the apparatus. When the charging 
vessel requires replenishing, the intermediate valve between the two cylin- 
ders is shut, and the charging vessel filled with a fresh supply of wet mate- 
rial; the vacuum still remains unimpaired in the bottom cylinder, and has 
to be restored only in the top cylinder after the charging vessel has been 
closed agaii\. 

In this vacuum the boiling-point of the water contained in the wet mate- 
rial is brought down as low as 110° F. The difference between this tem- 
perature and that of the heating surfaces is amply sufficient for obtaining 
good results from the employment of exhaust steam for heating all the 
surfaces except the revolving drum of tubes. The water contained in 
the solid substance to be dried evaporates as soon as the latter is heated 
to about 110° F., and as long as there is any moisture to be removed the 
solid substance is not heated above this temperature. 

Wet grains from a brewery or distillery, containing from 75% to 78% of 
water, have by this drying process been converted from a worthless incum- 
brance into a valuable food-stuff. The water is removed by evaporation 
only, no previous mechanical pressing being resorted to. 

At Guinness's brewery in Dublin two of these machines are employed. 
In each of these the top cylinder is 20 ft. 4 in. long and 2 ft. 8 in. diam., 
and the screw working inside it makes 7 revs, per min.; the bottom 
cylinder is 19 ft. 2 in. long and 5 ft. 4 in. diam., and the drum of the tubes 
inside it makes 5 revs, per min. The drying surfaces of the two cylinders 
amount together to a total area of about 1000 sq. ft., of which about 40% 
is heated by exhaust steam direct from the boiler. There is only one air- 
pump, which is made large enough for three machines; it is hori- 
zontal, and has only one air-cylinder, which is double-acting, 17 3/ 4 in. 
diam. and 173/4 in. stroke; and it is driven at about 45 revs, per min. 
As the result of about eight months' experience, the two machines 
have been drying the wet grains from about 500 cwt. of malt per day of 
24 hours. 

Roughly speaking, 3 cwt. of malt gave 4 cwt. of wet grains, and the 
latter yield 1 cwt. of dried grains; 500 cwt. of malt will therefore yield 
about 670 cwt. of wet grains, or 335 cwt. per machine. The quantity of 
water to be evaporated from the wet grains is from 75% to 78% of their 
total weight, or, say, about 512 cwt. altogether, being 256 cwt. per 
machine. 

Driers and Drying. 

(Contributed by W. B. Ruggles, 1909.) 

Materials of different physical and chemical properties require different 
types of drying apparatus. It is therefore necessary to classify mate- 
rials into groups, as below, andj design different machines for each 
group. 

Group A: Materials which may be heated to a high temperature and 
are not injured by being in contact with products of combustion. These 
include cement rock, sand, gravel, granulated slag, clay, marl, chalk, ore, 
graphite, asbestos, phosphate rock, slacked lime, etc. 

The most simple machine for drying these materials is a single revolving 
shell with lifting flights on the inside, the shell resting on bearing wheels 
and having a furnace at one end and a stack or fan at the other. The 
advantage of this style of machine is its low cost of installation and the 
small number of parts. The disadvantages are great cost of repairs and 
excessive fuel consumption, due to radiation and high temperature of the 
stack gases. If the material is fed from the stack and towards the furnace 
end, the shell near the furnace gets red-hot, causing excessive radiation and 
frequent repairs. Should the feed be reversed the exhaust temperature 



548 HEAT, 

must be kept above 212° F M or recondensation will take place, wetting the 
material. 

in order to economize fuel the shell is sometimes supported at the 
ends and brickwork is erected around the shell, the hot gases passing 
-under the shell and back through it. Although this method is more 
economical in the use of fuel, the cost of installation and the cost of 
repairs are greater. 

Group B: Materials such as will not be injured by the products of com- 
bustion but cannot be raised to a high temperature on account of driving 
off water of crystallization, breaking up chemical combinations, or on 
account of danger from ignition. Included in these are gypsum, fluor- 
spar, iron pyrites, coal, coke, lignite, sawdust, leather scraps, cork chips, 
tobacco stems, fish scraps, tankage, peat, etc. Some of these materials 
may be dried in a single-shell drier and some in a bricked -in machine, 
but none of them in a satisfactory way on account of the difficulty of 
regulating the temperature and, in some cases, the danger of explosion of 
dust. 

Group C: Materials which are not injured by a high temperature but 
which cannot be allowed to come into contact with products of combus- 
tion. These are kaolin, ocher and other pigments, fuller's earth, which is 
to be used in filtering vegetable or animal oils, whiting and similar earthy 
materials, a large proportion of which would be lost as dust in direct-heat 
drying. These may be dried by passing through a single-shell drier 
incased in brickwork and allowing heat to come into contact with the 
shell only, but this is an uneconomical machine to operate, due to the 
high temperature of the escaping gases. 

Group D: Organic materials which are used for food either by man or 
the lower animals, such as grain which has been wet, cotton seed, starch 
feed, corn germs, brewers' grains, and breakfast foods, which must be 
dried after cooking. These, of course, cannot be brought into contact 
with furnace gases and must be kept at a low temperature. For these 
materials a drier using either exhaust or live steam is the only practical 
one. This is generally a revolving shell in which are arranged steam 
pipes. Care should be exercised in selecting a steam drier which has 
perfect and automatic drainage of the pipes. The condensed steam 
always amounts to more than the water evaporated from the material. 

Group E: Materials which are composed wholly or contain a large pro- 
portion of soluble salts, such as nitrate of soda, nitrate of potash, car- 
bonates of soda or potash, chlorates of soda or potash, etc. These in 
drying form a hard scale which adheres to the shell, and a rotary drier 
cannot be profitably used on account of frequent stops for cleaning. The 
only practical machine for such materials is a semicircular cast-iron 
trough having a shaft through the center carrying paddles that con- 
stantly stir up the material and feed it through the drier. This machine 
has brick side walls and an exterior furnace; the heat from the furnace 
passing under the shell and back through the drying material or out 
through a stack or fan without passing through the material, as may be 
desired. Should the material also require a low temperature, the same 
type of drier can be used by substituting steam-jacketed steel sections 
instead of cast iron. 

The efficiency of a drier is the ratio of the theoretical heat required to 
do the drying to the total heat supplied. The greatest loss is the heat 
carried out by the exhaust or waste gases; this may be as great as 40% 
of the total heat from the fuel, or with a properly designed drier may be 
as small as 8%. The radiation from the shell or walls may be as high as 
25% or as low as 4%. The heat carried away by the dried material may 
amount under conditions of careless operation to as much as 25% or may 
be as low as nothing. 

A properly designed drier of the direct-heat type for either group " A " 
or "B" will give an efficiency of from 75% to 85%; a bricked-in return- 
draught single-shell drier, from 60% to 70%; and a single-shell straight- 
draught dryer, from 45%, to 55%. A properly designed indirect-heat 
drier for group "C" will give an efficiency of 50'% to 60%, and a poorly 
designed one may not give more than 30%; The best designed steam 
drier for group "D," in which the losses in the boiler producing the 
steam must be considered, will not often give an efficiency of more than 



EVAPORATION AND DRYING. 



549 



42%; and, while a poorly designed one may have an equal efficiency, its 
capacity may be not more than one-half of a good drier of equal size. 
The drier described for group " E" will not give an efficiency of more than 



Performance of Different Types of Driers. 

(W. B. Ruggies.) 



Type of drier 



Material 

Moisture, initial, per cent 

Moisture, final, per cent 

Calorific value of fuel, B.T.TJ 

Fuel consumed per hour, lbs 

Water evaporated per hour, lbs.. 
Water evap. per pound fuel, lbs.. 

Material dried per hour, lbs ' 

Fuel per ton dried material, lbs. . . 
Heat lost in exhaust air, per cent 
Heat lost by radiation, etc., per 

centi 

Heat used to evaporate water, 

per cent 

Heat used to raise temperature of 

material, per cent 

Total efficiency, per cent 







.. 








3i 


-fi£ 


Jfi'1 


»."§ 








-g-c-s 






Is* 


o a 1 

Is 


III 


'Mg 


Sand. 


Coal. 


Cement 
slurry. 


Lime- 
stone. 


4.58 


10.2 


61.2 


3.6 








40.7 


0.5 


12100 


12290 


13200 


13180 


398 


213.6 


667 


460 


2196 


924.2 


4057 


1325 


5.3 


4.3 


6.1 


2.3 


36460 


8300 


7680 


41400 


21.8 


51.3 


17.3 


22.2 


11.3 


42.8 


38.4 


38.2 


7.6 


7.7 


12.5 


15.6 


52.5 


39.4 


52.0 


24.4 


28.6 


10.1 


7.1 


21.8 




81.1 


49.5 


59.1 


46.2 



in r~ 
Nitrate 
of soda. 
7.2 
0.3 
13600 
87 
349 

4.0 
4581 
38.0 
40.7 

13.8 

33.1 

12.4 
45.5 



Performance of a Steam Drier. 

Material: Starch feed. Moisture, initial 39.8%, final 0.22%. Dried 
material per hour, 831 lbs. Water evaporated per hour, 548 lbs. Steam 
consumed per hour, 793 lbs. Water evaporated per pound steam, 
0.691 lb. Temperature of material, moist, 58°, dry, 212°. Steam pres- 
sure, 98 lbs. gauge. 

Total heat to evaporate 548 lbs. water at 58° into steam, 

548 X (154.2 + 969.7) = 615,897 B.T.TJ. 
Heat supplied by 793 lbs. steam condensed to water at 212°, 

793 X (1188.2 - 180.3) = 799,265 B.T.U. 
Heat used to evaporate water, 

(615,897 ■*■ 799,265) = 77.1%. 
Heat used to raise temp, of material, 

(831 X 154 X 0.492) = 62,963 = 7.9%. 
. 100 - (77.1 



Loss by radiation 
Total efficiency . 



- 7.9) = 15%. 
, , 85.0%, 



550 



Water Evaporated and Heat Required for Drying. 

M = percentage of moisture in material to be dried. 

Q = lbs. water evaporated per ton (2000 lbs.) of dry material. 

H = British thermal units required for drying, per ton of dry material. 



M 


Q 


H 


M 


Q 


H 


M 


Q 


H 


1 


20.2 


85,624 


14 


325.6 


424,884 


35 


1,077 


1,269,240 


2 


40.8 


108,696 


15 


352.9 


458,248 


40 


1,333 


1,555,960 


3 


61.9 


130,424 


16 


381.0 


489,720 


45 


1,636 


1,895,320 


4 


83.3 


156,296 


17 


409.6 


521,752 


50 


2,000 


2,303,000 


5 


105.3 


180,936 


18 


439.0 


554,680 


55 


2,444 


2,800,280 


6 


127.7 


206,024 


19 


469.1 


588,392 


60 


3,000 


3,423,000 


7 


150.5 


231,560 


20 


500.0 


623,000 


65 


3,714 


4,222,680 


8 


173.9 


257,768 


21 


531.6 


658,392 


70 


4,667 


5,290,040 


9 


197.8 


284,536 


22 


564.1 


694,792 


75 


6,000 


6,783,000 


10 


222.2 


311,864 


23 


597.4 


732,088 


80 


8,000 


9,023,000 


11 


247.2 


339,864 


24 


631.6 


770,392 


85 


11,333 


12,755,960 


12 


272.7 


368,424 


25 


666.7 


809,704 


90 


18,000 


20,223,000 


13 


298.9 


397,768 


30 


857.0 


1,022,840 


95 


38,000 


42,623,000 



Formulae: Q = 



100 



• M' 



H = 1120 Q 4- 63,000. 



The value of H is found on the assumption that the moisture is heated 
from 62° to 212° and evaporated at that temperature, and that the 
specific heat of the material is 0.21. [2000 X (212 - 62) X 0.21] = 63,000. 

Calculations for Design of Drying Apparatus. — A most efficient 
system of drying of moist materials consists in a continuous circulation of a 
volume of warm dry air over or through the moist material.lthen passing 
the air charged with moisture over the cold surfaces of condenser coils to 
remove the moisture, then heating the same air by steam-heating coils 
or other means, and again passing it over the material. In the design of 
apparatus to work on this system it is necessary to know the amount 
of moisture to be removed in a given time, and to calculate the volume of 
air that will carry that moisture at the temperature at which it leaves the 
material, making allowance for the fact that the moist, warm air on leaving 
the material may not be fully saturated, and for the fact that the cooled 
air is nearly or fully saturated at the temperature at which it leaves the 
cooling coils. A paper by Wm. M. Grosvenor, read before the Am. Inst, 
of Chemical Engineers (Heating and Ventilating Mag., May, 1909) con- 
tains a "humidity table" and a "humidity chart" which greatly facilitate 
the calculations required. The table is given in a condensed form below. 
It is based on the following data: Density of air + 0.04% CO2 = 

001293052 
1 + 0.00367 X Temp. C. (in Kg * per CU " m<) - Density ° f Water Vap ° r 
=0.62186 X density of air. Density at partial pressure -*■ density at 760 
m.m. = partial pressure -5- 760 m.m. Specific heat of water vapor = 0.475; 
sp. ht. of air = 0.2373. Kg. per cu. meter X 0.062428 = lbs. per cu. ft. 
The results given in the table agree within 1/4% with the figures of the 
U. S. Weather Bureau. (Compare also the tables of H. M. Prevost 
Murphy, given under "Air," page 586.) The term "humid heat" in 
the heading of the table is defined as the B.T.U. required to raise 
1° F. one pound of air plus the vapor it may carry when saturated at 
the given temperature and pressure; and °° humid volume" is the 
volume of one pound of air when saturated at the given temperature 
and pressure. 



RADIATION OF HEAT. 



551 



Humidity Table. 





Vapor 


Temp. 
F. 


Tension, 

Milli- 


meters of 




(Mercury. 


32 


4.569 


35 


5.152 


40 


6.264 


45 


7.582 


50 


9.140 


55 


10.980 


60 


13.138 


65 


15.660 


70 


18.595 


75 


22.008 


80 


25.965 


85 


30.573 


90 


35.774 


95 


41.784 


100 


48.679 


105 


56.534 


110 


65.459 


115 


75.591 


120 


87.010 


125 


99.024 


130 


114.437 


135 


130.702 


140 


148.885 


145 


169.227 


150 


191.860 


155 


216.983 


160 


244.803 


165 


275.592 


170 


309.593 


175 


347.015 


180 


388.121 


185 


433.194 


190 


482.668 


195 


536.744 


200 


595.771 


205 


660.116 


210 


730.267 



Lbs. 
Water 
Vapor 
per lb. 

Air. 



.003761 

.0042435 

.0050463 

.0062670 

.0075697 

.0091163 

.010939 

.013081 

.015597 

.018545 

.021998 

.026026 

.030718 

.036174 

.042116 

.049973 

.058613 

.068662 

.080402 

.094147 

.11022 

.12927 

.15150 

.17816 

.21005 

.24534 

.29553 

.35286 

.42756 

.52285 

.64942 

.82430 

1.00805 

1 .4994 

2.2680 

4.2272 
15.8174 



Humid 
Heat, 
B.T.U. 



Humid 
Volume 
cu.ft 



.2391 
.2393 
.2398 
.2403 
.2409 
.2416 
.2425 
.2435 
.2447 
.2461 
.2478 
.2497 
.2519 
.2545 
.2575 
.2610 
.2651 
.2699 
.2755 
.2820 
.2896 
.2987 
.3093 
.3219 
.3371 
.3553 
.3776 
.4054 
.4405 
.4856 
.5458 
.6288 
.7519 
.9494 
1.3147 
2.1562 
15.9148 



12.462 
12.549 
12.695 
12.843 
12.999 
13.159 
13.326 
13.501 
13.683 
13.876 
14.081 
14.301 
14.539 
14.793 
15.071 
15.376 
15.711 
16.084 
16.499 
16.968 
17.499 
18.103 
18.800 
19.609 
20.559 
21.687 
23.045 
24.708 
26.790 
29.454 
32.967 
37.796 
44.918 
56.302 
77.304 
131.028 
562.054 



Density, lbs. 

per cu.ft. at 760 

Millimeters. 



Dry 
Air. 



.080726 
.080231 
.079420 
.078641 
.077867 
.077109 
.076363 
.075635 
.074921 
.074218 
.073531 
.072852 
.072189 
.071535 
.070894 
.070264 
.069647 
.069040 
.068443 
.067857 
.067380 
.066713 
.066156 
,065601 
.065154 
.064539 
.064016 
.063502 
.062997 
.062500 
.062015 
.061529 
.061053 
.060588 
.060127 
.059674 
.059228 



Sat'd 
Mix. 



.080556 
.080085 
.079181 
.078348 
.077511 
.076685 
.075865 
.075039 
.074219 
.073471 
.072644 
.071744 
.070894 
.070051 
.069179 
.068288 
.067383 
.066447 
.065477 
.064480 
.063449 
.062374 
.061255 
.060104 
.058865 
.057570 
.056218 
.054795 
.053305 
,051708 
.050035 
.048265 
.046391 
.044405 
.042308 
.040075 
.037323 



Volume in cu. 
ft. per lb. of 



Dry 
Air. 



12.388 
12.464 
12.590 
12.718 
12.842 
12.968 
13.095 
13.222 
13.348 
13.474 
13.600 
13.726 
13.852 
13.979 
14.106 
14.232 
14.358 
14.484 
14.611 
14.736 
14.863 
14.989 
15.116 
15.242 
15.368 
15,494 
15.621 
15.748 
15.874 
16.000 
16.126 
16.253 
16.379 
16.505 
16.631 
16.758 
16.884 



Sat'd 
Mix. 



12.414 
12.496 
12.629 
12.763 
12.901 
13.041 
13.180 
13.325 
13.471 
13.624 
13.777 
13.938 
14.106 
14.275 
14.455 
14.643 
14.840 
15.050 
15.272 
15.509 
15.761 
16.032 
16.325 
16.643 
16,993 
17,370 
17,788 
18.250 
18.761 
19.339 
19.987 
20.719 
21.557 
22.521 
23.638 
24.954 
26.796 



RADIATION OF HEAT, 

Radiation of heat takes place between bodies at all distances apart, and 
follows the laws for the radiation of light. 

The heat rays proceed in straight lines, and the intensity of the rays 
radiated from any one source varies inversely as the square of their 
distance from the source. 

This statement has been erroneously interpreted by some writers, who 
have assumed from it that a boiler placed two feet above a fire would re- 
ceive by radiation only one-fourth as much heat as if it were only one foot 
above. In the case of boiler furnaces the side walls reflect those rays that 
are received at an angle, — following the law of optics, that the angle of 
incidence is equal to the angle of reflection, — with the result that the 
intensity of heat two feet above the fire is practically the same as at one 
foot above, instead of only one-fourth as much. 

The rate at which a hotter body radiates heat, and a colder body 
absorbs heat, depends upon the state of the surfaces of the bodies as 
well as on their temperatures. The rate of radiation and of absorption 
are increased by darkness and roughness of the surfaces of the bodies, 
and diminished by smoothness and polish. For this reason the covering 



552 



of steam pipes and boilers should be smooth and of a light color: uncovered 
pipes and steam-cylinder covers should be polished. 

The quantity of heat radiated by a body is also a measure of its heat- 
absorbing power under the same circumstances. When a polished body 
is struck by a ray of heat, it absorbs part of the heat and reflects the rest. 
The reflecting power of a body is therefore the complement of its absorb- 
ing power, which latter is the same as its radiating power. 

The relative radiating and reflecting power of different bodies has been 
determined by experiment, as shown in the table below, but as far as 
quantities of heat are concerned, says Prof. Trowbridge (Johnson's 
Cyclopaedia, art. Heat), it is doubtful whether anything further than the 
said relative determinations can, in the present state of our knowledge, 
be depended upon, the actual or absolute quantities for different tem- 
peratures being still uncertain. The authorities do not even agree on the 
relative radiating powers. Thus, Leslie gives for tin plate, gold, silver, 
and copper the figure 12, which differs considerably from the figures in 
the table below, given by Clark, stated to be on the authority of Leslie, 
De La Provostaye and Desains, and Melloni. 

Relative Radiating and Reflecting Power of Different Substances. 





u 






. 






°.« 


bfl 




MS 


W) 




■ji^ 


.s • 




•J^ss 






.2 s ! 






,c3 O £ • 


o & 




^-Q O 






"$£> o 


cfl O 






^ 




#& 


$P* 




100 





Zinc, polished 

Steel, polished 

Platinum, polished. 


19 


81 




100 
100 






17 

24 


83 


Carbonate of lead . . . 


76 


Writing-paper 


98 


2 


Platinum in sheet . . 


17 . 


83 


Ivory, jet, marble... 


93 to 98 


7 to 2 


Tin 


15 


85 


Ordinary glass 


90 


10 


Brass, cast, dead 






Ice 


85 


15 


polished 


11 


89 


Gum lac 


72 


28 


Brass, bright pol- 






Silver-leaf on glass . . 


27 


73 


ished 


7 


93 


Cast iron, bright pol- 






Copper, varnished. . 


14 


86 




25 
23 


75 

77 


Copper, hammered . 
Gold, plated 


7 
5 


93 


Mercury, about 


95 


Wrought iron, pol- 






Gold on polished 








23 


77 




3 


97 




Silver, polished 












3 


97 









Experiments of Dr. A. M. Mayer give the following: The relative radia- 
tions from a cube of cast iron, having faces rough, as from the foundry, 
Elaned, " drawfiled," and polished, and from the same surfaces oiled, are as 
elow (Prof. Thurston, in Trans. A. S. M. E., vol. xvi): 





Rough. 


Planed. 


Drawfiled. 


Polished. 




100 
100 


60 
32 


49 
20 


45 




18 







It here appears that the oiling of smoothly polished castings, as of 
cylinder-heads of steam-engines, more than doubles the loss of heat by 
radiation, while it does not seriously affect rough castings. 

" Black Body " Radiation. Stefan and Boltzman's Law. (Eng'g, 
March 1, 1907.) — Kirchhoff defined a black body as one that would absorb 
all radiations falling on it, and would neither reflect nor transmit any. 
The radiation from such a body is a function of the temperature alone, 



CONDUCTION AND CONVECTION OF HEAT. 



553 



and is identical with the radiation inside an inclosure all parts of which 
have the same temperature. By heating the walls of an inclosure as 
uniformly as possible, and observing the radiation through a very small 
opening, a practical realization of a black body is obtained. Stefan and 
Boltzman's law is: The energy radiated by a black body is proportional 
to the fourth power of the absolute temperature, or E = K (2' 4 — T *), 
where E = total energy radiated by the body at T to the body at T , and 
K is a constant. The total radiation from other than black bodies increases 
more rapidly than the fourth power of the absolute temperature, so that 
as the temperature is raised the radiation of all bodies approaches that of 
the black body. A confirmation of the Stefan and Boltzman law is given 
in the results of experiments by Lummer and Kuribaum, as below (T = 
290 degrees C, abs. in all cases). 

T=492. 654. 795. 1108. 1481. 1761, 

b (Black body 109.1 108.4 109.9 109.0 110.7 

™ m * Polished platinum.. 4.28 6.56 8.14 12.18 16.69 19.64 
Ti ~ r * (l r0 n oxide 33.1 33.1 36.6 46.9 653 

CONDUCTION AND CONVECTION OF HEAT. 

Conduction is the transfer of heat between two bodies or parts of a 
body which touch each other. Internal conduction takes place between 
the parts of one continuous body, and external conduction through the 
surface of contact of a pair of distinct bodies. 

The rate at which conduction, whether internal or external, goes on, 
being proportional to the area of the section or surface through which it 
takes place, may be expressed in thermal units per square foot of area per 
hour. 

Internal Conduction varies with the heat conductivity, which depends 
upon the nature of the substance, and is directly proportional to the 
difference betw r een the temperatures of the two faces of a layer, and in- 
versely as its thickness. The reciprocal of the conductivity is called the 
internal thermal resistance of the substance. If r represents this resist- 
ance, x the thickness of the layer in inches, T' and T the temperatures 
on the two faces, and q the quantitv in thermal units transmitted per 

T' — T 
hour per square foot of area, q = — (Rankine.) 

Peclet gives the following values of r: 

Gold, platinum, silver. 0.0016 J Lead....... 0.0090 

Copper 0.0018 Marble . 0.0716 

Iron 0.0043 Brick.. 0.1500 

Zinc . 0.0045 I 



Relative Heat-conducting Power of Metals. 

Metals. *C.&J. fW.&F. 

Silver, 1000 1000 

Gold 981 532 

Gold, with 1 % of silver. 840 

Copper, rolled 845 736 

Copper, cast 811 ... 

Mercury 677 

Mercury, with 1.25% of 

tin 412 

Aluminum . 665 

Zinc: 

cast vertically 628 

cast horizontally. . . 608 

rolled 641 

* Calvert & Johnson. 



Metals. 


*C.&J. 


tW.&F 


Cadmium 


. 577 




Wrought iron. 


. 436 


119 


Tin 


.. 422 


145 


Steel 


. 397 


116 


Platinum 


. 380 


84 


Sodium 


. 365 




Cast iron 


. 359 




Lead 


. 287 


85 


Antimony: 






cast horizontally. 


. 215 




cast vertically. . . 


. 192 




Bismuth 


. 61 


18 



\ Weidemann & Franz. 



Influence of a Non-metallic Substance in Combination on the 
Conducting Power of a Metal. 
Influence of carbon on iron: 

Wrought iron 436 

Steel.". . 397 

Cast iron 359 



Cast copper 811 

Copper with 1 % of arsenic. . . . 570 

with 0.5% of arsenic. . 669 

with 0.25% of arsenic. 771 



554 HEAT. 

The Rate of External Conduction through the bounding surface 
between a solid body and a fluid is approximately proportional to the 
difference of temperature, when that is small; but when that difference is 
considerable, the rate of conduction increases faster than the simple ratio of 
that difference. (Rankine.) 

If r, as before, is the coefficient of internal thermal resistance, e and e' 
the coefficient of external resistance of the two surfaces, x the thickness of 
the plate, and T' and T the temperatures of the two fluids in contact 

T' — T 

with the two surfaces, the rate of conduction is a = — — — Accord- 

e + e' + rx 

ing to Peclet, e+ e f = -r-y ^-y • in which the constants A and 

A. [1 -f- ±S ( i — 1 )\ 

B have the following values: 

B for polished metallic surfaces 0.0028 

B for rough metallic surfaces and for non-metallic surfaces . . 0.0037 

A foe polished metals, about 0.90 

A for glassy and varnished surfaces 1 . 34 

A for dull metallic surfaces 1 . 58 

A for lampblack 1 . 78 

When a metal plate has a liquid at each side of it, it appears from experi- 
ments by Peclet that B = 0.058, A = 8.8. 

The results of experiments on the evaporative power of boilers agree 
very well with the following approximate formula for the thermal resist- 
ance of boiler plates and tubes: 

, _ a 
e+ e - (r _ T y 

which gives for the rate of conduction, per square foot of surface per hour, 

a 

This formula is proposed by Rankine as a rough approximation, near 
enough to the truth for its purpose. The value of a lies between 160 and 
200. Experiments on modern boilers usually give higher values. 

Convection, or carrying of heat, means the transfer and diffusion of the 
heat in a fluid mass by means of the motion of the particles of that mass. 

The conduction, properly so called, of heat through a stagnant mass of 
fluid is very slow in liquids, and almost, if not wholly, inappreciable in 
gases. It is only by the continual circulation and mixture of the particles 
of the fluid that uniformity of temperature can be maintained in the fluid 
mass, or heat transferred between the fluid mass and a solid body. 

The free circulation of each of the fluids which touch the side of a solid 
plate is a necessary condition of the correctness of Rankine's formulae for 
the conduction of heat through that plate; and in these formula? it is 
implied that the circulation of each of the fluids by currents and eddies is 
such as to prevent any considerable difference of temperature between the 
fluid particles in contact with one side of the solid plate and those at con- 
siderable distances from it. 

When heat is to be transferred by convection from one fluid to another, 
through an intervening layer of metal, the motions of the two fluid masses 
should, if possible, be in opposite directions, in order that the hottest par- 
ticles of each fluid may be in communication with the hottest particles of 
the other, and that the minimum difference of temperature between the 
adjacent particles of the two fluids may be the greatest possible. 

Thus, in the surface condensation of steam, by passing it through metal 
tubes immersed in a current of cold water or air, the cooling fluid should 
be made to move in the opposite direction to the condensing steam. 

Coefficients of Heat Conduction of Different Materials. (W. 
Nusselt, Zeit des Ver. Deut. Ing., June, 1908. Eng. Digest, Aug., 1908.) — 
The materials were inclosed between two concentric metal vessels, the 
Inner of which contained an electric heating device. 

It was found that the materials tested all followed Fourier's law, the 
quantity of heat transmitted being directly proportional to the extent of 
surface, the duration of flow and the temperature difference between the 
inner and outer surfaces; and inversely proportional to the thickness of 
the mass of material. It was also found that the coefficient of conduction 
increased as the temperature increased. The table gives the British 
equivalents of the average coefficients obtained. 



CONDUCTION AND CONVECTION OF HEAT. 



555 



Coefficients of Heat Conduction at Different Temperatures for 
Various Insulating Materials. 

(B.T.U. per hour = Area of surface in square feet X coefficient 4- thick- 
ness in inches.) 



Lb. per 
cu. ft. 


M aterials. 


32° 
F. 


212° 
F. 


392° 
F. 


572° 
F. 


752° 
F. 


10. 




0.250 
0.266 
0.306 
0.314 
0.379 

0.403 


0.387 
0.403 
0.411 
0.419 
0.476 

0.508 


0.443 






8.5 








6.3 










9.18 


Silk, tufted 








5.06 










11.86 


Charcoal (carbonized cabbage 








13.42 


Sawdust (0.443 at 1 12° F.) 








10. 


Peat refusef (0.443 at 77° F.) 












21.85 


Kieselguhr (infusorial earth), 


0.419 


0.532 


0.596 


0.629 




12.49 


Asphalt-cork composition (0.492 
at65°F.) 




25.28 




0.484 
0.516 


0.613 
0.629 


J. 653 
3.742 






12.49 




0.854 


0.961 


12.17 


Peat refusef (0.564 at 68° F.) 




36.2 


Kieselguhr, dry and compacted 
(0.669 at 302° F.; 0.991 at 662° F.) . 












43.07 


Composition,^ compacted (0.806 
at 302° F.; 0.967 at 428° F.) 












22.47 


Porous blast-furnace slag (0.766 
at 112° F.) 












35.96 

34.33 


Asbestos (1.644 at 1112° F.) 

Slag concrete || (1.532 at 112° F.). 


1.048 


1.346 


1.451 


1.499 


1.548 


18.23 


Pumice stone gravel (1.612 at 
112° F.) 












128.5 


Portland cement, neat (6.287 at 
95° F.) 



























* Tufted, oily, and containing foreign matter. Used in Linde's 
apparatus, f Hygroscopic; measurements made in moist zones, t Cork, 
asbestos, kieselguhr and chopped straw, mixed with a binder and made 
in sheets for application to steam pipes in successive layers, the whole 
being wrapped in canvas and painted. § Kieselguhr, mixed with a binder 
and burned; very porous and hygroscopic. §§ Ingredients of (J) mixed 
with water and compacted. || 1 part cement, 9 parts porous blast-furnace 
slag, by volume. 

Heat Resistance, the Reciprocal of Heat Conductivity. (W. 
Kent, Trans. A. S. M. E., xxiv, 278.) — The resistance to the passage of 
heat through a plate consists of three separate resistances; viz., the 
resistances of the two surfaces and the resistance of the body of the plate, 
which latter is proportional to the thickness of the plate. It is probable 
also that the resistance of the surface differs with the nature of the body 
or medium with which it is in contact. 

A complete set of experiments on the heat-resisting power of heat- 
insulating substances should include an investigation into the difference 
in surface resistance when a surface is in contact with air and when it is 
in contact with another solid body. Suppose we find that the total resist- 
ance of a certain non-conductor may be represented by the figure 10, and 
that similar pieces all give the same figure. Two pieces in contact give 16. 
One piece of half the thickness of the others gives 8. What is the resist- 
ance of the surface exposed to the air in either piece, of the surface in 
contact with another surface, and of the interior of the body itself? Let 
the resistance of the material itself, of the regular thickness, be rep- 
resented by A, that of the surface exposed to the air by a, and that of the 
surface in contact with another surface by c. 



556 



HEAT. 



We then have for the three cases, 

Resistance of one piece A 4- 2 a =» 10 

of two pieces in contact .... 2A+2c+2a=-16 
of the thin piece 1/2 A + 2 a = 8 

These three equations contain three unknown quantities. Solving the 
equations we find A = 4, a = 3, and c = 1. Suppose that another 
experiment be made with the two pieces separated by an air space, and 
that the total resistance is then 22. If the resistance of the air space be 
represented by s we have the two equations: Resistance of one piece, 
A + 2 a = 10 ; resistance of two pieces and air space, 2A+4a+s= 22, 
from which we find s =' 2. Having these results we can easily estimate 
what will be the resistance to heat transfer of any number of layers of the 
material, whether in contact or separated by air spaces. 

The writer has computed the figures for heat resistance of several 
insulating substances from the figures of conducting power given in a table 
published by John E. Starr, in Ice and Refrigeration, Nov., 1901. Mr. 
Starr's figures are given in terms of the B.T.U. transmitted per sq. ft. of 
surface per day per degree of difference of temperatures of the air adjacent 
to each surface. The writer's figures, those in the last column of the table 
given herewith, are calculated by dividing Mr. Starr's figures by 24, to 
obtain the hourly rate, and then taking their reciprocals. They may be 
called "coefficients of heat resistance" and defined as the reciprocals of 
the B.T.U. per sq. ft. per hour per degree of difference of temperature. 

Heat Conducting and Resisting Values of Different Insulating 
Materials. 



Insulating Material. 


Conductance, 
B.T.U. per 
sq. ft. per 
Day per De- 
gree of Differ- 
ence of Tem- 
perature. 


Coefficient 

of Heat 

Resistance. 

C. 


1. 

2. 

3. 
4. 


5/8-in. oak board, 1 in. lampblack, 7/g-in. pine 

board (ordinary family refrigerator) 

7/s-in. board, I in. pitch, 7/s-in. board 

7/g-in. board, 2 in. pitch, 7/s-in. board 

7/s-in. board, paper, 1 in. mineral wool, paper, 


5.7 
4.89 

4.25 

4.6 

3.62 

3.38 
3.90 

2.10 

4.28. 

3.71 

3.32 

1.35 . 

1.80 

2.10 

1.20 
0.90 
1.70 
3.30 

2.70 

2.52 
2.48 


4.21 
4.91 
5.65 

5.22 


5. 


7/8-in. board, paper, 21/oin. mineral wool, 


6.63 


6. 


7/8-in. board, paper, 2 1/2 in. calcined pumice, 


7.10 -» 


7 




6.15 


8. 


7/8-in. board, paper, 3 in., sheet cork, 7/s-in. 


11.43 


9. 


Two 7/8-in. boards, paper, solid, no air space, 


5.61 


10. 


Two 7/8-in. boards, paper, 1 in. air space, 


6.47 


11. 


Two 7/ 8 -in. boards, paper, 1 in. hair felt, 


7.23 


12. 


Two 7/8-in. boards, paper, 8 in. mill shav- 


17.78 


n 




13 33 


14 




11.43 


15. 
1ft 


Two 7/8-in. boards, paper, 3 in. air, 4 in. 
sheet cork, paper, two 7/g-in. boards 


20.00 
26.67 


17 




14.12 


18 




7.27 


19. 

20. 
21. 


Four double 7/s-in. boards (8 boards), with 
paper between, three 8-in. air spaces ...._. 

Four 7/g-in. boards, with three quilts of 1/4-m 
hair between, papers separating boards . . 

7/s-in. board, 6 in. patented silicated straw- 
board, finished inside with thin cement.. 


8.89 
9.52 
9.68 



CONDUCTION AND CONVECTION OF HEAT. 



537 



Analyzing some of the results given in the last column of the table, we 
observe that, comparing Nos. 2 and 3, 1 in. added thickness of pitch 
increased the coefficient 0.74; comparing Nos. 4 and 5, li/2iri. of mineral 
wool increased the coefficient 1.11. If we assume that the 1 in. of mineral 
wool in No. 4 was equal in heat resistance to the additional U/2 in. added 
in No. 5, or 1.11 reciprocal units, and subtract this from 5.22, we get 4.11 
as the resistance of two 7/g-in. boards and two sheets of paper. This 
would indicate that one 7/ 8 -in. board and one sheet of paper give nearly 
twice as much resistance as 1 in. of mineral wool. In like manner any 
number of deductions may be drawn from the table, and some of them 
will be rather questionable, such as the comparison of No. 15 and No. 16, 
showing that 1 in. additional sheet cork increased the resistance given by 
four sheets 6.67 reciprocal units, or one-third the total resistance of No. 15. 
This result is extraordinary, and indicates that there must have been 
considerable differences of conditions during the two tests. 

For comparison with the coefficients of heat resistance computed from 
Mr. Starr's results we may take the reciprocals of .the figures given by 
Mr. Alfred R. Wolff as the result of German experiments on the heat 
transmitted through various building materials, as below: 

K = B.T.U. transmitted per hour per sq. ft. of surface, per degree F. 
difference of temperature. 

C = coefficient of heat resistance = reciprocal of K. 

The irregularity of the differences of C computed from the original 
values of K for each increase of 4 inches in thickness of the brick walls 
indicates a difference in the conditions of the experiments. The average 
difference of C for each 4 inches of thickness is about 0.80. Using this 
average difference to even up the figures we find the value of C is expressed 
by the approximate formula C = 0.70 + 0.20 t, in which t is the thickness 
in inches. The revised values of C, computed by this formula, and the 
corresponding revised values of K, are as follows: 



Thickness, 
in. 


}< 


8 


12 


16 


20 


24 


28 


32 


36 


40 


C 

K, revised. 
K, original. 
Difference.. 


1.50 
0.667 
0.68 
0.013 


2.30 
0.435 
0.46 
0.025 


3.10 
0.323 
0.32 
0.003 


3.90 
0.256 
0.26 
0.004 


4.70 
0.213 
0.23 
0.017 


5.50 
0.182 
0.20 
0.018 


6.30 
0.159 
0.174 
0.015 


7.10 
0.141 
0.15 
0.009 


7.90 
0.127 
0.129 
0.002 


8.70 
0.115 
0.115 
0.0 



The following additional .values of C are computed from Mr. Wolff's 
figures for K : 

K C 
Wooden beam construction, planked over or 
ceiled : 

As flooring . 083 12. 05 

As ceiling . 104 9.71 

Fireproof construction, Moored over: 

As flooring . 124 8 . 06 

As ceiling . 145 6 . 90 

Single window 1 . 030 . 97 

Single skylight 1.118 . 89 

Double window . 518 1 . 93 

Double skylight 0.621 1.61 

Door 0.414 2.42 

It should be noted that the coefficient of resistance thus defined will be 
approximately a constant quantity for a given substance under certain 
fixed conditions, only when the difference of temperature of the air on its 
two sides is small — say less than 100° F. When the range of tem- 
perature is great, experiments on heat transmission indicate that the 
quantity of heat transmitted varies, not directly as the difference of tem- 
perature, but as the square of that difference. In this case a coefficient 



&8 



of resistance with a different definition may be found — viz., that obtained 
from the formula a= (T - t)' 2 h- q, in which a is the coefficient, T— t the 
range of temperature, and q the quantity of heat transmitted, in British 
thermal units per square foot per hour. 

Steam-pipe Coverings. 

Experiments by Prof. Ordway, Trans. A. S. M. E., vi, 168; also Circular No. 
27 of Boston Mfrs. Mutual Fire Ins. Co., 1890. 



Substance 1 inch thick. Heat 
applied, 310° F. 


Pounds of 

Water 

heated 

10° F., per 

hour, 
through 
1 sq. ft. 


British 
Thermal 
Units per 
sq. ft. per 
minute. 


Solid Mat- 
ter in 1 sq. 
ft., 1 inch 
thick, 
parts in 
1000. 


tJ8 
Us 

If 

.Si ft 

< 




8.1 
9.6 

10.4 
10.3 
9.8 
10.6 
11.9 
13.9 
35.7 
12.4 
42.6 
13.7 
15.4 
14.5 
15.7 
20.6 
30.9 
49.0 
48.0 
62.1 
13. 
14. 
21. 
21.7 
14.6 
18. 
18.7 
16.7 
22. 
21. 
27. 
30.9 


1.35 
1.60 
1.73 
1.72 
1.63 
1.77 
1.98 
2.32 
5.95 
2.07 
7.10 
2.28 
2.57 
2.42 
2.62 
3.43 
5.15 
8.17 
8.00 
10.35 
2.17 
2.33 
3.50 
3.62 
2.43 
3. 

3.12 
2.78 
3.67 
3.50 
4.50 
5.15 


56 

50 

20 
185 

56 
244 

53 
119 
506 

23 
285 

60 
150 

60 
112 
253 
368 

81 



529 


944 




950 




980 




815 




944 




756 




947 




881 




494 


10. Loose calcined magnesia 

1 1 . Compressed calcined magnesia . . 

12. Light carbonate of magnesia. . . . 

13. Compressed carb. of magnesia.. . 


977 
715 
940 
850 
940 




888 


16. Ground chalk (Paris white) 


747 
632 




919 




1000 


20. Sand 


471 






22. Paper 









































































It will be observed that several of the incombustible materials are 
nearly as efficient as wool, cotton, and feathers, with which they may be 
compared in the preceding table. The materials which may be con- 
sidered wholly free from the danger of being carbonized or ignited by 
slow contact with pipes or boilers are printed in Roman type. Those 
which are more or less liable to be carbonized are printed in italics. 

The results Nos. 1 to 20 inclusive were from experiments with the 
various non-conductors each used in a mass one inch thick, placed on a 
flat surface of iron kept heated by steam to 310° F. The substances 
Nos. 21 to 32 were tried as coverings for two-inch steam-pipe; the results 
being reduced to the same terms as the others for convenience of com- 
parison. 



CONDUCTION AND CONVECTION OF HEAT. 559 



Experiments on still air gave results which differ little from those of 
Nos. 3, 4, and 6. The bulk of matter in the best non-conductors is 
relatively too small to have any specific effect except to trap the air and 
keep it stagnant. These substances keep the air still by virtue of the 
roughness of their fibers or particles. The asbestos, No. 18, had smooth 
fibers. Asbestos with exceedingly fine fiber made a somewhat better 
showing, but asbestos is really one of the poorest non-conductors. It 
may be used advantageously to hold together other incombustible sub- 
stances, but the less of it the better. A "magnesia" covering, made of 
carbonate of magnesia with a small percentage of good asbestos fiber 
and containing 0.25 of solid matter, transmitted 2.5 B.T.U. per square 
foot per minute, and one containing 0.396 of solid matter transmitted 
3.33 B.T.U. 

Any suitable substance which is used to prevent the escape of steam 
heat should not be less than one inch thick. 

Any covering should be kept perfectly dry, for not only is water a good 
carrier of heat, but it has been found that still water conducts heat about 
eight times as rapidly as still air. 

Tests of Commercial Coverings were made by Mr. Geo. M. Brill 
and reported in Trans. A. S. M. E., xvi, 827. A length of 60 feet of 8-inch 
steam-pipe was used in the tests, and the heat loss was determined by the 
condensation. The steam pressure was from 109 to 117 lbs. gauge, and 
the temperature of the air from 58° to 81° F. The difference between the 
temperature of steam and air ranged from 263° to 286°, averaging 
272°. 

The following are the principal results: 



Kind of Covering. 


M 

> 
o 
O 

"o 

01 . 

.3 O 

JS C 


Jg 

=•= 

° a 

3& 


4) 

ft 

0) 
ft . 


B.T.U. per sq. ft. per 
hour per degree of av- 
erage difference of 
temperature. 


J ft 

s§ 

8-^ 
SK 

a °?£ 

lag* 

CO 


""■ > 
o 

w 

o 

o © <0 


. ft 

o.S" 

~ °-% 






0.846 
0.120 
0.080 
0.089 
0.157 
0.109 


12.27 
1.74 
1.16 
1.29 
2.28 
1.59 


2.706 
0.384 
0.256 
0.285 
0.502 
0.350 


'6!726 

0.766 
0.757 
0.689 
0.737 


100. 
14.2 
9.5 
10.5 
18.6 
12.9 


2.819 




1.25 
1.60 
1.30 
1.30 
1.70 


0.400 




0.267 




297 


Fire-felt 


523 


Manville sectional 


0.564 


Manv. sect and hair-felt 


2.40 


0.066 


0.96 


0.212 


0.780 


7.8 


0.221 


Manville wool-cement . . . 


2.20 


0.108 


1.56 


0.345 


0.738 


12.7 


0.359 


Champion mineral wool . 


1.44 


0.099 


1.44 


0.317 


0.747 


11.7 


0.33t) 


Hair-felt 


0.82 
0.75 


0.132 
0.298 


1.91 

4.32 


0.422 
0.953 


0.714 
0.548 


15.6 
35.2 


0.439 




0.993 




0.75 


0.275 


3.99 


0.879 


0.571 


32.5 


0.919 







Tests of Pipe Coverings by an Electrical Method. (H. G. Stott, 
Power, 1902.) — A length of about 200 ft. of 2-in. pipe was heated to a 
known temperature by an electrical current. The pipe was covered with 
different materials, and the heat radiated by each covering was deter- 
mined by measuring the current required to keep the pipe at a constant 
temperature. A brief description of the various coverings is given below. 

No. 2. Solid sectional covering, 1 1/2 in. thick, of granulated cork 
molded under pressure and then baked at a temperature of 500° F.; 
1/8 in. asbestos paper next to pipe. 

No. 3. Solid 1-in. molded sectional, 85% carbonate of magnesia. 



560 HEAT. 

No. 4. Solid 1-in. sectional, granulated cork molded under pressure 
and baked at 500° F.; i/s in. asbestos next to pipe. 

No. 5. Solid 1-in. molded sectional, 85% carbonate of magnesia; out- 
side of sections covered with canvas pasted on. 

. No. 6. Laminated 1-in. sectional, nine layers of asbestos paper with 
granulated cork between; outside of sections covered with canvas, Vs in. 
asbestos paper next to pipe. 

No. 7. Solid 1-in. molded sectional, of 85% carbonate of magnesia; 
outside of sections covered with light canvas. 

No. 8. Laminated 1-in. sectional, seven layers of asbestos paper 
indented with 1/4-in. square indentations, which serve to keep the asbestos 
layers from coming in close contact with one another; i/s in. asbestos 
paper next to pipe. 

No. 9. Laminated 1-in. sectional, 64 layers of asbestos paper, in which 
were embedded small pieces of sponge; outside covered with canvas. 

No. 10. Laminated 1 1/2-in. sectional, 12 plain layers of asbestos paper 
with corrugated layers between, forming longitudinal air cells; 1/8 in. 
asbestos paper next to pipe; sections wired on. 

No. 11. Laminated 1-in. sectional, 8 layers of asbestos paper with 
corrugated layers between, forming small air ducts radially around the 
covering. 

No. 12. Laminated li/4-in. sectional, 6 layers of asbestos paper 
with corrugated layers; outside of sections covered with two layers of 
canvas. 

No. 15. "Remanit," composed of 2 layers wound in reverse direction 
with ropes of carbonized silk. Inner layer 21/2 in. wide and 1/2 in. thick; 
outer layer 2 in. wide and 3/ 4 in. thick, over which was wound a network 
of fine wire; Vs in. asbestos next to pipe. Made in Germany. 

No. 16. 2 1/2-in. covering, 85% carbonate of magnesia, 1/2-in. blocks 
about 3 in. wide and 18 in. long next to pipe and wired on; over these 
blocks were placed solid 2-in. molded sectional covering. 

No. 17. 2 1/2-in. covering, 85% magnesia. Put on in a 2-in. molded 
section wired on; next to the pipe and over this a 1/2-in. layer of magnesia 
plaster. 

No. 18. 2 1/2-in. covering, 85% carbonate of magnesia. Put on in two 
solid 1-in. molded sections with 1/2-in. layer of magnesia plaster between; 
two 1-in. coverings wired on and placed so as to break joints. 

No. 19. 2-in. covering, of 85% carbonate of magnesia, put on in two 
1-in. layers so as to break joints. 

No. 20. Solid 2-in. molded sectional, 85% magnesia. 

No. 21. Solid 2-in. molded sectional, 85% magnesia. 

Two samples covered with the same thickness of similar material give 
different results; for example, Nos. 3 and 5, and also Nos. 20 and 21. 
The cause of this difference was found to be in the care with which the 
joints between sections were made. A comparison between Nos. 19 and 
20, having the same total thickness, but one applied in a solid 2-in. section, 
and the other in two 1-in. sections, proved the desirability of breaking 
joints. 

An attempt was made to determine the law governing the effect of 
increasing the thickness of the insulating material, and for all the 85% 
magnesia coverings the efficiency varied directly as the square root of the 
thickness, but the other materials tested did not follow this simple law 
closely, each one involving a different constant. 

To determine which covering is the most economical the following 
quantities must be considered: (1) Investment in covering. (2) Cost 
of coal required to supply lost heat. (3) Five per cent interest on 
capital invested in boilers and stokers rendered idle through having to 
supply lost heat. (4) Guaranteed life of covering. (5) Thickness of 
covering. 

The coverings Nos. 2 to 15 were finished on the outside with resin paper 
and 8-ounce canvas ; the others had canvas pasted on outside of the sec- 
tions, and an 8-oz. canvas finish. The following is a condensed statement 
of the results with the temperature of the pipe corresponding to 160 lb. 
steam pressure. 



CONDUCTION AND CONVECTION OF HEaI. 



561 



Electrical Test of Steam-Pipe Coverings. 



Covering. 



Solid cork 

85 % magnesia. 

Solid cork 

85% magnesia 

Laminated asbestos cork 

85% magnesia 

Asbestos air cell [indent] 

Asbestos sponge felted 

Asbestos air cell [long] 

" Asbestoscel " [radial]. 

Asbestos air cell [long] 

" Remanit" [silk] wrapped 

85 % magnesia, 2" sectional and 1/2' 

block 

85 % magnesia, 2" sectional and 1/2' 

plaster 

85% magnesia, two 1 " sectional 

85% magnesia, two \" sectional 

85% magnesia, 2" sectional ........... 

85% magnesia, 2" sectional 

Bare pipe [from outside tests] 



Aver. 
Thick- 
ness. 



1.68 
1.18 
1.20 
1.19 
1.48 
1.12 
1.26 
1.24 
1.70 
1.22 
1.29 
1.51 

2.71 

2.45 
2.50 
2.24 
2.34 
2.20 



B.T.U. 
Loss 

per sq. 
ft. at 
160 1b. 
Pres. 



B.T.U. 
per sq. 
ft. per 
Hr. per 

Deg. 
Diff. of 
Temp. 



1.672 
2.008 
2.048 
2.130 
2.123 
2.190 
2.333 
2.552 
2.750 
2.801 
2.812 
1.452 

1.381 

1.387 
1.412 
1.465 
1.555 
1.568 
13. 



0.348 
0.418 
0.427 
0.444 
0.442 
0.456 
0.486 
0.532 
0.573 
0.584 
0.586 
0.302 



0.289 
0.294 
0.305 
0.324 
0.314 
2.708 



Per 
cent 
Heat 

Saved 
by 

Cover- 
ing. 



87.1 
84.5 
84.2 
83.6 
83.7 
83.2 
83.1 
80.3 
78.8 
78.5 
78.4 



88.7 
89.0 
88.7 
88.0 
87.9 



Transmission of Heat, through Solid Plates, from Water to Water. 

(Clark, S. E.) — M. Peclet found, from experiments made with plates of 
wrought iron, cast iron, copper, lead, zinc, and tin, that when the fluid 
in contact with the surface of the plate was not circulated by artificial 
means, the rate of conduction was the same for different metals and for 
plates of the same metal of different thicknesses. But when the water 
was thoroughly circulated over the surfaces, and when these were perfectly 
clean, the quantity of transmitted heat was inversely proportional to the 
thickness, and directly as the difference in temperature of the two faces 
of the plate. When the metal surface became dull, the rate of trans- 
mission of heat through all the metals was very nearly the same. 

It follows, says Clark, that the absorption of heat through metal plates 
is more active whilst evaporation is in progress — ■ when the circulation of 
the water is more active — than while the water is being heated up to the 
boiling-point. 

Transmission from Steam to Water. — M. Peclet's principle is 
supported by the results of experiments made in 1867 by Mr. Isherwood on 
the conductivity of different metals. Cylindrical pots, 10 inches in 
diameter, 21 1/4 inches deep inside, and Vs inch, 1/4 inch, and 3/ 8 inch 
thick, turned and bored, were formed of pure copper, brass (60 copper 
and 40 zinc), rolled wrought iron, and remelted cast iron. They were 
immersed in a steam bath, which was varied from 220° to 320° F. Water 
at 212° was supplied to the pots, which were kept filled. It was ascer- 
tained that the rate of evaporation was in the direct ratio of the difference 
of the temperatures inside and outside of the pots; that is, that the rate 
of evaporation per degree of difference of temperatures was the same for 
all temperatures; and that the rate of evaporation was exactly the same 
for different thicknesses of the metal. The respective rates of conductiv- 
ity of the several metals were as follows, expressed in weight of water 
evaporated from and at 212° F. per square foot of the interior surface of 
the pots per degree of difference of temperature per hour, together with 
the equivalent quantities of heat-units: 



562 



Water at 212°. 

Copper . 665 lb. 

Brass .577 " 

Wrought iron . 387 " 

Cast iron 327 " 



Heat-units. 


Ratio 


642.5 
556.8 
373.6 
315.7 


1.00 
0.87 

.58 
.49 



Whitham, "Steam Engine Design," p. 283, also Trans. A. S. M. E., ix, 
425, in using these data in deriving a formula for surface condensers, calls 
these figures those of perfect conductivity, and multiplies them by a 
coefficient C, which he takes at 0.323, to obtain the efficiency of con- 
denser surface in ordinary use, i.e., coated with saline and greasy deposits. 

Transmission of Heat from Steam to Water through Coils of Iron 
Pipe. — H. G. C. Kopp and F. J. Meystre (Stevens Indicator, Jan., 1894) 
give an account of some experiments on transmission of heat through 
coils of pipe. They collate the results of earlier experiments as follows, 
for comparison: 







Steam con- 


Heat trans- 








densed per 


mitted per 








square foot 


square foot 








per degree 


per degree 






*£ 


difference of 


difference of 






3 


temperature 


temperature 




<s 


CO 


per hour. 


per hour. 


Remarks. 




35 








0) 














eS 


Jl 

^2 




.SP 


Bj-I-'H 




w 


O 


ffi a 


^- 


W* 


&tm 




Laurens . 


Copper coils . . 
2 Copper coils 


0.292 


0.981 
1.20 


315 


974 
1120 




Havrez . . 


Copper coil . . . 


6.268 


1.26 


280 


1200 










0.24 




215 


( Steam pressure 
\ =100. 
( Steam pressure 
\ =10. 








0.22 




208.2 








Box 


Iron tube 


0.235 
0.196 
0.206 




230 
207 
210 






Havrez . . 


Cast-iron boiler 


0.077 


0.105 


82 


100 





From the above it would appear that the efficiency of iron surfaces is 
less than that of copper coils, plate surfaces being far inferior. 

In all experiments made up to the present time, it appears that the 
temperature of the condensing water was allowed to rise, a mean between 
the initial and final temperatures being accepted as the effective tempera- 
ture. But as water becomes warmer it circulates more rapidly, thereby 
causing the water surrounding the coil to become agitated and replaced 
by cooler water, which allows more heat to be transmitted. 

Again, in accepting the mean temperature as that of the condensing 
medium, the assumption is made that the rate of condensation is in direct 
proportion to the temperature of the condensing water. 

In order to correct and avoid any error arising from these assumptions 
and approximations, experiments were undertaken, in which all the condi- 
tions were constant during each test. 

The pressure was maintained uniform throughout the coil, and pro- 
vision was made for the free outflow of the condensed steam, in order to 
obtain at all times the full efficiency of the condensing surface. The con- 
densing water was continually stirred to secure uniformity of temperature, 
which was regulated by means of a steam-pipe and a cold-water pipe 
entering the tank in which the coil was placed. 



CONDUCTION AND CONVECTION OF HEAT. 



563 



The following is a condensed statement of the results. 

Heat Transmitted per Square Foot of Cooling Surface, per Hour, 
per Degree of Difference of Temperature. (British Thermal Units.) 



Temperature 
of Condens- 
ing Water. 


1-in. Iron Pipe; 

Steam inside, 

60 lbs. Gauge 

Pressure. 


U/2-in. Pipe; 

Steam inside, 

10 lbs. 

Pressure. 


1 1/2-in. Pipe; 

Steam outside, 

10 lbs. 

Pressure. 


1 1/2-in. Pipe; 

Steam inside, 

60 lbs 

Pressure. 


80 


265 
269 
272 
277 
281 
299 
313 


128 
130 
137 
145 
158 
174 


200 
230 
260 
267 
271 
270 




100 
120 
140 
160 
180 
200 


239 
247 
276 
306 
349 
419 











The results indicate that the heat transmitted per degree of difference of 
temperature in general increases as the temperature of the condensing 
water is increased. 

The amount transmitted is much larger with the steam on the outside of 
the coil than with the steam inside the coil. This may be explained in 
part by the fact that the condensing water when inside the coil flows over 
the surface of conduction very rapidly, and is more efficient for cooling 
than when contained in a tank outside of the coil. 

This result is in accordance with that found by Mr. Thomas Craddock, 
which indicated that the rate of cooling by transmission of heat through 
metallic surfaces was almost wholly dependent on the rate of circulation of 
the cooling medium over the surface to be cooled. 

Transmission of Heat in Condenser Tubes. (Eng'g, Dec. 10, 1875, 
p. 449.) — In 1874 B. C. Nichol made experiments for determining the 
rate at which heat was transmitted through a condenser tube. The 
results went to show that the amount of heat transmitted through the 
walls of the tube per estimated degree of mean difference of temperature 
increased considerably with this difference. For example: 

Estimated mean difference of 
temperature between inside and 
outside of tube, degrees Fahr. . . . 

Heat-units transmitted per hour 
per square foot of surface per 
degree of mean diff. of temp 



Vertical Tube. Horizontal Tube. 



128 151.9 152.9 111.6 146.2 150.4 



422 531 561 610 737 



823 



These results seem to throw doubt upon Mr. Isherwood's statement that 
the rate of evaporation per degree of difference of temperature is the same 
for all temperatures. 

Mr. Thomas Craddock found that water was enormously more efficient 
than air for the abstraction of heat through metallic surfaces in the process 
of cooling. He proved that the rate of cooling by transmission of heat 
through metallic surfaces depends upon the rate of circulation of the cool- 
ing medium over the surface to be cooled. A tube filled with hot water, 
moved by rapid rotation at the rate of 59 ft. per second, through air, lost as 
much heat in one minute as it did in still air in 12 minutes. In water, at a 
velocity of 3 ft. per second, as much heat was abstracted in half a minute 
as was abstracted in one minute when it was at rest in the water. Mr. 
Craddock concluded, further, that the circulation of the cooling fluid 
became of greater importance as the difference of temperature on the 
two sides of the plate became less. (Clark, R. T. D., p. 461.) 

G. A. Orrok (Power, Aug. 11, 1908) gives a diagram showing the relation 
of the B.T.U. transmitted per hour per sq. ft. of surface per degree of 
difference of temperature to the velocity of the water in the condenser 
tubes, in feet per second, as obtained by different experimenters. Approx- 
imate figures taken from the several curves are given below. 



564 





Tubes. 


Velocity of Water, Feet per 
Second. 




Authority. 


0.5 


.| 2 1 3] 4 1 5 ■:■]« 




B.T.U. per sq. ft. per hr. per 
deg. diff. 








325 
420 
540 
500 
365 
560 


400 
470 
370 
530 
590 


465 
525 
405 
560 


520 
560 
435 
585 


550 
585 
460 
615 


















470 








650 


5. Hepburn 

6. Hepburn . . . 


1 1/4-in. horiz. copper. . . . 
1 1/4-in. horiz. corrugated 
1 1/2-in. horiz. corrugated 


250 
360 
'.60 






















8. Weighton... 

9. Allen 


380 
225 


615 

290 


760 
365 


865 


940 























No. 1, water flowing up. Nos. 2 and 3, water flowing down. 

Transmission of Heat in Feed-water Heaters. (W. R. Billings, 
The National Engineer, June, 1907.) — Experiments show that the rate of 
transmission of heat through metal surfaces from steam to water increases 
rapidly with the increased rate of flow of the water. Mr. Billings there- 
fore recommends the use of small tubes in heaters in which the water is 
inside of the tubes. He says: A high velocity ,through the tubes causes 
friction between the water and the walls of the tubes; this friction is not 
the same as the friction between the particles of water themselves, and it 
tends to break up the column of water and bring fresh and cooler particles 
against the hot walls of the tubes. 

The following results were obtained in tests: 

1 1/4-in. smooth tubes { Jj Z i|§ " 5 570 6?0 

1 1/2-in. corrugated tubes { JjZ 3? £ 4 f \ 4 J| 7 || 

V = velocity of the water, ft. per min. U = B.T.U. transmitted per 
sq. ft. per hour per degree difference of temperature. (See Condensers.) 

In calculations of heat transmission in heaters it is customary to take 
as the mean difference of temperature the difference between the tem- 
perature of the steam and the arithmetical mean of the initial and final 
temperatures of the water; thus if S = steam temperature, / = initial 
and F = final temperature of the water, and D = mean difference, then 
D = S — 1/2 (/ + F). Mr. Billings shows that this is incorrect, and on 
the assumption that the rate of transmission through any portion of the 
surface is directly proportional to the difference he finds the true mean 
F — I 

to be D = -r = f-r= =7 j-^ =7-, • (This formula was derived by 

hyp. log [(S - I) -*- (S - F)] 
Cecil P. Poole in 1899, Power, Dec, 1906.) 

The following table is calculated from the formula: 



Degrees of 


Difference Between Steam Temperature and Actual 
Average Temperature of Water. 




Vacuum Heaters Between Engine and Condenser. 


Initial 


26" Vac. Temp. 126° F. 


24" Vac. Temp. 141° F. 


Temperature 
of Water. 


Final Temp, of Water. 


Final Temp, of Water. 




105 


110 


115 


120 


105 


110 


115 


120 


125 


130 


40 


46.1 
42.8 
39.3 
35.6 
31.8 


41.6 
38.4 
35.3 
31.9 

28.3 


36.9 
33.6 
30.7 
27.6 

24.5 


30.1 
27.6 
25.0 
22.4 
19.6 


62.9 
59.2 
55.5 
51.6 
47.6 


60.2 
56.6 
52.1 

48.2 
44.2 


55.3 
51.8 
48.4 
45.0 
41.2 


50.9 

47.7 
44.4 
41.0 
37.5 


46.1 
43.2 
40.1 
36.9 
33.6 


40.6 


50 


37.9 


60 

70 

80 


35.0 

32.2 
29.2 











CONDUCTION AND CONVECTION OF HEAT. 



565 





Atmospheric Heaters. 


Initial Temp. 


Atmos. Press. Temp. 
212° F. 


o 
a 
Be 

~3 


Atmos. Press. Temp. 
212° F. 


of Water. 


Final Temp, of Water. 


Final Temp, of Water. 




192 


196 


200 


204 


208 


210 


192 


196 


200 


204 


208 


210 


40 

50 

60 

70 

80 


70.6 
67.9 
65.1 
62.2 
59.4 


65.7 
63.1 
60.4 
57.7 
54.9 


60.1 
57.6 
55.2 
52.6 
50.0 


53.5 

51.2 
48.9 
46.6 
44.2 


44.8 
42.8 
40.7 
38.7 
36.6 


38.0 
36.4 
34.7 
32.9 
31.0 


105 
110 
115 
120 
125 


51.9 
50.3 

48.8 
47.2 
45.6 


47.9 
46.4 
45.0 
43.5 
41.9 


43.4 
42.1 
40.6 
39.2 
37.8 


38.2 
36.9 
35.7 
34.4 
33.1 


31.4 
30.2 
29.2 
28.0 
26.9 


26.4 
25.5 
^4.5 
23.5 
?.?. 5 







The error in using the arithmetic mean for the value of D is not impor- 
tant if F is very much lower than S, but if it is within 10° of S then the 
error may be a large one. With S = 212, / = 40, F = 110, the arith- 
metic mean difference is 137, and the value by the logarithmic formula 
131, an error of less than 5%; but if F is 204, the arithmetic mean is 90, 
and the value by the formula 53.5. 

It should be observed, however, that the formula is based on an assump- 
tion that is probably greatly in error for high temperature differences, 
i.e., that the transmission of heat is directly proportional to the tem- 
perature difference. It may be more nearly proportional to the square 
of the difference, as stated by Rankine. This seems to be indicated by 
the results of heating water by steam coils, given below. 

Heating Water by Steam Coils. — A catalogue of the American 
Radiator Co. (1908) gives a chart showing the pounds of steam condensed 
per hour per sq. ft. of iron, brass and copper pipe surface, for different 
mean or average differences of temperature between the steam and the 
water. Taking the latent heat of the steam at 966 B.T.U. per lb., the fol- 
lowing figures are derived from the table. 



Mean 
Temp. 


Lb. Steam Condensed 

per Hour per Sq. Ft. 

of Pipe. 


Lb. Steam Condensed 

per Hour per Sq. Ft. 

per Deg. Diff. 


B.T.U. per Sq. 
Ft. per Hour 
per Deg. Diff. 


Diff. 


Iron. 


Brass. 


Copper 


Iron. 


Brass. 


Copper 


Iron. 


Brass 


Cop. 


50 
100 
150 

200 


7.5 
18.5 
32.2 

48 


12.5 

38 

76.5 

128 


14.5 
43.5 
87.8 
144 


0.150 
0.185 
0.215 
0.240 


0.250 
0.380 
0.510 
0.640 


0.290 
0.435 
0.585 
0.720 


101 
179 
208 
232 


198 
367 
493 
618 


289 
415 
565 
695 



The chart is said to be plotted from a large number of tests with pipes 
placed vertically in a tank of water, about 20 per cent being deducted 
from the actual results as a margin of safety. 

W. R. Billings (Eng. Rec, Feb., 1898) gives as the results of one set of 
experiments with a closed feed-water heater: 

Mean temp, diff., deg. F 5 6 8 11 15 18 

B.T.U. per sq. ft. per hr. per deg. diff. 67 79 89 114 129 139 

Heat Transmission through Cast-iron Plates Pickled in Nitric 
Acid. — Experiments by R. C. Carpenter (Trans. A. S. M. E., xii, 179) 
show a marked change in the conducting power of the plates (from 
steam to water), due to prolonged treatment with dilute nitric acid. 



566 



HEAT. 



The action of the nitric acid, by dissolving the free iron and not attack- 
ing the carbon, forms a protecting surface to the iron, which is largely 
composed of carbon. The following is a summary of results: 



Character of Plate6, each plate 8.4 in. 
by 5.4 in., exposed surface 27 sq. ft. 



Cast iron — untreated skin on, but 

clean, free from rust, 

Cast iron — nitric acid, I % sol., 9 days . . 
1% sol., 18 days 
1% sol., 40 days 
5% sol., 9 days.. 
5% sol., 40 days 
Plate of pine.wood, same dimensions as 
the plate of cast iron 



Increase 
in Tem- 
perature 
of 3.125 
lbs. of 
Water 
each 
Minute. 



Proportionate 

Thermal Units 

Transmitted for 

each Degree of 

Difference of 

Temperature per 

Square Foot per 

Hour. 



13.90 
11.5 
9.7 
9.6 
9.93 
10.6 

0.33 



113.2 
97.7 
80.08 
77.8 
87.0 
77.4 



Rela- 
tive 
Trans- 
mission 

of 
Heat. 



100.0 
86.3 
70.7 
68.7 
76. 8 
68. 5 



1.6 



The effect of covering cast-iron surfaces with varnish has been investi- 
gated by P. M. Chamberlain. He subjected the plate to the action of strong 
acid for a few hours, and then applied a non-conducting varnish. One 
surface only was treated. Some of his results are as follows: 



cro 


f 170. 




152. 


fen"©- 


169. 


ft3 <u^- 


162. 


wjZ two 1 " 




•Sfc-S 1 ' 


166. 


3 Pus ** 




ss'i 


113. 



117. 



As finished — greasy. 

washed with benzine and dried. 
Oiled with lubricating oil. 
After exposure to nitric acid sixteen hours, then oiled 

(linseed oil). 
After exposure to hydrochloric acid twelve hours, then 
oiled (linseed oil). 
After exposure to sulphuric acid 1, water 2, for 48 
hours, then oiled, varnished, and allowed to dry for 
24 hours. 



Transmission of Heat through Solid Plates from Air or other Dry 
Gases to Water. (From Clark on the Steam Engine.) — The law of the 
transmission of heat from hot air or other gases to water, through metallic 
plates, has not been exactly determined by experiment. The general 
results of experiments on the evaporative action of different portions of 
the heating surface of a steam-boiler point to the general law that the 
quantity of heat transmitted per degree difference of temperature is 
practically uniform for various differences of temperature. 

The communication of heat from the gas to the plate surface is much 
accelerated by mechanical impingement of the gaseous products upon the 
surface. 

Clark says that when the surfaces are perfectly clean, the rate of trans- 
mission of heat through plates of metal from air or gas to water is greater 
for copper, next for brass, and next for wrought iron. But when the 
surfaces are dimmed or coated, the rate is the same for the different 
metals. 

With respect to the influence of the conductivity of metals and of the 
thickness of the plate on the transmission of heat from burnt gases to 
water, Mr. Napier made experiments with small boilers of iron and copper 
placed over a gas-flame. The vessels were 5 inches in diameter and 2 1/2 
inches deep. From three vessels, one of iron, one of copper, and one 
of iron sides and copper bottom, each of them 1/30 inch in thickness, 



CONDUCTION AND CONVECTION OF HEAT. 567 

equal quantities of water were evaporated to dryness, in the times as 
follows: 

Water. Iron Vessel. Copper Vessel. Iron V^S?? 1 *' 

4 ounces 19 minutes 18.5 minutes 

11 " 33 " 30.75 " 

5 J/2 " 50 44 " 

4 " 35.7 " 36.83 minutes 

Two other vessels of iron sides 1/30 inch thick, one having a 1/4-Itich 
copper bottom and the other a 1/4-inch lead bottom, were tested against 
the iron and copper vessel, 1/33 inch thick. Equal quantities of water were 
evaporated in 54, 55, and 531/2 minutes respectively. Taken generally, 
the results of these experiments show that there are practically but slight 
differences between iron, copper, and lead in evaporative activity, and 
that the activity is not affected by the thickness of the bottom. 

Mr. W. B. Johnson formed a like conclusion from the results of his 
observations of two boilers of 160 horse-power each, made exactly alike, 
except that one had iron flue-tubes and the other copper flue-tubes. No 
difference could be detected between the performances of these boilers. 

Divergencies between the results of different experimenters are attrib- 
utable probably to the difference of conditions under which the heat was 
transmitted, as between water or steam and water, and between gaseous 
matter and water. On one point the divergence is extreme: the rate of 
transmission of heat per degree of difference of temperature. Whilst from 
400 to 600 units of heat are transmitted from water to water through iron 
plates, per degree of difference per square foot per hour, the quantity of 
heat transmitted between water and air, or other dry gas, is only about 
from 2 to 5 units, according as the surrounding air is at rest or in move- 
ment. In a locomotive boiler, where radiant heat was brought into play, 
17 units of heat were transmitted through the plates of the fire-box per 
degree of difference of temperature per square foot per hour. 

Transmission of Heat through Plates from Flame to Water. — 
Much controversy has arisen over the assertion, by some makers of live- 
steam feed-water "heaters that if the water fed to a boiler was first heated to 
the boiling point before being fed into the boiler, by means of steam taken 
from the boiler, an economy of fuel would result; the theory being that 
the rate of transmission through a plate to water was very much greater 
when the water was boiling than when it was being heated to the boiling 
point, on account of the greatly increased rapidity of circulation of the 
water when boiling. (See Eng'g, Nov. 16, 1906, and Eng. Review [London], 
Jan., 1908.) Two experiments by Sir Wm, Anderson (1872), with a steam- 
jacketed pan, are quoted, one of which showed an increased transmission 
when boiling of 133%, and the other of 80%; also an experiment by 
Sir F. Bramwell, with a steam-heated copper pan, which showed a gain of 
164% with boiling water. On the other hand, experiments by S. B. Bil- 
brough (Transvaal Inst. Mining Engineers, Feb., 1908) showed in tests 
with a flame-heated pan that there was no difference in the rate of trans- 
mission whether the water was cold or boiling. W. M. Sawdon (Power, 
Jan. 12, 1909) objects to Mr. Bilbrough's conclusions on the ground that 
no corrections for radiation were made, and finds by a similar experiment, 
with corrections, that the increased rate of transmission with boiling water 
is at least 38%. All of these experiments were on a small scale, and in 
view of their conflict no conclusions can be drawn from them as to the 
value of live-steam feed-water heating in improving the economy of a 
steam boiler. 

A. Bleehynden's Tests. — A series of steel plates from 0.125 in. to 
1.187 in. thick were tested with hot gas on one side and w r ater on the other 
with differences of temperature ranging from 373° to 1318° F. Trans.) 
Inst. Naval Architects, 1894.) Mr. Blechynden found that the heat 
transmitted is proportional to the square of the difference between the 
temperatures at the two sides of the plate, or: Heat transmitted per sq. 
ft. -4- (diff. of temp.) 2 = a constant. A study of the results of these 
tests is made in Kent's " Steam Boiler Economy," p. 235, and it is shown 
that the value of a in Rankine's formula q =(T\— T) 2 -=-a, which a is the 
reciprocal of Mr. Bleehynden's constant and is a function of the thickness 
of the plate. One of the plates, A, originally 1.187 in. thick, was reduced 



568 



in four successive operations, by machining to 0.125 in. Another, B, was 
tested in four thicknesses. The othe; plates were tested in one or two 
thicknesses. Each plate was found to have a law of transmission of its 
own. For plate A the value of a is represented closely by the formula 
a = 40 ■+- 20 t, in which t is the thickness in inches. The formula a = 
40 + 20 t ± 10 covers the whole range of the experiments. The whole 
range of values is 38.6 to 71.9, which are very low when compared with 
values of a computed from the results of boiler tests, which are usually 
from 200 to 400, the low values obtained by Blechynden no doubt being 
due to the exceptionally favorable conditions of his tests as compared 
with those of boiler tests. Rankine says the value of a lies between 160 
and 200, but values below 200 are rarely found in tests of modern types 
of boilers. (See Steam-Boilers.) 

Cooling of Air. — H. F. Benson {Am. Mach., Aug. 31, 1905) derives 
the following formula for transmission of heat from air to water through 
copper tubes. It is assumed that the rate of transmission at any point of 
the surface is directly proportional to the difference of temperature 
between the air and water. 

Let A = cooling surface, sq. ft.; K = lb. of air per hour; S a = specific 
heat of air; T ai = temp, of hot inlet air; T ao =temp. of cooled outlet air; 
d = actual average diff. of temp, between "the air and the water; U = 
B.T.U. absorbed by the water per degree of diff. of temp, per sq. ft. per 
hour. W = lb. of water per hour; T Wl = temp, of inlet water; T w% = 
temp, of outlet water. Then 



AdU = KS a (T, 

rf = [(r ai -r a2 )-(r, 

AU = 
T W2 = 



«i 



T a2 ); A = KS a (T ai - T tt2 ) + dU. 
-T^Jl+iog [(T ai -T W2 ) + (T a2 -T Wl ). 

KS a W T ai - T W2 

W-KS a l ° g eT a2 - T Wl ' 
{S a K + W)(T ai -T a2 ) + T Wl . 



The more cooling water used, the lower is the temperature T wy Also 
the less T W2 is, the larger d becomes and the less surface is needed. About 
10 is the largest value of W IK that it is economical to use, as there is a 
saving of less than 0.5% in increasing it from 10 to 15. When desirable 
to save water it will be advisable to make W IK = 5. Values of U 
obtained by experiment with a Wainwright cooler made with corrugated 
copper tubes are given in the following table. K and W are in lb. per 
minute, B a = B.T.U. from air per min., B w = B.T.U. from water per 
min., Vw = velocity of water, ft. per min. 



T 


T a 2 


T w 


T W2 


K 


W 


B a 


B w 


V w 


U 


221.0 


76.3 


50.0 


169.0 


125.2 


28.50 


4303 


3392 


2.20 


6.75 


217.0 


64.3 


45.8 


146.4 


122.8 


36.73 


4452 


3695 


2.84 


7.12 


224.0 


63.3 


45.7 


149.2 


126.3 


40.30 


4819 


4171 


3.11 


7.91 


209.6 


54.0 


43.8 


125.9 


122.1 


50.00 


4511 


4105 


3.86 


8.81 


214.5 


46.3 


43.0 


106.2 


124.6 


68.95 


4976 


4357 


5.32 


10.55 


234.6 


63.6 


52.6 


120.2 


124.4 


73.25 


5051 


4152 


5.65 


8.41 


214.2 


43.5 


43.0 


94.7 


117.3 


79.84 


4753 


4128 


6.16 


.14.32 


242.9 


61. 7 


55.3 


114.0 


133.6 


92.72 


5649 


5443 


7.15 


10.01 


223.0 


46.0 


40.1 


79.1 


130.5 


114.80 


5484 


4477 


8.86 


7.8) 


239.3 


57.5 


51.0 


95.2 


130.0 


125.70 


"612 


5556 


9.70 


9.3T 


246.0 


58.0 


52.3 


95.1 


133.8 


145.90 


5977 


6244 


11.26 


10.57 



Sixteen other tests were made besides those given above, and their 
plotted results all come within the field covered by those in the table. 



CONDUCTION AND CONVECTION OF HEAT. 



569 



There is apparently an error in the last line of the table, for the heat 
gained by the water could not be greater than that lost by the air. The 
excess lost by the air may be due to radiation, but it shows a great irregu- 
larity. It appears that for velocities of water between 2.2 and 5.3 ft. per 
min. the value of U increases with the velocity, but for higher velocities 
the value of U is very irregular, and the cause of the irregularity is not 
explained. 

Chas. L. Hubbard (The Engineer, Chicago, May IS, 1902) made some 
tests by blowing air through a tight wooden box which contained a nest 
of 30 li/2-in. tin tubes, of a total surface of about 20 sq. ft., through 
which cold water flowed. The results were as follows: 



Cu. ft. of air per minute 

Velocity over cooling surface 

Initial temperature of air 

Drop in temperature 

Average temp, of water 

Average temp, of air 

Difference 

B.T.U. per hour per sq. ft. per degree 
difference 



268 


268 


469 


469 


636 


638. 


638 


1116 


1116 


1514 


72° 


72° 


72° 


74° 


74° 


8° 


12° 


8° 


10° 


8° 


50° 


43° 


48° 


48° 


50° 


68° 


66° 


68° 


69° 


70° 


18° 


23° 


20° 


21° 


20° 


6.5 


7.6 


10.2 


12.1 


13.8 



636 

1514 

74° 

10° 

44° 



Transmission of Heat through Plates and Tubes from Steam or 
Hot Water to Air. — The transfer of heat from steam or water through 
a plate or tube into the surrounding air is a complex operation, in which 
the internal and external conductivity of the metal, the radiating power 
of the surface, and the convection of heat in the surrounding air, are all 
concerned. Since the quantity of heat radiated from a surface varies with 
the condition of the surface and with the surroundings, according to laws 
not yet determined, and since the heat carried away by convection varies 
with the rate of the flow of the air over the surface, it is evident that no 
general law can be laid down for the total quantity of heat emitted. 

The following is condensed from an article on "Loss of Heat from 
Steampipes," in The Locomotive, Sept. and Oct., 1892. 

A hot steam-pipe is radiating heat constantly off into space, but at the 
same time it is cooling also by convection. Experimental data on which 
to base calculations of the heat radiated and otherwise lost by steam-pipes 
are neither numerous nor satisfactory. 

In Box's " Practical Treatise on Heat" a number of results are given for 
the amount of heat radiated by different substances when the temperature 
of the air is 1° Fahr. lower than the temperature of the radiating body. A 
portion of this table is given below. It is said to be based on Peclet's 
experiments. 



Heat Units Radiated per Hour, per Square Foot of Surface, 
for 1° Fahrenheit Excess in Temperature. 



Glass 0.5948 

Cast iron, new 0.6480 

Common steam-pipe, in- 
ferred 0.6400 

Cast and sheet iron, rusted . . 0.6S68 
Wood, building stone, and 
brick 0.7358 



Copper, polished 0.0327 

Tin, polished 0.0440 

Zinc and brass, polished. . . 0.0491 

Tinned iron, polished 0.0858 

Sheet iron, polished 0.0920 

Sheet lead ' 0.1329 

Sheet iron, ordinary 0.5662 

When the temperature of the air is about 50° or 60° Fahr., and the radiat- 
ing body is not more than about 30° hotter than the air, we may calculate 
the radiation of a given surface by assuming the amount of heat given off 
by it in a given time to be proportional to the difference in temperature 
between the radiating body and the air. This is " Newton's law of cooling. " 
But when the difference in temperature is great, Newton's law does not 
hold good; the radiation is no lonsrer proportional to the difference in tem- 
perature, but must be calculated by a complex formula established experi- 
mentally by Dulong and Petit. Box has computed a table from this 



570 



formula, which greatly facilitates its application, and which is given 
below: 

Factors for Reduction to Dulong's Law of Radiation. • 



Differences in Tem- 


Temperature of the Air 


an the Fahrenheit Scale. 


perature between 
Radiating Body 
























and the Air. 


32° 


50° 


59° 


68° 


86° 


IQ4° 


122° 


140° 


158° 


176° 


194° 


212 c 


Deg. Fahr. 


























18 


1.00 


1.07 


1.12 


1.16 


1.25 


1.36 


1.47 


1.58 


1.70 


1.85 


1.99 


2.15 


36 


1.03 


1.11 


1.16 


1.21 


1.30 


1.40 


1.52 


1.68 


1.76 


1.91 


2.06 


2.23 


54 . 


1.07 


1.16 


1.20 


1.25 


1.35 


1.45 


1.58 


1.70 


1.83 


l.9=> 


2.14 


2.31 


72 


1.12 


1.20 


1.25 


1.30 


1.40 


1.52 


1.64 


1.76 


1.90 


2.07 


2.23 


2.40 


90 


1.16 


1.25 


1.31 


1.36 


1.46 


1.58 


1.71 


1.84 


1.98 


2.15 


2.33 


2.51 


108 


1.21 


1.31 


1.36 


1.42 


1.52 


1.65 


1.78 


1.92 


2.07 


2.28 


2.42 


2.62 


126 


1.26 


1.36 


1.42 


1.48 


1.60 


1.72 


1.86 


2.00 


2.16 


2.34 


2.52 


2.72 


144 


1.32 


1.42 


1.48 


1.54 


1.65 


1.79 


1.94 


2.08 


2.24 


2.44 


2.64 


2.83 


162 


1.37 


1.48 


1.54 


1.60 


1.73 


1.86 


2.02 


2.17 


2.34 


2.54 


2.74 


2.96 


180 


1.44 


1.55 


1.61 


1.68 


1.81 


1.95 


2.11 


2.27 


2.46 


2.66 


2.87 


3.10 


198 


1.50 


1.62 


1.69 


1.75 


1.89 


2.04 


2.21 


2.38 


2.56 


2.78 


3.00 


3.24 


216 


1.58 


1.69 


1.76 


1.83 


1.97 


2.13 


2.32 


2.48 


2.68 


2.91 


3.13 


3.38 


234 


1.64 


1.77 


1.84 


1.90 


2.06 


2.23 


2.43 


2.52 


2.80 


3 03 


3.28 


3 46 


252 


1.71 


1.85 


1.92 


2.00 


2.15 


2.33 


2.52 


2.71 


2.92 


3.18 


3.43 


3.70 


270 


1.79 


1.93 


2.01 


2.09 


2.26 


2.44 


2.64 


2.84 


3.06 


3.32 


3.58 


3.87 


288 


1.89 


2.03 


2.12 


2.20 


2.37 


2.56 


2.78 


2.99 


3.22 


3.50 


3.77 


4.07 


306 


1.98 


2.13 


2.22 


2.31 


2.49 


2.69 


2.90 


3.12 


3.37 


3.66 


3 95 


4.26 


324 


2.07 


2.23 


2.33 


2.42 


2.62 


2.81 


3.04 


3.28 


3.53 


3.84 


4.14 


4.46 


342 


2.17 


2.34 


2.44 


2.54 


2.73 


2.95 


3.19 


3.44 


3.70 


4.02 


4.34 


4.68 


360 


2.27 


2.45 


2.56 


2.66 


2.86 


3.09 


3.35 


3.60 


3.88 


4.22 


4.55 


4.91 


378 


2.39 


2.57 


2.68 


2.79 


3.00 


3.24 


3.51 


3.78 


4.08 


4.42 


4.77 


5.15 


396 


2.50 


2.70 


2.81 


2.93 


3.15 


3.40 


3.68 


3.97 


4.28 


4.64 


5.01 


5.40 


414 


2.63 


2.84 


2.95 


3.07 


3.31 


3.56 


3.87 


4.12 


4.48 


4.87 


5.26 


5.67 


432 


2.76 


2.98 


3.10 


3,23 


3.47 


3.76 


4.10 


4.32 


4.61 


5.12 


5.53 


6.04 



The loss of heat by convection appears to be independent of the nature 
of the surface, that is, it is the same for iron, stone, wood, and other 
materials. It is different for bodies of different shape, however, and it 
varies with the position of the body. Thus a vertical steam-pipe will not 
lose so much heat by convection as a horizontal one will; for the air 
heated at the lower part of the vertical pipe will rise along the surface of 
the pipe, protecting it to some extent from the chilling action of the sur- 
rounding cooler air. For a similar reason the shape of a body has an 
important influence on the result, those bodies losing most heat whose 
forms are such as to allow the cool air free access to every part of their 
surface. The following table from Box gives the number of heat units 
that horizontal cylinders or pipes lose by convection per square foot of 
surface per hour, for one degree difference in temperature between the 
pipe and the air. 

Heat Units Lost by Convection from Horizontal Pipes, per Square 
Foot of Surface per Hour, for a Temperature 
Difference of 1° Fahr. 



External 

Diameter 

of Pipe 

in Inches. 


Heat 

Units 
Lost. 


External 
Diameter 

of Pipe 
in Inches. 


Heat 
Units 
Lost. 


External 
Diameter 
of Pipe 
in In ;hes. 


Heat 
Units 
Lost. 


2 
3 
4 
5 
6 


0.728 
0.626 
0.574 
0.544 
0.523 


7 
8 
9 
10 
12 


0.509 
0.498 
489 
482 
0.472 


18 
24 
36 
48 


0.455 
0.447 
438 
434 









THERMODYNAMICS. 



571 



The loss of heat by convection is nearly proportional to the difference 
in temperature between the hot body and the air, but the experiments of 
Dulong and Peclet show that this is not exactly true, and we may here also 
resort to a table of factors for correcting the results obtained by sample 
proportion. 

Factors for Reduction to Dulong's Law of Convection. 



Difference 




Difference 




Difference 




in Temp, 
between Hot 




in Temp. 




in Temp. 




Factor. 


between Hot 


Factor. 


between Hot 


Factor. 


Body and 




Body and 




Body and 




Air. 




Air. 




Air. 




18° F. 


0.94 


180° F. 


1.62 


342° F. 


1.87 


36° 


1.11 


198° 


1.65 


360° 


1.90 


54° 


1.22 


216° 


1.68 


378° 


1.92 


72° 


1.30 


234° 


1.72 


396° 


1.94 


90° 


1.37 


252° 


1.74 


414° 


1.96 


108° 


1.43 


270° 


1.77 


432° 


1.98 


126° 


1.49 


288° 


1.80 


450° 


2.00 


144° 


1.53 


306° 


1.83 


468° 


2.02 


162° 


1.58 


324° 


1.85 













Example in the Use of the Tables. — Required the total loss of heat 
by both radiation and convection, per foot of length of a steam-pipe 211/32 
in. external diameter, steam pressure 60 lbs., temperature of the air in the 
room 68° Fahr. 

Temperature corresponding to 60 lbs. equals 307°; temperature dif- 
ference = 307° - 68 = 239°. 

Area of one foot length of steam-pipe = 211/32 X 3.1416 -*- 12 = 
0.614 sq. ft. 

Heat radiated per hour per square foot per degree of difference, from 
table, 0.64. 

Radiation loss per hour by Newton's law = 239° X 0.614 ft. X 0.64 = 
93.9 heat units. Same reduced to conform with Dulong's law of radiation: 
factor from table for temperature difference of 239° and temperature of 
air 68° = 1.93. 93.9 X 1.93 = 181.2 heat units, total loss by radiation. 

Convection loss per square foot per hour from a 211/32-inch pipe: by 
interpolation from table, 2" = 0.728, 3" = 0.626, 211/32" = 0.693. 

Area, 0.614 X 0.693 X 239° = 101.7 heat units. Same reduced to 
conform with Dulong's law of convection: 101.7 X 1.73 (from table) = 
175.9 heat units per hour. Total loss by radiation and convection = 
181.2 + 175.9 = 357.1 heat units per hour. Loss per degree of difference 
of temperature per linear foot of pipe per hour = 357.1 -*■ 239 = 1.494 
heat units = 2.433 per sq. ft. 

It is not claimed, says The Locomotive, that the results obtained by this 
method of calculation are strictly accurate. The experimental data are 
not sufficient to allow us to compute the heat-loss from steam-pipes with 
any great degree of refinement; yet it is believed that the results obtained 
as indicated above will be sufficiently near the truth for most purposes. 
An experiment by Prof. Ordway, in a pipe 211/32 in. diam. under the above 
conditions (Trans. A. S. M. E., v. 73), showed a condensation of steam of 
181 grams per hour, which is equivalent to a loss of heat of 358.7 heat 
units per hour, or within half of one per cent of that given by the above 
calculation. 

The quantity of heat given off by steam and hot-water radiators in 
ordinary practice of heating buildings by direct radiation varies from 1.25 
to about 3.25 heat units per hour per square foot per degree of difference 
of temperature. (See Heating and Ventilation.) 

THERMODYNAMICS. 

Thermodynamics, the science of heat considered as a form of energy, 
is useful in advanced studies of the theory of steam, gas, and air engines, 
refrigerating machines, compressed air, etc. The method of treatment 
adopted by the standard writers is severely mathematical, involving 
constant application of the calculus. The student will find the subject 



572 HEAT. 

thoroughly treated in the works by Rontgen (Dubois's translation). Wood, 
Peabody, and Zeuner. 

First Law of Thermodynamics. — Heat and mechanical energy are 
mutually convertible in the ratio of about 778 foot-pounds for the British 
thermal unit. (Wood.) 

Second Law of Thermodynamics. — The second law has by different 
writers been stated in a variety of ways, and apparently with ideas so 
diverse as not to cover a common principle. (Wood, Therm., p. 389.) 

It is impossible for a self-acting machine, unaided by any external 
agency, to convert heat from one body to another at a higher temperature. 
(Clausius.) 

If all the heat absorbed be at one temperature, and that rejected be at 
one lower temperature, then will the heat which is transmuted into work 
be to the entire heat absorbed in the same ratio as the difference between 
the absolute temperature of the source and refrigerator is to the absolute 
temperature of the source. In other words, the second law is an expression 
for the efficiency of the perfect elementary engine. (Wood.) 

The expression - = x „ — - 2 may be called the symbolical or 

algebraic enunciation of the second law, — the law which limits the 
efficiency of heat engines, and which does not depend on the nature of the 
working medium employed. (Trowbridge.) Qx and T\ = quantity and 
absolute temperature of the heat received; Qi and Ti = quantity and 
absolute temperature of the heat rejected. 
Ti — Ti 
The expression ^ represents the efficiency of a perfect heat 

engine which receives all its heat at the absolute temperature T\, and 
rejects heat at the temperature Ti, converting into work the difference 
between the quantity received and rejected. 

Example. — What is the efficiency of a perfect heat engine which 
receives heat at 388° F. (the temperature of steam of 200 lbs. gauge 
pressure) and rejects heat at 100° F. (temperature of a condenser, pressure 
1 lb. above vacuum)? 



388 + 459.2 

In the actual engine this efficiency can never be attained, for the difference 
between the quantity of heat received into the cylinder and that rejected 
into the condenser is not all converted into work, much of it being lost by 
radiation, leakage, etc. In the steam engine the phenomenon of cylinder 
condensation also tends to reduce the efficiency. 

The Carnot Cycle. — Let one pound of gas of a pressure p\, volume vi 
and absolute temperature T\ be enclosed in an ideal cylinder, having non- 
conducting walls but the bottom a perfect con- 
ductor, and having a moving non-conducting 
frictionless piston. Let the pressure and volume 
of the gas be represented by the point A on the 
pv or pressure-volume diagram, Fig. 136, and 
let it pass through four operations, as follows: 

1. Apply heat at a temperature of T\ to the 

bottom of the cylinder and let the gas expand, 

doing work against the piston, at the constant 

temperature T\, or isothermally, to p 2 w>. or B. 

F , Q /> 2 - Remove the source of heat and put a non- 

r ig. ido. conducting cover on the bottom, and let the gas 

expand adiabatically, or without transmission of heat, to pzm, or C, while 

its temperature is being reduced to T-i. 

3. Apply to the bottom of the cvlinder a cold body, or refrigerator, of 
the temperature T2, and let the gas be compressed by the piston isother- 
mally to the point D, or p 4 ?>4, rejecting heat into the cold body. 

4. Remove the cold body, restore the non-conducting bottom, and 
compress the gas adiabatically to A , or the original pivi, while its tempera- 
ture is being raised to the original T\. The point D on the isothermal 
line CD is chosen so that an adiabatic line passing through it will also pass 
through A, and so that v\/v\ = m/vz. 

The area aABCc represents the work done by the gas on the piston; 



p 

A 






( 


\\b 




D^ 


"l C 


a 


d 


b \c 



THERMODYNAMICS. 573 

the area CDAac the negative work, or the work done by the piston on the 
gas; the difference, ABCD, is the net work. 

la. The area aABb represents the work done during isothermal expan- 
sion. It is equal in foot-pounds to Wi = pm log e {V2/v\), where pi = the 
initial absolute pressure in lbs. per sq. ft. and vi = the initial volume in 
cubic feet. It is also equal to the quantity of heat supplied to the gas,= 
Ui = RTi log e (i>2/m). R is a constant for a given gas, = 53.35 for air. 

2a. The area bBCc is the work done during adiabatic expansion, = Wz 

= _ 1 1 — (— ) \ . y being the ratio of the specific heat at constant 

pressure to the specific heat at constant volume. For air y = 1.406. 
The loss of intrinsic energy = K v (Ti — Ti) ft.-lbs. K v = specific heat 
at constant volume X 778. 

3a. CDdc is the work of isothermal compression, = Wz = piv\ logg 
(vz/vt) = heat rejected = JJ% = RTi log e (vz/vt). 

4a. DAad is the work of adiabatic compression 



= Wi 



■v^-en 



which is the same as Wi and therefore, being negative, cancels it, and the 

net work ABCD = Wi — Wz. The gain of intrinsic energy is K v (Ti — Ti). 

Comparing la and 3a, we have pm = pivi;pzvz = pm; vi/vz = vi/vi =r. 

Wi = pivi logg r = RTi log e r; Wz = pm log e r = RTi log e r. 

R(Ti-T2)\og e r _ Ti-Tz _T 1 

RTi\og e r ~~ T\ "* T\ 

M 7-1 Vx-Vt 



>&"-■ 



Ui 



Entropy. — In the pv or pressure-volume diagram, energy exerted or 
expended is represented by an area the lines of which show the changes 
of the values of p and v. In the Carnot cycle these changes are shown 
by curved lines. If a given quantity of heat Q is added to a substance 
at a constant temperature, we may represent it by a rectangular area 
in which the temperature is represented by a vertical line, and the base 
is the quotient of the area divided by the length of the vertical line. To 
this quotient is given the name entropy. When the temperature at 
which the heat is added is not constant a more general definition is 
needed, viz.: Entropy is length on a diagram the area of which represents 
a quantity of heat, and the height at any point represents absolute tempera- 
ture. The value of the increase of entropy is given in the language of 

calculus, E = I -t^p, which may be interpreted thus: increase of entropy 

between the temperatures T* and Ti equals the summation of all the 
quotients arising by dividing each small quantity of heat added by 
the absolute temperature at which it is added. It is evident that if 
the several small quantities of heat added are equal, while the values of 
T constantly increase, the quotients are not equal, but are constantly 
decreasing. The diagram, called the temperature-entropy diagram, or 
the 0<£, theta-phi, diagram, is one in which the abscissas, or horizontal 
distances, represent entropy, and vertical distances absolute temperature. 
The horizontal distances are measured from an arbitrary vertical line 
representing entropy at 32° F., and values of entropy are given as values 
beyond that point, while the temperatures are measured above absolute 
zero. Horizontal lines are isothermals, vertical lines adiabatics. The use- 
fulness of entropy in thermodynamic studies is due to the fact that in 
manv cases it simplifies calculations and makes it possible to use alge- 
braic or graphical methods instead of the more difficult methods of the 
calculus. 




574 HEAT. 

The Carnot Cycle in the Temperature-Entropy Diagram. — Let a 

pound of gas having a temperature Ti and entropy E be subjected to the 
four operations described above. (1) Ti being 
constant, heat (area aABc, Fig. 137) is added and 
the entropy increases from A to B\ isothermal 
expansion. (2) No heat is transferred, as heat, 
but the temperature is reduced from T\ to Tr, 
entropy constant ; adiabatic expansion. (3) Heat 
is rejected at the constant temperature T z , the 
area CcaD being subtracted; entropy decreases 
from C to D; isothermal compression. (4) En- 
tropy constant, temperature increases from D to 
A, or from Ti to T\\ no heat transferred as heat; 
adiabatic compression. The area aJL.Bc repre- 
sents the total heat added during the cycle, the 
area cCDa the heat rejected; the difference, or the 
Fig 137 area ^4 i?CD, is the heat utilized or converted into 

work. The ratio of this area to the whole area 
aABc is the efficiency; it is the same as the ratio (Ti — T2) **- Ti. It 
appears from this diagram that the efficiency may be increased by in- 
creasing T\ or by decreasing T2; also that since Ti cannot be lowered by 
any self-acting engine below the temperature of the surrounding atmos- 
phere, say 460°+ 62° F.= 522° F., it is not possible even in a perfect 
engine to obtain an efficiency of 50 per cent unless the temperature of 
the source of heat is above 1000° F. It is shown also by this diagram 
that the Carnot cycle gives the highest possible efficiency of a heat engine 
working between any given temperatures Ti and Ti, and that the admis- 
sion and rejection of heat each at a constant temperature gives a higher 
efficiency than the admission or rejection at any variable temperatures 
within the range Ti — Tt. 

The Reversed Carnot Cycle — Refrigeration. — Let a pound of cool 
gas whose temperature and entropy are represented by the "state- 
point" D on the diagram (1) receive heat at a constant temperature Ti 
(the temperature of a refrigerating room) until its entropy is C; (2) then 
let it be compressed adiabatically (no heat transmission, CB) to a high 
temperature T\; (3) then let it reject heat into the atmosphere at this 
temperature T\ (isothermal compression); (4) then let it expand adia- 
batically, doing work, as through a throttled expansion cock, or by 
pushing a piston, it will then cool to a temperature which may be far 
below that of the atmosphere and be used to absorb heat from the 
atmosphere. (See Refrigeration.) 

Principal Equations of a Perfect Gas. — Notation: P = pressure in 
lbs. per sq. ft. V = volume in cu. ft. P0F0, pressure and volume at 
32° F. T, absolute temperature = t° F. + 459.4. C p , specific heat at 
constant pressure. C v , specific heat at constant volume. K p = C p X 778; 
K v = C v X 778 ; specific heats taken in foot-pounds of energy. R, a 
constant, =? K p — K v . y = C p /C v . r = ratio of isothermal expansion 
or compression = P2/Pior V1/V2. 

For air: C p = 0.2375; C v = 0.1689; K p = 184.8; K v = 131.4; 
R = 53.35; y = 1.406. 

Boyle's Law, PV = constant when T is constant. P1V1 = P2V2. 
For 1 lb. air P V = 2116.2 X 12.387 = 26,224 ft.-lbs. 

Charles's Law, P1V1/T1 = P2V2/T2; P1F1 = P F X 7\/T : T = 32 
+ 459.4 = 491.4; P1V1 for air = 26,224 h- 491.4 = 53.35. 

General Equation, PV = RT. R is a constant which is different for 
different gases. 

Internal or Intrinsic Energy K v (Ti - 1\) = R (Ti- To) + (y — 1) 
= P\V\ -f- (v — 1) == amount of heat in a body, measured above abso- 
lute zero. For air at 32° F., K v (Ti - T ) = 131.4 X 491.4 = 64,570 
ft.-lbs. When air is expanded or compressed isothermally, PV = con- 
stant, and the internal energy remains constant, the work done in expan- 
sion = the heat added, and the work done in compression = the heat 
rejected. 



THERMODYNAMICS. 575 

Work done by Adiabatic Expansion, no transmission of heat, from Pi Vi to 
p 2 7 2 = p l y l \\ - (Vi/Vi) y \ -*- (y - 1), = (PiVi - P2V2) +'(y - 1) 

= P1V1 { 1 - (P*/Pi)~ } - (7 - 1). 

"FTorfc 0/ Adiabatic Compression from PiFi to P2F2 (P2 here being the 
higher pressure) = Pi V\ {( Vi/ V2) 7_1 - 1} -*- (7 - 1) = (Pj F 2 -P1F1) + 7 - 1 

=PiVi {(P2/P1) y -}}-*■ (v-i). 

Loss 0/ Intrinsic Energy in adiabatic expansion, or gain in compression 
==K v (Ti— a^), Ti being the higher temperature. 

TForfc of Isothermal Expansion, temperature constant, = heat expended 
= Pi Vi log e Vt/ Vi = Pi Vi log e r= RT log e r. 

Work of Isothermal Compression from Pi to P2 = PiFi log e Pi/P 2 
= PTlog e r= heat discharged. 

Relation between Pressure, Volume and Temperature: 

7-1 

t 2 = ri (£*) v = r 1 (-ft) 7-1 , Pi vv = p 2 v»y . 

For air, v = 1,406; 7 - 1 = 0.406; 1/7 = 0.711; 1/(7 - 1) = 2.463; 
7/(7-1) = 3.463; (7 - l)/7 = 0.289. 

Differential Equations of a Perfect Gas. Q = quantity of heat. 4> == 
entropy. 

, v jyur. d<f> = C v -yr + (C p -C v ) -y-o 

T dT dP 

upui -r (v v -C p ) p dV. d<f>=C p -Y + (C v - C p ) -p- • 

T T dP dV 

dQ=C vp -dP+C pp -dV. d^C v a -f+c p ?y> 

02 - 41 - c v iog e Q + (Cp - cy iog 6 £ • 
^ - 0i <r c p iog e |> + (c v - c p ) iog e £ 

2 -0i = CVog e g+c-plogg^. 

Work of Isothermal Expansion, W= P1V1 C 2 ~ = PiFi log. =&'• 

J Ti " F i 

Heat supplied during isothermal expansion, 

J*Vz dy y 

v ^-={C v -CJTi\og e g. 

Heat added = work done= ARTilog e Vi/Vi = AP1F1 log e V2/V1; (A — 
1/778). 

Work of adiabatic expansion, 

w- fW-v™ pff.^h-Y^V, 

JFi JFi FY V- 1 I W ) 



576 




Fig. 138. 



Construction of the Curve PV n = C. (Am. Mach., June 21, 1900.) — 
Referring to Fig. 138, on a system of rectangular coordinates YOX lay 

off OB = pi and BA = vi. 
Draw OJ, extended, at 
any convenient angle a, 
say 15°, with OX, and OC 
at an angle /3 with OY. /3 
is found from the equation 
1 + tan § =[l + tan a] n . 
Draw AJ parallel to YO. 
From B draw BC at 45° 
with BO, and draw CE 
parallel to OX. From J 
draw JH at 45° with AJ, 
and draw HE and HJi 
parallel to YO. The inter- 
section of CE and HE is 
the second point on the 
curve, or P2V2. From Ji 
draw JiHi at 45° to #«/i 
and draw the vertical 
JiHiR. Draw DK at 45° 
to DOi and i£.R parallel 
to OX. R is the third 
point on the curve, and 
so on. 

Conversely, if we have 
a curve for which we wish 
to derive an exponent, we can, by working backward, locate the lines 
OC and OJ, measure the angles a and 0, and solve for n. 

The smaller the angle a is taken the more closely the points of the curve 
may be located. If a = the curve is the isothermal curve, pv = con- 
stant. If a = 15° and = 21 c 30' the curve is the adiabatic for air, 
n = 1.41. (See Index of the Curve of an Air Diagram, p. 611). 

Temperature-Entropy Diagram of Water and Steam. — The line 
OA, Fig. 139, is the origin from which entropy is measured on horizontal 
lines, and the line Og is the line of zero 
temperature, absolute. The diagram 
represents the changes in the state 
of one pound of water due to the 
addition or subtraction of heat or to 
changes in temperature. Any point on 
the diagram is called a " state point." 
A is the state of 1 lb. of water at 
32° F. or 492° abs., B the state at 
212°, and C at 392° F., correspond- 
ing to about 226 lbs. absolute pres- 
sure. At 212° F. the area OABb is 
the heat added, and Ob is the increase 
of entropy. At 392° F., bBcC is the 
further addition of heat, and the 
entropy, measured from OA, is Oc. 
The two quantities added are nearly 
the same, but the second increase 
of entropy is the smaller, since the 
mean temperature at which it is 
added is higher. If Q = the quantity 
of heat added, and T\ and Ti are 
respectively the lower and the 
higher temperatures, the addition of 
entropy, <j>, is approximately Q -4- 1/ 2 (T 2 + Ti) = 180 -^ 1/2 (672 + 492) 
= 0.3093. More accurately it is i = log e (T2/T1) = 0.3119. In both of 
these expressions it is assumed that the specific heat of water = 1 at all 
temperatures, which is not strictly true. Accurate values of the entropy 
of water, taking into account the variation in specific heat, will be found 
in Peabody's Steam Tables.' 

J^et the 1 lb. of water at the state B have heat added to it at the con- 



P.° Abs. 
392-1852 



212- 



672 



32- 






T 



d 



■ Entropy - 



Fig. 139. 



PHYSICAL PROPERTIES OF GASES. 577 

stant temperature of 212° F. until it is evaporated. The quantity of 
heat added will be the latent heat of evaporation at 212° (see Steam 
Table) or L = 969.7 B.T.U., and it will be represented on the diagram by 
the rectangle bBFf. Dividing by T 2 = 672, the absolute temperature, 
gives fa - fa = 1.443 = BF. Adding fa = 0.312 gives fa = 1.755, the 
entropy of 1 lb. steam at 212° F. measured from water at 32° F. 

In like manner if we take L = 835 for steam at 852° abs., fa — fa = 
0.980 = CE, and fa = entropy of water at 852° = 0.558, the sum fa = 
1.538 = Oe on the diagram. 

E is the state point of dry saturated steam at 852° abs. and F the 
state point at 672°. The line EFG is the line of saturated steam and the 
line ABC the water line. The line CE represents the increase of entropy 
in the evaporation of water at 852° abs. If entropy CD only is added, 
or cCDd of heat, then a part of the water will remain unevaporated, 
viz.: the fraction DE/CE of 1 lb. The state point D thus represents wet 
steam having a dryness fraction of CD IDE. 

If steam having a state point E is expanded adiabatically to 672° 
abs. its state point is then ei, having the same entropy as at E, a total 
heat less by the amount represented by the area BCEe, and a dryness 
fraction Be/BF. If it is expanded while remaining saturated, heat 
must be added equal to eEFf, and the entropy increases by ef. 

If heat is added to the steam at E, the temperature and the entropy 
both increase, the line EH representing the superheating, and the area 
EH, down to the line Og, is the heat added. If from the state point H 
the steam is expended adiabatically, the state point follows the line FJ 
until it cuts the line EFG lt when the steam is dry saturated, and if it 
crosses this line the steam becomes wet. 

If the state point follows a horizontal line to the left, it represents 
condensation at a constant temperature, the amount of heat rejected 
being shown by the area under the horizontal line. If heat is rejected 
at a decreasing temperature, corresponding with the decreasing pressure 
at release in a steam engine, or condensation in a cylinder at a decreasing 
pressure, the state point follows a curved line to the left, as shown in 
the dotted curved line on the diagram. 

In practical calculations with the entropy-temperature diagram it is 
necessary to have at hand tables or charts of entropy, total heat, etc., 
such as are given in Peabody's Steam Tables, Ripper's Steam Engine, 
and other works. The diagram is of especial service in the study of 
steam turbines, and an excellent chart for this purpose will be found in 
Moyer's Steam Turbine. It gives for all pressures of steam from 0.5 
to 300 lbs. absolute, and for different degrees of dryness up to 300° of 
superheating, the total heat contents, in B.T.U. per pound, the entropy, 
and the velocity of steam through nozzles. 



PHYSICAL PROPERTIES OP GASES. 

(Additional matter on this subject will be found under Heat, Air, Gas 
and Steam.) 

When a mass of gas is inclosed in a vessel it exerts a pressure against the 
walls. This pressure is uniform on every square inch of the surface of the 
vessel; also, at any point in the fluid mass the pressure is the same in every 
direction. 

In small vessels containing gases the increase of pressure due to weight 
may be neglected, since all gases are very light; but where liquids are 
concerned, the increase in pressure due to their weight must always be 
taken into account. 

Expansion of Gases, Mariotte's Law. — The volume of a gas dimin- 
ishes in the same ratio as the pressure upon it is increased, if the tem- 
perature is unchanged. 

This law is by experiment found to be very nearly true for all gases, and 
is known as Boyle's or Mariotte's law. 

If p = pressure at a volume v, and p\ = pressure at a volumelvi, pivi = 

= a constant. 



578 PHYSICAL PROPERTIES OF GASES. 

The constant, C, varies with the temperature, everything else remaining 
the same. 

Air compressed by a pressure of seventy-five atmospheres has a volume 
about 2% less than that computed from Boyle's law, but this is the greatest 
divergence that is found below 160 atmospheres pressure. 

Law of Charles. — The volume of a perfect gas at a constant pressure 
is proportional to its absolute temperature. If v be the volume of a gas 
at 32° F., and vi the volume at any other temperature, ti, then 

(ti+ 459.2\. /, • tx - 32° 



,-(i 



491.2 )' -- V^ 491.2 r°' 
or vi = [1 + 0.002036 (h - 32°)] v . 
If the pressure also change from p to pi, 

Po /ti+ 459. 2\ 

The Densities of the elementary gases are simply proportional to their 
atomic weights. The density of a compound gas, referred to hydrogen 
as 1, is one-half its molecular weight; thus the relative density of CO2 is 
1/2 (12 4- 32) = 22. 

Avogadro's Law. — Equal volumes of all gases, under the same con- 
ditions of temperature and pressure, contain the same number of molecules. 

To find the weight of a gas in pounds per cubic foot at 32° F., multiply 
half the molecular weight of the gas by 0.00559. Thus 1 cu. ft. marsh- 
gas, CH 4 , 

= 1/2 (12 + 4) X 0.00559 = 0.0447 lb. 

When a certain volume of hydrogen combines with one-half its volume of 
oxygen, there is produced an amount of water vapor which will occupy the 
same volume as that which was occupied by the hydrogen gas when at the 
same temperature and pressure. 

Saturation Point of Vapors. — A vapor that is not near the satura- 
tion point behaves like a gas under changes of temperature and pressure; 
but if it is sufficiently compressed or cooled, it reaches a point where it 
begins to condense: it then no longer obeys the same laws as a gas, but 
its pressure cannot be increased by diminishing the size of the vessel con- 
taining it, but remains constant, except when the temperature is changed. 
The only gas that can prevent a liquid evaporating seems to be its own 
vapor. 

Dalton's Law of Gaseous Pressures. — Every, portion of a mass of 
gas inclosed in a vessel contributes to the pressure against the sides of the 
vessel the same amount that it would have exerted by itself had no other 
gas been present. 

Mixtures of Vapors and Gases. — The pressure exerted against the 
interior s of a vessel by a given quantity of a perfect gas inclosed in it is the 
sum of the pressures which any number of parts into which such quan- 
tity might be divided would exert separately, if each were inclosed in a 
vessel of the same bulk alone, at the same temperature. Although this 
law is not exactly true for any actual gas, it is very nearly true for many. 
Thus if 0.080728 lb. of air at 32° F., being inclosed in a vessel of one cubic 
foot capacity, exerts a pressure of one atmosphere, or 14.7 pounds, on each 
square inch of the interior of the vessel, then will each additional 0.080728 
lb. of air which is inclosed, at 32°, in the same vessel, produce very nearly 
an additional atmosphere of pressure. The same law is applicable to 
mixtures of gases of different kinds. For example, 0.12344 lb. of carbonic- 
acid gas, at 32°, being inclosed in a vessel of one cubic foot in capacitv, 
exerts a pressure of one atmosphere; consequently, if 0.080728 lb. of air 
and 0.12344 lb. of carbonic acid, mixed, be inclosed at the temperature 
of 32°, in a vessel of one cubic foot of capacity, the mixture will exert a 
pressure of two atmospheres. As a second example: Let 0.080728 lb. 



PHYSICAL PROPERTIES OF GASES. 579 

of air, at 212°, be inclosed in a vessel of one cubic foot; it will exert a 
pressure of 

21 9 -t- 4-^Q 9 
32 + 459 2 = 1 ' 366 atmos P heres - 

Let 0.03797 lb. of steam, at 212°, be inclosed in a vessel of one cubic 
foot ; it will exert a pressure of one atmosphere. Consequently, if 0.080728 
lb. of air and 0.03797 lb. of steam be mixed and inclosed together, at 212°, 
in a vessel of one cubic foot, the mixture will exert a pressure of 2.366 
atmospheres. It is a common but erroneous practice, in elementary 
books on physics, to describe this law as constituting a difference between 
mixed and homogeneous gases; whereas it is obvious that for mixed and 
homogeneous gases the law of pressure is exactly the same, viz.. that the 
pressure of the whole of a gaseous mass is the sum of the pressures of all 
its parts. This is one of the laws of mixture of gases and vapors. 

A second law is that the presence of a foreign gaseous substance in con- 
tact with the surface of a solid or liquid does not affect the density of the 
vapor of that solid or liquid unless there is a tendency to chemical com- 
bination between the two substances, in which case the density of the 
vapor is slightly increased. (Rankine, S. E., p. 239.) 

If 0.591 lb. of air, = 1 cu. ft. at 212° and atmospheric pressure, is con- 
tained in a vessel of 1 cu. ft. capacity, and water at 212° is introduced, 
heat at 212° being furnished by a steam jacket, the pressure will rise to 
two atmospheres. 

If air is present in a condenser along with water vapor, the pressure is 
that due to the temperature of the vapor plus that due to the quantity of 
air present. 

Flow of Gases. — By the principle of the conservation of energy, it 
may be shown that the velocity with which a gas under pressure will 
escape into a vacuum is inversely proportional to the square root of its 
density; that is, oxygen, which is sixteen times as heavy as hydrogen, 
would, under exactly the same circumstances, escape through an opening 
only one fourth as fast as the latter gas. 

Absorption of Gases by Liquids. — Many gases are readily absorbed 
by water. Other liquids also possess this power in a greater or less 
degree. Water will, for example, absorb its own volume of carbonic-acid 
gas, 430 times its volume of ammonia, 2 V3 times its volume of chlorine, 
and only about V20 of its volume of oxygen. 

The weight of gas that is absorbed by a given volume of liquid is pro- 
portional to the pressure. But as the volume of a mass of gas is less as 
the pressure is greater, the volume which a given amount of liquid can 
absorb at a certain temperature will be constant, whatever the pressure. 
Water, for example, can absorb its own volume of carbonic-acid gas at 
atmospheric pressure; it will also dissolve its own volume if the pressure 
is twice as great, but in that case the gas will be twice as dense, and con- 
sequently twice the weight of gas is dissolved. 

Liquefaction of Gases.— Liquid Air. (A. L. Rice, Trans. A.S.M. E., 
xxi, 156.)— Oxygen was first liquefied in 1877 by Cailletet and Pictet, 
working independently. In 1884 Dewar liquefied air, and in 1898 he 
liquefied hydrogen at a temperature of - 396.4° F., or only 65° above the 
absolute zero. The method of obtaining the low temperatures required 
for liquefying gases was suggested by Sir W. Siemens, in 1857. It consists 
in expanding a compressed" gas in "a cvlinder doing work, or through a 
small orifice, to a lower pressure, and using the cold gas thereby produced 
to cool, before expansion, the gas coming to the apparatus. Hampson 
claims to have condensed about 1.2 quarts of liquid air per hour at an 
expenditure of 3.5 H.P. for compression, using a pressure of 120 atmos- 
pheres expanded to 1, and getting 6.6 per cent of the air handled as 
liquid. 

The following table gives some physical constants of the principal gases 
that have been liquefied. The critical temperature is that at which the 
properties of a liquid and its vapor are indistinguishable, and above which 
the vapor cannot be liquefied by compression. The critical pressure is 
the pressure of the vapor at the critical temperature. 



580 











Temp, 
of 












Criti- 


Satu- 










Criti- 


cal 


rated 


Freez- 


Density of 






cal 


Pres- 


Vapor 


ing 


Liquid at 






Temp. 


sure in 


at 


Point. 


Temperature 






Deg. F. 


Atmo- 
spheres 


Atmos. 
Pres- 
sure 

Deg. F. 


Deg. F. 


Given. 




H 2 


689 


200 


212 


32 


1 at 39° F. 


Ammonia 


NH 4 


266 


115 


— 27 


—107 


0. 6364 at 32° F. 




C 2 Ho 


98.6 




—121 


—113.8 




Carbon Dioxide. . . . 


C0 2 


88 


75 


—112 


— 69 


0.83 at 32° F. 




C 2 H 4 
CH 4 


50 
—115.2 


51.7 
54.9 


—150 
-263.4 


—272 
—302.4 






1 0.415 1 




1 at— 263° F. | 




o 2 


—182 


50.8 


—294.5 




J 1.124 I 




\ at — 294° F. 1 




A 


—185.8 


50.6 


—304.6 


—309.3 


f about 1 .5 ) 




I at —305° F. J 




CO 


-219.1 
—220 


35.5 
39 


—310 
—312.6 


—340.6 




Air 


f 0.933 ) 
\ at —313° F.f 




N 2 


—231 


35 


—318 


—353.2 


i 0.885 ) 
tat— 318° F. } 






H 2 


—389 


20 


—405 













; 



AIR. 

Properties of Air. — Air is a mechanical mixture of the gases oxygen 
and nitrogen, with about 1% by volume of argon. Atmospheric air of 
ordinary purity contains about 0.04% of carbon dioxide. The com- 
position of air is variously given as follows: 





By Volume. 


By Weight 






N 


O 


Ar 


N 


O 


Ar 


1 


79.3 
79.09 
78.122 
78.06 


23.7 
20.91 
20.941 
21. 




77 

76.85 
75.539 
75.5 


23 

23.15 
23.024 
23.2 




2 






3 


0.937 
0.94 


1.437 


4 


1.3 







(1) Values formerly given in works on physics. (2) Average results 
of several determinations, Hempel's Gas Analysis. (3) Sir Wm. Ramsay, 
Bull. U. S. Geol. Survey, No. 330. (4) A. Leduc, Comptes Rendus, 1896, 
Jour. F. /., Jan., 1898. Leduc gives for the density of oxygen relatively 
to air 1.10523; for nitrogen 0.9671: for argon, 1.376. 

The weight of pure air at 32° F. and a barometric pressure of 29.92 
inches of mercury, or 14.6963 lbs. per sq. in., or 2116.3 lbs. per sq. ft., is 
080728 lb. per cubic foot. Volume of 1 lb. = 12.387 cu. ft. At any 
other temperature and barometric pressure its weight in lbs. per cubic 



AIR. 



581 



foot is W ■■ 



1.3253 X B 



where B = height of the barometer, T= tem- 



459.2+ T ' 

perature Fahr., and 1.3253 = weight in lbs. of 459.2 eu. ft. of air at 0° F. 
and one inch barometric pressure. Air expands 1/491.2 of its volume at 
32° F. for every increase of 1° F., and its volume varies inversely as the 
pressure. 

The Air-manometer consists of a long, vertical glass tube, closed at 
the upper end, open at the lower end, containing air, provided with a 
scale, and immersed, along with a thermometer, in a transparent liquid, 
such as water or oil, contained in a strong cylinder of glass, which com- 
municates with the vessel in which the pressure is to be ascertained. The 
scale shows the volume occupied by the air in the tube. 

Let i>o be that volume, at the temperature of 32° Fahrenheit, and mean 
pressure of the atmosphere, p ; let vi be the volume of the air at the tem- 
perature t, and under the absolute pressure to be measured pi; then 

(JL± 459.2°) povo 



Pressure of the Atmosphere at Different Altitudes. 

At the sea level the pressure of the air is 14.7 pounds per square inch; at 
1/4 of a mile above the sea level it is 14.02 pounds; at 1/2 mile, 13.33; at 
3/4 mile, 12.66; at 1 mile, 12.02; at IV4 mile, 11.42; at 1 1/2 mile, 10.88; and 
at 2 miles, 9.80 pounds per square inch. For a rough approximation we 
may assume that the pressure decreases 1/2 pound per square inch for 
every 1000 feet of ascent. 

It is calculated that at a height of about 31/2 miles above the sea level 
the weight of a cubic foot of air is only one-half what it is at the surface of 
the earth, at seven miles only one-fourth, at fourteen miles only one- 
sixteenth, at twenty-one miles only one sixty-fourth, and at a height of 
over forty-five miles it becomes so attenuated as to have no appreciable 
weight. 

The pressure of the atmosphere increases with the depth of shafts, equal 
to about one inch rise in the barometer for each 900 feet increase in depth: 
this may be taken as a rough-and-ready rule for ascertaining the depth of 
shafts. 

Pressure of the Atmosphere per Square Inch and per Square Foot 
at Various Readings of the Barometer. 

Rule. — Barometer in inches X 0.4908 = pressure per square inch; 
pressure per square inch X 144 = pressure per square foot. 



Barometer. 


Pressure 
per Sq. In. 


Pressure 
per Sq. Ft. 


Barometer. 


Pressure 
per Sq. In. 


Pressure 
per Sq. Ft. 


in. 


lbs. 


lbs* 


in. 


lbs. 


lbs.* 


28.00 


13.74 


1978 


29.75 


14.60 


2102 


28.25 


13.86 


1995 


30.00 - 


14.72 


2119 


28.50 


13.98 


2013 


30.25 - 


14.84 


2136 


28.75 


14.11 


2031 


30.50 


14.96 


2154 


29.00 


14.23 


2049 


30.75 


15.09 


2172 


29.25 


14.35 


2066 


31.00 


15.21 


2190 


29.50 


14.47 


2083 









* Decimals omitted. 
For lower pressures see table of the Properties of Steam. 



582 



AIR. 



Barometric Readings corresponding with Different 
Altitudes, in French and English Measures. 



Alti- 
tude. 


Read- 




Reading 




Reading 




Reading 


ing of 


Altitude. 


of 


Alti- 


of 


Altitude. 


of 


Barom- 




Barom- 


tude. 


Barom- 




Barom- 




eter. 




eter. 




eter. 




eter. 


meters 


mm. 


feet. 


inches. 


meters. 


mm. 


feet. 


inches. 





762 


0. 


30. 


1147 


660 


3763.2 


25.98 


21 


760 


68.9 


29.92 


1269 


650 


4163.3 


25.59 


127 


750 


416.7 


29.52 


1393 


640 


4568.3 


25.19 


234 


740 


767.7 


29.13 


1519 


630 


4983.1 


24.80 


342 


730 


1122. I 


28.74 


1647 


620 


5403.2 


24.41 


453 


720 


1486.2 


28.35 


1777 


610 


5830.2 


24.01 


564 


710 


1850.4 


27.95 


1909 


600 


6243. 


23.62 


678 


700 


2224.5 


27.55 


2043 


590 


6702.9 


23.22 


793 


690 


2599.7 


27.16 


2180 


580 • 


7152.4 


22.83 


909 


680 


2962.1 


26.77 


2318 


570 


7605.1 


22.44 


1027 


670 


3369.5 


26.38 


2460 


560 


8071. 


22.04 



Boiling Point of Water. — JTemperature in degrees F., barometer in 
in. of mercury. 



In. 


.0 


.1 


.2 


.3 


.4 


.5 


.6 


.7 


.8 


.9 


28 
29 
30 


208.7 
210.5 
212.1 


208.9 
210.6 
212.3 


209.1 
210.8 
212.4 


209.2 
210.9 
212.6 


209.4 
211.1 
212.8 


209.5 
211.3 
212,9 


209.7 
211.4 
213.1 


209.9 
211.6 
213.3 


210.1 
211.8 
213.5 


210.3 
212.0 
213.6 



Leveling by the Barometer and by Boiling Water. (Trautwine.) 
— Many circumstances combine to render the results of this kind of 
leveling unreliable where great accuracy is required. It is difficult to 
read off from an aneroid (the kind of barometer usually employed for 
engineering purposes) to within from two to five or six feet, depending on 
its size. The moisture or dryness of the air affects the results; also winds, 
the vicinity of mountains, and the daily atmospheric tides, which cause 
incessant and irregular fluctuations in the barometer. A barometer 
hanging quietly in a room will often vary 1/4 of an inch within a few 
hours, corresponding to a difference of elevation of nearly 100 feet. No 
formula can possibly be devised that shall embrace these sources of 
error. 

To Find the Difference in Altitude of Two Places. — Take from the 
table the altitudes opposite to the two boiling temperatures, or to the two 
barometer readings. Subtract the one opposite the lower reading from 
that opposite the upper reading. The remainder will be the required 
height, as a rough approximation. To correct this, add together the 
two thermometer readings, and divide the sum by 2, for their mean. 
From table of corrections for temperature, take out the number under 
this mean. Multiply the approximate height just found by this 
number. 

At 70° F. pure water will boil at 1° less of temperature for an average of 
about 550 feet of elevation above sea level, up to a height of 1/2 a mile. 
At the height of 1 mile, 1° of boiling temperature will correspond to about 
560 feet of elevation. In the table the mean of the temperatures at the 
two stations is assumed to be 32° F., at which no correction for temperature 
is necessary in using the table. 



AIR. 



583 





„ 


O -K 










. 




fl <U j< 

p§ ft s* 


PQ 


Altitud 
above 

Sea leve 
Feet. 


PQ a .H fa 


85 

PQ 


Altitud 

above 

Sea leve 

Feet. 


Boiling 
point 

in Deg 
Fahr. 


a . 

PQ 


^ 02 


184° 


16.79 


15,221 


196 


21.71 


8,4^1 


208 


27.73 


2,063 


185 


17.16 


14,649 


197 


22.17 


7,932 


208.5 


28.00 


1,809 


186 


17.54 


14,075 


198 


22.64 


7,381 


209 


28.29 


1,539 


187 


17.93 


13,498 


199 


23.11 


6,843 


209.5 


28.56 


1,290 


188 


18.32 


12,934 


200 


23.59 


6,304 


210 


28.85 


1,025 


189 


18.72 


12,367 


201 


24.08 


5,764 


210.5 


29.15 


754 


190 


19.13 


11,799 


202 


24.58 


5,225 


211 


29.42 


512 


191 


19.54 


11,243 


203 


25.08 


4,697 


211.5 


29.71 


255 


192 


19.96 


10,685 


204 


25.59 


4,169 


212 


30.00 


S.L,= 


193 


20.39 


10,127 


205 


26.11 


3,642 


212.5 


30.30 


—261 


194 


20.82 


9,579 


206 


26/4 


3,115 


213 


30.59 


—511 


195 


21.26 


9,031 


207 


27.18 


2,589 













Corrections for Temperature. 



Mean temp. F. in shade. 0, 10° I 20° 30° 40° I 50° 60° I 70° I 80° I 90° I 100° 
Multiply by ^33 .9541.975 .996 1.0161 1.036 1 .058J 1 .079[l . 1 00 [ 1 . 1 21 1 1 .1 42 



Moisture in the Atmosphere. — Atmospheric air always contains a 
smalt quantity of carbonic acid (see Ventilation), and a varying quantity 
of aqueous vapor or moisture. The relative humidity of the air at any time 
is the percentage of moisture contained in it as compared with the amount 
it is capable of holding at the same temperature, 

The degree of saturation or relative humidity of the air is determined 
by the use of the dry and wet bulb thermometer, The degree of satura- 
tion for a number of different readings of the thermometer is given in the 
following table, condensed from the Hygrometric Tables of the U. S. 
Weather Bureau: 















Relative 


Humidity, 


Per 


Cent. 


















ic 


Difference between the Dry and Wet Thermometers, Deg. F. 


» Or' 

£ « • 


1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


15 


16 


17 


18 


19 


20 


21 


22 


23 


24 


26 


23 


30 


Relative Humidity, Saturation being 100. (Barometer = 30 ins.) 


32 


89 


79 


69 


59 


49 


39 


30 


20 


11 


2 


1 
































40 


92 


83 


75 


68 


60 


52 


45 


37 


29 


23 


15 7 

































50 


93 


87 


80 


74 


67 


61 


55 


49 


43 


38 


3227 


21 


16 


11 


5 

























60 


94 


89 


83 


78 


73 


68 


63 


58 


53 


48 


43 39 


34 


30 


26 


21 


17 


13 


9 


5 


1 














70 


95 


90 


8ft 


81 


77 


72 


68 


64 


59 


55 


51 


48 


44 


40 


36 


33 


29 


25 


22 


19 


15 


12 


9 


6 








80 


96 


91 


87 


83 


79 


75 


72 


68 


64 


61 


57 


54 


50 


47 


44 


41 


38 


35 


32 


29 


26 


23 


20 


18 


12 


7 




90 


96 


92 


89 


85 


81 


78 


74 


71 


68 


65 


61 


58 


55 


52 


49 


47 


44 


41 


39 


36 


34 


31 


29 


26 


22 


17 


13 


100 


96 


93 


8? 


86 


83 


80 


77 


73 


70 


68 


65 


62 


59 


56 


54 


51 


49 


46 


44 


41 


39 


37 


35 


33 


28 


24 


21 


110 


97 


93 


90 


87 


84 


81 


78 


75 


73 


70 


67 


65 


62 


60 


57 


55 


52 


50 


48 


46 


44 


42 


40 


38 


34 


30 


26 


120 


97 


94 


91 


88 


85 


87 


80 


77 


74 


7? 


69 


67 


65 


62 


60 


58 


55 


53 


51 


49 


47 


45 


43 


41 


38 


34 


31 


140 


97 


95 


52 


89 


87 


84 


2 


79 


77 


75 


73 


70 


68 


66 


64 


62 


:0 


58 


56 


54 


53 


51 


49 


47 


44 


41 


38 



Moistnre in Air at FHfferent Pressures and Temperatures. (H. M. 

Prevost Murphy, Enn. News, June 18, 1908.) — 1. The maximum amount 
of moisture that pure air can contain depends only on its temperature 
and oressure, and has an unvarying value for each condition. 



584 air. 

2. The higher the temperature of the air, the greater is the amount 
of moisture that it can contain. 

3. The higher the pressure of the air, the smaller is the amount of 
moisture that it can contain. 

4. When air is compressed, the rise of temperature due to the com- 
pression, in all cases found in practice, far more than offsets the opposite 
effect of the rise of pressure on the moisture-carrying capacity of the air. 
Water is deposited, therefore, by compressed air as it passes from the com- 
pressor to the various portions of the system. 

Suppose that a certain amount of atmospheric air enters a compressor 
and that it contains all the moisture possible at the existing outside tem- 
perature and pressure. As this air is compressed its moisture-carrying 
capacity rapidly increases, consequently all the moisture is retained by 
the air and passes with it into the main or storage reservoir. Now if 
this air is permitted to pass from the reservoir into the various parts of 
the system before being cooled to the outside temperature, it will carry 
more moisture than it is capable of holding when the temperature 
finally drops to the normal point, and this excess quantity will be de- 
posited, because, the pressure being high, the air cannot hold as much 
moisture as it did at the same temperature and only atmospheric pressure. 
In order to reduce the moisture to a minimum, it is desirable to cool 
the air to the outside temperature before it leaves the reservoir, thereby 
causing it to deposit all of its excess moisture, which may be easily removed 
by drain cocks. 

Although compressed air may be properly dried before leaving the 
main reservoirs, some moisture may be temporarily deposited when the 
air is subsequently expanded to lower pressures, as its moisture-carry- 
ing capacity is usually affected more by the drop in temperature, result- 
ing from the expansion, than by the drop in pressure, but when the air 
again attains the outside temperature, the moisture thus deposited will 
be re-absorbed if it is freely exposed to the compressed air. 

In order to determine what percentage of moisture pure air can contain 
at various pressures and temperatures, to ascertain how low the "rela- 
tive humidity" of the atmosphere must be in order that no water will be 
deposited in any part of a compressed-air system and also to find to what 
temperature air drawn from a saturated atmosphere must be cooled in 
order to cause the deposition of moisture to commence, the following 
formulae and tables are used, based on Dalton's law of gaseous pressures, 
which may be stated as follows: 

The total pressure exerted against the interior of a vessel by a given 

quantity of a mixed gas enclosed in it is the sum of the pressures which 

each of the component gases, or vapors, would exert separately if it were 

enclosed alone in a vessel of the same bulk, at the same temperature. 

[The derivation of the formulae is given at length in the original paper.] 

Formulae for the Weight, in Lbs., of 1 Cu. Ft. of Dry Air, of 1 Cu. 

Ft. of Saturated Steam or Water Vapor and the Maximum Weight 

of Water Vapor that 1 Lb. of Pure Air Can Carry at Any Pressure 

and Temperature. (Copyright, 1908, by H. M. Prevost Murphy.) 

The values K and H being given in the table for various temperatures, 

t, in Fahrenheit degrees, the formulae are: 

Weight of 1 cu. ft. saturated steam = "' " — • 

H = elastic force or tension of water vapor or saturated steam, in in. of 
mercury corresponding to the temperature t (Fahr.) = 2.036 X (gauge pres- 
sure + atmospheric pressure, in pounds per square inch). 

K = the ratio of the weight of a volume of saturated steam to an equal 
volume of pure dry air at the same temperature and pressure, 

n ah so. 0092 * 
= - 6113+ 850=T 
Values of K and H corresponding to the various temperatures t are 
given in the table below. 
w ., + ,, .. . . 1.325271 M 2.698192 P 

Weight of 1 cu. ft. pure dry air- 4592+ ^ = 4 59.2-M ' 

M = absolute pressure in inch of mercury. 

P = absolute pressure in pounds per square inch. 



AIR. 



585 



W= maximum weight, in lbs., of water vapor, that 1 lb. of pure air 
can contain, when the temperature of the mixture is t, and the total, or 
observed, absolute pressure in pounds per square inch is P, 



2.036 P-H 



Note. — The results obtained by the use of any of the above formulae 
agree exactly with the average data for air and steam weights as given 
by the most reliable authorities and careful experiments, for all pressures 
and temperatures; the value of K being correct for all temperatures up 
to the critical steam temperature of 689° F. 

Values of "K" and " H" Corresponding to Temperatures t from 
- 30° to 434° F. 



t 


K 


H 


t 


K 


H 


t 


K 


H 


t 


K 


H 


t 


K 


H 


-30 


.6082 


.0099 


64 


.6188 


.5962 


158 


.6323 


9.177 


252 


.6501 


62.97 


344 


.6739 


254.2 


-28 


.6084 


.0111 


66 


.6190 


.6393 


160 


.6326 


9.628 


254 


.6505 


65.21 


346 


.6745 


261.0 


-26 


.6086 


.0123 


68 


.6193 


.6848 


162 


.6330 


10.10 


256 


.6510 


67.49 


348 


.6751 


268.0 


-24 


.6088 


.0137 


70 


.6196 


.7332 


164 


.6333 


10.59 


258 


.6514 


69.85 


350 


.6757 


275.0 


-22 


.6090 


.0152 


72 


.6198 


.7846 


166 


.6336 


11.10 


260 


.6518 


72.26 


352 


.6763 


282.2 


-20 


.6092 


.0168 


74 


.6201 


8391 


168 


.6340 


11.63 


262 


.6523 


74.75 


354 


.6770 


289.6 


-18 


.6094 


.0186 


76 


.6203 


8969 


170 


.6343 


12.18 


264 


.6528 


77.30 


356 


.6776 


297.1 


-16 


.6096 


.0206 


78 


.6206 


9585 


172 


.6346 


12.75 


266 


.6532 


79.93 


358 


.6783 


304.8 


-14 


.6098 


.0227 


80 


.6209 


1.024 


174 


.6350 


13.34 


268 


.6537 


82.62 


360 


.6789 


312.6 


-12 


.6100 


.0250 


82 


.6211 


1.092 


176 


.6353 


13.96 


270 


.6541 


85.39 


362 


.6795 


320.6 


-10 


.6102 


.0275 


84 


.6214 


1.165 


178 


.6357 


14.60 


272 


.6546 


88.26 


364 


.6803 


328.7 


- 8 


.6104 


.0303 


86 


.6217 


1.242 


180 


.6360 


15.27 


274 


.6551 


91.18 


366 


.6809 


337.0 


- 6 


.6107 


.0332 


88 


.6219 


1.324 


182 


.6364 


15.97 


276 


.6555 


94.18 


368 


.6816 


345.4 


- 4 


.6109 


.0365 


90 


.6222 


1.410 


184 


.6367 


16.68 


278 


.6560 


97.26 


370 


6822 


354.0 


- 2 


6111 


.0400 


92 


.6225 


1.501 


186 


.637! 


17.43 


280 


.6565 


100.4 


372 


6829 


362.8 





.6113 


.0439 


94 


.6227 


1.597 


188 


.6374 


18.20 


282 


.6570 


103.7 


374 


.6836 


371.8 


2 


.6115 


.0481 


96 


.6230 


1.698 


190 


.6377 


19.00 


284 


.6575 


107.0 


376 


.6843 


380.9 


4 


.6117 


0526 


98 


.6233 


1.805 


192 


.6381 


19.83 


286 


.6580 


110.4 


378 


.6850 


390.2 


6 


.6120 


0576 


100 


.6236 


1.918 


194 


.6385 


20.69 


288 


.6584 


113.9 


380 


6857 


399.6 


8 


.6122 


0630 


102 


.6238 


2.036 


196 


.6389 


21.58 


290 


.6590 


117.5 


382 


6865 


409.3 


10 


.6124 


0690 


104 


.6241 


2.161 


198 


.6393 


22.50 


292 


.6594 


121.2 


384 


6871 


419.1 


12 


.6126 


.0754 


106 


.6244 


2.294 


200 


.6396 


23.46 


294 


.66C0 


125.0 


386 


.6879 


429.1 


14 


.6128 


.0824 


108 


.6247 


2.432 


202 


.6400 


24.44 


296 


.6604 


128.8 


388 


6886 


439.3 


16 


.6131 


.0^00 


110 


6250 


2.578 


204 


.6404 


25.47 


298 


.6610 


132.8 


390 


6893 


449.6 


18 


.6133 


.0983 


112 


6253 


2.731 


206 


.6407 


26.53 


300 


.6615 


136.8 


392 


6901 


460.2 


20 


.6135 


.1074 


114 


.6256 


2.892 


208 


.6411 


27.62 


302 


.6620 


141.0 


394 


6908 


470.9 


22 


.6137 


.1172 


116 


.6258 


3.061 


210 


.6415 


28.75 


304 


.6625 


145.3 


396 


6915 


481.9 


24 


.6140 


.1279 


118 


.6261 


3.239 


212 


.6419 


29.92 


306 


.6631 


149.6 


398 


6923 


493.0 


26 


.6142 


1396 


120 


.6264 


3.425 


214 


.6423 


31.H 


308 


.6636 


154.1 


400 


6931 


504.4 


28 


.6144 


.1523 


122 


.6267 


3.621 


216 


.6426 


32.38 


310 


.6641 


1587 


402 


.6939 


515.9 


30 


.6147 


.1661 


124 


.6270 


3.826 


218 


.6430 


33.67 


3:2 


.6647 


163.3 


404 


.6947 


527.6 


32 .6149 


.1811 


126 


.6275 


4.042 


220 


.6434 


35.01 


314 


.6652 


168.1 


406 


.6955 


539.5 


34 


.6151 


.1960 


128 


.6276 


4.267 


222 


.6438 


36.38 


316 


.6658 


173.0 


408 


.6962 


551.6 


36 


.6154 


.2120 


130 


.6279 


4.503 


224 


.6442 


37.80 


318 


.6663 


178.0 


410 


.6970 


564.0 


38 


.6156 


2292 


132 


.6282 


4.750 


226 


.6446 


39.27 


320 


.6669 


183.1 


412 


.6979 


576.5 


40 


.6158 


>76 


134 


.6285 


5.008 


228 


.6451 


40.78 


322 


.6674 


188.3 


414 


.6987 


589.3 


42 


.6161 


.2673 


136 


6288 


5.280 


230 


.6455 


42.34 


324 


.6680 


193.7 


416 


6995 


602.2 


44 


.6163 


.2883 


138 


.6291 


5.563 


232 


.6458 


43.95 


326 


.6686 


199.2 


418 


.7003 


615.4 


46 


.6166 


.3109 


140 


.6294 


5.859 


234 


.6463 


45.61 


328 


.6691 


204.8 


420 


.7012 


628.8 


48 


.6168 


.3350 


142 


.6298 


6.167 


236 


.6467 


47.32 


330 


.6697 


210.5 


422 


.7021 


642.5 


50 


.6170 


3608 


144 


.6301 


6.490 


238 


.6471 


49.08 


332 


.6703 


216.4 


424 


.7029 


656.3 


52 


.6173 


.3883 


146 


.6304 


6. £27 


240 


.6475 


50.89 


334 


.6709 


222.4 


426 


.7037 


670.4 


54 


.6175 


.4176 


148 


.6307 


7.178 


242 


.6479 


52.77 


336 


.6715 


228.5 


428 


.7046 


684.7 


56 


.6178 


.4490 


150 


.6310 


7.545 


244 


.6484 


54.69 


338 


.6721 


234.7 


430 


.7055 


699.2 


58 


.6180 


.4824 


152 


.6313 


7.929 


246 


.6488 


56.67 


340 


.6727 


241.1 


432 


.7064 


713.9 


60 


.6183 


.5180 


154 


.6317 


8.328 


248 


.6492 


58.71 


342 


.6733 


247.6 


434 


.7073 


728.9 


62 


.6185 


.5559 


156 


.6320 


8.7441 250 


.6496 


60.81 















586 



Applications of the Formulae and Tables. 

Example 1. — How low must the relative humidity be, when the 
atmospheric pressure is 14.7 lb. per sq. in. and the outside temperature 
is 60°, in order that no moisture may be deposited in any part of a com- 
pressed air system carrying a constant gauge pressure of 90 lb. per sq. in.? 

Ans. — The maximum amount of moisture that 1 lb. of pure air can 
contain at 90 lb. gauge, = 104.7 lb. (absolute pressure) and 60° F., is 



W = 



KH 



0.6183X0.5180 



2.036 P-H 2.036X104.7-0.5180 



= 0.0015061b. 



The maximum weight of moisture that 1 lb. of air can contain at 60° 
F. and 14.7 lb. (absolute pressure) is 



W (at 14.7) = 



0.6183X0.5180 
2.036X14.7-0.5180 



= 0.01089 1b. 



In order that no moisture may be deposited, the relative humidity 
must not be above 

(0.001506 -*- 0.01089) X 100 = 13.83%. 

Weights in Pounds, of Pure Dry Air, Water Vapor and Saturated 

Mixtures of Air and Water Vapor at Various Temperatures, at 

Atmospheric Pressure, 29.921 In. of Mercury or 14.6963 

Lb. Per Sq. In. Also the Elastic Force or Pressure 

of the Air and Vapor Present in Saturated 

Mixtures. 

(Copyright, 1908, by H. M. Prevost Murphy.) 







Saturated Mixtures of Air and Water Vapor. 


tt fl 03 
S 03 03 

ft^H 5 
KS 


03 ^ 

O o >> 
M.2 03 


U O § 

o ft" 
fa 03 03 


Elastic Force 
of the Air 

alone, when 
Saturated, Ins. 

of Mercury. 


Weight of the 
Vapor in 1 Cu. 
Ft. of the Mix- 
ture, or Wt. of 1 
Cu. Ft. of Satu- 
rated Steam. 


2c& u 

•& - 03 

.£p.5"J3 

"5 u +> 


log 


55 a 





0.086354 


0.0439 


29.877 


0.000077 


0.086226 


0.086303 


0.000898 


12 


0.084154 


0.0754 


29.846 


0.000130 


0.083943 


0.084073 


0.001548 


22 


0.082405 


0.1172 


29.804 


0.000198 


0.082083 


0.082281 


0.002413 


32 


0.080728 


0.1811 


29.740 


0.000300 


0.080239 


0.080539 


0.003744 


42 


0.079117 


0.2673 


29.654 


0.000435 


0.078411 


0.078846 


0.005554 


52 


0.0775169 


0.3883 


29.533 


0.000621 


0.076563 


0.077184 


0.008116 


62 


0.076081 


0.5559 


29.365 


0.000874 


0.074667 


0.075541 


0.011709 


72 


0.074649 


0.7846 


29.136 


0.001213 


0.072690 


0.073903 


0.016691 


82 


0. 073270 


1.092 


28.829 


0.001661 


0.070595 


0.072256 


0.023526 


92 


0.071940 


1.501 


28.420 


0.002247 


0.068331 


0.070578 


0.032877 


102 


0.070658 


2.036 


27.885 


0.002999 


0.065850 


0.068849 


0.045546 


112 


0.069421 


2.731 


27.190 


0.003962 


0.063085 


0.067047 


0.062806 


122 


0.068227 


3.621 


26.300 


0.005175 


0.059970 


0.065145 


0.086285 


132 


0.067073 


4.750 


25.171 


0.006689 


0.056425 


0.063114 


0. 1 18548 


142 


0.065957 


6.167 


23.754 


0.008562 


0.052363 


0.060925 


0.163508 


152 


0.064878 


7.929 


21.992 


0.010854 


0.047686 


0.058540 


0.227609 


162 


. 063834 


10.097 


19.824 


0.013636 


0.042293 


0.055929 


0.322407 


172 


0.062822 


12.749 


17.172 


0.016987 


0.036055 


0.053042 


0.471146 


182 


0.061843 


15.965 


13.956 


0.021000 


0.028845 


0.049845 


0.728012 


192 


0.060893 


19.826 


10.095 


0.025746 


0.020545 


0.046291 


1.25319 


202 


0.059972 


24.442 


5.479 


0.031354 


0.010982 


0.042336 


2.85507 


212 


0.059079 


29.921 


0.000 


0.037922 


0.000000 


0.037922 


Infinite. 



air. 587 

Note. — Air is said to be saturated with water vapor when it contains 
the maximum amount possible at the existing temperature and pressure. 

Example 2. — When compressing air into a reservoir carrying a con- 
stant gauge pressure of 75 lb., from a saturated atmosphere of 14.7 lb. 
abs. press, and 70° F., to what temperature must the air be cooled after 
compression in order to cause the deposition of moisture to commence? 

Ans. — First find the maximum weight of moisture contained in 
1 lb. of pure air at 14.7 lb. pressure and 70° F. 

w KH 0.6 196 X 0.7332 . M ___ ., 

W = 2.036 P- H ~ 2WX 14.7 - 0.7332 = °- 01556 lb ' 

The temperature to which the air must be cooled in order to cause 
the deposition of moisture may be found by placing this value of 0.01556 
together with P equal to 75 + 14.7 in the equation thus: 

o ni ccc _ KH = K.H 

2.036 X 89.7 -if 182.63 - H 

9 849 

or H — n ni ' " 7 - r > , and the temperature which satisfies this equation 
0.0155b + K 

is found by aid of the table [by trial and error] to be approximately 
129° F. 

Example 3. — When the outside temperature is 82° F., and the 
pressure of the atmosphere is 14.6963 lb. per sq. in., the relative humid- 
ity being 100%, how many cu. ft. of free air must be compressed 
and delivered into a reservoir at 100 lb. gauge in order to cause 1 lb. of 
water to be deposited when the air is cooled to 82° F.? 

Ans. — Weight of moisture mixed with 1 lb. of air at 82° F., and 
atmospheric pressure = 0.023526 lb. For 100 lb. gauge pressure, 

IF— ™ = °- 6211 X 1092 = 0002918 1b 

2.036 P - H 2.036 X 114.6963 - 1.092 »- w ^ iai »- 

Weight of moisture deposited by each lb. of compressed air = 0.023526 
- 0.002918 = 0.020608 lb. Each cu. ft. of the moist atmosphere con- 
tains 0.070595 lb. of pure, air, therefore the number of cu. ft. that must 
be delivered to cause 1 lb. of water to be deposited is 

Example 4. — Under the same conditions as stated in Example 3, 
what is the loss in volumetric efficiency of the plant when the excess 
moisture is properly trapped in the main reservoirs? 

Ans. — Before compression, each pound of air is mixed with 0.023526 
lb. of water vapor and the weight of 1 cu. ft. of the mixture is 0.072256 lb., 
consequently the volume of the mixture is 

1.023526 -h 0.072256 = 14.165 cu. ft. 

For 100 lb. gauge pressure and 82° F. as shown in Example 3, 1 lb. 
of air can hold 0.002918 lb. of water in suspension, having deposited 
0.020608 lb. in the reservoir. The weight of 1 cu. ft. of water vapor at 
82° is 0.001661 lb., consequently -by Dalton's law the volume of the mix- 
ture of 1 lb. of air and 0.002918 lb. of water vapor at 100 lb. gauge press- 
ure is the same as that of the vapor or saturated steam alone; that is, 
0.002918 -** 0.001661 = 1.757 cu. ft. 

By Mariotte's law, the volume of the 1.757 cu. ft. of mixed gas at 
114.6963 lb. absolute when expanded to atmospheric pressure will be 

(114.6963 -r 14.6963) X 1.757 = 13.712 cu. ft,; 
consequently the decrease of volume, that is, the loss of volumetric 
efficiency, is 
14.165 - 13.712 = 0.453 cu. ft., or (0.453 + 14.165) X 100 = 3.2%. 

This example shows that, particularly in warm, moist climates, there 
is a very appreciable loss in the efficiency of compressors, due to the 
condensation of water vapor. 

Specific Heat of Air at Constant Volume and at Constant Pressure. 
— Volume of 1 lb. of air at 32° F. and pressure of 14.7 lbs. per sq. in. = 
12.387 cu. ft. = a column 1 sq. ft. area X 12.387 ft. high. Raising tem- 



588 air. 

perature 1° F. expands it 1/492, or to 12.4122 ft. high — a rise of 0.02522 
foot. 

Work done = 2116 lbs. per sq. ft. X .02522 = 53.37 foot-pounds, or 
53.37 -*- 778 = 0.0686 heat units. 

The specific heat of air at constant pressure, according to Regnault, is 
0.2375; but this includes the work of expansion, or 0.0686 heat units; hence 
the specific heat at constant •volume = 0.2375 - 0.0686 = 0.1689. 

Ratio of specific heat at constant pressure to specific heat at constant 
volume = 0.2375 -h 0.1689 = 1.406. (See Specific Heat, p. 534.) 

Flow of Air through Orifices. — The theoretical velocity in feet per 
second of jlow of any fluid, liquid, or gas through an orifice is v =\ / 2 gh 
= 8.02 Vft, in which h = the " head" or height of the fluid in feet required 
to produce the pressure of the fluid at the level of the orifice. (For gases 
the formula holds good only for small differences of pressure on the two 
sides of the- orifice.) The quantity of flow in cubic feet per second is equal 
to the product of this velocity by the area of the orifice, in square feet, 
multiplied by a "coefficient of flow," which takes into account the con- 
traction of the vein or flowing stream, the friction of the orifice, etc. 

For air flowing through an orifice or short tube, from a reservoir of the 
pressure pi into a reservoir of the pressure pi, Weisbach gives the following 
values for the coefficient of flow, obtained from his experiments. 

Flow of Air through an Orifice. 
Coefficient c in formula v = c V2 gh. 

Diam. 1 cm. = 0.394 in.: 

Ratio of pressures .. . 1.05 1.09 1.43 1.65 1.89 2.15 

Coefficient 555 .589 .692 .724 .754 . 788 

Diam. 2.14 cm. = 0.843 in.: 

Ratio of pressures .. . 1.05 1.09 1.36 1.67 2.01 

Coefficient 558 .573 .634 .678 .723 

Flow of Air through a Short Tube. 

Diam. 1 cm., = 0.394 in., length 3 cm. = 1.181 in. 

Ratio of pressures pi-^-pi. . . 1.05 1.10 1.30 

Coefficient 730 .771 .830 

Diam. 1.414 cm. = 0.557 in., length 4.242 cm. = 1.670 in.: 

Ratio of pressures 1 . 41 1 . 69 

Coefficient 813 .822 

Diam. 1 cm. = 0.394 in., length 1.6 cm. = 0.630 in. Orifice rounded: 

Ratio of pressures 1.24. 1.38 1.59 1.85 2.14 ... 

Coefficient 979 .986 .965 .971 .978... 

Clark (Rules, Tables, and Data, p. 891) gives, for the velocity of flow 
of air through an orifice due to small differences of pressure, 

V = cy^X773.2 X 
or, simplified, 

V = 352 Cy (1 + .00203 (t 

in which V = velocity in feet per second; 2 g = 64.4; h = height of the 
column of water in inches, measuring the difference of pressure; t = the 
temperature Fahr. ; and p = barometric pressure in inches of mercury. 
773.2 is the volume of air at 32° under a pressure of 29.92 inches of mercury 
when that of an equal weight of water is taken as 1. 

For 62° F., the formula becomes V = 363 C ^h/p, and if p = 29.92 
inches, V = 66.35 C ^h. 

The coefficient of efflux C, according to Weisbach, is: 
For conoidal mouthpiece, of form of the contracted vein, 

with pressures of from 0.23 to 1.1 atmospheres. ... C = 0.97 to 0.99 

Circular orifices in thin plates C = 0.56 to 0.79 

Short cylindrical mouthpieces C = 0.81 to 0.84 

The same rounded at the inner end C = 0.92 to 0.93 

Conical converging mouthpieces C = 0.90 to 0.99 




FLOW OF AIR THROUGH ORIFICES. 589 

R. J. Durley, Trans. A. S. M. E., xxvii, 193, gives the following: 
The consideration of the adiabatic flow of a perfect gas through a 
frictionless orifice leads to the equation 



-=V^f^-f:[(#-@r] • • • a> 

W = weight of gas discharged per second in pounds. 
A = area of cross section of jet in square feet. 
Pi = pressure inside orifice in pounds per square foot. 
. P2 = pressure outside orifice. 

Vi = specific volume of gas inside orifice in cu. ft. per lb. 
y = ratio of the specific heat at constant pressure to that at constant 
volume. 

For air, where y = 1.404, we have for a circular orifice of diameter d 
inches, the initial temperature of the air being 60° Fahr. (or 521° abs.), 



W = 0.000491 d 2 Pi\/(pj ~ (jrj 



(2) 



In practice the flow is not frictionless, nor is it perfectly adiabatic, and 
the amount of heat entering or leaving the gas is not known. Hence the 
weight actually discharged is to be found from the formulas by introducing 
a coefficient of discharge (generally less than unity) depending on the 
conditions of the experiment and on'the construction of the particular 
form of orifice employed. 

If we neglect the changes of density and temperature occurring as the 
air passes through the orifice, we may obtain a simpler though approxi- 
mate formula for the ideal discharge: 



V£- 



(3) 



in which d = diam. in inches, i = difference of pressures measured in 
inches of water, P = mean absolute pressure in lbs. per sq. ft., and T = 
absolute temperature on the Fahrenheit scale = degrees F. + 461. In 
the usual case, in which the discharge takes place into the atmosphere, 
P is approximately 2117 pounds per square foot and 



pp \/i 



W = 0.6299 d* U ~ (4) 

To obtain the actual discharge the values found by the formula are to be 
multiplied by an experimental coefficient C, values of which are given in 
the table below. 

Up to a pressure of about 20 ins. of water (or 0.722 lbs. per sq. in.) above 
the atmospheric pressure, the results of formulae (2) and (4) agree very 
closely. At higher differences of pressure divergence becomes noticeable. 

They hold good only for orifices of the particular form experimented 
with, and bored in plates of the same thickness, viz.: iron plates 0.057 in. 
thick. 

The experiments and curves plotted from them indicate that: — 

(1) The coefficient for small orifices increases as the head increases, but 
at a lesser rate the larger the orifices, till for the 2-in. orifice it is almost 
constant. For orifices larger than 2 ins. it decreases as the head increases, 
and at a greater rate the larger the orifice. 

(2) The coefficient decreases as the diameter of the orifice increases, and 
at a greater rate the higher the head. 

(3) The coefficient does not change appreciably with temperature 
(between 40° and 100° F.). 

(4) The coefficient (at heads under 6 ins.) is not appreciably affected 
by the size of the box in which the orifice is placed if the ratio of the areas 
pf the box and orifice is at least 20 : 1. 



590 



AIR. 



Mean Discharge in Pounds per Square Foot of Orifice per Second 
as Found from Experiments. 



Diameter 


1-inch 

Head 

Discharge 

per Sq. Ft. 


2-inch Head 


3-inch Head 


4-inch 

Head 

Discharge 

per Sq. Ft. 


5-inch 

Head 

Discharge 

per Sq. Ft. 


Orifice, 
Inches. 


Discharge 
per Sq. Ft. 


Discharge 
per Sq. Ft. 


0.3125 


3.060 


4.336 


5.395 


6.188 


7.024 


0.5005 


3.012 


4.297 


5.242 


6.129 


6.821 


1.002 


3.058 


4.341 


5.348 


6.214 


6.838 


1.505 


3.050 


4.257 


5.222 


6.071 


6.775 


2.002 


2.983 


4.286 


5.284 


6.107 


6.788 


2.502 


3.041 


4.303 


5.224 


5.991 


6.762 


3.001 


3.078 


4.297 


5.219 


6.033 


6.802 


3.497 


3.051 


4.258 


5.202 


5.966 


6.814 


4.002 


3.046 


4.325 


5.264 


5.951 


6.774 


4.506 


3.075 


4.383 


5.508 


6.260 


7.028 



Coefficients of Discharge for Various Heads and Diameters of 
Orifice. 



Diameter 

of Orifice, 

Inches. 


1-inch 


2-inch 


3-inch 


4-inch 


5-inch 


Head. 


Head. 


Head. 


Head. 


Head. 


5 /l6 


0.603 


0.606 


0.610 


0.613 


0.616 


V2 


0.602 


0.605 


0.608 


0.610 


0.613 


1 


0.601 


0.603 


0.605 


0.606 


0.607 


H/2 


0.601 


0.601 


0.602 


0.603 


0.603 


2 


0.600 


0.600 


0.600 


0.600 


0.600 


21/2 


0.599 


0.599 


0.599 


0.598 


0.598 


3 


0.599 


0.598 


0.597 


0.596 


0.596 


31/2 


0.599 


0.597 


0.596 


0.595 


0.594 


4 


0.598 


0.597 


0.595 


0.594 


0.593 


41/2 


0.598 


0.596 


0.594 


0.593 


0.592 



Corrected Actual Discharge in Pounds per Second at 60° F. and 

14.7 lbs. Barometric Pressure for Circular Orifices in 

Plate 0.057 in. Thick. 





Diameter of Orifice in Inches. 


^ 
W3 


0.3125 


0.500 


1.000 


1.500 


2.000 


2.500 


3.000 


3.500 


4.000 


4.500 


5.000 


V? 


0.00114 


0.00293 


0.0117 


0.0263 


0.0468 


0.0732 


0.105 


0.143 


0.187 


0.237 


0.292 


I 


0.00162 


0.00416 


0.0166 


0.0373 


0.0663 


0.103 


0.149 


0.202 


0.264 


0.334 


0.413 


Mh 


0.00199 


0.00510 


0.0203 


0.0457 


0.0811 


0.127 


0.182 


0.248 


0.323 


0.409 


0.505 


2 


0.00231 


0.00590 


0.0235 


0.0528 


0.0937 


0.146 


0.210 


0.285 


0.373 


0.471 


0.582 


2V> 


0.00259 


0.00662 


0.0263 


0.1591 


0.105 


0.163 


0.235 


0.319 


0.416 


0.526 


0.649 


3 


0.00285 


0.00726 


0.0289 


0.0648 


0.115 


0.179 


0.257 


0.349 


0.455 


0.575 


0.710 


3V-> 


0.00308 


0.00786 


0.0312 


0.0700 


0.124 


0.193 


0.277 


0.377 


0.491 


0.621 


0.766 


4 


0.00330 


0.00842 


0.0334 


0.0749 


0.133 


0.206 


0.296 


0.402 


0.525 


0.663 


0.817 


41/9 


0.00351 


0.00895 


0.0355 


0.0794 


0.141 


0.219 


0.314 


0.426 


0.556 


0.702 


0.865 


5 


0.00371 


0.00945 


0.0375 


0.0838 


0.148 


0.231 


0.331 


0.449 


0.586 


0.739 


0.912 


5V-> 


0.00390 


0.00993 


0.0393 


0.0879 


0.155 


0.242 


0.347 


0.471 


0.613 


0.774 


0.953 


6 


0.00408 


0.01049 


0.0411 


0.0918 


0.162 


0.252 


0.362 


0.492 


0.640 


0.808 


0.995 



FLOW OF AIR IN PIPES. 



591 



Flow of Air in Pipes. — Hawksley (Proc. Inst. C 
that his formula for flow of water in pipes, v = 48 



E., xxxiil. 55) states 

i/'-r~ i ma y also be 
employed for flow of air. In this case H = height n feet of a column of 
air required to produce the pressure causing the flow, or the loss of head 
for a given flow; v = velocity in feet per second, D = diameter in feet, 
L = length in feet. 

If the head is expressed in inches of water, h, the air being taken at 
62°F., its weight per cubic foot at atmospheric pressure = 0.0761 lb. 

Then /f= jlfy v ? = 68.3 h. If d = diameter in inches, D= ^ , and 



the formula becomes v = 114.5 



V^. 



rf = diameter in inches, and L=length in feet 
The quantity in cubic feet per second s 



in which /i=inches of water column, 

Lv 2 , Lv 2 



o,8 Ml f^=o.e 2 , 5 ^ :rf = V ' ^ ;ft =^ T . 



The horse-power required to drive air through a pipe is the volume Q in 
cubic feet per second multiplied by the pressure in pounds per square foot 
and divided by 550. Pressure in pounds per square foot = P = inches 
of water column X 5.196, whence horse-power = 



H.P. 



= QP_ 

550 



Qh 
105.9 



Q*L 



Volume of Air Transmitted in Cubic Feet per Minute in 
Pipes of Various Diameters. 



o ■ 


Actual Diameter of Pipe in Inches. 








1 


2 


3 


4 


5 


6 


8 


10 


12 


16 


20 


24 


> 






2.95 




















i 


327 


1 .31 


5.24 


8.18 


11 78 


20,94 


32.73 


47.12 


83.77 


1309 


188.5 


2 


655 


2.62 


5.89 


10.47 


16.36 


23.56 


4L89 


65.45 


94.25 


167.5 


261.8 


377.0 


3 


982 


3.93 


8.84 


15.7 


24.5 


35.3 


62.8 


98.2 


141. 4 


251.3 


392.7 


565.5 


4 


1.31 


5.24 


11.78 


20.9 


32.7 


47.1 


83.8 


131 


188 


335 


523 


754 


■> 


1 64 


6.54 


14 7 


26.2 


41.0 


59.0 


104 


163 


235 


419 


654 


942 


6 


1 96 


7 85 


17 7 


31.4 


49.1 


70.7 


125 


196 


283 


502 


785 


1131 


7 


2 29 


9 16 


20.6 


36.6 


57.2 


82.4 


146 


229 


330 


586 


916 


1319 


8 


2 62 


10 5 


23 5 


41.9 


65,4 


94 


167 


262 


377 


670 


1047 


1508 


9 


2 95 


11 78 


26 5 


47 


73 


106 


188 


294 


424 


754 


1178 


1696 


in 


3 27 


13.1 


29 4 


52 


82 


118 


209 


327 


471 


833 


1309 


1885 


12 


3 93 


15 7 


35 3 


63 


98 


141 


251 


393 


565 


1005 


1571 


2262 


15 


4 91 


19 6 


44 2 


78 


122 


177 


314 


491 


707 


1256 


1963 


2827 


18 


5.89 


23 5 


53 


94 


147 


212 


377 


589 


848 


1508 


2356 


3393 


2D 


6 54 


26.2 


59 


105 


164 


235 


419 


654 


942 


1675 


2618 


3770 


?A 


7 85 


31 4 


71 


125 


196 


283 


502 


785 


1131 


2010 


3141 


4524 


75 


8 18 


37 7 


73 


131 


204 


294 


523 


818 


1178 


2094 


3272 


4712 


7* 


9.16 


36 6 


8? 


146 


229 


330 


586 


916 


1319 


2346 


3665 


5278 


30 


9.8 


39.3 


88 


157 


245 


353 


628 


982 


1414 


2513 


3927 


5655 



592 air. 

In Hawksley's formula and its derivatives the numerical coefficients are 
constant. It is scarcely possible, however, that they can be accurate 
except within a limited range of conditions. In the case of water it is 
found that the coefficient of friction, on which the loss of head depends 
varies with the length and diameter of the pipe, and with the velocity as 
well as with the condition of the interior surface. In the case of air and 
other gases we have, in addition, the decrease in density and consequent 
increase in volume and in velocity due to the progressive loss of head from 
one end of the pipe to the other. 

Clark states that according to the experiments of D'Aubuisson and those 
of a Sardinian commission on the resistance of air through long conduits 
or pipes, the diminution of pressure is very nearly directly as the length, 
and as the square of the velocity and inversely as the diameter. The 
resistance is not varied by the density. 

If these statements are correct, then the formulae h — — r and h = ~-r. 

cd c'd 5 

and their derivatives are correct in form, and they may be used when the 
numerical coefficients c and c' are obtained by experiment. 

If we take the forms of the above formulae as correct, and let C be a 
variable coefficient, depending upon the length, diameter, and condition 
of surface of the pipe, and possibly also upon the velocity, the tempera- 
ture and the density, to be determined by future experiments, then for 
h = head in inches of water, d = diameter in inches, L = length in feet, 
v = velocity in feet per second, and Q = quantity in cubic feet per 

second: 

„Jhd , Lv 2 . Lv* 



\ L ; d ~ C 2 /* ; h ~ C*d ; 



. 33683 Q 2 L . 33683 Q 2 L 

= V — c*h' h = cw ' 

For difference or loss of pressure p in pounds per square inch, 
h = 27.71 p; *Jh = 5.264 Vp; 

V = 5.264 C Vf* ^L- -J^_ 



' L * 27.71 C 2 p' * 21.11 C 2 d' 



Q = 0.02871 C ^~; d = i/- 3 



1213 Q 2 L . 1213 Q*L 

C 2 p ' P C 2 d 5 



(For other formulae for flow of air, see Mine Ventilation.) 
Loss of Pressure in Ounces per Square Inch. — B. F. 

Company uses the following formulae: 



.-■V^ 



in which pi = loss of pressure in ounces per square inch, v = velocity of 
air in feet per second, and L = length of pipe in feet. If p is taken in 
pounds per square inch, these formulae reduce to 



J dpi. j 0.0000025 L& 



p = 0.0000025 -~; v = 632.5 T 

I v 2 
These are deduced from the common formula (Weisbach's), p=f-j-^— • 

in which /= 0.000 1608. They correspond to the formulae given above 
when C is taken at 120.15, Hawksley's formula for the same notation 
giving 114.5. Using the notation given in the formulae for compressed 
air, where Q is taken in cu. ft. per minute, Sturtevant's formula gives a 
value of C = 57.1, Hawksley's 54.4. The figure 60 is commonly used, 
assuming a density of air of 0.761 lb. per cu. ft. 

The following table is condensed from one given in the catalogue of 
B. F. Sturtevant Company. 



AIR. 



593 



Loss of Pressure in Pipes 100 ft. Long,* in Ounces per Sq. In. 



*g 








Diameter of Pipe in Inches. 












1 


2 


5 


4 


5 


6 


7 


8 


9 


10 


II 


12 


600 


0.400 


0.200 


0.133 


0.100 


0.080 


0.067 


0.057 


0.050 


0,044 


0.040 


036 


0.033 


1700 


1.600 


0.800 


0.533 


0.400 


0.320 


0.267 


0.229 


0.200 


0.178 


0.160 


145 


0.133 


1800 


3.600 


1.800 


1.200 


0.900 


0.720 


0.600 


0.514 


0.450 


0.400 


0.360 


327 


0.300 


7400 


6.400 


3.200 


2.133 


1.600 


1.280 


1 .067 


0.914 


0.800 


0.711 


0.640 


582 


0.533 


3000 


10.0 


5.0 


3.333 


2.5 


2.0 


1.667 


1.429 


1.250 


1.111 


1.000 


909 


0.833 


1600 


14.4 


7.2 


4.8 


3.6 


2.88 


2.4 


2.057 


1.8 


1.6 


1.44 


1,309 


1.200 


4700 




9.8 


6.553 


4.9 


3.92 


3.267 


2.8 


2.45 


2 178 


1 96 


1 782 


1.633 


4800 




12.8 


8.533 


6.4 


5.12 


4.267 


3.657 


3.2 


2 844 


2 56 


2 327 


2.133 


6000 




20. 


13.333 


10.0 


8.0 


6.667 


5.714 


5.0 


4.444 


4.0 


3.636 


3.333 




14 


16 


18 


20 


22 


24 


28 


32 


36 


40 


44 


48 


6011 


.029 


.026 


.022 


.020 


.018 


.017 


.014 


.012 


.011 


.010 


.009 


.008 


l?00 


.114 


.100 


.089 


.080 


.073 


..067 


.057 


.050 


044 


.040 


036 


.033 


1800 


.257 


.225 


.200 


.180 


.164 


.156 


.129 


.112 


.100 


.090 


.082 


.075 


7,400 


.457 


.400 


.356 


.320 


.291 


.267 


.239 


.200 


.178 


.160 


.145 


.133 


3600 


1.029 


.900 


.800 


.720 


.655 


.600 


.514 


.450 


.400 


.360 


.327 


.300 


47,00 


1.400 


1.225 


1.089 


.980 


.891 


.817 


.700 


.612 


.544 


.490 


.445 


.408 


4800 


1.829 


1.600 


1.422 


1.280 


1.164 


1.067 


.914 


.800 


711 


640 


582 


.533 


6000 


2.857 


2.500 


2.222 


2.000 


1.818 


1.667 


1.429 


1.250 


1.111 


1.000 


.909 


.833 



* For any other length the loss is proportional to the length. 

Effect of Bends in Pipes. (Norwalk Iron Works Co.) 
Radius of elbow, in diameter 

of pipe = 5 3 2 1 1/2 1 1/4 1 3/4 l/ 2 

Equivalent lengths of straight 

pipe, diams. 7.85 8.24 9.03 10.36 12.72 17.51 35.09 121.2 

Friction of Air in Passing through Valves and Elbows. W. L. 
Saunders, Compressed Air, Dec, 1902. —The following figures give the 
length in feet of straight pipe which will cause a reduction in pressure equal 
to that caused by globe valves, elbows, and tees in different diameters of 
pipe. 

Diam. of pipe, in.. 1 li/ 2 2 2i/ 2 3 3i/ 2 4 5 6 7 8 10 
Globe Valves ..... 2 4 7 10 13 16 20 28 36 44 53 70 
Elbows and Tees .23 5 7 9 11 13 19 24 30 35 47 

Compressed-air Transmission. (Frank Richards, Am. Mach., March 
8, 1894.) — The volume of. free air transmitted may be assumed to be 
directly as the number of atmospheres to which the air is compressed. 
Thus, if the air transmitted be at 75 pounds gauge-pressure, or six atmos- 
pheres, the volume of free air will be six times the amount given in the 
table (page 591). It is generally considered that for economical trans- 
mission the velocity in main pipes should not exceed 20 feet per second. 
In the smaller distributing pipes the velocity should be decidedly less 
than this. 

The loss of power in the transmission of compressed air in general is not 
a serious one, or at all to be compared with the losses of power in the opera- 
tion of compression and in the re-expansion or final application of the 
air. 

The formulas for loss by friction are all unsatisfactory. The statements 
of observed facts in this line are in a more or less chaotic state, and self- 
evidently unreliable. 

A statement of the friction of air flowing through a pipe involves at least 
all the following factors: Unit of time, volume of air, pressure of air, diam- 



594 



eter of pipe, length of pipe, and the difference or pressure at the ends of 
the pipe or the head required to maintain the flow. Neither of these 
factors can be allowed its independent and absolute value, but is subject to 
modifications in deference to its associates. The flow of air being assumed 
to be uniform at the entrance to the pipe, the volume and flow are not 
uniform after that. The air is constantly losing some of its pressure and 
its volume is constantly increasing. The velocity of flow is therefore also 
somewhat accelerated continually. This also modifies the use of the 
length of the pipe as a constant factor. 

Then, besides the fluctuating values of these factors, there is the condi- 
tion of the pipe itself. The actual diameter of the pipe, especially in the 
smaller sizes, is different from the nominal diameter. The pipe may be 
straight, or it may be crooked and have numerous elbows. 

Formulae for Flow of Compressed Air in Pipes. — The formulae on 
pages 591 and 592 are for air at or near atmospheric pressure. For com- 
pressed air the density has to be taken into account. A common formula 
for the flow of air, gas, or steam in pipes is 



4& 



in which Q — volume in cubic feet per minute, p = difference of pressure 
in lbs. per sq. in. causing the flow, d = diameter of pipe in in., L = length 
of pipe in ft., w = density of the entering gas or steam in lbs. per cu. ft., 
and c = a coefficient found by experiment. Mr. F. A. Halsey in calculat- 
ing a table for the Rand Drill Co.'s Catalogue takes the value of c at 58, 
basing it upon the experiments made by order of the Italian government 
preliminary to boring the Mt. Cenis tunnel. These experiments were made 
with pipes of 3281 feet in length and of approximately 4, 8, and 14 in. 
diameter. The volumes of compressed air passed ranged between 16.64 
and 1200 cu. ft. per minute. The value of c is quite constant throughout 
the range and shows little disposition to change with the varying diameter 
of the pipe. It is of course probable, says Mr. Halsey, that c would be 
smaller if determined for smaller sizes of pipe, but to offset that the actual 
sizes of small commercial pipe are considerably larger than the nominal 
sizes, and as these calculations are commoniy made for the nominal 
diameters it is probable that in those small sizes the loss would really be 
less than shown by the table. The formula is of course strictly applicable 
to fluids which do not change their density, but within the change of 
density admissible in the transmission of air for power purposes it is prob- 
able that the errors introduced by this change are less than those due to 
errors of observation in the present state of knowledge of the subject. 
Mr. Halsey's table is condensed below. 





Cubic feet of free air compressed to a gauge-pressure of 80 lbs. 
and passing through the pipe each minute. 




50 


100 


200 


400 


800 


1000 


1500 


2000 


3000 


4000 


5000 


ii 

5 


Loss of pressure in lbs. per square inch for each 1000 ft. of 
straight pipe. 


H/4 

H/2 
2 

21/2 
3 

31/2 


3.61 
1.45 
0.20 
0.12 


5.8 
1.05 
0.35 
0.14 


4.30 
1.41 
0.57 
0.26 
0.14 


5.80 
2.28 
1.05 
0.54 
0.18 


4.16 
2.12 
0.68 
0.28 
0.07 


6.4 
3.27 
1.08 
0.43 
0.10 


7.60 
2.43 
1.00 
0.24 
0.08 


4.32 
1.75 
0.42 
0.14 


9.6 
3.91 
0.93 
0.30 
0.12 


7.10 
1.68 
0.55 
0.22 
0.10 




4 








5 








6 








10.7 


8 










2.59 


10 










0.84 


12 














0.34 


14 


















0.16 

























595 



To apply the formula given above to air of different pressures it may be 
given other forms, as follows: 

Let Q = the volume in cubic feet per minute of the compressed air; Q\ = 
the volume before compression, or "free air," both being taken at mean 
atmospheric temperature of 62° F.; wi = weight per cubic foot of Qi = 
0.0761 lb.; r = atmospheres, or ratio of absolute pressures, = (gauge- 
pressure + 14.7) -s- 14.7; w = weight per cu. ft. of Q; p = difference of 
pressure, in lbs. per sq. in., causing the flow; d = diam. of pipe in in.; 
L = length of pipe in ft.; c = experimental constant. Then 



▼ wL' 



Q = 3.625 c 



fl 



■■ rwi = 0.0761 r; 
pd^r \ 



I - WO.O 



.LQ*r 



7lqv = 

V c 2 p 



pd r °r 



y/ox 



c 2 pr 



- 0.0761^= 0.0761 ^ 2 - 
c 2 d 3 c 2 rfV 



The value of c according to the Mt. Cenis experiments is about 58 for 
pipes 4, 8, and 14 in. diameter, 3281 ft. long. In the St. Gothard experi- 
ments it ranged from 62.8 to 73.2 (see table below) for pipes 5.91 and 7.87 
in. diameter, 1713 and 15,092 ft. long. Values derived from Darcy's 
formula for flow of water in pipes, ranging from 45.3 for 1 in. diameter to 
63.2 for 24 in., are given under "Flow of Steam," p. 845. For approxi- 
mate calculations the value 60 may be used for all pipes of 4 in. diameter 
and upwards. Using c = 60, the above formulae become 



Q - 



217.5 



/pdfi 
rL' 



= 217.5 



LQH 



<l 



f pd 5 r 

V —• 



LQi* 



p == 0.00002114 



LQ*r 



,W 



Loss of Pressure in Compressed Air Pipe-main, at St. 
Tunnel. (E. Stockalper.) 


Gothard 




03 

a 

03 

Q 
a 
"3 


Volume per second 
of free air, or equi- 
valent volume at 
atmospheric pres- 
sure and 32° F. 


03 03 'S 

tC OJ g 

ftftC 
o> S v 

asa 

"o O o3 

> 


fl 03 U 
H3 ft*; 

c3 0^> 
03 13 — ' 

2 


o . 

MM 


.2 a 
>>8 
. n ® 

O °3 

O (L, 


Observed Pressures. 




03 

s 

ft 


43 M 

c3 G 

g.2'3. 


03 

43 ft 

*'ft 

03^ 

g § 


Loss of 
Pressure. 


«S| a| 9 


lbs. 
per 
sq.in. 


% 


II 
IS 

> 


No. 

'{ 

2 ! 


in. 
7.87 
5.91 
7.87 
5.91 
7.87 
5.91 


cu.ft. 
} 33.056 { 

j 22.002 { 

1 18.364 { 


cu.ft. 
6.534 
7.063 
5.509 
5.863 
5.262 
5.580 


den. 
.00650 
.00603 
.00514 
.00482 
.00449 
.00423 


lbs. 

2.669 

2.669 

1.776 

1.776 

1.483 

1.483 


feet. 
19.32 
37.14 
16.30 

i 5 " 58 

29.34 


5.60 
5.24 
4.35 
4.13 
3.84 
3.65 


at. 
5.24 
5.00 
4.13 


5.292 
3.528 
3.234 


6.4 
4.6 
5.1 


73.2 
63.9 
70.7 


A 


3.65 
3.54 


2.793 
1.617 


5.0 
3.0 


67.6 

62.8 



The length of the pipe 7.87 in. in diameter was 15,092 ft., and of the 
smaller pipe 1712.6 ft. The mean temperature of the air in the large pipe 
was 70°F. and in the small pipe 80° F. 

Flow of Air in Long Pipes with Large Differences of Pressure..— The 
formulae given above are applicable strictly only to cases in which the 



596 



difference of pressure at the two ends of the pipe is small, and the density 
of the air, therefore, nearly constant. For long pipes with considerable 
difference of pressure the density decreases and the velocity increases 
during the flow from one end of the pipe to the other. Church (Mechs. of 
Eng'g, p. 790) develops a formula for flow in long pipes under the assump- 
tions of uniform decrease of density and of constant temperature, the 
loss of heat by adiabatic expansion being in great part made up by the 
heat generated by friction. Using the same notation as above Church's 

4 fl W 2 Vi 
formula is 1/2 [Pi 2 — P2 2 ] = % 9W "77 • f Dein S tne coefficient of friction, 

A the area of the pipe in square inches, and w the density of air at the 
entrance. The value of /is given at 0.004 to 0.005. 

J. E. Johnson, Jr. (Am. Mach., July 27, 1899) gives Church's formula 
in a simpler form as follows: Px 2 — p 2 2 = KQ 2 L -s- d 5 , in which p x and 
p 2 are the initial and final pressures in lbs. per sq. in., Q the volume of 
free air (that is the volume reduced to atmospheric pressure) in cubic 
feet per minute, d the diameter of the pipe in inches, L the length in feet, 
and K a numerical coefficient, which from the Mt. Cenis and St. Gothard 
experiments has a value of about 0.0006. E. A. Rix, in a paper on the 
Compression and Transmission of Illuminating Gas, read before the 
Pacific Coast Gas Ass'n, 1905, says he uses Johnson's formula, with a 
coefficient of 0.0005, which he considers more nearly correct than 0.0006. 
For gas the velocity varies inversely as the square root of the density, 
and for gas of a density G, relative to air as 1, Rix gives the formula 
Pi 2 - P2 2 = 0.0005 V^ X Q 2 L/dK 

Measurement of the Velocity of Air in Pipes by an Anemometer. 
— Tests were made by B. Donkin, Jr. (Inst. Civil Engrs., 1892), to com- 
pare the velocity of air in pipes from 8 in. to 24 in. diam., as shown by an 
anemometer 23/4 in. diam. with the true velocity as measured by the time 
of descent of a gas-holder holding 1622 cubic feet. A table of the results 
with discussion is given in Eng'g News, Dec. 22, 1892. In pipes from 8 in. 
to 20 in. diam. with air velocities of from 140 to 690 feet per minute the 
anemometer showed errors varying from 14.5% fast to 10% slow. With 
a 24-inch pipe and a velocity of 73 ft. per minute, the anemometer gave 
from 44 to 63 feet, or from 13.6 to 39.6% slow. The practical conclusion 
drawn from these experiments is that anemometers for the measurement 
of velocities of air in pipes of these diameters should be used with great 
caution. The percentage of error is not constant, and varies considerably 
with the diameter of the pipes and the speeds of air. The use of a baffle 
consisting of a perforated plate, which tended to equalize the velocity in 
the center and at the sides in some cases diminished the error. 

The impossibility of measuring the true quantity of air by an anemometer 
held stationary in one position is shown by the following figures, given by 
Wm. Daniel (Proc. Inst. M. E., 1875), of the velocities of air found at 
different points in the cross-sections of two different airways in a mine. 

Differences of Anemometer Readings in Airways. 
8 ft. square. 



1712 


1795 


1859 


1329 


1622 


1685 


1782 


1091 
1049 


1477 


1344 


1524 


1262 


1356 


1293 


1333 



1170 


1209 
1104 


1288 


948 


1177 


1134 


1049 


1106 



Average 1132. 
Average 1469. 

Equalization of Pipes. — It is frequently desired to know what number 
of pipes of a given size are equal in carrying capacity to one pipe of a 
larger size. At the same velocity of flow the volume delivered by two 
pipes of different sizes is proportional to the squares of their diameters; 



AIR. 



597 



thus, one 4-inch pipe will deliver the same volume as four 2-inch pipes. 
With the same head, however, the velocity is less in the smaller pipe, and 
the volume delivered varies about as the square root of the fifth power 
(i.e., as the 2.5 power). The following table has been calculated on this 
basis. The figures opposite the intersection of any two sizes is the num- 
ber of the smaller-sized pipes required to equal one of the larger. Thus 
one 4-inch pipe is equal to 5.7 two-inch pipes. 





1 


2 


3 


4 


5 


6 


7 


6 


9 


10 


12 


14 


16 


18 


20 


24 


2 


577 


~T~ 






























3 


15.6 


2.8 


1 




























4 


32.0 


5.7 


2.1 


1 


























5 


55.9 


9.9 


3.6 


1.7 


1 
























6 


88.2 


15.6 


5.7 


2.8 


1.6 


1 






















7 


130 


22.9 


8.3 


4.1 


2.3 


1.5 


1 




















8 


181 


32.0 


11.7 


5.7 


3.2 


2.1 


1.4 


1 


















9 


243 


43.0 


15.6 


7.6 


4.3 


2.8 


1.9 


1.3 


1 
















10 


316 


55.9 


20.3 


9.9 


5.7 


3.6 


2.4 


1.7 


1.3 


1 














11 


401 


70.9 


25.7 


12.5 


7.2 


4.6 


3.1 


2.2 


1.7 


1.3 














12 


499 


88.2 


32.0 


15.6 


8.9 


5.7 


3.8 


2.8 


2.1 


1.6 


1 












13 


609 


108 


39.1 


19.0 


10.9 


7.1 


4.7 


3.4 


2.5 


1.9 


1.2 












14 


733 


130 


47.0 


22.9 


13.1 


8.3 


5.7 


4.1 


3.0 


2.3 


1.5 


1 










15 


871 


154 


55.9 


27.2 


15.6 


9.9 


6.7 


4.8 


3.6 


2.8 


1.7 


1.2 










16 




181 


65.7 


32.0 


18.3 


11.7 


7.9 


5.7 


4.2 


3.2 


2.1 


1.4 


1 








17 




211 


76.4 


37.2 


21.3 


13.5 


9.2 


6.6 


4.9 


3.8 


2.4 


1.6 


1.2 








18 




243 


88.2 


43.0 


24.6 


15.6 


10.6 


7.6 


5.7 


4.3 


2.8 


1.9 


1.3 


1 






19 




278 


101 


49.1 


28.1 


17.8 


12.1 


8.7 


6.5 


5.0 


3.2 


2.1 


1.5 


1.1 






20 




316 


115 


55.9 


32.0 


20.3 


13.8 


9.9 


7.4 


5.7 


3.6 


2.4 


1.7 


1.3 


1 




22 




401 


146 


70.9 


40.6 


25.7 


17.5 


12.5 


9.3 


7.2 


4.6 


3.1 


2.2 


1.7 


1.3 




24 




499 


181 


88.2 


50.5 


32.0 


21.8 


15.6 


11.6 


8.9 


5.7 


3.8 


2.8 


2.1 


1.6 


1 


26 




609 


221 


108 


61.7 


39.1 


26.6 


19.0 


14.2 


10.9 


7.1 


■ 4.7 


3.4 


2.5 


1.9 


1.2 


28 




733 


266 


130 


74.2 


47.0 


32.0 


22.9 


17.1 


13.1 


8.3 


5.7 


4.1 


3.0 


2.3 


1.5 


30 




871 


316 


154 


88.2 


55.9 


38.0 


27.2 


20.3 


15.6 


9.9 


6.7 


4.8 


3.6 


2.8 


1.7 


36 






499 
733 


243 
357 
499 
670 
871 


130 
205 
286 
383 
499 


88.2 

130 

181 

243 

316 


60.0 
88.2 
123 
165 
215 


43.0 
63.2 
88.2 
118 
154 


32.0 
47.0 
62.7 
88.2 
115 


24.6 
36.2 
50.5 
67.8 
88.2 


15.6 
19.0 
32.0 
43.0 
55.9 


10.6 
15.6 
21.8 
29.2 
38.0 


7.6 
11.2 
15.6 
20.9 
27.2 


5.7 
8.3 
11.6 
15.6 
20.3 


4.3 
6.4 
8.9 
12.0 
15.6 


2.8 


42 






4.1 


48 






5.7 


54 








7.6 


60 








9.9 



WIND. 

Force of the Wind. — Smeaton in 1759 published a table of the 
velocity and pressure of wind, as follows: 

Velocity and Force of Wind, in Founds per Square Inch. 



0)73 


45 * m 




I* 

1.47 






0.005 


2.93 


0.020 


4.4 


0.044 


5.87 


0.079 


7.33 


0.123 


8.8 


0.177 


10.25 


0.241 


11.75 


0.315 


13.2 


0.400 


14.67 


0.492 


17.6 


0.708 


20.5 


0.964 


22.00 


1.107 


23.45 


1.25 



Common Appella- 
tion of the 
Force of Wind. 



Hardly perceptible. 
Just perceptible. 



Gentle, pleasant 
wind. 



■ Pleasant, brisk gale 



m 3 


a 












S 03 


pmcu 


18 


26.4 


1.55 


20 


29.34 


1.968 


25 


36.67 


3.075 


30 


44.00 


4.429 


35 


51.34 


6.027 


40 


58.68 


7.873 


45 


66.01 


9.963 


50 


73.35 


12.30 


55 


80.7 


14.9 


60 


88.00 


17.71 


65 


95.3 


20.85 


70 


102.5 


24.1 


75 


110.00 


27.7 


80 


117.36 


31.49 


100 


146.67 


49.2 



Common Appella- 
tion of the 
Force of Wind. 



Very brisk. 
High wind. 
^Very high storm. 

Great storm. 

| Hurricane. 

I Immense hurri- 



598 air. 

The pressures per square foot in the above table correspond to the 
formula P — 0.005 V 2 , in which V is the velocity in miles per hour. 
Eng'g News, Feb. 9. 1893, says that the formula was never well established, 
and has floated chiefly on Smeaton's name and for lack of a better. It 
was put forward only for surfaces for use in windmill practice. The 
trend of modern evidence is that it is approximately correct only for such 
surfaces, and that for large, solid bodies it often gives greatly too large 
results. Observations by others are thus compared with Smeaton's 
formula: 

Old Smeaton formula • P = 0.005 V 2 

As determined by Prof. Martin P — 0.004 V 2 

" Whipple and Dines P = 0.0029 V 2 

At 60 miles per hour these formulas give for the pressure per square foot, 
18, 14.4, and 10.44 lbs., respectively, the pressure varying by all of them as 
the square of the velocity. Lieut. Crosby's experiments (Eng'g, June 13, 
1890), claiming to prove that P = fV instead of P = fV 2 , are discredited. 

Experiments by M. Eiffel on plates let fall from the Eiffel tower in Paris 
gave coefficients of V 2 ranging from 0.0027 for small plates to 0.0032 for 
plates 10 sq. ft. area. For plates larger than 10 sq. ft. the coefficient 
remained constant at 0.0032. — Eng'g, May 8, 1908. 

A. R. Wolff (" The Windmill as a Prime Mover," p. 9) gives as the theo- 
retical pressure per sq. ft. of surface, P = dQv/g, in which d = density of 

air in pounds per cu. ft. = — 'j-^- -; p being the barometric pres- 
sure per square foot at any level, and temperature of 32° F., t any 
absolute temperature, Q = volume of air carried along per square foot in 
one second, i> = velocity of the wind in feet per second, = 32.16. Since 
Q = v cu. ft. per sec, P=dv 2 /g. Multiplying this by a coefficient 0.93 
found by experiment, and substituting the above value of d, he obtains 

D 0.017431 X V A u o, 1CC ir, 

P = ,- - , and when p = 21 16.5 lb. per sq. ft., or average 

t x y-i*> _ . 018743 

V 2 

u ... .... i i r. 36.8929 

atmospheric pressure at the sea-level, P = . , an ex- 

UL^lb 

v 2 
pression in which the pressure is shown to vary with the temperature; 
and he gives a table showing the relation between velocity and pressure 
for temperatures from 0° to 100° F., and velocities from 1 to 80 miles per 
hour. For a temperature of 45° F. the pressures agree with those in 
Smeaton's table, for 0° F. they are about 10 per cent greater, and for 100°, 
10 per cent less. 

Prof. H. Allen Hazen, Eng'g News, July 5, 1890, says that experiments 
with whirling arms, by exposing plates to direct wind, and on locomotives 
with velocities running up to 40 miles per hour, have invariably shown the 
resistance to vary with V 2 . The coefficient of V 2 has been found in some 
experiments with very short whirling arms and low velocities to vary with 
the perimeter of the plate, but this entirely disappears with longer arms 
or straight line motion, and the only quection now to be determined is 
the value of the coefficient. Perhaps some of the best experiments for 
determining this value were tried in France in 1886 by carrying flat 
boards on trains. The resulting formula in this case was, for 44.5 miles 
per hour, p = 0.00535 SV 2 . 

Prof. Kernot, of Melbourne (Eng. Rec, Feb. 20, 1894), states that 
experiments at the Forth Bridge showed that the average pressure on sur- 
faces as large as railway carriages, houses, or bridges never exceeded two- 
thirds of that upon small surfaces of one or two square feet, and also that 
an inertia effect, which is frequently overlooked, may cause some forms 
of anemometer to give false results enormously exceeding the correct 
indication. Experiments made by Prof. Kernot at speeds varying from 
2 to 15 miles per hour agreed with the earlier authorities. The pressure 
upon one side of a cube, or of a block proportioned like an ordinary 
carriage, was found to be 0.9 of that upon a thin plate of the same area. 
The same result was obtained for a square tower. A square pyramid, 
whose height was three times its base, experienced 0.8 of the pressure 
upon a thin plate equal to one of its sides, but if an angle was turned to 



WINDMILLS. 599 

the wind the pressure was increased by fully 20%. A bridge consisting 
of two plate-girders connected by a deck at the top was found to expe- 
rience 0.9 of the pressure on a thin plate equal in size to one girder, when 
the distance between the girders was equal to their depth, and this was 
increased by one-fifth when the distance between the girders was double 
the depth. A lattice-work in which the area of the openings was 55% of 
the whole area experienced a pressure of 80% of that upon a plate of the 
same area. The pressure upon cylinders and cones was proved to be equal 
to half that upon the diametral planes, and that upon an octagonal prism 
to be 20% greater than upon the circumscribing cylinder. A sphere was 
subject to a pressure of 0.36 of that upon a thin circular plate of equal 
diameter. A hemispherical cup gave the same result as the sphere; when 
its concavity was turned to the wind the pressure was 1.15 of that on a 
flat plate of equal diameter. When a plane surface parallel to the direc- 
tion of the wind was brought nearly into contact with a cylinder or sphere, 
the pressure on the latter bodies was augmented by about 20%, owing to 
the lateral escape of the air being checked. Thus it is possible for the 
security of a tower or chimney to be impaired by the erection of a building 
nearly touching it on one side. 

Pressures of Wind Registered in Storms. — Mr. Frizell has examined 
the published records of Greenwich Observatory from 1849 to 1869, and 
reports that the highest pressure of wind he finds recorded is 41 lb. per 
sq. ft., and there are numerous instances in which it was between 30 and 
40 lb. per sq. ft. Prof. Henry says that on Mount Washington, N. H., a 
velocity of 150 miles per hour has been observed, and at New York City 
60 miles an hour, and that the highest winds observed in 1870 were of 72 
and 63 miles per hour, respectively. Lieut. Dunwoody, U. S. A., says, 
in substance, that the New England coast is exposed to storms which 
produce a pressure of 50 lb. per sq. ft. — Eng. News, Aug. 20, 1880. 

WINDMILLS. 

Power and Efficiency of Windmills. — Rankine, S. E., p. 215, gives 
the following: Let Q — volume of air which acts on the sail, or part of a 
sail, in cubic feet per second, v = velocity of the wind in feet per second, 
s = sectional area of the cylinder, or annular cylinder of wind, through 
which the sail, or part of the sail, sweeps in one revolution, c = a coeffi- 
cient to be found by experience; then Q =cvs. Rankine, from experi- 
mental data given by Smeaton, and taking c to include an allowance for 
friction, gives for a wheel with four sails, proportioned in the best manner, 
c = 0.75. Let A = weather angle of the sail at any distance from the 
axis, i.e., the angle the portion of the sail considered makes with its plane 
of revolution. This angle gradually diminishes from the inner end of the 
sail to the tip; u = the velocity of 'the same portion of the sail, and E = 
the efficiency. The efficiency is the ratio of the useful work performed to 
the whole energy of the stream of wind acting on the surface s of the wheel, 
which energy is D s v 3 ■*- 2 g, D being the weight of a cubic foot of air. 
Rankine's formula for efficiency is 

E -D^J2- 9 =C \l sin2 ^ -%V ~ COS2A + /) -/}, 

in which c = 0.75 and /is a coefficient of friction found from Smeaton's 
data = 0.016. Rankine gives the following from Smeaton's data: 

A = weather-angle =7° 13° 19° 

F-fi) = ratio of speed of greatest 
efficiency, for a given 
weather-angle, to that 

of the wind . . .' =2.63 1.86 1.41 

E = efficiency = . 24 . 29 0.31 

Rankine gives the following as the best values for the angle of weather 
at different distances from the axis: 

Distance in sixths of total radius 12 3 4 5 6 

Weather angle. . 18° 19° 18° 16° 121/2° 7° 

But Wolff (p. 125) shows that Smeaton did not term these the best 
angles, but simply says they "answer as well as any," possibly any that 



600 AIR. 



were in existence in his time. Wolff says that they " cannot in the nature 
of things be the most desirable angles." Mathematical considerations, 
he says, conclusively show that the angle of impulse depends on the 
relative velocity of each point of the sail and the wind, the angle growing 
larger as the ratio becomes greater. Smeaton's angles do not fulfil this 
condition. Wolff develops a theoretical formula for the best angle of 
weather, and from it calculates a table of the best angles for different 
relative velocities of the blades and the wind, which differ widely from 
those given by Rankine. 

A. R. Wolff, in an article in the American Engineer, gives the following 
(see also his treatise on Windmills) : 

Let c = velocity of wind in feet per second; 

n = number of revolutions of the windmill per minute; 

60. &it fo, b x be the breadth of the sail or blade at distances Z , h, It, 
l s , and I, respectively, from the axis of the shaft; 

Z = distance from axis of shaft to beginning of sail or blade proper. 

I = distance from axis of shaft to extremity of sail proper; 

Vo, vi, V2, v 3 , v x = the velocity of the sail in feet per second at dis- 
tances la, Zi, h, h, I, respectively, from the axis of the shaft; 

a , ai, <Z2, az, a x = the angles of impulse for maximum effect at dis- 
tances To, h, h, h, I, respectively, from the axis of the shaft; 

a = the angle of impulse when the sails or blocks are plane surfaces 
so that there is but one angle to be considered; 

N = number of sails or blades of windmill; 

K = 0.93; 

d = density of wind (weight of a cubic foot of air at average tem- 
perature and barometric pressure where mill is erected) ; 
W = weight of wind-wheel in pounds; 

/ = coefficient of friction of shaft and bearings; 

D = diameter of bearing of windmill in feet. 




The effective horse-power of a windmill with plane sails will equal 

- to) Kc* 
550 g 



(I - Z ) KcUN „ . ( I . vo V 

Xmean of j v (sin a cos a)b cos a 



/ v x \ 

r (sin a cos a) b x 



fWX 0.05236 nD 
l > ~ -550 



2 sin 2 a x - 1 n fw X 0.05236 nD . 
sin 2 a r °x) 550 



The effective horse-power of a windmill of shape of sail for maximum 
effect equals 

N (Z-Z )Kdc 3 v „/2sin 2 a -l, 2 sin 2 01 - 1 . 

• — n "' X mean of I r-^ 6 , — — ^— s 5i . . . 

2200 g \ sin 2 a sin 2 ai . 

in 2 a x - 1 v 

sin 2 a x b x)~ 

The mean value of quantities in brackets is to be found according to 
Simpson's rule. Dividing I into 7 parts, finding the angles and breadths 
corresponding to these divisions by substituting them in quantities within 
brackets will be found satisfactory. Comparison of these formulae with 
the only fairly reliable experiments in windmills (Coulomb's) showed a 
close agreement of results. 

Approximate formulae of simpler form for windmills of present con- 
struction can be based upon the above, substituting actual average values 
for a, c, d, and e, but since improvement in the present angles is possible, 
it is better to give the formulae in their general and accurate form. 

Wolff gives the following table, based on the practice of an American 
manufacturer. Since its preparation, he says, over 1500 windmills have 
been sold on its guaranty (1885), and in all cases the results obtained did 
not vary sufficiently from those presented to cause any complaint. The 
actual results obtained are in close agreement with those obtained by 
theoretical analysis of the impulse of wind upon windmill blades. 



WINDMILLS. 



601 









Capacity of 


the Windmill. 








_; 


a 


J 






h 


3.53 . 


i 


S? 


^ • 


Gallons of Water raised per Minute 


3 cS 


O 3 a)T3 


"8 


^W 


"s-s 




to an Elevation of 


a 
.2 


^S 










srage No. o 
er Day 
hich this 
ill be obta 


03 

a 




3 03 







— o o 




25 


50 


75 


100 


150 


200 


> 


ri 


feet. 


feet. 


feet. 


feet. 


feet. 


feet. 


> ft? P 
< 


wheel 






















81/2 ft. 
10 " 


16 
16 
16 


70 to 75 
60 to 65 
55 to 60 


6.162 
19.179 
33.941 


3.016 
9.563 
17.952 










0.04 
0.12 
0.21 


8 


6.638 
11.851 


4.750 
8.485 






8 


12 " 


5.680 




8 


14 " 


16 


50 to 55 


45.139 


22.569 


15.304 


11.246 


7.807 


4.998 


0.28 


8 


16 " 


16 


45 to 50 


64.600 


31.654 


19.542 


16.150 


9.771 


8.075 


0.41 


8 


18 " 


16 


40 to 45 


97.682 


52.165 


32.513 


24.421 


17.485 


12.211 


0.61 


8 


20 " 


16 


35 to 40 


124.950 


63.750 


40.800 


31.248 


19.284 


15.938 


0.78 


8 


25 " 


16 


30 to 35 


212.381 


106.964 


71.604 


49.725 


37.349 


26.741 


1.34 


8 



These windmills are made in regular sizes, as high as sixty feet diameter 
of wheel; but the experience with the larger class of mills is too limited to 
enable the presentation of precise data as to their performance. 

If the wind can be relied upon in exceptional localities to average a 
higher velocity for eight hours a day than that stated in the above table, 
the performance or horse-power of the mill will be increased, and can be 
obtained by multiplying the figures in the table by the ratio of the cube 
of the higher average velocity of wind to the cube of the velocity above 
recorded. 

He also gives the following table showing the economy of the windmill. 
All the items of expense, including both interest and repairs, are reduced 
to the hour by dividing the costs per annum by 365 X 8 = 2920; the 
interest, etc., for the twenty-four hours being charged to the eight hours of 
actual work. By multiplying the figures in the 5th column by 584, the 
first cost of the windmill, in dollars, is obtained. 

Economy of the Windmill. 







64 

11 
o o 
<i ft 

a Z . 


ige Number of 
rs per Day during 
h this Quantity 
be raised. 


Expense of Actual Useful Power 


4S 




1 
'js . 

03 o 

fe u 

r* 03 

«M ft 

o . 


Developed, in Cents, per Hour. 


Designe 
tion o: 
Mill. 


Interest on 
b Cost (First 
, including 

of Windmill, 
p, and Tower, 
oer Annum). 


Repairs and 
-eciation (5% 
irst Cost per 

am). 


I 

a 

03 
< 


O 

o 
to 


"3 
o 
H 


o . 




°c3 


■a o 




»^S c 


pto a 








S £ 2 




"3 

O 




33 Oj3 — 


fc.s o o3^ 


*< »Va 


to 






l aS 


wheel 




















81/2 f 


t. 370 


0.04 


8 


0.25 


0.25 


0.06 


0.04 


0.60 


15.0 


10 


' 1151 


0.12 


8 


0.30 


0.30 


0.06 


0.04 


0.70 


5.8 


12 


' 2036 


0.21 


8 


0.36 


0.36 


0.06 


0.04 


0.82 


5.9 


14 


' 2708 


0.28 


8 


0.75 


0.75 


0.06 


0.07 


1.63 


5.8 


16 


' 3876 


0.41 


8 


1.15 


1.15 


0.06 


0.07 


2.43 


5.9 


18 


' 5861 


0.61 


8 


1.35 


1.35 


0.06 


0.07 


2.83 


4.6 


20 


' 7497 


0.79 


8 


1.70 


1.70 


0.06 


0.10 


3.56 


4.5 


25 


4 12743 


1.34 


8 


2.05 


2.05 


0.06 


0.10 


4.26 


3.2 



12. 


16. 


20. 


25. 


30 


10.2 


19.3 


25.3 


28.1 


25 


20.2 


26.1 


28. 


27.5 




4.8 


12.7 


18.8 


23.3 


25 


6.2 


11.9 


14.7 


16. 





602 air. 

Prof. De Volson Wood (Am. Mach., Oct. 29, 1896) quotes some results 
by Thos. O. Perry on three wheels, each 5 ft. diam.: A, a good "stock" 
wheel, B and C, improved wheels. Each wheel was tested with a dyna- 
mometer placed 1 ft. from the axis of the wheel, and it registered a 
constant load at that point of 1.9 lbs. The velocity of the wind in each 
test was 8.45 miles per hour = 12.4 ft. per second. The number of turns 
per minute was: A, 30.67; B, 38.13; C, 56.50. The efficiency was: A, 
0.142; B, 0.176; C, 0.261. The work of wheel C was 674.5 ft. lb. per 
min. = 0.020 H.P. Assuming that the power increases as the square 
of the diameter and as the cube of the velocity, a wheel of the quality of 
C, 121/2 ft. diam., with a wind velocity of. 17 miles per hour, would be re- 
quired for 1 H.P.; but wheel C had an exceptionally high efficiency, and 
such a high delivery would not likely be obtained in practice. 

Prof. O. P. Hood (Am. Mach., April 22, 1897) quotes the following 
results of experiments by E. C. Murphy; the mills were tested by pumping 
water: 

Wind, miles per hour 

Strikes per min., Mill No. 1, 8-ft. wheel 
Strokes per min., Mill No. 2, 8-ft. wheel 
Strokes per min., Mill No. 3, 12-ft. wheel 
Strokes per min., Mill No. 4, 12-ft. wheel 

Mill No. 3 was loaded nearly 90% heavier than mill No. 4. 

In a 25-mile wind, seven 12-ft. mills developed, respectively, 0.379, 
0.291, 0.309, 0.6, 0.247, 0.219, and 0.184 H.P.; and five 8-ft. mills, 0.043, 
0.099, 0.059, 0.099, and 0.005 H.P. These effects include the effects of 
pumps of unknown and variable efficiency. The variations are largely 
due to the variable relation of the fixed load on the mill to the most 
favorable load which that mill might carry at each wind velocity. With 
each mill the efficiency is a maximum only for a certain load and a certain 
velocity, and for different loads and velocities the efficiency varies greatly. 
The useful work of mill No. 3 was equal to 0.6 H.P. in a 25-mile wind, 
and its efficiency was 5.8%. In a 16-mile wind the efficiency rose to 12.1%, 
and in a 12-mile wind it fell to 10.9%. The rule of the power developed, 
varying as the cube of the velocity, is far from true for a single wheel 
fitted with a single non-adjustable pump, and can only be true when the 
work of the pump per stroke is adjusted by varying the stroke of the 
pump, or by other means, for each change of velocity. 

R. M. Dyer (The Iowa Engineer, July, 1906: also Mach'y, Aug., 1907) 
gives a brief review of the history of windmills, and quotes experiments 
by T. O. Perry, E. C. Murphy, Prof. F. H. King, and the Aermotor Co. 
Mr. Perry's experiments are reported in pamphlet No. 20 of the Water 
Supply and Irrigation Papers of the U. S. Geological Survey, Mr. Murphy's 
in pamphlets Nos. 41 and 42 of the same Papers, and Prof. King's, in 
Bulletin No. 82 of the Agricultural Experiment Station of the University 
of Wisconsin. The Aermotor Co.'s experiments are described in catalogues 
of that company. Some of Mr. Dyer's conclusions are as follows: 

Experiments showed that 7/8 of the zone of interruption could be covered 
with sails ; that the gain in power in from 3/ 4 to 7/g of the surface, was so small 
that the use of the additional material was not justifiable; that the sail 
surface should extend only two-thirds the distance from the outer diam- 
eter to the center; that a wheel running behind the carrying mast is not 
nearly as efficient as one running in front of the mast; that there should 
be the least possible obstruction behind the wheel; that to be efficient 
the velocity of the travel of the vertical circumference of the wheel 
should be from 1 to IV4 times the velocity of the wind, hence the 
necessity of back gearing to reduce the pump speed to 40 strokes per 
minute as a maximum, which is the limit of safety at which ordinary 
pumps can be operated. 

I hold that no manufacturer will be able to produce a marketable 
motor which will absorb and deliver, when acted upon by an elastic fluid, 
like air, in which it is entirely surrounded and submerged, more than 
35% of the kinetic energy of the impinging current. 

Theoretical demonstrations show that the kinetic energy of the air, 
impinging on the intercepted area of a wheel, varies as the cube of the 
wind velocity; consequently, the power of windmills of the same type 



WINDMILLS. 603 

varies theoretically as the square of the diameter, and as the cube of the 
wind velocity; but as a wheel is designed to give its best efficiency in low 
winds, say 10 to 15 miles per hour, we cannot expect that the same 
angle of sail would obtain the same percentage of efficiency in winds of 
considerably higher velocity. 

The ordinary wheel works most efficiently under wind velocities of from 
10 to 12 miles per hour; such wheels will give reasonable efficiency in from 
5- to 6-mile winds, while, if the wind blows more than 12 miles per hour, 
there will be power to spare. Our wheel must work in light winds, such 
being nearly always present, while the higher velocities only occur at 
intervals. Mills built for grinding purposes, or geared mills, will develop 
power almost approaching to the cube of the wind velocity, within reason- 
able limits, as their speed need not be kept down to a certain number of 
revolutions per minute, as in the case of the pumping mill. 

Should this theoretic condition hold, the following table, showing the 
amount of power for different sizes of mills at different wind velocities, 
would apply: Figures show Horse Power. 

5 10 15 20 25 30 35 40 

Size. mile. mile. mile. mile. mile. mile. mile. mile. 

8ft 0.0110.088 0.297 0.704 1.375 2.176 

12ft 0.025 0.20 0.675 1.6 3.125 5.4 8.57 12.8 

16 ft 0.045 0.36 1.215 2.88 5.52 9.75 15.3 21.04 

These figures have been proven by laboratory tests at velocities ranging 
from 10 to 25 miles per hour and more practically by the Murphy tests on 
mills actually in use, which show very close relation at the wind velocities 
at which the mills are best adapted. 

The Murphy figures are as follows: 



Size of mill. 


10 mile. 


15 mile. 


20 mile. 


12 ft. 


0.21 H.P. 


0.58 H.P. 


1.05 H.P. 


16 ft. 


0.29 


0.82 


1.55 



For higher wind velocities the Murphy values fall much under the 
theoretical values, but the range of velocities over which his experiments 
extend does not justify any change in the general law except inasmuch 
as common sense teaches us that theoretic conditions can rarely be 
attained in actual practice. 

In view of the fact that a windmill does not work as efficiently in high 
winds as in winds under 20 miles per hour my experience would lead me 
to believe that the following figures (H.P.) would be the probable exten-. 
sion of the Murphy tests: 

ck™ ~t ™ni 25-mile 30-mile 35-mile 40-mile 

Size ot mill. wind wind ^^ ^jncL 

12 ft. 2.5 4 5 6 

16 ft. 4. 6 8 10 

A 20-ft. mill would deliver approximately 50% greater than a 16-ft. 

The foregoing table must be translated with reasonable allowances for 
conditions under which wind wheels must work and which cannot well 
be avoided, e.g: Pumping mills must be made to regulate off at a certain 
maximum speed to prevent damage to the attached pumping devices. 
The regulating point is usually between 20- and 25-mile wind velocities, 
so that no matter how much higher the wind velocity may be the power 
absorbed and delivered by the wheel will be no greater than that indicated 
at the regulating point. 

Electric storage and lighting from the power of a windmill has been 
tested on a large scale for several years by Charles F. Brush, at Cleveland, 
Ohio. In 1887 he erected on the grounds of his dwelling a windmill 56 ft. 
in diameter, that operates with ordinary wind a dynamo at 500 revolutions 
per minute, with an output of 12,000 watts — 16 electric horse-power — 
charging a storage system that gives a constant lighting capacity of 100 
16 to 20 candle-power lamps. The current from the dynamo is auto- 



604 



matically regulated to commence charging at 330 revolutions and 70 volts, 
and cutting the circuit at 75 volts. Thus, by its 24 hours' work, the 
storage system of 408 cells in 12 parallel series, each cell having a capacity 
of 100 ampere-hours, is kept in constant readiness for all the requirements 
of the establishment, it being fitted up with 350 incandescent lamps, 
about 100 being in use each evening. The plant runs at a mere nominal 
expense for oil, repairs, and attention. (For a fuller description of this 

Elant, and of a more recent one at Marblehead Neck, Mass., see Lieut. 
ewis's paper in Engineering Magazine, Dec, 1894, p. 475.) 



COMPRESSED AIR. 

Heating of Air by Compression. — Kimball, in his treatise on Physi- 
cal Properties of Gases, says: When air is compressed, all the work which 
is done in the compression is converted into heat, and shows itself in the 
rise in temperature of the compressed gas. In practice many devices are 
employed to carry off the heat as fast as it is developed, and keep the tem- 
perature down. But it is not possible in any way to totally remove this 
difficulty. But, it may be objected, if all the work done in compression is 
converted into heat, and if this heat is got rid of as soon as possible, then 
the work may be virtually thrown away, and the compressed air can have 
no more energy than it had before compression. It is true that the com- 
pressed gas has no more energy than the gas had before compression, if 
its temperature is no higher, but the advantage of the compression lies in 
bringing its energy into more available form. 

The total energy of the compressed and uncompressed gas is the same 
at the same temperature, but the available energy is much greater in the 
former. 

When the compressed air is used in driving a rock-drill, or any other 
piece of machinery, it gives up energy equal in amount to the work it does, 
and its temperature is accordingly greatly reduced. 

Causes of Loss of Energy in Use of Compressed Air. (Zahner, on 
Transmission of Power by Compressed Air.) — 1. The compression of 
air always develops heat, and as the compressed air always cools down to 
the temperature of the surrounding atmosphere before it is used, the 
mechanical equivalent of this dissipated heat is work lost. 

2. The heat of compression increases the volume of the air, and hence 
it is necessary to carry the air to a higher pressure in the compressor in 
order that we may finally have a given volume of air at a given pressure, 
and at the temperature of the surrounding atmosphere. The work spent 
in effecting this excess of pressure is work lost. 

3. Friction of the air in the pipes, leakage, dead spaces, the resistance 
offered by the valves, insufficiency of valve-area, inferior workmanship, 
and slovenly attendance, are all more or less serious causes of loss of 
power. 

The first cause of loss of work, namely, the heat developed by compres- 
sion, is entirely unavoidable. The whole of the mechanical energy which 
the compressor-piston spends upon the air is converted into heat. This 
heat is dissipated by conduction and radiation, and its mechanical equiva- 
lent is work lost. The compressed air, having again reached thermal 
equilibrium with the surrounding atmosphere, expands and does work in 
virtue of its intrinsic energy. 

The intrinsic energy of a fluid is the energy which it is capable of exert- 
ing against a piston in changing from a given state as to temperature and 
volume to a total privation of heat and indefinite expansion. 

Adiabatic and Isothermal Compression. — Air may be compressed 
either adiabatically , in which all the heat resulting from compression is 
retained in the air compressed, or isothermally , in which the heat is removed 
as rapidly as produced, by means of some form of refrigerator. 



COMPRESSED AIR. 



605 



Volumes, Mean Pressures per Stroke, Temperatures, etc., In the 
Operation of Air-compression from 1 Atmosphere and 60° Fahr. 

(F. Richards, Am. Mach., March 30, 1893.) 



































i- a 




o s 


<D O 


o 






"3 a 




© a 


<D O 




e 




<% 


< 


ft o 


as 


a 


o3 




§ 


< 


ft o 


as. 


3 


3 


0) 


^H 


jH-13 


2 


£ u 


17 


3 


<2 


*& 


u 

I s 

o 
> 


£ 


2 *-> 


'£ 


6 

h 
bo 

3 

o 


n 

o 

a 
3 




P o 

"o 


u <o 




ol 

.o 

a 

a 


a3 

i 

bfl 
3 

s 


-3 

a 



a 
< 


'^1 

a§ 


Oh 'oT H 

all 


5p 

flgo 


a 

a 


1 


2 


3 


4 


5 


6 


7 


1 

80 


2 


3 


4 


5 


6 


7 





1 


1 


1 








60° 


6.442 


.1552 


.266 


27.38 


36.64 


432 


1 


1.068 


.9363 


.95 


.96 


.975 


71 


85 


6.782 


.1474 


.2566 


28.16 


37.94 


447 


2 


1. 136 


.8803 


.91 


J. 87 


1.91 


80.4 


90 


7.122 


.1404 


.248 


28.89 


39.18 


459 


3 


1.204 


.8305 


.876 


2.72 


2.8 


88.9 


95 


7.462 


.134 


.24 


29.57 


40.4 


472 


4 


1.272 


.7861 


.84 


3.53 


3.67 


98 


100 


7.802 


.1281 


.2324 


30.21 


41.6 


485 


5 


1.34 


.7462 


.81 


4.3 


4.5 


106 


105 


8.142 


.1228 


.2254 


30.81 


42.78 


496 


10 


1.68 


.5952 


.69 


7.62 


8.27 


145 


110 


8.483 


.1178 


.2189 


31.39 


43.91 


507 


15 


2.02 


.495 


.606 


10.33 


11.51 


178 


115 


8.823 


.1133 


.2129 


31.98 


44.98 


518 


20 


2.36 


.4237 


.543 


12.62 


14.4 


207 


120 


9.163 


.1091 


.2073 


32.54 


46.04 


529 


25 


2.7 


.3703 


.494 


14.59 


17.01 


234 


125 


9.503 


.1052 


.2020 


33.07 


47.06 


540 


30 


3.04 


.3289 


.4538 


16.34 


19.4 


252 


130 


9.843 


.1015 


.1969 


33.57 


48.1 


550 


35 


3.381 


.2957 


.42 


17.92 


21.6 


281 


135 


10.183 


.0981 


.1922 


34.05 


49.1 


560 


40 


3.721 


.2687 


.393 


19.32 


23.66 


302 


140 


10.523 


.095 


.1878 


34.57 


50.02 


570 


45 


4.061 


.2462 


.37 


20.57 


25.59 


321 


145 


10.864 


.0921 


.1837 


35.09 


51. 


580 


50 


4.401 


.2272 


.35 


21.69 


27.39 


339 


150 


11.204 


.0892 


.1796 


35.48 


51.89 


589 


55 


4.741 


.2109 


.331 


22.76 


29.11 


357 


160 


11.88 


.0841 


.1722 


36.29 


53.65 


607 


60 


5.081 


.1968 


.3144 


23.78 


30.75 


375 


170 


12.56 


.0796 


.1657 


37.2 


55.39 


624 


65 


5.422 


.1844 


.301 


24.75 


32.32 


389 


180 


13.24 


.0755 


.1595 


37.96 


57.01 


640 


70 


5.762 


.1735 


.288 


25.67 


33.83 


405 


190 


13.93 


.0718 


.154 


38.68 


58.57 


657 


75 


6.102 


.1639 


.276 


26.55 


35.27 


420 


200 


14.61 


.0685 


.149 


39.42 


60.14 


672 



Column 3 gives the volume of air after compression to the given pressure 
and after it is cooled to its initial temperature. After compression air 
loses its heat very rapidly, and this column may be taken to represent the 
volume of air after compression available for the purpose for which the 
air has been compressed. 

Column 4 gives the volume of air more nearly as the compressor has to 
deal with it. In any compressor the air will lose some of its heat during 
compression. The slower the compressor runs the cooler the air and the 
smaller the volume. 

Column 5 gives the mean effective resistance to be overcome by the air- 
cylinder piston in the stroke of compression, supposing the air to remain 
constantly at its initial temperature. Of course it will not so remain, but 
this column is the ideal to be kept in view in economical air-compression. 

Column 6 gives the mean effective resistance to be overcome by the pis- 
ton, supposing that there is no cooling of the air. The actual mean effec- 
tive pressure will be somewhat less than as given in this column; but for 
computing the actual power required for operating air-compressor cylin- 
ders, the figures in this column may be taken and a certain percentage 
added — say 10 per cent — and the result will represent very closely the 
power required by the compressor. 

The mean pressures given being for compression from one atmosphere 
upward, they will not be correct for computations in compound com- 
pression or for any other initial pressure. 



606 



AIR. 



Loss due to Excess of Pressure caused by Heating in the Com- 
pression-cylinder. — If the air during compression were kept at a con- 
stant temperature, the compression-curve of an indicator-diagram taken 
from the cylinder would be an isothermal curve, and would follow the law 

of Boyle and Mariotte, pv = a constant, or pm = p v , or pi = p — , pct'o 

being the pressure and volume at the beginning of compression, and 
P1V1 the pressure and volume at the end, or at any intermediate point. 
But as the air is heated during compression the pressure increases faster 
than the volume decreases, causing the work required for any given pres- 
sure to be increased. If none of the heat were abstracted by radiation or 
by injection of water, the curve of the diagram would be an adiabatic 



curve, with the equation p\ ■■- 



°©r 



Cooling the air during com- 



pression, or compressing it in two cylinders, called compounding, and 
cooling the air as it passes from one cylinder to the other, reduces the 
exponent of this equation, and reduces the quantity of work necessary to 
effect a given compression. F. T. Cause (Am. Mach., Oct. 20, 1892), 
describing the operations of the Popp air-compressors in Paris, says: 
The greatest saving realized in compressing in a single cylinder was 33 per 
cent of that theoretically possible. In cards taken from the 2000 H.P. 
compound compressor at Quai De La Gare, Paris, the saving realized is 
85 per cent of the theoretical amount. Of this amount only 8 per cent is 
due to cooling during compression, so that the increase of economy in the 
compound compressor is mainly due to cooling the air between the two 
stages of compression. A compression-curve with exponent 1.25 is the 
best result that was obtained for compression in a single cylinder and 
cooling with a very fine spray. The curve with exponent 1.15 is that 
which must be realized in a single cylinder to equal the present economy 
of the compound compressor at Quai De La Gare. 



Horse-power required to com- 
press and deliver One Cubic Foot 
6t Free Air per minute to a given 
pressure with no cooling of the air 
during the compression; also the 
horse power required, supposing the 
air to be maintained at constant 
temperature during the compression. 



Gauge- 


Air not 


pressure. 


cooled. 


5 


0.0196 


10 


0.0361 


20 


0.0628 


30 


0.0846 


40 


0.1032 


50 


0.1195 


60 


0. 1342 


70 


0.1476 


80 


0.1599 


90 


0.1710 


100 


0.1815 



H.P. required to compress and 
deliver One Cubic Foot of Com- 
pressed Air per minute at a given 
pressure (the air being measured at 
the atmospheric temperature) with 
no cooling of the air during the 
compression; also supposing the air 
to be maintained at constant tem- 
perature during the compression. 



Gauge- 


Air not 


Air constant 


pressure. 


cooled. 


temperature 


5 


0.0263 


0.0251 


10 


0.0606 


0.0559 


20 


0.1483 


0.1300 


30 


0.2573 


0.2168 


40 


0.3842 


0.3138 


50 


0.5261 


0.4166 


60 


0.6818 


0.5266 


70 


0.8508 


0.6456 


80 


1.0302 


0.7700 


90 


1.2177 


0.8979 


100 


1.4171 


1.0291 



Air constant 
temperature. 

0.0188 

0.0333 

0.0551 

0.0713 

0.0843 

0.0946 

0.1036 

0.1120 

0.1195 

0.1261 

0.1318 

The horse-power given above is the theoretical power, no allowance 
being made for friction of the compressor or other losses, which may 
amount to 10 per cent or more. 

Formulae for Adiabatic Compression or Expansion of Air (or 
Other Sensibly Perfect Gas). 

Let air at an absolute temperature Ti, absolute pressure pi, and volume 
vi be compressed to an absolute pressure pi and corresponding volume v% 
and absolute temperature Tr, or let compressed air of an initial pressure, 
volume, and temperature pi, Vt, and Ti be expanded to pi, vi, and Tk, there 
being no transmission of heat from or into the air during the operation. 



COMPRESSED AIR. 607 

Then the following equations express the relations between pressure, 
volume, and temperature (see works on Thermodynamics): 



vi = /P2\ 071 . P2 = MV- 41 . vi = /TjV- 

V2 \Pl) ' pX \V2/ ' V2 \tJ 

T2 _ M\°-« Tj. _ /P2\°-- 9 V2 = (T2\ 3 

Ti W ' Tx \px) ' px \tJ 



The exponents are derived from the ratio c^. -*- c v = k of the specific 
heats of air at constant pressure and constant volume. Taking k = 
1.406, I -r- fe= 0.711; l-'l= 0.406; 1 4- (k - 1) = 2.463; fc ■*■ 
(ft - 1) = 3.463; (k - 1) -j- k = 0.289. 

Work of Adiabatic Compression of Air. — If air is compressed in a 
cylinder without clearance from a volume vi and pressure px to a smaller 
volume V2 and higher pressure p>, work equal to pxVx is done by the external 
air on the piston while the air is drawn into the cylinder. Work is then 
done by the piston on the air, first, in compressing it to the pressure pa 
and volume V2, and then in expelling the volume V2 from the cylinder 

against the pressure p 2 . If the compression is adiabatic, p t Vi — P2V2 — 
constant, k = 1.406. 

The work of compression of a given quantity of air is 

PiVi \ tyA*- 1 _ -, j _ Ptvi J (PA k I , 

k-ll Kvz) ) ~ k - 1 | W ) 

2.463 Vl vx { g) 041 - 1 } = 2.463 ft* { (f)^- 1 } • 
The work of expulsion is P2V2 = PxVx I 



The total work is the sum of the work of compression and expulsion less 
the work done on the piston during admission, and it equals 



pwx 



ffective pressure during the stroke is 



px and P2 are absolute pressures above a vacuum in atmospheres or in 
pounds per square inch or per square foot. 

Example. — Required the work done in compressing 1 cubic foot of 
air per second from 1 to 6 atmospheres, including the work of expulsion 
from the cylinder. 

P2 ■*• px = 6; 6 029 - 1 = 0.681; 3.463 X 0.681 = 2.358 atmospheres 
X 14.7 = 34.661b. per sq. in. mean effective pressure, X 144 = 4991 lb. 
per sq. ft., XI ft. stroke =4991 ft .-lb.,-*- 550 ft.-lb. per second = 9.08 H.P. 

If R = ratio of pressures = P2 + Px, and if Vi = 1 cubic foot, the work 
done in compressing 1 cubic foot from px to P2 is, in foot-pounds, 

3.463 Pi (E 029 - 1), 

Px being taken in lb. per sq. ft. For compression at the sea level Pi may 
be taken at 14 lbs. per sq. in. = 2016 lb. per sq. ft., as there is some loss 
of pressure due to friction of valves and passages. 

Horse-power required to compress and deliver 100 cubic feet of free air 
per minute = 1.511 P t (E°- 29 - 1); P x being the pressure of the free air in 
pounds per sq. in., absolute. 

Example. To compress 100 cu. ft. from 1 to 6 atmospheres. Fi = 1.47; 
R = 6; 1.511 X 14.7 X 0.68.1 = 15.13 H.P. 



608 air. 



Indicator-cards from compressors in good condition and under working* 
speeds usually follow the adiabatic line closely. A low curve indicates 
piston leakage. Such cooling as there may be from the cylinder-jacket 
and the re-expansion of the air in clearance-spaces tends to reduce the 
mean effective pressure, while the "camel-backs" in the expulsion-line, 
due to resistance to opening of the discharge-valve, tend to increase it. 

Work of one stroke of a compressor, with adiabatic compression, in foot- 
pounds, 

W = 3.463 P1V1 (R - 29 - 1), 

in which P t ■= initial absolute pressure in lb. per sq. ft., and V t = volume 
traversed by piston in cubic feet. 

The work done during adiabatic compression (or expansion) of 1 pound 
of air from a volume vi and pressure p\ to another volume vi and pressure 
Vi is equal to the mechanical equivalent of the heating (or cooling). If 
t\ is the higher and fa the lower temperature, Fahr., the work done is 
c v J (ti — k) foot-pounds, c v being the specific heat of air at constant 
volume = 0.1689, and J = 778, c v J = 131.4. 

The work during compression also equals 

R a being the value of pv •*- absolute temperature for 1 pound of air =■ 
53.37. 

The work during expansion is 

2.463 ** [l -(g)" 29 ] - 2.463 «, [(g) °' 2 " - l], 

in which pivi are the initial and P2V2 the final pressures and volumes. 
Compressed-air Engines, Adiabatic Expansion. — Let the initial 

pressure and volume taken into the cylinder be p x lb. per sq. ft. and v x 
cubic feet; let expansion take place to pi and vi according to the adiabatic 
law pivi 1 - 41 = P2V2 1 - il ; then at the end of the stroke let the pressure drop 
to the back-pressure p 3 , at which the air is exhausted. Assuming no 
clearance, the work done by one pound of air during admission, measured 

above vacuum, is pm, the work during expansion is 2.463 piVi 1 — 

(p 2 \ 0.29-1 
— J , and the negative or back pressure work is — p 3 V2. The total 

work is piVi + 2.463 PtVi 1 — (— J — p 3 V2, and the mean effective pres- 

sure is the total work divided by v%. 

If the air is expanded down to the back-pressure pz the total work is 

3.463^, { 1 -(g) 0!9 }, 

or, in terms of the final pressure and volume, 

3.463^2 {(g) 029 -l}. 
and the mean effective pressure is 

3.463 P3 {(g)°;%l}. 

The actual work is reduced by clearance. When this is considered, the 
product of the initial pressure pi by the clearance volume is to be sub- 
tracted from the total work calculated from the initial volume vi, including 
clearance. (Seep. 931, under "Steam-engine.") 



COMPRESSED AIR. 



609 



Mean Effective Pressures of Air Compressed Adiabatically. 

(F. A. Halsey, Am. Mach., Mar. 10, 1898.) 







M.E.P. from 






M.E.P. from 


R. 


P> 29 . 


14 lbs. 
Initial. 


R. 


fio.29. 


14 lbs. 
Initial. 


1.25 


1.067 


3.24 


4.75 


1.570 


27.5 


1.50 


1.125 


6.04 


5 


1.594 


28.7 


1.75 


1.176 


8.51 


5.25 


1.617 


29.8 


2 


1.223 


10.8 


5.5 


1.639 


30.8 


2.25 


1.265 


12.8 


5.75 


1.660 


31.8 


2.5 


1.304 


14.7 


6 


1.681 


32.8 


2.75 


1.341 


16.4 


6.25 


1.701 


33.8 


3 


1.375 


18.1 


6.5 


1.720 


34.7 


3.25 


1.407 


19.6 


6.75 


1.739 


35.6 


3.5 


1.438 


21.1 


7 


1.757 


36.5 


3.75 


1.467 


22.5 


7.25 


1.775 


37.4 


4 


1.495 


23.9 


7.5 


1.793 


38.3 


4.25 


1.521 


25.2 


8 


1.827 


39.9 


4.5 


1.546 


26.4 









R = final -4- initial absolute pressure. 

M.E.P. = mean effective pressure, lb. per sq. in., based on 14 lb. initial. 

Compound Compression, with Air Cooled between the Two Cyl- 
inders. (Am. Mach., March 10 and 31, 1898.) — Work in low-pressure 
cylinder = W\, in high-pressure cylinder W 2 . Total work 

Wt + W 2 = 3.46 PiVt [rjO-29 + #0.29 x r t -<■■» - 2]. 
ri = ratio of pressures in 1. p. cyl., r 2 = ratio in h.p. cyl., R = nr 2 . When 
n = r 2 = Vp, the sum W t + W 2 is a minimum. Hence for a given total 
ratio of pressures, R, the work of compression, will be least when the ratios 
of the pressures in each of the two cylinders are equal. 

The equation may be simplified, when r x = ^R, to the following: 
Wi + W 2 = 6.92 PiFi [fl°-»5 _ i]. 
Dividing by V t gives the mean effective pressure reduced to the low- 
pressure cylinder M.E.P. = 6.92 P x [i2°-i« - 1]. 

In the above equation the compression in each cylinder is supposed to 
be adiabatic, but the intercooler is supposed to reduce the temperature 
of the air to that at which compression began. 

Horse-power required to compress adiabatically 100 cu. ft. of free air 
per minute in two stages with intercooling, and with equal ratio of com- 

Rression in each cylinder, = 3.022 P x (R° 145 — 1); Pi being the pressure in 
)s. per sq. in., absolute, of the free air, and R the total ratio of compression. 
Example. To compress 100 cu. ft. per min. from 1 to 6 atmospheres, 
P = 14.7; R = 6; 3.022 X 14.7 X 0.2964 = 13.17 H.P. 

Mean Effective Pressures of Air Compressed in Two Stages, assum- 
ing the Intercooler to Reduce the Temperature to that at which 
Compression Began. (F. A. Halsey, Am. Mach., Mar. 31, 1898.) 



R. 


#0.145. 


M.E.P. 
from 
14 lbs. 

Initial. 


Ultimate 
Saving 

by Com- 
pound- 
ing, %. 


R. 


#0.145. 


M.E.P. 

from 
14 lbs. 
Initial. 


Ultimate 
Saving 

by Com- 
pound- 
ing, %. 


5.0 


1 .263 


25.4 


11.5 


9.0 


1.375 


36.3 


15.8 


5.5 


1.280 


27.0 


12.3 


9.5 


1.386 


37.3 


16.2 


6.0 


1.296 


28.6 


12.8 


10 


1.396 


38.3 


16.6 


6.5 


1.312 


30.1 


13.2 


11 


1.416 


40.2 


17.2 


7.0 


1.326 


31.5 


13.7 


12 


1.434 


41.9 


17.8 


7.5 


1.336 


32.8 


14.3 


13 


1.451 


43.5 


18.4 


8.0 


1.352 


34.0 


14.8 


14 


1.466 


45.0 


19.0 


8.5 


1.364 


35.2 


15.3 


15 


1.481 


46.4 


19.4 



610 



AIR. 



R = final -*■ initial absolute pressure. 

M.E.P. = mean effective pressure, lb. per sq. in., based on 14 lb. absolute 
Initial pressure reduced to the low-pressure cylinder. 

Table for Adiabatic Compression or Expansion of Air. 

(Proc. Inst. M.E., Jan., 1881, p. 123.) 



Absolute Pressure. 


Absolute Temperature. 


Volume. 


Ratio of 


Ratio of 


Ratio of 


Ratio of 


Ratio of 


Ratio of 


Greater 


Less to 


Greater 


Less to 


Greater 


Less to 


to Less. 


Greater. 


to Less. 


Greater. 


to Less. 


Greater. 


(Expan 


(Compres 


(Expan- 


(Compres- 


(Compres- 


(Expan- 


sion.) 


sion.) 


sion.) 


sion.) 


sion.) 


sion.) 


1.2 


0.833 


1.054 


0.948 


1.138 


0.879 


1.4 


0.714 


1.102 


0.907 


1.270 


0.788 


1.6 


0.625 


1.146 


0.873 


1.396 


0.716 


1.8 


0.556 


1.186 


0.843 


1.518 


0.659 


2.0 


0.500 


1.222 


0.818 


1.636 


0.611 


2.2 


0.454 


1.257 


0.796 


1.750 


0.571 


2.4 


0.417 


1.289 


0.776 


1.862 


0.537 


2.6 


0.385 


1.319 


0.758 


1.971 


0.507 


2.8 


0.357 


1.348 


0.742 


2.077 


0.481 


3.0 


0.333 


1.375 


0.727 


2.182 


0.458 


3.2 


0.312 


1.401 


0.714 


2.284 


0.438 


3.4 


0.294 


1.426 


0.701 


2.384 


0.419 


3.6 


0.278 


1.450 


0.690 


2.483 


0.403 


3.8 


0.263 


1.473 


0.679 


2.580 


0.388 


4.0 


0.250 


1.495 


0.669 


2.676 


0.374 


4.2 


0.238 


1.516 


0.660 


2.770 


0.361 


4.4 


0.227 


1.537 


0.651 


2.863 


0.349 


4.6 


0.217 


1.557 


0.642 


2.955 


0.338 


4.8 


0.208 


1.576 


0.635 


3.046 


0.328 


5.0 


0.200 


1.595 


0.627 


3.135 


0.319 


6.0 


0.167 


1.681 


0.595 


3.569 


0.280 


7.0 


0.143 


1.758 


0.569 


3.981 


0.251 


8.0 


0.125 


1.828 


0.547 


4.377 


0.228 


9.0 


0.111 


1.891 


0.529 


4.759 


0.210 


10.0 


0.100 


1.950 


0.513 


5.129 


0.195 



Mean Effective Pressures for the Compression Part only of the 
Stroke when Compressing and Delivering Air from One Atmos- 
phere to given Gauge-pressure in a Single Cylinder. (F. Richards, 
Am. Mach., Dec. 14, 1893.) 



Gauge- 


Adiabatic 


Isothermal 


Gauge- 


Adiabatic 


Isothermal 


Pressure. 


Compression. 


Compression. 


Pressure. 


Compression. 


Compression. 


1 


0.44 


0.43 


45 


13.95 


12.62 


2 


0.96 


0.95 


50 


15.05 


13.48 


3 


1.41 


)4 


55 


15.98 


14.3 


4 


1.86 


1.84 


60 


16.89 


15.05 


5 


2.26 


2.22 


65 


17.88 


15.76 


10 


4.26 


4.14 


70 


18.74 


16.43 


15 


5.99 


5.77 


75 


19.54 


17.09 


20 


7.58 


7.2 


80 


20.5 


17.7 


25 


9.05 


8.49 


85 


21.22 


18.3 


30 


10.39 


9.66 


90 


22.0 


18.87 


35 


11.59 


10.72 


95 


22.77 


19.4 


40 


12.8 


11.7 


100 


23.43 


19.92 



AIR COMPRESSION AT ALTITUDES. 



611 



The mean effective pressure for compression only is always lower than 
the mean effective pressure for the whole work. 

To find the Index of the Curve of an Air-diagram. If PiVx be 
pressure and volume at one point on the curve, and PV the pressure and 

volume at another point, then -=- = {r/) > in which x is the index to be 

found. Let P + Pi = R, and Vi -*■ V = r; then R = r x ; log R =x log r, 

whence x = log R -s- log r. (See also graphic method on page 576.) 

Mean and Terminal Pressures of Compressed Air used Expansively 
for Gauge Pressures from 60 to 100 lb. 

(Frank Richards, Am. Mach., April 13, 1893.) 



J 










Initial Pressure. 








60 


70 


80 


90 


100 


o 
M 

'o 


3 2 

§ ft 


H ft 


gft 


"c3 ® 


i 6 
la 


*3 g 

H ft 


6 

dig 

§^g 

ft 


"3 ai 
H ft 




"3 ? 

w 


.25 


23.6 


io.es 


28.74 


12.07 


33.89 


JS.49 


39.04 


14.91 


44.19 


1.33 


.30 


28.9 


13.77 


34.75 


0.6 


40.61 


2.44 


46.46 


4.27 


53.32 


6.11 


# 


32.13 


0.96 


38.41 


3.09 


44.69 


5.22 


50.98 


7.35 


57.26 


9.48 


.35 


33.66 


2.33 


40.15 


4.38 


46.64 


6.66 


53.13 


8.95 


59.62 


11.23 


1 


35.85 


3.85 


42.63 


6.36 


49.41 


7.88 


56.2 


11.39 


62.98 


13.89 


.40 


37.93 


5.64 


44.99 


8.39 


52.05 


11.14 


59.11 


13.88 


66.16 


16.64 


.45 


41.75 


10.71 


49.31 


12.61 


56.9 


15.86 


64.45 


19.11 


72.02 


22.36 


.50 


45.14 


13.26 


53.16 


17. 


61.18 


20.81 


69.19 


24.56 


77.21 


28.33 


.60 


50.75 


21.53 


59.51 


26.4 


68.28 


31.27 


77.05 


36.14 


85.82 


41.01 


* 


51.92 


23.69 


60.84 


28.85 


69.76 


34.01 


78.69 


39.16 


87.61 


44.32 


.!• 


53.67 


27.94 


62.83 


33.03 


71.99 


38.68 


81.14 


44.33 


90.32 


49.97 


54.93 


30.39 


64.25 


36.44 


73.57 


42.49 


82.9 


48.54 


92.22 


54.59 


.75 


56.52 


35.01 


66.05 


41.68 


75.59 


48.35 


85.12 


55.02 


94.66 


61.69 


.80 


57.79 


39.78 


67.5 


47.08 


77.2 


54.38 


86.91 


61.69 


96.61 


68.99 


Jo 


59.15 


47.14 


69.03 


55.43 


78.92 


63.81 


88.81 


72. 


98.7 


80.28 


59.46 


49.65 


69.38 


58.27 


79.31 


66.89 


89.24 


75.52 


99.17 


87.82 



Pressures in italics are absolute; all others are gauge pressures. 

AIR COMPRESSION AT ALTITUDES. 

(Ingersoll-Rand Co. Copyright, 1906, by F. M. Hitchcock.) 

Multipliers to Determine the Volume of Free Air which, when 

Compressed, is Equivalent in Effect to a Given Volume of Free 

Air at Sea Level. 



Alti- 


Barometric 
Pressure. 


Gauge Pressure (Pounds). 




tude, 
Feet. 












In. of 
Mercury. 


Lb. per 
Sq. In. 


60 


80 


100 


125 


150 


1,000 


28.88 


14.20 


1.032 


1.033 


1.034 


1.035 


1.036 


2,000 


27.80 


13.67 


1.064 


1.066 


1.068 


1.071 


1.072 


3,000 


26.76 


13.16 


1.097 


1.102 


1.105 


1.107 


1.109 


4,000 


25.76 


12.67 


1 .132 


1.139 


1.142 


1.147 


1.149 


5,000 


24.79 


12.20 


1.168 


1.178 


1.182 


1.187 


1.190 


6,000 


23.86 


11.73 


1.206 


1.218 


1.224 


1.231 


1.234 


7,000 


22.97 


11.30 


1.245 


1.258 


1.267 


1.274 


1.278 


8,000 


22.11 


10.87 


1.287 


1.300 


1.310 


1.319 


1.326 


9,000 


21.29 


10.46 


1.329 


1.346 


1.356 


1.366 


1.374 


10,000 


20.49 


10.07 


1.373 


1.394 


1.404 


1,416 


1.424 



612 



Horse-power Developed in Compressing One Cubic Foot of Free Air 
at Various Altitudes from Atmospheric to Various Pressures. 

Initial Temperature of the Air in Each Cylinder Taken as 60° F.; Jacket 
Cooling not Considered ; Allowance made for usual losses. 





Simple Compression. 


Two Stage Compression. 


Altitude, 
Feet. 


Gauge Pressure 
(Pounds). 


Gauge Pressure (Pounds). 




60 


80 


100 


60 


80 


100 


125 


150 





0.1533 


0.1824 


0.2075 


0.1354 


0.1580 


0.1765 


0.1964 


0.2138 


1,000 


0.1511 


0.1795 


0.2040 


0.1332 


0.1553 


0.1734 


0.1926 


0.2093 


2,000 


0.1489 


0.1766 


0.2006 


0.1310 


0.1524 


0.1700 


0.1887 


0.2048 


3,000 


0.1469 


0.1739 


0.1971 


0.1286 


0.1493 


0.1666 


0.1848 


0.2003 


4,000 


0.1448 


0.1712 


0.1939 


0.1263 


0.1464 


0.1635 


0.1810 


0.1963 


5,000 


0.1425 


0.1685 


0.1906 


0.1241 


0.1438 


0.1600 


0.1772 


0.1921 


6,000 


0.1402 


0.1656 


0.1872 


0.1218 


0.1409 


0.1566 


0.1737 


0.1879 


7,000 


0.1379 


0.1628 


0.1839 


0.1197 


0.1383 


0.1536 


0.1700 


0.1838 


8,000 


0.1358 


0.1600 


0.1807 


0.1173 


0.1358 


0.1504 


0. 1662 


0.1797 


9,000 


0.1337 


0.1572 


0.1774 


0.1151 


0.1329 


0.1473 


0.1627 


0.1758 


10,000 


0.1316 


0.1547 


0.1743 


0.1132 


0.1303 


0.1442 


0.1592 


0.1717 



Example. — Required the volume of free air which when compressed 
to 100 lb. gauge at 9,000 ft. altitude will be equivalent to 1,000 cu. ft. 
of free air at sea level; also the power developed in compressing this 
volume to 100 lb. gauge in two stage compression at this altitude. 

From first table the multiplier is 1.356. Equivalent free air = 1,000 X 
1.356 = 1,356 cu. ft. 

From second table, power developed in compressing 1 cu. ft. of free air 
is 0.1473 H.P.; 1,356 X 0.1473 = 199.73 H.P. 

The Popp Compressed-air System in Paris. — A most extensive 
system of distribution of power by means of compressed air is that of 
M. Popp, in Paris. One of the central stations is laid out for 24,000 
horse-power. For a very complete description of the system, see Engineer- 
ing, Feb. 15, June 7, 21, and 28, 1889, and March 13 and 20, April 10, and 
May 1, 1891. Also Proc. Inst. M. E., July, 1889. A condensed descrip- 
tion will be found in Modern Mechanism, p. 12. 

Utilization of Compressed Air in Small Motors. — In the earliest 
stages of the Popp system in Paris it was recognized that no good results 
could be obtained if the air were allowed to expand direct into the motor; 
not only did the formation of ice due to the expansion of the air rapidly 
accumulate and choke the exhaust, but the percentage of useful work 
obtained, compared with that put into the air at the central station, was 
so small as to render commercial results hopeless. 

After a number of experiments M. Popp adopted a simple form of 
cast-iron stove lined with fire-clay, heated either by a gas jet or by a 
small coke fire. This apparatus answered the desired purpose until a 
better arrangement was perfected, and the type was accordingly adopted 
throughout the whole system. The economy resulting from the use of 
the improved form was very marked. 

It was found that more than 70% of the total heating value of the fuel 
employed was absorbed by the air and transformed into useful work. 
The efficiency of fuel consumed in this way is at least six times greater 
than when utilized in a boiler and steam-engine. According to Prof. 
Riedler, from 15% to 20% above the power at the central station can be 
obtained by means at the disposal of the power users. By heating the 
air to 480° F. an increased efficiency of 30% can be obtained. 

A large number of motors in use among the subscribers to the Com- 
pressed Air Company of Paris are rotary engines developing 1 H.P. and 
less, and these in the early times of the industry were very extravagant 
in their consumption. Small rotary engines, working cold air without 
expansion, used as high as 2330 cu. ft. of air per brake H.P. per hour, 
and with heated air 1624 cu. ft. Working expansively, a 1-H.P. rotary 
engine used 1469 cu. ft. of cold air, or 960 cu. ft. of heated air, and a 



COMPRESSED AIR TRANSMISSION. 613' 

2-H.P. rotary engine 1059 cu. ft. of cold air, or 847 cu. ft. of air, heated 
to about 122° F. 

The efficiency of this type of rotary motors, with air heated to 122° F., 
may now be assumed at 43%. 

Tests of a small Riedinger rotary engine, used for driving sewing- 
machines and indicating about 0.1 H.P., showed an air-consumption of 
1377 cu. ft. per H.P. per hour when the initial pressure of the air was 
86 lb. per sq. in. and its temperature 54° F., and 988 cu. ft. when the air 
was heated to 338° F., its pressure being 72 lb. With a 1/2-H.P. variable- 
expansion rotary engine the air-consumption was from 800 to 900 cu. ft. 
per H.P. per hour for initial pressures of 54 to 85 lb. per sq. in. with the 
air heated from 336° to 388° F., and 1148 cu. ft. with cold air, 46° F., and 
an initial pressure of 72 lb. The volumes of air were all taken at atmos- 
pheric pressure. 

Trials made with an old single-cylinder 80-horse-power Farcot steam- 
engine, indicating 72 H.P., gave a consumption of air per brake H.P. as 
low as 465 cu. ft. per hour. The temperature of admission was 320° F., 
and of exhaust 95° F. 

Prof. Elliott gives the following as typical results of efficiency for 
various systems of compressors and air-motors: 

Simple compressor and simple motor, efficiency 39 . 1 % 

Compound compressor and simple motor, " 44.9 

" compound motor, efficiency. 50.7 
Triple compressor and triple motor, " .55.3 

The efficiency is the ratio of the I.H.P. in the motor cylinders to the 
I.H.P. in the steam-cylinders of the compressor. The pressure assumed 
is 6 atmospheres absolute, and the losses are equal to those found in Paris 
over a distance of 4 miles. 

Summary of Efficiencies of Compressed-air Transmission at Paris, 
between the Central Station at St. Fargeau and a 10-horse-power 
Motor Working with Pressure Reduced to 41/2 Atmospheres. 

(The figures below correspond to mean results of two experiments cold and 

two heated.) 

One indicated horse-power at central station gives 0.845 I.H.P. in com- 
pressors, and corresponds to the compression of 348 cu. ft. of air per hour 
from atmospheric pressure to 6 atmospheres absolute. 

0.845 I.H.P. in compressors delivers as much air as will do 0.52 I.H.P. 
in adiabatic expansion after it has fallen to the normal temperature of the 
mains. 

The fall of pressure in mains between central station and Paris (say 5 
kilometres) reduces the possibility of work from 0.52 to 0.51 I.H.P. 

The further fall of pressure through the reducing valve to 41/2 atmos- 
pheres (absolute) reduces the possibility of work from 0.51 to 0.50. 

Incomplete expansion, wire-drawing, and other such causes reduce the 
actual I.H.P. of the motor from 0.50 to 0.39. 

By heating the air before it enters the motor to about 320° F., the 
actual I.H.P. at the motor is, however, increased to 0.54. The ratio of 
gain by heating the air is, therefore, 0.54 -f- 0.39 = 1.38. 

In this process additional heat is supplied by. the combustion of about 
0.39 lb. of coke per I.H.P. per hour, and if this be taken into account, the 
real indicated efficiency of the whole process becomes 0.47 instead of 0.54. 

Working with cold air the work spent in driving the motor itself reduces 
the available horse-power from 0.39 to 0.26. 

Working with heated air the work spent in driving the motor itself 
reduces the available horse-power from 0.54 to 0.44. 

A summary of the efficiencies is as follows: 

Efficiency of main engines 0.845. 

Efficiency of compressors 0.52 -4- 0.845 = 0.61. 

Efficiency of transmission through mains 0.51 -4- 0.52 = 0.98. 

Efficiency of reducing valve 0.50 -4- 0.51 = 0.98. 

The combined efficiency of the mains and reducing valve between 5 and 
4V2 atmospheres is thus 0.98 X 0.98 = 0.96. If the reduction had been 



614 



AIR. 



to 4, 3V2, or 3 atmospheres, the corresponding efficiencies would have 
been 0.93, 0.89, and 0.85 respectively. 

Indicated efficiency of motor 0.39 -4- 0.50 = 0.78. 

Indicated efficiency of whole process with cold air 0.39. Apparent 
indicated efficiency of whole process with heated air 0.54. 

Real indicated efficiency of whole process with heated air 0.47. 

Mechanical efficiency of motor, cold, 0.67. 

Mechanical efficiency of motor, hot, 0.81. 

Ingersoll-Sergeant Standard Air Compressors. 

(Ingersoll-Rand Co., 1908.) 





Diam.of Cyl., In. 


a 

Si 


02 


£ 
> 




MS 


| 


ft 

0> 



w 


el'd 


Class and Type. 


Steam. 


Air. 


.So 





r-; 


bfl 


i 

h5 


it 


A-1* 
Straight Line 
Steam Driven. 


10 

12 

14 
16 
18 
20 

22 
24 




10,1/4 

12l/ 4 
HI/4 
I6I/4 
I8I/4 
20l/ 4 
221/4 
241/4 




12 
14 
18 
18 
24 
24 
24 
30 


160 
155 
120 
120 
94 
94 
94 
80 


177 
285 
381 
498 
656 
807 
973 
1223 


50-100 
50-100 
50-100 
50-100 
50-100 
50-100 
50-100 
50-100 


23- 35 
37- 57 
50- 76 
65-100 
86-131 
106-161 
127-194 
161-242 


113 
200 
340 
340 
520 
520 
520 
710 


A-2* 
Straight Line 
Steam Driven 
Compound Air. 


12 
14 
16 
18 
20 
22 
24 
26 




71/2 
91/4 
IOI/4 
121/4 
131/4 
141,4 
151/4 
I6I/4 


121/4 
Ml/4 
I.6I/4 

2OI/4 
221/4 
241/4 
261/4 


12 
14 
18 

18 
24 
24 
24 
30 


160 
155 
135 
135 
110 
110 
110 
90 


252 
375 
550 
702 
940 
1131 
1333 
1606 


90-110 
90-110 
90-110 
90-110 
90-110 
90-110 
90-110 
90-110 


40- 45 
60- 66 
89- 97 
113-124 
151-166 
182-193 
214-236 
258-284 


145 
230 
435 
435 
640 
640 
640 
950 



B,* Straight line, belt driven. .Same as A-1 in sizes up to 16 1/4 X ISin. 

C, Duplex Corliss Steam, Duplex air. j ?f S n f ^l manWo 22nd" 

C-2, Compound Corliss Steam .Compound air.f ] a rd lize^ 









IOI/4 
I21/4 
HI/4 
I6I/4 
I8I/4 
201/4 




12 

14 

18 
18 
24 
24 


160 
155 
120 
120 
100 
100 


352 
568 
763 
994 
1338 
1674 


60-100 
60-100 
65-100 
70-100 
70-100 
70-100 


50- 67 
81-108 
113-146 
154-189 
207-256 
259-320 


240 


D-1* 






400 








6?5 








6?5 








1050 








105Q 








IOI/4 
HI/4 

HI/4 
151/4 
171/4 
18 1/4 
201/ 4 


16 1/4 
I81/ 4 
221/4 
251/4 
281/4 
301/4 
321/4 


12 
14 
18 
18 

24 
24 
24 


160 
155 
120 
120 
100 
100 
100 


444 
638 
925 
1205 
1622 
1857 
2130 


80-100 
80-100 
80-100 
80-100 
80-100 
80-100 
80 


65- 72 
93-104 
134-150 
174-194 
235-263 
269-300 
309 


?40 








400 


D-2J 






6?5 








6?5 








1050 








1050 








1050 



E.* Straight line, belt driven 


same sizes as F-1. 






F-1* 
Straight Line 
Steam Driven. 


6 
8 

10 
12 




6 

8 
10 
121/4 


1 6 

8 

10 

1 12 


150 
150 
150 
150 


29 
69 
134 
233 


45-100 
50-100 
55-100 
60-100 


4- 6 

91/2-14 
19-27 
35-47 


21 
32 
46 
63 



* Built in intermediate sizes for lower pressures. 

t Most economical form of compressor, t For sea level; also built with 
larger low pressure cylinders for altitudes of 5,000 and 10,000 ft. 



AIR COMPRESSORS. 



615 



Ingersoll-Sergeant Standard Air Compressors.— Continued. 





Diam.of Cyl., In. 


G 
aT 

o 

OS 


G 

ft 
> 






o 
ft 

i ■ 

1 

55- 70 
85-114 
119-152 
160-200 
218-267 
273-335 
328-402 




Class and Type. 


Steam. 


Air. 


-.2 


4 

9 


o 

fa 


4 


o 

h3 


fa 


G-1* 

Duplex and Half 

Duplex 

Steam Driven. 


10 

12 
14 
16 
18 
20 
22 




IOI/4 
121/4 
141/ 4 
I6I/4 
I8I/4 
201/ 4 
221/4 




12 
14 

18 
18 
24 
24 
24 


160 
155 
120 
120 
100 
100 
100 


352 
568 
763 
994 
1338 
1674 
2010 


50-100 
60-100 
55-100 
70-100 
70-100 
70-100 
70-100 


330 
480 
800 
800 
1450 
1450 
1450 


G-2f 
Duplex Steam, 
Compound Air. 


10 

12 
14 
16 
18 
20 
22 
22 




101/4 
11 1/4 

141/4 
151/4 
171/4 
I8I/4 
201/4 
221/4 


I6I/4 
I8I/4 
221/ 4 
251/4 
281/4 
301/4 
321/4 
341/4 


12 

14 
18 
18 
24 
24 
24 
24 


160 
153 
120 
120 
100 
100 
100 
100 


444 
638 
925 
1205 
1622 
1857 
2130 
2390 


80-100 

80-100 

80-100 

80-100 

80-100 

100 

100 

80 


67- 75 

97-108 

140-157 

182-204 

245-274 

314 

360 

361 


330 
480 
800 
800 
1475 
1475 
1475 
1475 


H-1* 

Duplex Steam, 

Duplex Air. 


6 
8 

10 
12 
14 
16 




6 

8I/4 
101/4 
121/4 
141/4 
161/4 




6 
8 

10 
12 
14 
16 


150 
150 
150 
150 
140 
135 


58 
140 
272 
472 
680 
986 


50-100 
55-100 
60-100 
60-100 
65-100 
70-100 


71/2-1H/2 
20- 28 
40- 54 
70- 94 
106-136 
160-197 


115 
150 
180 
220 
383 
585 


H-2'j 

Duplex Steam, 
Compound Air. 


6 
8 

10 
12 
14 
16 




7 

91/4 
101/4 
121/4 
141/4 
I6I/4 


10 

141/4 
161/4 

I8I/4 
221/4 
251/4 


6 
8 
10 
12 
14 
16 


150 
150 
150 
150 
140 
135 


81 
215 
348 
526 
841 
1205 


80-100 
80-100 
80-100 
80-100 
80-100 
80-100 


121/2-141/2 

33-37 

53-59 

80-90 
129-144 
182-204 


115 
150 
180 
220 
383 
585 








6 

8I/4 
101/4 
121/4 
141/4 
161/4 




6 
8 
10 
12 
14 
16 


150 
150 
150 
150 
140 
135 


58 
140 
272 
472 
680 
986 


50-100 
55-100 
60-100 
60-100 
65-100 
70-100 


7-11 
19-27 
39-53 
67-90 
101-130 
153-190 


83 








1?5 


Duplex 
Belt Driven. 






135 






17? 






315 








479 
















7 

91/4 
IOI/4 
121/4 
141/4 
161/ 4 


10 

141/4 
161/4 
I8I/4 
221/4 
251/4 


6 
8 
10 
12 

14 
16 


150 
150 
150 


81 
215 
348 


80-100 
80-100 
80-100 
80-100 


12-14 
31-35 
51-57 

77-86 


83 








1?5 


J-2J 

Duplex Compound 

Belt Driven. 






135 






150 526 
140! 841 


117 






80-1001 12-138 


315 








135 


1 1205 


80-1 00 


I 176-198 


429 



* Built in intermediate sizes for lower pressures. 

t For sea level ; also built with larger low pressure cylinders for alti- 
tudes of 5,000 and 10,000 ft. 

X For sea level; also built in the 4 largest sizes with larger low pressure 
cylinders for altitudes of 5,000 and 10,000 ft. 

Many other styles of compressors are also built. Among them are the 
following: 

Rand-Corliss, compound condensing steam, compound air; capacities. 
750 to 7670 cu. ft. of free air per min.; steam cylinders, 10 and IS to 28 and 
52 in.; air cylinders, 11 1/2 and 18 to 33 and 52 in.; stroke 30 to 48 in.; 
I.H. P., from 114 to 1166. 



616 



AIR. 



"Vertical duplex single acting, belt driven; capacities, 16.6 to 321 cu. ft. 
of free air per min. ; air cylinders, 4V2 to 12 in. ; stroke 41/2 to 14in. ; I.H.P., 
2.5 to 66. 

Duplex steam, non condensing, compound air; capacities, 343 to 2209 
cu. ft. of free air per min. ; steam cylinders, 10 to 20 in. ; air cylinders, 9 
and 14 to 19 and 30 in.; stroke, 16 to 30 in.; I.H.P., 53 to 380. 

Compound steam, non condensing, duplex air; capacities, 349 to 1962 
cu. ft. of free air per min.; steam cylinders, 10 and 16 to 20 and 32 in.; 
air cylinders, 10 to 20 in.; stroke, 16 to 30 in.; I.H.P., 62 to 392. 

Straight line, steam driven; capacities, 42 to 630 cu. ft. of free air per 
min.; steam cylinders, 6 to 12 in.; air cylinders, 6 to 19 in.; stroke, 8 to 
16 in.; I.H.P., 8.2 to 54. 

Cubic Feet of Air Required to Run Rock Drills at Various Pressures 
and Altitudes. 

(Ingersoll-Rand Co., 1908.) 

Table I. — cubic feet of free air required to run one drill. 





Size and Cylinder Diameter of Drill. 




A 35 


A 32 
A 86 


B 


C 


D 


D 


D 


E 


F 


F 


G 


H 


H9 


?„ a 






























2" 


21/4" 


21/2" 


23/ 4 " 


3" 


31/8" 


33/ie" 


31/4" 


31/2" 


35/ 8 " 


41/4" 


5" 


51/2" 


60 


50 


60 


68 


82 


90 


95 


97 


100 


108 


113 


130 


150 


164 


70 


56 


68 


77 


93 


102 


108 


110 


113 


124 


129 


147 


170 


181 


80 


63 


76 


86 


104 


114 


120 


123 


127 


131 


143 


164 


190 


207 


90 


70 


84 


95 


115 


126 


133 


136 


141 


152 


159 


182 


210 


230 


100 


77 


92 


104 


126 


138 


146 


149 


154 


166 


174 


199 


240 


252 



Table II. — multipliers to give capacity of compressor to operate 
FROM 1 TO 70 rock drills at various altitudes. 



< > 














Number of Drills. 












it 

< 


1 
1. 


2 

1.8 


3 

2.7 


4 

3.4 


5 

4.1 


6 

4.8 


7 

5.4 


8 

6.0 


9 

6.5 


10 
7.1 


15 


20 
11.7 


25 
13.7 


30 


40 
21,4 


50 





9.5 


15.8 


25.5 


1000 


1 03 


1.85 


2.78 


3.5 


4.22 


4.94 


5.56 


6.18 


6.69 


7.3 


9.78 


12.05 


14.1 


16.3 


22.0 


26.26 


2000 


1.07 


1.92 


2.89 


3.64 


4.39 


5.14 


5.78 


6.42 


6.95 


7.60 


10.17 


12.52 


14.66 


16.9 


22.9 


27.28 


300C 


1.10 


1 98 


2.97 


3.74 


4.51 


5.28 


5.94 


6.6 


7.15 


7.81 


10.45 


12.87 


15.07 


17.38 


23.54 


28.05 


5000 


1 17 


2 10 


3 16 


3.98 


48 


5 62 


6.32 


7.02 


7.61 


8.31 


11.12 


13.69 


16.03 


18,49 


25.04 


29.84 


8000 


1 26 


2 27 


3 40 


4.28 


5 17 


6.05 


6.8 


7.56 


8.19 


8.95 


11.97 


14.74 


17.26 


19.9 


26.96 


32.13 


10000 


1 32 


238 


3.56 


4,49 


5.41 


6.34 


7.13 


7.92 


8.58 


9.37 


12.54 


15.44 


18.08 


20.86 


28.25 


33.66 


15000 


1.43 


2.57 


3.86 


4.86 


5.86 


6.86 


7.72 


8.58 


9.3 


10.15 


13.58 


16.73 


19.59 


22.59 


30.6 


36.49 



Example. — Required the amount of free air to operate thirty 5-inch 
"H" drills at 8,000 ft. altitude, using air at a gauge pressure of 80 lb. per 
sq. in. From Table I, we find that one 5-inch " H " drill operating at 80 lb. 
gauge pressure requires 190 cu. ft. of free air per minute. From Table 
II, the factor for 30 drills at 8,000 feet altitude is 19.9; 190 X 19.9 => 
3781 = the displacement of a compressor under average conditions, to 
which must be added pipe line losses. 



COMPRESSED AIR. 



617 



The tables above are for fair conditions in ordinary hard rock. In 
soft material, where the drilling time is short more drills can be run with 
a given compressor than when working in hard material. In tunnel 
work, more rapid progress can be made if the drills are run at high air 
pressure, and it is advisable to have an excess of compressor capacity 
of about 25%. No allowance has been made in the tables for friction 
or pipe line losses. 

Steam Required to Compress 100 Cu. Ft. of Free Air. (O. S. 

Shantz, Power, Feb. 4, 1908.) — The following tables show the number of 
pounds of steam required to compress 100 cu. ft. of free air to different 
gauge pressures, by means of steam engines using from 12 to 40 lbs. of 
steam per I.H.P. per hour. The figures assume adiabatic compression 
in the air cylinders, with intercooling to atmospheric temperature in the 
case of two-stage compression, and 90% mechanical efficiency of the 
compressor. 

Steam Consumption of Air Compressors — Single-Stage Compression. 



Air. 


Steam per I.H.P. Hour. Lbs. 


Gauge 




























Pres- 




























sure. 


12 


14 


16 


18 


20 


22 


24 


26 


28 


30 


32 


36 


40 


20 


1.36 


1 58 


1 82 


2 04 


2 26 


2 49 


2 72 


2 94 


3 17 


3 40 


3 61 


4 08 


4.54 


30 


1,84 


2 14 


2 45 


2.76 


3.06 


3,37 


3 68 


3 98 


4 29 


4 60 


4 90 


5,51 


6.12 


40 


2 26 


2 64 


3 02 


3.39 


3.77 


4.15 


4 52 


4 90 


5.26 


5 65 


6 03 


6.78 


7.50 


50 


2.62 


3 06 


3 50 


3.93 


4.36 


4.80 


5.25 


5.68 


6.10 


6.55 


7.00 


8.86 


8.71 


60 


2.92 


3 4! 


3 90 


4.38 


4.80 


5.36 


5.85 


6,32 


6.80 


7 30 


7.80 


8.76 


9.71 


70 


3 22 


3 76 


4 30 


4 83 


5 36 


5 90 


6.45 


6 97 


7 50 


8 05 


8 60 


9 66 


10.70 


80 


3.50 


4 08 


4 67 


5 25 


5.84 


6 42 


7 00 


7 59 


8 15 


8 75 


9 34 


10.50 


11.61 


90 


3.72 


4 34 


4 96 


5 58 


6.20 


6 82 


7.45 


8 05 


8.66 


9 30 


9 94 


11.15 


12.35 


100 


3.96 


4 61 


5 29 


5.95 


6.60 


7.25 


7,92 


8 58 


9 22 


9 90 


10 56 


11 88 


13.15 


110 


4.18 


4 87 


5 58 


6 26 


6 96 


7 66 


8.36 


9 05 


9.75 


10 45 


11 15 


12 52 


13,90 


120 


4.38 


5.11 


5.85 


6.57 


7.30 


8.04 


8.76 


9.50 


10.20 


10.95 


11.66 


13.13 


14.55 



Two-Stage Compression. 



70 


2 82 


3 25 


3 76 


4 23 


4,69 


5,16 


5.63 


6,10 


6 56 


7 04 


7.50 


8.45 


9 35 


80 


3.01 


3 51 


4 03 


4 52 


5,02 


5.53 


6.03 


6.53 


7.03 


7.53 


8.03 


9.05 


10.01 


90 


3.19 


3,72 


4.26 


4.79 


5.32 


5.85 


6.38 


6.91 


7.44 


7.98 


8.50 


9.57 


10.60 


100 


3 37 


3 93 


4 50 


5 05 


5 61 


6,19 


6 74 


7 30 


7 85 


8 42 


8 99 


10,10 


11.20 


110 


3 54 


4 14 


4 74 


5 32 


5.91 


6.51 


7.10 


7 70 


8.27 


8.86 


9.46 


10.64 


11.80 


120 


3,69 


4 30 


4,93 


5 54 


6.15 


6.78 


7.38 


8,00 


8.61 


9.24 


9 85 


11.05 


12.27 


130 


3.83 


4 46 


5 11 


5,75 


6 38 


7.03 


7.66 


8.30 


8.92 


9,57 


10.20 


11,48 


12.72 


140 


3 96 


4 62 


5 29 


5 94 


6 60 


7 26 


7 92 


8 60 


9 23 


9 90 


10 56 


11 88 


13 15 


150 


4.10 


4.76 


5.46 


6.14 


6.81 


7.50 


6.74 


8.86 


9.55 


10.20 


10.90 


12.26 


13.60 



Compressed-air Table for Pumping Plants. 

(Ingersoll-Rand Co., 1908.) 

The following table shows the pressure and volume of air required for 
any size pump for pumping by compressed air. Reasonable allowances 
have been made for loss due to clearances in pump and friction in pipe. 

To find the amount of air and pressure required to pump a given quan- 
tity of water a given height, find the ratio of diameters between water 
and air cylinders, and multiply the number of gallons of water by the 
figure found in the column for the required lift. The result is the number 
of cubic feet of free air. The pressure required on the pump will be found 
directly above in the same column. For example: The ratio between 
cylinders being 2 to 1, required to pump 100 gallons, height of lift 250 



618 



AIR. 



feet. We find under 250 feet at ratio 2 to 1 the figures 2.11 ; 2.11 X 100 « 
211 cubic feet of free air. The pressure required is 34.38 pounds deliv- 
ered at the pump piston. 



Ratio of 
Diameters. 




Perpendicular Height, in Feet, to which the "Water 
is to be Pumped. 


25 


50 


75 


100 


125 


150 


175 


200 


250 


300 


400 


i j. i ( 


A 
B 

A 
B 
A 
B 
A 
B 
A 
B 
A 
B 


13.75 
0.21 


27.5 
0.45 

12.22 
0.65 


41.25 
0.60 

18.33 
0.80 

13.75 
0.94 


55.0 

0.75 
24.44 

0.95 
19.8 

1.14 
13.75 

1.23 


68.25 

0.89 
30.33 

1.09 
22.8 

1.24 
17.19 

1.37 
13.75 

1.53 


82.5 

1.04 
36.66 

1.24 
27.5 

1.30 
20.63 

1.52 
16.5 

1.68 
13.2 

1.79 


96.25 

1.20 
42.76 

1.39 
32.1 

1.54 
24.06 

1.66 
19.25 

1.83 
15.4 

1.98 


110.0 

1.34 
48.88 

1.53 
36.66 

1.69 
27.5 

1.81 
22.0 

1.97 
17.6 

2.06 








1 to 1 | 








1 1/2 to 1 { 


61.11 

1.83 
45.83 

1.99 
34.38 

2.11 
27.5 

2.26 
22.0 

2.34 


73.32 

2.12 
55.0 
•2.39 
41.25 

2.40 
33.0 

2.56 
26.4 

2.62 


97.66 
2.70 
73 33 


1 3/ 4 to 1 | 






2 88 


r 






55 


2 to 1 J 








7 98 


21/4 to 1 { 








44.0 










3 15 


( 










35 ?. 


2 1/ 2 to I | 












3.18 

















A = air-pressure at pump. B = cubic feet of free air per gallon of water. 



Compressed-air Table for Hoisting-engines. 

(Ingersoll-Rand Co., 1908.) 

The following table gives an approximate idea of the volume of free air 
required for operating hoisting-engines, the air being delivered to the 
engine at 60 lbs. gauge. There are so many variable conditions to the 
operation of hoisting-engines in common use that accurate computations 
can only be offered when fixed data are given. In the table the engine is 
assumed to actually run but one-half of the time for hoisting, while the 
compressor runs continuously. If the engine runs less than one-half the 
time, the volume of air required will be proportionately less, and vice 
versa. The table is computed for maximum loads, which also in practice 
may vary widely. From the intermittent character of the work of a 
hoisting-engine the parts are able to resume their normal temperature 
between the hoists, and there is little probability of freezing up the 
exhaust-passages. 



Volume of Free Air Required for Operating Hoisting-engines, the 
Air Compressed to 60 Pounds Gauge Pressure. 

Single-cylinder Hoisting-engine. 



Diam. of 

Cylinder, 

Inches. 


Stroke, 
Inches. 


Revolu- 
tions per 
Minute. 


Normal 
Horse- 
power. 


Actual 
Horse- 
power. 


Weight 
Lifted, 
Single 
Rope. 


Cubic Ft. 
of Free Air 
Required. 


5 
5 

61/4 
7 

8I/4 
8 1/2 
10 


6 
8 
8 
10 
10 
12 
12 


200 
160 
160 
125 
125 
110 
110 


3 

4 
6 
10 
15 
20 
25 


5.9 
6.3 
9.9 
12.1 
16.8 
18.9 
26.2 


600 
1 000 
1,500 
2,000 
3,000 
5 000 
6,000 


75 
80 
125 
151 
170 
238 
330 



- 



COMPRESSED AIR. 



619 



Double-cylinder Hoisting-engine. 



Diam. of 
Cylinder, 
Inches. 


Stroke, 
Inches. 


Revolu- 
tions per 
Minute. 


Normal 
Horse- 
power. 


Actual 
Horse- 
power. 


Weight 
Lifted, 
Single 
Rope. 


Cubic Ft. 
of Free Air 
Required. 


5 
5 

6I/4 

81/4 
81/2 

10 

121/4 

14 


6 
8 
8 
10 
10 
12 
12 
15 
18 


200 
160 
160 
125 
125 
110 
110 
100 
90 


6 
8 
12 
20 
30 
40 
50 
75 
100 


11.8 
12.6 
19.8 
24.2 
33.6 
37.8 
52.4 
89.2 
125. 


1,000 
1,650 
2,500 
3,500 
6,000 
8 000 
10,000 


150 
160 
250 
302 
340 
476 
660 
1,125 
1,587 



Practical Results with Compressed Air. — ■ Compressed-air System 
at the Chqpin Mines, Iron Mountain, Mich. — These mines are three miles 
from the falls which supply the power. There are four turbines at the 
falls, one of 1000 horse-power and three of 900 horse-power each. The 
pressure is 60 pounds at 60° Fahr. Each turbine runs a pair of compress- 
ors. The pipe to the mines is 24 ins. diameter. The power is applied at 
the mines to Corliss engines, running pumps, hoists, etc., and direct to 
rock-drills. 

A test made in 1888 gave 1430.27 H.P. at the compressors, and 390.17 
H.P. as the sum of the horse-power of the engines at the mines. There- 
fore, only 27% of the power generated was recovered at the mines. This 
includes the loss due to leakage and the loss of energy in heat, but not the 
friction in the engines or compressors. (F. A. Pocock, Trans. A. I. M. E., 
1890.) 

W. L. Saunders (Jour. F. I., 1892) says: "There is not a properly designed 
compressed-air installation in operation to-day that loses over 5% by 
transmission alone. The question is altogether one of the size of pipe; 
and if the pipe is large enough, the friction loss is a small item. 

" The loss of power in common practice, where compressed air is used 
to drive machinery in mines and tunnels, is about 70% . In the best prac- 
tice, with the best air-compressors, and without reheating, the loss is about 
60%. These losses may be reduced to a point as low as 20% by combin- 
ing the best systems of reheating with the best air-compressors." 

Gain due to Reheating. — Prof. Kennedy says compressed-air trans- 
mission system is now being carried on, on a large commercial scale, 
in such a fashion that a small motor four miles away from the central 
station can indicate in round numbers 10 horse-power, for 20 horse- 
power at the station itself, allowing for the value of the coke used in heat- 
ing the air. 

The limit to successful reheating lies in the fact that air-engines can- 
not work to advantage at temperatures over 350°. 

The efficiency of the common system of reheating is shown by the re- 
sults obtained with the Popp system in Paris. Air is admitted to the 
reheater at about 83°, and passes to the engine at about 315°, thus being 
increased in volume about 42%. The air used in Paris is about 11 cubic 
feet of free air per minute per horse-power. The ordinary practice in 
America with cold air is from 15 to 25 cubic feet per minute per horse- 
power. When the Paris engines were worked without reheating the air 
consumption was increased to about 15 cubic feet per horse-power per 
minute. The amount of fuel consumed during reheating is trifling. 

Effect of Temperature of Intake upon the Discharge of a Com- 
pressor. — Air should be drawn from outside the engine-room, and 
from as cool a place as possible. The gain in efficiency amounts to one 
per cent for every five degrees that the air is taken in lower than the 
temperature of the engine-room. The inlet conduit should have an area 
at least 50% of the area of the air-piston, and should be made of wood, 
brick, or other non-conductor of heat. 

Discharge of a compressor having an intake capacity of 1000 cubic feet . 
per minute, and volumes of the discharge reduced to cubic feet at atmos- 
pheric pressure and at temperature of 62 degrees Fahrenheit: 

Temperature of Intake, F 0° 32° 62° 75° 80° 90° 100° 110° 

Volume discharged, cubic ft. 1135 1060 1000 975 966 949 932 916 



620 



AIR. 



Compressed-Air Motors with a Return-Air Circuit. — In the ordinary 
use of motors, such as rock-drills, the air, after doing its work in the motor, 
is allowed to escape into the atmosphere. In some systems, however, 
notably in the electric air-drill, the air exhausted from the cylinder of the 
motor is returned to the air compressor. A marked increase in economy 
is claimed to have been effected in this way (Cass. Mag., 1907). 

Intercoolers for Air Compressors. — H. V. Haight (Am. Mach., 
Aug. 30, 1906). In multi-stage air compressors, the^efficiency is greater 
the more nearly the temperature of the air leaving the intercooler ap- 
proaches that of the air entering it. The difference of these temperatures 
for given temperatures of the entering water and air is diminished by in- 
creasing the surface of the intercooler and thereby decreasing the ratio 
of the quantity of air cooled to the area of cooling surface. Numerous 
tests of intercoolers with different ratios of quantity of air to area of sur- 
face, on being plotted, approximate to a straight-line diagram, from which 
the following figures are taken: 

Cu. ft. of free air per min. per sq. ft. of air cooling surface 5 10 15 
Diff . of temp. F°. between water entering and air leaving 12.5° 25° 37.5°. 

Centrifugal Air Compressors. — (Eng. News, Nov. 19, 1908.) The 
General Electric Co. has placed on the market a line of centrifugal air 
compressors with pressure ratings from 0.75 to 4.0 lbs. per sq. in. and 
capacities from 750 to 28,000 cu. ft. of free air per minute. The com- 
pressor consists essentially of a rotating impeller surrounded by a suit- 
able casing with an intake opening at the center and a discharge opening 
at the circumference. It is similar to the centrifugal pump, the efficiency 
depending largely upon the design of the impeller and casing. 

The compressors are driven by Curtis steam turbines or by electric 
motors especially designed for them. With "squirrel-cage" induction 
motors, since the speed cannot be varied, care must be taken to specify 
a pressure sufficiently high to cover the operating requirements, because 
at constant speed the pressure cannot be varied without altering the 
design of the impeller. For foundry cupola service direct-current motors 
can be compound wound so as to automatically increase the speed should 
the volume of air delivered decrease, thus increasing the pressure of the 
air and preventing undue reduction of flow of air through the cupola 
when it chokes up. Further adjustments of pressure can be made by 
changing the speed of the motor by means of the field rheostat. 



Standard 


Single 


-Stage Centrifugal Air 


Compressors (1909). 




Standard Con- 


Minimum Speed 


Maximum Speed 






ditions. 


Conditions. 


Conditions. 


Pipe 


R.P.M. 














Diam- 


Lbs. 

per Sq. 

In. 


Cu. Ft. 
per Min. 


Lbs. 

per Sq. 

In. 


Cu. Ft. 
per Min. 


Lbs. 

per Sq. 

In. 


Cu. Ft. 
per Min. 


eter 
Inches. 


3450 


1.0 


800 


0.75 


1,100 


1.25 


600 


10 


3450 


1.0 


1,600 


0.75 


2,100 


1.25 


1,300 


12 


3450 


1.0 


3,200 


0.75 


4,100 


1.25 


2,600 


12 


3450 


1.0 


4,500 


0.75 


5,900 


1.25 


3,800 


16 


3450 


1.0 


7,200 


0.75 


8,800 


1.25 


6,000 


20 


3450 


1.0 


10,200 


0.75 


12,000 


1.25 


8,700 


26 


1725 


1.0 


25,000 


0.75 


31,000 


1.25 


21,000 


36 


3450 


2.0 


750 


1.5 


1,000 


2.50 


500 


8 


3450 


2.0 


1,600 


1.5 


2,100 


2.50 


1,200 


10 


3450 


2.0 


2,500 


1.5 


3,300 


2.50 


1,900 


12 


3450 


2.0 


4,200 


1.5 


5,400 


2.50 


3,300 


16 


3450 


2.0 


6,200 


1.5 


8,000 


2.50 


5,000 


20 


1725 


2.0 


15,000 


1.5 


19,000 


2.50 


11,000 


26 


1725 


2.0 


28,000 


1.5 


36,000 


2.50 


24,000 


36 


3450 


3.25 


1,250 


2.5 


1,800 


4.00 


900 


8 


3450 


3.25 


2,400 


2.5 


3,200 


4.00 


1,900 


12 


3450 


3.25 


3,800 


2.5 


5,000 


4.00 


3,000 


14 


3450A.C.&tur. 


3.25 


9,000 


2.5 


11,500 


4.00 


7,500 


24 


1725 D.C. 


3.25 


9,000 


2.5 


11.000 


4.00 


6,400 


24 


3450A.C.&tur. 


3.25 


18,000 


2.5 


23; 000 


4.00 


15,000 


26 


1725 D.C. 


3.25 


18,000 


2.5 


23,500 


4.00 


14,000 


26 



HIGH-PRESSURE CENTRIFUGAL FANS. 621 



Multi-stage compressors have been built of the following sizes. 

Cu. ft. free air per min. Pressures. Rated speed. 

22,500 10 to 25 lbs. 1,800 r.p.m. 

8,000 8 to 15 lbs. 3,750 r.p.m. 

3,450 25 to 35 lbs. 3,450 r.p.m. 

From a curve of the load characteristics of a compressor rated at 1.7 
lbs. pressure and 750 cu. ft. per min. the following figures are derived. 
The actual efficiency is not given: 

Delivery, cu. ft. per min.* 200 400 600 700 800 900 1000 

Discharge pressure, lbs. per sq. in. 1.641.75 1.82 1.811.80 1.72 1.00 1.46 

Effy. per cent of maximum 49 77 95 99 100 99 96 

* Reduced to atmospheric pressure and 60° F. 

As in the case of centrifugal pumps, the pressure depends on the 

Seripheral velocity of the impeller. The volume of free air delivered is 
mited, however, by the capacity of the driver, and hence must be re- 
duced proportionately to the increase in pressure, otherwise the driver 
might become overloaded. 

The power required to drive centrifugal compressors varies approxi- 
mately with the volume of air delivered when operating at a constant 
speed. This gives flexibility and economy to the centrifugal type where 
variable loads are required, satisfactory efficiency being obtained between 
the limits of 25% and 125% of the rated load. 

When the compressor is operated as an exhauster against atmospheric 
pressure, the rated pressure P in lbs. per square inch must be multiplied 
by 14.7 and then divided by 14.7 + P. The result represents the vacuum 
obtained in lbs. per square inch below atmosphere. 

High-Pressure Centrifugal Fans. — (A. Rateau, Engg., Aug. 16, 1907.) 
In 1900, a single wheel fan driven by a steam turbine at 20,200 revs, per 
min. gave an air pressure of 8i/4lbs. per sq. in.; an output of 26.7 cu. ft. 
free air per second; useful work in H.P. adiabatic compression, 45.5; 
theoretical work in H.P. of steam-flow, 162; efficiency of the set, fan and 
turbine, 28%. An efficiency of 30.7% was obtained with an output of 
23 cu. ft. per sec. and 132 theoretical H.P. of steam. The pressure 
obtained with a fan is — ■ all things being equal — proportional to the 
specific weight of the gas which flows through it; therefore, if, instead of 
air at atmospheric pressure, air, the pressure of which has already been 
raised, or a gas of higher density, such as carbonic acid, be used, com- 
paratively higher pressures still will be obtained, or the engine can run at 
lower speeds for the same increase of pressure. 

Multiple Wheel Fans. — The apparatus having a single impeller gives 
satisfaction only when the duty and speed are sufficiently high. The 
speed is limited by the resistance of the metal of which the impeller is 
made, and also by the speed of the motor driving the fan. But by con- 
necting several fans in series, as is done with high-lift centrifugal pumps, 
it is possible to obtain as high a pressure as may be desired. 

Turbo-Compressor, Bethune Mines, 1906. — This machine compresses air 
to 6 and 7 atmospheres by utilizing the exhaust steam from the winding- 
engines. It consists of four sets of multi-cellular fans through which the 
air flows in succession. They are fitted on two parallel shafts, and each 
shaft is driven by a low-pressure turbine. A high-pressure turbine is 
also mounted on one of the shafts, but supplies no work in ordinary times. 
An automatic device divides the load equally between the two shafts. 
Between the two compressors are fitted refrigerators, in which cold water 
is made to circulate by the action of a small centrifugal pump keyed at 
the end of the shaft. In tests at a speed of 5000 r.p.m., the volume of 
air drawn per second was 31.7 cu. ft. and the discharge pressure 119.5 lb. 
per sq. in. absolute. These conditions of working correspond to an effect- 
ive work in isothermal compression of 252 H.P. The efficiency of the 
compressor has been as high as 70%. The results of two tests of the 
compressor are given below. In the first test the air discharged, reduced 
to atmospheric pressure, was 26 cu. ft. per sec; in the second test it was 
46 cu. ft. 



2d. 


3d. 


4th. 


23.37 


38.69 


66.44 


39.98 


66.44 


102.60 


4660 


4660 


4660 


67.8 


63. 


66. 


205. 


216. 


215.6 


122. 


114.8 


105.8 


137.2 


153. 


149.6 


60.5 


54. 


46.2 


2d. 


3d. 


4th. 


21.31 


37.33 


65.12 


38.22 


65.12 


99.66 


5000 


4840 


4840 


69.8 


64.4 


68.5 


208.4 


208.4 


199.6 


131. 


123.8 


100.4 


66.6 


58.7 


48.6 



622 



First Test. 
Stages. 1st. 

Abs. pressure at inlet, lbs. per sq. in. ... 15. 18 

Abs. pressure at discharge 24. 10 

Speed, revs, per rain 4660 

Temperature of air at inlet, deg. F. ... 57.2 
Temperature of air at discharge, deg. F. 171 . 

Adiabatic rise in temp., deg. F 106. 

Actual rise in temperature, deg. F. ... 113.8 
Efficiency, per cent 60 . 5 

Second Test. 
Stages. 1st. 

Abs. pressure at inlet, lbs. per sq. in. . . . 15. 18 

Abs. pressure at discharge 23 . 52 

Speed, revs, per min 5000 

Temp, of air at inlet, deg. F 55. 

Temp, of air at discharge, deg. F 160. 7 

Adiabatic rise in temp., deg. F 102.2 

Efficiency, per cent 62 . 3 

The Gutehoffnungshiitte Co. in Germany have in course of construc- 
tion several centrifugal blowing-machines to be driven by an electric 
motor, and up to 2000 H.P. Several machines are now being designed 
for Bessemer converters, some of which will develop up to 4000 H.P. 
The multicellular centrifugal compressors are identical in every point 
with centrifugal pumps. In the new machines cooling water is intro- 
duced inside the diaphragms, which are built hollow for this purpose, 
and also inside the diffuser vanes. By this means it is hoped to reduce 
proportionally the heating of the air: thus approaching isothermal com- 
pression much more nearly than is done in the case of reciprocating 
compressors. 

Test of a Hydraulic Air Compressor. — (W. O. Webber, Trans. 
A. S. M. E., xxii, 599.) The compressor embodies the principles of 
the old trompe used in connection with the Catalan forges some centuries 
ago, modified according to principles first described by J. P. Frizell, in 
Jour. F. I., Sept., 1880, and improved by Charles H. Taylor, of Montreal. 
(Patent July 23, 1895.) It consists principally of a down-flow passage 
having an enlarged chamber at the bottom and an enlarged tank at 
the top. A series of small air pipes project into the mouth of the water 
inlet and the large chamber at the upper end of the vertically descending 
passage, so as to cause a number of small jets of air to be entrained by the 
water. At the lower end of the apparatus, deflector plates in connection 
with a gradually enlarging section of the lower end of the down-flow pipe 
are used to decrease the velocity of the air and water, and cause a partial 
separation to take place. The deflector plates change the direction of 
the flow of the water and are intended to facilitate the escape of the air, 
the water then passing out at the bottom of the enlarged chamber into an 
ascending shaft, maintaining upon the air a pressure due to the height of 
the water in the uptake, the compressed air being led on from the top 
of the enlarged chamber by means of a pipe. The general dimensions of 
the compressor plant are: 

Supply penstock, 60 ins. diam.; supply tank at top, 8 ft. diam. X 10 ft. 
high; air inlets (feeding numerous small tubes), 34 2-in. pipes; down tube, 
44 ins. diam.; down tube, at lower end, 60 ins. diam.; length of taper in 
down tube, 20 ft.; air chamber in lower end of shaft, 16 ft. diam.; total 
depth of shaft below normal level of head water, about 150 ft.; normal 
head and fall, about 22 ft.; air discharge pipe, 7 ins. diam. 

It is used to supply power to engines for operating: the printing depart- 
ment of the Dominion Cotton Mills, Magog, P. Q., Canada. 

There were three series of tests, viz.: (1) Three tests at different rates 
of flow of water, the compressor being as originally constructed. (2) Four 
tests at different rates of flow of water, the compressor inlet tubes for air 
being increased bv 30 3/ 4 -in. pipes. (3) Four tests at different rates of 
flow of water, the compressor inlet tubes for air being increased by 153/4-in. 
pipes. 



HYDRAULIC AIR COMPRESSION. 



623 



The water used was measured by a weir, and the compressed air by air 
meters. The table on p. 623 shows the principal results: 

Test 1, when the flow was about 3800 cu. ft. per min., showed a decided 
advantage by the use of 30 3/ 4 -in. extra air inlet pipes. Test 5 shows, 
when the flow of water is about 4200 cu. ft. per mm., that the economy 
is highest when only 15 extra air tubes are employed. Tests 8 and 9 show, 
when the flow is about 4600 cu. ft. per min., that there is no advantage in 
increasing the air-inlet area. Tests 10 and 11 show that a flow of 5000 
or more cu. ft. of water is in excess of the capacity of the plant. These 
four tests may be summarized as follows: 

The tests show: (1) That the most economic rate of flow of water with 
this particular installation is about 4300 cu. ft. per min. (2) That this 
plant has shown an efficiency of 70.7 % under such a flow, winch is ex- 
cellent for a first installation. (3) That the compressed air contains only 
from 30 to 20% as much moisture as does the atmosphere. (4) That the 
air is compressed at the temperature of the water. 

Using an old Corliss engine without any changes in the valve gear 
as a motor there was recovered 81 H.P. This would represent a total 
efficiency of work recovered from the falling water, of 51.2%. When 
the compressed air was preheated to 267° F. before being used in the 
engine, 111 H.P. was recovered, using 115 lbs. coke per hour, which would 
equal about 23 H.P. The efficiency of work recovered from the falling 
water and the fuel burned would be, therefore, about 61 1/2%. On the basis 
of Prof. Riedler's experiments, which require only about 425 cu. ft. of air 
per B.H.P. per hour, when preheated to 300° F. and used in a hot-air 
jacketed cylinder, the total efficiency secured would have been about 
871/2%. 



Test No 

Flow of water, cu. ft. per min.. . 

Available head in ft 

Gross water, H.P 

Cu. ft. air, at atmos. press., per 

minute 

Pressure of air at comp., lbs 

Effective work in compressing, 

H.P 

Efficiency of compressor, % 

Temp, of external air, deg. F — 
Temp, of water and comp. air, 

deg. F t 

Ratio of water to air, volumes... 
Moisture in external air, p. c. of 

saturation 

Moisture in comp. air, p. c. of 

saturation 



1 


3 


4 


5 


7 


8 


3772 
20.54 
146.3 


3628 
20.00 
136.9 


4066 
20.35 
156.2 


4.292 
19.51 
158.1 


4408 
19.93 
165.8 


4700 
19.31 
171.4 


864 

51.: 


901 
53.7 


967 
53.2 


1148 
53.3 


1091 
53.7 


1103 
52.9 


83.3 
56.8 
68.3 


88.2 
64.4 
57.7 


94.3 
60.3 
66.4 


111.74 
70.7 
65.2 


107 
64.5 
59.7 


106.8 
62.2 
65 


66 
4.37 


65.5 
4.03 


66.4 
4.20 


66.5 
3.74 


67 
4.04 


66.5 
4.26 


61 


77.5 


71 


68 


90 


60.5 


51.5 


44 


38.5 


35 


29 


31.2 



10 



5058 
18.75 
179.1 

1165 
53.3 

113.4 
63.3 

64.2 

66 
4.34 



30 



Tests 1, 4, and 7 were made with the original air inlets; 2, 5, 8 and 10 
with the inlets increased by 153/ 4 -in. pipes, and 3, 6, 9 and 11 with the 
inlets increased by 30 3/4-in. pipes. Tests 2, 6, 9 and 11 are omitted here. 
They gave, respectively, 55.5, 61.3, 62, and 55.4% efficiency. 

Three other hydraulic air-compressor plants are mentioned in Mr. 
Webber's paper, some of the principal data of which are given below: 

Peterboro, Norwich, Cascade 

Ont. Conn. Range, 

Wash. 

Head of water 14 ft. 18* ft. 45 ft. 

Gauge pressure 25 lbs. 85 lbs. 85 lbs. 

Diam. of shaft 42 in. 24 ft. 

Diam. of compressor pipe 18 ft. 13 ft. 3 ft. 

Depth below tailrace 64 ft. 215 ft. 

Horse-power 1365 200 

In the Cascade Range plant there is no shaft, as the apparatus is con, 
structed against the vertical walls of a canyon. The diameter of the up- 
flow pipe is 4'ft. 9 in. 



624 



A description of the Norwich plant is given by J. Herbert Shedd in a 
paper read before the New England Water Works Assn., 1905 {Compressed ' 
Air, April, 1906). The shaft, 24 ft. diam., is enlarged at the bottom into 
a chamber 52 ft. diam., from which leads an air reservoir 100 ft. long, 18 ft. 
wide and 15 to 20 ft. high. Suspended in the shaft is a downfiow pipe 
14 ft. diam. connected at the top with a head tank, and at the bottom with 
the air-chamber, from which a 16-in. main conveys the air four miles to 
Norwich, where it is used in engines in several establishments. 

Pneumatic Postal Transmission. — A paper by A. Falkenau 
(Eng'rs Club of Philadelphia, April, 1894), entitled the " First United States 
Pneumatic Postal System," gives a description of the system used in 
London and Paris, and that recently introduced in Philadelphia between 
the main post-office and a substation. In London the tubes are 2 1/4 and 
3-inch lead pipes laid in cast-iron pipes for protection. The carriers 
used in 21/4-inch tubes are but 11/4 inches diameter, the remaining space 
being taken up by packing. Carriers are despatched singly. First, 
vacuum alone was used; later, vacuum and compressed air. The tubes 
used in the Continental cities in Europe are wrought iron, the Paris tubes 
being 21/2 inches diameter. There the carriers are despatched in trains 
of six to ten, propelled by a piston. In Philadelphia the size of tube 
adopted is 6i/s inches, the tubes being of cast iron bored to size. -The 
lengths of the outgoing and return tubes are 2928 feet each. The pressure 
at the main station is 7 lb., at the substation 4 lb., and at the end of the 
return pipe atmospheric pressure. The compressor has two air-cylinders 
18 X 24 in. Each carrier holds about 200 letters, but 100 to 150 are 
taken as an average. Eight carriers may be despatched in a minute, 
giving a delivery of 48,000 to 72,000 letters per hour. The time required 
in transmission's about 57 seconds. 

Pneumatic postal transmission tubes were laid in 1898 by the Batcheller 
Pneumatic Tube Co. between the general post-offices in New York and 
Brooklyn, crossing the East River on the Brooklyn bridge. The tubes 
are cast iron, 12-ft. lengths, bored to 8 1/8 in. diameter. The joints are 
bells, calked with lead and yarn. There are two tubes, one operating 
in each direction. Both lines are operated by air-pressure above the 
atmospheric pressure. One tube is operated by an air-compressor in the 
New York office and the other by one located in the Brooklyn office. 

The carriers are 24 in. long, in the form of a cylinder 7 in. diameter, 
and ar€ made of steel, with fibrous bearing-rings which fit the tube. Each 
carrier will contain about 600 ordinary letters, and they are despatched 
at intervals of 10 seconds in each direction, the time of transit between 
the two offices being 31/2 mi nut es, the carriers travelling at a speed of 
from 30 to 35 miles per hour. 

One of the air-compressors is of the duplex type and has two steam- 
cylinders 10 X 20 in. and two air-cylinders 24 X 20 in., delivering 
1570 cu. ft. of free air per minute, at 75 r.p.m. The power is about 50 H.P. 

Two other duplex air-compressors have steam-cylinders 14 X 18 in. 
and air-cylinders 261/4 X 18 in. They are designed for 80 to 90 r.p.m. 
and to compress to 20 lb. per sq. in. 

Another double line of pneumatic tubes has been laid between the 
main office and Postal Station H, Lexington Ave. and 44th St., in New 
York City. This line is about 31/2 miles in length. There are three 
intermediate stations. The carriers can be so adjusted when they are 
put into the tube that thev will traverse the line and be discharged auto- 
matically from the tube at the station for which they are intended. The 
tubes are of the same size as those of the Brooklyn line and are operated 
in a similar manner. The initial air-pressure is about 12 to 15 lb. On 
the Brooklyn line it is about 7 lb. 

There is also a tube svstem between the New York Post-office and the 
Produce Exchange. For a very complete description of the system and 
its machinery see "The Pneumatic Despatch Tube System," by B. C. 
Batcheller, J. B. Lippincott Co., Philadelphia, 1897. 

The Mekarski Compressed-air Tramwav at Berne, Switzerland. 
(Eng'g News, April 20, 1893.) — The Mekarski system has been intro- 
duced in Berne, Switzerland, on a line about two miles long, with grades 
of 0.25% to 3.7% and 5.2%. The air is heated by passing it through 
superheated water at 330° F. It thus becomes saturated with steam, 
which subsequently partly condenses, its latent heat being absorbed by 
the expanding air. The pressure in the car reservoirs is 440 lb. per sq. in. 



OPERATION OF PUMPS BY COMPRESSED AIR. 625 

The engine is constructed like an ordinary steam tramway locomotive, 
and drives two coupled axles, the wheel-base being 5.2 ft. It has a pair 
of outside horizontal cylinders, 5.1 X 8.6 in.; four coupled wheels, 27.5 
in. diameter. The total weight of the car including compressed air is 
7.25 tons, and with 30 passengers, including the driver and conductor, 
about 9.5 tons. 

The authorized speed is about 7 miles per hour. Taking the resistance 
due to the grooved rails and to curves under unfavorable conditions at 

30 lb. per ton of car weight, the engine has to overcome on the steepest 
grade, 5%, a total resistance of about 0.63 ton, and has to develop 25 
H.P. At the maximum authorized working pressure in cylinders of 176 
lb. per sq. in. the motors can develop a tractive force of 0.64 ton. This 
maximum is, therefore, just sufficient to take the car up the 5.2% grade, 
while on the flatter sections of the line the working pressure does not 
exceed 73 to 147 lb. per sq. in. Sand has to be frequently used to increase 
the adhesion on the 2% to 5% grades. 

< Between the two car frames are suspended ten horizontal compressed- 
air storage-cylinders, varying in length according to the available space, 
but of uniform inside diameter of 17.7 in., composed of riveted 0.27-in. 
sheet iron, and tested up to 588 lb. per sq. in., and having a collective 
capacity of 64.25 cu. ft., and two further small storage-cylinders of 
5.3 cu. ft. capacity each, a total capacity for the 12 storage-cylinders 
per car of 75 cu. ft., divided into two groups, the working and the reserve 
battery, of 49 cu. ft. and 26 cu. ft. capacity respectively. 

From the results of six official trips, the pressure and the mean con- 
sumption of air during a double trip per motor car are as follows: 

Pressure of air in storage-cylinders at starting, 440 lb. per sq. in. ; at end 
of up-trip, 176 lb., reserve, 260 lb.; at end of down-trip, 103 lb., reserve, 
176 lb. Consumption of air during up-trip, 92 lb., during down-trip, 

31 lb. The working experience of 1891 showed that the air consumption 
per motor car for a double trip was from 103 to 154 lb., mean 123 lb., 
and. per car mile from 28 to 42 lb., mean 35 lb. 

The disadvantages of this system consist in the extremely delicate adjust- 
ment of the different parts of the system, in the comparatively small 
supply of air carried by one motor car, which necessitates the car return- 
ing to the depot for refilling after a run of only four miles or 40 minutes, 
although on the Nogent and Paris lines the cars, which are, moreover, 
larger, and carry outside passengers on the top, run seven miles, and the 
loading pressure is 547 lb. per sq. in. as against only 440 lb. at Berne. 

For description of the Mekarski system as used at Nantes, France, see 
paper by Prof. D. S. Jacobus, Trans. A. S. M. E., xix. 553. 

American Experiments on Compressed Air for Street Railways. 
— Experiments have been made in Washington, D. C, and in New York 
City on the use of compressed air for street-railway traction. The air 
was compressed to 2000 lb. per sq. in. and passed through a reducing- 
valve and a heater before being admitted to the engine. The system has 
since been abandoned. For an extended discussion of the relative merits 
of compressed air and electric traction, with an account of a test of a 
four-stage compressor giving a pressure of 2500 lb. per sq. in., see Eng'g 
News, Oct. 7 and Nov. 4, 1897. A summarized statement of the probable 
efficiency of compressed-air traction is given as follows: Efficiency of com- 
pression to 2000 lb. per sq. in. 65%. By wire-drawing to 100 lbs. 57.5% 
of theavailable energy of the air will be lost, leaving 65 X 0.425 = 27.625% 
as the net efficiency of the air. This may be doubled by heating, making 
55.25%, and if the motor has an efficiency of 80% the net efficiency of 
traction by compressed air will be 55.25 X 0.80 = 44.2%. For a descrip- 
tion of the Hardie compressed-air locomotive, designed for street-railway 
work, see Eng'g News, June 24, 1897. For use of compressed air in mine 
haulage, see Eng'g News, Feb. 10, 1898. 

Operation of 31ine Pumps by Compressed Air. — The advantages 
of compressed air over steam for the operation of mine pumps are: Absence 
of condensation and radiation losses in pipe lines ; high efficiency of com- 
pressed-air transmission; ease of disposal of exhaust; absence of danger 
from broken pipes. The disadvantage is that, at a given initial pressure 
without reheating, a cylinder full of air develops less power than steam. 
The power end of the pump should be designed for the use of air, with 
low clearances and with proper proportions of air and water ends, with 
regard to the head under which the pump is to operate. Wm. Cox (Comp. 



626 



Air Mag., Feb., 1899) states the relations of simple or single-cylinder 
pumps to be A/W = l hh/p, where A = area of air cylinder, sq. in., W 
= area of water cylinder, sq. in., h = head, ft., and p = air pressure, lb. 
per sq. in. Mr. Cox gives the volume V of free air in cu. ft. per minute 
to operate a direct-acting, single-cylinder pump, working without cut off, 
to be 

V = 0.093 W 2 hG/P. 

Where W 2 = volume of 1 cu. ft. of free air corresponding to 1 cu. ft. of 
free air at pressure P, G = gallons of water to be raised per minute, P = 
receiver-gauge pressure of air to be used, and h = head in feet under 
which pump works. This formula is based on a piston speed of 100 ft. 
per minute and 15% has been added to the volume ot air to cover losses. 
The useful work done in a pump using air at full pressure is greater at 
low pressures than at high, and the efficiency is increased. High pressures 
are not so economical for simple pumps as low pressures. As high-pressure 
air is required for drills, etc., and as the air for pumps is drawn from the 
same main, the air must either be wire-drawn into the pumps, or a reducing 
valve be inserted between the pump and main. Wire-drawing causes a 
low efficiency in the pump. If a reducing valve is used, the increase of 
volume will be accompanied with a drop in temperature, so that the full 
value of the increase is not realized. Part of the lost heat may be regained 
by friction, and from external sources. The efficiency of the system may 
be increased by the use of underground receivers for the expanded air 
before it passes to the pump. If the receiver be of ample size, the air 
will regain nearly its normal temperature, the entrained moisture will be 
deposited and freezing troubles avoided. By compounding the pumps, 
the efficiency may be increased to about 25 per cent. In simple pumps it 
ranges from 7 to 16 per cent. For much further information on this sub- 
ject, see Peele's " Compressed- Air Plant for Mines," 1908. 

FANS AND BLOWERS. 

Centrifugal Fans. — The ordinary centrifugal fan consists of a number 
of blades fixed to arms revolving at high speed. The width of the blade 
is parallel to the shaft. The experiments of W. Buckle (Proc. Inst. M. E., 
1847) are often quoted as still standard. Mr. Buckle's conclusions, how- 
ever, do not agree with those of modern experimenters, nor do the propor- 
tions of fans as determined by him have any similarity to those of modern 
fans. His results are presented here merely for purposes of reference and 
comparison. The experiments were made on fans of the " paddle-wheel" 
type, and have no bearing on the more modern multivane fans of the 
"Sirocco" type. 

From his experiments Mr. Buckle deduced the following proportions for 
a fan: 1. The width of the vanes should be one-fourth the diameter; 
2. The diameter of the inlet opening in the sides of the fan chest should 
be one-half the diameter of the. fan; 3. The length of the vanes should be 
one-fourth the diameter of the fan. These rules do not agree with those 
adopted by modern manufacturers, nor do the rules adopted by different 
manufacturers agree among themselves. An examination of 18 commer- 
cial sizes of fans, of the ordinary steel-plate type, built by two prominent 
manufacturers, A and B, shows the following proportions based on the 
diameter of the fan wheel, D, in inches: 



Proportions of Fans, Rectangular Blades. 






A 

Max. 


A 

Min. 


A 

Av. 


B 

Max. 


B 

Min. 


B 

Av. 


Buckle. 


Diam. inlet 
Width of blade . 


0.666D 
0.435D 


0.618D 
0.380D 


0.636D 
0.398D 


0.495D 
0.366D 


0.430D 
0.333D 


0.476D 
0.356D 


0.5D 
0.25D 



The rules laid down by Buckle do not give a fan the highest commer- 
cial efficiency without loss of mechanical efficiency. By commercial effi- 
ciency is meant the ratio of the volume of air delivered per revolution to 
the cubical contents of the wheel, if the wheel be considered a solid whose 
dimensions are those of the wheel. This ratio is also known as the volu- 
metric efficiency. Inasmuch as the loss due to friction of the air entering 
the fan will be less with a large inlet than with a small one, in a wheel of 



FANS AND BLOWERS. 627 

given diameter, more power will be consumed in delivering a given volume 
of air with a small inlet than with a larger one. 

In the ordinary fan the number of vanes varies from 4 to 8, while with 
multivane fans it is 60 or more. The number of vanes has a direct relation 
to the size of the inlet. This is made as large as possible for the reason 
given above. Any increase in the diameter of the inlet necessarily de- 
creases the depth of the blade, thus diminishing the capacity and pressure. 
To overcome this decrease, the number of blades is increased to the limit 
placed by constructional considerations. A properly proportioned fan is 
one in which a balance is obtained between these two features of maxi- 
mum inlet and maximum number of blades. Generally speaking, in a 
purely centrifugal fan, increased pressure is obtained with the increase in 
depth of the blade. This appears to be due to the greater area of blade 
working on the air. A smaller wheel, with a greater number of blades, 
aggregating a larger blade area, gives a higher pressure than a larger 
wheel with less total blade area. 

In some cases two fans mounted on one shaft may be more useful than 
a single wide one, as in such an arrangement twice the area of inlet opening 
is obtained, as compared with a single wide fan. Such an arrangement 
may be adopted where occasionally half the full quantity of air is required, 
as one of the fans may be put out of gear and thus save power. 

Rules for Fan Design. — It is impossible to give any general rules 
or formulae covering the proportions of parts of fans and blowers. There 
are no less than 14 variables involved in the construction and operation of 
fans, a slight change in any one producing wide variations in the perform- 
ance. The design of a new fan by manufacturers is largely a matter of 
trial and error, based on experiments, until a compromise with all the 
variables is obtained which most nearly conforms to the given conditions. 

Pressure Due to Velocity of the Fan Blades. — The pressure of the 
air due to the velocity of the fan blades may be determined by the formula 

H = -^— , deduced from the law of falling bodies, in which H is the " head " 

or height of a homogeneous column of air one-inch square whose weight is 
equal to the pressure per square inch of the air leaving the fan, v is the 
velocity of the air leaving the fan in feet per second, and q the acceleration 
due to gravity. The pressure of the air is increased by increasing the 
number of revolutions per minute of the fan. Wolff, in his "The Wind- 
mill as a Prime Mover," p. 17, argues that it is an error to take // = v 2 
■*■ 2 g, the formula according to him being H = v 2 -s- g. See also Trow- 
bridge (Trans. A. S. M. E., vii., 536). This law is analogous to that of 
the pressure of a fluid jet striking a plane surface perpendicularly and 
escaping at right angles to its original path, this pressure being twice that 
due the height calculated from the formula h = v 2 -*- 2 g. (See Hawksley, 
Proc. Inst. M. E., 1882.) Later authorities and manufacturers, however, 
base all their calculations on the former formula. 

Buckle says: " From the experiments it appears that the velocity of the 
tips of the fan is equal to nine-tenths of the velocity a body would acquire 
in falling the height of a homogeneous column of air equivalent to the 
density." D. K. Clark (R. T. & D., p. 924), paraphrasing Buckle, appar- 
ently, says: " It further appears that the pressure generated at the circum- 
ference is one-ninth greater than that which is due to the actual circumfer- 
ential velocity of the fan." The two statements, however, are not in 

harmony, for if „ = oWi^?, H = Q -^^= 1.234^and not ff g - 

If we take the pressure as that equal to a head or column of air of twice 
the height due the velocity, as stated by Trowbridge, the paradoxical 
statements of Buckle and Clark — which would indicate that the actual 
pressure is greater than the theoretical — are explained, and the formula 

becomes H = 0.617 — and v = 1.273 ^gH = 0.9 ^2gH, in which H is 

the head of a column producing the pressure, which is equal to twice the 
theoretical head due the velocity of a falling body (k = v 2 /2 g), multiplied 
by the coefficient 0.617. The difference between 1 and this coefficient ex- 
presses the loss of pressure due to friction, to the fact that the inner por- 
tions of the blade have a smaller velocity than the outer edge, and probably 
to other causes. The coefficient 1 .273 means that the tip of the blade must 
be given a velocity 1.273 times that theoretically required to produce the 
head H. 



628 air. 

Commenting on the above paragraphs and the formulae below, the B. F. 
Sturtevant Co., in a letter to the author, says: "Let us assume that the 
fan considered is of the centrifugal type, which is a wheel in a spiral casing. 
In any case of centrifugal fan the pressure at the fan outlet is wholly 
dependent upon the load on the fan, and, therefore, the pressure cannot 
well be expressed by a formula, unless it includes some term which is an 
expression in some way of the load upon the fan. The actual pressure 
depends upon the design of both wheel and housing, upon the blade area 
and also upon the form of the blades. With a curved blade running with 
the concave side forwara it is possible to obtain a much higher pressure 
than if the blade is running with the convex side forward. This can only 
be shown by tests, and can be figured out by blade-velocity diagrams." 

It should be noted, however, that while the fan with a blade concaved 
in the direction of rotation has the highest efficiency, all other things being 
equal, the noise of operation is increased. A blade convex in the direction 
of rotation runs more quietly, and in most situations it is necessary to 
sacrifice efficiency in order to obtain quiet operation. 

To convert the head H expressed in feet to pressure in lb. per sq. in. 
multiply it by the weight of a cubic foot of air at the pressure and tempera- 
ture of the air expelled from the fan (about 0.08 lb. usually) and divide by 
144. Multiply this by 16 to obtain pressure in ounces per sq. in. or by 
2.035 to obtain inches of mercury, or by 27.71 to obtain pressure in inches 
of water c olum n. Taking 0.08 as the weight of 1 cu. ft. of air, and 
v - 0.9 ^2 gH, 

p lb. per sq. in. = 0.00001066 v 2 ; v = 310 VP_nearly; 

pi ounces per sq. in. = 0.0001706 v 2 ; v= 80 \/Pi " 
p 2 inches of mercury = 0.00002169 v 2 \ v = 220 VP2 " 
ps inches of water = 0.0002954 v 2 ; v= 60 VP3 " 

in which v = velocity of tips of blades in feet per second. 

Testing the above formula by one of Buckle's expeiiments with a vane 
14 inches long, we have p = 0.00001066 v 2 = 9.56 oz. The experiment 
gave 9.4 oz. 

Testing it by the experiment of H. I. Snell, given below, in which the 
circumferential speed was about 150 ft. per second, we obtain 3.85 ounces, 
while the experiment gave from 2.38 to 3.50 ounces, according to the 
amount of opening for discharge. _ 

Taking the formula v = 80 Vp x> we have for different pressures in 
ounces per square inch the following velocities of the tips of the blades in 
feet per second: 

pi = ounces per square inch. 2 3 4 5 6 7 8 10 12 14 

v = feet per second 113 139 160 179 196 212 226 253 277 299 

A rule in App. Cyc. Mech., article " Blowers," gives the following veloci- 
ties of circumference for different densities of blast in ounces: 3,170 ; 4, 180; 
5, 195; 6, 205; 7, 215. 

The same article gives the following tables, the first of which shows that 
the density of blast is not constant for a given velocity, but depends on the 
ratio of area of nozzle to area of blades: 

Velocity of circumference, feet per second.. . 150 150 150 170 200 200 220 

Area of nozzle -5- area of blades 2 1 1/2 1/4 1/2 Ve Vs 

Density of blast, oz. per square inch 12 3 4 4 6 6 

Quantity of Air op a Given Density Delivered by a Fan. 
Total area of nozzles in square feet X velocity in feet per minute corre- 
sponding to density (see table) = air delivered in cubic feet per minute, 
discharging freely into the atmosphere (approximate). See p. 642. 



Density, Velocity, 

ounces feet per 

per sq. in. minute. 

1 5,000 

2 7,000 

3 8,600 

4 10,000 



Density, Velocity, 

ounces feet per 

per sq. in. minute. 

5 11,000 

6 12,250 

7 13,200 

8 14,150 



Density, Velocity, 

ounces feet per 

per sq. in. minute. 

9 15,000 

10 15,800 

11 16,500 

12 17,300 



FANS AND BLOWERS. 



629 



" Blast Area," or " Capacity Area." When the fan outlet is small 
the velocity of the outflow is equal to the peripheral velocity of the fan. 

Start with the outlet closed; then if the opening be slowly increased 
while the speed of the fan remains constant the air will continue to flow 
with the same velocity as the fan tips until a certain size of outlet is 
reached. If the outlet is still further increased the pressure within the 
casing will drop, and the velocity of outflow will become less than the 
tip velocity. The size of the outlet at which this change takes place is 
called the blast area, or capacity area, of the fan. This varies somewhat 
with different types and makes of fans, but for the common form of 
blower it is approximately, DW -4- 3, in winch D is the diameter of the 
fan wheel and W its width at the circumference. — (C. L. Hubbard.) 

This established capacity area has no relation to the area of the outlet 
in the casing, which may be of any size, but is usually about twice the 
capacity area. The velocity of the air discharged through this latter 
area is practically that of the circumference of the wheel, and the pressure 
created is that corresponding thereto. — W. B. Snow. 

Experiments with Blowers. (Henry I. Snell, Trans. A. S. M. E., ix. 
51.) — The following tables give velocities of air discharging through an 
aperture of any size under the given pressures into the atmosphere. The 
volume discharged can be obtained by multiplying the area of discharge 
opening by the velocity, and this product by the coefficient of contraction: 
0.65 for a thin plate and 0.93 when the orifice is a conical tube with a con- 
vergence of about 3.5 degrees, as determined by the experiments of Weis- 
bach. 

The tables are calculated for a barometric pressure of 14.69 lb . ( = 
235 oz.), and for a temperature of 50° Fahr., from the formula V = "^2 gh. 

Allowances have been made for the effect of the compression of the air, 
but none for the heating effect due to the compression. 

At a temperature of 50 degrees, a cubic foot of air weighs 0.078 lb., and 
calling g = 32.1602, the above formula may be reduced to 



V x = 60 \ / 31.5812 X (235 + P)X P, 

where V t = velocity in feet per minute, P = pressure above atmosphere, 
or the pressure shown by gauge, in oz. per square inch. 





Corre- 






Corre- 




Pressure 


sponding 


Velocity due 


Pressure 


sponding 


Velocity due 


per sq. in., 


Pressure, 


to Pressure, 


per sq. in., 


Pressure, 


to Pressure, 


in. of water. 


oz. per sq. 
in. 


ft. per min. 


in. of water. 


oz. per sq. 
in. 


ft. per min. 


V32 


0.01817 


696.78 


5/8 


0.36340 


3118.38 


Vl6 


0.03634 


987.66 


3/ 4 


0.43608 


3416.64 


1/8 


0.07268 


1393.75 


7/8 


0.50870 


3690.62 


3/16 


0.10902 


1707.00 


1 


0.58140 


3946.17 


1/4 


0.14536 


1971.30 


11/4 


0.7267 


4362.62 


5/16 


0.18170 


2204.16 


11/2 


0.8721 


4836.06 


3/8 


0.21804 


2414.70 


13/4 


1.0174 


5224.98 


1/2 


0.29072 


2788.74 


2 


1.1628 


5587.58 



Pres- 
sure, 
oz.per 
sq. in. 

0.25 
0.50 
0.75 
1.00 
1.25 
1.50 
1.75 
2.00 



Velocity 
due to 

Pressure ; 
ft. per. 
min. 

2,582 
3,658 
4,482 
5,178 
5,792 
6,349 
6,861 
7,338 



Pres- 
sure, 
oz.per 
sq. in. 

2.25 
2.50 
2.75 
3.00 
3.50 
4.00 
4.50 
5.00 



Velocity 
due to 

Pressure 
ft. per 
min. 

7,787 
8,213 
8,618 
9,006 
9,739 
10,421 
11,065 
11,676 



Pres- 
sure, 
oz.per 
sq. in. 

5.50 
6.00 
6.50 
7.00 
7.50 
8.00 
9.00 
10.00 



Velocity 
due to 

Pressure, 
ft. per 



12,259 
12,817 
13,354 
13,873 
14,374 
14,861 
15,795 
16,684 



Pres- 
sure, 
oz. per 



11.00 
12.00 
13.00 
14.00 
15.00 
16.00 



Velocity 
due to 
Pressure, 
ft. per 
min. 

17,534 
18,350 
19,138 
19,901 
20,641 
21,360 



630 



Pressure in 
ounces per 
square inch. 


Velocity in feet 
per minute. 


Pressure in ounces 
per square inch. 


Velocity in feet 
per minute. 


0.01 
0.02 
0.03 
0.04 
0.05 


516.90 
722.64 
895.26 
1033.86 
1155.90 


0.06 
0.07 
0.08 
0.09 
0.10 


1266.24 
1367.76 
1462.20 
1550.70 
1635.00 



Experiments on a Fan with Varying Discharge-opening. 
Revolutions nearly constant. 



© 
ft 
w 

3 

.2© 


© • 
|| 


3 
© 


I 

<! © ■ 

ftS 

'ot3 © 


1 

o 


Izj'S © 


heoret. Vol. per 
min. that may be 
discharged with 
1 H.P.at corresp. 
Pressure. 


O © 


3 3 

o.S 

©S 


© a 


© s 

> 3 

n 


© bfl « 

3^ 3 
■£ © e 


ft 
1 

o 


• ft 
3g| 


.£ * 3 

J ©S 


K 


< 


o 


> 


W 


< 


H 


H 


1519 



6 


3.50 
3.50 



406 


0.80 
1.15 




1048 
1048 




1479 


353 


0.337 


1480 


10 


3.50 


676 


1.30 


520 


1048 


0.496 


1471 


20 


3.50 


1353 


1.95 


694 


1048 


0.66 


1485 


28 


3.50 


1894 


2.55 


742 


1048 


0.709 


1485 


36 


3.40 


2400 


3.10 


774 


1078 


0.718 


1465 


40 


3.25 


2605 


3.30 


790 


1126 


0.70 


1468 


44 


3.00 


2752 


3.55 


115 


1222 


0.635 


1500 


48 


3.00 


3002 


3.80 


790 


1222 . 


0.646 


1426 


89.5 


2.38 


3972 


4.80 


827 


1544 


0.536 



The fan wheel was 23 in. diam., 65/s in. wide at its periphery, and had 
an inlet 12 1/2 in. diam. on either side, which was partially obstructed by 
the pulleys, which were 59/i6 in. diam. It had eight blades, each of an 
area of 45.49 sq. in. The discharge of air was through a conical tin tube 
with sides tapered at an angle of 31/2 degrees. The actual area of opening 
was 7% greater than given in the tables, to compensate for the vena con- 
tracta. 

In the last experiment, 89.5 sq. in. represents the actual area of the 
mouth of the blower less a deduction for a narrow strip of wood placed 
across it for the purpose of holding the pressure-gauge. In calculating the 
volume of air discharged in the last experiment the value of vena contracta 
is taken at 0.80. 

Experiments were undertaken for the purpose of showing the results 
obtained by running the same fan at different speeds with the discharge- 
opening the same throughout the series. The discharge-pipe was a conical 
tube 8 1/2 in. inside diam. at the end, having an area of 56.74 sq. in., which 
is 7% larger than 53 sq. in.; therefore 53 sq. in., equal to 0.368 square feet, 
is called the area of discharge, as that is the practical area by which the 
volume of air is computed. 



FANS AND BLOWERS. 



631 



Experiments on a Fan with Constant Discharge-opening and 
Varying Speed. — The first four columns are given by Mr. Snell, the 
others are calculated by the author. 





m 


c 




°S 


k^\ * 


°'\1 


8 b 

ft3 . 


i 


| 


d 


pi 

3 


3^ 
® 




H ft 




H « 




o 

w 




i 


1* 


-5 Pi 


1 
o 
ft 

1 

o 


•'o t *l 


s 2 „ 


+> ft 


«-. PI .1. 


la 


ft 
>> 


> 

0> 


| 


21 

O h 


• --0 

■in 


■s»-5 

in 


2 W 

'o Sri 


■-2 » 
g.S ft 


II 


o 
'3 


Ph 


£ 


> 


w 


^> 


> 


o 


> 


H 


H 


600 


0.50 


1336 


0.25 


60.2 


56.6 


85.1 


3,630 


0.182 


73 


800 


0.88 


1787 


0.70 


80.3 


75.0 


85.6 


4,856 


0.429 


61 


1000 


1.38 


2245 


1.35 


100.4 


94 


85.4 


6,100 


0.845 


63 


1200 


2.00 


2712 


2.20 


120.4 


113 


85.1 


7,370 


1.479 


67 


1400 


2.75 


3177 


3.45 


140.5 


133 


84.8 


8,633 


2.283 


66 


1600 


3.80 


3670 


5.10 


160.6 


156 


82.4 


9,973 


3.803 


74 


1800 


4.80 


4172 


8.00 


180.6 


175 


82.4 


11,337 


5.462 


68 


2000 


5.95 


4674 


11.40 


20Q.7 


195 


85.6 


12,701 


7.586 


67 



Mr. Snell has not found any practical difference between the mechanical 
efficiencies of blowers with curved blades and those with straight radial 
ones. From these experiments, says Mr. Snell, it appears that we may 
expect to receive back 65% to 75% of the power expended, and no more. 
The great amount of power often used to run a fan is not due to the fan 
itself, but to the method of selecting, erecting, and piping it. (For opin- 
ions on the relative merits of fans and positive rotary blowers, see discus- 
sion of Mr. Snell's paper, Trans. A. S. M. E., ix. 66, etc.) 

Comparative Efficiency of Fans and Positive Blowers. (H. M. 
Howe, Trans. A. I. M. E., x. 482.) — Experiments with fans and positive 
(Baker) blowers working at moderately low pressures, under 20 ounces, 
show that they work more efficiently at a given pressure when delivering 
large volumes (i.e., when working nearly up to their maximum capacity) 
than when delivering comparatively small volumes. Therefore, when 
great variations in the quantity and pressure of blast required are liable 
to arise, the highest efficiency would be obtained by having a number of 
blowers, always driving them up to their full capacity, and regulating the 
amount of blast by altering the number of blowers at work, instead of 
having one or two very large blowers and regulating the amount of blast 
by the speed of the blowers. 

There appears to be little difference between the efficiency of fans and 
of Baker blowers when each works under favorable conditions as regards 
quantity of work, and wnen each is in good order. 

For a given speed of fan \y diminution in the size of the blast-orifice 
decreases the consumption ?t power and at the -same time raises the pres- 
sure of the blast; but r; increases the consumption of power per unit of 
orifice for a given pressure of blast. When the orifice has been reduced to 
the normal si^e for any given fan, further diminishing it causes but slight 
elevation of the blast pressure; and, when the orifice becomes compara- 
tively small, further diminishing it causes no sensible elevation of the 
blast pressure, which remains practically constant, even when the orifice is 
entirely closed. 

Many of the failures of fans have been due to too low speed, to too small 
pulleys, to improper fastening of belts, or to the belts being too nearly ver- 
tical: in brief, to bad mechanical arrangement, rather than to inherent 
defects in the principles of the machine. 

If several fans are used, it is probably essential to high efficiency to pro- 
vide a separate blast pipe for each (at least if the fans are of different size 
or speed), while any number of positive blowers may deliver into the same 
pipe without lowering their efficiency. 



632 



AIR. 



Capacity of Fans and Blowers. — The following tables supplied (1909) 
by the American Blower Co., Detroit, show the capacities of exhaust fans 
and volume and pressure blowers. The tables are all based on curves 
established by experiment. The pressures, volumes and horse-powers 
were all actually measured with the apparatus working against maintained 
resistances formed by restrictions equivalent to those found in actual prac- 
tice, and which experience shows will produce the best results. 

Speed, Capacity and Horse-power of Steel Plate Exhaust Fans. 

(American Blower Co., Type E, 1908.) 











1/2 oz. pres- 


3/4 oz. pres- 


I oz. pres- 


2 oz. pres- 










sure. 


sure. 


sure. 


sure. 






























*° J 


a 


!s.s 




& 


h 




& 


h 




3 


i 




a> 


£ 


6 




■ 0> 






a . 






a . 






A . 






ft . 




f! 

Ba 




a) a- 

as 

- 1 


id 

Pm 


£3 
11 






£3 

31 


tl 

Jl 

2 a 


P4 


£"3 
2 c 


^ 

(B 2 

S a 


3 

p4 


. a> 
2 a 

■S'i 


J Si 


fc 


Q 
16 


Q 
10 


985 


O 


pq 
0.30 


1200 





0.56 


PI 
1390 


O 


pq 
0.85 


PI 

1966 





n 


25 


61/8 


1,09 


1,345 


1,555 


2,200 


2.40 


30 


19 


vy* 


12 


830 


1,580 


43 


1012 


1,940 


0.80 


1170 


2,240 


1.22 


1655 


3,175 


3.46 


35 


22 


81/8 


14 


715 


2,155 


59 


876 


2,635 


1 08 


1010 


3,040 


1.66 


1430 


4,310 


4.70 


40 


25 


93/8 


16 


630 


2,820 


77 


772 


3,450 


1 41 


1890 


3.980 


2 17 


1260 


5,640 


6.15 


43 


28 


107/s 


18 


563 


3,560 


97 


689 


4,360 


1 78 


1795 


5,030 


2 74 


1125 


7,140 


7.79 


50 


31 


123/ 8 


20 


508 


4,400 


1.20 


622 


5,390 


2 20 


1719 


6,220 


3 39 


1015 


8,820 


9 63 


55 


34 


131/m 


22 


464 


5,330 


1.45 


567 


6,525 


2.66 


1655 


7,530 


4.10 


927 


10,650 


11.60 


60 


38 


141/9 


24 


413 


6,350 


1.73 


309 


7,775 


3 18 


1587 


8,960 


4 89 


830 


12,700 


13 85 


70 


44 


131/8 


27 


373 


7,440 


2.02 


459 


9,120 


3.72 


1530 


10,500 


5.72 


750 


14,875 


16,20 


80 


30 


l61/ 2 


29 


328 


10,050 


2.75 


402 


12,100 


4.94 


1464 


13,980 


7.62 


656 


19,800 


21.60 



Speed, Capacity and Horse-power of Volume Blowers. 

(American Blower Co., Type V, 1909.) 











1/2 oz. pres- 


3/4 oz. pres- 


1 oz. pres- 


1 1/2 oz. pres- 






-i 




sure. 


sure. 


sure. 




sure. 






















"S.9 


_ft 

0) 


l-~ 




ft . 


i 




a . 


£ 




0) 

ft . 


i 




ft . 


k 






u s 


fc'u 




























-2"a5 


^T3 






J Si 




tin 3 


A |R 




«£"§ 


-^ m 






*% 


"S 


2 » 

S3 £ 


£* 

."2S 


S.I 


3 


3*1 


2 a 


Pm 


fl 

3l 


2 a 


9 

Pm 


3l 


■36 

S a 


Pm 


2 c 

■Si 


la 


fc 


Q 


£ 


Q 


K 


O 


« 


rt 





ffl 


pej 





pq 


« 





P3 


1 


8I/9 


7. 


41/9 


1850 


223 


0.06 


2270 


273 


0.11 


2620 


315 


0.17 


3210 


386 


0.32 


? 


101/1 


23/r 


51/9 


1535 


332 


0.09 


1880 


407 


0.17 


2170 


469 


0.26 


2660 


576 


0.48 


3 


12 


31/4 


6 1/9 


1310 


464 


13 


1600 


569 


0.23 


1830 


656 


0.36 


2273 


805 


0.66 


4 


151/9 


43/9 


8 1/9 


1015 


705 


22 


1240 


975 


0.40 


1433 


1122 


0.61 


1760 


1377 


1.13 


5 


19 


51/8 


103/ 8 


830 


1185 


32 


1013 


1450 


0.59 


1170 


1675 


0.92 


1435 


2055 


1.68 


6 


221/9 


61/. 


17.3/8 


700 


1686 


46 


858 


2065 


0.84 


990 


2385 


1.30 


1213 


2930 


2.40 


7 


7.6 


71/9 


HI/4 


606 


7735 


61 


742 


2740 


1.12 


838 


3160 


1.72 


1030 


3880 


3.18 


8 


291/9 


8I/0 


161/1 


534 


7.910 


79 


654 


3560 


1 45 


753 


4110 


2.24 


928 


5040 


4.13 


9 


33 


91/2 


181/4 


477 


3660 


1.00 


585 


4490 


1.83 


673 


5175 


2.82 


823 


6350 


5.20 



Note: This table also applies to Type V, cast-iron exhaust fans. 



FANS AND BLOWERS. 



633 



Steel Pressure Blowers for Cupolas (Average Application). 

(American Blower Co., 1909.) 



^ 


.15 
"o 

s 

141/2 


.ft 

ft.S 

-S 

S 


II 

o 


!l 

5 


3 
O 

< 


Oz. 


2 


3 


4 


5 


6 


7 


8 


9 


* 


In. 


3.46 


5.19 


6.92 


8.65 


10.38 


12.12 


13.83 


15.56 


6 


H.P. 

const, 
at 1000 
cu. ft. 


1.242 


1.86 


2.48 


3.10 


3.73 


4.35 


4.95 


5.58 


1 


13/8 


3.80 


53/4 


0.18 


R.P.M. 
C.F. 
H.P. 


1960 
361 
0.45 


2400 
434 
0.81 


2770 
500 
1.24 


3095 
560 
1.74 


3390 
610 

2.28 


3666 
665 
2.89 


3915 
708 
3.51 


4150 
752 
4.20 


2 


17 


15/8 


4.45 


63/ 4 


0.2485 


R.P.M. 
C.F. 
H.P. 


1675 
498 
0.62 


2050 
600 
1.12 


2362 
691 
1.72 


2645 
774 
2.40 


2895 
843 
3.15 


3130 
916 
3.99 


3340 
978 
4.84 


3540 
1038 
5.79, 


3 


191/2 


17/8 


5.11 


73/4 


0.327 


R.P.M. 
C.F. 
H.P. 


1460 
655 
0.82 


1785 
789 
1.47 


2060 
910 
2.26 


2300 
1018 
3.16 


2520 
1110 
4.15 


2730 
1207 
5.25 


2910 
1286 
6.36 


3085 
1365 
7.62 


4 


22 


21/8 


5.76 


83/4 


0.4176 


R.P.M. 
C.F. 
H.P. 


1292 
838 
1.04 


1582 
1006 
1.87 


1825 
1162 
2.88 


2040 
1300 
4.03 


2235 
1415 
5.28 


2420 
1540 
6.70 


2585 
1643 
8.14 


2740 
1746 
9.74 


5 
6 
7 
8 
9 


241/ 2 


23/8 


6.41 


93/4 


0.519 


R.P.M. 
C.F. 
H.P. 


1162 
1040 
1.30 


1422 
1250 
2.33 


1640 
1442 
3.58 


1835 
1612 
5.00 


2010 
1760 
6.57 


2175 
1915 
8.34 


2320 
2040 
10.10 


2460 
2166 
12.10 


27 


27/8 
33/8 


7.06 
8.39 


103/4 


0.63 


R.P.M. 
C.F. 
H.P. 


1055 
1262 
1.57 


1290 
1520 
2.83 


1490 
1750 
4.34 


1665 
1960 
6.08 


1825 
2135 
7.96 


1975 
2375 
10.10 


2105 
2475 
12.25 


2233 
2630 
14.12 


32 


121/2 


0.852 


R.P.M. 
C.F. 
H.P. 


889 
1705 
2.12 


1087 
2055 
3.83 


1255 
2366 
5.86 


1405 
2650 
8.23 


1535 
2890 
10.78 


1660 
3140 
13.66 


1775 
3350 
16.60 


1880 
3555 
19.83 


37 


37/8 


9.70 


14 


1.069 


R.P.M. 
C.F. 
H.P. 


769 
2140 
2.66 


940 
2575 
4.79 


1085 
2970 
7.36 


1212 
3325 
10.3 


1328 
3620 
13.5 


1446 
3940 
17.15 


1533 
4200 
20. CO 


1625 
4460 
24.90 


42 


43/8 


10.98 


16 


1.396 


R.P.M. 
C.F. 
H.P. 


679 
2800 
3.48 


830 
3370 
6.27 


958 
3880 
9.63 


1072 
4340 
13.46 


1172 
4730 
17.65 


1270 
5150 
22.40 


1355 
5500 
27.25 


1435 
5825 
32.50 


10 


47 


47/8 


12.30 


171/2 


1.67 


R.P.M. 
C.F. 
H.P. 


606 
3350 
4.17 


742 
4025 
7.5 


855 
4640 
11.5 


956 
5200 
16.12 


1048 
5660 
21.12 


1133 
6160 
26.80 


1210 
6570 
32.55 


1280 
6970 
38.90 


11 


52 


53/8 


13.6 


191/4 


2.02 


R.P.M. 
C.F. 
H.P. 


548 
4050 
5.03 


670 
4870 
9.06 


774 
5610 
13.9 


865 
6290 
19.5 


947 
6850 
25.55 


1025 
7450 
32.40 


1093 
7950 
39.33 


1160 
8440 
47.10 


12 


57 


57/8 


14.92 


21 


2.405 


R.P.M. 
C.F. 
H.P. 


500 
4820 
6.00 


611 
5800 
10.78 


705 
6700 
16.62 


789 
7490 
23.25 


863 
8160 
30.45 


934 
8870 
38.60 


996 
9460 
46.85 


1056 
10040 
56.10 



634 



Steel Pressure Blowers for Cupolas (Average Application).— 

Continued. 





"a3 

CD 

J3 






S.S 


3 


Oz. 


10 


11 


12 


13 


14 


15 


16 





In. 


17 28 


19,02 


20.75 


22.5 


24.22 


25.95 


27.66 






P-fl 


d"cu 
5 ® 


o g_ 


*o£ 




















H.P. 
















6 


<3 
5 


T3 

5 




.g'S 

Q 




const, 
at 1000 
cu. ft. 


6.20 


6.82 


7.44 


8.07 


8.69 


9.30 


9.92 




17 


15/8 


4.45 


63/ 4 


0.2485 


R.P.M. 
C.F. 
H.P. 


3740 
1093 
6.78 


3920 
1148 
7.83 


4090 
1196 
8.9 










?. 










































R.P.M. 


3255 


3415 


3570 


3710 


3955 


3985 


4120 


3 


191/-, 


17/8 


5.11 


73/4 


0.327 


C.F. 


1440 


1510 


1575 


1642 


1700 


1762 


1820 














H.P. 


8.93 


10.3 


11.72 


13.26 


14.75 


16.4 


18.05 














R.P.M. 


2890 


3030 


3163 


3290 


3420 


3535 


3650 


4 


22 


21/8 


5.76 


83/4 


0.4176 


C.F. 


1840 


1930 


2012 


2095 


2175 


2250 


2325 














H.P. 


11.40 


13.16 


14.96 


16.9 


18.9 


20.9 


23.1 














R.P.M. 


2595 


2720 


2845 


2960 


3075 


3180 


3280 


5 


24 V, 


23/ 8 


6.41 


93/ 4 


0.519 


C.F. 


2280 


2395 


2500 


2605 


2700 


2800 


2885 














H.P. 


14.13 


16.33 


18.6 


21.05 


23.45 


26.05 


23.66 














R.P.M. 


2355 


2470 


2580 


2685 


2790 


2885 


2980 


6 


27 


27/8 


7.06 


103/4 


0.63 


C.F. 


2770 


2910 


3033 


3165 


3280 


3395 


3500 














H.P. 


17.18 


19.85 


22.6 


25.55 


28.50 


31.55 


34.7 














R.P.M. 


1983 


2080 


2170 


2260 


2345 


2430 


2510 


7 


32 


33/s 


8.39 


121/^ 


0.852 


C.F. 


3750 


3930 


4110 


4276 


4430 


4590 


4730 














H.P. 


23.25 


26.80 


30.6 


34.5 


38.5 


42.7 


47. 














R.P.M. 


1715 


1800 


1880 


1955 


2030 


2100 


2170 


8 


37 


37/8 


9.70 


14 


1.069 


C.F. 


4700 


4930 


5150 


5360 


5560 


5760 


5940 














H.P. 


29.15 


33.66 


38.33 


43.25 


48.30 


53.55 


59. 














R.P.M. 


1515 


1590 


1660 


1728 


1792 


1855 


1916 


9 


42 


43/ 8 


10.98 


16 


1.396 


C.F. 


6150 


6450 


6730 


7010 


7270 


7525 


7760 














H.P. 


38.15 


44.00 


50.15 


56.60 


63.2 


70. 


77. 














R.P.M. 


1352 


1418 


1480 


1540 


1600 


1655 


1710 


10 


47 


47/ 8 


12.30 


171/9 


1.67 


C.F. 


7350 


7715 


8055 


8390 


8700 


9010 


9300 














H.P. 


45.60 


52.66 


60. 


67.66 


75.6 


83.9 


92.25 














R.P.M. 


1222 


1282 


1340 


1393 


1447 


1498 


1546 


11 


52 


53/8 


13.6 


191/-) 


2.02 


C.F. 


8900 


9330 


9750 


10140 


10520 


10890 


11220 














H.P. 


55.20 


63.6 


72.5 


82. 


91.5 


101.2 
1363 


111.33 














R.P.M. 


1113 


1168 


1220 


1270 


1318 


1410 


12 


57 


57/ 8 


14 92 


21 


2.405 


C.F. 


10580 


11100 


11600 


12080 


12520 


12960 


13380 














H.P. 


65.5 


75.70 


86.33 


97.5 


109 


120.5 


132.75 


Cai 


ition in Regard to 


Use of Fan and Blower Tables. — Many en- 


gineei 
their 


s report that some 
fans and underestima 


manufacturers' tables overrate the capacity of 
te the horse-power required to drive them. In 


some 


cases the complaints 


may be due to restricted air outlets, long and 


crook 


gd pipes, slipping of 


belts, too small engines, etc. It may also be 


due t 


d the fact that the \ 


olumes are stated without being accompanied 


1 


sy in 


form 


ation 


as t 


o the 


maintai 


tied r 


esista 


nee, a 


nd th 


3 volu 


mes gi 


ven 



FANS AND BLOWEKS. 



635 



may be those delivered with an unrestricted inlet and outlet. As this 
condition is not a practical one, the volume delivered in an installation 
is much smaller than that given in the tables. The underestimating of 
horse-power required may be due to the fact that the volumes given in 
tables are for operation against a practical resistance, and in an installa- 
tion it might be that the resistance was low, consequently the volume 
and also the horse-power required would be greater. 

Capacity of Sturtevant High-Pressure Blowers (1908). 



Number of 
blower. 


Capacity in cubic feet 
per minute, 1/2 lb. pres- 
sure. 


Revolutions per 
minute. 


Inside dia. 

of inlet 
and outlet, 

inches. 


Approx. 
weight, 
pounds.* 


000 


1 to 5 


200 to 1000 


13/s 


40 


00 


5 to 25 


375 to 800 


11/2 


80 





25 to 45 


370 to 800 


21/2 


140 


1 


45 to 130 


240 to 600 


3 


330 


2 


130 to 225 


300 to 500 


4 


550 


3 


225 to 325 


380 to 525 


4 


760 


4 


325 to 560 


350 to 565 


6 


1,080 


5 


560 to 1,030 


300 to 475 


8 


1,670 


6 


1,030 to 1,540 


290 to 415 


10 


2,500 


7 


1,540 to 2,300 


280 to 410 


10 


3,200 


8 


2,300 to 3,300 


265 to 375 


12 


4,700 


9 


3,300 to 4,700 


250 to 350 


16 


6,100 


10 


4,700 to 6,000 


260 to 330 


16 


8,000 


11 


6,000 to 8,500 


220 to 310 


20 


12,100 


12 


8,500 to 11,300 


190 to 250 


24 


18,700 


13 


11,300 to 15,500 


190 to 260 


30 


22,700 



* Of blower for 1/2 lb. pressure. 



Performance of a No. 7 Steel Pressure Blower under Varying 
Conditions of Outlet. 

Per cent of 
Rated Ca- 
pacity 20 40 60 80 100 120 140 160 180 200 220 240 

Rated H.P. 28 42 57 72 86 100 116 130 144 159 173 187 202 

Total pres- 
sure, oz 10.2 11.4 11.912.0 11.9 11.410.910.3 9.7 9.1 8.5 7.9 7.2 

Static pres- 
sure, oz ..10.211.2 11.611.411.0 10.2 9.2 8.0 6.6 5.0 3.5 1.9 0.3 

Efficiency, per 

cent 26 40 50 56 60 62 61 59 56 52 48 45 

The above figures are taken from a plotted curve of the results of 
a test by the Buffalo Forge Co. in 1905. A letter describing the test 
says : 

The object was to determine the variation of pressure, power and 
efficiency obtained at a constant speed with capacities varying from zero 
discharge to free delivery. A series of capacity conditions were secured 
by restricting the outlet of the blower by a series of converging cones, 
so arranged as to make the convergence in each case very slight, and of 
sufficient length to avoid any noticeable inequality in velocities at the 
discharge orifice. The fan was operated as nearly at constant speed as 
possible. The velocity of the air at the point of discharge was measured 
by a Pitot tube and draft gauge of usual construction. Readings were 
taken over several points of the outlet and the average taken, although 



636 



AIR. 



the variation under nearly all conditions was scarcely perceptible. A 
coefficient of 93% was assumed for the discharge orifice. The pressure 
was taken as the reading given by the Pitottube and draft gauge at 
outlet. The agreement of this reading with the static pressure in a 
chamber from which a nozzle was conducted had been checked by a 
previous test in which the two readings, i.e., velocity and static pressure, 
were found to agree exactly within the limit of accuracy of the draft 
gauge, which was about 0.01 in., or, in this case, within 1% The horse- 
power was determined by means of a motor which had been previously 
calibrated by a series of brake tests. Variations in speed were assumed 
to produce variation in capacity in proportion to the speed, variation in 
pressure to the square of the speed, and variation in H.P. in proportion to 
the cube of the speed. These relations had been previously shown to 
hold true for fans in other tests. They were also checked up by oper- 
ating the fan at various speeds and plotting the capacities directly with 
the speed as abscissa, the pressure with the square of the speed as abscissa, 
and the horse power with the cube of the speed as abscissa. These were 
found, as in previous cases, to have a practically straight-line relation, in 
which the line passed through the origin. 

Effect of Resistance upon the Capacity of a Fan. — A study of the 
figures in the above table shows the importance of having ample capacity 
in the air mains and delivery pipes, and of the absence of sharp bends 
or other obstructions to the flow which may increase the resistance or 
pressure against which the fan operates. The fan delivering its rated 
capacity against a static pressure of 10.2 ounces delivers only 40 % 
of that capacity, with the same number of revolutions, if the pressure is 
increased to 11.6 ounces; the power is reduced only to 57%, instead of 
40%, and the efficiency drops from 60% to 40%. 



Dimensions of Sirocco Fans. 

(American Blower Co., 1909.) 





© • 
P-..S 

03 >> 


-T3 


.9 

2g" 


°.S ° 


"£.9 


a 



t a 1 


"S«4-l 

03 6* 
a> 03 


"- 1 i i 1 


3 a- 




3£ 


£-2 

3! a 


"o 

6 


i< 


las-? 


;5T2 


SUO 

gffl 


is 


«3 


gJ« 


"jscs 




S 


£"* 


48 


H 


w 


£ 


A 


% 


i 


< 


<~ 


^ 


6 


3 


56 


11" 


4 


10" 


.23 


.123 


.11 


.12 


3" 


9 


41/2 


48 


127 


V 4" 


6 


v y 


.49 


.349 


.25 


.35 


41/4" 


12 


6 


64 


226 


V 9" 


8 


V 7" 


.85 


.616 


.44 


.60 


53/4" 


15 


71/2 


64 


353 


2' 4" 


10 


2' 0" 


1.46 


.957 


.69 


.92 


71/4" 


18 


9 


64 


509 


2' 10" 


12 


2' 5" 


1.87 


1.37 


1.00 


1.40 


8 1/2" 


21 


101/2 


64 


693 


y a" 


14 


2' 10" 


2.40 


1.87 


1.34 


1.87 


10" 


24 


12 


64 


904 


y 8" 


16 


y 3" 


3.14 


2.46 


1.78 


2.40 


1 1 1/2" 


27 


131/2 


64 


1144 


4' 3" 


18 


y 7" 


4.59 


3.11 


2.25 


3.14 


13" 


30 


15 


64 


1413 


4' 7" 


20 


if o" 


5.58 


3.83 


2.78 


3.83 


141/2" 


36 


18 


64 


2036 


5' 6" 


24 


4' 10" 


7.87 


5.50 


4.00 


5.58 


17" 


42 


21 


64 


2770 


6' 5" 


28 


5' 7" 


10.56 


7.47 


5.44 


7.47 


20" 


48 


24 


64 


3617 


T 3" 


32 


6' 5" 


13.6 


9.79 


7.11 


9.85 


23" 


54 


27 


64 


4578 


8' 2" 


36 


T 3" 


17.0 


12.3 


9.00 


12.3 


26" 


60 


30 


64 


5652 


9' 1" 


40 


8' 0" 


20.9 


15.2 


11.11 


15.3 


281/ 2 " 


66 


33 


64 


6839 


9/ ir 


44 


8' 10" 


25.2 


18.4 


13.41 


18.3 


311/2" 


72 


36 


64 


8144 


1C 10" 


43 


9' 7" 


29.8 


22.2 


16.00 


22.3 


341/2" 



Sirocco or Multivane Fans. — • There has recently (1909) come into use 
a fan of radically different proportions and characteristics from the ordi- 
nary centrifugal fan. This fan is composed of a great number of shallow 
vanes, ranging from 48 to 64, set close together around the periphery of 
the fan wheel. Over a large range of sizes, 64 vanes appear to give the 



Speed, Capacities and Horse-power of Sirocco Fans. (American 
Blower Co., 1909.) 



The figures given represent dynamic pressures in oz. per sq. in. 
static pressure, deduct 28.8%; for velocity pressure, deduct 71.2%. 


For 


si 




o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


6 


Cu.ft. 
R.P.M. 
B.H.P. 


155 
1,145 
.0185 


220 
1,615 
.052 


270 
1,980 
.095 


310 
2,290 
.147 


350 

2,560 
.205 


380 
2,800 
.270 


410 

3,025 

.34 


440 

3,230 

.42 


490 

3,616 

.58 


540 

3,960 

.76 


9 


Cu.ft. 
R.P.M. 
B.H.P. 


350 
762 
.042 


500 
1,076 
.118 


610 
1,320 
.216 


700 
1,524 
.333 


790 
1,700 
.463 


860 
1,866 
.610 


930 

2,020 

.77 


1,000 

2,152 

.95 


1,110 
2,408 
1.32 


1,220 
2,640 
1.73 


12 


Cu.ft. 
R.P.M. 
B.H.P. 


625 
572 
.074 


880 
808 
.208 


1,080 
990 
.381 


1,250 
1,145 

.588 


1,400 

1,280 

.82 


1,530 
1,400 
1.08 


1,650 
1,512 
1.36 


1,770 
1,615 
1.66 


1,970 
1,808 

2.32 
3,090 
1,444 

3.65 
4,450 
1,204 

5.25 
6,060 
1,032 

7.15 

7.900 

904 

9.3 


2,170 
1,980 
3.05 


15 


Cu. ft. 
R.P.M. 
B.H.P. 


975 
456 
.115 


1,380 
645 
.326 


1,690 
790 
.600 


1,950 
912 
.923 


2,180 
1,020 
1.29 


2,400 
1,120 
1.69 


2,590 
1,210 
2.14 


2,760 
1,290 

2.61 
3,980 
1,076 

3.75 


3,390 

1,580 

4.8 


18 


Cu. ft. 
R.P.M. 
B.H.P. 


1,410 
381 
.167 


1,990 
538 
.470 


2,440 
660 
.862 


2,820 
762 
1.33 


3,160 
850 
1.85 


3,450 
933 
2.43 


3,720 
1,010 
3.07 


4,880 

1,320 

6.9 


21 


Cu. ft. 
R.P.M. 
B.H.P. 


1,925 
326 
.227 


2,710 
462 
.640 


3,310 
565 
1.17 


3,850 
652 
1.81 


4,290 
730 
2.53 


4,700 
800 
3.33 


5,070 
864 
4.18 


5,420 
924 
5.11 


6,620 

1,130 

9.4 


24 


Cu. ft. 
R.P.M. 
B.H.P. 


2,500 
286 
.296 


3,540 
404 
.832 


4,340 
495 
1.53 


5,000 
572 
2.35 


5,600 
640 

3.28 


6,120 
700 
4.32 


6,620 
756 
5.44 


7,080 
807 
6.64 


8,680 
990 
12.2 


27 


Cu. ft. 
R.P.M. 
B.H.P. 


3,175 
254 
.373 


4,490 
359 
1.05 


5,500 
440 
1.94 


6,350 
508 
2.98 


7,100 
568 
4.16 


7,780 
622 
5.48 


8,400 
672 
6.90 


8,980 
718 
8.44 


10,050 
804 
11.8 


11,000 
880 
15.5 


30 


Cu. ft. 
R.P.M. 
B.H.P. 


3,910 
228 
.460 


5,520 
322 
1.30 


6,770 
395 
2.40 


7,820 
456 
3.68 


8,750 
510 
5.15 


9,600 
560 
6.75 


10,350 
604 
8.53 


11,050 
645 
10.4 


12,350 
722 
14.5 


13,550 
790 
19.1 


36 


Cu. ft. 
R.P.M. 
B.H.P. 


5,650 
190 
.665 


7,950 
269 
1.87 


9,750 
330 
3.44 


11,300 
381 
5.30 


12,640 
425 
7.40 


13,800 
466 
9.72 


14,900 

504 

12.25 


15,900 
538 
15.0 


17,800 
602 
20.9 


19,500 
660 
27.5 


42 


Cu. ft. 
R.P.M. 
B.H.P. 


7,700 
163 
.903 


10,850 
231 
2.55 


13,300 
283 
4.69 


15,400 
326 

7.24 


17,170 
365 
10.1 


18,800 
400 
13.3 


20,300 
432 
16.7 


21,700 
462 
20.4 


24,250 
516 

28.5 


26,600 

566 

37.5 


48 


Cu. ft. 
R.P.M. 
B.H.P. 


10,000 
143 
1.18 


14,150 
202 
3.32 


17,350 

248 
6.10 


20,000 
286 
9.40 


22,400 
320 
13.1 


24,500 
350 
17.2 


26,500 

378 

21.75 


28,300 
403 
26.6 


31,600 
452 
37.1 


34,700 
495 
48.8 


54 


Cu. ft. 
R.P.M. 
B.H.P. 


12,700 
127 
1.49 


17,950 

179 

4.20 


22,000 
220 
7.75 


25,400 
254 
11.9 


28,400 
284 
16.6 


31,100 
311 
21.9 


33,600 
336 
27.6 


35,900 
359 
33.7 


40,200 
402 
47.1 


44,000 
440 
62. 


60 


Cu. ft. 
R.P.M. 
B.H.P. 


15,650 
114 
1.84 


22,100 
161 
5.20 


27,100 

198 

9.58 


31,300 
228 
14.7 


35,000 
255 
20.6 


38,400 
280 
27.0 


41,400 
302 
34.1 


44,200 
322 
41.6 


49,400 
361 

58.2 


54,200 
396 
76.5 


66 


Cu. ft. 
R.P.M. 
B.H.P. 


18,950 

104 

2.23 


26,800 

147 

6.30 


32,850 
180 
11.6 


37,900 
208 
17.8 


42,300 
232 
24.9 


46,400 
254 
32.7 


50,100 
275 
41.2 


53,600 
294 
50.4 


60,000 
328 
70.4 


65,700 
360 
92.6 


72 


Cu. ft. 
R.P.M. 
B.H.P. 


22,600 

95 

2.66 


31,800 
134 

7.48 


39,000 
165 
13.7 


45,200 

190 

21.2 


50,600 
212 
29.6 


55,200 
233 

38.9 


59,600 
252 
49.0 


63,600 
269 
59.8 


71,200 
301 
83.6 


78,000 
330 
110. 


78 


Cu. ft. 
R.P.M. 
B.H.P. 


26,400 

88 

3.10 


37,350 
124 
8.77 


45,800 
153 
16.1 


52,800 
176 
24.8 


59,100 

197 

34.7 


64,700 
215 
45.6 


70,000 
233 
57.5 


74,700 
248 
70.2 


83,500 
278 
98. 


91,600 
305 
129. 


84 


Cu. ft. 
R.P.M. 
B.H.P. 


30,800 

81 

3.61 


43,400 
115 
10.2 


53,200 
142 
18.7 


61,600 
163 
28.9 


68,700 
182 
40.4 


75,200 
200 
53.0 


81,200 
216 
66.8 


86,800 
231 
81.7 


97,100 
258 
114. 


106,400 
283 
150. 


90 


Cu. ft, 
R.P.M. 
B.H.P. 


35,250 

76 

4.14 


49,800 
107 
11.7 


61,000 
132 
21.5 


70,500 
152 
33.1 


78,800 
170 
46.2 


86,400 
186 
60.7 


93,300 
201 
76.7 


99,600 
214 
93.6 


111,200 
241 
131. 


122.000 
264 
172. 



638 



AIR. 



best results. The vanes, measured radially, have a depth 1/ie the fart 
diameter. Axially, they are much longer than those of the ordinary fan, 
being 3/ 5 the fan diameter. The fan occupies about 1/2 the space, and is 
about 2/3 the weight of the ordinary fan. The vanes are concaved in the 
direction of rotation and the outer edge is set forward of the inner edge. 
The inlet area is of the same diameter as the inner edge of the blades. 
Usually the inlet is on one side of the fan only, and is unobstructed, the 
wheel being overhung from a bearing at the opposite end. A peculiarity 
of this type of fan is that the air leaves it at a velocity about 80 per 
cent in excess of the peripheral speed of the blades. The velocity of 
the air through the inlet is practically uniform over the entire inlet 
area. The power consumption is relatively low. This type of fan was 
invented by S. C. Davidson of Belfast, Ireland, and is known as the 
"Sirocco" fan. It is made under that name in this country by the 
American Blower Co., to which the author in indebted for the preceding 
tables. 

A Test of a " Sirocco " Mine Fan at Llwnypia, Wales, is reported in 
Eng'g., April 16, 1909. The fan is 11 ft. 8 in. diam., double inlet, direct- 
coupled to a 3-phase motor. Average of three tests: Revs, per min., 184; 
peripheral speed, 6,705 ft. per min.; water-gauge in fan drift and in main 
drift, each 6 in.; area of drift, 184.6 sq. ft.; av. velocity of air, 1842 
ft. per min; volume of air, 340,033 cu. ft. per min.; H.P. input at motor, 
420; Brake H.P. on fan shaft, 390; Indicated H.P. in air, 321.5; efficiency 
of motor, 93%; mechanical efficiency of fan, 82.43%; combined mechan- 
ical efficiency of fan and motor, 76.6%. 

The Sturtevant Multivane Fan. A modification of the Sirocco fan 
has been developed by the B. F. Sturtevant Co., in which the blades are 
made with spoon-shaped serrations along their iength. The advantage 
claimed for this construction is that the air is discharged more evenly 
along the length of the blade. The following table shows the sizes, capac- 
ities and horse-power required by the fan. 



Sizes, Capacities and Horse-power of Multivane Fans. 

(B. F. Sturtevant Co., 1909.) 



Height 
of Fan 


Resistance, 1/2 In. 


Resistance, 1 In. 


Resist 


ance, 1 1/2 In. 
















Casing 
















1 


inches * 


Vol. 


R.P.M. 


H.P. 


Vol. 


R.P.M. 


H.P. 


Vol. 


R.P.M. 


H.P. 


30 


1,800 


695 


0.45 


2,560 


985 


1.2 


3,100 


1,200 


2.3 


35 


2,600 


580 


0.65 


3,700 


820 


1.8 


4,500 


1,000 


3.4 


40 


3,550 


500 


0.90 


5,000 


700 


2.5 


6,200 


860 


4.5 


50 


4,620 


435 


1.15 


6,500 


615 


3.3 


8,000 


750 


6.0 


60 


7,220 


350 


1.8 


10,200 


490 


5.0 


12,500 


600 


9.3 


70 


10,400 


290 


2.6 


14,700 


410 


7.3 


18,000 


500 


13.4 


80 


14,000 


250 


3.5 


20,000 


350 


10 


24,500 


430 


18.0 


100 


23,500 


190 


5.8 


33,300 


275 


16.5 


40,800 


335 


30.0 


120 


35,000 


160 


8.8 


49,700 


225 


25 


61,000 


275 


45.0 


150 


48,800 


135 


12.0 


69,000 


190 


34 


85,000 


233 


63.0 


170 


65,000 


115 


16.0 


92,000 


165 


46 


112,500 


200 


85.0 



* Full housing. Bottom horizontal discharge. 

The above table gives the volumes and horse-powers of Sturtevant 
multivane fans operating against a continuously maintained resistance, 
handling air at 65° F. The table is compiled for single-inlet fans, but 
when used with double inlet the volumes will be considerably increased 
(about 15-20%), and the power will also be greater (about 25-35%). It 
is possible to handle any of the volumes given against any stated pressure 
with quite an appreciable saving in power as compared with the table 
horse-power by using a larger fan, and by so doing obtaining lower veloci- 



FANS AND BLOWERS. 639 

ties through the fan. It is also possible to handle any stated volume 
against any pressure given in the table with a considerably smaller fan, 
but when this is done it requires an increase in horse-power due to the 
greater velocity, which is increased in proportion to the decrease in size 
and to the lower mechanical efficiency of an overloaded fan. By main- 
tained resistance is meant a static pressure existing in the air after it 
leaves the fan outlet, if the fan is applied to a blowing system. With the 
suction system, maintained resistance is the static suction existing in the 
duct just outside the fan inlet. If the fan is so placed in the system that 
there is resistance to the flow of air on both inlet and outlet, the maintained 
resistance against which the fan operates is the sum of the static suction 
existing in the air just before entering the inlet and the static pressure in 
the air just outside the fan outlet. In ordinary draw-through heating 
systems a maintained suction is encountered in the fan inlet due to the 
resistance of the heater, and the maintained pressure is created in the fan 
outlet due to the piping system. The volumes given are computed from 
tests in which the average velocity over rectangular or circular pipes is 
taken as 91% of that velocity (not velocity head) which is read at the 
center of the pipe by means of the Pitot tube. This method of computing 
velocity is conservative, especially for pipes having large sectional area. 

High-Pressure Centrifugal Fans. (See page 620.) 
Methods of Testing Fans. 

(Compiled by B. F. Sturtevant Co., 1909.) 

Various methods are used in testing centrifugal fans, some of which, 
being crude, credit fans with performances somewhat different from the 
true performance. Some of the formulae used in determining the per- 
formances of a fan are given below: 

h v — Velocity head, in. of water; h t — Total or Impact head, in. of 
water; h s = Static head, in. of water; Q = Cu. ft. per min.; v— Velocity, 
ft. per min.; w = Density of air, lb. per cu. ft.; A = Area of outlet pipe, 
sq. ft.; A.H.P S . = Air horse-power crediting the fan with the energy due 
to static pressure only; A.H.Pj. = Air horse-power, crediting the fan with 
both the energy due to static pressure and the kinetic energy in the dis- 
charge; B.H,P.= Brake horse-power. 



r^. «?-io»7l/5 : 



A.H.P S . = Q X h s X 0.0001575; A.H.P^. ~QXh t X 0.0001575. 

Mechanical Efficiency = A.H.P.-f-B.H.P. 
Volumetric Efn'y= Volume per Revolution -f- Cubical Contents of wheel: 
Anemometer Method. Anemometers are subject to considerable error 
as they are very delicate and must be handled with care. Should they be 
placed in a draft where the velocity is much over 1000 ft. per min. they 
are apt to be damaged by bending the blades. The methods of calibrating 
these instruments are faulty, and give some chance of error, even though 
the instrument be in the same condition as when calibrated. Unless it 
is frequently calibrated, the instrument may not be true to its calibra- 
tion curve, which is often a source of considerable error. An anemometer 
is seldom adapted to taking readings at the fan outlet, or within pipes, as 
the velocity in most cases exceeds the limitations of the instrument. 
Therefore, readings are usually taken at a point where the velocity is 
lower, and consequently over areas of various shapes with unknown co- 
efficients, thus introducing another source of error. Unless the flow of 
air is constant, faulty readings are obtained, due to the inertia of the 
instrument, which results in the fan being credited with a volume greater 
than the true volume. 



640 air. 

Water-Gauge Readings at End of Tapered Cone. In this method, 
cones are placed on the fan outlet, or on the end of a short outlet pipe. 
The readings at the end of the cone vary widely, due to the large number 
of variable eddies. The pressure reading at the end of the cone is a total 
of two components, static pressure and velocity pressure. Unless the 
static pressure is deducted from the total pressure the true velocity pressure 
is not obtained. 

Air-tight Room with Sliding Door. This method consists of the fan dis- 
charging its air into a closed room whose outlet is a sliding door. In this 
method, the readings generally take into account not only the volumetric 
performance but also the static pressure in the room, against which the 
fan delivers air. All tests by this method must be corrected for leakage of 
air from the room, the leakage factor being much larger than would be sup- 
posed. A variable coefficient of orifice is encountered, since at no two 
Sositions of the sliding door is either the area or shape of orifice the same, 
headings taken at the door, by anemometers, are subject to the errors of 
these instruments. If water-gauge readings are taken at the door, the 
results are in error if it is assumed that all pressure at the door is velocity 
pressure. Static readings should be made at each station and deducted 
from the total observed pressure in order to get the velocity head. Even 
then it is difficult to get a true static reading at the door, as the stream 
lines are not all perpendicular to the plane of the orifice. 

Pitot Tube in Center of Discharge Pipe. This method requires a dis- 
charge pipe of the same size as the outlet of the fan. In the center of 
this pipe and at such a distance from the fan outlet that eddies are prac- 
tically eliminated, is placed a Pitot tube. The discharge pipe is of such 
length beyond the tube that when restricted at its end, the stream lines in 
the vicinity of the tube are not materially affected. By this method the 
static and total pressures are observed with considerable accuracy. The 
velocity pressure is determined by subtracting the static pressure from 
the total pressure. By applying a proper coefficient to the readings at 
the center the average velocity over the full discharge area is obtained. 
It is possible to make a more complete test by placing several Pitot tubes 
in the discharge pipe at different points in a cross-section, thereby obtain- 
ing an average. But it is found that by taking readings at a distance of 
eight or ten diameters from the fan outlet very good results are obtained 
with one tube placed in the center of the section of the pipe, whose read- 
ings are corrected by a proper coefficient. For medium-size pipes it is 
found that a coefficient of 0.91 applied to the velocity read at the center 
of the discharge pipe gives good and conservative results. [Other author- 
ities give 0.87 as the value of this coefficient. See Pitot Tube, under 
Illuminating Gas.] 

I Experiments with the tapered cone method and the Pitot tube in the 
center of pipe method show that the former credits a fan with greater 
volume than the latter, and also show that there is a variable relation 
between these two methods as regards the volume of air credited to the 
fan when it is handling a certain volume of air. The difference in volumes 
credited the fan becomes greater as the size of the discharge pipe increases. 
In tests on two fans of different sizes, but of symmetrical design, the Pitot 
tube in the center of the pipe will record symmetrical results under given 
conditions, while with the tapered cone the results obtained with the 
larger fan and larger discharge pipe are beyond those which would have 
been expected from the symmetry of the fan. 

From the above formulas the air horse-power is a function of two vari- 
ables, volume and pressure. Opinions vary as to the pressure which 
should be credited to the fan. It is claimed that the fan should be 
credited with the difference between the static pressure in the medium 
from which the fan is drawing air and the static pressure in the discharge 
pipe. It is also claimed that the fan should also be credited with the 
kinetic energy in the air in the discharge pipe or with the difference be- 
tween the static pressure in the medium from which the fan is drawing air 
and the total or impact pressure in the discharge pipe. Efficiencies de- 
termined by crediting the fan with the former pressure may be called 
static efficiencies, and those determined by crediting the fan with the 
latter pressure may be called impact efficiencies. 

The work of compression is negligible, as these methods have to do with 
air under low pressure. When readings are taken on the suction side of 



FANS AND BLOWERS. 641 

the fan, for the purpose of determining static efficiency, the fan is often 
erroneously credited with a pressure equal to the difference between the 
medium into which the fan is discharging and the negative static pressure 
in the pipe leading to the fan inlet, whereas it should be credited only with 
the difference between the static pressure in the discharging medium and 
the impact pressure in the inlet pipe. The static suction has a greater 
negative value than the impact pressure at the same point. -which is the 
result of the reduction of pressure caused by the air entering the system 
changing from rest, or zero velocity, to a finite velocity which it has at the 
point of measurement. If the object is to determine the impact efficiency 
where readings are taken at the suction side of the fan, the pressure with 
which the fan should be credited is the difference between the impact read- 
ing at the fan discharge and the impact reading obtained in the inlet pipe. 
This total pressure with which the fan is credited may also be expressed as 
the difference between the static pressure in the discharge pipe and the 
static suction in the inlet pipe, plus the increase of the velocity pressure 
in the outlet pipe over the velocity pressure in the inlet pipe. 

From the above methods it is seen that volumetric and mechanical 
efficiencies of wide variety are obtained, and that where a test is of any 
importance it is essential that it be made on the most correct lines. Using 
a Pitot tube in the center of the pipe through which air flows, affords the 
best means of getting the true pressures as a whole and their separate 
components, and, consequently, is most accurate in determining the 




JE33- 




Fig. 140 

volume flowing. Fig. 140 shows diagrammat cally the method of test 
where the Pitot tube is used in the center of the discharge pipe. It also 
shows how readings could be taken by the cone method at the end of a 
discharge pipe. The details of the Pitot tube in what is considered its 
best form are also shown. The impact or total pressure is obtained at the 
end of the horizontal tube nearest the fan, and read by a water gauge 
connected to the vertical tube communicating with this point. The 
static pressure is obtained at the slots in the side of the outer horizontal 
tube which communicates with the second vertical tube, to which a water 
gauge may be connected. 

Efficiency of Fans. — Much useful information on the theory and 
practice of fans and blowers, with results of tests of various forms, will be 
found in Heating and Ventilation, June to Dec. 1897, in papers by Prof. 
R. C. Carpenter and Mr. W. G. Walker. It is shown by theory that the 
volume of air delivered is directly proportional to the speed of rotation, 
that the pressure varies as the square of the speed, and that the horse- 
power varies as the cube of the speed. For a given volume of air moved 
the horse-power varies as the square of the speed, showing the great advan- 
tage of large fans at slow speeds over small fans at high speeds delivering 
the same volume. The theoretical values are greatly modified by varia- 
tions in practical conditions. Professor Carpenter found that with three 
fans running at a speed of 6200 ft. per minute at the tips of the vanes, and 



642 



AIR. 



an air-pressure of 2 1/2 in. of water column, the mechanical efficiency, or the 
horse-power of the air delivered divided by the power required to drive the 
fan, ranged from 32% to 47%, under different conditions, but with slow 
speeds it was much less, in some cases being under 20%. Mr. Walker in 
experiments on disk fans found efficiencies ranging all the way from 7.4% 
to 43%, the size of the fans and the speed being constant, but the shape and 
angle of the blades varying. It is evident that there is a wide margin for 
improvements in the forms of fans and blowers, and a wide field for experi- 
ment to determine the conditions that will give maximum efficiency. 

Flow of Air through an Orifice. 

VELOCITY, VOLUME, AND H.P. REQUIRED WHEN AIR UNDER GIVEN PRESSURE 
IN OUNCES PER SQ. IN. IS ALLOWED TO ESCAPE INTO THE ATMOSPHERE. 

(B. F. Sturtevant Co.) 



.si 




.5 • 


u 

ft 


f 8g 


s 


ftp, 


6" 
■a! 


a 


1% -a 

J3 • g 


* a 
so"! 


ftft 


g! 

£§.S 


u 




J2 K .ts 


j ? d c 

OCMO 


ftg 

is « 

o2'g 




lis 


11 


2 • & 

" M > a 


0+3 ^ 

S2.>* 
a mo 


^ . 

is.s 

S2 3 


fc 


Ph 


> 


> 


w . 


M 


fin 


> 


> 


ffl 


W- 


1/8 


0.216 


1.828 


12.69 


0.00043 


0.0340 


2 


7.284 


50.59 


0.02759 


0.5454 


1/4 


0.432 


2,585 


17.95 


0.00122 


0.0680 


21/8 


7.507 


52.13 


. 0.03021 


0.5795 


3/8 


0.648 


3.165 


21.98 


0.00225 


0.1022 


21/4 


7,722 


53.63 


0.03291 


0.6136 


■ 1/2 


0.864 


3.654 


25.37 


0.00346 


0.1363 


23/s 


7.932 


55.08 


0.03568 


0.6476' 


5/8 


1.080 


4,084 


28.36 


0.00483 


0.1703 


Vr/l 


8,136 


56.50 


0.03852 


0.6818 


3/4 


1.296 


4.473 


31.06 


0.00635 


0.2044 


25/s 


8,334 


57.88 


0.04144 


0.7160 


7/8 


1.512 


4.830 


33.54 


0.00800 


0.2385 


23/4 


8.528 


59.22 


0.04442 


0.7500 


1 


1.728 


5.162 


35.85 


0.00978 


0.2728 


27/8 


8,718 


60.54 


0.04747 


0.7841 


U/8 


1.944 


5.473 


38.01 


0.01166 


0.3068 


3 


8,903 


61.83 


0.05058 


0.8180 


1V4 


2.160 


5,768 


40.06 


0.01366 


0.3410 


31/8 


9,084 


63.08 


0.05376 


0.8522 


13/8 


2.376 


6.048 


42.00 


0.01575 


0.3750 


31/4 


9,262 


64.32 


0.05701 


0.8863 


H/2 


2.59? 


6.315 


43.86 


0.01794 


0.4090 


33/s 


9.435 


65.52 


0.06031 


0.9205 


15/8 


2.808 


6.571 


45.63 


0.02022 


0.4431 


31/2 


9.606 


66.71 


0.06368 


0.9546 


13/4 


3.024 


6.818 


47.34 


0.02260 


0.4772 


35/8 


9,773 


67.87 


0.06710 


0.9887 


17/8 


3.240 


7,055 


49.00 


0.02505 


0.5112 


33/4 
37/ 8 


9,938 
10,100 


69.01 
70.14 


0.07058 
0.07412 


1.0227 
1 .0567 


(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


(1) 


(3) 


(4) 


(5) 


(6) 



The headings of the 3d and 4th columns in the above table have been 
abridged from the original, which read as follows: Velocity of dry air, 
50° F., escaping into the atmosphere through any shaped orifice in any 
pipe or reservoir in which the given pressure is maintained. Volume of 
air in cubic feet which may be discharged in one minute through an orifice 
having an effective area of discharge of one square inch. The 6th column, 
not in the original, has been calculated by the author. The figures repre- 
sent the horse-power theoretically required to move 1000 cu. ft. of air of 
the given pressures through an orifice, without allowance for the work of 
compression or for friction or other losses of the fan. These losses may 
amount to 60% or more of the given horse-power. 

The change in density which results from a change in pressure has been 
taken into account in the calculations of the table. The volume of air at 
a given velocity discharged through an orifice depends upon its shape, and 
is always less than that measured by its full area. For a given effective 
area the volume is proportional to the velocity. The power required to 
move air through an orifice is measured by the product of the velocity and 
the total resisting pressure. This power for a given orifice varies as the 
cube of the velocity. For a given volume it varies as the square of the 
velocity. In the movement of air by means of a fan there are unavoidable 
resistances which, in proportion to their amount, increase the actual power 
considerably above the amount here given. 



FANS AND BLOWERS. 



643 



Pipe Lines for Fans and Blowers. — In installing fans and blowers 
careful consideration should be given to the pipe line conducting the air 
from the fan or blower. Bends and turns in the pipe, even of long radii, 
will cause considerable drop in pressure, and in straight pipe the friction of 
the moving air is a source of considerable loss. The friction increases with 
the length of the pipe and is inversely as the diameter. It also varies as the 
square of the velocity. In long runs of pipe, the increased cost of a larger 
pipe can often be compensated by the decreased cost of the motor and 
power for operating the blower. 

The advisability of using a large pipe for conveying the air is shown by 
the following table which gives the size of pipe which should be used for 
pressure losses not exceeding one-fourth and one-half ounce per square 
inch, for various lengths of pipe. 



Diameters of Blast Pipes. 

(B. F. Sturtevant Co., 1908.) 



0, 


h 
a 


'3 


Length of Pipe in Feet. 


c 
o 


20 1 40 1 


60 1 80 1 100 1 120 1 140 


"8 u 


2 ~ 


43g 

D 


Diameter of Pipe with Drop of 


§1 


1/4 


1/2 


1/4 


1/2 


V4 


1/2 


1/4 


1/2 


1/4 


1/2 


1/4 


1/2 


1/4 


1/2 


H 


a 
23 


Oz. 
6 


Oz. 
5 


Oz. 
7 


Oz. 
6 


Oz. 
7 


Oz. 
6 


Oz. 
8 


Oz. 
7 


Oz. 
9 


Oz. 
8 


Oz. 
9 


Oz. 
8 


Oz. 
9 


Oz. 


1 


500 


8 


2 


27 


1,000 


8 


7 


9 


8 


10 


9 


11 


9 


11 


10 


12 


11 


12 


11 


3 


30 


1,500 


10 


8 


11 


10 


11 


10 


12 


11 


13 


11 


13 


12 


14 


12 


4 


32. 


2,000 


11 


9 


12 


11 


13 


12 


14 


12 


15 


13 


15 


14 


16 


14 


5 


36 


2,500 


12 


10 


14 


12 


15 


13 


15 


14 


16 


14 


17 


15 


17 


15 


6 


39 


3,000 


13 


11 


15 


13 


16 


14 


17 


15 


18 


15 


18 


16 


18 


16 


7 


42 


3,500 


13 


12 


15 


13 


17 


15 


17 


15 


18 


16 


19 


17 


20 


18 


8 


45 


4,000 


15 


12 


16 


15 


18 


15 


18 


16 


19 


17 


20 


18 


21 


18 


9 


48 


4,500 


15 


13 


17 


15 


18 


16 


19 


17 


20 


18 


21 


19 


22 


19 


10 


54 


5,000 


15 


13 


18 


15 


19 


17 


20 


18 


21 


18 


22 


19 


23 


20 


11 


54 


5,500 


16 


14 


18 


16 


20 


17 


21 


18 


22 


19 


23 


20 


23 


20 


12 


60 


6,000 


17 


14 


19 


17 


20 


17 


21 


19 


22 


20 


23 


21 


24 


21 


13 


60 


6,500 


17 


14 


19 


17 


21 


18 


23 


19 


23 


20 


24 


21 


25 


22 


14 


60 


7,000 


18 


15 


20 


18 


22 


19 


23 


20 


24 


21 


25 


22 


26 


23 


15 


66 


7,500 


18 


16 


21 


IS 


22 


19 


24 


21 


25 


22 


26 


22 


27 


23 


16 


66 


8,000 


18 


16 


22 


18 


23 


20 


24 


22 


26 


22 


26 


23 


27 


24 


17 


66 


8.500 


18 


16 


22 


18 


23 


20 


24 


22 


26 


22 


27 


24 


28 


24 


18 


72 


9,000 


18 


17 


22 


18 


24 


21 


25 


22 


27 


23 


27 


24 


28 


25 


19 


72 


9,500 


20 


17 


23 


20 


24 


22 


26 


23 


28 


23 


28 


25 


29 


26 


20 


72 


10,000 


20 


18 


23 


20 


25 


22 


27 


23 


28 


24 


29 


25 


30 


26 


21 


78 


10,500 


21 


18 


24 


21 


26 


23 


27 


23 


29 


25 


30 


26 


30 


26 


22 


78 


11,000 


21 


18 


24 


21 


27 


23 


28 


24 


29 


26 


30 


27 


31 


27 


23 


78 


11,500 


21 


19 


25 


21 


27 


24 


28 


25 


30 


26 


30 


27 


31 


27 


24 


84 


12,000 


22 


19 


25 


22 


28 


24 


28 


25 


31 


26 


31 


27 


32 


28 


25 


84 


12,500 


22 


19 


26 


22 


28 


24 


29 


26 


31 


27 


32 


28 


33 


28 


26 


84 


13,000 


22 


19 


26 


22 


28 


24 


29 


26 


31 


27 


32 


28 


33 


28 


27 


90 


13.500 


23 


20 


26 


23 


28 


24 


30 


26 


31 


27 


32 


28 


34 


28 


28 


90 


14,000 


23 


20 


27 


23 


29 


25 


30 


27 


32 


28 


33 


29 


34 


29 


29 


90 


14,500 


23 


20 


27 


23 


29 


26 


31 


27 


32 


28 


33 


29 


34 


30 


30 


90 


15,000 


24 


21 


27 


24 


29 


26 


31 


27 


32 


28 


34 


30 


35 


30 



644 air. 



The minimum radius of each turn should be equal to the diameter of the 
pipe. For each turn thus made add three feet in length, when using this 
table. If the turns are of less radius, the length added should be increased 
proportionately. 

The above table has been constructed on the following basis: A loss of, 
say, 1/2 oz. pressure was allowed as a standard for the transmission of a 
given quantity of air through a given length of pipe of any diameter. The 
increased loss due to increasing the length of pipe was compensated for by 
increasing the diameter sufficiently to keep the loss still at 1/2 oz. Thus, 
if 2500 cu. ft. of air is to be delivered per minute through 100 ft. of pipe 
with a loss of not more than 1/2 oz., a 14-in. pipe will be required. If it is 
necessary to increase the length of pipe to 140 ft., a pipe 15 in. diameter 
will be required if the loss in pressure is not to exceed 1/2 oz. In deciding 
the size of pipe the loss in pressure in the pipe must be added to the pres- 
sure to be maintained at the fan or blower, if the tabulated efficiency of 
the latter is to be secured at the delivery end of the pipe. 

Centrifugal Ventilators for Mines. — Of different appliances for ven- 
tilating mines various forms of centrifugal machines having proved their 
efficiency have now almost completely replaced all others. Most if not all 
of the machines in use in this country are of this class, being either open- 
periphery fans, or closed, with chimney and spiral casing, of a more or less 
modified Guibal type. The theory of such machines has been demonstrated 
by Mr. Daniel Murguein " Theories and Practices of Centrifugal Ventilating 
Machines," translated by A. L. Stevenson, and is discussed in a paper by R. 
Van A. Norris, Trans. A. I. M. E., xx. 637. From this paper the following 
formulae are taken: 

Let a = area in sq. ft. of an orifice in a thin plate, of such area that its 
resistance to the passage of a given quantity of air equals the 
resistance of the mine; 

= orifice in a thin plate of such area that its resistance to the pas- 
sage of a given quantity of air equals that of the machine; 

Q = quantity of air passing in cubic feet per minute; 

V = velocity of air passing through a in feet per second; 
V = velocity of air passing through o in feet per second; 

h = head in feet air-column to produce velocity V; 

ho — head in feet air-column to produce velocity V . 

Q = 0.65aV; V = ^Ygh; Q = 0.65a ^ / 2~gh; 

a = . = equivalent orifice of mine; 

0.65 vigft 

or, reducing to water-gauge in inches and quantity in thousands of cubic 
feet per minute, 



0.403 Q 
Vw.G. ; 



•-V* 



O 2 

- — — = equivalent orifice of machine. 



65 2 h 2 g 

The theoretical depression which can be produced by any centrifugal 
ventilator is double that due to its tangential speed. The formula 

77 = Tl _ YL 
2o 2g' 

in which T is the tangential speed, V the velocity of exit of the air from the 
space between the blades, and H the depression measured in feet of air- 
column, is an expression for the theoretical depression which can be pro- 
duced by an uncovered ventilator; this reaches a maximum when the air 
leaves the blades without speed, that is, V = 0, and H = T 2 -*■ 2 g. 

Hence the theoretical depression which can be produced by any uncov- 
ered ventilator is equal to the height due to its tangential speed, and one* 



MINE-VENTILATING FANS. 



645 



half that which can be produced by a covered ventilator with expanding 
chimney. Practical considerations in the design of the fan wheel and 
casing will probably cause the actual results obtained with fans to vary 
considerably from these formulae. 

So long as the condition of the mine remains constant: 

(1) The volume produced by any ventilator varies directly as the speed 
of rotation. 

(2) The depression produced by any ventilator varies as the square of 
the speed of rotation. 

(3) For the same tangential speed with decreased resistance the quantity 
of air increases and the depression diminishes. 

The following table shows a few results, selected from Mr. Norris's paper, 
giving the range of efficiency which may be expected under different cir- 
cumstances. Details of these and other fans, with diagrams of the results, 
are given in the paper. 

Experiments on Mine-Ventilating Fans. 





05 

?9 


i 

05 . 

as 


"3 

*S 45 


3 c 



°1 


05 05 

u 


"'S.& 

«H 05 . 




05 


i05 

E.a 

O M 


4 . 


82 

11 




.2«r 


Is 


m O 
03 > 




-J 





tj'o 


^ 


a 05* 

05 g 


03 


3 3 

o.a 


■si 


"a 

3 a 


3 a 


11 

2<S 


-2 a 

3 ft 05 




B.t! 

O c3 


3ft 


05 05 

"3 c 

Sfi'Sb 


o-o.X 


u< 




Ph 


o 


O 








K 


M 


H 


W 


r 


5517 


236,684 


2818 


3040 


4290 


1.80 


67.13 


88.40 


75.9 


■* 


A 


100 


6282 


336,862 


3369 


3040 


5393 


2.50 


132.7C 


155.43 


85.4 


L« 




111 


6973 


347,396 


3130 


3040 


5002 


3.20 


175.17 


209.64 


83.6 


f«" 


1 


123 


7727 


394,100 


3204 


3040 


5100 


3.60 


223.56 


295.21 


75.7 


J« 


B{ 


100 


6282 


188,888 


1889 


1520 


3007 


1.40 


41.67 


97.99 


42.5 


130 


8167 


274,876 


2114 


1520 


3366 


2.00 


86.63 


194.95 


44.6 


22 


*{ 


59 


3702 


59,587 


1010 


1520 


1610 


1.20 


11.27 


16.76 


67.83 




83 


5208 


82,969 


1000 


1520 


1593 


2.15 


27.86 


48.54 


57.38 




*{ 


40 


3140 


49,611 


1240 


3096 


1580 


0.87 


6.80 


13.82 


49.2 


32 


70 


5495 


137,760 


1825 


3096 


2507 


2.55 


55.35 


67.44 


82.07 




-{ 


50 


2749 


147,232 


2944 


1522 


5356 


0.50 


11.60 


28.55 


40.63 




69 


3793 


205,761 


2982 


1522 


5451 


1.00. 


32.42 


45.98 


70.50 


83 


96 


5278 


299,600 


3121 


1522 


5676 


2.15 


101.50 


120.64 


84.10 






200 


7540 


133,198 


666 


746 


1767 


3.35 


70.30 


102.79 


68.40 


26.9 


V 


200 


7540 


180,809 


904 


746 


2398 


3.05 


86.89 


129.07 


67.30 


38.3 




200 


7540 


209,150 


1046 


746 


2774 


2.80 


92.50 


150.08 


61.70 


46.3 




10 


785 


28,896 


2890 


3022 


3680 


0.10 


0.45 


1.30 


35. . 






20 


1570 


57,120 


2856 


3022 


3637 


0.20 


1.80 


3.70 


49. 






25 


1962 


66,640 


2665 


3022 


3399 


0.29 


2.90 


6.10 


48. 






30 


2355 


73,080 


2436 


3022 


3103 


0.40 


4.60 


9.70 


47. 


52 


G< 


35 


2747 


94,080 


2688 


3022 


3425 


0.50 


7.40 


15.00 


48. 




40 


3140 


112,000 


2800 


3022 


3567 


0.70 


12.30 


24.90 


49. 






50 


3925 


132,700 


2654 


3022 


3381 


0.90 


18.80 


38.80 


48. 






60 


4710 


173,600 


2893 


3022 


3686 


1.35 


36.90 


66.40 


55. 






70 


5495 


203,280 2904 


3022 


3718 


1.80 


57.70 


107.10 


54. 




I 


80 1 


6280 


222,3201 2779 


3022 


3540 


2.25 


78.80 


152.60 


52. 





Type of fan. 


Diam. 


Width. 


No. inlets. 


Diam. 
inlets. 


A. Guibal, double 

B. Same, only left hand running 

C. Guibal 


20 ft. 

20 

20 

25 

171/2 

12 

25 


6 ft. 
6 
6 
8 
4 
10 
8 


4 
4 
2 
1 

4 
2 
1 


8 ft. 10 in. 
8 10 
8 10 


D. Guibal 


11 6 




8 


F. Capell 


7 


G. Guibal .' 


12 







646 



AIR. 



An examination of the detailed results of each test in Mr. Norris's table 
shows a mass of contradictions from which it is exceedingly difficult to 
draw any satisfactory conclusions. The following, he states, appear to be 
more or less warranted by some of the figures: 

1. Influence of the Condition of the Airways on the Fan. — Mines with 
varying equivalent orifices give air per 100 ft. speed of tip of fan, within 
limits as follows, the quantity depending on the resistance of the mine: 



Equivalent 
orifice, 
sq.ft. 


Cu.ft. air 

per 100 ft. 

speed of fan. 


Average. 


Equivalent 
orifice, 
sq. ft. 


Cu.ft. air 

per 100 ft. 

speed of fan. 


Average. 


Under 20 
20 to 30 
30 to 40 
40 to 50 


1100 to 1700 
1300 to 1800 
1500 to 2500 
2300 to 3500 
2700 to 4800 


1300 
1600 
2100 
2700 
3500 


60 to 70 
70 to 80 
80 to 90 
90 to 100 
100 to 114 


3300 to 5100 
4000 to 4700 
3000 to 5600 


4000 
4400 
4800 


50 to 60 


5200 to 6200 


5700 



The influence of the mine on the efficiency of the fan does not seem to be 
very clear. Eight fans, with equivalent orifices over 50 square feet, give 
efficiencies over 70%; four, with smaller equivalent mine-orifices, give 
about the same figures; while, on the contrary, six fans, with equivalent 
orifices of over 50 square feet, give lower efficiencies, as do ten fans, all 
drawing from mines with small equivalent orifices. It would seem that, 
on the whole, large airways tend to assist somewhat in attaining high 
efficiency. 

2. Influence of the Diameter of the Fan. — This seems to be practically nil, 
the only advantage of large fans being in their greater width and the lower 
speed required of the engines. 

3. Influence of the Width of a Fan. — This appears to be small as regards 
the efficiency of the machine; but the wider fans are, as a rule, exhausting 
more air. However, increasing the width of the fan of a given diameter 
causes an increase in the velocity of the air through the wheel inlet, and 
this increased velocity will become at a certain point a serious loss and 
will decrease the mechanical efficiency. 

4. Influence of Shape of Blades. — This appears, within reasonable limits, 
to be practically nil. Thus, six fans with tips of blades curved forward, 
three fans with flat blades, and one with blades curved back to a tangent 
with the circumference, all give very high efficiencies — over 70 per cent. 
A prominent manufacturer claims, however, that his tests show a higher 
efficiency with vanes curved forward as compared with straight or back- 
wardly curved vanes. 

5. influence of the Shape of the Spiral Casing. — This appears to be 
considerable. The shapes of spiral casing in use fall into two classes, 
the first presenting a large spiral, beginning at or near the point of cut-off, 
and the second a circular casing reaching around three-quarters of the 
circumference of the fan, with a short spiral reaching to the evasee 
chimney. 

Fans having the first form of casing appear to give in almost every case 
high efficiencies. 

Fans that have a spiral belonging to the first class, but very much con- 
tracted, give only medium efficiencies. It seems probable that the proper 
shape of spiral casing would be one of such form that the air between each 
pair of blades could constantly and freely discharge into the space between 
the fan and casing, the whole being swept along to the evasee. chimney. 
This would require a spiral beginning near the point of cut-off, enlarging by 
gradually increasing increments, to allow for the slowing of the air caused 
by its friction against the casing, and reaching the chimney with an area 
such that the air could make its exit with its then existing speed — some- 
what less than the periphery-speed of the fan. 

6. Influence of the Shutter. — The shutter certainly appears to be an ad- 
vantage, as by it the exit area can be regulated to suit the varying quantity 
of air given by the fan, and in this way re-entries can be prevented. It is 
not uncommon to find shutterless fans, into the chimneys of which bits of 
paper may be dropped, which are drawn into the fan, make the circuit, and 
are again thrown out. This peculiarity has not been noticed with fans 
provided with shutters. 



DISK FANS. 647 



7. Influence of the Speed at which a Fan is Run. — It is noticeable that 
most of the fans giving high efficiency were running at a rather high 
periphery velocity. The best speed seems to be between 5000 and 6000 
feet per minute. The fans appear to reach a maximum efficiency at some- 
where about the speed given, and to decrease rapidly in efficiency when 
this maximum point is passed. The same manufacturer mentioned in 
note 4 states that the efficiency is not affected by the tip speed, providing 
that the comparison is always made at the same point in the efficiency 
curve. 

In discussion of Mr. Norris's paper, Mr. A. H. Storrs says: From the " cu- 
bic feet per revolution" and "cubical contents of fan-blades," as given in 
the table, we find that the enclosed fans empty themselves from one-half to 
twice per revolution, while the open fans are emptied from one and three- 
quarters to nearly three times; this for fans of both types, on mines covering 
the same range of equivalent orifices. One open fan, on a very large 
orifice, was emptied nearly four times, while a closed fan, on a still 
larger orifice, only shows one and one-half times. For the open fans the 
"cubic feet per 100 ft. motion" is greater, in proportion to the fan 
width and equivalent orifice, than for the enclosed type. Notwithstand- 
ing this apparently free discharge of the open fans, they show very low 
efficiencies. 

As illustrating the very large capacity of centrifugal fans to pass air, if 
the conditions of the mine are made favorable, a 16-ft. diam. fan, 4 ft. 6 in. 
wide, at 130 revolutions, passed 360,000 cu. ft. per min., and another, of 
same diameter, but slightly wider and with larger intake circles, passed 
500,000 cu. ft., the water-gauge in both instances being about 1/2 in- 

T. D. Jones says: The efficiency reported in some cases by Mr. Norris is 
larger than I have ever been able to determine by experiment. My own 
experiments, recorded in the Pennsylvania Mine Inspectors' Reports from 
1875 to 1881, did not show more than 60% to 65%. 

DISK FANS. 

Efficiency of Disk Fans. — ■ Prof. A. B. W. Kennedy (Industries, Jan. 
17, 1890) made a series of tests on two disk fans, 2 and 3 ft. diameter, 
known as the Verity Silent Air-propeller. The principal results and 
conclusions are condensed below. 

In each case the efficiency of the fan, that is, the quantity of air delivered 
per effective horse-power, increases very rapidly as the speed diminishes, 
so that lower speeds are much more economical than higher ones. On the 
other hand, as the quantity of air delivered per revolution is very nearly 
constant, the actual useful work done by the fan increases almost directly 
with its speed. Comparing the large and small fans with about the 
same air delivery, the former (running at a much lower speed, of course) 
is much the more economical. Comparing the two fans running at the 
same speed, however, the smaller fan is very much the more economical. 
The delivery of air per revolution of fan is very nearly directly propor- 
tional to the area of the fan's diameter. 

The air delivered per minute by the 3-ft. fan is nearly 12.5 R cubic feet 
(R being the number of revolutions made by the fan per minute). For 
the 2-ft. fan the quantity is 5.7R cubic feet. For either of these or any 
other similar fans of which the area is A square feet, the delivery will be 
about 1.8 AR cubic feet. Of course any change in the pitch of the blades 
might entirely change these figures. 

The net H.P. taken up is not far from proportional to the square of the 
number of revolutions above 100 per minute. Thus for the 3-ft. fan the 

net Hp - is mooT ' while < OT the 2 " ft - fan the net H - p is S 

The denominators of these two fractions are very nearly proportional 
inversely to the square of the fan areas or the fourth power of the fan 
diameters. The net H.P. required to drive a fan of diameter D feet or 
area A square feet, at a speed of R revolutions per minute, will therefore 
, 1-.+ 1 D*(R- 100) 2 A* (#-100) 2 

be approximately 17 Q0Q 0QQ or 1Q 4Q0>000 - 

The 2-ft. fan was noiseless at all speeds. The 3-ft. fan was also noiseless 
up to over 450 revolutions per minute. 



648 



Speed of fan, revolutions per minute . . 

Net H.P. to drive fan and belt 

Cubic feet of air per minute 

Mean velocity of air in 3-ft. flue, feet 

per minute 

Mean velocity of air in flue, same 

diameter as fan 

Cu. ft. of air per min. per effective H.P 
Motion given to air per rev. of fan, ft.. 
Cubic feet of air per rev. of fan 



Propeller, 
2 ft. diam. 



750 
0.42 
4,183 

593 

1,330 
9,980 
1.77 
5.58 



676 
0.32 
3,830 

543 

1,220 

11,970 

1.81 

5.66 



577 
0.227 
3,410 



1,085 
15,000 



5.90 



Propeller, 
3 ft. diam. 



576 
1.02 
7,400 



7,250 
1.82 
12.8 



459 
0.575 
5,800 



10,070 
1.79 
12.6 



373 
0.324 
4,470 



13,800 
1.70 
12.0 



Experiments made with a Blackman Disk Fan, 4 ft. diam. by Geo. 
A. Suter, to determine the volumes of air delivered under various con- 
ditions, and the power required; with calculations of efficiency and ratio 
of increase of power to increase of velocity, by G. H. Babcock. (Trans. 
A. S. M. E., vii. 547): 



.s 
a 

« 

> 


Cu. ft. of Air 
delivered 
per min., 


gin 

o 

w 


i.a 

60 


h 

■si's 

•2 £w 


pi • 


■s-SB 

& 


8 8 

a^ 
k Hi 

m 


IS 

!■« 

a*- 


>> 

is 

W 


350 


25,797 
32,575 
41,929 
47,756 
For 


0.65 
2.29 
4.42 
7.41 
series 














1 682 


440 
534 
612 




1.257 
1.186 
1.146 
1.749 


1.262 
1.287 
1.139 
1.851 


3.523 
1.843 
1.677 
11.140 


5.4 
2.4 
3.97 
4. 




.9553 
1.062 
.9358 








340 


20,372 
26,660 
31,649 
36,543 
For 


0.76 
1.99 
3.86 
6.47 
series 














.7110 


453 
536 
627 




1.332 
1.183 
1.167 
1.761 


1.308 
1.187 
1.155 
1.794 


2.618 
1.940 
1.676 
8.513 


3.55 
3.86 
3.59 
3.63 




.6063 
.5205 
.4802 








340 


9,983 

13,017 

17,018 

118,649 

For 


1.12 
3.17 
6.07 
8.46 
series 


0.28 
0.47 
0.75 
0.87 












.3939 


430 
534 
570 


1.265 
1.242 
1.068 
1.676 


1.304 
1.307 
1.096 
1.704 


2.837 
1.915 
1.394 
7.554 


3.93 
2.25 
3.63 
3.24 


1.95 
1.74 
1.60 
1.81 


.3046 
.3319 
.3027 


330 


8,399 
10,071 
11,157 
For 


1.31 

3.27 

6.00 

series 


0.26 
0.45 
0.75 












.2631 


437 
516 


1.324 
1.181 
1.563 


1.199 
1.108 
1.329 


3.142 
1.457 
4.580 


6.31 
3.66 
5.35 


3.06 
4.96 
3.72 


.2188 
.2202 



Nature of the Experiments. — First Series: Drawing air through 30 ft. 
of 48-in. diam. pipe on inlet side of the fan. 

Second Series: Forcing air through 30 ft. of 48-in. diam. pipe on outlet 
side of the fan. 

Third Series: Drawing air through 30 ft. of 48-in. pipe on inlet side of 
the fan — the pipe being obstructed by a diaphragm of cheese-cloth. 

Fourth Series: Forcing air through 30 ft. of 48-in. pipe on outlet side 
of fan — the pipe being obstructed by a diaphragm of cheese-cloth. 

Mr. Babcock says concerning these experiments: The first four experi- 
ments are evidently the subject of some error, because the efficiency is 
such as to prove on an average that the fan was a source of power sufficient 
to overcome all losses and help drive the engine besides. The second 
series is less questionable, but still the efficiency in the first two experi- 
ments is larger than might be expected. In the third and fourth series 
the resistance of the cheese-cloth in the pipe reduces the efficiency largely, 
as would be expected. In this case the value has been calculated from 



POSITIVE ROTARY BLOWERS. 649 



the height equivalent to the water-pressure, rather than the actual veloc- 
ity of the air. 

This record of experiments made with the disk fan shows that this kind 
of fan is not adapted for use where there is any material resistance to the 
flow of the air. In the centrifugal fan the power used is nearly propor- 
tioned to the amount of air moved under a given head, while in this fan 
the power required for the same number of revolutions of the fan increases 
very materially with the resistance, notwithstanding the quantity of air 
moved is at the same time considerably reduced. In fact from the inspec- 
tion of the third and fourth series of tests, it would appear that the power 
required is very nearly the same for a given pressure, whether more or 
less air be in motion. It would seem that the main advantage, if any, 
of the disk fan over the centrifugal fan for slight resistances consists in the 
fact that the delivery is the full area of the disk, while with centrifugal 
fans intended to move the same quantity of air the opening is much 
smaller. 

It will be seen by columns 8 and 9 of the table that the power used in- 
creased much more rapidly than the cube of the velocity, as in centrifugal 
fans. The different experiments do not agree with each other, but a 
general average may be assumed as about the cube root of the eleventh 
power. 

Capacity of Disk Fans. (C. L. Hubbard, The Metal Worker, Sept. 5, 
1908.) — The rated capacities given in catalogues are for fans revolving 
in free air — that is, mounted in an opening without being connected with 
ducts or subject to other frictional resistance. 

The following data, based upon tests, apply to fans working against a 
resistance equivalent to that of a shallow heater of open pattern, and 
connecting with ducts of medium length through which the air flows at a 
velocity not greater than 600 or 800 ft. per minute. Under these con- 
ditions a good type of fan will propel the air in a direction parallel to the 
shaft, a distance equal to about 0.7 of its diameter at each revolution. 
From this we have the equation Q = 0.7 D X R X A, in which Q = cu. 
ft. of air discharged per minute; D = diam. of fan, in ft.; R = revs, per 
min.; A = area of fan, in sq. ft. The following table is calculated on this 
basis. 
Diam. of fan, in. 

18 24 30 36 42 48 54 60 72 84 96 
Cu. ft per rev. 

1.85 4.40 8.59 14.8 23.6 35.2 50.1 68.7 118.7188.6 281.5 

Revolutions per min. for velocity of air through fan = 1000 ft. per min. 
952 714 571 476 408 357 317 286 238 204 179 
The velocity of the air through the fan is proportional to the number 
of revolutions. For the conditions stated the H.P. required per 1000 cu. 
ft. of air moved will be about 0.16 when the velocity through the fan is 
1000 ft. per min., 0.14 for a velocity of 800 ft., and 0.18 for 1200 ft. For 
a fan moving in free air the required speed for moving a given volume of 
air will be about 0.6 of the number of revolutions given above and the 
H.P. about 0.3 of that required when moving against the resistance stated. 

POSITIVE ROTARY BLOWERS. 

Rotary Blowers, Centrifugal Fans, and Piston Blowers. (Cata- 
logue of the Connersville Blower Co.) — In ordinary work the advantage 
of a positive blower over a fan begins at about 8 oz. pressure, and the 
efficiency of the positive blower increases from 8 oz. as the pressure goes 
up to a point where the ordinary centrifugal fan fails entirely. The 
highest efficiency of rotary blowers is when they are working against 
pressures ranging between 1 and 8 lbs. 

Fans, when run at constant speed, cannot be made to handle a constant 
volume of fluid when the pressure is variable; and they cannot give a high 
efficiency except for low and uniform pressures. 

When a fan blower is used to furnish blast for a cupola it is driven at a 
constant speed, and the amount of air discharged by it varies according 
to the resistance met with in the cupola. With a positive blower running 
at a constant speed, however, there is a constant volume of air forced 
into the cupola, regardless of changing resistance. 



650 



AIR. 



A rotary blower of the two-impeller type is not an economical com- 
pressor, because the impellers are working against the full pressure at all 
times, while in an ideal blowing engine the theoretical mean effective 
pressure on the piston, when discharging air at 15 lbs. pressure, is IH/2 lbs. 
For high pressures, on account of the increase of leakage and the increase 
of power required because it does not compress gradually, the rotary 
blower must give way to the piston type of machine. Commercially, the 
line is crossed at about 8 lbs. pressure. 

1. A fan is the cheapest in first cost, and if properly applied may be 
used economically for pressures up to 8 oz. 

2. A rotary blower costs more than a fan, but much less than a blowing 
engine; is more economical than either between 8 oz. and 8 lbs. pressure, 
and can be arranged to give a constant pressure or a constant volume. 

3. Piston machines cost much more than rotary blowers, but should 
be used for continuous duty for pressures above 8 lbs., and may be econom- 
ical if they are properly constructed and not run at too high a piston speed. 

The horse-power required to operate rotary blowers is proportional to 
the volume and pressure of air discharged. In making estimates for 
power it is safe to assume that for each 1000 cu. ft. of free air discharged, 
at one pound pressure, 5 H.P. should be provided. . 

Test of a Rotary Blower. (Connersville Blower Co.) — The test was 
made in 1904 on two 39 X 84 in. blowers coupled direct to two 12 and 24 X 
36 in. compound Corliss engines. The results given below are for the 
combined units. 



Air pressure, lbs 

Engine, I.H.P 

Displacement, cu.f t 
Efficiency 




19.30 



0.05 
23.76 
19,212 



0.5 

52.83 
18,727 
68.5 



1.0 
100.91 

18,508 
79 



1.5 
132.67 
18,344 



2. 
176.11 
18,200 
85.6 



2.5 
223.20 
18,028 



3. 

256.87 

17,966 

86 



3.5 

287.56 
17,863 
85.9 



In calculating the efficiency the theoretical horse-power was taken as 
the power required to compress adiabatically and to discharge the net 
amount of air at the different pressures and at the same altitude. The 
test was made up to 3.5 lbs. only. Estimated efficiencies for higher 
pressures from an extension of the plotted curve are: 6 lbs. 84%, 8 lbs. 
82%, 10 lbs. 79.5%. The theoretical discharge of the blower was 19,250 
cu. ft. ' 





Capacity of Rotary 


Blowers for 


Cupolas 


. 


Cu.ft 


Revs. 


Tons 


Suitable 


Cu. ft. 


Revs. 


Tons 


Suitable 


per 


per 


per 


for cupola 


per 


per 


per 


for cupola 


rev. 


min. 


hour. 


in. diam.* 


rev. 


min. 


hour. 


in. diam. 


1.5 


( 200 

1 400 


1 
2 


} 18 to 20 


45 


f 135 
} 165 


12 
15 


I 54 to 66 


3.3 


| 175 
\ 335 


1 
2 


} 24 to 27 




( 200 
( 130 


18 
15 


) 


6 


j 185 

\ 275 


2 
3 


} 28 to 32 


57 


X 155 
t 185 


18 
21 


> 60 to 72 


10 


S 200 
\ 250 


4 
5 


\ 32 to 38 


65 


( 140 
X 160 


18 
21 


> 66 to 84 




( 150 


4 


) 




( 185 


24 


13 


X 190 


5 


\ 32 to 40 




( 125 


21 


) 




( 175 


6 1/ 2 


) 


84 


X 145 


24 


> 72 to 90 




( 150 


5 


) 




t 160 


27 


) 


17 


X 205 


6 1/2 


\ 36 to 45 




( 120 


24 


) 




( 250 


8 1/ 2 


) 


100 


X 135 


27 


> 84 to 96 




( 166 


8 


) 




I 160 


30 


) 


24 


X 200 


10 


\ 42 to 54 




( 115 


27 


1 Two 




( 240 


12 


) 


118 


X 130 


30 


( cupolas 




( 150 


10 


) 




I 140 


33 


> 60 to 66 


33 


X 180 
( 210 


12 
14 


> 48 to 60 











* Inside diam. The capacity in tons per hour is based on 30,000 cu. ft. 
of air per ton of iron melted. 



STEAM-JET BLOWER AND EXHAUSTER. 



651 



For smith fires; an ordinary fire requires about 60 cu. ft. per min. 

For oil furnaces ; an ordinary furnace burns about 2 gallons of oil per 
hour and 1800 cu. ft. of air should be provided for each gallon of oil. For 
each 100 cu. ft. of air discharged per minute at 16 oz. pressure, 1/2 H.P. 
should be provided. 
Sizes of small blowers . 173 288 576 cu. in. per rev. 

Revs, per min 800 to 1500 500 to 900 300 to 600 

Diam. of outlet, in. . . . 2 1/2 2 1/2 3 

Rotary Gas Exhausters. 



Cu. ft. per rev. 
Rev. per min.. 
Diam. of pipe open- 
ing 

Cu. ft. per rev 
Rev. per min.. 
Diam. pipe opening 



2/3 


IV? 


3.3 


6 


10 


13 


17 


24 


200 


180 


170 


160 


150 


150 


140 


130 


4 


6 


8 


10 


12 


12 


16 


16 


45 


57 


65 


. 84 


100 


118 


155 


200 


no 


100 


95 


90 


85 


82 


80 


80 


20 


24 


-24 


30 


30 


30 


36 


36 



33 

120 

20 
300 
75 
42. 



There is no gradual compressing of air in a rotary machine, and the 
unbalanced areas of the impellers are working against the full difference 
of pressure at all times. The possible efficiency of such a machine under 
ordinary temperature and conditions of atmosphere, assuming no me- 
chanical friction, leakage, nor radiation of heat of compression, would be 
as follows: 

Gauge pres. lb 1 2 3 4 5 10 15 

Efficiency % 97.5 95.5 93.3 91.7 90 82.7 76.7 

The proper application of rotary positive machines when operating in 
air or gas under differences of pressures from 8 oz. to 5 lbs. is where con- 
stant quantities of fluid are required to be delivered against a variable 
resistance, or where a constant pressure is required and the volume is 
variable. These are the requirements of gas works, pneumatic-tube 
transmission (both the vacuum and pressure systems), foundry cupolas, 
smelting furnaces, knobbling fires, sand blast, burning of fuel oil, con- 
veying granular substances, the operation of many kinds of metallurgical 
furnaces, etc. — J. T. Wilkin, Trans. A. S. M. E„ Vol. xxiv. 



STEAM-JET BLOWER AND EXHAUSTER. 

A blower and exhauster is made by L. Schutte & Co., Philadelphia, on 
the principle of the steam-jet ejector. The following is a table of capa- 
cities: 





Quantity of 
Air per hr. 

in 
cubic feet. 






Size 

No. 


Quantity of 
Air per hr. 

in 
cubic feet. 






Size 
No. 


Diameter of 
Pipes in inches. 


Diameter of 
Pipes in inches. 


Steam. 


Air. 


Steam. 


Air. 


. 000 
00 

1 

2 
3 
4 


1,000 
2,000 
4,000 
6,000 
12,000 
18,000 
24,000 


1/2 
3/ 4 

11/4 
U/2 
2 
2 


1 

U/2 
2 

21/2 
3 

31/2 
4 


5 
6 
7 
8 
9 
10 


30,000 
36,000 
42,000 
48,000 
54,000 
60,000 


21/2 

21/2 

3 

3 

31/2 

31/2 


5 
6 
6 

7 
7 
8 



The admissible vacuum and counter-pressure, for which the apparatus 
is constructed, is up to a rarefaction of 20 inches of mercury, and a 
counter-pressure up to one-sixth of the steam-pressure. 

The table of capacities is based on a steam-pressure of about 60 lbs., 
and a counter-pressure of about 8 lbs. With an increase of steam- 
pressure or decrease of counter-pressure the capacity will largely increase. 



652 



Another steam-jet blower is used for boiler-firing, ventilation, and 
similar purposes where a low counter-pressure or rarefaction meets the 
requirements. 

The volumes as given in the following table of capacities are under the 
supposition of a steam-pressure of 45 lbs. and a counter-pressure of, say, 
2 inches of water: 



Size 
No. 


Cubic 

feet of 

Air 

delivered 

per hour. 


Diam. 

of 
Steam- 
pipe in 
inches. 


Dian 
inche 

Inlet. 


i. in 

SOf— 

Disch 


Size 
No. 


Cubic 
feet of Air 
delivered 
per hour. 


Diam. 

of 
Steam- 
pipe in 
inches. 


Diam. in 
inches of— 

Inlet. Disch 


00 



1 

2 

3 


6,000 
12,000 
30,000 
60,000 
125,000 


3/8 

V2 
1/2 
3/4 

1 


4 
5 
8 
11 
14 


3 
4 
6 
8 
10 


4 
6 
8 
10 


250,000 

500,000 

1,000,000 

2,000,000 


1 

U/4 
H/2 
2 


17 
24 
32 
42 


14 
20 
27 
36 



The Steam-jet as a Means for Ventilation. — Between 1810 and 
1850 the steam-jet was employed to a considerable extent for ventilating 
English collieries, and in 1852 a committee of the House of Commons 
reported that it was the most powerful and at the same time the cheapest 
method for the ventilation of mines; but experiments made shortly after- 
wards proved that this opinion was erroneous, and that furnace ventila- 
tion was less than half as expensive, and in consequence the jet was soon 
abandoned as a permanent method of ventilation. 

For an account of these experiments see Colliery Engineer, Feb., 1890. 
The jet, however, is sometimes advantageously used as a substitute, for 
instance, in the case of a fan standing for repairs, or after an explosion, 
when the furnace may not be kept going, or in the case of the fan having 
been rendered useless. 



BLOWING-ENGINES. 

Corliss Horizontal Cross-compound Condensing Blowing-engines. 

(Philadelphia Engineering Works.) 



Indicated 
Horse-power. 


u 

ftfl 

> 8 


Cu. ft. 

Free 
Air per 

min. 


U 2 <» 

03 w fl 

3 


i i 

•.S3 


i * 


.5 .S 

J -So 


p. 


< 


..s-sw 


15 Exp. 
125 lbs. 
Steam. 


13 Exp. 
100 lbs. 
Steam. 


< 




1,572 
2,280 
1,290 
2,060 


40 
60 
40 
60 


30,400 
45,600 
30,400 
45,600 


} ,2 


44 
42 


78 
72 


(2) 84 
(2) 84 


60 
60 


505,000 
475,000 


605,000 
550,000 


1,050 
1,596 


1,340 

1,980 


40 
60 

40 
60 


30,400 
45,600 
26,800 
39,600 


} ,0 


32 
40 


60 
72 


(2) 84 
(2) 78 


60 
60 


355,000 
445,000 


436,000 
545,000 




1,152 
1,702 


40 
60 


26,800 
39,600 


}« 


38 


70 


(2) 78 


60 


425,000 


491,000 




938 
1,386 


40 
60 


26,800 
39,600 


}.. 


36 


66 


(2) 78 


60 


415,000 


450,000 




780 
1,175 


4U 
60 


15,680 
23,500 


I" 


34 


60 


(2) 72 


60 


340,000 


430,000 




548 
821 


40 
60 


15,680 
23,500 


},0 


28 


50 


(2) 72 


60 


270,000 


300,000 



Vertical engines are built of the same dimensions as above, except that 
the stroke is 48-in. instead of 60, and they' are run at a higher number of 
revolutions to give the same piston-speed and the same I.H.P. 



HEATING AND VENTILATION. 653 

The calculations of power, capacity, etc., of blowing-engines are the 
same as those for air-compressors. They are built without any provision 
for cooling the air during compression. About 400 feet per minute is the 
usual piston-speed for recent forms of engines, but with positive air-valves, 
which have been introduced to some extent, this speed may be increased. 
The efficiency of the engine, that is, the ratio of the I.H.P. of the air- 
cylinder to that of the steam-cylinder, is usually taken at 90 per cent, the 
losses by friction, leakage, etc., being taken at 10 per cent. 



HEATING AND VENTILATION. 

Ventilation. (A. R. Wolff, Stevens Indicator, April, 1890.) — The 
popular impression that the impure air falls to the bottom of a crowded 
room is erroneous. There is a constant mingling of the fresh air admitted 
with the impure air due to the law of diffusion of gases, to difference of 
temperature, etc. The process of ventilation is one of dilution of the 
impure air by the fresh, and a room is properly ventilated in the opinion 
of the hygienists when the dilution is such that the carbonic acid in the 
air does not exceed from 6 to 8 parts by volume in 10,000. Pure country 
air contains about 4 parts C0 2 in 10,000, and badly-ventilated quarters 
as high as 80 parts. 

An ordinary man exhales 0.6 of a cubic foot of C0 2 per hour. New 
York gas gives out 0.75 of a cubic feet of C0 2 for each cubic foot of gas 
burnt. An ordinary lamp gives out 1 cu. ft. of C0 2 per hour. An 
ordinary candle gives out 0.3 cu. ft. per hour. One ordinary gaslight 
equals in vitiating effect about 51/2 men, an ordinary lamp 12/3 men, and 
an ordinary candle 1/2 man. 

To determine the quantity of air to be supplied to the inmates of an un- 
lighted room, to dilute the air to a desired standard of purity, we can 
establish equations as follows: 

Let v = cubic feet of fresh air to be supplied per hour; 

r = cubic feet of CO2 in each 10,000 cu. ft. of the entering air; 
R = cubic feet of CO2 which each 10,000 cu. ft. of the air in the room 

may contain for proper health conditions ; 
n = number of persons in the room; 
0.6 = cubic feet of CO2 exhaled by one man per hour. 



during one hour. 

This value divided by v and multiplied by 10,000 gives the proportion 
of CO2 in 10,000 parts of the air in the room, and this should equal R, the 
standard of purity desired. Therefore 



10 ' 000 [gjfe +( H 



nrtu 6000 n 

or v = — • 

R—r 



If we place r at 4 and R at 6, v = 6000 n -*■ (6 - 4) = 3000 n, or the 
quantity of air to be supplied per person is 3000 cubic feet per hour. 

If the original air in the room is of the purity of external air, and the 
cubic contents of the room is equal to 100 cu. ft. per inmate, only 3000 — 
100 = 2900 cu. ft. of fresh air from without will have to be supplied the 
first hour to keep the air within the standard purity of 6 parts of CO2 in 
10,000. If the cubic contents of the room equals 200 cu. ft. per inmate, 
only 3000 - 200 = 2800 cu. ft. will have to be supplied the first hour to 
keep the air within the standard purity, and so on. 

Again, if we only desire to maintain a standard of purity of 8 parts 
of carbonic acid in 10,000, the equation gives as the required air-supply 
per hour 

v= s _ . - w = 1500 n, or 1500 cu. ft. of fresh air per inmate per hour. 



654 



HEATING AND VENTILATION. 



Cubic feet of air containing 4 parts of carbonic acid in 10,000 necessary 
per person per hour to keep the air in room at the composition of 



parts of C0 2 in 10,000. 
cubic feet. 



6 7 8 9 10 15 20 

3000 2000 1500 1200 1000 545 375 

If the original air in the room is of purity of external atmosphere (4 parts 
of carbonic acid in 10,000), the amount or air to be supplied the first hour, 
for given cubic spaces per inmate, to have given standards of purity not 
exceeded at the end of the hour, is obtained from the following table: 



Cubic 
Feet of 


Proportion of Carbonic Acid in 10,000 Parts of the Air, not to 
be Exceeded at End of Hour. 


m Space 
in Room. 


6 7 8 9 10 | 15 | 20 


Individ- 
ual. 


Cubic Feet of Air, of Composition 4 Parts of Carbonic Acid in 
10,000, to be Supplied the First Hour. 


100 
200 
300 
400 
500 
600 
700 


2900 
2800 
2700 
2600 
2500 
2400 
2300 
2200 
2100 
2000 
1500 
1000 
500 


1900 
1800 
1700 
1600 
1500 
1400 
1300 
1200 
1100 
1000 
500 
None 


1400 
1300 
1200 
1100 
1000 
900 
800 
700 
600 
500 
None 


1100 
1000 
900 
800 
700 
600 
500 
400 
300 
200 
None 


900 
800 
700 
600 
500 
400 
300 
200 

too 

None 


445 
345 
245 
145 

45 
None 


275 
175 
73 

None 


800 






900 






1000 






1500 






2000 








2500 



























It is exceptional that systematic ventilation supplies the 3000 cubic 
feet per inmate per hour, which adequate health considerations demand. 
For large auditoriums in which the cubic space perindi vidual is great, andin 
which the atmosphere is thoroughly fresh before the rooms are occupied, 
and the occupancy is of two or three hours' duration, the systematic air- 
supply may be reduced, and 2000 to 2500 cubic feet per inmate per hour 
is a satisfactory allowance. 

In hospitals where, on account of unhealthy excretions of various kinds, 
the air-dilution must be largest, an air-supply of from 4000 to 6000 cubic 
feet per inmate per hour should be provided, and this is actually secured 
in some hospitals. A report dated March 15, 1882, by a commission ap- 
pointed to examine the public schools of the District of Columbia, says: 
" " In each class-room not less than 15 square feet of floor-space should be 
allotted to each pupil. In each class-room the window-space should not 
be less than one-fourth the floor-space, and the distance of desk most 
remote from the window should not be more than one and a half times the 
height of the top of the window from the floor. The height of the class- 
room should never exceed 14 feet. The provisions for ventilation should 
be such as to provide for each person in a class-room not less than 30 cubic 
feet of fresh air per minute (1800 per hour), which amount must be intro- 
duced and thoroughly distributed without creating unpleasant draughts, 
or causing any two parts of the room to differ in temperature more than 
2° Fahr., or the maximum temperature to exceed 70° Fahr. " [The provi- 
sion of 30 cu. ft. per minute for each person in a class-room is now (1909) 
required by law in several states.] 

' When the air enters at or near the floor, it is desirable that the velocity 
of inlet should not exceed 2 feet per second, which means larger sizes of 
register openings and flues than are usually obtainable, and much higher 
velocities of inlet than two feet per second are the rule in practice. 
The velocity of current into vent-flues can safely be as high as 6 or even 
10 feet per second, without being disagreeably perceptible. 

The entrance of fresh air into a room is coincident with, or dependent 
on, the removal of an equal amount of air from the room. The ordinary 
means of removal is the vertical yent-duct, rising to the top of the build- 



HEATING AND VENTILATION. 



655 



lng Sometimes reliance for the production of the current in this vent- 
duct is Placed solely on the difference of temperature of the air in the 
room and that of the external atmosphere; sometimes a steam coil is 
placed within the flue near its bottom to heat the air within the duct • 
sometimes steam pipes (risers and returns) run up the duct performing 
the same functions ; or steam jets within the flue, or exhaust fans driven 
by steam or electric power, act directly as exhausters; sometimes the 
heating of the air in the flue is accomplished by gas-jets. 

The draft of such a duct is caused by the difference of weight of the 
heated air in the duct, and of a column of equal height and cross-sectional 
area of the external air. 

Let d = density, or weight in pounds, of a cubic foot of the external air 

Let di = density, or weight in pounds, of a cubic foot of the heated air 
within the duct. 

Let h = vertical height, in feet, of the vent-duct. 

h (d — di) = the pressure, in pounds per square foot, with which the 
air is forced into and out of the vent-duct. 

This pressure expressed in height of a column of air of density within 
the vent-duct is h (d - d{) -s- d. 

Or, if t = absolute temperature of external air, and h = absolute tem- 
perature of the air in the vent-duct, then the pressure =/i (ti — t) ■'■*• t. 

The theoretical velocity, in feet per second, with which the air would 
travel through the vent-duct under this pressure is 



v=y 



2gh(t 1 -t) 



/ 



h(h-t) _ 



The actual velocity will be considerably less than this, on account of loss 
due to friction. This friction will vary with the form and cross- sectional 
area of the vent-duct and its connections, and with the degree of smooth- 
ness of its interior surface. On this account, as well as to prevent leakage 
of air through crevices in the wall, tin lining of vent-flues is desirable. 

The loss by friction maybe estimated at approximately 50%, and the 
actual velocity of the air as it flows through the vent-duct is 



v=-i/ 2gh — ^ — , or, approximately, v=4y h~ 



(ti-t) 
t 

If V = velocity of air in vent-duct, in feet per minute, and the external 
air be at 32° Fahr., since the absolute temperature on Fahrenheit scale 
equals thermometric temperature plus 459.4, 

from which has been computed the following table: 

Quantity of Air, in Cubic Feet, Discharged per Minute through a 
Ventilating Duct, of which the Cross-sectional Area is One 
Square Foot (the External Temperature of Air being 32° Fahr.). 



Height of 


Excess of Temperature of Air in Vent-duct above 
that of External Air. 


feet. 


5° 


10° 


15° 


20° 


25° 


30° 


50° 


100° 


150° 


10 


77 
94 
108 
121 
133 
143 
153 
162 
171 


108 
133 
153 
171 
188 
203 
217 
230 
242 


133 
162 

188 
210 
230 
248 
265 
282 
297 


153 

188 
217 
242 
265 
286 
306 
325 
342 


171 
210 
242 
271 
297 
320 
342 
363 
383 


188 
230 
265 
297 
325 
351 
375 
398 
419 


242 
297 
342 
383 
419 
453 
484 
514 
541 


342 
419 
484 
541 
593 
640 
683 
723 
760 


419 


15 


514 


20 


593 


25 


663 


30 


726 


35 


784 


40 


838 


45 


889 


50 


937 







656 HEATING AND VENTILATION. 



Multiplying the figures in preceding table by 60 gives the cubic feet 
of air discharged per hour per square foot of cross-section of vent-duct. 
Knowing the cross-sectional area of vent-ducts we can find the total dis- 
charge; or for a desired air-removal, we can proportion the cross-sectional 
area of vent-ducts required. 

Heating and Ventilating of Large Buildings. (A. R. Wolff, Jour. 
Frank. Inst., 1893.) — The transmission of heat from the interior to the 
exterior of a room or building, through the walls, ceilings, windows, etc., 
is calculated as follows: 

S = amount of transmitting surface in square feet ; 
t = temperature F. inside, t = temperature outside; 

K = a coefficient representing, for various materials composing build- 
ings, the loss by transmission per square foot of surface in British 
thermal units per hour, for each degree of difference of tempera- 
ture on the two sides of the material; 

Q = total heat transmission = SK (t— to). 

This quantity of heat is also the amount that must be conveyed to the 
room in order to make good the loss by transmission, but it does not 
cover the additional heat to be conveyed on account of the change of 
air for purposes of ventilation. (See Wolff's coefficients below, page 
659.) 

These coefficients are to be increased respectively as follows: 10% when 
the exposure is a northerly one, and winds are to be counted on as impor- 
tant factors; 10% when the building is heated during the daytime only, 
and the location of the building is not an exposed one: 30% when the 
building is heated during the daytime only, and the location of the build- 
ing is exposed; 50% when the building is heated during the winter months 
intermittently, with long intervals (say days or weeks) of non-heating. 

The value of the radiating-surface is about as follows: Ordinary bronzed 
cast-iron radiating-surfaces, in American radiators (of Bundy or similar 
type), located in rooms, give out about 250 heat-units per hour for each 
square foot of surface, with ordinary steam-pressure, say 3 to 5 lbs, per 
sq. in., and about 0.6 this amount with ordinary hot-water heating. 

Non-painted radiating-surfaces, of the ordinary " indirect " type 
(Climax or pin surfaces), give out about 400 heat-units per hour for each 
square foot of heating-surface, with ordinary steam-pressure, say 3 to 
5 lbs. per sq. in.; and about 0.6 this amount with ordinary hot-water 
heating. 

A person gives out about 400 heat-units per hour; an ordinary gas- 
burner, about 4800 heat-units per hour; an incandescent electric (16 
candle-power) light, about 1600 heat-units per hour. 

The following example is given by Mr. Wolff to show the application of 
the formula and coefficients: 

Lecture-room 40 X 60 ft., 20 ft. high, 48,000 cubic feet, to be heated 
to 69° F.; exposures as follows: North wall, 60 X 20 ft., with four windows, 
each 14X8 feet, outside temperature 0° F. Room beyond west wall and 
room overhead heated to 69°, except a double skylight in ceiling, 14 X 24 
ft., exposed to the outside temperature of 0°. Store-room beyond east 
wall at 36°. Door 6X12 ft. in wall. Corridor beyond south wall heated 
to 59°. Two doors, 6 X 12, in wall. Cellar below, temperature 36°. 

If we assume that the lecture-room must be heated to 69° F. in the 
daytime when unoccupied, so as to be at this temperature when first 
persons arrive, there will be required, ventilation not being considered, 
and bronzed direct low-pressure steam-radiators being the heating media, 
about 113,550 -*- 250 = 455 sq. ft. of radiating-surface. 

If we assume that there are 160 persons in the lecture-room, and we 
provide 2500 cubic feet of fresh air per person per hour, we will supply 
160 X 2500 = 400,000 cubic feet of air per hour (i.e., over eight changes 
of contents of room per hour). 

To heat this air from 0° F. to 69° F. will require 400,000 X 0.01785 X 
69 = 492.660 thermal units per hour (0.01785 being the product of the 
weight of a cubic foot, 0.075, by the specific heat of air, 0.238). Accord- 
ingly there must be provided 492,660 -*• 400 = 1232 sq. ft. of indirect 



HEATING AND VENTILATION. 



657 



surface, to heat the air required for ventilation, in zero weather. If the 
room were to be warmed entirely indirectly, that is, by the air supplied 
to room (including the heat to be conveyed to cover loss by transmission 
through walls, etc.), there would have to be conveyed to the fresh-air 
supply 492,660 + 118,443 = 611,103 heat-units. Tins would imply the 
provision of an amount of indirect heating-surface of the "Climax" type 
of 611,103 ■*■ 400 = 1527 sq. ft., and the fresh air entering the room 
would have to be at a temperature of about 86° F., viz., 



69° + 



118,413 



400,000 X 0.01785 



, or( 



i + 17 = 



5 F. 



The above calculations do not, however, take into account that 160 
persons in the lecture-room give out 160 X 400 = 64,000 thermal units 
per hour; and that, say, 50 electric lights give out 50 X 1600 = 80,000 
thermal units per hour; or, say, 50 gaslights, 50X4800 = 240,000 
thermal units per hour. The presence of 160 people and the gaslighting 
would diminish considerably the amount of heat required. Practically, 
it appears that the heat generated by the presence of 160 people, 64,000 
heat-units, and by 50 electric lights, 80,000 heat-units, a total of 144,000 
heat-units, more than covers the amount of heat transmitted through 
walls, etc. Moreover, that if the 50 gaslights give out 240,000 thermal 
units per hour, the air supplied for ventilation must enter considerably 
below 69° Fahr., or the room will be heated to an unbearably high temper- 
ature. If 400,000 cubic feet of fresh air per hour are supplied, and 240,000 
thermal units per hour generated by the gas must be abstracted, it means 

that the air must, under these conditions, enter ■ ' = 

about 34° less than 86°, or at about 52° Fahr. Furthermore, the addi- 
tional vitiation due to gaslighting would necessitate a much larger supply 
of fresh air than when the vitiation of the atmosphere by the people alone 
is considered, one gaslight vitiating the air as much as five men. 

The following table shows the calculation of heat transmission (some 
figures changed from the original) : 



1 T3 


Kind of Transmitting 
Surface. 


3-8.9 


Calculation 
of Area of 
Transmit- 
ting Sur- 
face. 


U 

02 


3 




69° 




36" 
36" 
24" 
36" 


63x22-448 

4x 8x 14 
42x22- 72 

6x12 
45x22- 72 

6x12 
17x22- 72 

6x12 
32x42-336 
14x24 
62x42 


938 

448 
852 

72 
918 

72 
302 

72 

1,008 

336 

2,604 


10 
83 
4 
19 
2 
5 
1 
5 
10 
35 
4 


9,380 

37,186 

3,408 

1,368 


69 




K 




33 




in 




1,836 


in 




360 


in 




302 


in 




360 


69 


Roof 


10,080 


m 




11,760 


n 


Floor 


10,416 




Supplementary allowance, north c 
Supplementary allowance, north c 

Exposed location and intermitten 








mtside 


wall, 10%.. 


86,454 
938 






% 


3,718 




day or night use, 


$0% 






91,110 
27,333 










118,443 









658 



HEATING AND VENTILATION. 



STANDARD VALUES FOR USE IN CALCULATION OF HEATING 
AND VENTILATING PROBLEMS. 

Heating Value of Coal. 



Anthracite.... . . . 

Semi-anthracite . 
Semi-bituminous 

Bit. eastern 

Bit. western 

Lignite 



Volatile 
Matter in 
the Com- 
bustible, 
per cent. 



3 to 7.5 
7.5 to 12.5 
12.5 to 25 
25 to 40 
35 to 50 
Over 50 



Heating Value 

per lb. 

Combustible, 

B.T.U. 



14,700 to 14,900 
14,900 to 15,500 
15,500 to 16,000 
14,800 to 15,000 
13,500 to 14,800 
11,000 to 13,500 



14,800 
15,200 
15,750 
15,150 
14,150 
12,250 



Air-dried 

Coal, 
per cent. 



Ash in 
Air-dried 

Coal, 
per cent. 



0.5to 1.0 
0.5tol.O 
0.5to 1.0 

1. to 4. 

4. to 14. 
10. to 18. 



10. to 18. 
10. to 18. 

5. to 10. 

5. to 15. 
10. to 25. 

5. to 25. 



Average Heating Value of Air-Dried Coal.— Anthracite, 12,600; semi- 
anthracite, 12,950; semi-bituminous, 14,450; bituminous eastern, 13,250; 
bituminous western, 10,400; lignite, 9,700. 

Eastern bituminous coal is that of the Appalachian coal field extending 
from Pennsylvania and Ohio to Alabama. Western bituminous coal 
is that of the great coal fields west of Ohio. 

Steam Boiler Efficiency. — The maximum efficiency obtainable with 
anthracite in low-pressure steam boilers, water heaters or hot-air furnaces 
is about 80 per cent, when the thickness of the coal bed and the draft 
are such as to cause enough air to be supplied to effect complete combus- 
tion of the carbon to CO2. With coals high in volatile matter the max- 
imum efficiency is probably not over 70 per cent. Very much lower 
efficiencies than these figures are obtained when the air supply is either 
deficient or greatly in excess, or when the furnace is not adapted to burn 
the volatile matter in the coal. D. T. Randall, in tests made in 1908 for 
the U. S. Geological Survey, with house-heating boilers, obtained effi- 
ciencies ranging from 0.62 with coke, 0.61 with anthracite, and 0.58 with 
semi-bituminous, down to 0.39 with Illinois coal. 

Available Heating Value of the Coal. — Using the figures given above as 
the average heating value of coal stored in a dry cellar, we have the follow- 
ing as the probable maximum values in British Thermal Units, of the 
heat available for furnishing steam or heating water or air, for the several 
efficiencies stated: 



Eff'y 0.80 

B.T.U. 10,080 



Semi- An. 


Semi-Bit. 


Bit. East. 


Bit. West. 


Lignite. 


0.77 
9,933 


0.75 
10,837 


0.70 
9,275 


0.65 
6,760 


0.60 

5,820 



For average values in practice, about 10 per cent may be deducted from 
these figures. (It is possible that an efficiency higher than 80% may be 
obtained with anthracite in some forms of air-heating furnaces in which 
the escaping chimney gases. are cooled, by contact with the cold air inlet 
pipes, to comparatively low temperatures.) 

The value 10,000 B.T.U. is usually taken as the figure to be used in 
calculation for design of heating and ventilating apparatus. For coals 
with lower available heating values proper reductions must be made. 



HEATING AND VENTILATING PROBLEMS. 



659 



Heat Transmission through Walls, Windows, etc., in B.T.U. per 
sq, ft. per Hour per Degree of Difference of Temperature. 

Brick Walls. 



Thick- 
ness, 
In. 


Wolff. 


Hauss. 


Average, 
B.T.U. * 


Thickness, 
In. 


Wolff. 


Hauss. 


Average. 
B.T.U.* 


4 


0.66 




0.537 


25 




0.18 


0.188 


43/ 4 




0.48 


0.508 


28 


0.18 




0.172 


8 


0.45 




0.397 


30 




0.16 


0.163 


10 




0.34 


0.351 


32 


0.16 




0.154 


12 


0.33 




0.313 


35 




0.13 


0.143 


15 




0.26 


0.272 


36 


0.145 




0.140 


16 


0.27 




0.260 


40 


0.13 


0.12 


0.128 


20 


0.23 


0.22 


0.222 


45 




0.11 


0.116 


24 


0.20 




0.194 











* The average figure for brick walls was obtained by plotting the 
reciprocals of Wolff's and Hauss's figures and drawing a straight line 
between them, representing the average heat resistances, and then taking 
the reciprocals of the resistances for different thicknesses. The resist- 
ance corresponds to the straight line formula B = 0.12+ 0.165 t, where 
t = thickness in inches. (Hauss's figures are from a paper by Chas. 
F. Hauss, of Antwerp, Belgium, in Trans. A. S. H. V. E., 1904.) 

Solid Sandstone Walls. (Hauss.) 

Thickness, in. . . 12 16 20 24 28 32 36 40 44 48 
B.T.U 0.45 0.39 0.35 0.32 0.29 0.26 0.24 0.22 0.20 0.19 

For limestone walls, add 10 per cent. 



Wolff. Hauss 
B.T.U. B.T.U. 



Wolff. Hauss. 
B.T.U. B.T.U. 



Glass Surfaces. 

Vault light 

Single window 

Double window 

Single skylight 

Double skylight 



Doors. 

Door 

1-in. pine 

2-in. pine 



Partitions. 
Solid plaster, 

13/ 4 to2l/4in.. 

2 1/2 to 3 1/4 in . . 

Fireproof 

2-in. pine board. . . . 



1.42 
1.20 
0.56 
1.03 
0.50 



0.40 
0.28 



0.30 
0.28 



1.00 
0.46 
1.06 
0.48 



0.60 
0.48 



Floors . 

Joists with double 
floor 

Concrete floor 

Fireproof construc- 
tion, planked over. 

Wooden beam con- 
struction, planked 
over 

Concrete floor 
brick arch 

Stone floor on arches 

Planks laid on earth. 

Planks laid on as- 
phalt 

Arch with air space . . 

Stones laid on earth. 

Ceilings. 
Joists with single 

floor 

Arches with air space 



0.10 
0.31 



0.22 
0.20 
0.16 

0.20 
0.09 
0.08 



0.10 
0.14 



660 



HEATING AND VENTILATION. 



Allowances for Exposures. — Wolff adds 25% for north and west ex- 
posures, 15% for east, and 5% for south exposures, also 10% additional 
for reheating, and 10% to the transmission through floor and ceilings. 
The allowance for reheating Mr. Wolff explains as follows in a letter to 
the author, Mar. 10, 1905. The allowance is made on the basis that the 
apparatus will not be run continuously ; in other words, that it will not be 
run at all, or only lightly, overnight. The rooms will cool off below the 
required temperature of 70°, and to be able to heat up quickly in the 
morning an allowance of 10% is made to the transmission figures to meet 
this condition. Hauss makes allowances as follows: 5% for rooms with 
unusual exposure; 10% where exposures are north, east, northeast, 
northwest and west; 31/3% where the height of ceiling is more than 13 ft.; 
6 2 /3% where it is more than 15 ft.; 10% where it is more than 18 ft. For 
rooms heated daily, but where heating is interrupted at night, add 

A = 0.0025 [(N - 1) Wi] h- Z. 
For rooms not heated daily, add B = [0.1 W (8 - Z)] -*- Z. 
In these formulas W\ = B.T.U. transmitted per hour by exposed sur- 
faces; W = total B.T.U. necessary, including that for ventilation or 
changes of air; N = time from cessation of heating to time of starting 
fire again, hours; Z = time necessary after fire is started until required 
room temperature is reached, hours. 

Allowance for Exposure and for Leakage. — In calculations of the 
quantity of heat required by ordinary residences, the formula total heat 

/W nC\ 

— (Ti— To) (-T-+ ^ + ^fi7 * s commonly used. Ti = temp, of room, 

To = outside temp., W = exposed wall surface less window surface, 
G = glass surface, C = cubic contents of room, n = number of changes 
of air per hour. The factor n is usually assumed arbitrarily or guessed 
at; some writers take its value at 1, others 1 for the rooms, 2 for the halls, 
etc.; others object to the use of C as a factor, saying that the allowance for 
exposure and leakage should be made proportional to the exposed wall 
and glass surface since it is on these surfaces that the leakage occurs, 
and omitting the term wC/56 they multiply the remainder of the ex- 
pression by a factor for exposure, c = 1.1 to 1.3, depending on the direc- 
tion of the exposure. To show what different results may be obtained 
by the use of the two methods, the following table is calculated, apply- 
ing both to six rooms of widely differing sizes. Two sides of each room, 
north and east, are exposed. Ti = 70; T = 0; G = 1/5 (W + G). 













$ 


s 












**! 


Total Wall, 


Q> 


+ 


+ 


<© 






a 


Size, ft. 


3 


(W + G) 







"* 


to 


O* 


&5 

CO 










11 


sq. ft. 


O 


II s 


$ 
g 


A 


10x10x10 


1,000 


20x10= 200 


40 


5 


5,600 


1,250 


1,120 


1,680 


B 


10x20x10 


2,000 


30x10= 300 


60 


62/3 


8,400 


2,500 


1,680 


2,520 


C 


20x20x12 


4,800 


40x12= 480 


96 


10 


13,440 


6,000 


2,688 


4,032 


D 


20x40x14 


11,200 


60x14= 840 


168 


171/3 


23,520 


14.000 


4,704 


7,0:6 


E 


40x40x15 


24.000 


80x15=1200 


240 


20 


33.600 


30.000 


6,720 


10.080 


F 


40x80x16 


51,200 


120x16=1920 


384 


262/3 


54,460 


64.000 


10.892 


16.338 



The figures in the column headed H = 70 (W/4 + G) represent the 
heat transmitted through the walls, those in the column 70 C/56 are the 
heat required for one change of air per hour; 0.2 H is the heat correspond- 
ing to an allowance of 20% for exposure and leakage, and 0.3 H corre- 
sponds to an allowance of 30%. For the small rooms A and B the 
difference between 70 C/56 and 0.2 H or 0.3 H is not of great importance, 
but it becomes very important in the largest rooms; in room F the differ- 
ence between 70 C/56 and 0.2 H is nearly equal to the total heat trans- 
mitted through the walls, indicating that the use of the cubic contents 
as a factor in calculations of large rooms is likely to lead to great errors. 
This is due to the fact that the ratio C ■*■ (W + G) varies greatly with 
different sizes of rooms. 



HEATING BY HOT-AIR FURNACES. 661 

With forced ventilation, the quantity of heat needed depends chiefly 
upon the number of persons to be provided for. Assuming 2000 cu. ft. 
per hour per person, heated from 0° to 70°, and 1, 2 and 4 persons per 
100 sq. ft. of floor surface, the heat required for the air is as follow.s: 
Room A B C D E F 

1 person per 100 sq. ft. 2,500 5,000 10,000 20,000 40,000 80,000 

2 persons per 100 sq. ft. 5,000 10,000 20,000 40,000 80,000 160,000 
4 persons per 100 sq. ft. 10,000 20,000 40,000 80,000 160,000 320,000 
Ratio of last line toff.. 1.8 2.4 3.0 3.4 4.8 5.9 

Heating "by Hot-air Furnaces. — A simple formula for calculating the 
total heat in British Thermal Units required for heating and ventilating 

tt W\ nC~\ 

C l^ + T/ + ~~^6>\^ 1 ~' 11 ^' (See notation above.) 

The formula is derived as follows: The heat transmitted through 1 sq. ft. 
of single glass window is approximately 1 B.T.U. per hour per degree of 
difference of temperature, and that through 1 sq. ft. of 16-in. brick wall 
about 0.25 B.T.U. (For more accurate calculations figures taken from 
the tables (p. 659) should be used.) The specific heat of air is taken at 
0.238, and the weight of 1 cu. ft. air at 70° F. at 0.075 lb. per cu. ft. 
The product of these figures is 0.01785, and its reciprocal is 56. 

For a difference T\ - T = 70°, 0.01785 X 70 = 1.2495, we may, 
therefore, write the formula 

Total heat = 70 [ c (^ + x)] + 125 A 

= heat conducted through walls + heat exhausted in 
ventilation. 

A is the cubic feet of air (measured at 70°) supplied to and exhausted 
from the building. This formula neglects the heat conducted through 
the roof, for which a proper addition should be made. 

There are two methods of heating by hot-air furnaces; one in which 
all the air for both heating and ventilation is taken from outdoors and 
exhausted from the building, and the other in which only the air for 
ventilation is taken from outdoors, and additional air is recirculated 
through the furnace from the building itself. The first method is an 
exceedingly wasteful one in cold weather. By the second it is possible 
to heat a building with no greater expenditure of fuel than is required 
for steam or hot-water heating. 

Example. — Required the amount of heat and the quantity of air to be 
circulated by the two methods named for a building which has G = 400, 
W = 2400, C = 16,000, n = 2, T\ = 70°, T = 0°, T 2 , the temperature 
at which the air leaves the furnace, being taken for three cases as 100°, 
120°, and 140°. Assume c, the coefficient for exposure, including heat 
lost through roof, = 1.2. When only enough air for ventilation is taken 
into and exhausted from the building, the formula gives 
70 X 1.2 (500 + 400) + 1.25 X 32,000 = 115,600 B.T.U. = 75,600 for 
heat + 40,000 for ventilation. 

Suppose all the air required for heating is taken from outdoors at 0° F., 
and all exhausted at 70 , the quantity, A, then, instead of being 32,000 
cu. ft., has to be calculated as follows: 

Total heat = c (g + ^\ (Ti- T ) + A X 0.01785 X (Ti - T ) 

= 0.01785 A (T 2 - T ). 
Heat supplied by furnace = heat for conduction + heat for ventilation 

From which we find A = c (g + ^) (Ti - T ) ■*■ 0.01785 (T 2 -Ti) 
= 75,600 -h 0.01785 (T 2 - 70°). 

For the value of r 2 T 2 = 100 7 7 2 = 120 r 2 = 140 

A = cu. ft 141,117 84,706 60,504 

Heat lost by exhausting this air at 70° . . . 176,396 105,882 75,630 

Adding 75,600 loss by walls gives total . . . 251,996 181,482 152,230 
Excess above 115,600 actually required 

for heating and ventilating, % 118.0 57.0 31.7 



662 



HEATING AND VENTILATION. 



British Thermal Units Absorbed in Heating 1 Cu. Ft. of Air, or given 
up in cooling it. — (The air is measured at 70° F.) 

10° 20 30 40 50 56 60 70 80 90 100 101 120 126 130 140 
0.18 0.36 0.54 0.71 0.89 1. 1.07 1.25 1.43 1.61 1.78 1.96 2.14 2.25 2.32 2.5 



Area in Square Inches of Pipe required to Deliver 100 Cu. Ft. of 
Air per Minute, at Different Velocities. — The air is measured at the 
temperature of the air in the pipe. 

Velocity per second 2 3 

Area, sq. in 120 80 



5 6 7 8 9 10 
48 40 34.3 30 26.7 24 



The quantity of air required for ventilation or heating should be 
figured at a standard temperature, say 70° F., but when warmer air is 
to be delivered into the room through pipes, the area of the pipes should 
be calculated on the basis of the temperature of the warm air, and not on 
that of the room. 

Example. — A room requires to be supplied with 1000 cu. ft. per min. 
at 70° F. for ventilation, but the air is also used for heating and is delivered 
into the room at 120° F. Required, the area of the delivery pipe, if the 
velocity of the heated air in the pipe is 6 ft. per second. 

From the table of volumes, given on the next page, 1000 cu. ft. at 70° 
= 1094 cu. ft. at 120°. From the above table of areas, at 6 ft. velocity 
40 sq. in. area is required for 100 cu. ft., therefore 1094 cu. ft. will require 
10.94 X 40 = 437.6 sq. in. or about 3 sq. ft. 



Carrying Capacity of Air Pipes. 





Area in 
sq. in. 


Area, 
sq.ft. 


Velocity, Feet per Second. 


Diam. 


3 


4 


5 


6 


7 


8 








Cu. Ft. 


per Min. 




5 


19.63 


.1364 


24.6 


32.7 


40.9 


49.1 


57.3 


65.5 


6 


28.27 


.1963 


35.3 


47.1 


58.9 


70.7 


82.4 


94.2 


7 


38.48 


.2673 


48.1 


64.2 


80.2 


96.2 


112. 


128. 


8 


50.27 


.3491 


62.8 


83.8 


105. 


126. 


147. 


168. 


9 


63.62 


.4418 


80.0 


106. 


133. 


159. 


186. 


212. 


10 


78.54 


.5454 


98.2 


131. 


164. 


196. 


229. 


262. 


11 


95.03 


.6600 


119. 


158. 


198. 


238. 


277. 


317. 


12 


113.1 


.7854 


141. 


188. 


236. 


283. 


330. 


377. 


13 


132.7 


.9218 


166. 


221. 


277. 


332. 


387. 


442. 


14 


153.9 


1.069 


192. 


257. 


321. 


385. 


449. 


513. 


15 


176.7 


1.227 


221. 


294. 


368. 


442. 


515. 


589. 


11.3 


100. 


0.694 


125. 


167. 


208. 


250. 


292. 


333. 


13.6 


144. 


I. 


180. 


240. 


300. 


360. 


420. 


480. 



The figures in the table give the carrying capacity of pipes in cu. ft. 
of air at the temperature of the air flowing in the pipes. To reduce the 
figures to cu. ft. at a standard temperature (such as 70° F.) divide by 
the ratio of the volume per cu. ft. of the air in the pipe to that of the air 
of the standard temperature, as in the following table: 



HEATING BY HOT-AIR FURNACES. 



663 





Volume of 


Air a 


t Different Temperatures. 








(Atmospheric pressure.) 




Fahr. 
Deg. 


Cu. Ft. 
in 1 lb. 


Compar- 
ative 
Volume. 


Fahr. 
Deg. 


Cu. Ft. 
in 1 lb. 


Compar- 
ative 
Volume. 


Fahr. 
Deg. 


Cu.Ft. 
in 1 lb. 


Compar- 
ative 
Volume. 





11.583 


0.867 


90 


13.845 


1.038 


160 


15.603 


1.169 


32 


12.387 


0.928 


100 


14.096 


1.056 


170 


15.854 


1.188 


40 


12.586 


0.943 


110 


14.346 


1.075 


180 


16.106 


1.207 


50 


12.840 


0.962 


120 


14.596 


1.094 


190 


16.357 


1.226 


62 


13.141 


0.985 


130 


14.848 


1.113 


200 


16.608 


1.245 


70 


13.342 


1.000 


140 


15.100 


1.132 


210 


16.860 


1.264 


80 


13.593 


1.019 


150 


15.351 


1.151 


212 


16.910 


1.267 



Sizes of Air Pipes Used in Furnace Heating. (W. G. Snow, Eng. 
News, April 12, 1900.) 











Length of Room, Ft. 










W'th. 

of 
Room 

Ft. 


10 


12 


14 


16 


18 


20 


22 


24 


26 


28 


30 


Diameter of Pipe, Ins. 


8.... 


8, 7 
8, 7 


8,7 
9,8 
9,8 


9,8 
9, 8 
10, 8 
10,8 


9, 8 
10, 8 
10, 8 
10,9 
11,9 
















10.... 


10, 8 

10, 9 

11, 9 

11, 9 

12, 10 


10, 9 

11, 9 

11, 9 

12, 10 

12, 10 

13, 11 












12.... 


11, 9 

12, 10 

12, 10 

13, 11 
13, 11 


12, 10 

12, 10 

13, 10 
13, 11 
13, 11 








14.... 




13, 10 
13, 10 

13, 11 

14, 12 


13, 10 

13, 11 

14, 12 
14, 12 




16.... 






13 11 


18.... 








14 12 


20.... 










14, 12 

















The first figure in each column shows the size of pipe for the first floor 
and the second figure the size for the second floor. Temperature at regis- 
ter, 140°; room, 70°; outside, 0°. Rooms 8 to 16 ft. in width assumed to 
be 9 ft. high; 18 to 20 ft. width, 10 ft. high. When first-floor pipes are 
longer than 15 ft. use one size larger than that stated. For third floor, 
use one size smaller than for second floor. For rooms with three expo- 
sures, increase the area of pipe in proportion to the exposure. 

The table was calculated on the following basis: 

The loss of heat is calculated by first reducing the total exposure to 
equivalent glass surface. This is done by adding to the actual glass 
surface one-quarter the area of exposed wood and plaster or brick walls 
and V20 the area of floor or ceiling. Ten per cent is added where the 
exposure is severe. The window area assumed is 20 % of the entire ex- 
posure of the room. 

Multiply the equivalent of glass surface by 85. The product will be 
the total loss of heat by transmission per hour. 

Assuming the temperature of the entering air to be 140° and that of 
the room to be 70°, the air escaping at approximately the latter tempera- 
ture will carry away one-half the heat brought in. The other half, corre- 
sponding to the drop in temperature from 140° to 70°, is lost by trans- 
mission. With outside temperature zero, each cubic foot of air at 140° 
brings into the room 2.2 heat units.. Since one-half of this, or 1.1 heat 
units, can be utilized to offset the loss by transmission, to ascertain the 
volume of air per hour at 140° required to heat a given room, divide the 
loss of heat by transmission by 1.1. This result divided by 60 gives the 
number of cubic feet per minute. In calculating the table, maximum 
velocities of 280 and 400 ft. were used for pipes leading to the first and 
second floors respectively. The size of the smaller pipes was based on 
lower velocities, according to their size, to allow for their greater resist- 
ance and loss of temperature. 



664 



HEATING AND VENTILATION. 



Furnace-Heating with Forced Air Supply. (The Metal Worker, 
April 8, 1905.) —Tests were made of a Kelsey furnace with the air supply 
furnished by a 48-in. Sturtevant disk fan driven by a 5 H.P. electric 
motor. A connection was made from the air intake, between the fan and 
the furnace, to the ash pit so that the rate of combustion could be regu- 
lated independently of the chimney-draft condition. The furnace had 
4.91 sq. ft. of grate surface and 238 sq. ft. of heating surface. The volume 
of air was determined by anemometer readings at 24 points in a cross- 
section of a rectangular intake of 11.88 sq. ft. area. The principal 
results obtained in two tests of 8 hours each are as follows: 

Av. temp, of the cold air 

Per cent humidity of the cold air 

Av. temp, of the warm air 

Air delivered to heater, cu. ft. per hour. . . . 

B.T.U. absorbed by the dry air per hour. . . 

B.T.U. absorbed by the vapor per hour .... 

Avge. no. of pounds of coal burned per hour 

B.T.U. given by the coal per hour 529,200 

Per cent efficiency of the furnace 

Grate Surface and Rate of Burning Coal. 

In steam boilers for power plants, which are constantly attended by 
firemen, coal is generally burned at between 10 and 30 lbs. per sq. ft. 
of grate per hour. In small boilers, house heaters and furnaces, which 
even in the coldest weather are supplied with fresh coal only once in 
several hours, it is necessary to burn the coal at very much slower rates. 
Taking a cubic foot of coal as weighing 60 lbs., in a bed 12 inches deep, 
and 1 sq. ft. of grate area, it would be one-half burned away in 71/2 hours 
at a rate of burning of 4 lbs. per sq. ft. of grate per hour. This figure, 
4 lbs., is commonly taken in designing grate surface for house-heating 
boilers and furnaces. Using this figure we have the following as the 
rated capacity of different areas of grate surface. 



39° 


58° 


71 


56 


135° 


152° 


250,896 


249,195 


451,872 


421,496 


2,016 


3,102 


36 


33.5 


529,200 


492,450 


85.7 


86.2 



Rated Capacity of Furnaces and Boilers for House Heating. 






Coal- 
burning 
Capacity 




Equiv. 
lbs. 


Equiv. 


Equiv. 


Diam. 




Capacity, 


lbs. 


cu. ft. 


of 


Area in — 


B.T.U. 


Steam 


Air per 


Air at 


Round 


per 


Evap. 


Hour 


70° 


Grate. 




Hour. 


Hour. 


212° per 
Hour. 


Heated 
100°. 


Heated 
100°. 


ins. 


^q.in. 


sq.ft. 


lbs. 


(a) 


(b) 


(O 


(d) 


12 


113.1 


.785 


3.142 


31,420 


32.5 


1,320 


17,610 


14 


153.9 


1.069 


4.276 


42,760 


44.3 


1,797 


23,970 


16 


201.1 


1.396 


5.585 


55,850 


57.8 


2,347 


31,300 


18 


254.5 


1.76'/ 


7.069 


70,690 


73.2 


2,970 


39,620 


20 


314.2 


2.182 


8.728 


87,280 


90.4 


3,667 


43,920 


22 


380.1 


2.640 


10.560 


105,600 


109.4 


4,437 


59,190 


24 


452.4 


3.142 


12.566 


125,660 


130.1 


5,280 


70,430 


26 


530.9 


3.687 


14.748 


147,480 


152.7 


6,197 


82,670 


28 


615.8 


4.276 


17.104 


171,040 


177.1 


7,187 


95,870 


30 


706.9 


4.909 


19.636 


196,360 


203.3 


8,260 


110,190 


32 


804.2 


5.585 


22.340 


223,400 


231.3 


9,387 


125,220 


34 


907.9 


6.305 


25.220 


252,200 


261.2 


10,597 


141,350 


36 


1017.9 


7.069 


28.276 


282,760 


292.8 


11,881 


V58.490 



Figures in column (b) = (a) -s- 965.7. 

Figures in column (c) = (a) -h (100 X 0.238). 

Figures in column (d) = (c) X 13.34. 

Latent heat of steam at 212° = 965.7 B.T.U. [new steam tables give 
970.4]. 

Specific heat of air = 0.238. 

Note that the figures in the last three columns are all based on the rate 
of combustion of 4 lbs. of coal per sq. ft. of grate per hour, which is taken 
as the standard for house heating. For heating schoolhouses and other 
large buildings where the furnace is fed with coal more frequently a 



4 


2.775 


40,000 


27,750 


41.25 


28.61 


156.5 


108.7 



STEAM-HEATING. 665 

much higher actual capacity may be obtained from the grate surface 
named. A committee of the Am. Soc. H. and V. Engrs. in 1909 says: 

The grate surface to be provided depends on the rate of combustion, 
and this in turn depends on the attendance and draft, and on the size of 
the boiler. Small boilers are usually adapted for intermittent attention 
and a slow rate of combustion. The larger the boiler, the more attention 
is given to it, and the more heating surface is provided per square foot 
of grate. The following rates of combustion are common for internally 
fired heating boilers: 

Sq. ft. of grate 4 to 8 10 to 18 20 to 30 

Lbs. coal per sq. ft. grate per hr. not over 4 6 10 

Capacity of 1 sq. ft. and of 100 sq. in. of Grate Surface, for Steam, 
Hot-water, or Furnace Heating. 

(Based on burning 4 lbs. of coal per sq. ft. of grate per hour and 10,000 
B.T.U. available heating value of 1 lb. of coal.) 
1 sq. ft. 100 sq. ins. 

grate equals grate equals 

lbs. of coal per hour. 
B.T.U. per hour. 

lbs. of steam evap. from and at 212° per hr. 
sq. ft. of steam radiating surface = B.T.U. 
-4- 255.6*. 

261.4 181.5 sq. ft. of hot-water radiating surface = 

B.T.U. -J- 153 t- 
22,420. 15,570. cu. ft. of air (measured at 70° F.) per hour 

heated 100°. 
* Steam temperature 212°, room temperature 70°, radiator coefficient, 
that is the B.T.U, transmitted persq. ft. of surface per hour per degree of 
difference of temperature, 1.8. 

t Water temperature 160°, room temperature 70°, radiator co- 
efficient 1.7. 

For any other rate of combustion than 4 lbs., multiply the figures in the 
table by that rate and divide by 4. 

STEAM-HEATING. 

The Rating of House-heating Boilers. 

(W. Kent, Trans. A. S. H. V. E., 1909.) 
The rating of a steam-boiler for house-heating may be based upon one 
or more of several data: 1, square feet of grate-surface; 2, square feet of 
heating-surface; 3, coal-burning capacity; 4, steam-making capacity; 
5, square feet of steam-radiating-surface, including mains, that it will 
supply. In establishing such a rating the following considerations should 
be taken into account: 

1. One sq. ft. of cast-iron radiator surface will give off about 250 B.T.U. 
per hour under ordinary conditions of temperature of steam 21 2°, and 
temperature of room 70°. 

2. One pound of good anthracite or semi-bituminous coal under the 
best conditions of air-supply, in a boiler properly proportioned, will 
transmit about 10,000 B.T.U. to the boiler. 

3. In order to obtain this economical result from the coal the boilers 
should be driven at a rate not greatly exceeding 2 lbs. of water evaporated 
from and at 212° per sq. ft. of heating-surface per hour, corresponding 
to a heat transmission of 2 X 970 = 1940, or, say, approximately 2000 
B.T.U. per hour per sq. ft. of heating-surface. 

4. A satisfactory boiler or furnace for house-heating should not 
require coal to be fed oftener than once in 8 hours; this requires a rate 
of burning of only 3 to 5 pounds of coal per sq. ft. of grate per hour. 

5. For commercial and constructive reasons, it is not convenient to 
establish a fixed ratio of heating- to grate-surface for all sizes of boilers. 
The grate-surface is limited by the available area in which it may be 
placed, but on a given grate more heating-surface may be piled in one 
form of boiler than in another, and in boilers of one general form one 
boiler may be built higher than another, thus obtaining a greater amount 
of heating-surface. 



666 



HEATING AND VENTILATION. 



6. The rate of burning coal and the ratio of heating- to grate-surface 
both being variable, the coal-burning rate and the ratio may be so related 
to each other as to establish condition 3, viz., a rate of evaporation of 
2 lbs. of water from and at 212° per sq. ft. of heating-surface per hour. 
These general considerations lead to the following calculations: 
1 lb. of coal, 10,000 B.T.U. utilized in the boiler, will supply 10,000 *■ 
250 = 40 sq. ft. radiating-surface, and will require 10,000 4- 2000 = 
5 sq. ft. boiler heating-surface. 1 sq. ft. of boiler-surface will supply 
2000 -h 250 or 40 ■*- 5 = 8 sq. ft. radiating-surface. 



Low 
Boiler. 



Medi- 
um. 



High Boiler. 



1 sq. ft. of grate should burn 

1 sq. ft. of grate should develop. 

1 sq. ft. of grate will require 

1 sq. ft. of grate will supply 

Type of boiler, depending on 
ratio heating- -*- grate-surface, 



3 

30,000 
15 
120 



40,000 
20 
160 

B. 



5 lb. coal per hour. 
50,000 B.T.U. per hour. 
25 sq. ft. heating-surf. 
200 sq.ft. radiating-sur. 

C. 











Table of 


Ratings. 










6 

T3 

a 


1 


<2 
fa ™ 


13 £ 
3 n 


aJ§ 

> ,- 

H3 


gfa 


6 


03 

o 


fa " 


^5 


Is 


m fa 


ft 
>> 

H 


fa 

6 1 
xn 


go S 
W 


O <D 

o a 




PS 


05 

a 
H 


fa 

m 




5m 

6 ft 


!> a 


73 6* 


A 1... 


1 


15 


3 


30 


120 


B 8 


.. 8 


160 


32 


320 


1,280 


A 2... 


2 


30 


6 


60 


240 


V, 6 


6 


150 


30 


300 


1,200 


A 3... 


3 


45 


9 


90 


360 


(1 7 


7 


175 


35 


350 


1,400 


A A... 


4 


60 


12 


120 


480 


(1 8 


8 


200 


40 


400 


1,600 


A 5... 


5 


75 


15 


150 


600 


10 


.. 10 


250 


50 


500 


2,000 


B 4... 


4 


80 


16 


160 


640 


12 


.. 12 


300 


60 


600 


2,400 


B 5... 


5 


100 


20 


200 


800 


a 14 


.. 14 


350 


70 


700 


2,800 


B 6... 


6 


120 


24 


240 


960 


C 16 


.. 16 


400 


80 


800 


3,200 


B 7... 


7 


140 


28 


280 


1,120 















The table is based on the utilization in the boiler of 10,000 B.T.U. per 
pound of good coal. For poorer coal the same figures will hold good 
except the pounds coal burned per hour, which should be increased in 
the ratio of the B.T.U. of the good to that of the poor coal. Thus for 
coal from which 8000 B.T.U. can be utilized the coal burned per hour 
will be 25 per cent greater. 

For comparison with the above table the following figures are taken 
and calculated from the catalogue of a prominent maker of cast-iron 
boilers: 





















Coal 






H 


R 










5|* 


per 






Heat- 


Radiat- 


H 


R 


R 


B.T.U. 


Hour 


Height. 


G 


mg- 


ing-sur- 


— 


— 


~ 


per Hour 


per 




Grate. 


sur- 
face. 


face. 


G 


G 


H 


= Rx250 


« 


sq.ft. 

Grate 

* 


Low 


I 2.1 


45 


210 


21.5 


100 


4.7 


52,500 


1,167 


2.5 


1 4.7 


90 


600 


19.1 


128 


6.7 


150,000 


1,667 


3.2 


Medium.. 


( 4.2 


103 


600 


24.5 


143 


5.8 


150,000 


1,456 


3.6 


\ 8.2 


195 


1,500 


23.8 


183 


7.7 


375,000 


1,923 


4.6 


High 


( 6.7 
\ 14.7 


210 


1,200 


31.3 


179 


5.7 


300,000 


1,476 


4.5 


420 


3,300 


28.6 


225 


7.9 


825,000 


1,964 


5.6 



Equals B.T.U. per hour -h 10,000 G. 



STEAM-HEATING. 667 



Testing Cast-iron House-heating Boilers. 

The testing of the evaporating power and the economy of small-sized 
boilers is more difficult than the testing of large steam-boilers for the 
reason that the small quantity of coal burned in a day makes it impossible 
to procure a uniform condition of the coal on the grate throughout the 
test, and large errors are apt to be made in the calculation on account of 
the difference of condition at the beginning and end of a test. The 
following is suggested as a method of test which will avoid these errors. 

(a) Measure the grate-surface and weigh out an amount of coal equal 
to 30, 40, or 50 lbs. per sq. ft. of grate, according to the type A, B, or C, 
or the ratio of heating- to grate-surface. 

(b) Disconnect the steam-pipe, so that the steam may be wasted at 
atmospheric pressure. Fill the boiler with cold water to a marked level, 
and take the weight of this water and its temperature. 

(c) Start a brisk fire with plenty of wood, so as to cause the coal to 
ignite rapidly; feed the coal as needed, and gradually increase the thick- 
ness of the bed of coal as it burns brightly on top, getting the fire-pot full 
as the last of the coal is fired. Then burn away all the coal until it ceases 
to make steam, when the test may be considered as at an end. 

(d) Record the temperature of the gases of combustion in the flue every 
half-hour. 

(e) Periodically, as needed, feed cold water, which has been weighed, 
to bring the water level to the original mark. Record the time and the 
weight. 

Calculations. 

Total water fed to the boiler, including original cold 
water, pounds X (212° — original cold-water tem- 
perature) = B.T.U. 

Water apparently evaporated, pounds X 970 = B.T.U. 

Add correction for increased bulk of hot water: 

Original water, pounds X (62 " 3 ~ 59-8) X 970 = B.T.U. 

Total ' B.T.U. 

Divide by 970 to obtain equivalent water evaporation from and at 
212° F. 

Divide by the number of pounds of coal to obtain equivalent water per 
pound of coal, 

The last result may be considerably less than 10 pounds on account of 
imperfect combustion at the beginning of the test, excessive air-supply 
when the coal bed is thin in the latter half of the test, and loss by radiation, 
but the results will be fairly comparable with results from other boilers 
of the same size and run under the same conditions. The records of water 
fed and of temperature of gases should be plotted, with time as the base, 
for comparison with other tests. 

Proportions of House-heating Boilers. — A committee of the Am. 
Soc. Heating and Ventilating Engineers, reporting in 1909 on the method 
of rating small house-heating boilers, shows the following ratings, in square 
feet of radiating surface supplied by certain boilers of nearly the same 
nominal capacity, as given in makers' catalogues. 

Boiler A. B. C. D. E. F. 

Rated capacity. . 800 800 775 750 750 750 

Square inches of grate 616 740 648 528 630 648 

Ratio of grate to 100 sq. ft. of capacity 77 92.5 83.6 70.4 84 86.2 

Estimated rate of combustion 5.1 4.2 4.65 5.63 4.4 4.5 

The figures in the last line are lbs. of coal per sq. ft. of grate surface per 
hour, and are based on the assumptions of 10,000 B.T.U. utilized per 
lb. of coal and 270 B.T.U. transmitted by each sq. ft. of radiating sur- 
face per hour. 



668 



HEATING AND VENTILATION. 



The question of heating surface in a boiler seems to be an unknown 
quantity, and inquiry among the manufacturers does not produce much 
information on the subject." 

Following is the list of sizes and ratings of the "Manhattan" sectional 
steam boiler. The figures for sq. ft. of grate surface and for the ratio of 
heating to grate surface (approx.) have been computed from the sizes 
given in the catalogue (1909). 





"o ttf 




+3 a 


bi 




"3 oi 




-p a 




*S £ 


ll^-g 




03 03 


M G 


"8 T ; 


11^-t 




03 — ■ 
03 03 




£g 


Square f 
Direct R 
tion Boi 
will Sup 


Size of 


03 


O go 


u a 


Square f 
Direct R 
tion Boi 
will Sup 


Size of 


03^ h 


.20£ 
1^ 




Grate. 


8 zsu 






Grate. 


b 3 -2 






ins. 


sq.ft. 










ins. 


sq.ft. 






4 


450 


18x19 


2.37 


68 


29 


10 


2250 


24x63 


10.5 


212 


20 


5 


600 


18x25 


3.75 


84 


23 


6 


2200 


36x36 


9 


256 


28 


6 


750 


18x31 


3.87 


100 


26 


7 


2700 


36x43 


11.74 


298 


26 


7 


900 


18x37 


4.65 


116 


25 


8 


3200 


36x50 


13.33 


340 


26 


8 


1050 


18X43 


5.37 


132 


25 


9 


3700 


36x57 


14.25 


382 


26 


5 


1000 


24x30 


5 


111 


22 


10 


4200 


36x64 


16 


424 


26 


6 


1250 


24x36 


6 


128 


21 


11 


4700 


36x71 


17.5 


466 


27 


7 


1500 


24x43 


7.16 


149 


21 


12 


5200 


36x78 


19.5 


508 


26 


8 


1750 


24x50 


8.33 


170 


20 


13 


5700 


36x84 


21 


550 


26 


9 


2000 


24x57 


9.5 


191 


20 


14 


6200 


36X90 


22.5 


592 


26 



It appears from this list that there are three sets of proportions, corre- 
sponding to the three widths of grate surface. The average ratio of 
heating to grate surface in the three sets is respectively 25.0, 20.7, and 
25.8; the rated sq. ft. of radiating surface per sq. ft. of grate is 185, 208, 
and 259, and the sq. ft. of radiating surface per sq. ft. of boiler heating 
surface is 7.4, 10.1, and 9.8. Taking 10,000 B.T.U. utilized per lb. of 
coal, and 250 B.T.U. emitted per sq. ft. of radiating surface per hour, 
the rate of combustion required to supply the radiating surface is respec- 
tively 4.62, 5.22, and 6.40 lbs. per sq. ft. of grate per hour. 

Coefficient of Heat Transmission in Direct Radiation. — The value 
of K, or the B.T.U. transmitted per sq. ft. of radiating surface per hour 
per degree of difference of temperature between the steam (or hot water) 
and the air in the room, is commonly taken at 1.8 in steam heating, 
with a temperature difference of about 142°, and 1.6 in hot-water heat- 
ing, with a temperature difference averaging 80°. Its value as found by 
test varies with the conditions; thus the total heat transmitted is not 
directly proportional to the temperature difference, but increases at a 
faster rate; single pipes exposed on all sides transmit more heat than 
pipes in a group; low radiators more than high ones; radiators exposed 
to currents of cool air more than those in relatively quiet air; radiators 
with a free circulation of steam throughout more than those that are 
partly filled with water or air, etc. The total range of the value of K, 
for ordinary conditions of practice, is probably between 1.5 and 2.0 for 
steam-heating with a temperature difference of 140°, averaging 1.8, and 
between 1.2 and 1.7, averaging 1.6, for hot-water heating, with a tem- 
perature difference of 80%. 

C. F. Hauss, Trans. A. S. H. V. E., 1904, gives as a basis for calcula- 
tion, for a room heated to 70° with steam at IV2 lbs. gauge pressure 
(temperature difference 146° F.) 1 sq. ft. of single column radiator gives 
off 300 B.T.U. per hour; 2-column, 275; 3-column, 250; 4-column, 225. 

Value of K in Cast-iron Direct Radiators. (J. K. Allen, Trans. 
A. S. H. V. E., 1908.) Ts = temp, of steam; 2 7 1 = temp, of room. 
7/s-7\ = 110 120 130 140 150 160 

2-col. rad 1.71 1.745 1.76 1.82 1.855 1.895 

3-col. rad 1.65 1.695 1.745 1.79 1.835 1.885 

Ts-T t = 170 180 200 220 240 260 

2-col. rad 1.93 1.965 2.04 2.11 2.185 2.265 

3-col. rad 1.93 1.98 2.075 2.165 2.260 2.36 



STEAM-HEATING. 669 



B.T.TJ. Transmitted per Hour per Sq. Ft. of Heating Surface in 
Indirect Radiators. (W. S. Munroe, Eng. Rec, Nov. 18, 1899.) 

Cu. ft. of air per hour per sq. ft. of surface. 
100 200 300 400 500 600 700 800 900 
B.T.U. per hour per sq. ft. of heating surface. 
"Gold Pin ")(a). .. 200 325 450 560 670 780 870 950 1030 

radiator J (6) . . . 300 550 760 950 1130 1300 
"Whittier" (b)...250 400 520 620 710 

B.T.U. per hr. per sq. ft. per deg. diff. of temp.* 

Gold Pin (a) 1.3 2.2 3.0 3.7 4.5 5.2 5.8 6.3 6.9 

Gold Pin (6) 2.0 3.7 5.1 6.3 7.7 8.7 

Whittier (6) 1.7 2.7 3.5 4.1 4.7 

Temperature difference between steam and entering air, (a) 150; 
(&) 215. 

* Between steam and entering air. 

Short Rules for Computing Radiating-Surfaces. — In the early days 
of steam-heating, when little was known about " British Thermal Units," 
it was customary to estimate the amount of radiating-surface by dividing 
the cubic contents of the room to be heated by a certain factor supposed 
to be derived from "experience." Two of these rules are as follows: 

One square foot of surface will heat from 40 to 100 cu. ft. of space to 
75° in — 10° latitudes. This range is intended to meet conditions of 
exposed or corner rooms of buildings, and those less so, as intermediate 
ones of a block. As a general rule, 1 sq. ft. of surface will heat 70 cu. ft. 
of air in outer or front rooms and 100 cu. ft. in inner rooms. In large 
stores in cities, with buildings on each side, 1 to 100 is ample. The 
following are approximate proportions: 

One square foot radiating-surface will heat : 

In Dwellings, In Hall, Stores, In Churches, 
Schoolrooms, Lofts, Factories, Large Audito- 
Offices, etc. etc. riums, etc. 

Bv direct radiation. ... 60 to 80 ft. 75 to 100 ft. 150 to 200 ft. 

By indirect radiation.. 40 to 50 ft. 50 to 70 ft. 100 to 140 ft. 

Isolated buildings exposed to prevailing north or west winds should 
have a generous addition made to the heating-surface on their exposed 
sides. 

1 sq. ft. of boiler-surface will supply from 7 to 10 sq. ft. of radiating- 
surface, depending upon the size of boiler and the efficiency of its surface, 
as well as that of the radiating-surface. Small boilers for house use 
should be much larger proportionately than large plants. Each horse- 
power of boiler will supply from 240 to 360 ft. of 1-in. steam-pipe, or 
80 to 120 sq. ft. of radiating-surface. Under ordinary conditions 1 
horse-power will heat, approximately, in — 

Brick dwellings, in blocks, as in cities 15,000 to 20,000 cu. ft. 

Brick stores, in blocks 10,000 " 15,000 

Brick dwellings, exposed all round 10,000 " 15,000 

Brick mills, shops, factories, etc 7,000 " 10,000 " 

Wooden dwellings, exposed 7,000 " 10,000 

Foundries and wooden shops 6,000 " 10,000 

Exhibition buildings, largely glass, etc 4,000 " 15,000 

Such "rules of thumb," as they are called, are generally supplanted by 
the modern "heat-unit" methods. 

Carrying Capacity of Pipes in Low-Pressure Steam Heating. (W. 

Kent, Trans. A. S, H. V. E., 1907,) — The following table is based on an 
assumed drop of 1 pound pressure per 1000 feet, not because that is 
the drop which should always be used — in fact the writer believes that 
In large installations a far greater drop is permissible — but because it 
gives a basis upon which the flow for any other drop may be calculated, 



670 



HEATING AND VENTILATION. 



merely by multiplying the figures in the tables by the square root of the 
assigned drop. The formula from which the tables are calculated is the 



well known one. 



i, W = c -v' 



w (pi — gg) d 5 



, in which W = weight of steam 



in lbs. per minute; w = weight of steam in pounds per cubic foot, at 
the entering pressure, j> x ; p^ the pressure at the end of the pipe; d the 
actual diameter of standard wrought-iron pipe in inches, and L the length 
in feet. The coefficients c are derived from Darcy's experiments on flow 
of water in pipes, and are believed to be as accurate as any that have 
been derived from the very few recorded experiments on steam. 



Nominal diam. of pipe. 

Value of c — 

Nominal diam. of pipe. 
Value of c — 



V?, 


3/ 4 


1 


U/4 


IV?, 


2 


21/?, 


3 


it 8 


42 


4i i 


48 


50 


V2 i 


54.8 


56.2 


4 


41/9 


5 


6 


7 


8 


9 


10 


57.8 


58.3 


58.7 


59.5 


60.2 


60.8 


61.3 


61.7 



31/2 

57.1 

12 

62.1 



Flow of Steam at Low Pressures in Pounds per Hour for a Uni- 
form Drop at the Rate of One Pound per 1000 Feet 
Length of Straight Pipe. 



Nominal 
Diam. 

of 
Pipe. 



Steam Pressures, by Gauge, at Entrance of Pipe. 



0.3 1.3 2.3 8.3 4.3 5.3 6.3 8.3 10.3 



Flow of Steam, Pounds per Hour. 



1/2 

1 3/4 
11/4 
11/2 
2... 
21/2 

31/2 
4... 
4l/ 2 

7... 
8... 
9... 
10.. 
12.. 



19 

40 

61 

120 

195 

345 

505 

701 

938 

1252 

2011 

2936 

4082 

5462 

7314 

11550 



2 


4.3 


4.4 


4.6 


4.7 


4.8 


4.9 


5.1 


7 


10.0 


10.3 


10.5 


10.8 


11.0 


11.3 


11.8 





19.6 


20.2 


20.7 


21.2 


21.7 


22.3 


23.2 


1 


41.3 


42.5 


43.7 


44.8 


45.9 


46.9 


49.0 


4 


63.2 


65.1 


66.8 


68.6 


70.3 


71.9 


75.0 


8 


124.5 


128.2 


131.6 


135.0 


138.3 


141.5 


147.7 


7 


201.8 


207.5 


213.2 


218.7 


224.0 


229.2 


239.2 


5 


356.1 


366.5 


376.4 


386.1 


395.5 


404.7 


422.4 


3 


520.8 


535.9 


550.5 


564.7 


578.5 


591.8 


618.0 


4 


723.0 


744.0 


764.4 


784.2 


803.4 


822.0 


857.4 


7 


967.6 


995.8 


1023. 


1049. 


1075. 


1100. 


1148. 




1291. 


1328. 


1364. 


1399. 


1433. 


1467. 


1531. 




2074. 


2134. 


2192. 


2248. 


2303. 


2356. 


2459. 




3027. 


3115. 


3199. 


3281. 


3362. 


3440. 


3590. 




4208. 


4331. 


4448. 


4564. 


4674. 


4783. 


4991. 




3630. 


5794. 


5951. 


6102. 


6252. 


6396. 


6678. 




7536. 


7758. 


7968. 


8172. 


8370. 


8562. 


8940. 




11916. 


12264. 


12594. 


12918. 


13236. 


13542. 


14136. 



5.3 
12.3 
24.2 
50.9 
78.0 
153.6 
248.8 
439.3 
642.6 
891.6 
1193. 
1592. 
2557. 
3733. 
5191. 
6942. 
9294. 
14700. 



For any other drop of pressure per 1000 feet length, multiply the fig- 
ures in the table by the square root of that drop. 

In all cases the judgment of the engineer must be used in the assump- 
tion of the drop to be allowed. For small distributing pipes it will gen- 
erally be desirable to assume a drop of not more than one pound per 
1000 feet to insure that each single radiator shall always have an ample 
supply for the worst conditions, and in that case the size of piping given 
in the table up to two inches may be used; but for main pipes supplying 
totals of more than 500 square feet, greater drops may be allowed. 



STEAM-HEATING. 



671 



Proportioning Pipes to Radiating Surface. 

Figures Used in Calculation of Radiating Surface. 

P = Pressure by gauge, lbs. per sq. in. 
0. 0.3 1.3 2.3 3.3 4.3 5.3 6.3 8.3 10.3 

L = latent heat of evaporation, B.T.U. per lb.* 
965.7 965.0 962.6 960.4 958.3 956.3 954.4 952.6 949.1 945.8 

Temperature Fahrenheit, 1\. 
212. 213. 216.3 219.4 222.4 225.2 227.9 230.5 235.4 240.0 
Ti= Ti— 70°, difference of temperature. 
146.3 149.4 152.4 155.2 157.9 160.5 165.4 170.0 



142. 

Hi = 



143. 
Tt X l.i 



heat transmission per sq. ft. radiating surface, B.T.U. 
per hour. 
255.6 257.4 263.3 268.9 274.3 279.2 284.2 288.9 297.7 306.0 

#1-*- L = steam condensed per sq. ft. radiating surface, lbs. per hour. 
0.2647 0.267 0.274 0.280 0.286 0.292 0.298 0.303 0.314 0.324 

Reciprocal of above = radiating surface per lb. of steam condensed per 

hour. 
3.78 3.75 3.65 3.57 3.50 3.42 3.36 3.30 3.18 3.09 

The last three lines of figures are based on the empirical constant 1.8 
for the average British thermal units transmitted per square foot of radi- 
ating surface per hour per degree of difference of temperature. This 
figure is approximately correct for several forms of both cast-iron radia- 
tors and pipe coils, not over 30 inches high and not over two pipes in 
width. 



Radiating Surface Supplied by Different Sizes of Pipe. 

On basis of steam in pipe at 0.3 and 10.3 lbs. gauge pressure, tempera- 
ture of room 70°, heat transmitted per square foot radiating surface 257.4 
and 306 British thermal units per hour, and drop of pressure in pipe at 
the rate of 1 lb. per 1000 feet length; = pounds of steam per hour in the 
table on the preceding page, 1st column, X 3.75, and last column, X 3.09. 



Size of 
Pipe. 


Radiating 
Surface, 
Sq. Ft. 


Size of 
Pipe, 


Radiating 
Surface, 
Sq. Ft. 


Size of 
Pipe. 


Radiating 
Surface, 

Sq. Ft. 


In. 


0.3 1b. 


10.3 lb. 


In, 


0.3 1b. 


10.3 1b. 


In. 


0.3 1b. 


10.31b. 


V2 
3/4 

1 

H/4 

H/2 

2 


16 
36 
71 
150 
230 
453 


16 
38 
75 
157 
241 
475 


21/2 

3 

31/2 

4 

41/2 


734 
1,296 
1,895 
2,630 
3,520 
4,695 


769 
1,357 
1,986 
2,755 
3,686 
4,919 


6 
7 
8 
9 
10 
12 


7,541 
11,010 
15,307 
20,482 
27,427 
43,312 


7,901 
11,535 
16,040 
21,451 
28,718 
45,423 



For greater drops than 1 lb. per 1000 ft. length of pipe, multiply the 
figures by the square root of the drop. 

* The latest steam tables (1909) give somewhat higher figures, but the 
difference is unimportant here. 



672 



HEATING AND VENTILATION. 



Sizes of Steam Pipes in Heating Plants. — G. W. Stanton, in Heating 
and Ventilating Mag., April, 1908, gives tables for proportioning pipes to 
radiating surface, from which the following table is condensed: 



Sup- 
ply 


Radiating Surface Sq 


.Ft. 


Returns. 


Drips. 


Connections. 


Pipe. 
Ins. 


A 


B 


C 


D 


B 


dD 


A 


BidD 


Ai 


AaBA 


B 2 C 2 


1 

11/4 

H/2 

2 

21/2 


24 

60 

125 

250 

600 

800 

1,000 

1,600 

1,900 

2,300 

4,100 

6,500 

9,600 

13,600 


60 

100 

200 

400 

700 

1,000 

1,600 

2,300 

3,200 

4,100 

6,500 

9,600 

13,600 


36 

72 

120 

280 

528 

900 

1,320 

1,920 

2,760 

3,720 

6,000 

9,000 

12,800 

17,800 

23,200 

37,000 

54,000 

76,000 


60 

120 

240 

480 

880 

1,500 

2,200 

3,200 

4,600 

6,200 

10,000 

15,000 

21,600 

30,000 

39,000 

62,000 

92,000 

130,000 


1 
1 

11/4 
H/2 

2 
2 

21/2 

21/2 

21/2 

3 

3 

31/2 

4 


1 
1 

11/4 

U/2 

2 

21/2 

21/2 

3 

3 

31/2 

31/2 

4 

4 

41/2 

5 

6 

7 

8 


3/4 

3/4 
1 

11/4 
H/4 
U/2 
1 L/2 
U/2 


3/4 

, 3/4 

1 

11/4 

11/4 

11/4 

11/4 


H/4 
H/2 

2 

21/2 

3 

31/2 

4 

41/2 


1 

U/4 
U/2 
2 


1 
1 

11/4 
U/2 


3 






31/2 






4 






41/2 






6 
7 
8 
9 
10 


Supply mains and risers 
are of the same size. 
Riser connections on 
the two-pipe system to 
be the same size as the 
riser. 


12 






14 






16 























5 lb. pressure. Ai, 



300 400 500 


600 


700 


800 


900 


1000 


. 58 0.5 . 45 


0.41 


0.38 


0.35 


0.33 


0.32 



A. For single-pipe steam-heating system 
riser connections. Ai, radiator connections. 

B. Two-pipe system to 5 lb. pressure; Bi, Ci, radiator connections, 
supply; Bi, Ci, radiator connections, return. 

C. D. Two-pipe system 2 and 5 lbs. respectively, mains and risers not 
over 100 ft. length. For other lengths, multiply the given radiating 
surface by factors, as below: 

Length, ft.... 200 
Factor 0.71 

Mr. Stanton says: Theoretically both supply and return mains could 
be much smaller, but in practice it has been found that while smaller 
pipes can be used if a job is properly and carefully figured and propor- 
tioned and installed, for work as ordinarily installed it is far safer to use 
the sizes that have been tried and proven. By using the sizes given a 
job will circulate throughout with 1 lb. steam pressure at the boiler. 

Resistance of Fittings. — Where the pipe supplying the radiation con- 
tains a large number of fittings, or other conditions make such a refine- 
ment necessary, it is advisable to add to the actual distance of the radia- 
tion from the source of supply a distance equivalent to the resistance 
offered by the fittings, and by the entrance to the radiator, the value of 
which, expressed in feet of pipe of the same diameter as the fitting, will 
be found in the accompanying table. Power, Dec, 1907. 

Feet op Pipe to be Added for Each Fitting. 



Size Pipe. 


1 


U/4 


U/2 


2 


21/2 


3 


31/2 


4 


41/2 


5 


6 


7 


8 


9 


10 


Elbows... 


3 


4 


5 


7 


8 


10 


12 


13 


15 


17 


20 


23 


27 


30 


33 


Globe V.. 


7 


8 


10 


13 


17 


20 


23 


27 


30 


33 


40 


47 


53 


60 


67 


Entrance 


5 


6 


8 


10 


12 


15 


18 


20 


23 


25 


30 


35 


40 


45 


50 



STEAM-HEATING. 673 

Overhead Steam-pipes. (A. R. Wolff, Stevens Indicator, 1887.) — 
When the overhead system of steam-heating is employed, in which sys- 
tem direct radiating-pipes, usually 1 1/4 in. in diam., are placed in rows 
overhead, suspended upon horizontal racks, the pipes running horizon- 
tally, and side by side, around the whole interior of the building, from 2 
to 3 ft. from the walls, and from 2 to 4 ft. from the ceiling, the amount 
of li/4-in. pipe required, according to Mr. C. J. H. Woodbury, for heating 
mills (for which use this system is deservedly much in vogue), is about 
1 ft. in length for every 90 cu. ft. of space. Of course a great range of 
difference exists, due to the special character of the operating machinery 
in the mill, both in respect to the amount of air circulated by the ma- 
chinery, and also the aid to warming the room by the friction of the 
journals. 

Removal of Air from Radiators. Vacuum Systems. — In order 
that a steam radiator may work at its highest capacity it is necessary 
that it be neither water-bound nor air-bound. Proper drainage must 
therefore be provided, and also means for continuously, or frequently, 
removing air from the system, such as automatic air- valves on each 
radiator, an air-pump or an air-ejector on a chamber or receiver into 
which the returns are carried, or separate air-pipes connecting each 
radiator with a vacuum chamber. When a vacuum- system is used, 
especially with a high vacuum, much lower temperatures than usual may 
be used in the radiators, which is an advantage in moderate weather. 

Steam-consumption in Car-heating. 

C, M. & St. Paul Railway Tests. (Engineering, June 27, 1890, p. 764.) 

Outside Temperature. Inside Temperature. ^IfcL^Uonr! 011 

40 70 70 lbs. 

30 70 85 

10 70 100 

Heating a Greenhouse by Steam. — Wm. J. Baldwin answers a 
question in the American Machinist as below: With five pounds steam- 
pressure, how many square feet or inches of heating-surface is necessary 
to heat 100 square feet of glass on the roof, ends, and sides of a green- 
house in order to maintain a night heat of 55° to 65°, while the thermom- 
eter outside ranges at from 15° to 20° below zero; also, what boiler- 
surface is necessary? Which is the best for the purpose to use — 2" pipe 
or 1 1/4" pipe? 

Ans. — Reliable authorities agree that 1.25 to 1.50 cubic feet of air in 
an enclosed space will be cooled per minute per sq. ft. of glass as many 
degrees as the internal temperature of the house exceeds that of the air 
outside. Between + 65° and —20° there will be a difference of 85°, or, 
say, one cubic foot of air cooled 127.5° F. for each sq. ft. of glass for the 
most extreme condition mentioned. Multiply this by the number of 
square feet of glass and by 60, and we have the number of cubic feet of 
air cooled 1° per hour within the building or house. Divide the number 
thus found by 48, and it gives the units of heat required, approximately. 
Divide again by 953, and it will give the number of pounds of steam that 
must be condensed from a pressure and temperature of five pounds 
above atmosphere to water at the same temperature in an hour to main- 
tain the heat. Each square foot of surface of pipe will condense from 
1/4 to nearly 1/2 lb. of steam per hour, according as the coils are exposed 
or well or poorly arranged, for which an average of 1/3 lb. may be taken. 
According to this, it will require 3 sq. ft. of pipe surface per lb. of steam 
to be condensed. Proportion the heating-surface of the boiler to have 
about one fifth the actual radiating-surface, if you wish to keep steam 
over night, and proportion the grate to burn not more than six pounds 
of coal per sq. ft. of grate per hour. With very slow combustion, such 
as takes place in base-burning boilers, the grate might be proportioned 
for four to five pounds of coal per hour. It is cheaper to make coils of 
H/4" pipe than of 2", and there is nothing to be gained by using 2" pipe 
unless the coils are very long. The pipes in a greenhouse should be 
under or in front of the benches, with every chance for a good circulation 



674 HEATING AND VENTILATION. 



of air. "Header" coils are better than "return-bend" coils for this 
purpose. 

Mr. Baldwin's rule may be given the following form: Let H = heat- 
units transferred per hour, T = temperature inside the greenhouse, t == 
temperature outside, S = sq. ft. of glass surface; then H — 1.5 S (T — t) 
X 60 + 48 = 1.875 S (T - t). Mr. Wolff's coefficient K for single sky- 
lights gives H = 1.03 S (T - t), and for single windows, 1.20 S (T - t). 

Heating a Greenhouse by Hot Water. — W. M. Mackay, of the 
Richardson & Boynton Co., in a lecture before the Master Plumbers' 
Association, N. Y., 1889, says: I find that while greenhouses were for- 
merly heated by 4-inch and 3-inch cast-iron pipe, on account of the large 
body of water which they contained, and the supposition that they gave 
better satisfaction and a more even temperature, florists of long experi- 
ence who have tried 4 inch and 3-inch cast-iron pipe, and also 2-inch 
wrought-iron pipe for a number of years in heating their greenhouses 
by hot water, and who have also tried steam-heat, tell me that they get 
better satisfaction, greater economy, and are able to maintain a more 
even temperature with 2-inch wrought-iron pipe and hot water than by 
any other system they have used. They attribute this result principally 
to the fact that this size pipe contains less water and on this account the 
heat can be raised and lowered quicker than by any other arrangement 
of pipes, and a more uniform temperature maintained than by steam or 
any other system. 

HOT-WATER HEATING. 

The following notes are from the catalogue of the Nason Mfg. Co.: 

There are two distinct forms or modifications of hot-water apparatus, 
depending upon the temperature of the water. 

In the first or open-tank system the water is never above 212° tempera- 
ture, and rarely above 200°. This method always gives satisfaction 
where the surface is sufficiently liberal, but in making it so its cost is 
considerably greater than that for a steam-heating apparatus. 

In the second method, sometimes called (erroneously) high-pressure 
hot-water heating, or the closed-system apparatus, the tank is closed. 
If it is provided with a safety-valve set at 10 lbs. it is practically as safe 
as the open-tank system. 

Law of Velocity of Flow. — The motive power of the circulation in a 
hot-water apparatus is the difference between the specific gravities of 
the water in the ascending and the descending pipes. This effective 
pressure is very small, and is equal to about one grain for each foot in 
height for each degree difference between the pipes; thus, with a height 
of 12 in "up" pipe, and a difference between the temperatures of the 
up and down pipes of 8°, the difference in their specific gravities is equal 
to 8.16 grains (0.001166 lb.) on each square inch of the section of return- 
pipe, and the velocity of the circulation is proportioned to these differ- 
ences in temperature and height. 

Main flow-pipes from the heater, from which branches may be taken, 
are to be preferred to the practice of taking off nearly as many pipes from 
the heater as there are radiators to supply. 

It is not necessary that the main flow and return pipes should equal in 
capacity that of all their branches. The hottest water will seek the 
highest level, while gravity will cause an even distribution of the heated 
water if the surface is properly proportioned. 

It is good practice to reduce the size of the vertical mains as they ascend, 
say at the rate of one size for each floor. 

As with steam, so with hot water, the pipes must be unconfined to allow 
for expansion of the pipes consequent on having their temperatures in- 
creased. 

An expansion tank is required to keep the apparatus filled with water, 
which latter expands 1/24 of its bulk on being heated from 40° to 212°, 
and the cistern must have capacity to hold certainly this increased bulk. 
It is recommended that the supply cistern be placed on level with or 
above the highest pipes of the apparatus, in order to receive the air which 
collects in the mains and radiators, and capable of holding at least 1/20 of 
the water in the entire apparatus. 

Arrangement of Mains for Hot-water Heating. (W. M. Mackay, 
Lecture before Master Plumbers' Assoc, N. Y., 1889). — There are two 
different systems of mains in general use, either of which, if properly 



HOT-WATER HEATING. 675 

placed, will give good satisfaction. One is the taking of a single large- 
flow main from the heater to supply all the radiators on the several floors, 
with a corresponding return main of the same size. The other is the tak- 
ing of a number of 2-inch wrought-iron mains from the heater, with the 
same number of return mains of the same size, branching off to the several 
radiators or coils with 1 1/4-inch or 1-inch pipe, according to the size of 
the radiator or coil. A 2-inch main will supply three 1 1/4-inch or four 
1-inch branches, and these branches should be taken from the top of the 
horizontal main with a nipple and elbow, except in special cases where it 
it is found necessary to retard the flow of water to the near radiator, for 
the purpose of assisting the circulation in the far radiator; in this case 
the branch is taken from the side of the horizontal main. The flow and 
return mains are usually run side by side, suspended from the basement 
ceiling, and should have a gradual ascent from the heater to the radiators 
of at least 1 inch in 10 feet. It is customary, and an advantage where 
2-inch mains are used, to reduce the size of the main at every point where 
a branch is taken off. 

The single or large main system is best adapted for large buildings; but 
there is a limit as to size of main which it is not wise to go beyond — 
generally 6-inch, except in special cases. 

The proper area of cold-air pipe necessary for 100 square feet of indi- 
rect radiation in hot-water heating is 75 square inches, while the hot-air 
pipe should have at least 100 square inches of area. There should be a 
damper in the cold-air pipe for the purpose of controlling the amount of 
air admitted to the radiator, depending on the severity of the weather. 

Sizes of Pipe for Hot-water Heating. — A theoretical calculation of 
the required size of pipe in hot-water heating may be made in the follow- 
ing manner. Having given the amount of heat, in B.T.U. to be emitted 
by a radiator per minute, assume the temperatures of the water entering 
and leaving, say 160° and 140°. Dividing the B.T.U. by the difference 
in temperatures gives the number of pounds of water to be circulated, 
and this divided by the weight of water per cubic foot gives the number 
of cubic feet per minute. The motive force to move -this water, per 
square inch of the area of the riser, is the difference in weight per cu. ft. 
of water at the two temperatures, divided by 144, and multiplied by H, 
the height of the riser, or for Ti = 160 and T2 = 140, (61.37 - 60.98) 
f- 144 = 0.00271 lb. per sq. in. for each foot of the riser. Dividing 144 
by 61.37 gives 2.34, the ft. head of water corresponding to 1 lb. per sq. 
in., and 0.00271 X 2.34 = 0.0066 ft. head, or if the riser is 20 ft. high, 
20 X 0.0066 = 0.132 ft. head, which is the motive force to move the water 
over the whole length of the circuit, overcoming the friction of the riser, 
the return pipe, the radiator and its connections. If the circuit has a 
resistance equal to that of a 50-ft. pipe, then 50 -f- 0.132 = 380 is the 
ratio of length of pipe to the head, which ratio is to be taken with the 
number of cubic feet to be circulated, and by means of formulae for flow 
of water, such as Darcy's, or hydraulic tables, the diameter of pipe re- 
quired to convey the given quantity of water with this ratio of length of 
pipe to head is found. Tins tedious calculation is made more complicated 
by the fact that estimates have to be made of the frictional resistance of 
the radiator and its connections, elbows, valves, etc., so that in practice 
it is almost never used, and "rules of thumb" and tables derived from 
experience are used instead. 

On this subject a committee of the Am. Soc. Heating and Ventilating 
Engineers reported in 1909 as follows: 

The amount of water of a certain temperature required per hour by 
radiation may be determined by the following formula: 

20 X^o/x 60 = CU - ft - ° f WateF Per minUte - 

R = square feet of radiation; X = B.T.U. given off per hour by 1 sq. 
ft. of radiation (150 for direct and 230 for indirect) with water at 170°. 
Twenty is the drop in temperature in degrees between the water entering 
the radiation and that leaving it; 60.8 is the weight of a cubic foot of 
water at 170 degrees; 60 is to reduce the result from hours to minutes. 

The average sizes of mains, as used by seven prominent engineers in 
regular practice for 1800 square feet of radiation, are given below: 



676 



HEATING AND VENTILATION. 



2-pipe open-tank system, 100 ft. mains, 5-in. pipe = 26.6 ft. per min. 

1-pipe open-tank system, 100 ft. mains, 6-in. pipe = 18.4 ft. per min. 

Overhead open-tank system, 100 ft. mains, 4-in. pipe = 41.8 ft. per min. 

Overhead open-tank system, 100 ft. mains, 3-in. pipe = 72.1 ft. per 
min. 

For 1200 sq. ft. indirect radiation with separate main, 100 ft. long, 
direct from boiler, open system, the bottom of the radiator being 1 ft. 
above the top of the boiler — 5-in. pipe = 22.4 ft. per min. 

Capacity of Mains 100 ft. Long. 
Expressed in the number of square feet of hot-water radiating sur- 
face they will supply, the radiators being placed in rooms at 70° F., and 
20° drop assumed. 



Diameter of 
Pipes, Ins. 


Two-Pipe 

up Feed 

Open Tank. 


One-Pipe 

up Feed 

Open Tank. 


Overhead 
Open 
Tank. 


Overhead 
Closed 
Tank. 


Two-Pipe 
Open 
Tank. 


11/ 4 


75 

107 

200 

314 

540 

780 

1,060 

1,860 

2,960 

4,280 

5 ; 850 


45 

65 

121 

190 

328 

474 

645 

1,130 

1,800 

2,700 

3,500 


127 

181 

339 

533 

916 

1,334 

1,800 

3,150 

5,000 

7,200 

9,900 


250 
335 

667 
1,060 
1,800 
2,600 
3,350 
6,200 
9,800 
13,900 
19,500 


48 


11/2... 


69 


2 


129 


21/2 


202 


3. 


348 


31/2 


502 


4 . . 


684 


5 


1,200 


6 


1,910 


7 


2,760 


8 


3,778 







The figures are for direct radiation except the last column which is for 
indirect, 12 in. above boiler. 

Capacity of Risebs. 

Expressed in the number of sq. ft. of direct hot-water radiating sur- 
face they will supply, the radiators being placed in rooms at 70° F., and 
20° drop"assumed. The figures in the last column are for the closed-tank 
overhead system the others are for the open-tank system. 



Diameter 
of Riser. 
Inches. 


1st Floor. 


2d Floor. 


3d Floor. 


4th Floor. 


Drop 

Risers, not 

exceeding 

4 floors. 


1 


33 
71 
100 
187 
292 
500 


46 
104 
140 
262 
410 
755 


57 
124 
175 
325 
492 
875 


64 
142 
200 
375 
580 
1,000 


48 


11/ 4 


112 


11/2 


160 


2 


300 


21/2 


471 


3 . . . . . 


810 







All horizontal branches from mains to risers or from risers to radiators, 
more than 10 ft. long (unless within 15 ft. of the boiler), should be in- 
creased one size over that indicated for risers in the above table. 

For indirect radiation, the amount of surface may be computed as 
follows: 

Temperature of the air entering the room, 110° = T. 

Average temperature of the air passing through the radiator, 55°. 

Temperature of the air leaving the room, 70° = t. 

Velocity of the air passing through the radiator, 240 ft. per min. 

Cubic feet of air to be conveyed per hour, = C = (H X 55) -5- (T — t). 

H = exposure loss in B.T.TJ. per hour. 

Heat necessary to raise this air to the entering temperature from 
0° F., T X C + 55 = H. 



HOT-WATER HEATING. 



677 



The amount of radiation is found by dividing the total heat by the 
emission of heat by indirect radiators per square foot per hour per degree 
difference in temperature. This varies with the velocity, as shown below: 
Velocity, ft. per min..: . 174 246 300 342 378 400 428 450 474 492 
B.T.U 1.70 2.00 2.22 2.38 2.52 2.60 2.67 2.72 2.76 2.80 

The difference between 170 degrees (average temperature of the water 
in the radiator) and 55 degrees (average temperature of the air in the 
radiator) being 115, the emission at 240 ft. per min. is 2. per degree differ- 
ence or 230 B.T.U. 

Ordinarily the amount of indirect radiation required is computed by 
adding a percentage to the amount of direct radiation [computed by the 
usual rules], and an addition of 50% has been found sufficient in many 
cases; but in buildings where a standard of ventilation is to be maintained, 
the formula mentioned seems more likely to give satisfactory results. 
Free area between the sections of radiation to allow passage of the re- 
quired volume of air at the assumed velocity must be maintained. The 
cold-air supply duct, on account of less frictional resistance, may ordi- 
narily have 80% of the area between the radiator sections. The hot-air 
flues may safely be proportioned for the following air velocities per min- 
ute: First floor, 200 feet; second floor, 300 feet; third floor, 400 feet. 

Pipe Sizes for Hot-water Heating. 
Based on 20° difference in temperature between flow and return water. 



(C. L. Hubbard, 


The Engineer July 1 


1902. 


) 










Diam. of 
Pipe. 


' 


11/4 


11/2 2 21/2 3 31/2 4 | 5 6 7 


Length of 
Run. 


Square Feet of Direct Radiating Surface. 


Feet. 
100 


30 


60 
50 


100 
75 
50 


200 
150 
125 
100 
75 


350 
250 
200 
175 
150 
125 


550 
400 
300 
275 
250 
225 
200 
175 
150 


850 
600 
450 
400 
350 
325 
300 
250 
225 


1,200 
850 
700 
600 
525 
475 
450 
400 
350 








200 


1,400 
1,150 
1,000 
700 
850 
775 
725 
650 






300 






400 






1,600 
1,400 
1,300 
1,200 
'1,150 
1,000 




500 










600 










700 










1,700 


800 












1,600 


1000 












1.500 


















Square Feet of Indirect Radiation. 


100 
200 


15 


30 

20 


50 
30 


100 
70 


200 1 300 
120 200 


400 
300 


600 
400 


1,000 
700 
















Square Feet of Direct Radiating Surface. 


1st story 
2d " 


30 
55 
65 
75 
85 
95 


60 
90 
110 
125 
140 
160 


100 
140 
165 
185 
210 
240 


200 
275 
375 
425 
500 


350 

275 


550 


850 


















3d 














4th " 
















5th " 
















6th " 


































The size of pipe required to supply any given amount of hot-water 
radiating surface depends upon (1) The square feet of radiation; (2) its 
elevation above the boiler; (3) the difference in temperature of the water 
in the supply and return pipes; (4) the length of the pipe connecting the 
radiator with the boiler. 

In estimating the length of a pipe the number of bends and valves must 
be taken into account. It is customary to consider an elbow as equivalent 
to a pipe 60 diameters in length, and a return bend to 120 diameters. A 
globe valve may be taken about the same as an elbow. 

A series of articles on The Determination of the Sizes of Pipe for Hot 
Water Heating, by F. E. Geisecke, is printed in Domestic Engineering, 
beginning in May, 1909. 



678 



HEATING AND VENTILATION. 



Sizes of Flow and Return Pipes Approximately Proportioned to 
Surface of Direct Radiators for Gravity Hot-Water Heating. 

(G. W. Stanton, Heat. & Ventg. Mag., April, 1908.) 



Size 
of 

Mains. 



11/4 

U/2 

2 

21/2 

3 

31/2 

4 

41/2 

6 

7 

8 

9 
10 
11 
12 



In Cellar 

or 

Basement. 



On One 

or More 
Floors. 
Average. 



Branches of Mains. 



First Second 
Floor Floor 
10'-15\ 15'-25'. 



Third 
Floor 
25'-35\ 



Fourth 
or Fifth 
Floor 
35'-45'. 



Square Feet of Radiating Surface. 



100 

135 

225 

320 

500 

650 

850 

1,050 

1,350 

2,900 

3,900 

5,000 

6,300 

7,900 

9,500 

11,400 



135 

220 

350 

460 

675 

850 

1,100 

1,350 

1,700 

3,600 

4,800 

6,200 

7,700 

9,800 

11,800 

14,000 



50 
110 
180 
290 
400 
620 
820 
1,050 
1,325 



40 


45 


75 


80 


120 


135 


195 


210 


320 


350 


490 


525 


650 


690 


870 


920 


1,120 


1,185 


1,400 


1,485 



50 
85 
150 
230 
370 
550 
730 
970 
1,250 
1,560 



Note. — The heights of the several 
floors are taken as: 
1st. 10 to 15 ft.; 2d. 15 to 25 ft. 
3d. 25 to 35 ft.; 4th. 35 to 45 ft. 



Heating by Hot Water, with Forced Circulation. —The principal 
defect of gravity hot-water systems, that the motive force is only the 
difference in weight of two columns of water of different temperatures, is 
overcome by giving the water a forced circulation, either by means of a 
pump or by a steam ejector. For large installations a pump gives facili- 
ties for forcing the hot water to any distance required. The design of 
such a system is chiefly a problem in hydraulics. After determining the 
quantity of heat to be given out by each radiator, a certain drop in 
temperature is assumed, and from that the volume of water required by 
each radiator is calculated. The piping system then has to be designed 
so that it will carry the proper supply of water to each radiator without 
short-circuiting, and with a minimum total cost for power to force the 
water, for loss by radiation, and for interest, etc., on cost of plant. No 
short rules or formulae have been established for designing a forced hot- 
water system, and each case has to be stud : ed as an original problem to 
be solved by application of the laws of heat transmission and hydraulics. 
Forced systems using steam ejectors have come into use to some extent 
in Europe in small installations, and some of them are described in the 
Transactions of the Amer. Soc'y of Heating and Ventilating Engineers. 

A system of distributing heat and power to customers by means of hot 
water pumped from a central station was adopted by the Boston Heating 
Co. in 1888. It was not commercially successful. A description of the 
plant is given by A. V. Abbott in Trans. A. I. M. E., 1888. 

THE BLOWER SYSTEM OF HEATING. 

The* system provides for the use of a fan or blower which takes its sup- 
ply of fresh air from the outside of the building to be heated, forces it 
over steam coils, located either centrally or divided up into a number of 
independent groups, and then into the several ducts or flues leading to the 
various rooms. The movement of the warmed air is positive, and the 
delivery of the air to the various points of supply is certain and entirely 
independent of atmospheric conditions. 

Advantages and Disadvantages of the Plenum System. (Prof. 
W. F. Barrett, Brit. Inst. H. & V. Engrs., 1905.)— Advantages: (1) The 



THE BLOWER SYSTEM OF HEATING. 



679 



evenness of temperature produced; (2) the ventilation of the building 
is concurrent with its warming; (3) the air can be drawn from sources 
free from contamination and can be filtered from suspended impurities, 
warmed and brought to the proper hygrometric state before its intro- 
duction to the different rooms or wards; (4) the degree of temperature 
and of ventilation can be easily controlled in any part of the building, 
and (5) the removal of ugly pipes running through the rooms has a great 
architectural and esthetic advantage. 

Disadvantages: (1) The most obvious is that no windows can be 
opened nor doors left open; double doors with an air lock between must 
also be provided if the doors are frequently opened and closed; (2) the 
mechanical arrangements are elaborate and the system requires to be 
used with intelligent care; (3) the whole elaborate system needs to be 
set going even if only one or two rooms in a large building require to 
be warmed, as often happens in the winter vacation of a college; (4) the 
temporary failure of the system, through the breakdown of the engines 
or other cause, throws the whole system into confusion, and if, as in the 
Royal Victoria Hospital, the windows are not made to open, imminent 
danger results; (5) then, also, in the case of hospital wards and asylums 
it is possible that the outlet ducts may become coated with disease germs, 
and unless periodically cleansed, a back current through a high wind or 
temporary failure of the system may bring a cloud of these disease germs 
back into the wards. 

Heat Radiated from Coils in the Blower System. — The committee 
on Fan-blast Heating, of the A. S. H. V. E., in 1909, gives the following 
formula for amount of heat radiated from hot-blast coils with different 
velocities of air passing through the heater: £' = B.T.U. per sq. ft. of sur- 
face per hour per degree of difference bet wee n the average temperature of 
the air and the steam temperature, = ^4 V, in which V= velocity of the 
air through the free area of the coil in feet per second. A plotted curve 
of 20 tests of different heaters shows that the formula represents the aver- 
age results, but individual tests show a wide variation from the average, 
thus: For velocity 1000 ft. per min., average 9 B.T.U., range 7.5 to 11; 
1600 ft. per min., average 10.4, range 9.5 to 12. 

The committee also gives the following formula for the rise in tem- 
perature of each two-row section of a coil: 

(T s -T a )XHX E 
R = A X V m X W X 60 X 0.2377 ' 

F. rise for each two-row section; T s = tem- 
T a = temperature of air; H = square feet of sur- 
face in two-row sect ion; E = B.T.U. per degree difference between air 
and steam; E = V^ V s , in which V s = air velocity in ft. per sec; 
A = area through heater in sq. ft.; V m — velocity of air in ft. per min.; 
W = weight of 1 cu. ft. of air, lbs. 

The value of R is computed for each two-row section in a coil, and the 
results added. From a set of curves plotted from the formula the follow- 
ing figures are taken. 



In which R == 
perature of steam 











Number of Rows. 




< 


8 | 12 | 16 | 20 | 24 


28 




Temperature Rise, Degrees. 


Steam, 


80 lbs. 


V^ = 


1,200 


43 


83 


115 


144 


167 


189 


209 


Steam, 


80 lbs. 


V n = 


1,800 


36 


68 


96 


122 


145 


165 


182 


Steam, 


5 lbs. 


V m = 


1,200 


31 


53 


80 


100 


118 


133 


146 


Steam, 


5 lbs. 


Vm = 


1,800 


25 


48 


68 


86 


101 


115 


128 



A formula for the rise in temperature of air in passing through the 
coils of a hot-blast heater is given by E. F. Child in The Metal Worker, 

Oct. 5, 1907, as. -follows; R^ KDZ m N * ^V, in which #=rise in 



680 



HEATING AND VENTILATION. 



temperature of the air; K = a constant depending on the kind of heat- 
ing surface; D = an average of the summation of temperature differ- 
ences between the air and the steam = (Ti—T ) ■*■ log e [(T s — To) ■*> 
(T s — Ti)]; Z = number of sq. ft. of heating surface per sq. ft. of clear 
area per unit depth of heater, m = a power applicable to Z and depend- 
ing on the type of heating surface; N = number of units in depth of 
heater; V = velocity of the air at 70° F. in ft. per min. through the clear 
area; n = a root applicable to V and depending on experiment. 

For practical purposes and within the range of present knowledge on 
the subject the formula may be written R = 0.85 DZN -*■ %jv, and from 
this formula with T s = 227° and T = 0°, with different values of Ti, the 
temperature of the air leaving the- coils, a set of curves is plotted, from 
which the figures in the following table are taken. 





Sq. ft. of heating surface -=- sq. ft. free area through heater. 


Velocity, 
Ft. per Min. 


20 


30 1 40 50 | 60 I 70 1 80 I 90 1 100 1 120 




Rise in Temperature, Degrees F. 


500.. 


43 
38 
36 
34 
29 


63 
55 
52 
49 
42 


79 
70 
66 
63 
55 


95 

84 
79 
75 
66 


108 
97 
92 
87 
76 


120 
108 
102 
98 

86 


131 
118 
112 
108 
95 


141 
128 
121 
117 
104 


151 
138 
130 
125 
112 


170 


800 


157 


1000 


147 


1200 


140 


2000 


127 







Burt S. Harrison (Htg. and Ventg. Mag., Oct. and Nov., 1907) gives the 
following formula, R=- Tr= .(T-t) Ar , in which !F = temp. of steam 

\l Y Pi " ' U.^4 

in coils, £ = temp. of air entering coils, V = velocity of air through coils in 
ft. per sec, N= no. of rows of 1-in. pipe in depth of heater. Charts are 
given by means of which heaters may be designed for any set of con- 
ditions. 

Tests of Cast-iron Heaters for Hot-blast Work. — An extensive 
series of tests of the Amer. Radiator Co's, "Vento" cast-iron heater is 
described by Theo. Weinshank in Trans. A. S. H. V. E., 1908. The tests 
were made under the supervision of Prof. J. H. Kinealy. The principal 
results are given below. 

Tests of a" Vento " Cast- Iron Heater. 



Velocity, 
ft. per Min. 



1600 
1500 
1400 
1300 
1200 
1100 
1000 
900 



Number of sections heater is Number of sections heater ia 



Rise of temperature, K, per de- 
gree difference between tem- 
perature of steam and mean 
temperature of air for differ- 
ent velocities of air. 



0.124 
0.132 
0.139 
0.147 
0.154 
0.162 
0.170 
0.177 
0.185 



0.253 
0.261 
0.268 
0.276 
0.283 
0.291 
0.299 
0.306 
0.314 



0.761 
0.769 
0.776 
0.784 
0.791 
0.799 
0.807 
0.814 
0.822 



1 



3 



5 



Heat units transmitted per 
square foot of heating surface 
per hour per degree difference 
between the temperature of 
the steam and the mean tem- 
perature of the air. 



11.94 
11.91 
11.70 
11.50 
11.11 
10.72 
10.23 
9.59 
8.90 



12.17 
11.76 
11.28 
10.79 
10.21 
9.63 
8.99 
8.28 
7.56 



12.67 
12.11 
11.50 
10.89 
10.22 
9.55 
8.84 
8.08 
7.31 



12.67 
12.06 
11.41 
10.75 
10.05 
9.34 
8.61 
7.85 
7.08 



12.50 
11.86 
11.18 
10.51 
9.81 
9.09 
8.36 
7.60 
6.48 



12.20 
11.56 
10.89 
10.22 
9.52 
8.82 
8.10 
7.35 
6.60 



THE BLOWER SYSTEM OF HEATING. 



681 



Tests of a "Vento" Cast-iron Heater. — Continued. 



Velocity, 
ft. per min 



Final 


temperature, 


T, of 


air 


when entering heater at 0° F. 


Temperature of steam in 


heater, 227°. 


26.5 


51.0 


74.9 


94.7 


111.3 


125.2 


28.1 


52.4 


76.3 


95.8 


112.4 


126.0 


29 5 


53 8 


77 2 


96 7 


113 3 


126 8 


31 1 


55 


77 6 


97 9 


114 3 


127 7 


32 4 


56 4 


79 6 


99 


115 3 


128,7 


34 


57 7 


80 5 


100 


116 2 


129.6 


35 6 


59,1 


82 


100 1 


117 2 


130 5 


36.9 


60.1 


83 


102 1 


118 


131 3 


38.5 


61.6 


84.3 


103.1 


119.0 


132.3 



Friction loss in inches of water 
due to the sections. 



1600. 
1500 
1400 
1300 
1200 
1100 
1000 
900 



236 


288 


416 


543 


0.672 


207 


253 


366 


477 


0.590 


180 


220 


318 


415 


0.514 


156 


190 


274 


358 


0.443 


133 


162 


234 


306 


0.378 


111 


136 


197 


257 


0.318 


092 


112 


162 


212 


0.262 


074 


091 


132 


172 


0.212 


0.059 


0.072 


0.104 


0.136 


0.167 



0.800 
0.703 
0.613 
0.528 
0.450 
0.378 
0.312 
0.253 
0.200 



Formulae. — s = no. of sections; V = velocity, ft. per min., air measured 
at 70°; k = rise of temp, per degree difference; t = final temperature. 
/ = friction loss in in. of water, t = 454 k + (2 + k). k = s (0.167 - 

0.005 s) - 0.061 ( "gQQ 00 ) - /=(0.8 s+ 0.2) (F/4000) 2 . Values of k and 
/ when s = 2 or more. 



Factory Heating by the Fan System. 

In factories where the space provided per operative is large, warm air 
is recirculated, sufficient air for ventilation being provided by leakage 
through the walls and windows. The air is commonly heated by steam 
coils furnished with exhaust steam from the factory engine. When the 
engine is not running, or when it does not supply enough exhaust steam 
for the purpose, steam from the boilers is admitted to the coils through 
a reducing valve. The following proportions are commonly used in de- 
signing. Coils, pipes 1-in., set 2i/s in. centers; free area through coils, 
40% of cross area. Velocity of air through free area, 1200 to 1800 ft. 
per min. ; number of coils in series 8 to 20 ; circumferential speed of fan, 
4000 to 6000 ft. per min.; temperature of air leaving coils, 120° to 160° 
F.; velocity of air at outlet of coil stack, 3000 to 4000 ft. per min.; veloc- 
ity in branch pipes, 2000 to 2800 ft., the lower velocities in the longest 
pipes. 

In factories in which mechanical ventilation as well as heating is re- 
quired, outlet flues at proper points must be provided, to avoid the neces- 
sity of opening windows, and the outflow of air in them may be assisted 
either by exhaust fans or by steam coils in the flues. 



Cooling Air for Ventilation. 

The chief difficulty in the artificial cooling of air is due to the moisture 
it contains, and the great quantity of heat that has to be absorbed or 
abstracted from the air in order to condense this moisture. The cooled 
and moisture-laden air also needs to be partially reheated in order to 
bring it to a degree of relative humidity that will make it suitable for ven- 
tilation. To cool 1 lb. of dry air from 82° to 72° requires the abstracting 
of 10 X 0.2375 B.T.U. (0.2375 being the specific heat at constant pres- 
sure). If the air at 82° is saturated, or 100% relative humidity, it 
contains 0.0235 lb. of water vapor, while 1 lb. at 72° contains 0.0167 lb., 
so that 0.0068 lb. will be condensed in cooling from vapor at 82° to 
water at 72°. The total heat (above 32°) in 1 lb. vapor at 82° is 1095.6 
B.T.U. and that in 1 lb. of water at 72° is 40 B.T.U. The difference, 
1055.6 X 0.0068 = 7.178 B.T.U., is the amount of heat abstracted in 
condensing the moisture. The B.T.U. in 1 lb. vapor at 72° is 1091.2, 



682 



HEATING AND VENTILATION. 



and the B.T.U. abstracted in cooling the remaining vapor from 82° to 
72° is 0.0167 X (1095.6 - 1091.2) = 0.073 B.T.U. The sum, 7.251 
B.T.U. , is more than three times that required to cool the dry air from 
82° to 72°. Expressing these principles in formulae we have: 

Let T\ = original and Ti the final temperature of the air, 
a = vapor in 1 lb. saturated air at T\; b = do. at T2, 
H = relative humidity of the air at fi; ft = desired do. at T2, 
U = total heat, in B.T.U., in 1 lb. vapor at T\; u = do. at Ti, 
w = total heat in water at T2. 



Then total heat abstracted in cooling air from T\ to 7 7 2 = (aH — bh) X 
(17 - w) + bh (U - u) + 0.2375 (Ti - 7 T 2 ), or aHU - bhu - (aH - 
bh) w + 0.2375 (Ti - Ti), or aH (U - w) - bh (u - w) + 0.2375 (Ti - 
T2). 

Example. — Required the amount of heat to be abstracted per hour 
in cooling the air for an audience chamber containing 1000 persons, 
1500 cu. ft. (measured at 70° F.), being supplied per person per hour, 
the temperature of the air before cooling being 82°, with relative humid- 
ity 80%, and after cooling 72°, with humidity 70%. 



1000 X 1500 = 



1,500,000 cu. 
112,500 lbs. 



ft., at 0.075 lb. per cu. ft. 



For 1 lb. aH (U - w) - bh ( u - w) + 0.2375 (Ti - T2). 

0.0235 X 0.8 X (1095.6 - 40) - 0.0167 X 0.7 X (1091.2 - 40) 
+ 2.375 = 9.932 B.T.U. 
112,500 X 9.932 = 1.061,100 B.T.U. 

Taking 142 B.T.U. as the latent heat of melting ice, this amount is 
equivalent to the heat that would melt 7472 lbs. of ice per hour. 

See also paper by W. W. Macon, Trans. A. S. H. V. E., 1909, and Air- 
cooling of the New York Stock Exchange, Eng. Rec, April, 1905, and The 
Metal Worker, Aug. 5, 1905. 

Capacities of Fans or Blowers for Hot-Blast or Plenum Heating. 

(Computed by F. R. Still, American Blower Co., Detroit, Mich.) 



PQ.S 
"I 
w. 



<D 


ti. 
9, 





% <D 


ef 


<u 


^ 


Q3 

u ti-ti 


ti 


ti 

.2 

*0 03 


ti a 

0*03 

W <D 


Ft. of Ai 
ed per Mi 
an throug 
eater. 




fcti 


^Q 


3^W 


P 

42 


« 


W 





360 


21/9 


6,900 


48 


320 


3 


8,500 


54 


280 


4 


10,500 


60 


250 


5 


12,500 


66 


230 


6 


15,800 


72 


210 


8 


19,800 


84 


180 


10 


26,200 


96 


160 


12 


33,000 


108 


140 


15 


41,600 


120 


125 


18 


50,000 



415,200 

510,000 

630,000 

750,000 

948,000 

1,118,000 

1,572,000 

1,980,000 

2,496,000 

3,000,000 



V- 


£ 


a 





« 


1(35 


ti 


<D 


*$ 
$& 


tf °0 


<3% 


^ 


Oj> 


IjN 


2 C 


."S . ti 


PK£ 


&jfs 


< gj 


ti 0*0 
0m# 






oj ft 




§ ft<1 


-2-^ 8 
-3^ ft 


gS 


c3 03 01 

a; aft 


w 


> 


h 


W 


1,021,000 


900 


7.7 


1760 


1,255,000 






9.45 






1,550,000 






11.66 






1,845,000 






13.9 






2,335,000 






17.55 






2,900,000 






22. 






3,870,000 






29.1 






4,870,000 






36.7 






6,130,000 






46.3 






7,375,000 






55.5 










580 
714 
880 
1050 
1325 
1650 
2200 
2770 
3490 
4140 



PERFORMANCE OF HEATING GUARANTEE. 



683 



Capacities of Fans or Blowers for Hot-blast or Plenum Heating — 

Continued. 







1 


~£ 


T3 


T3 O) 




+= ® 


T3 — 


£.3 


fe « (3 

o - n o 
= faO 


M 

a 

o 

1 

o 

3 


i 
a 
O 

o>'3 

fa 03 


73 

a 

o 

°o' 

32 


'3 
& 

V 

1 

a 

<B 
02 


'3 

a 1 


'3 3 

W OQ 
>> • . 

So — 
O^ || 

t2 • o 


■-Soq 
o> — 

6® 


oj § 
^ ■ = i 

fa • • 

■o'c 


go . 

*©"3 

-■IS 


"Hi 

g> 
°fa 
°§ . 
^,2 s 


£ «fa 
IJi 

S'33 3 
^ fl.2 ^ 

© 03 -^"CS 


w 


J 


fa 


OS 


s 


ffl 


m 


m 


!> 


«l 


£ 


70 


1,740 


1055 


31/2 


2 


35 


525 


15 


8,700 


9.67 


8,200 


80 


2,142 


1295 


4 


2 


43 


645 


18 


10,700 


13.05 


10,000 


90 


2,640 


1600 


41/2 


21/2 


53 


795 


23 


13,200 


14.72 


12,500 


100 


3,150 


1900 


5 


21/2 


63 


945 


27 


15,800 


17.55 


15,000 


110 


3,975 


2410 


51/2 


3 


80 


1200 


34 


19,900 


22.20 


18,900 


120 


4,950 


2990 


6 


3 


100 


1500 


43 


25,000 


27.80 


23,800 


140 


6,600 


3990 


7 


31/2 


133 


1995 


57 


33,100 


36.80 


31,400 


160 


8,310 


5025 


8 


4 


167 


2505 


72 


41,700 


46.30 


39,600 


180 


10,470 


6325 


9 


4 l.'o 


211 


3165 


90 


52,500 


58.40 


50,000 


200 


12,420 


7560 


10 


5 


252 


3780 


108 


63,200 


70.25 


60,000 



Temperature of fresh air, 0°; of air from coils, 120°; of steam, 227°; 
Pressure of steam, 5 lbs. 

Peripheral velocity of fan-tips, 4000 ft.; number of pipes deep in coil, 
24; depth of coil, 60 inches ; area of coils approximately twice free area. 

Relative Efficiency of Fans and Heated Chimneys for Ventila- 
tion. — W. P. Trowbridge, Trans. A. S. M. E. vii. 531, gives a theoretical 
solution of the relative amounts of heat expended to remove a given 
volume of impure air by a fan and by a chimney. Assuming the total 
efficiency of a fan to be only 1/25, which is made up of an efficiency of 1/10 
for the engine, 5/ 10 for the fan itself, and s/ 10 for efficiency as regards 
friction, the fan requires an expenditure of heat to drive it of only 1/38 of 
the amount that would be required to produce the same ventilation by 
a chimney 100 ft. high. For a chimney 500 ft. high the fan will be 7.6 
times more efficient. 

The following figures are given by Atkinson (Coll. Engr., 1889), show- 
ing the minimum depth at which a furnace would be equal to a ventilating- 
machine, assuming that the sources of loss are the same in each case, i.e., 
that the loss of fuel in a furnace from the cooling in the upcast is equiva- 
lent to the power expended in overcoming the friction in the machine, 
and also assuming that the ventilating-machine utilizes 60 per cent of the 
engine-power. The coal consumption of the engine per I.H.P. is taken 
at 8 lbs. per hour. 

Average temperature in upcast 100° F. 150° F. 200° F. 

Minimum depth for equal economy.. 960 yards. 1040 yards. 1130 yards. 



PERFORMANCE OF HEATING GUARANTEE. 

Heating a Building to 70° F. Inside when the Outside Tempera- 
ture is Zero. — It is customary in some contracts for heating to guaran- 
tee that the apparatus will heat the interior of the building to 70° in zero 
weather. As it may not be practicable to obtain zero weather for the 
purpose of a test, it may be difficult to prove the performance of the 
guarantee unless an equivalent test may be made when the outside tem- 
perature is above zero, heating the building to a higher temperature 
than 70°. The following method was proposed by the author (Eng. Rec, 



684 HEATING AND VENTILATION. 



Aug. 11, 1894) for determining to what temperature the rooms should 
be heated for various temperatures of the outside atmosphere and of the 
steam or hot water in the radiators. 

Let S = sq. ft. of surface of the steam or hot-water radiator; 
W = sq. ft. of surface of exposed walls, windows, etc.; 
T s = temp, of the steam or hot water, 7 7 1 = temp, of inside of 
building or room, To = temp, of outside of building or room ; 
a = heat-units transmitted per sq. ft. of surface of radiator per 

hour per degree of difference of temperature; 
6 = average heat-units transmitted per sq. ft. of walls per hour 
per degree of difference of temperature, including allow- 
ance for ventilation. 
It is assumed that within the range of temperatures considered New- 
ton's law of cooling holds good, viz., that it is proportional to the differ- 
ence of temperature between the two sides of the radiating-surface. 

Then aS (T s - T t ) = bW (T t - To). Let ^ = C; then 



Ti==C (J 7 !- To); T t = 



aS 
T s + CT Q „ T s - T t 



1 + C ' Ti - To 
If T t = 70, and T = 0, C = -^ — 

Let T s '= 140° 160° 180° 200° 212° 220° 250° 300° 

Then (7= 1 1.286 1.571 1.857 2.029 2.143 2.571 3.286 

and from the formula 7\= (T s + CT ) + (1 + C) we find the inside 

temperatures corresponding to the given values of T s and T which 
should be produced by an apparatus capable of heating the building to 
70° in zero weather. 

For T = -20 - 10 10 20 30 40° F. 

Inside Temperatures T t . 

For Ts = 140° F. 60 65 70 75 80 85 90 

160 58.7 64.3 70 75.6 81.3 86.9 92.5 

180 57.8 63.9 70 76.1 82.2 88.4 94.5 

200 57.0 63.5 70 76.5 83.0 89.5 96.0 

212 56.6 63.3 70 76.7 83.4 90.1 96.8 

220 56.4 63.2 70 76.8 83.6 90.5 97.3 

250 55.6 62.8 70 77.2 84.4 91.6 98.8 

300 54.7 62.4 70 77.7 85.3 93.0 100.7 

J. K. Allen {Trans. A. S. H. V. E., 1908) develops a complex formula 
for the inside temperature which takes into consideration the fact that 
the coefficient of transmission of the radiator is not constant but in- 
creases with the temperature. With T s = 227 and a two-column cast-iron 
radiator he finds for T = -20-10 10 20 30 40 
7\ = 58 64 70 77.5 83 90 97 

For all values of T between — 10 and 40 these figures are within one 
degree of those computed by the author's method. 

ELECTRICAL HEATING. 

Heating by Electricity. — If the electric currents are generated by a 
dynamo driven by a steam-engine, electric heating will prove very ex- 
pensive, since the steam-engine wastes in the exhaust-steam and by 
radiation about 90% of the heat-units supplied to it. In direct steam- 
heating, with a good boiler and properly covered supply-pipes, we can 
utilize about 60% of the total heat value of the fuel. One pound of coal, 
with a heating value of 13,000 heat-units, would supply to the radiators 
about 13,000 X 0.60 = 7800 heat-units. In electric heating, suppose we 
have a first-class condensing-engine developing 1 H.P. for every 2 lbs. of 
coal burned per hour. This would be equivalent to 1,980,000 ft.-lbs. •+ . 



MINE-VENTILATION. 685 

778 = 2545 heat-units, or 1272 heat-units for 1 lb. of coal. The friction 
of the engine and of the dynamo and the loss by electric leakage and 
by heat radiation from the conducting wires might reduce the heat- 
units delivered as electric current to the electric radiator, and there con- 
verted into heat, to 50% of this, or only 636 heat-units, or less than one 
twelfth of that delivered to the steam-radiators in direct steam-heating. 
Electric heating, therefore, will prove uneconomical unless the electric 
current is derived from water or wind power which would otherwise be 
wasted. (See Electrical Engineering.) 

MINE-VENTILATION. 

Friction of Air in Underground Passages. — In ventilating a mine or 
other underground passage the resistance to be overcome is, according 
to most writers on the subject, proportional to the extent of the fric- 
tional surface exposed; that is, to the product lo of the length of the gang- 
way by its perimeter, to the density of the air in circulation, to the 
square of its average speed, v, and lastly to a coefficient k, whose numer- 
ical value varies according to the nature of the sides of the gangway and 
the irregularities of its course. 

The formula for the loss of head, neglecting the variation in density as 

unimportant, is p = , in which p = loss of pressure in pounds per 

square foot, 5 = square feet of rubbing-surface exposed to the air, v the 
velocity of the air in feet per minute, a the area of the passage in square 
feet, and k the coefficient of friction. W. Fairley, in Colliery Engineer, 
Oct. and Nov., 1893, gives the following formulae for all the quantities 
involved, using the same notation as the above, with these additions: 
h = horse-power of ventilation; I = length of air-channel; o = perimeter 
of air-channel; q = quantity of air circulating in cubic feet per minute; 
u — units of work, in foot-pounds, applied to circulate the air; w = water- 
gauge in inches. Then, 

_ ksv 2 __ ksv 2 q _ ksv 3 _ u _ q_ 
~ p u pv ~ pv ~ V ' 

o h = u = gP = 5.2 qw 
33,000 33,000 33,000* 
pa _ u _ p _ 5.2 w 



3 



sv 2 sv 3 
4. I - 



5. o - 



' kv 2 o 
pa 



I kvH 

ksv 2 _ u __ _ / "/ u Y ks ksv 3 u 

a q \Vksla q 



ks I v ' 

a u ksv 3 . I pa . lu 

8. q = va = - = — =^ Ts a = ^ rs a. 



7. pa = ksv 2 = I 4 / j— 1 ks = - ; pa 3 = ksq 2 . 



pa _ u_ _ qp_ _ vpa 

' kv 2 ~ kv 3 ~ kv 3 ~~ kv 3 



: 10. 



10. u = qp = vpa = ^^ = ksv 3 = 5.2 qw = 33,000 h 

a. - = u = g = //it = K Vm = * Im. 

pa a y ks y ks y ks 



686 HEATING AND VENTILATION. 

is. «• = | =, m w sg* 

V ksv 2 
14 - w = K2 = sT5' 
To find the quantity of air with a given horse-power and efficiency (e) 
of engine: 

h X 33,000 X e 

q = v ' 

The value of k, the coefficient of friction, as stated, varies according to 
the nature of the sides of the gangway. Widely divergent values have 
been given by different authorities (see Colliery Engineer, Nov., 1893), the 
most generally accepted one until recently being probably that of J. J. 
Atkinson, .0000000217, which is the pressure per square foot in decimals 
of a pound for each square foot of rubbing-surface and a velocity of one 
foot per minute. Mr. Fairley, in his "Theory and Practice of Ventilating 
Coal-mines," gives a value less than half of Atkinson's or .00000001; and 
recent experiments by D. Murgue show that even this value is high under 
most conditions. Murgue's results are given in his paper on Experi- 
mental Investigations in the Loss of Head of Air-currents in Under- 
ground Workings, Trans. A. I. M. E., 1893, vol. xxiii. 63. His coefficients 
are given in the following table, as determined in twelve experiments: 

Coefficient of Loss of 
Head by Friction. 
French. British. 

{Straight, normal section 00092 .000,000,00486 
Straight, normal section 00094 .000,000,00497 
Straight, large section 00104 .000,000,00549 
Straight, normal section 00122 .000,000,00645 

1 Straight, normal section 00030 .000,000,00158 
Straight, normal section 00036 .000,000,00190 
Continuous curve, normal section .00062 .000,000,00328 
Sinuous, intermediate section 00051 .000,000,00269 
Sinuous, small section 00055 . 000,000,00291 

t;™KotWI ( Straight, normal section 00168 .000,000,00888 

J ■ ™"f_ r ®° { Straight, normal section 00144 .000,000,00761 

gangways. ( slightly sinuous, small section. . . .00238 .000,000,01257 

The French coefficients which are given by Murgue represent the height 
of water-gauge in millimeters for each square meter of rubbing-surface 
and a velocity of one meter per second. To convert them to the British 
measure of pounds per square foot for each square foot of rubbing-surface 
and a velocity of one foot per minute they have been multiplied by the 
factor of conversion, .000005283. For a velocity of 1000 feet per minute, 
since the loss of head varies as v 2 , move the decimal point in the coefficients 
six places to the right. 

Equivalent Orifice. — ■ The head absorbed by the working-chambers 
of a mine cannot be computed a priori, because the openings, cross- 
passages, irregular-shaped gob-piles, and daily changes in the size and 
shape of the chambers present much too complicated a network for accu- 
rate analysis. In order to overcome this difficulty Murgue proposed in 
1872 the method of equivalent orifice. This method consists in substitut- 
ing for the mine to be considered the equivalent thin-lipped orifice, 
requiring the same height of head for the discharge of an equal volume 
of air. The area of this orifice is obtained when the head and the dis- 
charge are known, by means of the following formulae, as given by Fairley: 
Let Q = quantity of air in thousands of cubic feet per minute; 
w = inches of water-gauge; 
A = area in square feet of equivalent orifice. 
Then 

A = 0_*7J = Q. t Q = A^., „ = 0.1369X(2) ! . 
V w 2.7 v w ^.67 VA ' 

± „ . 0.38 Q , x , . . 0.403 Q ~ *,.. . 

* Murgue gives A = — -^, and Norns A = — -—■ • See page 644, ante. 



687 



Motive Column or the Head of Air Due to Differences of Tem- 
perature, etc. (Fairley.) 

Let M = motive column in feet ; 

T = temperature of upcast; 

/ = weight of one cubic foot of the flowing air; 

t = temperature of downcast; 
D = depth of downcast. 
Then 

„_ ^ T-t 5.2 Xw .„ ,, fXM v 

M = D m w trn or t ; p = / X M;w = — e 



T X 459 



/ 



5.2 



To find diameter of a round airway to pass the same amount of air as a 
square airway, the length and power remaining the same: 

Let D = diameter of round airway, A = area of square airway; = 



Vt 



A S X 3.1416 



perimeter of square airway. Then D s 

" 7854 3 X O 
If two fans are employed to ventilate a mine, each of which when 
worked separately produces a certain quantity, which may be indicated 
by A and B, then the quantit y of air t hat will pass when the two fans are 
worked together will be <\/A 3 + B 3 . (For mine-ventilating fans, see 
page 644.) 

WATER. 

Expansion of Water. — The following table gives the relative vol- 
umes of water at different temperatures, compared with its volume at 
4° C. according to Kopp, as corrected by Porter. 



Cent. 


Fahr. 


Volume. 


Cent. 


Fahr. 


Volume. 


Cent. 


Fahr. 


Volume. 


4° 


39.1° 


1.00000 


35° 


95 o 


1.00586 


70° 


158° 


1.02241 


5 


41 


1.00001 


40 


104 


1.00767 


75 


167 


1.02548 


10 


50 


1 .00025 


45 


113 


1.00967 


80 


176 


1.02872 


15 


59 


1.00083 


50 


122 


1.01186 


85 


185 


1.03213 


20 


68 


1.00171 


55 


131 


1.01423 


90 


194 


1.03570 


25 


77 


1.00286 


60 


140 


1.01678 


95 


203 


1.03943 


30 


86 


1.00425 


65 


149 


1.01951 


100 


212 


1.04332 



Weight of 1 cu. ft. at 39.1° F. = 62.4245 lb. h- 1.04332 = 59.833, 
weight of 1 cu. ft. at 212° F. 

Weight of Water at Different Temperatures. — The weight of 
water at maximum density, 39.1°, is generally taken at the figure given 
by Rankine, 62.425 lbs. per cubic foot. Some authorities give as low as 
62.379. The figure 62.5 commonly given is approximate. The highest 
authoritative figure is 62.428. At 62° F. the figures range from 62.291 to 
62.360. The figure 62.355 is generally accepted as the most accurate. 

At 32° F. figures given by different writers range from 62.379 to 62.418. 
Hamilton Smith, Jr. (from Rosetti) gives 62.416. 



Weight of Water at Temperatures above 200° F. 

Bornstein's Tables, 1905.) 



(Landolt and 





Lbs. 




Lbs. 




Lbs. 




Lbs. 




Lbs. 




Lbs. 


Deg. 


Per 


Deg. 


Per 


Deg. 


Per 


Deg. 


Per 


Deg. 


Per 


Deg. 


Per 


F. 


Cu. 


H'. 


Cu. 


F. 


Cu. 


F. 


Cu. 


H'. 


Cu. 


F. 


Cu. 




Ft. 




Ft. 




Ft. 




Ft. 


480 


Ft. 
49 7 


550 


Ft. 


200 


60.12 


270 


58.26 


340 


55.94 


410 


53.0 


45.6 


210 


59.88 


280 


57.96 


350 


55.57 


420 


52.6 


490 


49 2 


560 


44.9 


220 


59.63 


290 


57.65 


360 


55.18 


430 


52.2 


500 


48 7 


570 


44.1 


230 


59.37 


300 


57.33 


370 


54.78 


440 


51.7 


510 


48.1 


580 


43.3 


240 


59.11 


310 


57.00 


380 


54.36 


450 


51.2 


520 


47 6 


590 


42.6 


250 


58.83 


320 


56.66 


390 


53.94 


460 


50.7 


530 


47 


600 


41.8 


260 


58.55 


330 


56.30 


400 


53.5 


470 


50.2 


540 


46.3 







Weight of Water per Cubic Foot, from 32° to 212° F., and heat* 
units per pound, reckoned above 32° F.: The figures for weight of water 
in following table, made by interpolating the table given by Clark as cal- 
culated from Rankine's formula, with corrections for apparent errors, was 
published by the author in 1884, Trans. A. S. M. E., vi. 90. The figures 
for heat units are from Marks and Davis's Steam Tables, 1909. 



.fa 


i.2 

— 'Xi 


"3 

3 


& fa 


£ 2 


'3 

3 


k fa 


.8.2 

M (5 ° 


! 


| J* 


-Q 2 


'3 

3 


S-s 






B 3®, 


"5 

CD 


B££ 




a 


B 3.2 


"eS 
a> 


_H 


w 


H 


£ 


w 


H 


w 


H 


£ 


a 


32 


62.42 


0. 


78 


62.25 


46.04 


123 


61.68 


90.90 


168 


60.81 


135.86 


33 


62.42 


1.01 


79 


62.24 


47.04 


124 


61.67 


91.90 


169 


60.79 


136.86 


34 


62.42 


2.02 


80 


62.23 


48.03 


125 


61.65 


92.90 


170 


60.77 


137.87 


35 


62.42 


3.02 


81 


62.22 


49.03 


126 


61.63 


93.90 


171 


60.75 


138.87 


36 


62.42 


4.03 


82 


62.21 


50.03 


127 


61.61 


94.89 


172 


60.73 


139.87 


37 


62.42 


5.04 


83 


62.20 


51.02 


128 


61.60 


95.89 


173 


60.70 


140.87 


38 


62.42 


6.04 


84 


62.19 


52.02 


129 


61.58 


96.89 


174 


60.68 


141.87 


39 


62.42 


7.05 


85 


62.18 


53.02 


130 


61.56 


97.89 


175 


60.66 


142.87 


40 


62.42 


8.05 


86 


62.17 


54.01 


131 


61.54 


98.89 


176 


60.64 


143.87 


41 


62.42 


9.05 


87 


62.16 


55.01 


132 


61.52 


99.88 


177 


60 s 62 


144.88 


42 


62.42 


10.06 


88 


62.15 


56.01 


133 


61.51 


100.88 


178 


60.59 


145.88 


43 


62.42 


11.06 


89 


62.14 


57.00 


134 


61.49 


101.88 


179 


60.57 


146.88 


44 


62.42 


12.06 


90 


62.13 


58.00 


135 


61.47 


102.88 


180 


60.55 


147.88 


45 


62.42 


13.07 


91 


62.12 


59.00 


136 


61.45 


103.88 


181 


60.53 


148.88 


46 


62.42 


14.07 


92 


62.11 


60.00 


137 


61.43 


104.87 


182 


60.50 


149.89 


47 


62.42 


15.07 


93 


62.10 


60.99 


138 


61.41 


105.87 


183 


60.48 


150.89 


48 


62.41 


16.07 


94 


62.09 


61.99 


139 


61.39 


106.87 


184 


60.46 


151.89 


49 


62.41 


17.08 


95 


62.08 


62.99 


140 


61.37 


107.87 


185 


60.44 


152.89 


50 


62.41 


18.08 


96 


62.07 


63.98 


141 


61.36 


108.87 


186" 


60.41 


153.89 


51 


62.41 


19.08 


97 


62.06 


64.98 


142 


61.34 


109.87 


187 


60.39 


154.90 


52 


62.40 


20.08 


98 


62.05 


65.98 


143 


61.32 


110.87 


188 


60.37 


155.90 


53 


62.40 


21.08 


99 


62.03 


66.97 


144 


61.30 


111.87 


189 


60.34 


156.90 


54 


62.40 


22.08 


100 


62.02 


67.97 


145 


61.28 


112.86 


190 


60.32 


157.91 


55 


62.39 


23.08 


101 


62.01 


68.97 


146 


61.26 


113.86 


191 


60.29 


158.91 


56 


62.39 


24.08 


102 


62.00 


69.96 


147 


61.24 


114.86 


192 


60.27 


159.91 


57 


62.39 


25.08 


103 


61.99 


70.96 


148 


61.22 


115.86 


193 


60.25 


160.91 


58 


62.38 


26.08 


104 


61.97 


71.96 


149 


61.20 


116.86 


194 


60.22 


161.92 


59 


62.38 


27.08 


105 


61.96 


72.95 


150 


61.18 


117.86 


195 


60.20 


162.92 


60 


62.37 


28.08 


106 


61.95 


73.95 


151 


61.16 


118.86 


196 


60.17 


163.92 


61 


62.37 


29.08 


107 


61.93 


74.95 


152 


61.14 


119.86 


197 


60.15 


164.93 


62 


62.36 


30.08 


108 


61.92 


75.95 


153 


61.12 


120.86 


198 


60.12 


165.93 


63 


62.36 


31.07 


109 


61.91 


76.94 


154 


61.10 


121.86 


199 


60.10 


166.94 


64 


62.35 


32.07 


110 


61.89 


77.94 


155 


61.08 


122.86 


200 


60.07 


167.94 


65 


62.34 


33.07 


111 


61.88 


78.94 


156 


61.06 


123.86 


201 


60.05 


168.94 


66 


62.34 


34.07 


112 


61.86 


79.93 


157 


61.04 


124.86 


202 


60.02 


169.95 


67 


62.33 


35.07 


113 


61.85 


80.93 


158 


61.02 


125.86 


203 


60.00 


170.95 


68 


62.33 


36.07 


114 


61.83 


81.93 


159 


61.00 


126.86 


204 


59.97 


171.96 


69 


62.32 


37.06 


115 


61.82 


82.92 


160 


60.98 


127.86 


205 


59.95 


172.96 


70 


62.31 


38.06 


116 


61.80 


83.92 


161 


60.96 


128.86 


206 


59.92 


173.97 


71 


62.31 


39.06 


117 


61.78 


84.92 


162 


60.94 


129.86 


207 


59.89 


174.97 


72 


62.30 


40.05 


118 


61.77 


85.92 


163 


60.92 


130.86 


208 


59.87 


175.98 


73 


62.29 


41.05 


119 


61.75 


86.91 


164 


60.90 


131.86 


209 


59.84 


176.98 


74 


62.28 


42.05 


120 


61.74 


87.91 


165 


60.87 


132.86 


210 


59.82 


177.99 


75 


62.28 


43.05 


121 


61.72 


88.91 


166 


60.85 


133.86 


211 


59.79 


178.99 


76 


62.27 


43.04 


122 


61.70 


89.91 


167 


60.83 


134.86 


212 


59.76 


180.00 


77 


62.26 


45.04 


















~ 



Later authorities give figures for the weight of water which differ in the 
second decimal place only from those given above, as follows: 

50 60 70 80 90 
62.42 62.37 62.30 62.22 62.11 
110 120 130 140 150 

61.86 61.71 61.55 61.38 (jl. J8 
170 180 190 200 210 
60.80 60.50 60.36 60.13 59.88 



Temp. F 


..40 


Lbs, per cu. ft. 


..62.43 


Temp. F 


.100 


Lbs. per cu, ft. 


, 62.00 


Temp. F 


.160 


Lbs, per cu. ft, 


. 61.00 



689 



Comparison of Heads of Water in Feet with Pressures in Various 
Units. 

One foot of water at 39.1° Fahr. = 62.425 lbs. on the square foot; 

= . 4335 lbs. on the square inch; 

= 0.0295 atmosphere; 

= 0.8826 inch of mercury at 30°; 

_ 77 o of feet of air at 32° and 

1 atmospheric pressure ; 
One lb. on the square foot, at 39.1° Fahr.. = 0.01602 foot of water; 
One lb. on the square inch, at 39.1° Fahr .. = 2.307 feet of water; 
One atmosphere of 29 . 922 in. of mercury . . = 33 . 9 feet of water; 

One inch of mercury at 32. 1° = 1 . 133 feet of water; 

One foot of air at 32°, and 1 atmosphere. . = 0.001293 feet of water; 

One foot of average sea-water = 1 .026 foot of pure water; 

One foot of water at 62° F = 62 . 355 lbs. per sq. foot ; 

One foot of water at 62° F = . 43302 lb. per sq. inch; 

One inch of water at 62° F. = .5774 ounce = 0.036085 lb. per sq. inch; 
One lb. of water on the square inch at 62° F= 2. 3094 feet of water. 
One ounce of water on the square inch at 

62° F = 1 . 732 inches of water. 



Pressure in Pounds per Square Inch for Different Heads of Water. 

At 62° F. 1 foot head = 0.433 lb. per square inch, 0.433 X 144 = 62.352 
lbs. per cubic foot. 



Head, feet. 





1 


2 


3 


4 


5 


6 


7 


8 


9 







0.433 


0.866 


1.299 


1.732 


2.165 


2.598 


3.031 


3.464 


3.897 


10 


4.330 


4.763 


5.196 


5.629 


6.062 


6.495 


6.928 


7.361 


7.794 


8.227 


20 


8.660 


9.093 


9.526 


9.959 


10.392 


10.825 


11.258 


11.691 


12.124 


12.557 


30 


12.990 


13.423 


13.856 


14.289 


14.722 


15.155 


15.588 


16.021 


16.454 


16.887 


40 


17.320 


17.753 


18.186 


18.619 


19.052 


19.485 


19.918 


20.351 


20.784 


21.217 


50 


21.650 


22.083 


22.516 


22.949 


23.382 


23.815 


24.248 


24.681 


25.114 


25.547 


60 


25.980 


26.413 


26.846 


27.279 


27.712 


28.145 


28.578 


29.011 


29.444 


29.877 


70 


30.310 


30.743 


31.176 


31.609 


32.042 


32.475 


32.908 


33.341 


33.774 


34.207 


80 


34.640 


35.073 


35.506 


35.939 


36.372 


36.805 


37.238 


37.671 


38.104 


38.537 


90 


38.970 


39.403 


39.836 


40.269 


40.702 


41.135 


41.568 


42.001 


42.436 


42.867 



Head in Feet of Water, Corresponding to Pressures in Pounds per 
Square Inch. 

1 lb. per square inch = 2.30947 feet head, 1 atmosphere = 14.7 lbs. 
per sq. inch = 33.94 ft. head. 



Pressure. 





1 


2 


3 


4 


5 


6 


7 


8 


9 







2.309 


4.619 


6.928 


9.238 


11.547 


13.857 


16.166 


18.476 


20.785 


10 


23.0947 


25.404 


27.714 


30.023 


32.333 


34.642 


36.952 


39.261 


41.570 


43.880 


20 


46.1894 


48.499 


50.808 


53.118 


55.427 


57.737 


60.046 


62.356 


64.665 


66.975 


30 


69.2841 


71.594 


73.903 


76.213 


78.522 80.831 83.141 85.450 


87.760 


90.069 


40 


92.3788 


94.688 


96.998 


99.307 


101 .62103.931106.24 108.55 


110.85 


113.16 


50 


115.4735 


117.78 


120.09 


122.40 


124.71 127. 02 ! 129. 33 


131.64 


133.95 


136.26 


60 


138.5682 


140.88 


143.19 


145.50 


147.811150.12152.42 


154.73 


157.04 


159.35 


70 


161.6629 


163.97 


166.28 


168.59 


170.90 1 173.21 1175.52 


177.83 


180.14 


182.45 


80 


184.7576 


187.07 


189.38 


191.69 


194.00196.31 198.61 


200.92 


203.23 


205.54 


90 


207.8523 


210.16 


212.47 


214.78 


217.09 219.40 221 .71 


224.02 


226.33 


228.64 



690 



Pressure of Water due to its Weight. — The pressure of still water 
in pounds per square inch against the sides of any pipe, channel, or vessel 
of any shape whatever is due solely to the " head," or height of the 
level surface of the water above the point at which the pressure is con- 
sidered, and is equal to 0.43302 lb. per square inch for every foot of head, 
or 62.355 lbs. per square foot for every foot of head (at 62° F.). 

The pressure per square inch is equal in all directions, downwards, 
upwards, or sideways, and is independent of the shape or size of the 
containing vessel. 

The pressure against a vertical surface, as a retaining- wall, at any 
point is* in direct ratio to the head above that point, increasing from at 
the level surface to a maximum at the bottom. The total pressure 
against a vertical strip of a unit's breadth increases as the area of a 
right-angled triangle whose perpendicular represents the height of the 
strip and whose base represents the pressure on a unit of surface at the 
bottom; that is, it increases as the square of the depth. The sum of all 
the horizontal pressures is represented by the area of the triangle, and 
the resultant of this sum is equal to this sum exerted at a point one third 
of the height from the bottom. (The center of gravity of the area of a 
triangle is one third of its height.) 

The horizontal pressure is the same if the surface is inclined instead 
of vertical. 

(For an elaboration of these principles see Trautwine's Pocket-Book, 
or the chapter on Hydrostatics in any work on Physics. For dams, 
retaining-walls, etc., see Trautwine.) 

The amount of pressure on the interior walls of a pipe has no appreci- 
able effect upon the amount of flow. 

Buoyancy. — When a body is immersed in a liquid, whether it float or 
sink, it is buoyed up by a force equal to the weight of the bulk of the 
liquid displaced by the body. The weight of a floating body is equal to 
the weight of the bulk of the liquid that it displaces. The upward 
pressure or buoyancy of the liquid may be regarded as exerted at the 
center of gravity of the displaced water, which is called the center of 
pressure or of buoyancy. A vertical line drawn through it is called the 
axis of buoyancy or of flotation. In a floating body at rest a line joining 
the center of gravity and the center of buoyancy is vertical, and is called 
the axis of equilibrium. When an external force causes the axis of 
equilibrium to lean, if a vertical line be drawn upward from the center 
of buoyancy to this axis, the point where it cuts the axis is called the 
metacenter . If the metacenter is above the center of gravity the distance 
between them is called the metacentric height, and the body is then said 
to be in stable equilibrium, tending to return to its original position 
when the external force is removed. 

Boiling-point. — Water boils at 212° F. (100° C.) at mean atmos- 
pheric pressure at the sea-level, 14.696 lbs. per square inch. The tem- 
perature at which water boils at any given pressure is the same as the 
temperature of saturated steam at the same pressure. For boiling-point 
of water at other pressure than 14.696 lbs. per square inch, see table of 
the Properties of Saturated Steam. 

The Boiling-point of Water may be Raised. — When water is 
entirely freed of air, which may be accomplished by freezing or boiling, 
the cohesion of its atoms is greatly increased, so that its temperature 
may be raised over 50° above the ordinary boiling-point before ebullition 
takes place. It was found by Faraday that when such air-freed water 
did boil the rupture of the liquid was like an explosion. When water 
is surrounded by a film of oil, its boiling temperature may be raised 
considerably above its normal standard. This has been applied as a 
theoretical explanation in the instance of boiler explosions. 

The freezing-point also may be lowered, if the water is perfectly quiet, 
to - 10° C, or 18° Fahrenheit below the normal freezing-point. (Hamilton 
Smith, Jr., on Hydraulics, p. 13.) 

Freezing-point. — Water freezes at 32° F. at the ordinary atmos- 
pheric pressure, and ice melts at the same temperature. In the melting 
of 1 pound of ice into water at 32° F. about 142 heat-units are absorbed, 
or become latent; and in freezing 1 lb. of water into ice a like quantity 
of heat is given out to the surrounding medium. 

Sea-water freezes at 27° F. The ice is fresh. /Trautwine.) 



THE IMPURITIES OF WATER. 



691 



Ice and Snow. (From Clark.) — 1 cubic foot of ice at 32° F. weighs 
57.50 lbs.; 1 pound of ice at 32° F. has a volume of 0.0174 cu. ft. = 30.067 
cu. in. 

Relative volume of ice to water at 32° F., 1.0855, the expansion in 
passing into the solid state being 8.55%. Specific gravity of ice = 0.922, 
water at 62° F. being 1. 

At high pressures the melting-point of ice is lower than 32° F., being at 
the rate of 0.0133° F. for each additional atmosphere of pressure. 

The specific heat of ice is 0.504, that of water being 1. 

1 cubic foot of fresh snow, according to humidity of atmosphere: 
5 lbs. to 12 lbs. 1 cubic foot of snow moistened and compacted by 
rain: 15 lbs. to 50 lbs. (Trautwine.) 

Specific Heat of Water. (From Davis and Marks's Steam Tables.) 



Deg. Sp. 


Deg. 


Sp. 


Deg. 


Sp. 


Deg. 


Sp. 


Deg. 


k. 


Deg. 


Sp. 


F. Ht. 


F. 


Ht. 


F. 


Ht. 


F. 


Ht. 


F. 


F. 


Ht. 


20 1.0168 


120 


0.9974 


220 


1.007 


320 


1.035 


420 


1.072 


520 


1.123 


30 1.0098 


130 


0.9974 


230 


1.009 


330 


1.038 


430 


1.077 


530 


1.128 


40 1.0045 


140 


0.9986 


240 


1.012 


340 


1.041 


440 


1.082 


540 


1.134 


50 1.0012 


150 


0.9994 


250 


1.015 


350 


1.045 


450 


1.086 


550 


1.140 


60 0.9990 


160 


1.0002 


260 


1.018 


360 


1.048 


460 


1.091 


560 


1.146 


70 0.9977 


170 


1.0010 


270 


1.021 


370 


1.052 


470 


1.096 


570 


1.152 


80 0.9970 


180 


1.0019 


280 


1.023 


380 


1.056 


480 


1.101 


580 


1.158 


90 0.9967 


190 


1.0029 


290 


1.026 


390 


1.060 


490 


1.106 


590 


1.165 


100 0.9967 


200 


1.0039 


300 


1.029 


400 


1.064 


500 


1.112 


600 


1.172 


110 0.9970 


210 


1 .0050 


310 


1.032 


410 


1.068 


510 


1.117 







These figures are based on the mean value of the heat unit, that is, 
Vi80 of the heat needed to raise 1 lb. of water from 32° to 212°. 

Compressibility of Water. — Water is very slightly compressible. 
Its compressibility is from 0.000040 to 0.000051 for one atmosphere, 
decreasing with increase of temperature. For e-ch foot of pressure dis- 
tilled water will be diminished in volume 0.0000015 to 0.0000013. Water 
is so incompressible that even at a depth of a mile a cubic foot of water 
will weigh only about half a pound more than at the surface.. 



THE IMPURITIES OF WATER. 

(A. E. Hunt and G. H. Clapp, Trans. A.I. M. E., xvii. 338.) 

Commercial analyses are made to determine concerning a given water: 
(1) its applicability for making steam; (2) its hardness, or the facility 
with which it will "form a lather" necessary for washing; or (3) its 
adaptation to other manufacturing purposes. 

At the Buffalo meeting of the Chemical Section of the A. A. A. S. it 
was decided to report all water analyses in parts per thousand, hundred- 
thousand, and million. 

To convert grains per imperial (British) gallon into parts per 100,000, 
divide by 0.7. To convert parts per 100,000 into grains per U. S. gallon, 
multiply by 0.5835. To convert grains per U. S. gallon into parts per 
million multiply by 17.14. 

The most common commercial analysis of water is made to determine 
its fitness for making steam. Water containing more than '5 parts per 
100,000 of free sulphuric or nitric acid is liable to cause serious corrosion, 
not onlv of the metal of the boiler itself, but of the pipes, cylinders, pistons, 
and valves with which the steam comes in contact. 

The total residue in water used for making steam causes the interior 
linings of boilers to become coated, and often produces a dangerous hard 



692 WATER. 

scale, which prevents the cooling action of the water from protecting 
the metal against burning. 

Lime and magnesia bicarbonates in water lose their excess of carbonic acid 
on boiling, and often, especially when the water contains sulphuric acid, 
produce, wich the other solid residues constantly being formed by the 
evaporation, a very hard and insoluble scale. A larger amount than 100 
parts per 100,000 of total solid residue will ordinarily cause troublesome 
scale, and should condemn the water for use in steam-boilers, unless a 
better supply cannot be obtained. 

The following is a tabulated form of the causes of trouble with water 
for steam purposes, and the proposed remedies, given by Prof. L. M. 
Norton. 

Causes of Incrustation. 

1. Deposition of suspended matter. 

2. Deposition of deposed salts from concentration. 

3. Deposition of carbonates of lime and magnesia by boiling off 
carbonic acid, which holds them in solution. 

4. Deposition of sulphates of lime, because sulphate of lime is but 
slightlv soluble in cold water, less soluble in hot water, insoluble above 
27Q° F. 

5. Deposition of magnesia, because magnesium salts decompose at high 
temperature. 

6. Deposition of lime soap, iron soap, etc., formed by saponification of 
grease. 

Means for Preventing Incrustation. 

1. Filtration. 

2. Blowing off. 

3. Use of internal collecting apparatus or devices for directing the 
circulation. 

4. Heating feed-water. 

5. Chemical or other treatment of water in boiler. 

6. Introduction of zinc into boiler. 

7. Chemical treatment of water outside of boiler. 

Tabular View. 

Troublesome Substance. Trouble. Remedy or Palliation. 
Sediment, mud, clay, etc. Incrustation. Filtration; blowing off. 

Readily soluble salts. Blowing off. 

Bicarbonates of lime, magnesia,} .. f Sc^da^" of 

iroa - J t magnesia, etc. 

quinhatp nf limp " (Addition of carb. soda, 

bulpnate ot lime. { barium hydrate, etc. 

Chloride and sulphate of mag-) r> rtrrnoift „ (Addition of carbonate of 

nesium. \ Corrosion. | godai etc 

Carbonate of soda in large) p ,■•.„ (Addition of barium chlo- 

amounts. ( ^ nmm S- \ ride, etc. 

Acid (in mine waters). Corrosion. Alkali. 

Dissolved carbonle aeid and} Com>sion . j^oMef UrnTa*,^ ffi 

oxygen - m l ternal coating. 

Grease (from condensed water). lf^?5J°B ° r l Different cases require dif- 
• Primfne ■ ferent remedies. Consult 

Organic matter (sewage). \ corrosion or fjp ecialist on the sub ' 

( incrustation/ jec1. 

The mineral matters causing the most troublesome boiler-scales are 
bicarbonates and sulphates of lime and magnesia, oxides of iron and 
alumina, and silica. The analyses of some of the most common and 
troublesome boiler-scales are given in the following table: 



THE IMPURITIES OF WATER. 



693 





Analyses of Boiler-scale. (Chandler.) 








Sul- 
phate 

of 
Lime. 


Mag- 
nesia. 


Silica. 


Per- 
oxide 

of 
Iron. 


Water. 


Car- 
bonate 

of 
Lime. 


N.Y.C.&H.R 


.Ry.,No. 1 
No. 2 
No. 3 
No. 4 
No. 5 
No. 6 
No. 7 
No. 8 
No. 9 
No. 10 


74.07 
71.37 
62.86 
53.05 
46.83 
30.80 
4.95 
0.88 
4.81 
30.07 


9.19 
"\8.95 

2.61 

2.84 


0.65 
1.76 
2.60 
4.79 
5.32 
7.75 
2.07 
0.65 
2.92 
8.24 


0.08 


1.14 


14.78 


'.! "t 


0.92 


1.28 


12.62 


•I •< i 








:: :•: : 


1.08 
1.03 
0.36 


2.44 
0.63 
0.15 


26.93 
86.25 
93.19 


•i << . 

















Analyses in parts per 100,000 of Water giving Bad Results in 
Steam-boilers. (A. E. Hunt.) 





ll 

3 3 


03 

fl.S 

s : 
















i 




L"pq 

o e 


1§ 




.2 

0> 


3 






<v 




'•73 

O 
02 




is 

a -.. 
: ■ 
-"- : 


®T3 


O! 


c 


< 






oj 








71 OJ 

- - 

.2 o 


a 

3 


03 


zs 


6 




'S 


c3 


O 
13 


















a 

3 






.2-3 


53 CD 


o 


o 


3 




2 


o 


M 


2 




W 


w 


H 


H 


02 


u 


1-1 


o 


< 


o 




110 
151 

75 


25 

38 
89 


119 
190 
95 


39 
48 
170 


890 
360 
110 


590 
990 
?\ 


780 

38 
75 


30 
21 
10 


640 
30 
80 




Salt-well 


1310 




36 




no 


?1 


161 


V> 


710 


18 


70 










80 
32 
30 


70 
82 
50 


94 
61 
41 


81 
104 
68 


219 
28 
890 


210 
190 
42 


90 

38 
23 








• i >< 

























Many substances have been added with the idea of causing chemical 
action which will prevent boiler-scale. As a general rule, these do more 
harm than good, for a boiler is one of the worst possible places in which 
to carry on chemical reaction, where it nearly always causes more or less 
corrosion of the metal, and is liable to cause dangerous explosions. 

In cases where water containing large amounts of total solid residue is 
necessarily used, a heavy petroleum oil, free from tar or wax, which is not 
acted upon by acids or alkalies, not having sufficient wax in it to cause 
saponification, and which has a vaporizing-point at nearly 600° F., will 
give the best results in preventing boiler-scale. Its action is to form a 
thin greasy film over the boiler linings, protecting them largely from the 
action of acids in the water and greasing the sediment which is formed, 
thus preventing the formation of scale and keeping the solid residue 
from the evaporation of the water in such a plastic suspended condition 
that it can be easily ejected from the boiler by the process of "blowing 
off." If the water is not blown off sufficiently often, this sediment 
forms into a "putty" that will necessitate cleaning the boilers. Any 
boiler using bad water should be blown off every twelve hours. 



694 



WATER. 



Hardness of Water. — The hardness of water, or its opposite quality, 
indicated by the ease with which it will form a lather with soap, depends 
almost altogether upon the presence of compounds of lime and magnesia. 
Almost all soaps consist, chemically, of oleate, stearate, and palmitate of 
an alkaline base, usually soda and potash. The more lime and magnesia 
in a sample of water, the more soap a given volume of the water will 
decompose, so as to give insoluble oleate, palmitate, and stearate of 
lime and magnesia, and consequently the more soap must be added in 
order that the necessary quantity of soap may remain in solution to 
form the lather. The relative hardness of samples of water is generally 
expressed in terms of the number of standard soap-measures consumed 
by a gallon of water in yielding a permanent lather. 

In Great Britain the standard soap-measure is the quantity required to 
precipitate one grain of carbonate of lime: in the U. S. it is the quantity 
required to precipitate one milligramme. 

If a water charged with a bicarbonate of lime, magnesia, or iron 
is boiled, it will, on the excess of the carbonic acid being expelled, 
deposit a considerable quantity of the lime, magnesia, or iron, and con- 
sequently the water will be softer. The hardness of the water after 
this deposit of lime, after long boiling, is called the permanent hardness 
and the difference between it and the total hardness is called temporary 
hardness. 

Lime salts in water react immediately on soap-solutions, precipitating 
the oleate, palmitate, or stearate of lime at once. Magnesia salts, on the 
contrary, require some considerable time for reaction. They are, how- 
ever, more powerful hardeners; one equivalent of magnesia salts con- 
suming as much soap as one and one-half equivalents of lime. 

The presence of soda and potash salts softens rather than hardens 
water. Each grain of carbonate of lime per gallon of water causes an 
increased expenditure for soap of about 2 ounces per 100 gallons of water. 
(Eng'g News, Jan. 31, 1885.) 

Low degrees of hardness (down to 200 parts of calcium carbonate 
(CaCOs) per million) are usually determined by means of a standard 
solution of soap. To 50 c.c. of the water is added alcoholic soap solu- 
tion from a burette, shaking well after each addition, until a lather is 
obtained which covers the entire surface of the liquid when the bottle is 
laid on its side and which lasts five minutes. From the number of c.c. 
of soap solution used, the hardness of the water may be calculated by 
the use of Clark's table, given below, in parts of CaC03 per million. 



c.c. Soap 
Sol. 


Pts. 
CaCOs. 


c.c. Soap 
Sol. 


Pts. 
CaCOs. 


c.c. Soap 
Sol. 


Pts. 
CaCOs. 


c.c. Soap 
Sol. 


Pts. 
CaCOs. 


0.7 

1.0 

2.0 

3.0 




5 

19 

32 


4.0 

5.0 

6.0 

7.0 


46 

60 

74 

89 


8.0 

9.0. 

10.0 

11.0 


103 

118 

133 

.....148 


12.0 

13.0 

14.0 

15.0 


164 

.....180 
196 

212 









For waters which are harder than 200 parts per million, a solution of 
soap ten times as strong may be used, the end or determining point being 
reached when sufficient soap has been added to deaden the harsh sound 
produced on shaking the bottle containing the water. — A. H. Gill, En- 
gine-Room Chemistry. 

Purifying Feed-water for Steam-boilers. (See also Incrustation 
and Corrosion, p. 897.) — When the water used for steam-boilers con- 
tains a large amount of scale-forming material it is usually advisable to 
purify it before allowing it to enter the boiler rather than to attempt the 
prevention of scale by the introduction of chemicals into the boiler. 
Carbonates of lime and magnesia may be removed to a considerable 
extent by simple heating of the water in an exhaust-steam feed-water 
heater or, still better, by a live-steam heater. (See circular of the Hoppes 
Mfg. Co., Springfield, O.) When the water is very bad it is best treated 



PURIFYING WATER 695 

with chemicals — lime, soda-ash, caustic soda, etc. — in tanks, the pre- 
cipitates being separated by settling or filtering. For a description of 
several systems of water purification see a series of articles on the sub- 
ject by Albert A. Cary in Eng'g Mag., 1897. 

Mr. H. E. Smith, chemist of the Chicago, Milwaukee & St. Paul Ry. 
Co., in a letter to the author, June, 1902, writes as follows concerning 
the chemical action of soda-ash on the scale-forming substances in boiler 
waters: 

Soda-ash acts on carbonates of lime and magnesia in boiler water in the 
following manner: — The carbonates are held in solution by means of 
the carbonic acid gas also present which probably forms bicarbonates of 
lime and magnesia. Any means which will expel or absorb this carbonic 
acid will cause the precipitation of the carbonates. One of these means 
is soda ash (carbonate of soda), which absorbs the gas with the forma- 
tion of bicarbonate of soda. This method would not be practicable for 
softening cold water, but it serves in a boiler. The carbonates precipi- 
tated in this manner are in flocculent condition instead of semi-crystalline 
as when thrown down by heat. In practice it is desirable and sufficient 
to precipitate only a portion of the lime and magnesia in flocculent 
condition. As to equations, the following represent what occurs: — 

Ca (HC0 3 ) + Na 2 C0 3 = CaC0 3 + 2 NaHCOs. 
Mg (HCO3) + Na 2 C0 3 = MgCOs + 2 NaHCOs. 
(free) C0 2 + Na 2 C0 3 + H 2 = 2 NaHCOs. 

Chemical equivalents: — 106 pounds of pure carbonate of soda — 
equal to about 109 pounds of commercial 58 degree soda-ash — are 
chemically equivalent to — i.e., react exactly with — the following 
weights of the substances named: Calcium sulphate, 136 lbs.; magnesium 
sulphate, 120 lbs.; calcium carbonate, 100 lbs.; magnesium carbonate, 
84 lbs.; calcium chloride, 111 lbs.; magnesium chloride, 95 lbs. 

Such numbers are simply the molecular weights of the substances 
reduced to a common basis with regard to the valence of the component 
atoms. 

Important work in this line should not be undertaken by an amateur. 
" Recipes" have a certain field of usefulness, but will not cover the whole 
subject. In water purification, as in a problem of mechanical engineer- 
ing, methods and apparatus must be adapted to the conditions presented. 
Not only must the character of the raw water be considered but also the 
conditions of purification and use. 

Water-softening Apparatus. (From the Report of the Committee 
on Water Service, of the Am. Railway Eng'g and Maintenance of Way 
Assn., Eng. Rec, April 20, 1907). — Between three and four hours is nec- 
essary for reaction and precipitation. Water taken from running streams 
in winter should have at least four hours' time. At least three feet of 
the bottom of each settling tank should be reserved for the accumulation 
of the precipitates. 

The proper capacities for settling tanks, measured above the space 
reserved for sludge, can be determined as follows: a = capacity of soft- 
ener in gallons per hour; b = hours required for reaction and precipitation; 
c = number of settling tanks (never less than two) ; x = number of 
hours required to fill the portion of settling tank above the sludge portion; 
y = number of hours required to transfer treated water from one settling 
tank to the storage tank (y should never be greater than x). 

Where one pump alternates between filling and emptying settling 
tanks, x = y. Settling capacity in each tank= 2 ax = ab -s- (c — 1). 

For plants where the quantity of water supplied to the softener and the 
capacity of the plant are equal, the settling capacity of each tank is equal 
to ax. The number of hours required to fill all the settling tanks should 
equal the number of hours required to fill, precipitate and empty one 
tank, as expressed by the following equation: ex = x + b + y. 

Ify = x, ax = ab -s- (c — 2). 

If y = 1/2 x, ax = ab -s- (c — 1.5). 



696 



WATER. 



An article on "The Present Status of "Water Softening," by G. C. 
Whipple, in Cass. Mag., Mar., 1907, illustrates several different forms of 
water-purifying apparatus. A classification of degrees of hardness cor- 
responding to parts of carbonates and sulphates of lime and magnesia 
per million parts of water is given as follows: Very soft, to 10 parts; 
soft, 10 to 20; slightly hard, 25 to 50; hard, 50 to 100; very hard, 100 to 
200; excessively hard, 200 to 500; mineral water, 500 or more. The 
same article gives the following figures showing the quantity of chemicals 
required for the various constituents of hard water. For each part per 
million of the substances mentioned it is necessary to add the stated 
number of pounds per million gallons of lime and soda. 



For Each Part per Million of 


Pounds per Million 
Gallons. 




Lime. 


Soda. 


Free C0 2 


10.62 
4.77 
4.67 
0.00 

19.48 







9.03 









8.85 












The above figures do not take into account any impurities in the 
chemicals. These have to be considered in actual operation. 

An illustrated description of a water-purifying plant on the Chicago 
& Northwestern Ry. by G. M. Davidson is found in Eng. News, April 2, 
1903. Two precipitation tanks are used, each 30 ft. diam., 16 ft. high, 
or 70,000 gallons each. As some water is left with the sludge in the 
bottom after each emptying, their net capacity is about 60,000 gallons 
each. The time required for filling, precipitating, settling and trans- 
ferring the clear water to supply tanks is 12 hours. Once a month the 
sludge is removed, and it is found to make a good whitewash. Lime and 
soda-ash, in predetermined quantity, as found by analysis of the water, 
are used as precipitants. The following table shows the effect of treat- 
ment of well water at Council Bluffs, Iowa. 



Total solid matter, grains per gallon 

Carbonates of lime and magnesia 

Sulphates of lime and magnesia 

Silica and oxides of iron and aluminum. . 

Total incrusting solids 

Alkali chlorides 

Alkali sulphates 

Total non-in crusting solids 

Pounds scale-forming matter in 1000 gals 




The minimum amount of scaling matter which will justify treatment 
cannot be stated in terms of analysis alone, but should be stated in terms 
of pounds incrusting matter held in solution in a day's supply. Besides 
the scale-forming solids, nearly all water contains more or less free car- 
bonic acid. Sulphuric acid is also found, particularly in streams adjacent 
to coal mines. Serious trouble from corrosion will result from a small 
amount of this acid. In treating waters, the acids can be neutralized, 
and the incrusting matter can be reduced to at least 5 grains per gallon in 
most cases. 



HYDRAULICS. 



697 



Quantity of Pure Reagents Required to Remove One Pound op 
Incrusting or Corrosive Matter from the Water. 



Incrusting or Corrosive 

Substance Held in 

Solution. 



Amount of Reagent. (Pure.) 



Foaming Mat- 
ter Increased. 



Sulphuric acid 

Free carbonic acid 

Calcium carbonate 

Calcium sulphate 

Calcium chloride 

Calcium nitrate 

Magnesium carbonate. . . 
Magnesium sulphate 

Magnesium chloride 

Magnesium nitrate 



Calcium carbonate 

Magnesium carbonate. . 
Magnesium sulphate . . . 
*Calcium sulphate 



0.571b. lime plus 1 .08 lbs. soda ash 

1.27 lbs. lime 

0.56 1b. lime 

0.78 1b. soda ash 

. 96 lb . soda ash 

0.65 lb. soda ash 

1 .33 lbs. lime 

0.47 lb. lime plus 0.881b. soda ash. 
0.59 lb. lime plus 1.11 lbs. soda ash 
. 38 lb . lime plus . 72 lb . soda ash . 



1 .71 lbs. barium hydrate. 
4.05 lbs. barium hydrate. 
1 .42 lbs. barium hydrate. 
1 .26 lbs. barium hydrate. 



1.45 lbs. 

None 

None 

1.04 lbs. 

1.05 lbs. 
1.04 lbs. 
None 
1.18 lbs. 
1.22 lbs. 
1.15 lbs. 

None 
None 
None 
None 



* In precipitating the calcium sulphate, there would also be precipi- 
tated 0.74 lb. of calcium carbonate or 0.31 lb. of magnesium carbonate, 
the 1.26 lbs. of barium hydrate performing the work of 0.41 lb. of lime 
and 0.78 lb. of soda-ash, or for reacting on either magnesium or calcium 
sulphate, 1 lb. of barium hydrate performs the work of 0.33 lb. of lime 
plus 0.62 lb. of soda-ash, and the lime treatment can be correspondingly 
reduced. 

Barium hydrate has no advantage over lime as a reagent to precipitate 
the carbonates of lime and magnesia and should not be considered except 
in connection with the treating of water containing calcium sulphate. 



HYDRAULICS -FLOW OF WATER. 

Formulae for Discharge of Water through Orifices and Weirs. — 

For rectangular or circular orifices, with the head measured from center 
of the orifice to the surface of the still water in the feeding reservoir: 

Q = C ^2gHX a . (1) 

For weirs with no allowance for increased head due to velocity of 
approach: 

Q = CV 3 \ / 2gH XLH (2) 

For rectangular and circular or other shaped vertical or inclined orifices; 
formula based on the proposition that each successive horizontal layer of 
water passing through the orifice has a velocity due to its respective 
head: 

Q =cL 2/3 ^2gX (^Htf - V#jS) ( 3) 

For rectangular vertical weirsj 

Q =c2/ 3 V2gHXLh (4) 

Q — quantity of water discharged in cubic feet per second; C = ap- 
proximate coefficient for formulas (1) and (2): c = correct coefficient 
for (3) and (4). 

Values of the coefficients c and C are given below. 

g = 32.16; *^2g = 8.02; H = head in feet measured from center of 
orifice to level of still water; H b = head measured from bottom of 
orifice; H t = head measured from top of orifice; h = H, corrected for 
velocity of approach, V a = H + 1.33 V a 2 /2g for weirs with no end con- 
traction, and. H + 1.4 V^/2 g for weirs with end contraction; a= area in 
square feet; L=length in feet. 



HYDRAULICS. 



Flow of Water from Orifices. — The theoretical velocity of water 
flowing from an orifice is the same as the velocity of a falling body which 
has fallen from a height equal to the head of water, = V2 gH. The 
actual velocity at the smaller section of the vena contracta is substan- 
tially the sam e as the theoretical, but the velocity at the plane of the 
orifice is C ^2 gH, in which the coefficient C has the nearly constant 
value of 0.62. The smallest diameter of the vena contracta is therefore 
about 0.79 of that of the orifice. If C be the approximate coefficient 
= 0.62, and c the correct coefficient, the ratio C/c varies with different 
ratios of the head to the diameter of the vertical orifice, or to H/D. Ham- 
ilton Smith, Jr., gives the following: 

H/D=0.5 0.875 1. 1.5 2. 2.5 5. 10. 

C/c =0.9604 0.9849 0.9918 0.9965 0.9980 0.9987 0.9997 1. 

For vertical rectangular orifices of ratio of head to width W; 
¥ovH/W = 0.5 0.6 0.8 1 - 1.5 2. 3. 4. 5. 8. 

C/c= .9428 .9657 .9823 .9890 .9953 .9974 .9988 .9993 .9996 .9998 

For H -=- D or H -h W over 8, C = c, practically. 

For great heads, 312 ft. to 336 ft., with converging mouthpieces, c 
has a value of about one, and for small circular orifices in thin plates, 
with full contraction, c = about 0.60. 

Mr. Smith as the result of the collation of many experimental data of 
others as well as his own, gives tables of the value of c for vertical orifices, 
with full contraction, with a free discharge into the air, with the inner 
face of the plate, in which the orifice is pierced, plane, and with sharp 
inner corners, so that the escaping vein only touches these inner edges. 
These tables are abridged below. The coefficient c is to be used in the 
formulae (3) and (4) above. For formulae (1) and (2) use the coefficient 
C found from the values of the ratios C/c above. 



Values of Coefficient c for Vertical Orifices with Sharp Edges, 
Full Contraction, and Free Discharge into Air. (Hamilton 
Smith, Jr.) 



I'saj 


Square Orifices. Length of the Side of the Square, in feet. 


HI 


.02 


.03 


.04 


.05 


.07 


.10 


.12 


.15 


.20 


.40 


.60 


.80 


1.0 


Woo 










"7628 
.623 


T621 

.617 


.616 
.613 


T6TT 
.610 












0.4 






.643 
.636 


.637 
.630 




0.6 


660 


.645 


.605 


.601 


.598 


.596 




1.0 


648 


.636 


.628 


.622 


.618 


.613 


,610 


.608 


.605 


.603 


.601 


.600 


.599 


3.0 


632 


.622 


.616 


.612 


.609 


.607 


606 


.606 


.605 


.605 


.604 


.603 


.603 


6.0 


623 


.616 


.612 


.609 


607 


.605 


605 


.605 


.604 


.604 


.603 


.602 


.602 


10. 


616 


.611 


.608 


.606 


.605 


604 


.604 


.603 


.603 


.603 


.602 


.602 


.601 


20. 


606 


605 


604 


603 


602 


607, 


602 


602 


602 


,601 


.601 


.601 


.600 


100. (?) 


.599 


.598 


.598 


.598 


.598 


.598 


.598 


.598 


.598 


.598 


.598 


.598 


.598 









Circular Orifices. 


Diameters, in feet. 








H. 


.02 


.03 


.04 


.05 


.07 


.10 


.12 


.15 


.20 


.40 


.60 


.80 


1.0 


0.4 








.637 
,624 


.628 
.618 


.618 
.613 


.612 
,609 


.606 
.605 












0.6 


655 


.640 


,630 


.601 


596 


.593 


.590 




1.0 


644 


.631 


.623 


.617 


.612 


.608 


.605 


.603 


.600 


.598 


.595 


.593 


.591 


2. 


632 


.621 


.614 


610 


607 


.604 


.601 


,600 


.599 


.599 


.597 


.596 


.593 


4. 


,623 


.614 


609 


605 


603 


.602 


.600 


.599 


.599 


.598 


.597 


.597 


.596 


6. 


618 


.611 


607 


604 


602 


600 


.599 


.599 


.598 


.598 


.597 


.396 


.596 


10. 


611 


.606 


603 


601 


,599 


.598 


.598 


.597 


.597 


.597 


.596 


.596 


.595 


20. 


601 


600 


599 


598 


597 


596 


596 


596 


596 


596 


,596 


.595 


.594 


50.(?) 


596 


596 


595 


595 


594 


.594 


594 


.594 


.594 


.594 


.594 


.593 


.593 


100. (?) 


.593 


.593 


.592 


.592 


.592 


.592 


.592 


.592 .592 


.592 


.592 


.592 


.592 



HYDRAULIC FORMULA. 699 



HYDRAULIC FORMULAE. — FLOW OF WATER IN OPEN AND 
CLOSED CHANNELS. 

Flow of Water in Pipes. — The quantity of water discharged 
through a pipe depends on the "head"; that is, the vertical distance 
between the level surface of still water in the chamber at the entrance 
end of the pipe and the level of the center of the discharge end of the 
pipe; also upon the length of the pipe, upon the character of its interior 
surface as to smoothness, and upon the number and sharpness of the 
bends; but it is independent of the position of the pipe, as horizontal, . 
or inclined upwards or downwards. 

The head, instead of being an actual distance between levels, may be 
caused by pressure, as by a pump, in which case the head is calculated 
as a vertical distance corresponding to the pressure, 1 lb. per sq. in. 
= 2.309 ft. head, or 1 ft. head = 0.433 lb. per sq. in. 

The total head operating to cause flow is divided into three parts: 

1. The velocity -head, which is the height through which a body must 
fall in vacuo to acquire the velocity with which the water flows into the 
pipe = v 2 *■ 2 g, in which v is the velocity in ft. per sec. and 2 g = 64.32; 

2. the entry-head, that required to overcome the resistance to entrance 
to the pipe. With sharp-edged entrance the entry-head = about 1/2 the 
velocity-head; with smooth rounded entrance the entry-head is inap- 
preciable; 3. the friction-head, due to the frictional resistance to flow 
within the pipe. 

In ordinary cases of pipes of considerable length the sum of the entry 
and velocity heads required scarcely exceeds 1 foot. In the case of 
long pipes with low heads the sum of the velocity and entry heads is 
generally so small that it may be neglected. 

General Formula for Flow of Water in Pipes or Conduits. 



Mean velocity in ft. per sec. = c v'mean hydraulic radius X slope 

Do. for pipes running full = c \ X slope, 

in which c is a coefficient determined by experiment. (See pages following.) 



wet perimeter 



In pipes running full, or exactly half full, and in semicircular open 
channels running full it is equal to 1/4 diameter. 

The slope = the head (or pressure expressed as a head, in feet) 

-5- length of pipe measured in a straight line from end to end. 

In open channels the slope is the actual slope of the surface, or its 
fall per unit of length, or the sine of the angle of the slope with the horizon. 

Chezy's Formula: v = fVrVs = f v «; r = mean hydraulic 
radius, s = slope = head ■*- length, v = velocity in feet per second, all 
dimensions in feet. 

Quantity of Water Discharged. — If Q = discharge in cubic feet 
per second and a = area of channel, Q = av = ac VVs. 

a Vr is approximately proportional to the discharge. It is a maxi- 
mum at 308° of the circumference, corresponding to 19/20 of the diameter, 
and the flow of a conduit 19/20 full is about 5 per cent greater than that of 
one completely filled. 

Values of the Coefficient c. (Chiefly condensed from P. J. Flynn 
on Flow of Water.) — Almost all the old hydraulic formulae for finding the 



700 



HYDRAULICS. 



mean velocity in open and closed channels have constant coefficients, 
and are therefore correct for only a small range of channels. They have 
often been found to give incorrect results with disastrous effects. Gan- 
guillet and Kutter thoroughly investigated the American, French, and 
other experiments, and they gave as the result of their labors the formula 
now generally known as Kutter's formula. There are so many varying 
conditions affecting the flow of water, that all hydraulic formulae are 
only approximations to the correct result. 

When the surface-slope measurement is good, Kutter's formula will 
give results seldom exceeding 71/2% error, provided the rugosity coeffi- 
cient of the formula is known for the site. For small open channels 
Darcy's and Bazin's formulae, and for cast-iron pipes Darcy's formulae, 
are generally accepted as being approximately correct. 



Table giving Fall in Feet per Mile, the Distance on Slope corre- 
sponding to a Fall of 1 Ft., and also the Values of S and V$ 
for Use in the Formula V = C Vrs. . 

s = H -h L = sine of angle of slope = fall of water-surface (H), In 
any distance (L), divided by that distance. 



Fall in 


Slope, 


Sine of 


v7. 


Fall in 


Slope, 


Sine of 


V7. 


Feet 


1 Foot 


Slope, 


Feet 


1 Foot 


Slope, 


per Mi. 


in 


s. 




per Mi. 


in 


s. 




0.25 


21120 


0.0000473 


0.006881 


17 


310.6 


0.0032197 


0.056742 


.30 


17600 


.0000568 


.007538 


18 


293.3 


.0034091 


.058388 


.40 


13200 


.0000758 


.008704 


19 


277.9 


.0035985 


.059988 


.50 


10560 


.0000947 


.009731 


20 


264 


.0037879 


.061546 


.60 


8800 


.0001136 


.010660 


22 


240 


.0041667 


.064549 


.702 


7520 


.0001330 


.011532 


24 


220 


.0045455 


.067419 


.805 


6560 


.0001524 


.012347 


26 


203.1 


.0049242 


.070173 


.904 


5840 


.0001712 


.013085 


28 


188.6 


.0053030 


.072822 


1 


5280 


.0001894 


.013762 


30 


176 


.0056818 


.075378 


1.25 


4224 


.0002367 


.015386 


35.20 


150 


.0066667 


.081650 


1.5 


3520 


.0002841 


.016854 


40 


132 


.0075758 


.087039 


1.75 


3017 


.0003314 


.018205 


44 


120 


.0083333 


.091287 


2 


2640 


.0003788 


.019463 


48 


110 


.0090909 


.095346 


2.25 


2347 


.0004261 


.020641 


52.8 


100 


.010 


.1 


2.5 


2112 


.0004735 


.021760 


60 


88 


.0113636 


.1066 


2.75 


1920 


.0005208 


.022822 


66 


80 


.0125 


.111803 


3 


1760 


.0005682 


.023837 


70.4 


75 


.0133333 


.115470 


3.25 


1625 


.0006154 


.024807 


80 


66 


.0151515 


.123091 


3.5 


1508 


.0006631 


.025751 


88 


60 


.0166667 


.1291 


3.75 


1408 


.0007102 


.026650 


96 


55 


.0181818 


. 134839 


4 


1320 


.0007576 


.027524 


105.6 


50 


.02 


.141421 


5 


1056 


.0009470 


.030773 


120 


44 


.0227273 


.150756 


6 


880 


.0011364 


.03371 


132 


40 


.025 


.158114 


7 


754.3 


.0013257 


.036416 


160 


33 


.0303030 


.174077 


8 


660 


.0015152 


.038925 


220 


24 


.0416667 


.204124 


9 


586.6 


.0017044 


.041286 


264 


20 


.05 


.223607 


10 


528 


.0018939 


.043519 


330 


16 


.0625 


.25 


11 


443.6 


.0020833 


.045643 


340 


12 


.0833333 


.288675 


12 


440 


.0022727 


.047673 


528 


10 


.1 


.316228 


13 


406.1 


.0024621 


.04962 


660 


8 


.125 


.353553 


14 


377.1 


.0026515 


.051493 


880 


6 


.1666667 


.408248 


15 


352 


.0028409 


.0533 


1056 


5 


.2 


.447214 


16 


330 


.0030303 


.055048 


1320 


4 


.25 


.5 



HYDRAULIC FORMULA. 



701 



Values of V r for Circular Pipes, Sewers, and Conduits of Different 
Diameters. * 



running full or exactly half full. 



Diam., 


v7 


Diam., 


V7 


Diam., 


V7 


Diam., 


V r 


ft. in. 


in Feet. 


ft. in. 


in Feet. 


ft. 


in. 


in Feet. 


ft. in. 


in Feet. 


3/8 


0.088 


2 


0.707 


4 


6 


1.061 


9 


1.500 


1/2 


.102 


2 1 


.722 


4 


7 


1.070 


9 3 


1.521 


3/4 


.125 


2 2 


.736 


4 


8 


1.080 


9 6 


1.541 


1 


.144 


2 3 


.750 


4 


9 


1.089 


9 9 


1.561 


H/4 


.161 


2 4 


.764 


4 


10 


1.099 


10 


1.581 


H/2 


.177 


2 5 


.777 


4 


11 


1.109 


10 3 


1.601 


13/4 


.191 


2 6 


.790 


5 




1.118 


10 6 


1.620 


2 


.204 


2 7 


.804 


5 


1 


1.127 


10 9 


1.639 


21/2 


.228 


2 8 


.817 


5 


2 


1.137 


11 


1.658 


3 


.251 


2 9 


.829 


5 


3 


1.146 


11 3 


1.677 


4 


.290 


2 10 


.842 


5 


4 


1.155 


11 6 


1.696 


5 


.323 


2 11 


.854 


5 


5 


1.164 


11 9 


1.714 


6 


.354 


3 


.866 


5 


6 


1.173 


12 


1.732 


7 


.382 


3 1 


.878 


5 


7 


1.181 


12 3 


1.750 


8 


.408 


3 2 


.890 


5 


8 


1.190 


12 6 


1.768 


9 


.433 


3 3 


.901 


5 


9 


1.199 


12 9 


1.785 


10 


.456 


3 4 


.913 


5 


10 


1.208 


13 


1.803 


11 


.479 


3 5 


.924 


5 


11 


1.216 


13 3 


1.820 


1 


.500 


3 6 


.935 


6 




1.225 


13 6 


1.837 


1 1 


.520 


3 7 


.946 


6 


3 


1.250 


14 


1.871 


1 2 


.540 


3 8 


.957 


6 


6 


1.275 


14 6 


1.904 


1 3 


.559 


3 9 


.968 


6 


9 


1.299 


15 


1.936 


1 4 


.577 


3 10 


.979 


7 




1.323 


15 6 


1.968 


1 5 


.595 


3 11 


.990 


7 


3 


1.346 


16 


2. 


1 6 


.612 


4 


1. 


7 


6 


1.369 


16 6 


2.031 


1 7 


.629 


4 1 


1.010 


7 


9 


1.392 


17 


2.061 


1 8 


.646 


4 2 


1.021 


8 




1.414 


17 6 


2.091 


1 9 


.661 


4 3 


1.031 


8 


3 


1.436 


18 


2.121 


1 10 


.677 


4 4 


1.041 


8 


6 


1.458 


19 


2.180 


1 11 


.692 


4 5 


1.051 


8 


9 


1.479 


20 


2.236 



Kutter's Formula for measures in feet is 



0.00281\ s . 



Vr\ 



<V^s\ 



in which v = mean velocity in feet per second ; r = 



= hydraulic mean 



depth in feet = area of cross-section in square feet divided by wetted 
perimeter in lineal feet; s = fall of water-surface (h) in any distance (I) 

divided by that distance, = r ,= sine of slope; n = the coefficient of 

rugosity, depending on the nature of the lining or surface of the channel. 
If we let the first term of the right-hand side of the equation equal c, we 
have Chezy's formula, v = c ^rs = c X Vp X Vs. 

Values, of « in Kutter's Formula. — The accuracy of Kutter's for- 
mula depends, in a great measure, on the proper selection of the coefficient 



702 HYDRAULICS. 



of roughness n. Experience is required in order to give the right value to 
this coefficient, and to this end great assistance can be obtained, in making 
this selection, by consulting and comparing the results obtained from 
experiments on the flow of water already made in different channels. 

In some cases it would be well to provide for the contingency of future 
deterioration of channel, by selecting a high value of n, as, for instance, 
where a dense growth of weeds is likely to occur in small channels, and 
also where channels are likely not to be kept in a state of good repair. 

The following table, giving the value of n for different materials, is 
compiled from Kutter, Jackson, and Hering, and this value of n applies 
also in each instance to the surfaces of other materials equally rough. 

Value of n in Kutter's Formula for Different Channels. 

n = .009, well-planed timber, in perfect order and alignment; otherwise, 
perhaps .01 would be suitable. 

n = .010, plaster in pure cement; planed timber; glazed, coated, or 
enameled stoneware and iron pipes; glazed surfaces of every sort in 
perfect order. 

n = .011, plaster in cement with one-third sand, in good condition; 
also for iron, cement, and terra-cotta pipes, well joined, and in best order. 

n = .012, unplaned timber, when perfectly continuous on the inside; 
flumes. 

n = .013, ashlar and well-laid brickwork; ordinary metal; earthen and 
stoneware pipe in good condition, but not new; cement and terra-cotta 
pipe not well jointed nor in perfect order, plaster and planed wood in 
imperfect or inferior condition; and, generally, the materials mentioned 
with n = .010, when in imperfect or inferior condition. 

n = .015, second class or rough-faced brickwork; well-dressed stone- 
work; foul and slightly tuberculated iron; cement and terra-cotta pipes, 
with imperfect joints- and in bad order; and canvas lining on wooden 
frames. 

n = .017, brickwork, ashlar, and stoneware in an inferior condition; 
tuberculated iron pipes; rubble in cement or plaster in good order; fine 
gravel, well rammed, 1/3 to 2/3 inch diameter; and, generally, the materials 
mentioned with n = .013 when in bad order and condition. 

n = .020, rubble in cement in an inferior condition; coarse rubble, 
rough set in a normal condition; coarse rubble set dry: ruined brickwork 
and masonry; coarse gravel well rammed, from 1 to 11/3 inch diameter; 
canals with beds and banks of very firm, regular gravel, carefully trimmed 
and rammed in defective places ; rough rubble with bed partially covered 
with silt and mud; rectangular wooden troughs with battens on the 
inside two inches apart; trimmed earth in perfect order. 

n = .0225, canals in earth above the average in order and regimen. 

n = .025, canals and rivers in earth of tolerably uniform cross-section; 
slope and direction, in moderately good order and regimen, and free from 
stones and weeds. 

n = .0275, canals and rivers in earth below the average in order and 
regimen. 

n = .030, canals and rivers in earth in rather bad order and regimen, 
having stones and weeds occasionally, and obstructed by detritus. 

n = .035, suitable for rivers and canals with earthen beds in bad order 
and regimen, and having stones and weeds in great quantities. 

n = .05, torrents encumbered with detritus. 

Kutter's formula has the advantage of being easily adapted to a change 
in the surface of the pipe exposed to the flow of water, by a change in 
the value of n. For cast-iron pipes it is usual to use n = .013 to provide 
for the future deterioration of the surface. _ _ 

Reducing Kutter's formula to the form v = cX ^r X ^s, and taking 
n, the coefficient of roughness in the formula, = .011, .012, and .013, and 
s = .001, we have the following values of the coefficient c of different 
diameters of conduit. 



HYDRAULIC FORMULAE. 



703 



Talues of c in Formula » = cX ^r X v * for Metal Pipes and 
Moderately Smooth Conduits Generally. 

By Kutter's Formula. (# = .001 or greater.) 



Diameter. 


ti=.011 


w = .012 


n=.013 


Diameter. 


71= .011 


n=.012 


n= .013 


ft. in. 
1 


c= 
47.1 
61.5 
77.4 
87.4 
105.7 
116.1 
123.6 
133.6 
140.4 
145.4 
149.4 


c = 


c = 


ft. 
7 
8 
9 
10 
11 
12 
14 
16 
18 
20 


c= 

152.7 

155.4 

157.7 

159.7 

161.5 

163 

165.8 

168 

169.9 

171.6 


c= 

139.2 

141.9 

144.1 

146 

147.8 

149.3 

152 

154.2 

156.1 

157.7 


c= 
127 9 


2 






130 4 


4 






132.7 


6 
1 

1 6 
2 
3 
4 
5 
6 


77.5 
94.6 
104.3 
111.3 
120.8 
127.4 
132.3 
136.1 


69.5 
85.3 
94.4 
101.1 
110.1 
116.5 
121.1 
124.8 


134.5 
136.2 
137.7 
140.4 
142.1 
144.4 
146 













For circular pipes the hydraulic mean depth r equals 1/4 of the diameter. 

According to Kutter's formula the value of c, the coefficient of discharge, 
is the same for all slopes greater than 1 in 1000; that is, within these 
limits c is constant. We further find that up to a slope of 1 in 2640 
the value of c is, for all practical purposes, constant, and even up to a 
slope of 1 in 5000 the difference in the value of c is very little. This is 
exemplified in the following: 



Value of c for Different Values of vV and * in Kutter 
with « = .013. 


's Formula, 


Vr 


Slope. 
1 in 1000 


Slope. 
1 in 2500 


Slope. 
1 in 3333.3 


Slope. 
1 in 5000 


Slope. 
! in 10,000 


0.6 
1 

2 


93.6 
116.5 
142.6 


91.5 
115.2 
142.8 


90.4 
114.4 
143.0 


88.4 
113.2 
143.1 


83.3 
109.7 
143.8 



The reliability of the values of the coefficient of Kutter's formula for 
pipes of less than 6 in. diameter is considered doubtful. (See note under 
table on page 704.) 



Values of c 


for Earthen Channels, by Kutter's Formula, for Use 






in Formula 


v = t 


V rs . 






Coefficient of Roughness, 


Coefficient of Roughness, 






n=.0225. 






n=.035. 






vV in feet. 




^/r in feet. 




0.4 


1.0 


1.8 


2.5 


4.0 


0.4 


1.0 


1.8 


2.5 


4.0 


Slope, 1 in 


c 


c 


c 


c 


c 


c 


c 


c 


c 


c 


1,000 


35.7 


62.5 


80.3 


89.2 


99.9 


19.7 


37.6 


51.6 


59.3 


69.2 


1,250 


35.5 


62.3 


80.3 


89.3 


100.2 


19.6 


37.6 


51.6 


59.4 


69.4 


1,667 


35.2 


62.1 


80.3 


89.5 


100.6 


19.4 


37.4 


51.6 


59.5 


69.8 


2,500 


34.6 


61.7 


80.3 


89.8 


101.4 


19.1 


37.1 


51.6 


59.7 


70.4 


3,333 


34. 


61.2 


80.3 


90.1 


102.2 


18.8 


36.9 


51.6 


59.9 


71 


5,000 


33. 


60.5 


80.3 


90.7 


103.7 


18.3 


36.4 


51.6 


60.4 


72.2 


7,500 


31.6 


59.4 


80.3 


91.5 


106.0 


17.6 


35.8 


51.6 


60.9 


73.9 


10,000 


30.5 


58.5 


80.3 


92.3 


107.9 


17.1 


35.3 


51.6 


60.5 


75.4 


15,840 


28.5 


56.7 


80.2 


93.9 


112.2 


16.2 


34.3 


51.6 


62.5 


78.6 


20,000 


27.4 


55.7 


80.2 


94.8 


115.0 


15.6 


33.8 


51.5 


63.1 


80.6 



704 



HYDRAULICS. 



Darcy's Formula for clean iron pipes under pressure is 
rs \ 1/2 



0.00007726 +- 



Darcy's formula, as given by J. B. Francis, C. E., for old cast-iron pipe, 
lined with deposit and under pressure, is 



?-<$. 



.00082 (12rf + l/ 



in which d = diameter in feet. 

For Pipes Less_ than 5 inches in Diameter, coefficients (c) in the 
formula v = c ^rs, from the formula of Darcy, Kutter, and Fanning. 



Diam. 

in 
inches. 


Darcy, 

for Clean 

Pipes. 


Kutter, 

for 
«=.011 
s=.001 


Fanning, 

for Clean 

Iron 

Pipes. 


Diam. 

in 
inches. 


Darcy, 

for Clean 

Pipes. 


Kutter, 

for 
n=.011 
s= .001 


Fanning, 

for Clean 

Iron 

Pipes. 


t 


59.4 
65.7 

74.5 
80.4 
84.8 
88.1 


32. 

36.1 

42.6 

47.4 

51.9 

55.4 




13/4 

2 

21/2 

4 

5 


90.7 
92.9 
96.1 
98.5 
101.7 
103.8 


58.8 

61.5 

66. 

70.1 

77.4 

82.9 


92.5 
94.8 


, 3/ « 

U/4 






80.4 


96.6 
103.4 


11/2 


88. 







Mr. Flynn, in giving the above table, says that the facts show that the 
coefficients diminish from a diameter of 5 inches to! smaller diameters, 
and it is a safer plan to adopt coefficients varying with the diameter than 
a constant coefficient. No opinion is advanced as to what coefficients 
should be used with Kutter 's formula for small diameters. 



VELOCITY OF WATER IN OPEN CHANNELS. 

Irrigation Canals. — The minimum mean velocity required to pre- 
vent the deposit of silt or the growth of aquatic plants is in Northern 
India taken at 1 1/2 feet per second. It is stated that in America a higher 
velocity is required for this purpose, and it varies from 2 to 31/2 feet per 
second. The maximum allowable velocity will vary with the nature of 
the soil of the bed. A sandy bed will be disturbed if the velocity exceeds 
3 feet per second. Good loam with not too much sand will bear a velocity 
of 4 feet per second. The Cavour Canal in Italy, over a gravel bed, has a 
velocity of about 5 per second. (Flynn's "Irrigation Canals.") 

Mean Surface and Bottom Velocities. — According to the formula 
of Bazin, 

v= v max -25.4 ^rs; v = v&+ 10.87 vVs. 

.'. vjj = v — 10.87 "^rs, in which v = mean velocity in feet per second, 
r max = maximum surface velocity in feet per second, 1^= bottom velocity 
in feet per second, r = hydraulic mean depth in feet = area of cross-section 
in square feet divided by wetted perimeter in feet, s = sine of slope. 

The least velocity, or that of the particles in contact with the bed, is 
almost as much less than the mean velocity as the greatest velocity is 
greater than the mean. 

Rankine states that in ordinary cases the velocities may be taken as 
bearing to each other nearly the proportions of 3, 4, and 5. In very slow 
currents they are nearly as 2, 3, and 4, 



VELOCITY OF WATER IN OPEN CHANNELS. 



705 



Safe Bottom and Mean Velocities. — Ganguillet & Kutter give the 
following table of safe bottom and mean velocity in channels, calculated 
from the formula v = v^+ 10.87 ^rs: 



Material of Channel. 


Safe Bottom Velocity 
Vf), in feet per second. 


Mean Velocity v, in 
feet per second. 




0.249 
0.499 
1.000 
1.998 
2.999 
4.003 
4.988 
6.006 
10.009 


0.328 




0.656 




1.312 




2.625 


Pebbles 


3.938 




5.579 


Conglomerate, soft slate. . . . 


6.564 
8.204 




13.127 







Ganguillet & Kutter state that they are unable for want of observations 
to judge how far these figures are trustworthy. They consider them to be 
rather disproportionately small than too large, and therefore recommend 
them more confidently. 

Water flowing at a high velocity and carrying large quantities of silt is 
very destructive to channels, even when constructed of the best masonry. 

Resistance of Soils to Erosion by Water. — W. A. Burr, Eng 1 g 
News, Feb. 8, 1894, gives a diagram showing the resistance of various soils 
to erosion by flowing water. 

Experiments show that a velocity greater than 1.1 feet per second will 
erode sand, while pure clay will stand a velocity of 7.35 feet per second. 
The greater the proportion of clay carried by any soil, the higher the per- 
missible velocity. Mr. Burr states that experiments have shown that the 
line describing the power of soils to resist erosion is parabolic. From his 
diagram the following figures are selected as representing different classes 
of soils: 

Pure sand resists erosion by flow of 1.1 feet per second. 

Sandy soil, 15% clay 1.2 

Sandy loam, 40 % clay 1.8 

Loamy soil, 65% clay 3.0 

Clay loam, 85% clay 4.8 

Agricultural clay, 95% clay 6.2 

Clay 7 . 35 

Abrading and Transporting Power of Water. — Prof. J. LeConte, 
in his "Elements of Geology," states: 

The erosive power of water, or its power of overcoming cohesion, 
varies as the square of the velocity of the current. 

The transporting power of a current varies as the sixth power of the 
velocity. * * * If the velocity therefore be increased ten times, the 
transporting power is increased 1,000,000 times. A current running 
three feet per second, or about two miles per hour, will bear fragments 
of stone of the size of a hen's egg, or about three ounces weight. A 
current of ten miles an hour will bear fragments of one and a half tons, 
and a torrent of twenty miles an hour will carry fragments of 100 tons. 

The transporting power of water must not be confounded with its 
erosive power. The resistance to be overcome in the one case is weight, 
in the other, cohesion; the latter varies as the square: the former as the 
sixth power of the velocity. 

In many cases of removal of slightly cohering material, the resistance 
is a mixture of these two resistances, and the power of removing mate- 
rial will vary at some rate between v 2 and v 6 . 

Baldwin Latham has found that in order to prevent deposits of sewage 
silt in small sewers or drains, such as those from 6 inches to 9 inches 
diameter, a mean velocity of not less than 3 feet per second should be 
produced. Sewers from 12 to 24 inches diameter should have a velocity 



706 HYDRAULICS. 

of not less than 21/2 feet per second, and in sewers of larger dimensions 
in no case should the velocity be less than 2 feet per second. 

The specific gravity of the materials has a marked effect upon the 
mean velocities necessary to move them. T. E. Blackwell found that 
coal of a sp. gr. of 1.26 was moved by a current of from 1.25 to 1.50 ft. 
per second, while stones of a sp. gr. of 2.32 to 3.00 required a velocity of 
2.5 to 2.75 ft. per second. 

Chailly gives the following formula for finding the velocity required to 
move rounded stones or shingle: __ 

9 = 5.67 Vag, 
in which v = velocity of water in feet per second, a = average diameter 
in feet of the body to be moved, g = its specific gravity. 

Geo. Y. Wisner, Eng'g News, Jan. 10, 1895, doubts the general accuracy 
of statements made by many authorities concerning the rate of flow of 
a current and the size of particles which different velocities will move. 
He says: 

The scouring action of any river, for any given rate of current, must 
be an inverse function of the depth. The fact that some engineer has 
found that a given velocity of current on some stream of unknown depth 
will move sand or gravel has no bearing whatever on what may be ex- 
pected of currents of the same velocity in streams of greater depths. In 
channels 3 to 5 ft. deep a mean velocity of 3 to 5 ft. per second may 
produce rapid scouring, while in depths of 18 ft. and upwards current 
velocities of 6 to 8 ft. per second often have no effect whatever on the 
channel bed. 

Grade of Sewers. — The following empirical formula is given in Bau- 
meister's "Cleaning and Sewerage of Cities," for the minimum grade 
for a sewer of clear diameter equal to d inches, and either circular or 
oval in section: 

Minimum grade, in per cent, = - • 

o d + ou 

As the lowest limit of grades which can be flushed, 0.1 to 0.2 per cent 
may be assumed for sewers which are sometimes dry, while 0.3 per cent 
is allowable for the trunk sewers in large cities. The sewers should run 
dry as rarely as possible. 

FLOW OF WATER — EXPERIMENTS AND TABLES. 

The Flow of Water through New Cast-iron Pipe was measured by 
S. Bent Russell, of the St. Louis, Mo., Water-works. The pipe was 12 
inches in diameter, 1631 feet long, and laid on a uniform grade from 
end to end. Under an average total head of 3.36 feet the flow was 
43,200 cubic feet in seven hours; under an average head of 3.37 feet the 
flow was the same; under an average total head of 3.41 feet the flow 
was 46,700 cubic feet in 8 hours and 35 minutes. Making allowance for 
loss of head due to entrancejand to curves, it was found that the value 
of c in the formula v = c vVs was from 88 to 93. (Eng'g Record, April 
14, 1894.) 

Flow of Water in a 20-inch Pipe 75,000 Feet Long. — A com- 
parison of experimental data with calculations bv different formulae is 
given by Chas. B. Brush, Trans. A. S. C. E., 1888. The pipe experi- 
mented with was that supplying the city of Hoboken, N. J. 

Results Obtained by the Hackensack Water Co., from 1882-1887, 
in Pumping Through a 20-in. Cast-iron Main 75,000 Feet Long. 

Pressure in lbs. per sq. in. at pumping-station: 

95 100 105 110 115 120 125 130 

Total effective head in feet: 

55 66 77 89 100 

Discharge in U. S. gallons in 24 hours, 1 = 
2,848 3,165 3,354 3,566 3,804 
Theoretical discharge bv Darcy's formula: 
* 2,743 3,004 3,244 3,488 3,699 
Actual velocity in main in feet per second: 
2.00 2.24 2.36 2.52 2.68 



112 
1000: 
3,904 


123 
4,116 


135 
4,255 


3,915 


4,102 


4,297 


2.76 


2.92 


3.00 



FLOW OF WATER. 



707 



Flow of Water in Circular Pipes, Sewers, etc., Flowing Full. 
Based on Kutter's Formula, with n = .013. 

Discharge in cubic feet per second. 





Slope, or Head Divided by Length of Pipe. 




Diam- 










eter. 




















1 in 40 


1 in 70 


I in 100 


1 in 200 


1 in 300 


1 in 400 


1 in 500 


1 in 600 


5 in. 


0.456 


0.344 


0.288 


0.204 


0.166 


0.144 


0.137 


0.118 


6 " 


0.762 


0.576 


0.482 


0.341 


0.278 


0.241 


0.230 


0.197 


7 " 


1.17 


0.889 


0.744 


0.526 


0.430 


0.372 


0.355 


0.304 


8 " 


1.70 


1.29 


1.08 


0.765 


0.624 


0.54 


0.516 


0.441 


9 " 


2.37 


1.79 


1.50 


1.06 


0.868 


0.75 


0.717 


0.613 


s= 


1 in 60 


1 in 80 


1 in 100 


1 in 200 


1 in 300 


1 in 400 


1 in 500 


1 in 600 


10 in. 


2.59 


2.24 


2.01 


1.42 


1.16 


1.00 


0.90 


0.82 


11 " 


3.39 


2.94 


2.63 


1.86 


1.52 


1.31 


1.17 


1.07 


12 " 


4.32 


3.74 


3.35 


2.37 


1.93 


1.67 


1.5 


1.37 


13 " 


5.38 


4.66 


4.16 


2.95 


2.40 


2.08 


1.86 


1.70 


14 " 


6.60 


5.72 


5.15 


3.62 


2.95 


2.57 


2.29 


2.09 


s = 


1 in 100 


1 in 200 


1 in 300 


1 in 400 


1 in 500 


1 in 600 


1 in 700 


1 in 800 


15 in. 


6.18 


4.37 


3.57 


3.09 


2.77 


2.52 


2.34 


2.19 


16 " 


7.38 


5.22 


4.26 


3.69 


3.30 


3.01 


2.79 


2.61 


18 " 


10.21 


7.22 


5.89 


5.10 


4.56 


4.17 


3.86 


3.61 


20 " 


13.65 


9.65 


7.88 


6.82 


6.10 


5.57 


5.16 


4.83 


22 " 


17.71 


12.52 


10.22 


8.85 


7.92 


7.23 


6.69 


6.26 


s = 


1 in 200 


1 in 400 


1 in 600 


1 in 800 


1 in 1000 


1 in 1250 


1 in 1500 


1 in 1800 


2ft. 


15.88 


11.23 


9.17 


7.94 


7.10 


6.35 


5.80 


5.29 


2ft. 2in. 


19.73 


13.96 


11.39 


9.87 


8.82 


7.89 


7.20 


6.58 


2 " 4" 


24.15 


17.07 


13.94 


12.07 


10.80 


9.66 


8.82 


8.05 


2 " 6 " 


29.08 


20.56 


16.79 


14.54 


13.00 


11.63 


10.62 


9 69 


2 " 8 " 


34.71 


24.54 


20.04 


17.35 


15.52 


13.88 


12.67 


11.57 


s = 


1 in 500 


1 in 750 


1 in 1000 


1 in 1250 


lin 1500 


1 in 1750 


1 in 2000 


1 in 2500 


2ft. lOin. 


25.84 


21.10 


18.27 


16.34 


14.92 


13.81 


12.92 


11.55 


3 " 


30.14 


24.61 


21.31 


19.06 


17.40 


16.11 


15.07 


13.48 


3 " 2in. 


34.90 


28.50 


24.68 


22.07 


20.15 


18.66 


17.45 


15.61 


3 " 4 " 


40.08 


32.72 


28.34 


25.35 


23.14 


21.42 


20.04 


17.93 


3 " 6 " 


45.66 


37.28 


32.28 


28.87 


26.36 


24.40 


22.83 


20.41 


s= 


1 in 500 


1 in 750 


lin 1000 


1 in 1250 


lin 1500 


lin 1750 


1 in 2000 


1 in 2500 


3ft. 8in. 


51.74 


42.52 


36.59 


32.72 


29.87 


27.66 


25.87 


23.14 


3 " 10 " 


58.36 


47.65 


41.27 


36.91 


33.69 


31.20 


29.18 


26.10 


4 " 


65.47 


53.46 


46.30 


41.41 


37.80 


34.50 


32.74 


29.28 


4 " 6in. 


89.75 


73.28 


63.47 


56.76 


51.82 


47.97 


44.88 


40.14 


5 " 


118.9 


97.09 


84.08 


75.21 


68.65 


63.56 


59.46 


53.18 


s = 


1 in 750 


1 in 1000 


lin 1500 


1 in 2000 


1 in 2500 


1 in 3000 


1 in 3500 


1 in 4000 


5ft. 6in. 


125.2 


108.4 


88.54 


76.67 


68.58 


62.60 


57.96 


54.21 


6 " 


157.8 


136.7 


' 111.6 


96.66 


86.45 


78.92 


73.07 


68.35 


6 " 6 " 


195.0 


168.8 


137.9 


119.4 


106.8 


97.49 


90.26 


84.43 


7 " 


237.7 


205.9 


168.1 


145.6 


130.2 


118.8 


110.00 


102.9 


7 " 6 " 


285.3 


247.1 


201.7 


174.7 


156.3 


142.6 


132.1 


123.5 


s= 


1 in 1 500 


1 in 2000 


1 in 2500 


1 in 3000 


1 in 3500 


1 in 4000 


1 in 4500 


1 in 5000 


8 ft. 


239.4 


207.3 


195.4 


169.3 


156.7 


146.6 


138.2 


131.1 


8 " 6in. 


281.1 


243.5 


217.8 


198.8 


184.0 


172.2 


162.3 


154.0 


9 " 


327.0 


283.1 


253.3 


231.2 


214.0 


200.2 


188.7 


179.1 


9 " 6 " 


376.? 


326.4 


291.9 


266.5 


246.7 


230.8 


217.6 


206.4 


10 " 


431.4 


373.6 


334.1 


305.0 


282.4 


264.2 


249.1 


236.3 



708 



HYDKAULICS. 



For U. S. gallons multiply the figures in the table by 7.4805. 

For a given diameter the quantity of flow varies as the square root of 
the sine of the slope. From this principle the flow for other slopes than 
those given in the table may be found. Thus, what is the flow for a 
pipe 8 feet diameter, slope 1 in 125? From the table take Q = 207.3 
for slope 1 in 2000. The given slope 1 in 125 is to 1 in 2000 as 16 to 1, 
and the square root of this ratio is 4 to 1. Therefore the flow required 
is 207.3 X 4 = 829.2 cu. ft. 



Circular Pipes, Conduits, etc., Flowing Full. 

Values of the factor ac "^r in the formula Q = ac Vr X "^s corre- 
sponding to different values of the coefficient of roughness, n. (Based on 
Kutter's formula.) 









Value of ac V r. 






Diam. 














ft. in. 
















n=.0l0. 


w= .011. 


n=.012. 


w=.013. 


n=.015. 


n=.0l7. 


6 


6.906 


6.0627 


5.3800 


4.8216 


3.9604 


3.329 


9 


21.25 


18.742 


16.708 


15.029 


12.421 


10.50 


1 


46.93 


41 .487 


37.149 


33.497 


27.803 


23.60 


1 3 


86.05 


76.347 


68.44 


61.867 


51.600 


43.93 


1 6 


141.2 


125.60 


112.79 


102.14 


85.496 


72.99 


1 9 


214.1 


190.79 


171.66 


155.68 


130.58 


III. 8 


2 


307.6 


274.50 


247.33 


224.63 


188.77 


164 


2 3 


421.9 


377.07 


340.10 


309.23 


260.47 


223.9 


2 6 


559.6 


500.78 


452.07 


411.27 


347.28 


299.3 


2 9 


722.4 


647.18 


584.90 


532.76 


451.23 


388.8 


3 


911.8 


817.50 


739.59 


674.09 


570.90 


493.3 


3 3 


1128.9 


1013.1 


917.41 


836.69 


709.56 


613.9 


3 6 


1374.7 


1234.4 


1118.6 


1021.1 


866.91- 


750.8 


3 9 


1652.1 


1484.2 


1345.9 


1229.7 


1045 


906 


4 


1962.8 


1764.3 


1600.9 


1463.9 


1245.3 


1080.7 


4 6 


2682.1 


2413.3 


2193 


2007 


1711.4 


1487.3 


5 


3543 


3191.8 


2903.6 


2659 


2272.7 


1977 


5 6 


4557.8 


4111.9 


3742.7 


3429 


2934.8 


2557.2 


6 


5731.5 


5176.3 


4713.9 


4322 


3702.3 


3232.5 


6 6 


7075.2 


6394.9 


5825.9 


5339 


4588.3 


4010 


7 


8595.1 


7774.3 


7087 


6510 


5591.6 


4893.2 


7 6 


10296 


9318.3 


8501.8 


7814 


6717 


5884.3 


8 


12196 


11044 


10083 


9272 


7978.3 


6995.3 


8 6 


14298 


12954 


11832 


10889 


9377.9 


8226.7 


9 


16604 


15049 


13751 


12663 


10917 


9580 


9 6 


19118 


17338 


15847 


14597 


12594 


11061 


10 


21858 


19834 


18134 


16709 


14426 


12678 


10 6 


24823 


22534 


20612 


18996 


16412 


14434 


11 


28020 


25444 


23285 


21464 


18555 


16333 


11 6 


31482 


28593 


26179 


24139 


20879 


18395 


12 


35156 


31937 


29254 


26981 


23352 


20584 


12 6 


39104 


35529 


32558 


30041 


26012 


22938 


13 


43307 


39358 


36077 


33301 


28850 


25451 


13 6 


47751 


43412 


39802 


36752 


31860 


28117 


14 


52491 


47739 


43773 


40432 


35073 


30965 


14 6 


57496 


52308 


47969 


44322 


38454 


33975 


15 


62748 


57103 


52382 


48413 


42040 


37147 


16 


74191 


67557 


62008 


57343 


49823 


44073 


17 


86769 


79050 


72594 


67140 


58387 


51669 


18 


100617 


91711 


84247 


77932 


67839 


60067 


19 


115769 


105570 


96991 


89759 


78201 


69301 


20 


132133 


120570 


110905 


102559 


89423 


79259 



FLOW OF WATER IN PIPES. 



Flow of Water in Circular Pipes, Conduits, etc., Flowing under 
Pressure. 

Based on Darcy's formulae for the flow of water through cast-iron 
pipes. With comparison of results obtained by Kutter's formula, with 
n = 0.013. (Condensed from Flynn on Water Power.) 

Values of a, and also the values of the factors c V r and ac vV for use 

in the formulae Q = av; v = c V r x v's, and Q = ac Vr X v s. 

Q = discharge in cubic feet per second, a = area in square feet, v = 
velocity in feet per second, r = mean hydraulic depth, 1/4 diam. for 
pipes running full, s = sine of slope. 

(For values of V$ see page 700.) 







Clean Cast-iron 


Value of 


Old Cast 


-iron Pines 


Size 01 jripe. 


Pipes. 


ac VV by 


Lined with Deposit. 










Kutter's 

Formula, 

when 






d=diam. 
in 


a = area in 
square 


For 
Velocity, 


For Dis- 
charge, 


For 
Velocity, 


For 
Discharge, 


ft. in. 


feet. 


cV r . 


ac v r. 


n=.013. 


c^r. 


ac^7. 


3/8 


.00077 


5.251 


.00403 




3.532 


.00272 


1/2 


.00136 


6.702 


.00914 




4.507 


.00613 


3/4 


.00307 


, 9.309 


.02855 




6.261 


.01922 


1 


.00545 


11.61 


.06334 




7.811 


.04257 


H/4 


.00852 


13.68 


.11659 




9.255 


.07885 


H/2 


.01227 


15.58 


.19115 




10.48 


.12855 


13/ 4 


.01670 


17.32 


.28936 




11.65 


.19462 


2 


.02182 


18.96 


.41357 




12.75 


.27824 


21/2 


.0341 


21.94 


.74786 




14.76 


.50321 


3 


.0491 


24.63 


1.2089 




16.56 


.81333 


4 


.0873 


29.37 


2.5630 




19.75 


1.7246 


3 


.136 


33.54 


4.5610 




22.56 


3.0681 


6 


.196 


37.28 


7.3068 


4.822 


25.07 


4.9147 


7 


.267 


40.65 


10.852 




27.34 


7.2995 


8 


.349 


43.75 


15.270 




29.43 


10.271 


9 


.442 


46.73 


20.652 


15.03 


31.42 


13.891 


10 


.545 


49.45 


26.952 




33.26 


18.129 


11 


.660 


52.16 


34.428 




35.09 


23.158 




.785 


54.65 


42.918 


33.50 


36.75 


28.867 


1 2 


1.000 


59.34 


63.435 




39.91 


42.668 


1 4 


1.396 


63.67 


88.886 




42.83 


59.788 


1 6 


1.767 


67.75 


119.72 


102.14 


45.57 


80.531 


1 8 


2.182 


71.71 


156.46 




48.34 


105.25 


1 10 


2.640 


75.32 


198.83 




50.658 


133.74 




3.142 


78.80 


247.57 


224.63 


52.961 


166.41 


2 2 


3.687 


82.15 


302.90 




55.258 


203.74 


2 4 


4.276 


85.39 


365.14 




57.436 


245.60 


2 6 


4.909 


88.39 


433.92 


411.37 


59.455 


291.87 


2 8 


5.585 


91.51 


511.10 




61.55 


343.8 


2 10 


6.305 


94.40 


595.17 




63.49 


400.3 




7.068 


97.17 


686.76 


674.09 


65.35 


461.9 


3 2 


7.875 


99.93 


786.94 




67.21 


529.3 


3 4 


8.726 


102.6 


895.7 




69 


602 


3 6 


9.621 


105.1 


1011.2 


1021.1 


70.70 


680.2 


3 8 


10.559 


107.6 


1136.5 




72.40 


764.5 


3 10 


11.541 


110.2 


1271.4 




74.10 


855.2 




12.566 


112.6 


1414.7 


1463.9 


75.73 


951.6 


4 3 


14.186 


116.1 


1647.6 




78.12 


1108.2 


4 6 


15.904 


119.6 


1901.9 


2007 


80.43 


1279.2 


4 9 


17.721 


122.8 


2176.1 




82.20 


1456.8 




19.635 


126.1 


2476.4 


2659 


84.83 


1665.7 


3 3 


21.648 


129.3 


2799.7 




86.99 


1883.2 


5 6 


23.758 


132.4 


3146.3 


3429 


89.07 


2116.2 


3 9 


25.967 


135.4 


3516 




91.08 


2365 




28.274 


138.4 


3912.8 


4322 


93.08 


2631.7 


6 6 


33.183 


144.1 


4782.1 


5339 


96.93 


3216.4 




38.485 


149.6 


5757.5 


6510 


100.61 


3872.5 



710 



HYDRAULICS. 



Size of Pipe. 


Clean Cast-iron 
Pipes. 


Value of 

ac Vr by 
Kutter's 


Old Cast-iron Pipes 
Lined with Deposit. 














d=diam. 


a = area 


For 


For Dis- 


Formula, 


For 


For 


in 


in 


Velocity, 


charge, 


when 


Velocity, 


Discharge, 
ac V r. 


ft. in. 


square 
feet. 


cv;. 


ac^r. 


n=.013 


cV r . 


7 6 


44.179 


154.9 


6841.6 


7814 


104.11 


4601.9 


8 


50.266 


160 


8043 


9272 


107.61 


5409.9 


8 6 


56.745 


165 


9364.7 


10889 


111 


6299.1 


9 


63.617 


169.8 


10804 


12663 


114.2 


7267.3 


9 6 


70.882 


174.5 


12370 


14597 


117.4 


8320.6 


10 


78.540 


179.1 


14066 


16709 


120.4 


9460.9 


10 6 


86.590 


183.6 


15893 


18996 


123.4 


10690 


11 


95.033 


187.9 


17855 


21464 


126.3 


12010 


11 6 


103.869 


192.2 


19966 


24139 


129.3 


13429 


12 


113.098 


196.3 


22204 


26981 


132 


14935 


12 6 


122.719 


200.4 


24598 


30041 


134.8 


16545 


13 


132.733 


204.4 


27134 


33301 


137.5 


18252 


13 6 


143.139 


208.3 


29818 


36752 


140.1 


20056 


14 


153.938 


212.2 


32664 


40432 


142.7 


21971 


14 6 


165.130 


216.0 


35660 


44322 


145.2 


23986 


15 


176.715 


219.6 


38807 


48413 


147.7 


26103 


-15 6 


188.692 


223.3 


42125 


52753 


150.1 


28335 


16 


201.062 


226.9 


45621 


57343 


152.6 


30686 


16 6 


213.825 


230.4 


49273 


62132 


155 


33144 


17 


226.981 


233.9 


53082 


67140 


157.3 


35704 


17 6 


240.529 


237.3 


57074 


72409 


159.6 


38389 


18 


254.470 


240.7 


61249 


77932 


161.9 


41199 


19 


283.529 


247.4 


70154 


89759 


166.4 


47186 


20 


314.159 


253.8 


79736 


102559 


170.7 


53633 



Flow of Water in Pipes from. 3/ 8 Inch to 12 Inches Diameter for a 
Uniform Velocity of 100 Ft. per Min. 



Diam. 


Area 


Cu. Ft. 


U. S. 
Gallons 
per Min. 


Diam. 


Area 


Cu. Ft. 


U. S. 
Gallons 
per Min. 


in In. 


Sq. Ft. 


per. Min. 


in In. 


Sq. Ft. 


per Min. 


3/8 


.00077 


0.077 


.57 


4 


.0873 


8.73 


65.28 


1/2 


.00136 


0.136 


1.02 


5 


.136 


13.6 


102.00 


3/ 4 


.00307 


0.307 


2.30 


6 


.196 


19.6 


146.88 


1 


.00545 


0.545 


4.08 


7 


.267 


26.7 


199.92 


U/4 


.00852 


0.852 


6.38 


8 


.349 


34.9 


261.12 


H/2 


.01227 


1.227 


9.18 


9 


.442 


44.2 


330.48 


13/4 


.01670 


1.670 


12.50 


10 


.545 


54.5 


408.00 


2 


.02182 


2.182 


16.32 


11 


.660 


66.0 


493.68 


21/2 


.0341 


3.41 


25.50 


12 


.785 


78.5 


587.52 


3 


.0491 


4.91 


36.72 











Short Formulae. E. Sherman Gould, Eng. News, Sept. 6, 1900, 
shows that Darcy's formulae for cast-iron pipes may be reduced to the fol- 
lowing approximate forms, in which h is loss of head or drop of hydraulic 
grade line in feet per 1000, d in ft., v in ft. per sec, Q in cu. ft. per sec. 



8 in. to 48 in. diam. 



3 to 6 in. diam. 



(Rough, Q 2 = hd 5 ; 
(Smooth, Q 2 = 2hd 5 ; v 
(Rough, Q 2 = 0.785M5 
(Smooth, Q* = 1.57MS; 



= 1.27 VtfL 
= 1.80 VdflT 

v = 1.13 Vdh. 
v = 1.60 *Sdh. 



FLOW OF WATER IN PIPES. 



711 



Flow of Water in Circular Pipes from 3/ 8 Inch to 12 Inches 
Diameter. 

Based on Darcy's formula for clean cast-iron pipes. Q = ac vV Vg. 



Value 


Dia. 
in. 


Slope, or Head Divided by Length of Pipe. 


of acvr. 


1 in 10 


lin20 


1 in 40 


I in 60 


1 in 80 


1 in 100 


1 in 150 


1 in 200 








Quan 


tity in 


cubic 


feet per 


second. 






.00403 


3/s 


.00127 


.00090 


.00064 


.00052 


.00045 


.00040 


.00033 


.00028 


.00914 


l/o 


.00289 


.00204 


.00145 


.00118 


.00102 


.00091 


.00075 


.00065 


.02855 


3/1 


.00903 


.00638 


.00451 


.00369 


.00319 


.00286 


.00233 


.00202 


.06334 


1 


.02003 


.01416 


.01001 


.00818 


.00708 


.00633 


.00517 


.00448 


.11659 


11/4 


.03687 


.02607 


.01843 


.01505 


.01303 


.01166 


.00952 


.00824 


.19115 


\lfc 


.06044 


.04274 


.03022 


.02468 


.02137 


.01912 


.01561 


.01352 


.28936 


13/i 


.09140 


.06470 


.04575 


.03736 


.03235 


.02894 


.02363 


.02046 


.41357 


?, 


.13077 


.09247 


.06539 


.05339 


.04624 


.04136 


.03377 


.02927 


.74786 


2 l/o 


.23647 


.16722 


.11824 


.09655 


.08361 


.07479 


.06106 


.05288 


1.2089 


3 


.38225 


.27031 


.19113 


.15607 


.13515 


.12089 


.09871 


.08548 


2.5630 


4 


.81042 


.57309 


.40521 


.33088 


.28654 


.25630 


.20927 


.18123 


4.5610 


5 


1.4422 


1.0198 


.72109 


.58882 


.50992 


.45610 


.37241 


.32251 


7.3068 


6 


2.3104 


1.6338 


1.1552 


.94331 


.81690 


.73068 


.59660 


.51666 


10.852 


7 


3.4314 


2.4265 


1.7157 


1.4110 


1.2132 


1.0852 


.88607 


.76734 


15.270 


8 


4.8284 


3.4143 


2.4141 


1.9713 


1.7072 


1.5270 


1.2468 


1.0797 


20.652 


9 


6.5302 


4.6178 


3.2651 


2.6662 


2.3089 


2.0652 


1.6862 


1.4603 


26.952 


10 


8.5222 


6.0265 


4.2611 


3.4795 


3.0132 


2.6952 


2.2006 


1.9058 


34.428 


11 


10.886 


7.6981 


5.4431 


4.4447 


3.8491 


3.4428 


2.8110 


2.4344 


42.918 


12 


13.571 


9.5965 


6.7853 


5.5407 


4.7982 


4.2918 


3.5043 


3.0347 


Value of V s = 


0.3162 


0.2236 


0.1581 


0.1291 


0.1118 


0.1 


0.08165 


0.07071 



Value. Dia. ] Jn 250 , in300 , in350 , in 400 , in 450 , in500 
of acVr. in. 



1 in 550 1 in 600 



.00403 
.00914 
.02855 
.06334 
.11659 
.19115 
.28936 
.41357 
.74786 
1.2089 
2.5630 
4.5610 
7.3068 
10.852 
15.270 
20.652 
26.952 
34.428 
42.918 



1/2 

I 3 ' 4 

11/4 

»l/2 

13/ 4 

2 

21/2 

3 

4 

5 

6 

7 

8 

9 
10 
11 
12 



.00025 
.00058 
.00181 
.00400 
.00737 
.01209 
.01830 
.02615 
.04730 
.07645 
.16208 
.28843 
.46208 
.68628 
.96567 
1 3060 
1.7044 
2.1772 
2.7141 



.00023 
.00053 
.00165 
.00366 
.00673 
.01104 
.01671 
.02388 
.04318 
.06980 
.14799 
.26335 
.42189 
.62660 
.88158 
1.1924 
1.5562 
1 .9878 
2.4781 



.00022 
.00049 
.00153 
.00339 
.00623 
.01022 
.01547 
.02211 
.03997 
.06462 
. 13699 
.24379 
.39055 
.58005 
.81617 
1 . 1038 
1.4405 
1.8402 
2.2940 



.00020 
.00046 
.00143 
.00317 
.00583 
.00956 
.01447 
.02068 
.03739 
.06045 
.12815 
.22805 
.36534 
.54260 
.76350 
1.0326 
1 .3476 
1.7214 
2.1459 



.00019 
.00043 
.00134 
.00298 
.00549 
.00901 
.01363 
.01948 
.03523 
.05695 
.12074 
.21487 
.34422 
.51124 
.71936 
.97292 
1.2697 
1.6219 
2.0219 



.00018 
.00041 
.00128 
.00283 
.00521 
.00855 
.01294 
.01849 
.03344 
.05406 
.11461 
.20397 
.32676 
.48530 
.68286 
.92356 
1.2053 
1.5396 
1.9193 



.00017 
.00039 
.00122 
.00270 
.00497 
.00815 
.01234 
.01763 
.03189 
.05155 
. 10929 
.19448 
.31156 
.46273 
.65111 
.88060 
1.1492 
1.4680 
1.8300 



Value of ^S' 



.06324 .05774 .05345 .05 



.04711 



For U. S. gals, per sec, multiply the figures in the table by 7.4805 

" " min., " " " " ... 48.83 
" " hour, " " " " .. . 26929.8 
" 24hrs., " " " " ...646315. 

For any other slope the flow is proportional to the square root of the 
slope; thus, flow in slope of 1 in 100 is double that in slope of 1 in 400. 



712 



HYDRAULICS. 



Flow of Water in House-service Pipes. 

Mr. E. Kuichling, C. E., furnished the following table to the Thomson 
Meter Co.: 





. 


Discharge, 


or Quantity capable of being delivered, in 




•— 


Cubic Feet pei 


Minute, from the Pipe, under the 




•S ft .S 

3 d oj 

£&£ 
F4 


conditions 


specified in the first column. 


Condition of 
Discharge. 


Nominal Diameters of Iron or Lead Service-pipe in 
Inches. 




1/2 


5/8 


3/4 


1 


11/2 


2 


3 


4 


6 




30 


1.10 


1.92 


3.01 


6.13 


16.58 


33.34 


88.16 


173.85 


444.63 


Through 35 


40 


1.27 


2.22 


3.48 


7.08 


19.14 


38.50 


101.80 


200.75 


513.42 


feet of ser- 


50 


1.42 


2.48 


3.89 


7.92 


21.40 


43.04 


113.82 


224.44 


574.02 


vice-pipe, 


60 


1.56 


2.71 


4.26 


8.67 


23.44 


47.15 


124.68 


245.87 


628.81 


no back 


75 


1.74 


3.03 


4.77 


9.70 


26.21 


52.71 


139.39 


274.89 


703.03 


pressure. 


100 


2.01 


3.50 


5.50 


11.20 


30.27 


60.87 


160.96 


317.41 


811.79 




130 


2.29 


3.99 


6.28 


12.77 


34.51 


69.40 


183.52 


361.91 


925.58 




30 


0.66 


1.16 


1.84 


3.78 


10.40 


21.30 


58.19 


118.13 


317.23 


Through 100 


40 


0.77 


1.34 


2.12 


4.36 


12.01 


24.59 


67.19 


136.41 


366.30 


feet of ser- 


50 


0.86 


1.50 


2.37 


4.88 


13.43 


27.50 


75.13 


152.51 


409.54 


vice-pipe, 


60 


0.94 


1.65 


2.60 


5.34 


14.71 


30.12 


82.30 


167.06 


448.63 


no back 


75 


1.05 


1.84 


2.91 


5.97 


16.45 


33.68 


92.01 


186.78 


501.58 


pressure. 


100 


1.22 


2.13 


3.36 


6.90 


18.99 


38.89 


106.24 


215.68 


579.18 




130 


1.39 


2.42 


3.83 


7.86 


21.66 


44.34 


121.14 


245.91 


660.36 


Through 100 
feet of ser- 


30 


0.55 


0.96 


1.52 


3.11 


8.57 


17.55 


47.90 


97.17 


260.56 


40 


0.66 


1.15 


1.81 


3.72 


10.24 


20.95 


57.20 


116.01 


311.09 


50 


0.75 


1.31 


2.06 


4.24 


11.67 


23.87 


65.18 


132.20 


354.49 


vice-pipe, 
and 1 5 feet 
vertical 


60 


0.83 


1.45 


2.29 


4.70 


12.94 


26.48 


72.28 


146.61 


393.13 


75 


0.94 


1.64 


2.59 


5.32 


14.64 


29.96 


81.79 


165.90 


444.85 


100 


1.10 


1.92 


3.02 


6.21 


17.10 


35.00 


95.55 


193.82 


519.72 


rise. 


130 


1.26 


2.20 


3.48 


7.14 


19.66 


40.23 


109.82 


222.75 


597.31 




30 


0.44 


0.77 


1.22 


2.50 


6.80 


14.11 


38.63 


78.54 


211.54 


Through 100 


40 


0.55 


0.97 


1.53 


3.15 


8.68 


17.79 


48.68 


98.98 


266.59 


feet of ser- 


50 


0.65 


1.14 


1.79 


3.69 


10.16 


20.82 


56.98 


115.87 


312.08 


vice-pipe, 


60 


0.73 


1.28 


2.02 


4.15 


11.45 


23.47 


64.22 


130.59 


351.73 


and 30 feet 


75 


0.84 


1.47 


2.32 


4.77 


13.15 


26.95 


73.76 


149.99 


403.98 


vertical 


100 


1.00 


1.74 


2.75 


5.65 


15.58 


31.93 


87.38 


177.67 


478.55 


rise. 


130 


1.15 


2.02 


3.19 


6.55 


18.07 


37.02 


101.33 


206.04 


554.96 



In this table it is assumed that the pipe is straight and smooth inside; 
that the friction of the main and meter are disregarded; that the inlet 
from the main is of ordinary character, sharp, not flaring or rounded, and 
that the outlet is the full diameter of pipe. The deliveries given will be 
increased if, first, the pipe between the meter and the main is of larger 
diameter than the outlet; second, if the main is tapped, say for 1-inch 
pipe, but is enlarged from the tap to 1 1/4 or 1 1/2 inch; or, third, if pipe on 
the outlet is larger than that on the inlet side of the meter. The exact 
details of the conditions given are rarely met in practice; consequently 
the quantities of the table may be expected to be decreased, because the 
pipe is liable to be throttled at the joints, additional bends may inter- 
pose, or stop-cocks may be used, or the back-pressure may be increased. 



FLOW OF WATER THROUGH NOZZLES. 



713 



2 


OOfM^OOf 
O0> — TOO 


"T^OSift0>Nf\00OISO>OVC0-ift00^»0N0>0\ON0*00 
mrsiM^NONOiriNBiriOiri— ooovnOW — vo — l> — — ts»N>c 




TOOCNlNOONCNlONTONTONONONt->inpO|OTNOOOONO>oom — r*> — 
TTmmmNONOi>Nt-««aooooNO — NtfitiriiosoooN- mm nooo 






= 




rn OOn T — mO«»,NO — inONOOrnNOrnNOinT 
TOrNlm<NONONOONOOONONOOaoCNlrriNOO 


— ocoiniMfiOO — 


--(v|N(^t^T'\T'<riJMOin«*tsNOOi3vO^O--Nf 


ooor-»moo — Tno 


o 


tsoomOi>c 


mooorNjoNTminmooinNONomoooo — tcs 
onoono — tisaNifucoo- Motisoo- r~* 


iNCNicninNooinNO 


^S^SSi 


OfiNOO* — win — moo — am — NfN]iN.Nm 

mrrimrriTTTinininNONOrN.ooooONONO — 


m — oo — mTinm 






ON 


OMNOOTt 


mtta-fim(Ni(NitnoNtNO>NOvOi'iO>1 , NOl"t«i!<itiri 
OTN©NONOToooNoom — omtNoo — NMspNitnoNinrNtfi'NT 


l^jngia 


int^ON — minoo — Tt>.ONO — NooinoNNom 
CSCN|csirr 1 cn<N-vmTTTinmNONOt>.r«.r-.00ON 


OnON(SN-000 
OO — cn en Tin m 


co 


c^SSS^ 


OONNI-nOOOO^NnOOiMMIOOOvOCON 

ooNOTOinoNO — TinincNTrnomNomo 


— amONSONtsN 


c< °--- 


on — rn>nNOooominrNONToorNjNoo>'NjooT 
-N(N)N(NlNwt<N.rfiifiWtNj-ioiniri*NOt> 


ONmoovOT — ooin 
i^mooooono- — cnj 


- 


— iNQOc^irnnoc^rN^"t^o*\0' — ifi — o^^ON>or^O' — m — coin — TmNO 
OOMfMMn-NOa>-tn , t'VTm'-Ntr|00'--OONOMritN\OmlsNNIsO>00 


i-oo>-m 


lAONOvO-^iTlMOOflMNONinNM'C 

— — — — rNqtsjcsirgrNjcNrnmrnTTTTinin 


NONONOrNOOOOONON 


o 


On OO On — nO 
in On O no On 


Nt-OtmOv0t0>NN00(N)N01-!N-O000Mflf0\m'OM 

ifio^MOtntmN- — NOinoinooO'ONOintNiNoo^orNO>o 
— — — oonpnCNndon — NooMfNrwNiriNOinNMnacAN* 


«-> T !>. 00 On 


— rsitnTTint-NOOON — PNlTr^ON — rninoo — 
— — — — — --NNNNNmmwwt 


•vrr»O>t00N\OO 
TTTininNONOt-N 


« 


mo> in oao 

T in OO On — 
T TOO On On 


inr^r^mr^ONOfsrNinoNinONinooTOT — or->fNmmr^TON 

tfl!fiin00lstC0trflI>N9 0>0VN9NOv0 0\f^-0>0>^in-- 

f>T — r^mONONONOONOTr-iooToofNTrNiONONOoinoooNtNTON 


cnj m t m no 


PnOOOnOnOO — Nd^TiAtsCOO — IJtKOOOONtNOmNOeO 






T 


Oin no O — 

•Nttvo ooun. 
ooooons 


ONTONTr-NTinOTOOONCSTON — nOnO— m T On ctn. — oot>.o 
CNiTOmnqoNNONOooNOr>.in — oooNrnr>NorNooinomt^oor«. 
tono>— NOOONr>inr-ioomt>.0'— mcnf>iorv,CN)r>.inocninNO 


NNt^fl 


Nor>r>eocoo>o>o-NNTinrN><»o>ON'NT 


inMJO — TnOOOO 




T 


no — tiN,nfNiu>NmNO'NtotsoomoNO'ONO^ominl - (Ni 

in Csl — 00t0»t«0NNOONBCNlC0tA0\O— OOOOnO — in 


mT — ooor>.NOo 


— CNjfC|W*lT 


■NTinif\NONONNWCOaO> — NrnttmrNOO 


o-ofxiTNor^ON — 






en 


c*3Cc>$oo 


OCtOOOvCOMNl-tNOOINhNlNN— ^OINNtS 

r-N — tNOKitomN- inTtNor^mON — — 


— OONinOTr>ON 


<NCn1cO 


tnTTTinininNONOt>.t>.oooNOO — — mT 


inNONOooo — Nm 


« 


o in o no o 
08™^ — t 


t o T — lANto- r-jooinONOinrviininoo 
ooinONtsmm — inoooONor-jtviNor-s.inoT — 
tsONintNONtnNOO-NinMOOWN.OOtfioONO'NT 


— OO^NOIStsN^ 


O — — MfNl 


'Nmmm'N^mTTTiniriNONOr-.rNOOoooNO 


— i — CN m Tin no in. 


N 


-•nTNINOv 
n©00 <N T t>. 


moooOinTTNOinONOor>.rnNONOON — inooin 
m^ooTONmONrninNONO<Nm — noo — ONm 

OC — (Nit^tNONN^NOWnts- TOO— nOCN 


inToomrnONrnON 
rsNNCrNaiSN 


OO 


-NNNrvlNNwmWW , r^>flifMftNO-or> 


NOOCOaOO-N 


tN 


tNltf\ttMf\'O'Nt'<f^-O<0ONOO*(Nlin(NltCO — M3»O\N*iftinO\'O(N|tf\0000 

tAifMNON-Mm^rm*N»o(Nin'rNo(Ni'Nrt>ONrNiNoa.(NHftomoi'Too 


oooo — 


— — — — — — — pNjrNif-NirvjrNimmmmmTT 


tif\in«iC>ONN 


i 


CO— ■"T'TrNlONNOrNloOrnoOOONOTrviONNOOTr^.ONO — — O-in — — Ontj-oO — 
Cvlc«>,Tu-NNONOt>.OOaOONONO — CN]tni^iriNOOO>OCNl , r*tM>- TnO On — T 


OOOOOOOOOOO — — — NNNN 


CNirslrnrnmrnTT 


- 


oooom — no — — on too — ovoinoo- oo — in mm no o r^ 

Ov^Oitls- T-OOn — tOOMinoONO\N9CNl<OrflOOOONO 

o — — (N]N(^t^tiMn'Nr'NT'NrinininNO\oiN.»(cova>o- 


csmmmNor>oooN 


o 

i 

S 


m -0 no rq CS — pqornaooooONinON — O — tON^JB 
.O>m00O>r>.r>. — — r-N,OC-40000TinT000NOT — mT — 


OOnOnOOO— OOCNJO 


^•rstn in m O 
— CNmTm 


sONIN — nOON1 , -N^nCOOOOOO>nON 
(PInOnOInNQOOOONOO — NWiTtNOSINO^ — 


soomt-NOOOoo 
MTmr^orsTin 


N«\OOiNm8>(Nllft»-Nm»>ONOOOOOO-g 
— f*"N.NOO*cnNOO'mNOONC<"N.ONNOf s JONNOin(NONNOrc,0 — OO 


NnOOOOnOTCNO 


Qh nN t co' p>i r>.' 


.— in'oToo'm — oon^noooo — minNoomr^oTorNT— -oo 
pNiCNqmmmTinNONorNooorninrvON — NOOTONmtNogooNO 


m o o o o 

. — CNimT 


SS-S§l§?§|Sg§S||||l 


oooooooo 
soonOPnITnoSo 



714 HYDRAULICS. 



LOSS OF HEAD. 

The loss of head due to friction when water, steam, air, or gas of any 
kind flows through a straight tube is represented by the formula 



, ,42 D 2 . , «/64.4 hd 

h=f i: 2d' whence v= va T' 



in which I = the length and d = the diameter of the tube, both in feet; 
v = velocity in feet per second, and /is a coefficient to be determined by 
experiment. According to Weisbach, / == 0.00644, in which case 



4 /64.4 _ n „ _ n Jhd 

\-rj = 50, and v= 50 \ -— , 



which is one of the older formulae for flow of water (Downing's). Prof. 
Unwin says that the value of / is possibly too small for tubes of small 
bore, and he would put / =0.006 to 0.01 for 4-inch tubes, and / = 0.0084 
to 0.012 for 2-inch tubes. Another formula by Weisbach is 



»-(« 



0.0144 + 



0.01716\ I v* 



Rankine gives 



V v ) d 2g 

/_0.005(l +I f 5 ). 

From the general equation for velocity of flow of water v = c Vr Vs 

= for round pipes c J - 4/ - , we havei; 2 = c 2 - -j and h= —£?■, in which 

c is the coefficient c of Darcy's, Bazin's, Kutter's, or other formula 
as found by experiment. Since this coefficient varies with the condition 
of the inner surface of the tube, as well as with the velocity, it is to be 
expected that values of the loss of head given by different writers will 
vary as much as those of quantity of flow. 

The relation of the value of c in Chezy 's for mula V = c '^ / rs to the 



e of the coefficient of friction /is c = ^ 


/ 2 g/f. 




/= .0035 
c = 135.5 
/= .0070 
c= 95.8 


.0040 .0045 .0050 
127.8 119.6 113.4 
.0075 .0080 .0090 
92.6 89.7 84.5 


.0055 

108.1 

.010 

80.2 


.0060 .0065 

103.5 99.4 

.011 .012 

76.5 73.2 


60 70 
.018 .013 


80 90 100 110 
.010 .008 .0064 .0053 


120 
.0045 


130 140 - 150 
.0038 .0033 .0029 



Equations derived from the formulae. (Unwin.) 

Velocity, ft. per sec v= 4.012 >/dh/(Jl)= 1.273 Q/d*= c Vd/4 X ^s. 

Diameter, ft d= 0.0622 f vl/h = 1.128 ^Q /v. 

Quantity, cu. ft. per sec. Q= 3.149 ^hd 5 /fl. 
Head, ft h = 0.1008 fQH/d 5 . 

Rough preliminary calculations may be made by the following approx- 
imate formulae. They are least accurate for small pipes, s = slope, =h/l. 
New and clean pipes. Old and incrusted pipes. 

v = 56 Vds, v = 40 Vds^_ 

Q = 44 Vd^s. Q = 31.4 *Sd 5 s. 

d = 0.22^QVs. d = 0.252 ^/QVs. 

Flow of Water in Riveted Steel Pipes. — The laps and rivets tend 
to decrease the carrying capacity of the pipe. See paper on " New 
Formulas for Calculating the Flow of Water in Pipes and Channels," by 
W. E. Foss, Jour. Assoc. Eng. Soc, xiii, 295. Also Clemens Herschel's 
book on "115 Experiments on the Carrying Capacity of Large Riveted 
Metal Conduits," John Wiley & Sons, 1897. 



LOSS OF HEAD. 



715 



"Values of the Coefficient of Friction. Unwin's "Hydraulics" gives 
values of/, based on Darcy's experiments, as follows: Clean and smooth 
pipes, / = 0.005 (1 + 1/12 d). Incrusted pipes, / =0.01 (1 + l/i 2 d). In 
1886 Unwin examined all the more carefully made experiments on flow 
in pipes, including those of Darcy, classifying them according to the 
quality and condition of their surfaces, and showing the relation of the 
value of /to both diameter and velocity. The results agree fairly closely 
with the following values, / = a (1 + .p/d). 



Kind of pipe. 


Values of a for velocities in ft. per second. 


Values 
of j3. 


Drawn wrought iron . . 
Asphalted cast iron . . . 
Clean cast iron 


1-2 
.00375 
. 00492 
. 00405 


2-3 
.00322 
.00455 
.00395 


3-4 
.00297 
.00432 
.00387 


4-5 
.00275 
.00415 
.00382 


0.37 
0.20 
0.28 
0.26 



Incrusted cast iron at all velocities a = . 00855 



From the experiments of Clemens Herschel, 1892-6, on clean steel 

riveted pipes, Unwin derives the following values of / for different veloci- 
ties. 

Ft. per sec 1 2 3 4 5 6 

48-in. pipe, av.of 2. .0066 .0060 .0057 .0055 .0055 .0055 

42-in. pipe, av. of 2. .0067 .0058 .0054 .0054 .0054 .0054 

36-in. pipe 0087 .0071 .0060 .0053 .0047 .0042 

Unwin attributes the anomalies in this table to errors of observation. 
In comparing the results with those on cast-iron pipes, the roughness of 
the rivet heads and joints must be considered, and the resistance can 
only be determined by direct experiment on riveted pipes. 

Two portions of the 48-in. main were tested after being four years in 
use, and the coefficients derived from them differ remarkably. 

Ft. per sec 1 2 3 4 5 6 

Upper part 0106 .0080 .0075 .0073 .0072 .0072 

Lower part 0068 .0060 .0058 .0060 .0060 .0060 

Marx, Wing, and Hopkins in 1897 and 1899 made gaugings on a 6-ft. 
main, part of which was of riveted steel and part of wood staves. (Trans. 
A. S. C. E., xl, 471, and xliv, 34.) From these tests Unwin derives the 
following values of /. 

Ft. per sec. 1 1.5 2 2.5 3 4 5 5.5 

Steel pipe: 

1897. ../= .0053 .0052 .0053 .0055 .0055 .0052 

1899.../= .0097 .0076 .0067 .0063 .0061 .0060 .0058 .0058 

Wood staves: 

1897.../= .0064 .0053 .0048 0043 .0041 

1899.../= .0048 .0046 .0045 0044 .0043 .0043 .0043 

Freeman's experiments on fire hose pipes (Trans. A. S. C. E., xxi, 303) 
give the following values of/. 

Velocity, ft. per sec 4 6 10 15 20 

Unlined canvas 0095 .0095 .0093 .0088 .0085 

Rough rubber-lined cotton 0078 .0078 .0078 .0075 .0073 

Smooth rubber-lined cotton 0060 .0058 .0055 .0048 .0045 

The Resistance at the Inlet of a Pipe is equal to the frictional resist- 
ance of a straight pipe whose length is l = (1 +/o) d -j- 4 /. Values of / are: 
(A) for end of pipe flush with reservoir wall, 0.5; (B) pipe entering wall, . 
straight edges, 0.56; (C) pipe entering wall, sharp edges, 1.30; (Z>) bell- 
mouthed inlet, 0.02 to 0.05. Values of l /d are for 

A, 53 B, 75 C, 78 D, 115 

26 38 39 53 



/= 0.005 
0.010 



716 



HYDRAULICS. 



Multiplying these figures by d gives the length of straight pipe to be 
added to the actual length to allow for the inlet resistance. In long 
lengths of pipe the relative value of this length is so small that it may be 
neglected in practical calculations. — (Unwin.) 

Loss of Head in Pipe by Friction. — Loss of head by friction in 
each 100 feet in length of riveted pipe when discharging the following 
quantities of water per minute (Pelton Water-wheel Co.). 

V = velocity in feet per second; h = loss of head in feet; Q = dis- 
charge in cubic feet per minute. 





Inside Diameter of Pipe in Inches. 




7 


8 


9 


10 


11 


12 


V 


h 
0.338 


Q 

32 


h 


Q 


h 


Q 
53 


h 


Q 


h 


Q 


h 


Q 


2 


0.296 


41.9 


0.264 


0.237 


65.4 


0.216 


79.2 


0.198 


94 2 


3 


0.698 


48 1 


0.611 


62.8 


0.544 


79 5 


0.488 


98.2 


0.444 


119 


0.407 


141 


4 


1.175 


64.1 


1.027 


83.7 


0.913 


106 


0.822 


131 


0.747 


158 


0.685 


188 


5 


1.76 


80.2 


1.54 


105 


1.37 


132 


1.23 


163 


1.122 


198 


1.028 


235 


6 


2.46 


96.2 


2.15 


125 


1.92 


159 


1.71 


196 


1.56 


237 


1.43 


283 


7.0 


3.26 


112.0 


2.85 


146 


2.52 


185 


2.28 


229 


2.07 


277 


1.91 


330 




13 in. 


14 in. 


15 in. 


16 in. 


18 in. 


20 in. 


V 


h 


Q 


h 


Q 


h 


Q 


h 


Q 


h 


Q 


h 


Q 


2 


0.183 


110 


0.169 


128 


0.158 


147 


0.147 


167 


0.132 


212 


0.119 


262 


3 


.375 


166 


.349 


192 


.325 


221 


.306 


251 


.271 


318 


.245 


393 


4 


.632 


221 


.587 


256 


.548 


294 


.513 


335 


.456 


424 


.410 


523 


5 


.949 


276 


.881 


321 


.822 


368 


.770 


419 


.685 


530 


.617 


654 


6.0 


1.325 


332 


1.229 


385 


1.148 


442 


1.076 


502 


.957 


636 


.861 


785 


7.0 


1.75 


387 


1.63 


449 


1.52 


515 


1.43 


586 


1.27 


742 


1.143 


916 





22 in. 


24 in. 


26 in. 


28 in. 


30 in. 


36 in. 


V 


h 


Q 


h 


Q 


h 


Q 


h 


Q 


h 


Q 


h 


Q 


2 


0.108 


316 


0.098 


377 


0.091 


442 


0.084 


513 


0.079 


589 


0.066 


848 


3 


.222 


475 


.204 


565 


.188 


663 


.174 


770 


.163 


883 


.135 


1273 


4 


.373 


633 


.342 


754 


.315 


885 


.293 


1026 


.273 


1178 


.228 


1697 


5,0 


.561 


792 


.513 


942 


.474 


1106 


.440 


1283 


.411 


1472 


.342 


2121 


6 


.782 


950 


.717 


1131 


.662 


1327 


.615 


1539 


.574 


1767 


.479 


2545 


7.0 


1.040 


1109 


.953 


1319 


.879 


1548 


.817 


1796 


.762 


2061 


.636 


2868 



This table is based on Cox's reconstruction of Weisbach's formula, 
using the denominator 1000 instead of 1200, to be on the safe side, allow- 
ing 20% for the loss of head due to the laps and rivet-heads in the pipe. 

Example. — Given 200 ft. head and 600 ft. of 11-inch pipe, carrying 
119 cubic feet of water per minute. To find effective head: In right- 
hand column, under 11-inch pipe, find 119 cubic ft.; opposite this will 
be found the loss by friction in 100 ft. of length for this amount of water, 
which is 0.444. Multiply this by the number of hundred feet of pipe, 
which is 6, and we have 2.66 ft., which is the loss of head. Therefore 
the effective head is 200 - 2.66 = 197.34. 

Explanation. — The loss of head by friction in a pipe depends not 
only upon diameter and length, but upon the quantity of water passed 
through it. The head or pressure is what would be indicated by a 



LOSS OF HEAD. 



717 



pressure-gauge attached to the pipe near the wheel. Readings of gauge 
should be taken while the water is flowing from the nozzle. 

To reduce heads in feet to pressure in pounds multiply by 0.433. To 
reduce pounds pressure to feet multiply by 2.309. 

Cox's Formula. — Weisbach's formula for loss of head caused by the 
friction of water in pipes is as follows: 

17 • +• u a tn^AA , 0.01716\ L .V- 

Friction-head = (0.0144 H 7=—) g ,_ , , 

\ \/y / 5.367 a 

where L = length of pipe in feet ; 

V = velocity of the water in feet per second; 
d = diameter of pipe in inches. 

William Cox (Amer. Mach., Dec. 28, 1893) gives a simpler formula 
which gives almost identical results: 



H = friction-head in feet = 



Hd 
L 



d 
4F2+57- 



(1) 
(2) 



He gives a table by means of which the value of 
once obtained when V is known, and vice versa. 
4F2+57-2 



4724. 57 _ 2 



V 


0.0 


0.1 


0.2 


0.3 


0.4 


0.5 


0.6 


0.7 


0.8 


0.9 


1 


.00583 


.00695 


.00813 


.00938 


.01070 


.01208 


.01353 


.01505 


.01663 


.01828 


2 


.02000 


.02178 


.02363 


.02555 


.02753 


.02958 


.03170 


.03388 


.03613 


.03845 


3 


.04083 


.04328 


.04580 


.04838 


.05103 


.05375 


.05653 


.05938 


.06230 


.06528 


4 


.06833 


.07145 


.07463 


.07788 


.08120 


.08458 


.08803 


.09155 


.09513 


.09878 


5 


.10250 


.10628 


.11013 


.11405 


.11803 


.12208 


.12620 


.13038 


.13463 


.13895 


6 


.14333 


.14778 


.15230 


.15688 


.16153 


.16625 


.17103 


.17588 


.18080 


.18578 


7 


.19083 


.19595 


.20113 


.20638 


.21170 


.21708 


.22253 


.22805 


.22363 


.23928 


8 


.24500 


.25078 


.25663 


.26255 


.26853 


.27458 


.28070 


.28688 


.29313 


.29945 


9 


.30583 


.31228 


.31880 


.32538 


.33203 


.33875 


.34553 


.35238 


.35930 


.36628 


10 


.37333 


.38045 


.38763 


.39488 


.40220 


.40958 


.41703 


.42455 


.43213 


.43978 


11 


.44750 


.45528 


.46313 


.47105 


.47903 


.48708 


.49520 


.50338 


.51163 


.51995 


12 


.52833 


.53678 


.54530 


.55388 


.56253 


.57125 


.58003 


.58888 


.59780 


.60678 


13 


.61583 


.62495 


.63413 


.64338 


.65270 


.66208 


.67153 


.68105 


.69063 


.70028 


!4 


.71000 


.71978 


.72963 


.73955 


.74953 


.75958 


.76970 


.77988 


.79013 


.80045 


15 


.81083 


.82128 


.83180 


.84238 


.85303 


.86375 


.87453 


.88538 


.89630 


.90728 


16 


.91833 


.92945 


.94063 


.95188 


.96320 


.97458 


.98603 


.99755 


1 .00913 


1.02078 


17 


1.03250 


1.04428 


1.05613 


1.06805 


1.08003 


1 .09208 


1 . 10420 


1.11638 


1.12863 


1.14095 


18 


1.15333 


1.16578 


1.17830 


1 . 19088 


1.20353 


1.21625 


1 .22903 


1.24188 


1 .25480 


1.26778 


19 


1.28083 


1.29395 


1.30713 


1.32038 


1.33370 


1 .34708 


1 .36053 


1 .37405 


1 .38763 


1.40128 


20 


1.41500 


1.42878 


1.44263 


1 .45655 


1.47053 


1.48458 


1.49870 


1.51288 


1.52713 


1.54145 


21 


1 .55583 


1.57028 


1.58480 


1.59938 


1.61403 


1 .62875 


1.64353 


1.65838 


1.67330 


1 .68828 



The use of the formula and table is illustrated as follows: 

Given a pipe 5 inches diameter and 1000 feet long, with 49 feet head, 

what will the discharge be? 

If the velocity V is known in feet per second, the discharge is 0.32725 d a V 

cubic foot per minute. 



718 HYDRAULICS. 

By equation 2 we have 

4F2+5F- 2 = Hd 
1200 L 

whence, by table, V = real velocity = 8 feet per second. 

The discharge in cubic feet per minute, if V is velocity in feet per 
second and d diameter in inches, is 0.32725 dW, whence, discharge 

= 0.3275 X 25 X 8 = 65.45 cubic feet per minute. 

The velocity due the head, if there were no friction, is 8.025 V# 
= 56.175 feet per second, and the discharge at that velocity would be 

0.32725 X 25 X 56.175 = 460 cubic feet per minute. 

Suppose it is required to deliver this amount, 460 cubic feet, at a 
velocity of 2 feet per second, what diameter of pipe of the same length 
and under the same head will be required and what will be the loss of 
head by friction? j 



d = diameter = 



: V rxo^s - V2OT2B - V70S - 26 - 5 inches - 

Having now the diameter, the velocity, and the discharge, the friction- 
head is calculated by equation 1 and use of the table; thus, 

„ L4V 2 +5V~2 1000 ^ ftno 20 , „ , , 
H= d 1200— = 2-6T X °-° 2= 2675= °' 75 f ° 0t ' 

thus leaving 49 — 0.75 = say 48 feet effective head applicable to power- 
producing purposes. 

Problems of the loss of head may be solved rapidly by means of Cox's 
Pipe Computer, a mechanical device on the principle of the slide-rule, 
for sale by Keuffel & Esser, New York. 

Exponential Formulae. Williams and Hazen's Tables. — From 
Chezy's formula, v = c ^rs, it would appear that the velocity varies as 
the square root of the head, or that the head varies as the square of the 
velocity; this is not true, however, for c is not a constant, but a variable, 
depending on both r and s. Hazen and Williams, as a result of a study 
of the best records of experiments and plotting them on logarithmic ruled 
paper, found an exponential formula v = cr°' es s 0-54 , in which the coefficient 
c is practically independent of the diameter and the slope, and varies only 
with the condition of the surface. In order to equalize the numerical 
value of c to that of the c in the Chezy formula, at a slope of 0.001, they 
added the factor 0.001-0-04 to the formula, so that the working formula 
of Hazen and Williams is 

V = cr 0-63 §0-54 0.001- 0-04 . 

Approximate values given for c are: 

140 for the very best cast-iron pipe, laid straight and when new. 
130 for good, new cast-iron pipe, very smooth; good masonry aqueducts; 
small brass pipes.* 

1 20 for cast-iron pipe 5 years old ; riveted steel pipe, new. 

110 for cast-iron pipe 10 years old; steel pipe 10 years old; brick sewers. 

100 for cast-iron pipe 17 years old, roueh. 

90 for cast-iron pipe 26 years old, rough. 

80 for cast-iron pipe 37 years old , very rough. 

* 130 may also be used for straight lead, tin, and drawn copper pipes. 
Computations of the exponential formula are made by logarithms, or by 
the Hazen-Williams hydraulic slide rule. On logarithmic ruled paper 
values of v for different values of c, r and s may be plotted in straight 
lines. (See "Hydraulic Tables," by Williams and Hazen, John Wiley & 
Sons.) 



LOSS OF HEAD. 



719 



Friction Loss in Clean Cast-iron Pipe. 

Compiled from Weston's "Friction of Water in Pipes" as computed from 
formulas of Henry Darcy. 
Pounis loss per 1000 feet in pipe of given diameter. (Small lower 
figures give Velocity in Feet per Second.) 



U. S.Gals per 
Min. and (Cu. 
Ft. per Sec.) 


Diameter of Pipe in Inches. 


3 


4 


5 


6 


8 


10 


12 


14 


16 


20 


24 

0.00 
0.18 
0.01 
0.35 
0.02 
0.53 
0.03 
0.71 


30 


250 

(0.56) 
500 
(111) 
750 
(1.67) 
1,000 
(2.23) 


60 

11 
220 

23 
477 

34 


20 

6.4 

82 
13.0 
184 
19.0 
328 
26.0 


6.4 
4.0 

25.8 
8.2 

58.0 

12.2 
103.0 

16.3 


2.5 

2.8 
10.0 

6.0 
23.0 

8.0 
40.0 
11.0 


0.6 
1.6 
2.3 
3.2 
5.0 
4.8 
9.0 
6.4 


0.2 
1.2 
0.7 
2.4 
1.6 
3.1 
2.9 
4.1 


0.07 
0.7 
0.29 
1.4 
0.66 
2.1 
1.20 
2.8 


0.03 
0.52 
0.13 
1.04 
0.30 
1.56 
0.53 
2.08 


0.02 
0.4 
0.07 
0.8 
0.15 
1.2 
0.27 
1.6 


0.01 
. 26 
0.02 
0.51 
0.05 
0.77 
0.09 
1.0 


o.oo 

0.23 

6 6\ 

0.45 


1,250 






161.0 
20.4 

231.9 
24.5 


63.0 
14.0 
91.0 
17.0 

123.0 
20.0 

160.0 
23.0 


14.0 
8.0 
21.0 
10.0 
28.0 
11.0 
37.0 
13.0 


4.6 
5.1 
6.6 
6.1 

9.0 
7.1 
12.0 
8.2 


1.80 
3.6 
2.60 
4.3 
3.60 
5.0 
4.70 
5.7 


0.83 

2. GO 
1.10 
3.13 
1.6 
3. 65 
2.14 
4.17 


0.42 
2.0 
0.61 
2.4 
0.83 
2.8 
1.10 
3.2 


0.14 
1.3 
0.20 
1.5 
0.27 
l.S 
0.35 
2.0 


0.06 
. Ml 
0.08 
1.06 
0.11 
1.24 
0.14 
1.42 




(2.79) 
1,500 












03 


(3.34) 






68 


1,750 








(3.90) 










2,000 








05 


(4.46) 


















2,500 








58.0 
16.0 


18.0 
10.2 
26.0 
12.0 


7.30 
7.1 
10.00 

8.5 


3.34 
5.21 
4.81 
6.25 
8.55 
S.34 


1.70 
4.0 
2.40 
4.8 
4.30 
6.4 
6.80 
S.O 


0.55 

2.6 

0.79 

3.1 

1.40 

4.1 

2.20 

5.1 


0.22 
1.80 
0.32 
2.10 
0.56 
2 . 80 
1.00 
3.60 

1.30 

4.30 
1.70 

5.00 
2.20 
5.70 
2.80 
6.40 


07 


(5.57) 


Pipe 


inTn 






113 


3,000 

(6.68) 








10 


36 


48 








1 40 


4,000 








18 


(8.91) 
















1 80 


5,000 


0.11 
1.6 


0.03 
0.89 












79 


(11.14) 
































6,000 


0.16 
1.9 
0.23 
2.2 
0.29 
2.5 
0.37 
2.8 
0.45 
3.1 


0.04 
1.06 
0.05 
1.2 
0.07 
1.4 
0.09 
1.6 
0.11 
1.8 
















3.20 
6.1 
4.30 

7.1 


41 


(13.37) 
















2 70 


7,000 
















56 


(15.60) 
















3 20 


8,000 
















71 


(17.82) 


















3 60 


9,000 


















9? 


(20.05) 


















4 10 


10,000 


















1 13 


(22.28) 




















4.50 


Vel.ft.per sec. 
Hd.duevel.ft . 


1 
0.016 


2 
0.062 


3 

0.14 


4 
0.25 


5 

0.39 


6 

0.56 


7 
0.76 


8 
1.0 


9 
13 


10 
1.6 


11 

1.9 


12 

2.2 


Vel.ft.per sec. 
Hd.duevel.ft.. 


13 

2.6 


14 
3.1 


15 
3.5 


16 
4.0 


17 
4.5 


18 
5.0 


19 
5.6 


20 

6.2 


25 
9.3 


30 
14.0 


40 

24.8 


50 

38.8 



These losses are for new, clean, straight, tar-coated, cast-iron pipes. For 
pipes that have been in service a number of years the losses 
will be larger or. account of corrosion and incrustation, and 10 years 1.3 
the losses in the tables should be multiplied under average 20 " 1.6 
conditions by the factors opposite; but they must be used 30 " 2.0 
with much discretion, for some waters corrode pipes much 50 " 2.6 
more rapidly than others. 75 " 3.4 

The same figures may be used for wrought-iron pipes which are not 
subject to a frequent change of water. 



720 HYDRAULIC FORMULA. 

Approximate Hydraulic Formulae. (The Lombard Governor Co., 
Boston, Mass.) 

Head (H) in feet. Pressure (P) in lbs. per sq. in. Diameter (D) in 
feet. Area (A) in sq. ft. Quantity (Q) in cubic ft. per second. Time 
(T) in seconds. _ 

Spouting velocity = 8.02 V#. 

Time (7\) to acquire spouting velocity in a vertical pipe, or (Tt) in a 
pipe on an angle (0) from horizontal: 

T 1 = 8.02 Vff +■ 32.17, T 2 = 8.02 ^H h- 32.17 sin 0. 

Head (#) or pressure (P) which will vent any quantity (Q) through a 
round orifice of any diameter (Z>) or area (A): 

H=Q 2 + 14.1 D<,= Q 2 •+■ 23.75 A 2 ; P= Q* + 34.1 D 4 ,- Q 2 -h 55.3 A*. 

Quantity (Q) discharged through a round orifice of any diameter (Z>) or 
area (A) under any pressure (P) or under any head (H): 



Q = V > X 55.3 X A 2 = V PX34.1 X D 4 ; 

= V# x 23.75 X A 2 =V#x 14.71 XD*. 

Diameter (D) or area (A) of a round orifice to vent any quantity (Q) 
under any head (H) or under any pressure (P) : 



Z) = \/QH-3.84^iJ =V<9-!-5.8^P; A = Q + 4.89V# =Q-=-7.35 V>. 

Time (7 1 ) of emptying a vessel of any area (A) through an orifice of any 
area (a) anywhere in its side: T = 0.416 A Vf? -j- a. 

Time (T) of lowering a water level from (H) to (ft) in a tank of area A 
through an orifice of any area (a) in its side. J 7 = 0.416A(V# — \/j£) -s-a. 

Kinetic energy (K) or foot-pounds in water in a round pipe of any 
diameter (D) when moving at velocity (V): K = 0.76 X D 2 X L X V. 

Area (a) of an orifice to empty a tank of any area (A) in any time (T) 
from any head (H): a = T -t- 0.409 A V#. 

Area (a) of an orifice to lower water in a tank of area (A) from head (H) 
to (/*) in time (T): a = T -*- 0.409 X A X (V# - Vh). 

Compound Pipes and Pipes with Branches. (Unwin.) — Loss of 
head in a main consisting of different diameters. (1) Constant discharge. 
Total loss of head H = h x + h 2 + h 3 = 0.1008 /Q 2 (l 1 /d 1 ^ + h/d£ + h/d* 6 ). 

(2) Constant velocity in the main, the discharge jdiminishing from sec- 
tion to section. H = 0.0551 fv 5/ 2(i,/^Qi+ h/^Q*. + h/^Qz). Equiv- 
alent main of uniform diameter. Length of equivalent main 

I = d* (h/dj + h/d 2 5 + Zs/ds 6 ). 

Loss of head in a main of uniform diameter in which the discharge de- 
creases uniformly along its length, such as a main with numerous branch 
pipes uniformly spaced and delivering equal quantities: h = 0.0336 
fQ 2 l/d 5 , Q being the quantity entering the pipe. The loss of head is just 
one-third of the loss in a pipe carrying the uniform quantity Q through- 
out its length. 

Loss of head in a pipe that receives Q cu. ft. per sec. at the inlet, and 
delivers Q x cu. ft. at x ft. from the inlet, having distributed qx cu. ft. 
uniformly in that distance, h x = 0.1008 fx (Q x + 0.55 qx)/d 5 . 

Delivery by two or more mains, in parallel. Total discharge = Qt + Q 

+Qa = 3.149 */h/f (y df /l x W dtf> /h+^/ dy> /h) . Diameter of an equivalent 

main to discharge the same total quantity, d= (v^s+V^ +^dy>) 2 l^. 

Long Pipe Lines. — (1) Vyrnwy to Liverpool, 68 miles; 40 million gals. 
(British) per day. Three lines of cast-iron pipe, 42 to 39 in. diam. One 
of the 42-in. lines after being laid 12 years, with a hydraulic gradient of 



LOSS OF HEAD. 721 

4.5 ft. per mile, discharged 15 million gallons per day; velocity, 2.892 ft. 
per sec, /= 0.00574. 

(2) East Jersey riveted steel pipe line, Newark, N. J., 21 miles long, 48 
in. diam., 50 million U. S. gals, per day; velocity about 6 ft. per sec. 

(3) Perth to Coolgarlie, Western Australia, 351 miles, 30 in. steel pipe 
with lock-bar joints. Eight pumping stations in the line. Two tests 
showed delivery of 5 and 5.6 million gals, per day; hydraulic gradient, 
2.25 and 2.8 ft. per mile; velocity, 1.889 and 2.115 ft. per sec.;/= 0.00480 
and 0.00486. 

Rifled Pipes for Conveying Heavy Oils. (Eng. Rec, May 23, 1908.)— 
The oil from the California fields is a heavy, viscous fluid. Attempts 
to handle it in long pipe lines of the ordinary type have not been practi- 
cally successful. High pumping pressures are required, resulting in large 
expense for pipe and for pumping equipment. 

The method of pumping in the rifled-pipe line is to inject about 10 per 
cent of water with the oil and to give the oil and water a centrifugal 
motion, by means of the rifled pipe, sufficient to throw the water to the 
outside, where it forms a thin film of lubrication between the oil and the 
sides of the pipe that greatly reduces the friction. The rifled pipe de- 
livers at ordinary temperatures eight to ten times as much oil, through a 
long line, as does a line of ordinary pipe under similar conditions. An 
8-in. rifled pipe line 282 miles in length has been built from the Kern oil 
fields to Porta Costa, on tidewater near San Francisco. The pipe is 
rifled with six helical grooves to the circumference, these grooves making 
a complete turn through 360 deg. in 10 ft. of length. 

Loss of Pressure Caused by Valves and Fittings — The data given 
below are condensed from the results of experiments by John R. Freeman 
for the Inspection Department of the Assoc. Facty. Mut. Ins. Cos. ■ The 
friction losses in ells and tees are approximate. Fittings of the same nom- 
inal size with the different curvatures and different smoothness as made 
by different manufacturers will cause materially different friction losses. 
The figures are the number of feet of clean, straight pipe of same size 
which would cause the same loss as the fitting. Grinnell dry-pipe valve, 
6-in., 80 ft.; 4-in., 47 ft. Grinnell alarm check, 6-in., 100 ft.; 4-in., 47 ft. 
Pratt & Cady check valve, 6-in., 50 ft.; 4-in., 25 ft. 4-in. Walworth globe 
check valve, 6-in., 200 ft.; 4-in., 130 ft. 21/2 in. to 8-in. ells, long-turn, 
4 ft.; short-turn 9 ft. 3-in. to 8-in. tees, long-turn, 9 ft.; short-turn, 17 ft. 
One-eighth bend, 5 ft. 

Effect of Bends and Curves in Pipes. — Weisbach's rule for bends: 

Loss of head in feet = To. 131 + 1.847 (^) ?/2 ] X -—^ X ^, in which r 

= internal radius of pipe in feet, R = radius of curvature of axis of pipe, 
v = velocity in feet per second, and a = the central angle, or angle sub- 
tended by the bend. 

Hamilton Smith, Jr., in his work on Hydraulics, says: The experimental 
data at hand are entirely insufficient to permit a satisfactory analysis of 
this quite complicated subject; in fact, about the only experiments of 
value are those made by Bossut and Dubuat with small pipes. 

Curves. — If the pipe has easy curves, say with radius not less than 5 
diameters of the pipe, the flow will not be materially diminished, provided 
the tops of all curves are kept below the hydraulic grade-line and provision 
be made for escape of air from the tops of all curves. (Trautwine.) 

Williams, Hubbell and Fenkel (Trans. A.S.C.E., 1901) conclude from 
an extensive series of experiments that curves of short radius, down to 
about 21/2 diameters, offer less resistance to the flow of water than do 
those of longer radius, and that earlier theories and practices regarding 
curve resistance are incorrect. For a 90° curve in 30 in. cast-iron pipe, 
6 ft. radius, they found the loss of head 15.7% greater than that of a 
straight pipe of equal length; with 10 ft. radius, 17.3% greater; with 25 ft. 
radius, 52.7 % greater; and with 60 ft. radius, 90.2% greater, 

Hydraulic Grade-line. — In a straight tube of uniform diameter 
throughout, running full and discharging freely into the air, the hydraulic 
grade-line is a straight line drawn from the discharge end to a point imme- 
diately over the entry end of the pipe and at a depth below the surface 
equal to the entry and velocity heads. (Trautwine.) 

In a pipe leading from a reservoir, no part of its length should be above 
the hydraulic grade-line. 



722 HYDRAULICS. 



Air-bound Pipes. — A pipe is said to be air-bound when, in conse- 

Suence of air being entrapped at the high points of vertical curves in the 
ne, water will not flow out of the pipe, although the supply is higher than 
the outlet. The remedy is to provide cocks or valves at the high points, 
through which the air may be discharged. The valve may be made auto- 
matic by means of a float. 

Water-hammer. — Prof. I. P. Church gives the following formula for 
the pressure developed by the instantaneous closing of a valve in a water 
pipe: 

V = vCy/g, 
in which p is pressure in lbs. per sq. in., v velocity in inches per second, 
C velocity of pr essure wave in inches per second, and g = 386.4 ins. The 
value of C is ^gEEjt/y (tEx + 2 rE), in which E x = modulus of elasticity, 
30,000,000 for steel, E = bulk modulus of water = 300,000 lbs. per sq. in. 
at 50° F, y = 0.03604 = lbs. of water in 1 cu. in., t = thickness of pipe, 
ins., and r = internal radius of pipe, ins. Example, a 16-in. steel pipe 
with i/4-in. walls, and v = 60 ins. per second, gives a velocity of the pres- 
sure wave C = 44,285 ins. per second and a pressure per sq. in. of 2478 
lbs. If the elasticity of the pipe is not considered, the formula reduces 
top = 5.29 v, which in the example given gives a pressure of 317.4 lbs. 
per sq. in. 

Vertical Jets. (Molesworth.) — H = head of water, h = height of 
jet, d = diameter of jet, K = coefficient, varying with ratio of diameter 
of jet to head; then h = KH. 

If H = d X 300 600 1000 1500 1800 2800 3500 4500 
K w 0.96 0.9 0.85 0.8 0.7 0.6 0.5 0.25 

Water Delivered through Meters. (Thomson Meter Co.) — The 
best modern practice limits the velocity in water-pipes to 10 lineal feet 
per second. Assume this as a basis of delivery, and we find, for the sev- 
eral sizes of pipes usually metered, the following approximate results: 
Nominal diameter of pipe in inches: 

3/8 5/ 8 3/ 4 1 11/2 2 3 4 6 

Quantity delivered, in cubic feet per minute, due to said velocity: 
0.46 1.28 1.85 3.28 7.36 13.1 29.5 52.4 117.9 
Prices Charged for Water in Different Cities. (National Meter Co.) 

Average minimum price for 1000 gallons in 163 places 9.4 cents. 

Average maximum price for 1000 gallons in 163 places 28 " 

Extremes, 21/2 cents to 100 

FIRE-STREAMS. 

Fire-Stream Tables. — The table on the following page is condensed 
from one contained in the pamphlet of " Fire-Stream Tables" of the Asso~ 
ciated Factory Mutual Fire Ins. Cos., based on the experiments of John R. 
Freeman, Trans. A. S. C. E., vol. xxi, 1889. 

The pressure in the first column is that indicated by a gauge attached 
at the base of the play pipe and set level with the end of the nozzle. The 
vertical and horizontal distances, in 2d and 3d cols., are those of effective 
fire-streams with moderate wind. The maximum limit of a " fair stream " 
is about 10% greater for a vertical stream; 12% for a horizontal stream. 
In still air much greater distances are reached by the extreme drops. 
The pressures given are for the best quality of rubber-lined hose, smooth 
inside. The hose friction varies greatly in different kinds of hose, accord- 
ing to smoothness of inside surface, and pressures as much as 50% 
greater are required for the same delivery in long lengths of inferior 
rubber-lined or linen hose. The pressures at the hydrant are those while 
the stream is flowing, and are those required with smooth nozzles. Ring 
nozzles require greater pressures. With the same pressures at the base 
of the play pipe, the discharge of a3/ 4 -in. smooth nozzle is the same as that 
of a 7/8-in. ring nozzle; of a 7/g-in. smooth nozzle, the same as that of a 
1-in. ring nozzle. 

The figures for hydrant pressure in the body of the table are derived 
by adding to the nozzle or play-pipe pressure the friction loss in the 
hose, and also the friction loss of a Chapman 4-way independent gate 



FIRE-STREAMS. 



723 



hydrant ranging from 0.86 lb. for 200 gals, per min. flowing to 2.31 lbs. 
for 600 gals. 

The following notes are taken from the pamphlet referred to. The 
discharge as stated in Ellis's tables and in their numerous copies in trade 
catalogues is from 15 to 20% in error. 

In the best rubber-lined hose, 21/2-in. diam., the loss of head due to 
friction, for a discharge of 2-10 gallons per minute, is 14.1 lbs. per 100 ft. 
length; in inferior rubber-lined mill hose, 25.5 lbs., and in unlined linen 
hose, 33.2 lbs. 

Less than' a 1 1/8-in. smooth-nozzle stream with 40 lbs. pressure at the 
base of the play pipe, discharging about 240 gals, per min., cannot be 
called a first-class stream for a factory fire. 80 lbs. per sq. in. is con- 
sidered the best hydrant pressure for general use; 100 lbs. should not be 
exceeded, except for very high buildings, or lengths of hose over 300 ft. 

Hydrant Pressures Required with Different Sizes and Lengths of 

Hose. (J. R. Freeman, Trans. A. S. C. E., 1889.) 

3/4-inch smooth nozzle. 



,Q 


Fire- 
steam 
Distance. 


a 


Hydrant Pressure with Different Lengths of 


Hi 


Hose to Maintain Pressure at Base of Play Pipe. 


V 


Vert. 


Hor. 


6 

52 


50 ft. 


100 ft. 


200 ft. 


300 ft. 
12 


400 ft. 


500 ft. 


600 ft. 


800 ft. 


1000 

ft. 


10 


17 


19 


10 


11 


11 


13 


13 


14 


15 


16 


20 


33 


29 


73 


21 


22 


23 


24 


25 


26 


28 


30 


32 


30 


48 


37 


90 


31 


32 


34 


36 


38 1 


40 


41 


45 


49 


40 


60 


44 


104 


42 


43 


46 


48 


50 


53 


55 


60 


65 


50 


67 


50 


116 


52 


54 


57 


60 


63 


66 


69 


75 


81 


60 


72 


54 


127 


63 


65 


68 


72 


76 


79 


83 


90 


97 


70 


76 


58 


137 


73 


75 


80 


84 


88 


92 


97 


105 


114 


80 


79 


62 


147 


84 


86 


91 


96 


101 


106 


111 


120 


no 


90 


81 


65 


156 


94 


97 


102 


108 


113 


119 


124 


135 


146 


100 


83 


68 


164 


105 


108 


114 


120 


126 


132 


138 


150 


163 



7/8-inch smooth nozzle. 



10 


18 


21 


71 


11 


11 


13 


14 


15 


16 


17 


19 


?.?. 


20 


34 


33 


100 


22 


23 


25 


27 


30 


32 


34 


39 


43 


30 


49 


42 


123 


33 


34 


38 


41 


45 


48 


51 


58 


65 


40 


62 


49 


142 


43 


46 


50 


55 


59 


64 


68 


78 


87 


50 


71 


55 


159 


54 


57 


63 


69 


74 


80 


86 


97 


108 


60 


77 


61 


174 


65 


69 


75 


82 


89 


96 


103 


116 


130 


70 


81 


66 


188 


76 


80 


88 


96 


104 


112 


120 


136 


152 


80 


85 


70 


201 


87 


91 


101 


110 


119 


128 


137 


155 


173 


90 


88 


74 


213 


98 


103 


113 


123 


134 


144 


154 


174 


195 


100 


90 


76 


224 


109 


114 


126 


137 


148 


160 


171 


194 


216 



I-inch smooth nozzle. 



10 


18 


21 


93 


12 


12 


14 


16 


18 


20 


22 


26 


30 


20 


35 


37 


132 


23 


25 


29 


33 


37 


41 


45 


52 


60 


30 


51 


47 


161 


34 


37 


43 


49 


55 


61 


67 


79 


90 


40 


64 


55 


186 


46 


50 


58 


66 


73 


81 


89 


105 


120 


50 


73 


61 


208 


57 


62 


72 


82 


92 


102 


111 


131 


151 


60 


79 


67 


228 


69 


75 


87 


98 


110 


122 


134 


157 


181 


70 


85 


72 


246 


80 


87 


101 


115 


128 


142 


156 


183 


211 


80 


89 


76 


7.63 


97. 


100 


115 


131 


147 


162 


178 


209 


241 


90 


92 


80 


279 


103 


112 


130 


147 


165 


183 


200 


236 




100 


96 


83 


295 


115 


125 


144 


164 


183 


203 


223 













HYDRAULICS. 



Hydrant Pressures Required with Different Sizes and Lengths of 
Hose. — Continued. 



1 1/8-inch smooth nozzle. 





Fire- 
Steam 
Distance. 


a 

a 




Hydrant Pressure with Different Lens 


f ths of 




► 3 


Hose to Maintain Pressure at Base of Play Pipe. 


I 


Vert. 


Hor. 


$ 

119 


50 ft. 


100ft. 


200 ft. 
17 


300 ft. 


400 ft. 


500ft. 


600 ft. 


800 ft. 


1000 

ft. 


10 


18 


22 


12 


14 


20 


24 


27 


30 


36 


43 


20 


36 


38 


168 


25 


28 


34 


41 


47 


54 


60 


73 


85 


30 


52 


50 


206 


37 


42 


52 


61 


71 


80 


90 


109 


128 


40 


65 


59 


238 


50 


56 


69 


81 


94 


107 


120 


145 


171 


50 


75 


66 


266 


62 


70 


86 


102 


118 


134 


150 


181 


213 


60 


83 - 


72 


291 


74 


84 


103 


122 


141 


160 


180 


218 


256 


70 


88 


77 


314 


87 


98 


120 


143 


165 


187 


209 


254 




80 


92 
96 
99 


81 
85 
89 


336 
356 
376 


99 

112 
124 


112 
126 
140 


138 
155 

172 


163 
183 

204 


188 
212 
236 


214 
241 


239 






90 






ion 



















1 l/4-mch smooth nozzle. 



10 


19 


22 


148 


14 


16 


21 


26 


31 


36 


41 


51 


61 


20 


37 


40 


209 


27 


32 


42 


52 


62 


72 


82 


101 


121 


30 


53 


54 


256 


41 


49 


63 


78 


93 


108 


123 


152 


182 


40 


67 


63 


296 


55 


65 


84 


104 


124 


144 


164 


203 


243 


50 


77 


70 


331 


68 


81 


106 


130 


155 


180 


204 


254 




60 


85 
91 
95 
99 
101 


76 
81 
85 
90 
93 


363 
392 
419 

444 
468 


82 
96 
110 
123 
137 


97 
113 
129 
145 

162 


127 
148 
169 
190 
211 


156 
182 

208 
234 
261 


186 
217 

248 


216 
252 


245 






70 






80 








90 










100 

























1 3/8-inch smooth nozzle. 



10 

20 
30 

40 


20 
38 
55 
69 
79 
87 
92 
97 
100 
103 


23 
42 
56 
66 
73 
79 
84 
88 
92 
96 


182 
257 
315 
363 
406 
445 
480 
514 
545 
574 


16 
31 
47 
62 
78 
93 
109 
124 
143 
156 


,9 
39 
58 
77 
96 
116 
135 
154 
173 
193 


27 
53 
80 
107 
134 
160 
187 
214 
240 


34 
68 
103 
137 
171 
205 
239 


42 
83 
125 
166 
208 
250 


49 
98 
147 
196 

245 


56 
113 
169 
226 


71 
143 
214 


86 
173 
259 


50 






60 








70 










80 












90 














100 































FIEE-STREAMS. 



725 



Pump Inspection Table. 

Discharge of nozzles attached to 50 ft. of 21/2-m. best quality rubber- 
lined hose, inside smooth. (J. R. Freeman.) 



S2 






Size 


of Smooth Nozzle. 






Ring Nozzle. 


Kf=4 


13/4 


U/2 


13/8 


11/4 


11/8 


1 


7/8 


3/4 


13/8 


11/4 


11/8 


10 


193 


163 


146 


127 


107 


87 


68 


51 


118 


101 


84 


20 


274 


232 


206 


179 


151 


123 


96 


72 


167 


143 


119 


30 


335 


283 


251 


219 


184 


150 


118 


88 


205 


175 


145 


40 


387 


327 


291 


253 


213 


173 


136 


101 


237 


202 


168 


50 


432 


366 


325 


283 


238 


194 


152 


113 


264 


226 


188 


60 


473 


400 


357 


309 


261 


213 


167 


124 


289 


247 


205 


70 


510 


432 


385 


334 


281 


230 


180 


134 


313 


267 


222 


80 


546 


461 


412 


357 


301 


246 


192 


144 


334 


285 


237 


90 


579 


490 


437 


379 


319 


261 


204 


152 


355 


303 


252 


100 


610 


515 


461 


400 


337 


275 


215 


161 


374 


319 


266 



Friction Loss in Rubber-Lined Cotton Hose with Smoothest Lining. 



g 


Gallons per Minute Flowing. 


..0 


Velocity 






£02 
la 


Head 
V 2 - 20. 





100 


200 


300 


400 


500 


600 


700 


800 


1000 


a 




^£ 






S 


Friction Loss, Pounds per 100 ft. Length. 


■Ft. 


Lbs. 


2 


6.836 
5.170 


27.3 
70 7 


61.5 

46 5 


109 

8? 7 


171 

1?9 










5 
10 


0.39 
1.6 


0.17 


21/8 


189 








0.69 


21/4 


3.790 


15 ? 


34 1 


60 6 


94 7 


136 


186 






15 


3.5 


1.5 


23/s 


2.895 


11 6 


26 1 


46 3 


72.4 


104 


138 


185 




20 


6.2 


2.7 


lih 


2.240 


9 


20 2 


35 8 


56.0 


80.6 


110 


143 


224 


25 


9.7 


4.2 


25/8 


1.748 


7,0 


15 7 


28 


43.7 


62.9 


85.7 


112 


175 


30 


14.0 


6.1 


23/4 


1.391 


5 6 


12 5 


7.7. 3 


34 8 


50 1 


68 ,2 


89,0 


139 


35 


19.0 


8.2 


27/a 


1.097 


4 4 


9 9 


17 6 


71 A 


39 5 


53 8 


70.2 


110 


40 


24.8 


10.7 


3 


0.900 


3 6 


8 1 


14 A 


72 5 


32 A 


44 1 


57.6 


90 


45 


31.4 


13.6 


31/2 


0.416 


1 7 


3 7 


6 7 


10 A 


15,0 


20 A 


26.6 


41.6 


50 


38.8 


16.7 


4 


0.214 


0.9 


1.9 


3.4 


5.4 


7.7 


10.5 


13.7 


21.4 









The above table is computed on the basis of 14 lbs. per 100 ft. length 
of 21/2-in. hose with 250 gals, per min. flowing, as found in Freeman's 
tests, assuming that the loss varies as the square of the quantity, and for 
different diameters and the same quantity inversely as the 5th power of 
the diameter. 

Rated Capacities of Steam Fire-engines, which is perhaps one third 
greater than their ordinary rate of work at fires, are substantially as 
follows: 

3d size, 550 gals, per min., or 792,000 gals, per 24 hours. 

2d " 700 " " 1,008,000 

1st " 900 " ** 1,296,000 

1 ext., 1,100 " " 1,584,000 



726 HYDRAULICS. 



THE SIPHOK* 

The Siphon is a bent tube of unequal branches, open at both ends, and 
is used to convey a liquid from a higher to a lower level, over an interme- 
diate point higher than either. Its parallel branches being in a vertical 
plane and plunged into two bodies of liquid whose upper surfaces are at 
different levels, the fluid will stand at the same level both within and 
without each branch of the tube when a vent or small opening is made 
at the bend. If the air be withdrawn from the siphon through this vent, 
the water will rise in the branches by the atmospheric pressure without, 
and when the two columns unite and the vent is closed, the liquid will 
flow from the upper reservoir as long as the end of the shorter branch 
of the siphon is below the surface of the liquid in the reservoir. 

If the water was free from air the height of the bend above the supply 
level might be as great as 33 feet. 

If A = area of cross-section of the tube in square feet, H = the differ- 
ence in level between the two reservoirs in feet, D the density of the 
liquid in pounds per cubic foot, then ADH measures the inte nsity of the 
force which causes the movement of the fluid, and V = A ^ / 2gH = 8.02 
"^H is the theoretical velocity, in feet per second, which is reduced by 
the loss of head for entry and friction, as in other cases of flow of liquids 
through pipes. In the case of the difference of level being greater than 
33 feet, however, the velocity of the water in the shorter leg is limited 
to that due to a height of 33 feet, or that due to the difference between 
the atmospheric pressure at the entrance and the vacuum at the bend. 

Long Siphons. — Prof. Joseph Torrey, in the Amer. Machinist, de- 
scribes a long siphon which was a partial failure. 

The length of the pipe was 1792 feet. The pipe was 3 inches diameter, 
and rose at one point 9 feet above the initial level. The final level was 
20 feet below the initial level. No automatic air valve was provided. 
The highest point in the siphon was about one third the total distance 
from the pond and nearest the pond. At this point a pump was placed, 
whose mission was to fill the pipe when necessary. This siphon would 
flow for about two hours and then cease, owing to accumulation of air in 
the pipe. When in full operation it discharged 431/2 gallons per minute. 
The theoretical discharge from such a sized pipe with the specified head 
is 551/2 gallons per minute. 

Siphon on the Water-supply of Mount Vernon, N. T. (Eng'g 
News, May 4, 1893.) — A 12-inch siphon, 925 feet long, with a maximum 
lift of 22.12 feet and a 45° change in alignment, was put in use in 1892 
by the New York City Suburban Water Co. At its summit the siphon 
crosses a supply main, which is tapped to charge the siphon. The air- 
chamber at the siphon is 12 inches by 16 feet long. A 1/2-inch tap and 
cock at the top of the chamber provide an outlet for the collected air. 

It was found that the siphon with air-chamber as described would run 
until 125 cubic feet of air had gathered, and that this took place only 
half as soon with a 14-foot lift as with the full lift of 22.12 feet. The 
siphon will operate about 12 hours without being recharged, but more 
water can be gotten over by charging every six hours. It can be kept 
running 23 hours out of 24 with only one man in attendance. With the 
siphon as described above it is necessary to close the valves at each end 
of the siphon to recharge it. It has been found by weir measurements 
that the discharge of the siphon before air accumulates at the summit is 
practically the same as through a straight pipe. 

A successful siphon is described by R. S. Hale in Jour. Assoc. Eng. 
Soc, 1900. A 2-in. galvanized pipe had been used, and it had been nec- 
essary to open a waste-pipe and thus secure a continuous flow in order 
to keep the siphon in operation. The trouble seemed to be due to very 
small air leaks in the joints. When the 2-in. iron pipe was replaced by a 
1-in. lead pipe, the siphon was entirely successful. The maximum rise 
of the pipe above the level of the pond was 12 ft., the discharge about 
350 ft. below the level, and the length 500 ft. 



MEASUREMENT OF FLOWING WATER. 727 



MEASUREMENT OF FLOWING WATER. 

Piezometer. — If a vertical or oblique tube be inserted into a pipe 
containing water under pressure, the water will rise in the former, and the 
vertical height to which it rises will be the head producing the pressure 
at the point where the tube is attached. Such a tube is called a piezom- 
eter or pressure measure. If the water in the piezometer falls below 
its proper level it shows that'' the pressure in the main pipe has been 
reduced by an obstruction between the piezometer and the reservoir. If 
the water rises above its proper level, it indicates that the pressure there 
has been increased by an obstruction beyond the piezometer. 

If we imagine a pipe full of water to be provided with a number of pie- 
zometers, then a line joining the tops of the columns of water in them Is 
the hydraulic grade-line. 

Pitot Tube Gauge. — The Pitot tube is used for measuring the veloc- 
ity of fluids in motion. It has been used with great success in measuring 
the flow of natural gas. (S. W. Robinson, Report Ohio Geol. Survey, 1890.) 
(See also Van Nosh-and's Mag., vol. xxxv.) It is simply a tube so bent 
that a short leg extends into the current of fluid flowing from a tube, with 
the plane of the entering orifice opposed at right angles to the direction of 
the current. The pressure caused by the impact of the current is trans- 
mitted through the tube to a pressure-gauge of any kind, such as a column 
of water or of mercury, or a Bourdon spring-gauge. From the pressure 
thus indicated and the known density and temperature of the flowing gas 
is obtained the head corresponding to the pressure, and from this the 
velocity. In a modification of the Pitot tube described by Prof Robinson, 
there are two tubes inserted into the pipe conveying the gas, one of which 
has the plane of the orifice at right angles to the current, to receive the 
static pressure plus the pressure due to impact; the other has the plane of 
its orifice parallel to the current, so as to receive the static pressure only. 
These tubes are connected to the legs of a [/tube partly filled with mercury, 
which then registers the difference in pressure in the two tubes, from which 
the velocity may be calculated. Comparative tests of Pitot tubes with 
gas-meters, for measurement of the flow of natural gas, have shown an 
agreement within 3%. 

It appears from experiments made by W. M. White, described in a 
paper before the Louisiana Eng'g Socy., 1901, by Williams, Hubbell and 
Fenkel (Trans. A. S. C. E., 1901), and by W. B. Gregory (Tran s. A. S. 
M. E., 1903), that in the formula for the Pitot tube, V = c ^2 gH, in 
which V is the velocity of the current in feet per second, H the head in 
feet of the fluid corresponding to the pressure measured by the tube, 
and c an experimental coefficient, c = 1 when the plane at the point of 
the tube is exactly at right angles with the direction of the current, 
and when the static pressure is correctly measured. The total pressure 
produced by a jet striking an extended plane surface at right angles to 
it, and escaping parallel to the plate, equals twice the product of the 
area of the jet into the pressure calculated from the "head due the veloc- 
ity," and for this case H = 2 X V 2 /2 g instead of V 2 /2 g; but as found in 
White's experiments the maximum pressure at a point on the plate 
exactly opposite the jet corresponds to h = V 2 /2 g. Experiments made 
with four different shapes of nozzles placed under the center of a falling 
stream of water showed that the pressure produced was capable of sus- 
taining a column of water almost exactly equal to the height of the 
source of the falling water. 

Tests by J. A. Knesche (Indust. Eng'g, Nov., 1909), in which a Pitot 
tube was inserted in a 4-in. water pipe, gave C = about 0.77 for velocities 
of 2.5 to 8 ft. per sec, and smaller values for lower velocities. He holds 
that the coefficient of a tube should be determined by experiment before 
its readings can be considered accurate. 

Maximum and Mean Velocities in Pipes. — Williams, Hubbell and 
Fenkel (Trans. A. S. C. E.. 1901) found a ratio of 0.84 between the mean 
and the maximum velocities of water flowing in closed circular conduits, 
under normal conditions, at ordinary velocities; whereby observations of 
velocity taken at the center under such conditions, with a properly rated 
Pitot tube, may be relied on to give results within 3% of correctness. 



728 HYDRAULICS. 



The Venturi Meter, invented by Clemens Herschel, and described in 
a pamphlet issued by the Builders' Iron Foundry of Providence, R.L.is 
named from Venturi, who first called attention, in 1796, to the relation be- 
tween the velocities and pressures of fluids when flowing through converg- 
ing and diverging tubes. It consists of two parts — the tube, through 
which the water flows, and the recorder, which registers the quantity of 
water that passes through the tube. The tube takes the shape of two trun- 
cated cones joined in their smallest diameters by a short throat-piece. At 
the up-stream end and at the throat there are pressure-chambers, at 
which points the pressures are taken. 

The action of the tube is based on that property which causes the small 
section of a gently expanding frustum of a cone to receive, without material 
resultant loss of head, as much water at the smallest diameter as is dis- 
charged at the large end, and on that further property which causes the 
pressure of the water flowing through the throat to be less, by virtue of its 
greater velocity, than the pressure at the up-stream end of the tube, each 
pressure being at the same time a function of the velocity at that point and 
of the hydrostatic pressure which would obtain were the water motionless 
within the pipe. 

Tne recorder is connected with the tube by pressure-pipes which lead to 
it from the chambers surrounding the up-stream end and the throat of the 
tube. It may be placed in any convenient position within 1000 feet of the 
meter. It is operated by a weight and clockwork. The difference of pres- 
sure or head at the entrance and at the throat of the meter is balanced in 
the recorder by the difference of level in two columns of mercury in 
cylindrical receivers, one within the other. The inner carries a float, the 
position of which is indicative of the quantity of water flowing through 
the tube. By its rise and fall the float varies the time of contact between 
an integrating drum and the counters by which the successive readings 
are registered. 

There is no limit to the sizes of the meters nor the quantity of water 
that may be measured. Meters with 24-inch, 36-inch, 4S-inch, and even 
20-foot tubes can be readily made. 

Measurement by Venturi Tubes. (Trans. A. S. C. E., Nov., 1887, 
and Jan., 1888.) — Mr. Herschel recommends the use of a Venturi tube, in- 
serted in the force-main of the pumping engine, for determining the 
quantity of water discharged. Such a tube applied to a 24-inch main has 
a total length of about 20 feet. At a distance of 4 feet from the end 
nearest the engine the inside diameter of the tube is contracted to a throat 
having a diameter of about 8 inches. A pressure-gauge is attached to each 
of two chambers, the onesurrounding and communicating with the entrance 
or main pipe, the other with the throat. According to experiments made 
upon two tubes of this kind, one 4 in. in diameter at the throat and 12 in. 
at the entrance, and the other about 36 in. in diameter at the throat and 
9 feet at its entrance, the quantity of water which passes through the tube 
is very nearly the theoretical discharge through an opening having an area- 
equal to that of the throat, and a velocity which is that due to the difference 
in head shown by the two gauges. Mr. Herschel states that the coefficient 
for these two widely-varying sizes of tubes and for a wide range of velocity 
through the pipe, was found to be within two per cent, either way, of 98%. 
In other words, the quantity of water flowing through the tube per se cond 
is expressed within two per cent by the formula W= 0.98 X AX v/ 2 gh, 
in which A is the area of the throat of the tube, h the head, in feet, corre- 
sponding to the difference in the pressure of the water entering the tube and 
that found at the throat, and g = 32.16. 

Measurement of Discharge of Pumping-engines by means of 
Nozzles. (Trans. A. S. M. L., xii, 575.) — The measurement of water 
by computation from its discharge through orifices, or through the nozzles 
of fire-hose, furnishes a means of determining the quantity of water de- 
livered by a pumping-engine which can be applied without much difficulty. 
John R. Freeman, Trans. A. S. C. E., Nov., 1889, describes a series of ex- 
periments covering a wide range of pressures and sizes, and the results 
showed that the coefficient of discharge for a smooth nozzle of ordinary 
good form was within one-half of one per cent, either way, of 0.977; the 
diameter of the nozzle being accurately calipered, and the pressures being 
determined by means of an accurate gauge attached to a suitable piezom- 
eter at the base of the play-pipe. 



MEASUREMENT OF FLOWING WATER. 



729 



In order to use this method for determining the quantity of water dis- 
charged by a pumping-engine, it would be necessary to provide a pressure- 
box, to which the water would be conducted, and attach to the box as 
many nozzles as would be required to carry off the water. According to 
Mr. Freeman's estimate, four 1 1/4-inch nozzles, thus connected, with a 
pressure of 80 lbs. per square inch, would discharge the full capacity of a 
two-and-a-half-million engine. He also suggests the use of a portable 
apparatus with a single opening for discharge, consisting essentially of a 
Siamese nozzle, so-called, the water being carried to it by three or more 
lines of fire-hose. 

To insure reliability for these measurements, it is necessary that the 
shut-off valve in the force-main, or the several shut-off valves, should be 
tight, so that all the water discharged by the engine may pass through the 
nozzles. 

Flow through Rectangular Orifices. (Approximate. See p. 698.) 

Cubic Feet of Water Discharged per Minute through an Orifice 
One Inch Square, under any Head of Water from 3 to 72 Inches. 

For any other orifice multiply by its area in square inches. 
Formula, Q' = 0.624 "^ h" X a. Q' = cu. ft. per min.; a = area in sq. in. 





"S 




tj 




T3 




,_, 




T3 




T3 




-0 






























m M ■ 




M • 




"S M • 




n M • 




"S M • 




"S M • 




m M ' 


3 <n 


8 £ a 


.3 to 


,« d-5 


.3 m 


Sg.E 


£ b3 


a! £.3 


.3 "■' 


S 3 3 


rt ^ 


a? is. 3 


c „; 


•5-9 




^ J* a 




^-g S 




^| B 


'" £ 


&H^a 




fe -g 3 


'r 4 ' 


fe^'g 


"" a; 


feja a 


"^"o 


0^ 


-i 




51 




"3 O 


2 m t* 


■:: 




-3 


2 M ti 


-3-g 


2^" 


2.s 


'•§5 8. 


$ s 


|qS 


«.s 


|qI 


5.= 


^fla 


a - 

as . - 


-§3 » 


2.3 


■§5 ft 


2.3 


■§«& 


w 





13 





23 


' 


33 





3 
43 





53 





63 





3 


1.12 


2.20 


2.90 


3.47 


3.95 


4.39 


4.78 


4 


1.27 


14 


2.28 


24 


2.97 


34 


3.52 


44 


4.00 


54 


4.42 


64 


4.81 


5 


1.40 


15 


2.36 


25 


3.03 


35 


3.57 


45 


4.05 


55 


4.46 


65 


4.85 


6 


1.52 


16 


2.43 


26 


3.08 


36 


3.62 


46 


4.09 


56 


4.52 


66 


4.89 


7 


1.64 


17 


2.51 


27 


3.14 


37 


3.67 


47 


4.12 


57 


4.55 


67 


4.92 


8 


1.75 


18 


2.58 


28 


3.20 


38 


3.72 


43 


4.18 


58 


4.58 


68 


4.97 


9 


1.84 


19 


2.64 


29 


3.25 


39 


3.77 


49 


4.21 


59 


4.63 


69 


5.00 


10 


1.94 


20 


2.71 


30 


3.31 


40 


3.81 


50 


4.27 


60 


4.65 


70 


5.03 


II 


2.03 


21 


2.73 


31 


3.36 


41 


3.86 


51 


4.30 


61 


4.72 


71 


5.07 


12 


2.12 


22 


2.84 


32 


3.41 


42 


3.91 


52 


4.34 


62 


4.74 


72 


5.09 



Measurement of an Open Stream by Velocity and Cross-section. — 

Measure the depth of the water at from 6 to 12 points across the stream at 
equal distances between. Add all the depths in feet together and divide 
by the number of measurements made; this will be the average depth of 
the stream, which multiplied by its width will give its area or cross-section. 
Multiply this by the velocity of the stream in feet per minute, and the 
result will be the discharge in cubic feet per minute of the stream. 

The velocity of the stream can be found by laying off 100 feet of the bank 
and throwing a float into the middle, noting the time taken in passing over 
the 100 ft. Do this a number of times and take the average; then, divid- 
ing this distance by the time gives the velocity at the surface. As the top 
of the stream flows faster than the bottom or sides — the average velocity 
being about 83 % of the surface velocity at the middle — it is convenient to 
measure a distance of 120 feet for the float and reckon it as 100. 



730 HYDRAULICS. 



Miner's Inch Measurements. (Pelton Water Wheel Co.) 

The cut, Fig. 141, shows the form of measuring-box ordinarily used, ..__ 
the following table gives the discharge in cubic feet per minute of a miner's 
inch of water, as measured under the various heads and different lengths 
and heights of apertures used in California. 



and 




Fig. 141. 



Length 

of 
Opening 


Openings 2 Inches High. 


Openings 4 Inches High. 


Head to 


Head to 


Head to 


Head to 


Head to 


Head to 


inches. 


Center, 


Center, 


Center, 


Center, 


Center, 


Center, 




5 inches. 


6 inches. 


7 inches. 


5 inches. 


6 inches. 


7 inches. 




Cu. ft. 


Cu. ft. 


Cu.ft. 


Cu.ft. 


Cu.ft. 


Cu. ft. 


4 


1.348 


1.473 


1.589 


1.320 


1.450 


1.570 


6 


1.355 


1.480 


1.596 


1.336 


1.470 


1.595 


8 


1.359 


1.484 


1.600 


1.344 


1.481 


1.608 


10 


1.361 


1.485 


1.602 


1.349 


1.487 


1.615 


12 


1.363 


1.487 


1.604 


1.352 


1.491 


1.620 


14 


1.364 


1.488 


1.604 


1.354 


1.494 


1.623 


16 


1.365 


1.489 


1.605 


1.356 


1.496 


1.626 


18 


1.365 


1.489 


1.606 


1.357 


1.498 


1.628 


20 


1.365 


1.490 


1.606 


1.359 


1.499 


1.630 


22 


1.366 


1.490 


1.607 


1.359 


1.500 


1.631 


24 


1.366 


1.490 


1.607 


1.360 


1.501 


1.632 


26 


1.366 


1.490 


1.607 


1.361 


1.502 


1.633 


28 


1.367 


1.491 


1.607 


1.361 


1.503 


1.634 


30 


1.367 


1.491 


1.608 


1.362 


1.503 


1.635 


40 


1.367 


1.492 


1.608 


1.363 


1.505 


1.637 


50 


1.368 


1.493 


1.609 


1.364 


1.507 


1.639 


60 


1.368 


1.493 


1.609 


1.365 


1.508 


1.640 


70 


1.368 


1.493 


1.609 


1.365 


1.508 


1.641 


80 


1.368 


1.493 


1.609 


1.366 


1.509 


1.641 


90 


1.369 


1.493 


1.610 


1.366 


1.509 


1.641 


100 


1.369 


1.494 


1.610 


1.366 


1.509 


1.642 



Note. — The apertures from which the above measurements were ob- 
tained were through material 1 1/4 inches thick, and the lower edge 2 inches 
above the bottom of the measuring-box, thus giving full contraction, 



MEASUREMENT OF FLOWING WATER. 



731 



Flow of Water Over Weirs. Weir Dam Measurement. (Pelton 
Water Wheel Co.) — Place a board or plank in the stream, as shown in 
the sketch, at some point where a pond will form above. The length of 
the notch in the dam should be from two to four times its depth i'or'small 
quantities and longer for large quantities. The edges of the notch should 
be beveled toward the intake side, as shown. The overfall below the notch 
should not be less than twice its depth. Francis savs a fall below the 
crest equal to one-half the head is sufficient, but there must be a free access 
of air under the sheet. 




%'/,. 




Fig. 142. 

In the pond, about 6 ft. above the dam, drive a stake, and then obstruct 
the water until if rises precisely to the bottom of the notch and mark the 
stake at this level. Then complete the dam so as to cause all the water to 
flow through the notch, and, after time for the water to settle, mark the 
stake again for this new level. If preferred the stake can be driven with 
its top precisely level with the bottom of the notch and the depth of the 
water be measured with a rule after the water is flowing free, but the marks 
are preferable in most cases. The stake can then be withdrawn; and the 
distance between the marks is the theoretical depth of flow corresponding 
to the quantities in the weir table on the following page. 



Francis's Formulae for Weirs. 



As given by 
Francis. 



As modified by 
Smith. 



Weirs with both end contrac- 
tions 

Weirs with one end contrac- 
tion su; 



r^ed 00 ™™: } Q - 3.33 »% 3.29 (l + |) #> 

Q = 3.33 (I -0.1 h) /i 3/2 3.29 lh 3 ^ 

Weirs with full contraction . Q = 3.33 (1-0.2 h)h 3 h 3.29 (l - A) /i 3 /2- 

The greatest variation of the Francis formulae from the values of c given 
by Smith amounts to 3 V2%- The modified Francis formulae, says Smith, 



732 



HYDRAULICS. 



will give results sufficiently exact, when great accuracy is not required, 
within the limits of h, from 0.5 ft. to 2 ft., I being not less than 3 h. 

Q = discharge in cubic feet per second, I = length of weir in feet, h = 
effective head in feet, measured from the level of the crest to the level of 
still water above the weir. 

If Q' = discharge in cubic feet per minute, and V and h' are taken in 
inches, the first of the above formulae reduces to Q' = 0.4 l'h' 3/ 2 . From this 
formula the following table is calculated. The values are sufficiently 
accurate for ordinary computations of water-power for weirs without end 
contraction, that is, for a weir the full width of the channel of approach. 
For weirs with full end contraction multiply the values taken from the 
table by the length of the weir crest in inches less 0.2 times the head in 
inches, to obtain the discharge. 



Giving Cubic Feet of Water per Minute that will Flow over a Weir 
One Inch Wide and from i/s to 207/g Inches Deep. 

For other widths multiply by the width in inches. 



Depth. 




1/8 in. 


V4 in. 


3/8 in. 


1/2 in. 


5/8 in. 


3/ 4 in. 


7/8 in. 


in. 


cu. ft. 


cu. ft. 


cu. ft. 


cu. ft. 


cu. ft. 


cu. ft. 


cu. ft. 


cu. ft. 





.00 


.01 


.05 


.09 


.14 


.19 


.26 


.32 


1 


.40 


.47 


.55 


.64 


.73 


.82 


.92 


1.02 


2 


1.13 


1.23 


1.35 


1.46 


1.58 


1.70 


1.82 


1.95 


3 


2.07 


2.21 


2.34 


2.48 


2.61 


2.76 


2.90 


3.05 


4 


3.20 


3.35 


3.50 


3.66 


3.81 


3.97 


4.14 


4.30 


5 


4.47 


4.64 


4.81 


4.98 


5.15 


5.33 


5.51 


5.69 


6 


5.87 


6.06 


6.25 


6.44 


6.62 


6.82 


7.01 


7.21 


7 


7.40 


7.60 


7.80 


8.01 


8.21 


8.42 


8.63 


8.83 


8 


9.05 


9.26 


9.47 


9.69 


9.91 


10.13 


10.35 


10.57 


9 


10.80 


11.02 


11.25 


11.48 


11.71 


11.94 


12.17 


12.41 


10 


12.64 


12.88 


13.12 


13.36 


13.60 


13.85 


14.09 


14.34 


It 


14.59 


14.84 


15.09 


15.34 


15.59 


15.85 


16.11 


16.36 


12 


16.62 


16.88 


17.15 


17.41 


17.67 


17.94 


18.21 


18.47 


13 


18.74 


19.01 


19.29 


19.56 


19.84 


20.11 


20.39 


20.67 


14 


20.95 


21.23 


21.51 


21.80 


22.08 


22.37 


22.65 


22.94 


15 


23.23 


23.52 


23.82 


24.11 


24.40 


24.70 


25.00 


25.30 


16 


25'. 60 


25.90 


26.20 


26.50 


26.80 


27.11 


27.42 


27.72 


17 


28.03 


28.34 


28.65 


28.97 


29.28 


29.59 


29.91 


30.22 


18 


- 30.54 


30.86 


31.18 


31.50 


31.82 


32.15 


32.47 


32.80 


19 


33.12 


33.45 


33.78 


34.11 


34.44 


34.77 


35.10 


35 44 


20 


35.77 


36.11 


36.45 


36.78 


37.12 


37.46 


37.80 


38.15 



When the velocity of the approaching water is less than 1/2 foot per 
second, the result obtained by the table is fairly accurate. When the vel- 
ocity of approach is greater than 1/2 foot per second, a correction should be 
applied, see page 698. 

For more accurate computations, the coefficients of flow of Hamilton 
Smith, Jr., or of Bazin should be used. In Smith's Hydraulics will be found 
a collection of results of experiments on orifices and weirs of various shapes 
made by many different authorities, together with a discussion of their 
several formulae. (See also Trautwine's Pocket Book, Unwin's Hydrau- 
lics, and Church's Mechanics of Engineering.) 

Bazin's Experiments. — M. Bazin (Annates des Ponts et Chaussees, 
Oct., 1888, translated by Marichal and Trautwine, Proc. Engrs. Club of 
Phila., Jan., 1890) made an extensive series of experiments with a sharp- 
crested weir without lateral contraction, the air being admitted freely be- 
hind the falling sheet, and found values of m varying from 0.42 to 0.50, 
with variations of the length of the weir from 19 3/ 4 to 783/ 4 in., of the 
height of the crest above the bottom of the channel from 0.79 to 2.46 ft., 



MEASUREMENT OF FLOWING WATER. 



733 



and of the head from 1.97 to 23.62 in. From these experiments he deduces 
the following formula: 

Q = [0.425+ 0.21 (^JLj^LH V^gH, 

in which P is the height in feet of the crest of the weir above the bottom of 
the channel of approach, L the length of the weir, // the head, both in feet, 
and Q the discharge in cu. ft. per sec. This formula, says M. Bazin, is 
entirely practical where errors of 2% to 3% are admissible. The following 
table is condensed from M. Bazin's paper: 

Values of the Coefficient m in the Formula Q = mLH ^2 gH, for a 
Sharp-crested Weir without Lateral Contraction; the Air 
being Admitted Freely Behind the Falling Sheet. 





Height of Crest of Weir Above Bed of Channel. 


Head, H. 




























Feet... 0.66 


98 


1 31 


1.64 1.97 


2.62 


3.28 


4.92 


6.56 


00 




Inches 7.87 


11.81 


15.75 


19.69 23.62 


31.50 


39.38 


59.07 


78.76 


oo 


Ft 


Tn 


?n 


m 


m 


m m 


m. 


m 


m 




m 


0.164 


1 97 


0.458 


0.453 


'J. 451 


0.450;0.449 


0.449 


0.449 


0.448 


0.448 


0.4481 


230 


2 76 


0.455 


0.448 


J. 445 


0.4430.442 


0.441 


0.440 


0.440 


0.439 


0.4391 


0.295 


3.54 


0.457 


44/' 


J 442 


0.440,0.438 


0.436 


0.436 


0.435 


0.434 


0.4340 


0.394 


4 72 


0.462 


443 


J 442 


0.43810.436 


0.433 


0.432 


0.430 


0.430 


0.4291 


525 


6 30 


0.471 


453 


J, 44 


0.438 0435 


0.431 


0.429 


0.427 


0.426 


0.4246 


0.656 


7 87 


0.480 


o m 


J. 447 


0.440 


0.436 


0.431 


0.428 


0.425 


0.423 


0.4215 


787 


9 45 


0.488 


4Si 


) 452 


0.444 


0.438 


0.432 


0.428 


0.424 


0.422 


0.4194 


0.919 


11.02 


0.496 


472 


J. 457 


0.448 


441 


0.433 


0.429 


0.424 


0.422 


0.4181 


1.050 


12.60 
14.17 
15.75 
17,32 




0.478 
0.483 
0.489 
0.494 


J. 452 0.452 
0.457 0.456 


0.444 
0.448 
0.451 
0.454 


0.436 
0.438 
440 
0.442 


0.430 
0.432 
0.433 
0.435 


0.424 
0.424 
0.424 
0.425 


0.421 
0.421 
0.421 
0.421 


0.4168 


1.181 




0.4156 


1.312 




0.472 
0.476 


0.459 
0.463 


0.4144 


1.444 




0.4134 


1.575 


18.90 
20.47 
22.05 
23.62 






0.480 
0.483 
0.487 
0.490 


0.467 
0.470 
0.473 
0.476 


0.457 
0.460 
0.463 
0.466 


0.444 
0.446 
D.448 
0.451 


0.436 
0.438 
0.439 
0.441 


0.425 
0.426 
0.427 
0.427 


0.421 
0.421 
0.421 
0.421 


0.4122 


1.706 






0.4112 


1 837 






0.4101 


1.969 






0.4092 











A comparison of the results of this formula with those of experiments, 
says M. Bazin, justifies us in believing that, except in the unusual case of a 
very low weir (which should always be avoided), the preceding table will 
give the coefficient m in all cases within 1% ; provided, however, that the 
arrangements of the standard weir are exactly reproduced. It is especially 
important that the admission of the air behind the falling sheet be perfectly 
assured. If this condition is not complied with, m may vary within much 
wider limits. The type adopted gives the least possible variation in the 
coefficient. 

The Cippoleti, or Trapezoidal Weir. — Cippoleti found that by using 
a trapezoidal weir with the sides inclined 1 horizontal to 4 vertical, with 
end contraction, the discharge is equal to that of a rectangular weir 
without end contraction (that is with the width of the weir equal to the 
width of the channel) and is represented by the simple formula Q = 3.367 
Lff 3 /2. A. D. Flinn and C. W. D. Dyer (Trans. A. S. C. E., 1894), in 
experiments with a trapezoidal weir, with values of L from 3 to 9 ft. 
and of H from 0.24 to 1.40 ft., found the value of the coefficient to aver- 
age 3.334, the water being measured by a rectangular weir and the results 
being computed by Francis's formula, and 3.354 when Smith's formula 
was used. They conclude that Cippoleti's formula when applied to a 
properly constructed trapezoidal weir will give the discharge with an 
error due to combined inaccuracies, not greater than 1%. 



734 WATER-POWER. 



WATER-POWER, 

Power of a Fall of Water — Efficiency. — The gross power of a fall 
pf water is the product of the weight of water discharged in a unit of time 
Into the total head, i.e., the difference of vertical elevation of the upper 
surface of the water at the points where the fall in question begins and 
ends. The term "head" used in connection with water-wheels is the 
difference in height from the surface of the water in the wheel-pit to the 
surface in the pen-stock when the wheel is running. 

If Q = cubic feet of water discharged per second, D = weight of a cubic 
foot of water = 62.36 lbs. at 60° F., H = total head in feet; then 

DQH = gross power in foot-pounds per second, 
and DQH -i- 550 = 0.1134 QH = gross horse-power. 

Q' If y ft 9 9ft 

If Q' is taken in cubic feet per minute, H.P. = Q o nnn = .00189Q'#. 

A water-wheel or motor of any kind cannot utilize the whole of the head 
H, since there are losses of head at both the entrance to and the exit from 
the wheel. There are also losses of energy due to friction of the water in 
its passage through the wheel. The ratio of the power developed by the 
wheel to the gross power of the fall is the efficiency of the wheel. For 75% 

efficiency, net horse-power = 0.00142 Q'H = ^r^- 

70o 

A head of water can be made use of in one or other of the following ways, 
viz.: 

1st. By its weight, as in the water-balance and in the overshot-wheel. 

2d. By its pressure, as in turbines and in the hydraulic engine, hydraulic 
press, crane, etc. 

3d. By its impulse, as in the undershot-wheel, and in the Pelton wheel. 

4th. By a combination of the above. 

Horse-power of a Running Stream. — The gross horse-power is 
H.P. = QHX 62.36 -v- 550 = 0.1134 QH, in which Q is the discharge in 
cubic feet per second actually impinging on the float or bucket, and H = 

v 2 v 2 

theoretical head due to the velocity of the stream = -— = — — , in which 

2 g 64.4 
v is the velocitv in feet per second. If Q f be taken in cubic feet per minute, 
H.P. = 0.00189 Q'H. 

Thus, if the floats of an undershot-wheel driven by a current alone be 5 
feet X 1 foot, and the velocity of stream = 210 ft. per minute, or 31/2 ft. 
per sec, of which the theoretical head is 0.19 ft., Q = 5 sq. ft. X 210 = 1050 
cu. ft. per minute; H.P. = 1050 X 0.19 X 0.00189 = 0.377 H.P. 

The wheels would realize only about 0.4 of this power, on account of 
friction and slip, or 0.151 H.P., or about 0.03 H.P. per square foot of 
float, which is equivalent to 33 sq. ft, of float per H.P. 

Current Motors. — A current motor could only utilize the whole 
power of a running stream if it could take all the velocity out of the water, 
so that it would leave the floats or buckets with no velocity at all; or in 
other words, it would require the backing up of the whole volume of the 
stream until the actual head was equivalent to the theoretical head due to 
the velocity of the stream. As but a small fraction of the velocity of the 
stream can be taken up by a current motor, its efficiency is very small. 
Current motors may be used to obtain small amounts of power from large 
streams, but for large powers they are not practicable. 

Bernouilli's Theorem. — Energy of Water Flowing in a Tube. — 
v 2 f 

The head due to the velocity is — ; the head due to the pressure is— ; the 

head due to actual height above the datum plane is h feet. The total head 

v 2 f 

is the sum of these = \-h-\ — - in feet, in which v = velocity in feet per 

2 g w * 

second,/ = pressure in lbs. per sq. ft., w = weight of 1 cu. ft. of water — 



WATER-POWER. 735 

62.36 lbs. If p = pressure in lbs. per sq. in., — = 2.309 p. If a constant 

quantity of water is flowing through a tube in a given time, the velocity- 
varying at different points on account of changes in the diameter, the 
energy remains constant (loss by friction excepted) and the sum of the 
three heads is constant, the pressure head increasing as the velocity de- 
creases, and vice-versa. This principle is known as " Bernouilli's Theo- 
rem." 

In hydraulic transmission the velocity and the height above datum are 
usually small compared with the pressure-head. The work or energy of a 
given quantity of water under pressure = its volume in cubic feet X its 
pressure in lbs. per sq. ft.; or it Q = quantity in cubic feet per second, 
and p = pressure in lbs. per square inch, W = 144 pQ, and the H.P. 

-.:*££?. T 0.2618 pQ. 

Maximum Efficiency of a Long Conduit. — A. L. Adams and R. C. 
Gemmell (Eng'g News, May 4, 1893) show by mathematical analysis that 
the conditions for securing the maximum amount of power through a long 
conduit of fixed diameter, without regard to the economy of water, is that 
the draught from the pipe should be such that the frictional loss in the pipe 
will be equal to one-third of the entire static head. 

Mill-Power. — A "mill-power" is a unit used to rate a water-power 
for the purpose of renting it. The value of the unit is different in different 
localities. The following are examples (from Emerson): 

Holyoke, Mass. — Each mill-power at the respective falls is declared to 
be the right during 16 hours in a day to draw 38 cu. ft. of water per second 
at the upper fall when the head there is 20 feet, or a quantity proportionate 
to the height at the falls. This is equal to 86.2 horse-power as a maximum. 

Lowell, Mass. — The right to draw during 15 hours in the day so much 
water as shall give a power equal to 25 cu. ft. a second at the great fall, 
when the fall there is 30 feet. Equal to 85 H.P. maximum. 

Lawrence, Mass. — The right to draw during 16 hours in a day so much 
water as shall give a power equal to 30 cu. ft. per second when the head is 
25 feet. Equal to 85 H.P. maximum. 

Minneapolis, Minn. — 30 cu. ft. of water per second" with head of 22 feet. 
Equal to 74.8 H.P. 

Manchester, N.H. — Divide 725 by the number of feet of fall minus 1, 
and the quotient will be the number of cubic feet per second in that fall. 
For 20 feet fall this equals 38.1 cu. ft., equal to 86.4 H.P. maximum. 

Cohoes, N.Y. — " Mill-power" equivalent to the power given by 6 cu. ft. 
per second, when the fall is 20 feet. Equal to 13.6 H.P., maximum. 

Passaic, N.J. — Mill-power: The right to draw 8 1/2 cu. ft. of water per 
sec, fall of 22 feet, equal to 21.2 horse-power. Maximum rental $700 per 
year for each mill-power = $33.00 per H.P. 

The horse-power maximum above given is that due theoretically to the 
weight of water and the height of the fall, assuming the water-wheel to 
have perfect efficiency. It should be multiplied by the efficiency of the 
wheel, say 75% for good turbines, to obtain the H.P. delivered by the 
wheel. 

Value of a Water-power. — In estimating the value of a water- 
power, especially where such value is used as testimony for a plaintiff 
whose water-power has been diminished or confiscated, it is a common 
custom for the person making such estimate to say that the value is repre- 
sented by a sum of money which, when put at interest, would maintain a 
steam-plant of the same power in the same place. 

Mr. Charles T. Main (Trans. A. S. M. E., xiii. 140) points out that this 
system of estimating is erroneous; that the value of a power depends upon 
a great number of conditions, such as location, quantity of water, fall or 
head, uniformity of flow, conditions which fix the expense of dams, canals, 
foundations of buildings, freight charges for fuel, raw materials and finishc d 
product, etc. He gives an estimate of relative cost of steam and water- 
power for a 500 H.P. plant from which the following is condensed: 

The amount of heat required per H.P. varies with different kinds of 
business, but in an average plain cotton-mill, the steam required for heat- 
ing and slashing is equivalent to about 25% of steam exhausted from tlu; 
high-pressure cylinder of a compound engine of the power required to run 
that mill, the steam to be taken from the receiver. 



736 WATER-POWER. 



The coal consumption per H.P. per hour for a compound engine is taken 
at 1 3/4 lbs. per hour, when no steam is taken from the receiver for heating 
purposes. The gross consumption when 25% is taken from the receiver is 
about 2.06 lbs. 

75% of the steam is used as in a compound engine at 1.75 lbs.== 1.31 lbs, 
25% of the steam is used as in a high-pressure engine at 3.00 lbs. = .75 lb. 

2.06 lbs. 
The running expenses per H. P. per year are as follows: 
2.06 lbs. coal per hour = 21.115 lbs. for 10 1/4 hours or one day = 

6503.42 lbs. for 308 days, which, at $3.00 per long ton = $8.71 

Atendance of boilers, one man @ $2.00, and one man @ $1.25 = 2.00 
Attendance of engine, one man @ $3.50. 2.16 

Oil, waste, and supplies. . 80 

The cost of such a steam-plant in New England and vicinity of 500 
H. P. is about $65 per H.P. Taking the fixed expenses as 4% 
on engine, 5% on boilers, and 2% on other portions, repairs at 
2%, interest at 5%, taxes at 11/2% on s/4 cost, andinsurance at 
V2% on exposed portion, the total average per cent is about 
12V2%, or $65 X O.I21/2 = 8.13 

80 



Gross cost of power and low-pressure steam per H. P. $21 



Comparing this with water-power, Mr. Main says: "At Lawrence the 
cost of dam and canals was about $650,000, or $65 per H. P The cost 
per H. P. of wheel-plant from canal to river is about $45 per H. P. of 
plant, or about $65 per H. P. used, the additional $20 being caused by 
making the plant large enough to compensate for fluctuation of power 
due to rise and fall of river. The total cost per H. P. of developed plant 
is then about $130 per H. P. Placing the depreciation on the whole 
plant at 2%, repairs at 1%, interest at 5%, taxes and insurance at 1%, 
or a total of 9%, gives: 

Fixed expenses per H. P. $1.30 X .09 = $11.70 
Running expenses per H. P. (Estimated) 2.00 

$13.70 

"To this has to be added the amount of steam required for heating 
purposes, said to be about 25% of the total amount used, but in winter 
months the consumption is at least 371/2%. It is therefore necessary to 
have a boiler plant of about 37 1/?% of the size of the one considered with 
the steam-plant, costing about $"20 X 0.375 = $7.50 per H. P of total 
power used. The- expense of running this boiler-plant is, per H. P. of 
the total plant per year: 

Fixed expenses 121/2% on $7.50 $0.94 

Coal 3 . 26 

Labor 1 . 23 

Total $5.43 

Making a total cost per year for water-power with the auxiliary boiler 
plant $13.70 + $5.43 = $19.13 which deducted from $21.80 makes a 
difference in favor of water-power of $2.67, or for 10,000 H. P. a saving 
of $26,700 per year. 

"It is fair to say," says Mr. Main, "that the value of this constant 
power is a sum of money which when put at interest will produce the 
saving; or if 6% is a fair interest to receive on money thus invested the 
value would be $26,700 -*- 0.06 = $445,000." 

Mr. Main makes the following general statements as to the value of a 
water-power: "The value of an undeveloped variable power is usually 
nothing if its variation is great, unless it is to be supplemented by a 
steam-plant. It is of value then only when the cost per horse-power'for 
the double-plant is less than the cost of steam-power under the same 
conditions as mentioned for a permanent power, and its value can be 
represented in the same manner as the value of a permanent power has 
been represented. 



TURBINE WHEELS. 737 

"The value of a developed power is as follows: If the power can be 
run cheaper than steam, the value is that of the power, plus the cost of 
plant, less depreciation. If it cannot be run as cheaply as steam, con- 
sidering its cost, etc., the value of the power itself is nothing, but the 
value of the plant is such as could be paid for it new, which would bring 
the total cost of running down to the cost of steam-power, less deprecia- 
tion." 

Mr. Samuel Webber, Iron Age, Feb. and March, 1S93, writes a series of 
articles showing the development of American turbine wheels, and inci- 
dentally criticises the statements of Mr. Main and others who have 
made comparisons of costs of steam and of water-power unfavorable to 
the latter. He says: "They have based their calculations on the cost 
of steam, on large compound engines of 1000 or more H. P. and 120 
pounds pressure of steam in their boilers, and by careful 10-hour trials 
succeeded in figuring down steam to a cost of about $20 per H. P., ignor- 
ing the well-known fact that its average cost in practical use, except 
near the coal mines, is from $40 to $50. In many instances dams, 
canals, and modern turbines can be all completed for a cost of $100 per 
H. P.; and the interest on that, and the cost of attendance and oil, will 
bring water-power up to about $10 or $12 per annum; and with a man 
competent to attend the dynamo in attendance, it can probably be 
safely estimated at not over $15 per H. P." 

WATER-WHEELS. 

Water-wheels are classified as vertical wheels (including current motors, 
undershot, breast, and overshot wheels), turbine wheels, and impulse 
wheels. Undershot and breast wheels give very low efficiency, and are 
now no longer built. The overshot wheel when made of large diameter 
(wheels as high as 72 ft. diameter have been made) and properly designed 
have given efficiencies of over 80%, but they have been almost entirely 
supplanted by turbines, on account of their 'cumbersomeness, high cost, 
leakage, and inability to work in back water. 

Turbines are generally classified according to the direction in which the 
water flows through them, as follows: 

Tangential flow: Barker's mill. Parallel flow: Jonval. Radial out- 
ward flow: Fourneyron. Radial inward flow: Thompson vortex; Francis. 
Inward and downward flow: Central discharge, scroll wheels and earlier 
American type of wheels; Swain turbine. Inward, downward, and out- 
ward flow: The American type of turbine. 

TURBINE WHEELS. 

Proportions of Turbines. — Prof. De Volson Wood discusses at 
length the theory of turbines in his paper on Hydraulic Reaction Motors, 
Trans. A. S. M. E. xiv. 266. His principal deductions which have an 
immediate bearing upon practice are condensed in the following: 
Notation, 

Q = volume of water passing through the wheel per second, 

hi = head in the supply chamber above the entrance to the buckets, 

fa = head in the tail-race above the exit from the buckets, 

z\ = fall in passing through the buckets, 

H = h\ + zi — hi, the effective head, 

hi = coefficient of resistance along the guides, 

H2 = coefficient of resistance along the buckets, 

n = radius of the initial rim, 

r2 = radius of the terminal rim, 

V = velocity of the water issuing from supply chamber, 

vi = initial velocity of the water in the bucket in reference to the bucket, 

V2 = terminal velocity in the bucket, 

w = angular velocity of the wheel, 

a = terminal angle between the guide and initial rim = CAB, Fig. 143, 

Vi = angle between the initial element of bucket and initial rim = EAD, 

72 = GFl, the angle between the terminal rim and terminal element of 
the bucket, 

a = eb, Fig. 144 = the arc subtending one gate opening, 



738 



WATER-POWER. 



ai = the arc subtending one bucket at entrance. (In practice a\ is 
larger than a,) 

0-2 = gh, the arc subtending one bucket at exit, 

K = bf, normal section of passage, it being assumed that the passages 
and buckets are very narrow. 

k\ = bd, initial normal section of bucket, 
ki = gi, terminal normal section, 
ion — velocity of initial rim, 
wr2 = velocity of terminal rim, 
= HFI, angle between the terminal rim and actual direction of 
the water at exit, 

Y = depth of K, y, of oi, and yi of K<l, then 
K = Ya sin a; Ki = 2/iaisinyi; Ki = yiai sin 72. 



wr 2 




Fig. 143. 



Fig. 144. 



Three simple systems are recognized, n < r2, called outward flow; 
ri > r 2 , called inward flow: n = r2, called parallel flow. The first and 
second may be combined with the third, making a mixed system. 

Value of 72 {the quitting angle). — The efficiency is increased as 72 
decreases, and is greatest for 72 = 0. Hence, theoretically, the terminal 
element of the bucket should be tangent to the quitting" rim for best 
efficiency. This, however, for the discharge of a finite quantity of 
water, would require an infinite depth of bucket. In practice, there- 
fore, this angle must have a finite value. The larger the diameter of 
the terminal rim the smaller may be this angle for a given depth of wheel 
and given quantity of water discharged. In practice 72 is from 10° to 20°. 

In a wheel in which all the elements except 72 are fixed, the velocity of 
the wheel for best effect must increase as the quitting angle of the bucket 
decreases. 

Values of a + yi must be less than 180°, but the best relation cannot 
be determined by analysis. However, since the water should be de- 
flected from its course as much as possible from its entering to its leaving 
the wheel, the angle a for this reason should be as small as practicable. 

In practice, a cannot be zero, and is made from 20° to 30°. 

The value n = \Ari makes the width of the crown for internal flow 
about the same as for n = r-i V1/2 for outward flow, being approximately 
3 of the external radius. 



TURBINE WHEELS. 739 



Values of m and in. — The frictional resistances depend upon the con- 
struction of the wheel as to smoothness of the surfaces, sharpness of the 
angles, regularity of the curved parts, and also upon the speed it is run. 
These values cannot be definitely assigned beforehand, but Weisbach 
gives for good conditions in = m = 0.05 to 0.10. 

They are not necessarily equal, and m may be from 0.05 to 0.075, and m 
from 0.06 to 0.10 or even larger. 

Values of yi must be less than 180° — a. 

To be on the safe side, vi may be 20 or 30 degrees less than 180° — 2 a, 
giving 

yi = 180° - 2 a - 25 (say) = 155° - 2 a. 

Then if a = 30°, vi = 95°. Some designers make vi 90°; others more, 
and still others less, than that amount. Weisbach suggests that it be less, 
so that the bucket will be shorter and friction less. This reasoning appears 
to be correct for the inflow wheel, but not for the outflow wheel. In the 
Tremont turbines, described in the Lowell Hydraulic Experiments, this 
angle is 90°, the angle a 20°, and V2 10°, which proportions insured a posi- 
tive pressure in the wheel. Fourneyron made vi = 90°, and a from 30° to 
33°. which values made the initial pressure in the wheel near zero. 

Form of Bucket. — The form of the bucket cannot be determined analyti- 
cally. From the initial and terminal directions and the volume of the 
water flowing through the wheel, the area of the normal sections may be 
found. 

The normal section of the buckets will be: K == M; ki = — ; &2= — • 

V Vl V2 



The depths of those sections will be: 



, T K ki k? 

Y = — : : ?/i = : ; 7/2 : 



a sin a' " ai sin vi «2 sin V2 

The changes of curvature and section must be gradual, and the general 
form regular, so that eddies and whirls shall not be formed. For the same 
reason the wheel must be run with the correct velocity to secure the best 
effect. In practice the buckets are made of two or three arcs of circles, 
mutually tangential. 

The Value of w. — So far as analysis indicates, the wheel may run at any 
speed; but in order that the stream shall flow smoothly from the supply 
chamber into the bucket, the velocity V should be properly regulated. 

If /(1 == /(2 = o.lO, rs •*- ri = 1.40, a = 25°, vi = 90°, V2 = 12°, the 
velocity of the initial rim for outward flow will be for m aximu m efficiency 
0.614 of the velocity due to the head, or w n = .614 "^2 gH. 

The velocity due to the head would be V2 gH = 1.414 "^gH. 

For an inflow wheel for the ca.se in w hich n 2 = 2 r-?, and the other 
dimensions as given above, wn = 0.682 V«2 gH. 

The highest efficiency of the Tremont turbine, found experimentally, 
was 0.79375, and the corresponding velocity, 0.62645 of that due to the 
head, and for all velocities above and below this value the efficiency was 
less. 

In the Tremont wheel a = 20° instead of 25°, and 72 = 10° instead of 12°. 
These would make the theoretical efficiency and velocity of the wheel some- 
what greater. Experiment showed that the velocity might be consider- 
ably larger or smaller than this amount without much diminution of the 
efficiency. 

It was found that if the velocity of the initial (or interior) rim was not 
less than 44% nor more than 75 % of that due to the fall, the efficiency was 
75% or more. This wheel was allowed to run freely without any brake 
except its own f riction, and the velocity of the i nitial rim was observed to 
be 1.335 V2 gH, half of which is 0.6675 ^2 gH, which is not far from the 
velocity giving maximum effect; that is to say, when the gate is fully 
raised the coefficient of effect is a maximum when the wheel is moving with 
about half its maximum velocity. 

Number of Buckets. — Successful wheels have been made in which the 
distance between the buckets was as small as 0.75 of an inch, and others as 
much as 2.75 inches. Turbines at the Centennial Exposition had buckets 
from 41/2 inches to 9 inches from center to center. If too large they will 
not work properly. Neither should they be too deep. Horizontal parti- 



740 WATER-POWER. 



tions are sometimes introduced. These secure more efficient working in 
case the gates are only partly opened. The form and number of buckets 
for commercial purposes are chiefly the result of experience. 

Ratio of Radii. — Theory does not limit the dimensions of the wheel. In 
practice, 

for outward flow, ri -s- n is from 1.25 to 1.5.0; 

for inward flow, r2 -*■ n is from 0.66 to 0.80. 

It appears that the inflow-wheel has a higher efficiency than the outward- 
flow wheel. The inflow-wheel also runs somewhat slower for best effect. 
The centrifugal force in the outward-flow wheel tends to force the water 
outward faster than it would otherwise flow; while in the inward-flow 
wheel it has the contrary effect, acting as it does in opposition to the 
velocity in the buckets. 

It also appears that the efficiency of the outward-flow wheel increases 
slightly as the width of the crown is less and the velocity for maximum 
efficiency is slower; while for the inflow-wheek the efficiency slightly in- 
creases for increased width of crown, and the velocity of the outer rim at 
the same time also increases. 

Efficiency. — The exact value or the efficiency for a particular wheel 
must be found by experiment. 

It seems hardly possible for the effective efficiency to equal, much less 
exceed, 86%, and all claims of 90 or more per cent for these motors should 
be discarded as improbable. A turbine yielding from 75% to 80% is 
extremely good. Experiments with higher efficiencies have been reported. 

The celebrated Tremont turbine gave 79V4% without the "diffuser," 
which might have added some 2%. A Jonval turbine (parallel flow) was 
reported as yielding 0.75 to 0.90, but Morin suggested corrections reducing 
it to 0.63 to 0.71. Weisbach gives the results of many experiments, in 
which the efficiency ranged from 50% to 84%. Numerous experiments 
give E = 0.60 to 0.65. The efficiency, considering only the energy im- 
parted to the wheel, will exceed by several per cent the efficiency of the 
wheel, for the latter will include the friction of the support and leakage at 
the joint between the sluice and wheel, which are not included in the 
former; also as a plant the resistances and losses in the supply-chamber 
are to be still further deducted. 

The Crowns. — The crowns may be plane annular disks, or conical, or 
curved. If the partitions forming the buckets be so thin that they may be 
discarded, the law of radial flow will be determined by the form of the 
crowns. If the crowns be plane, the radial flow (or radial component) 
will diminish, for the outward-flow wheel, as the distance from the axis 
increases — the buckets being full — for the angular space will be greater. 

Prof. Wood deduces from the formulae in his paper the tables on the 
next page. 

It appears from these tables: 1. That the terminal angle, a, has 
frequently been made too large in practice for the best efficiency. 

2. That the terminal angle, a, of the guide should be for the inflow less 
than 10° for the wheels here considered, but when the initial angle of the 
bucket is 90°, and the terminal angle of the guide is 5° 28', the gain of 
efficiency is not 2% greater than when the latter is 25°. 

3. That the initial angle of the bucket should exceed 90° for best effect 
for out flow-wheels. 

4. That with the initial angle between 60° and 120° for best effect on 
inflow wheels the efficiency varies scarcely 1%. 

5. In the outflow-wheel, column (9) shows that for the outflow for best 
effect the direction of the quitting water in reference to the earth should be 
nearly radial (from 76° to 97°) , but for the inflow wheel the water is thrown 
forward in quitting. This shows that the velocity of the rim should some- 
what exceed the relative final velocity backward in the bucket, as shown 
in columns (4) and (5). . 

6. In these tables the velocities given are in terms of V2 gh, and the 
coefficients of this expression will be the part of the head which would 
produce that velocity if the water issued freely. There is only one case, 
column (5), where the coefficient exceeds unity, and the excess is so small 
it may be discarded ; and it may be said that in a properly proportioned 
turbine with the conditions here given none of the velocities will equal 
that due to the head in the supply-chamber when running at best effect 



TURBINE WHEELS. 



741 



V 


= 


0.67 
0.76 
0.84 
1.00 


Head 

Equivalent 

of Energy 

in quitting 

Water. 

2~g 


© 


as us a: a; 

— o _ <s 

© © © o 


Direc- 
tion of 
quitting 
Water. 



• 


vo O pq r^ 


Termi- 
nal 
Angle of 
Guide. 


« 


SS2:2 


Velocity of 
Exit from 
Supply- 
Chamber. 
V 


- 


mil 
>>>> 

ifi « MS 

o © o o 


Relative 
Velocity of 

Entrance. 


vO 


o o o o 


Relative 

Velocity of 

Exit. 


- 


caJ CaJ cd «=» 

1 cs 1 tsl cvjl cq 
>>>> 

© o co r^ 
— ' o o ©' 


■ *3 

C t- > 
gg II 


"* 


>>>> 

© o © © 


if* 


«n 


© ©' © © 


< >> 


N 


f 00 5- - 
00 oo CO O^ 
o ©' ©" ©' 


If 


- 


© © © © 

•G O «"-J >n 



Ha 
> 


1.48 
1.50 
1.55 
1.65 




as as a; a; 
© © ©' © 


«> 


© -o in r^ 


« 


CS "T © 


t^ 


1^1^ 
!«M!r^loal(N 
>>>> 

© © ©' ©' 


5 1 


© © © — 
©' © ©' o 


s 


1 CC!| Ct3| tCJi £33 

>>>> 

© © © ©' 




I&si&siEcji&s 
>>>> 
s § 5 I 

©' © ©' ©' 




1 E33 1 CC! f =E3 1 CCS 

>>>> 

r> vo o o 
©©'©©' 


K) 


© © C> CO 
© O © © 


£ 


• • 

© © © © 

« o» N m 



742 



WATER-POWER. 



7. The inflow turbine presents the best conditions for construction for 

Eroducinga given effect, the only apparent disadvantage being an increased 
rst cost due to an increased depth, or an increased diameter for producing 
a given amount of work. The larger efficiency should, however, more than 
neutralize the increased first cost. 

Tes^s of Turbines. — Emerson says that in testing turbines it is a 
rare thing to find two of the same size which can be made to do their best 
at the same speed. The best speed of one of the leading wheels is in- 
variably wide from the tabled rate. It was found that a 54-in. Leffel 
vvheel under 12 ft. head gave much better results at 78 revolutions per 
minute than at 90. 

Overshot wheels have been known to give 75% efficiency, but the 
average performance is not over 60%. 

A fair average for a good turbine wheel may be taken at 75%. In tests 
of 18 wheels made at the Philadelphia Water- works in 1859 and 1860, one 
wheel gave less than 50% efficiency, two between 50% and 60%, six 
between 60% and 70%, seven between 71% and 77%, two 82%, and one 
87.77%. (Emerson.) 

Tests of Turbine Wheels at the Centennial Exhibition, 1876. 
(From a paper by R. H. Thurston on The Systematic Testing of Turbine 
Wheels in the United States, Trans. A. S. M. E., viii. 359.) — In 1876 the 
judges at the International Exhibition conducted a series of trials of 
turbines. Many of the wheels offered for tests were found to be more or 
less defective in fitting and workmanship. The following is a statement 
of the results of all turbines entered which gave an efficiency of over 75%. 
Seven other wheels were tested, giving results between 65% and 75%. 



Maker's Name, or Name the 
Wheel is Known by. 


£S 

h . 


"3 i 
£S 

<d o cr 


¥ 

<a o »h 


Is 

32 • 

<V o *- 

OS 


3 m 

.25 

■s"3 

C+-, M 
W o *- 


Is 


3 A 

11 

rtrv. 
g c g? 




87.68 
83.79 
83.30 
82.13 
81.21 
78.70 
79.59 
77.57 
77.43 
76.94 
76.16 
75.70 
75.15 




86.20 


82.41 
70.79 




75.35 




















Thos. Tait 






70.40 
55.90 
68.60 
79.92 


66.35 




55.00 




'7K66 


71.01 
8K24 






51.03 
67.23 






Tyler Wheel 


69.59 










74.25 
' 73J3 
'74.89 






62.75 






E. T. Cope & Sons 


69.92 












70.87 
62.06 


71.74 






67.08 
71.90 


67.57 
70.52 




W. F. Mosser & Co 


66.04 









The limits of error of the tests, says Prof. Thurston, were very uncertain; 
they are undoubtedly considerable as compared with the later work done 
in the permanent flume at Holyoke — possibly as much as 4% or 5%. 

Experiments with "draught-tubes," or "suction-tubes," which were 
actually "diffusers" in their effect, so far as Prof. Thurston has analyzed 
them, indicate the loss by friction which should be anticipated in such 
cases, this loss decreasing as the tube increased in size, and increasing as 
its diameter approached that of the wheel — the minimum diameter tried. 
It was sometimes found very difficult to free the tube from air completely, 
and next to impossible, during the interval, to control the speed with the 
brake. Several trials were often necessary before the power due to the full 
head could be obtained. The loss of power by gearing and by belting was 
variable with the proportions and arrangement of the gears and pulleys, 
length of belt, etc., but averaged not far from 30% for a single pair of bevel- 



TURBINE WHEELS. 743 

gears, uncut and dry, but smooth for such gearing, and but 10% for the 
same gears, well lubricated, after they had been a short time in operation. 
The amount of power transmitted was, however, small, and these figures 
are probably much higher than those representing ordinary practice. 
Introducing a second pair — spur-gears — the best figures were but little 
changed, although the difference between the case in which the larger gear 
was the driver, and the case in which the small wheel was the driver, was 
perceivable, and was in favor of the former arrangement. A single straight 
belt gave a loss of but 2% or 3%, a crossed belt 6% to 8%, when transmit- 
ting 14 horse-power with maximum tightness and transmitting power. A 
"quarter turn" wasted about 10% as a maximum, and a "quarter twist" 
about 5%. 

Dimensions of Turbines. — For dimensions, power, etc., of standard 
makes of turbines consult the catalogues of different manufacturers. 
The wheels of different makers vary greatly in their proportions for any 
given capacity. 

Rating and Efficiency of Turbines. — The following notes and tables 
are condensed from a pamphlet entitled "Turbine Water-wheel Tests 
and Power Tables," by R. E. Horton. Water-supply and Irrigation 
Paper No. 180, U. S. Geol. Survey, 1906. 

Theory does not indicate the numbers of guides or buckets most desir- 
able. If, however, they are too few, the stream will not properly follow 
the flow lines indicated by theory. If the buckets are too small and too 
numerous, the surface-friction factor will be large. 

It is customary to make the number of guide chutes greater than the 
number of buckets, so that any object passing through the chutes will be 
likely to pass through the buckets also. 

With most forms of gates the size of the jet is decreased as the gate is 
closed, the bucket area remaining unchanged, so that the wheel operates 
mostly by reaction at full gate and by impulse to an increasing extent as 
the gate is closed. Hence, the speed of maximum efficiency varies as 
the gate is closed. The ratio peripheral velocity -s- velocity due head for 
maximum efficiency for a 36-inch Hercules turbine is given below: 

Proportional gate opening . . . Full . 806 . 647 . 489 379 

Maximum efficiency 85.6 87.1 86.3 80 73.1 

Periph. vel. -!- vel. due head. . . 677 . 648 . 641 . 603 . 585 

American turbine practice differs from European practice in that water 
wheels are placed on the market in standard or stock sizes, whereas in 
Europe, notably on the Continent, each turbine is designed for the special 
conditions under which it is to operate, the designs being based on mathe- 
matical theory and following chiefly the Jonval and Fourneyron types. 

Having been developed by experiment after successive Holyoke tests, 
American stock pattern turbines probably give their best efficiencies at 
about the head under which those tests are made — i.e., 14 to 17 ft. 
The shafts, runners, and cases are so constructed as to enable stock sizes 
of wheels to be used under heads ranging from 6 to 60 ft. For very low 
heads they are perhaps unnecessarily cumbersome. For heads exceed- 
ing 60 ft. American builders commonly resort to the use of bronze buckets 
and "special wheels," not designed along theoretical lines, as in Europe, 
but representing modifications of the standard patterns. 

The double Fourneyron turbine used in the first installation of the 
Niagara Falls Power Co. is operated under a head of about 135 ft. Two 
wheels are used, one being placed at the top and the other at the bottom 
of the globe penstock. The runner and buckets are attached to the verti- 
cal shaft. Holes are provided in the upper penstock drum to allow 
Water under full pressure of the head to pass through and act vertically 
against the upper runner. In this way the vertical pressure of the great 
column of water is neutralized and a means is provided to counterbalance 
the weight of the long vertical shaft and the armature of the dynamo at 
its upper end. These turbines discharge 430 cu. ft. per second, make 
250 rev. per min., and are rated at 5000 H.P. 

A Fourneyron turbine at Trenton Falls, N. Y., operates under 265 ft. 
gross head and has 37 buckets, each 5| in. deep and \% inch wide at the 
least section. The total area of outflow at the minimum section is 165 
sq. in. The wheel develops 950 H.P. 

The theoretical horse-power of a given quantity of water Q, in cu. ft. 
per min., falling through a height H, in ft., is H.P. = 0.00189 QH. 



744 V/ATER-POWER. 

In practice the theoretical power is multiplied by an efficiency factor E 
to obtain the net power available on the turbine shaft as determinable by 
dynamometrical test. 

Manufacturers' rating tables are usually based on efficiencies of about 
80%. In selecting turbines from a maker's list the rated efficiency may 
be obtained by the following formula: 

E = tabled efficiency. H.P. = tabled horse-power, and Q — tabled 

discharge (C.F.M.) for any head H. E = j^'°°° Q x'ff = 528 ' 8 U^H ' 

Relations of Power, Speed and Discharge. — Nearly all American turbine 
builders publish rating tables showing the discharge in cu. ft. per min., 
rev. per min., and H.P. for each size pattern under heads varying from 
3 or 4 ft. to 40 ft. or more. 

Examples of each size of a number of the leading types of turbines 
have been tested in the Holyoke flume. For such turbines the rating 
tables have usually been prepared directly from the tests. 

Let M, R, and Q denote, respectively, the H.P., r.p.m., and discharge 
in cu. ft. per min. of a turbine, as expressed in the tables, for any head 
H in feet. The subscripts 1 and 16 added signify the power, speed, and 
discharge for the particular heads 1 and 16 ft., respectively. 

Let P, N, and F denote coefficients of power, speed, and discharge, 
which represent, respectively, the H.P., r.p.m., and discharge in cu. ft. 
per sec. under a head of 1 ft. 

The speed of a turbine or the number of rev. per min. and the discharge 
are proportional to the square root of the head. The H.P. varies with 
the product of the head and discharge, and is consequently proportional 
to the three-halves power of the head. 

Given the values of M, R, and Q from the tables for any head H, these 
quantities for any other head h are: 

M H : M h :: H 3 /z : fc 3 /2 ; R H :R h : : H 1 ^ : fcV2 ; Q H :Q h :: H 1 ?? : %% 

If H and h are taken at 16 ft. and 1 ft., respectively, the values of the 
coefficients P, N, and F are: 

P = M 1G /H 3 /2 = M l6 /64 = 0.01562 M t6 

N = _R 16 /#V2= jj lfl /4 = 0.25 R l6 

F = Q 16 /60 #V2= Q 16 /240 = 0.00417 .Q l8 . 

P, N, and F, when derived for a given wheel, enable the power, speed, 
and discharge to be calculated without the aid of the tables, and for any 
head H, by means of the following formulas: 

M = MtH ^VHj. = PH 3 /2_ 

R = Rt Vg/ffi = N ^H _ 

Q = Qi ^H/Hi = 60 F y/H. 
Since at a head of 1 ft^ and M lt R u and Q t equal P, N, and 60 F, 
respectively, H 3 ^ and "^H x each equals 1. Calculations involving i? 3 /2 
may be facilitated by the use of the appended table of three-halves 
powers. Rating tables for sizes other than those tested are computed 
usually on the following basis: 

1. The efficiency and coefficients of gate and bucket discharge for the 
sizes tested are assumed to apply to the other sizes also. 

2. The discharge for additional sizes is computed in proportion to the 
measured area of the vent or discharge orifices. 

Having these data, together with the efficiency, the tables of discharge 
and horse-power can be prepared. The peripheral speed corresponding 
to maximum efficiency determined from tests of one size of turbine may 
be assumed to apply to the other sizes also. From this datum the revo- 
lutions per minute can be computed, the number of revolutions required 
to give a constant peripheral speed being inversely proportional to the 
diameter of the turbine. 

In point of discharge, the writer's observation has been that the rating 
tables are usually fairly accurate. In the matter of efficiency there are 
undoubtedly much larger discrepancies. 



TURBINE WHEELS. 



745 



Table of H / 2 for Calculating Horse-Power of Turbines. 



t3 


0.0 


0.2 


0.4 


0.6 


0.8 


3 ^ 

X^ 


0.0 


0.2 


0.4 


0.6 


0.8 





0.00 


0.09 


0.25 


0.46 


0.72 












1 


1.00 


1.32 


1.65 


2.02 


2.42 


51 


364.21 


366.36 


368.50 


370.66 


372.82 


2 


2.83 


3.26 


3.72 


4.19 


4.69 


52 


374.98 


377.14 


379.31 


381.48 


383.66 


3 


5.20 


5.72 


6.27 


6.83 


7.41 


53 


385.85 


388.03 


390.22 


392.4- 


394.61 


4 


8.00 


8.61 


9.23 


9.87 


10.52 


54 


396.81 


399.02 


401.23 


403.45 


405.6/ 


5 


11.18 


11.86 


12.55 


13.25 


13.97 


55 


407.89 


410.11 


412.35 


414.58 


416.82 


6 


14.70 


15.44 


16.19 


16.96 


17.73 


56 


419.07 


421.31 


423.56 


425.81 


428.07 


7 


18.52 


19.32 


20.13 


20.95 


21.78 


57 


430.34 


432.60 


434.87 


437.13 


439.43 


8 


22.63 


23.48 


24.35 


25.22 


26.11 


58 


441.71 


444.00 


446.29 


448.58 


450.88 


9 


27.00 


27.91 


28.82 


29.75 


30.68 


59 


453.09 


455.49 


457.80 


460.12 


462.43 


10 


31.62 


32.53 


33.54 


34.51 


35.49 


60 


464.75 


467.08 


469.41 


471.75 


474.08 


11 


36.48 


37.48 


38.49 


39.51 


40.53 


61 


476.42 


478.77 


481.12 


483.47 


485.82 


12 


41.57 


42.61 


43.66 


44.73 


45.79 


62 


488.19 


490.55 


492.92 


495.29 


497.67 


13 


46.87 


47.9 


49.05 


50.15 


51.26 


63 


500.04 


502.43 


504.82 


507.20 


509. GO 


14 


52.38 


53.51 


54.64 


55.79 


56.94 


64 


512.00 


514.40 


516.80 


519.22 


521.63 


15 


58.09 


59.26 


60.43 


61.61 


62.80 


65 


524.04 


526.46 


528.89 


531.31 


533.75 


16 


64.00 


65.20 


66.41 


67.63 


68.85 


66 


536.18 


538.62 


541.07 


543.51 


545.96 


17 


70.09 


71.33 


75.58 


73.84 


75.10 


67 


548.42 


550.87 


553.33 


555.80 


558.27 


18 


76.37 


77.64 


78.93 


80.22 


81.52 


68 


560.74 


563.22 


565.70 


568.18 


570.66 


19 


82.82 


84.13 


85.45 


86.77 


88.10 


69 


573.16 


575.65 


578.14 


580.65 


583.15 


20 


89.44 


90.79 


92.14 


93.50 


94.86 


70 


585.66 


588.17 


590.68 


593.20 


595.73 


21 


96.23 


97.61 


99.00 


100.39 


101.79 


71 


598.25 


600.79 


603.32 


605.85 


608.39 


22 


103.19 


104.60 


106.02 


107.44 


108.87 


72 


610.93 


613.43 


616.04 


618.59 


621.15 


23 


110.30 


111.74 


113.19 


114.65 


116.11 


73 


623.71 


626.27 


628.84 


631.41 


633.99 


24 


117.58 


119.05 


120.53 


122.01 


123.50 


74 


636.57 


639.15 


641.74 


644.33 


646.92 


25 


125.00 


126.50 


128.01 


129.53 


131.05 


75 


649.52 


652.11 


654,72 


657.33 


659.94 


26 


132.57 


134.11 


135.65 


137.19 


138.74 


76 


662.55 


665.17 


667.79 


670.41 


673.04 


27 


140.30 


141.86 


143.43 


145.00 


146.58 


77 


675.67 


678.20 


680.94 


683.58 


686.2 3 


28 


148.16 


149.75 


151.35 


152.95 


154.56 


78 


688.87 


691.52 


694.18 


696.84 


699.50 


29 


156.17 


157.79 


159.41 


161.04 


162.68 


79 


702.16 


704.83 


707.50 


710. 13 


712.85 


30 


164.32 


165.96 


167.61 


169.27 


170.93 


80 


715.54 


718.22 


720.92 


723.60 


726.30 


31 


172.60 


174.27 


175.95 


177.64 


179.33 


81 


729.00 


731.70 


734.40 


737.11 


739.82 


32 


181.02 


182.72 


184.42 


186.13 


187.85 


82 


742.54 


745.26 


747.98 


750.70 


753.43 


33 


189.57 


191.30 


193.03 


194.76 


196.51 


83 


756.16 


758.90 


761.63 


764.38 


767.12 


34 


198.25 


200.00 


201.76 


203.52 


205.29 


84 


769.87 


772.62 


775.37 


778.13 


780.89 


35 


207.06 


208.84 


210.62 


212.41 


214.20 


85 


783.66 


786.42 


789. 2 J 


791.97 


794.75 


36 


216.00 


217.80 


219.61 


221.42 


223.24 


86 


797.53 


800.31 


803.10 


805.89 


808.68 


37 


225.06 


226.89 


228.72 


230.56 


232.40 


87 


811.43 


814.27 


817.0/ 


819.88 


822.70 


38 


234.25 


236.10 


237.96 


239.82 


241.68 


88 


825.51 


828.32 


831.15 


833.97 


836.79 


39 


243.56 


245.43 


247.31 


249.20 


251.09 


89 


839.62 


842.45 


845.29 


848.13 


850.96 


40 


252.98 


254.88 


256.79 


258.70 


260.61 


90 


853.81 


856.66 


859.51 


862.37 


865.22 


41 


262.53 


264.45 


266.33 


268.31 


270.25 


91 


868.08 


870.94 


873.81 


876.68 


879.55 


42 


272.19 


274.1 -5 


276.09 


278.03 


280.01 


92 


882.43 


835.30 


888.1? 


891.07 


893.96 


43 


281.97 


283.9 \ 


285.91 


287.89 


289.88 


93 


896.86 


899.75 


902.6" 


905.55 


908.45 


44 


291.86 


293.8 


295.85 


297.85 


299.86 


94 


911.35 


914.27 


917.18 


920.10 


923.02 


45 


301.87 


303.88 


305.90 


307.93 


309.95 


95 


925.94 


928.87 


931.79 


934.73 


937.66 


46 


311.97 


314.02 


316.0^ 


318.11 


32-). 16 


96 


940.60 


943.54 


946.48 


949.43 


952.38 


47 


322.22 


324.27 


326.34 


328.41 


330.48 


97 


955.33 


958.29 


961.25 


964.21 


967.17 


48 


332.55 


334.63 


336.7? 


338.81 


340.90 


98 


970.14 


973 . 1 1 


976.09 


979.07 


982.05 


49 


343 00 


345. 10 


347.21 


349.3? 


351.43 


99 


985.03 


988.02 


991.01 


994.00 


996.99 


50 


353 55 


355.67 


357.80 


359.93 


362.07 


100 


1000.00 





















Rating Table for Turbines. 

Leffel Standard (New Type). Pivot Gate. [1900 list.] 



Diameter of 


Manufacturer's Rating for 
a Head of 16 Ft. 


Coefficients. 


Runner in 
Inches. 


H.P. 

( = M). 


Cu. Ft. 
per rain. 


Revs, 
per min. 


Power 

( = P). 


Dis- 
charge. 
( = F). 


Speed 

( = iV). 


10 

111/2 


3.70 
4.9 
6.5 
8.4 
11.00 
14.9 
19.4 
25.25 
33.61 
44.3 
58.2 
67.75 
84.1 
142 
168 
2C2 
247 


53 

201 

267 

348 

455 

602 

802 

1,043 

1,390 

1,831 

2,406 

2,800 

3,475 

5,858 

6,950 

8,340 

10,222 


535 
463 
404 
351 
306 
268 
233 
202 
176 
153 
134 
122 
110 
96 
87 
80 
72 


0.058 
.076 

.101 

.131 

.172 

.232 

.303 

.393 

.524 

.691 

.908 

1.058 

1.312 

2.215 

2.621 

3.151 

3.853 


0.220 

.838 

1.113 

1.451 

1.897 

2.510 

3.344 

4.339 

5.796 

7.635 

10.033 

11.676 

14.490 

24.428 

28.982 

34.778 

42.623 


133.8 
115.8 


131/4 


101.0 


151 4 


87.8 


171/2 

20 

23 

261/2 

30 1/2 


76.5 
67 

58.2 
50.5 

44 


35 


38.2 


40 

44 

43 


33.5 
30.5 
27.5 


56 


24 


61 


21.8 


66 


20 


74 


18 



Leffel Improved Samson. Pivot Gate. [1897 and 1900 lists.] 



20 


51.7 
68.3 
87.3 

116 

158 

207 

262 

324 

405 

497 

597 

708 


2,111 
2,792 
3,569 
4,751 
6,440 
8,446 
10,689 
13,196 
16,554 
20,292 
24,409 
28,906 


325 
283 
250 
217 
186 
163 
145 
130 
116 
105 
96 
88 


0.806 
1.065 
1.362 
1.810 
2.465 
3.229 
4.087 
5.054 
6.318 
7.753 
9.313 
11.045 


8.803 
11.643 
14.883 
19.812 
26.855 
35.220 
44.573 
55.027 
69.030 
84.618 
101.786 
120.538 


81 3 


23 . . 


70 8 


26.... 


62 5 


30 


54.3 


35 


46 5 


40 ... 


40 8 


45 


36 3 


50 


32.5 


56 . . 


29.0 


62.... 


26 3 


68 ... 


24.0 


74 


22.0 



Victor High Pressure Turbine. Cylinder Gate. [1903 list.] 
Ratings for 100 Ft. Head. 



14 


37 
50 


247 
332 


656 

574 


0.037 
.050 


0.412 
.553 


65.6 


16 


57.4 


is : 


66 


442 


510 


.066 


.733 


51.0 


20 


82 


542 


459 


.082 


.903 


45.9 


22 


106 
128 
151 
173 
191 
228 
272 
303 


707 
850 
1,001 
1,147 
1,265 
1,512 
1,805 
2,005 


417 
383 
353 
328 
306 
278 
255 
235 


.106 
.128 
.151 
.173 
.191 
.228 
.272 
.303 


1.178 
1.417 
1.668 
1.912 
2.108 
2.520 
3.008 
3.342 


41.7 


24 


38.3 


26 


35.3 


28 


32.8 


30 . . 


30.6 


33 


27.8 


36 . 


25.5 


39 


23.5 


42 


343 


2,277 


219 


.343 


3.795 


21.9 


45 


387 


2,563 


204 


.387 


4.272 


20.4 


43 


426 


2,820 


191 


.426 


4.700 


19.1 


51 


462 


3,063 


180 


.462 


5.105 


18.0 


54 


504 


3,340 


170 


.504 


5.567 


17.0 


57 


544 


3,605 


161 


.544 


6.008 


16.0 


60 


590 


3,907 


153 


.590 


6.512 


15.3 


63 


619 
680 
742 
799 


4,100 
4,505 
4,910 
5,290 


146 
139 
133 
127 


.619 
.680 

.742 
.799 


6.833 
7.508 
8.183 
8.817 


14.6 


66 


13.9 


69 


13.3 


72 


12.7 



am 



TURBINE WHEELS. 747 

The discharge of turbines is nearly always expressed in cubic feet per 
minute. The "vent" in square inches is also used by millwrights and 
manufacturers, although to a decreasing extent. The vent of a turbine 
is the area of an orifice which would, under any given head, theoretically 
discharge the same quantity of water that is vented or passed through a 
turbine under that same head when the wheel is so loaded as to be run- 
ning at maximum efficiency. 

If V = vent in sq. in., Q = discharge in cu. ft. per min. under a head H, 
F = dis charge in cu. ft. per sec. under a head of 1 foot, then Q = 60 F/144 
V2gH = 3.344 V^H, and V = 0.3 QI^H; also V= 17.94 F and F = 
0.0557 V. 

The vent of a turbine should not be confused with the area of the out- 
let orifice of the buckets. The actual discharge through a turbine is 
commonly from 40 to 60% of the theoretical discharge of an orifice whose 
area equals the combined cross-sectional areas of the outlet ports meas- 
ured in the narrowest section. 

The high-pressure turbine is a recent design (1903), and is tabled for 
heads of 70 to 675 feet. 

A 10,000 H.P. Turbine at Snoqualmie, Wash. (Arthur Giesler, 
Eng. News, Mar. 20, 1906.)— The fall is about 270 ft. high. The machin- 
ery is placed in an underground chamber excavated in the rock about 
250 ft. below the surface, and 300 ft. up-stream from the crest of the falls. 
A tail-race tunnel runs to the lower reach of the river. The wheel 'was 
designed by the Piatt Iron Works Co., Dayton, O., for an effective head 
of 260 ft. and 300 r.p.m., the latter being fixed by the limitations of 
dynamo design. There .was no precedent for a generator approximating 
10,000 H.P. running at such a speed. The turbine is a horizontal shaft 
machine, of the Francis type, radial inward flow with central axial dis- 
charge. The turbine proper has only one bearing, SS/s X 26 in., the gen- 
erator having three bearings. The draft tube is on the generator (front) 
side. The shaft-bearing, thrust-bearing and thrust-balancing devices are 
at the back side. The wheel is 66 in. outside diam. by 9 in. wide through 
the vanes. It has 34 vanes which extend a short distance beyond the 
end plate of the wheel on the discharge side. There are 32 guide vanes, 
of the swivel type, connected to a rotatable ring which is actuated by a 
Lombard governor. The turbine wheel or runner is an annular steel 
casting. It is bolted to a disk 46 in. diam., which is an ■enlargement of 
the 131/2 in. hollow nickel-steel shaft. A test for efficiency was made, in 
which the output was measured on the electrical side, and the input by 
the drop of head across the head gate. At 10,000 H.P. the efficiency 
shown was 84%, the figure being subject to the inaccuracy of the water 
measurement. The maximum capacity registered was 8250 K.W. or 
11.000 H.P. With the generator and the governor disconnected, with 
full gates and no load, the wheel ran at 505 r.p.m. 

Turbines of 13,500 H.P.— Four Francis turbines, with vertical shafts, 
rated at 13,500 H.P. each, have been built bv Allis-Chalmers Co., for the 
Great Northern Power Co., Duluth. Minn. The available head is 365 ft., 
and the wheels run at 375 r.p.m.; discharging, at full load, about 400 cu. 
ft. per second, each. The runners are 62 in. diam. The penstock for 
each wheel is 84 in. diam., reduced gradually to 66 in. at the wheel. 
(Bulletin No. 1613, A.-C. Co.) 

The " Fall-increaser " for Turbines. — A circular issued Nov., 1908, 
by Clemens Herschel, the inventor of the Venturi Meter, illustrates a 
device, based on the principle of the meter, for diminishing the back- 
water head which acts against the turbine. The surplus water, which 
would otherwise run to waste, is caused to flow into a tube of the Venturi 
shape, and the pressure in the narrow section, or throat of this tube, is 
less than that due to the head of the back-water into which the tube dis- 
charges. The throat is perforated with a great number of 6-in. holes, 
through wmich the discharge-water of the turbine is caused to flow, the 
velocity through the holes being never over 4 ft. per second. The circular 
says: 

The fall-increaser is a form of power-house foundation construction so 
made that by running through it water, which would otherwise waste 
over the dam, the fall acting on the turbines is increased, and the output 
of power is kept at its maximum quantity, in spite of the back-water 



748 WATER-POWER. 

which always accompanies an abundance of river flow passing down the 
river. 

The results show that fall-increasers add about 10% to the annual 
output of power with no appreciable increase in operating expenses. 

For half the days of the year the fall-increasers are shut down because 
there is not enough, or only enough, water to supply the plain turbines; 
but for the other half of the year the fall-increasers keep the output of 
power practically constant, and at the full output, where this power 
output would fall to half the full output or less if the fall-increasers had 
not been built. 

An illustrated description of the fall-increaser, with results of tests, is 
given in the Harvard Eng'Q Journal, June, 1908. See also U. S. Pat. 
No. 873,435 and Eng. News, June 11, 1908. 

TANGENTIAL OR I31PULSE WATER-WHEELS. 

The Pelton Water-wheel. — Mr. Ross E. Browne (Eng'g News, Feb. 
20, 1892) thus outlines the principles upon which this water-wheel is 
constructed: 

The function of a water-wheel, operated by a jet of water escaping 
from a nozzle, is to convert the energy of the jet, due to its velocity, into 
useful work. In order to utilize this energy fully the wheel-bucket, 
after catching the jet, must bring it to rest before discharging it, without 
inducing turbulence or agitation of the particles. 

This cannot be fully effected, and unavoidable difficulties necessitate 
the loss of a portion of the energy. The principal losses occur as follows: 
First, in sharp or angular diversion of the jet in entering, or in its course 
through the bucket, causing impact, or the conversion of a portion of the 
energy into heat instead of useful work. Second, in the so-called fric- 
tional resistance offered to the motion of the water by the wetted surfaces 
of the buckets, causing also the conversion of a portion of the energy into 
heat instead of useful work. Third, in the velocity of the water, as it 
leaves the bucket, representing energy which has not been converted into 
work. 

Hence, in seeking a high efficiency: 1. The bucket-surface at the en- 
trance will be approximately parallel to the relative course of the jet, and 
the bucket should be curved in such a manner as to avoid sharp angular 
deflection of the stream. If, for example, a jet strikes a surface at an 
angle and is sharply deflected, a portion of the water is backed, the 
smoothness of the stream is disturbed, and there results considerable 
loss by impact and otherwise. 

2. The path of the jet in the bucket should be short; in other words, 
the total wetted surface of the bucket should be small, as the loss by fric- 
tion will be proportional to this. 

3. The discharge end of the bucket should be as nearly tangential to 
the wheel periphery as compatible with the clearance of the bucketwhich 
follows; and great differences of velocity in the parts of the escaping 
water should be avoided. In order to bring the water to rest at the dis- 
charge end of the bucket, it is shown, mathematically, that the velocity 
of the bucket should be one half the velocity of the jet. 

A bucket, such as shown in Fig. 145, will cause the heaping of more or 
less dead or turbulent water at the point indicated by dark shading. 
This dead water is subsequently thrown from the wheel with considerable 
velocity, and represents a large loss of energy. The introduction of the 
wedge in the Pelton bucket (see Fig. 146) is an efficient means of avoiding 
this loss. 






Fig. 145. Fig. 146. Fig. 147. 

A wheel of the form of the Pelton (Fig. 147) conforms closely in con- 
struction to each of these requirements. [In wheels as now made (1909) 



TANGENTIAL OR IMPULSE WATER-WHEELS. 749 

the sharp corners shown in this bucket are eliminated. See catalogues 
of the Pelton Water Wheel Co., Joshua Hendy Iron Works, and Abner 
Doble Co., all of San Francisco.] 

Considerations in the Choice of a Tangential Wheel (Joshua 
Hendy Iron Works.) — The horse-power that can be developed by a tan- 
gential wheel does not depend upon the size of the wheel but. solely upon 
the head and volume of water available. The number of revolutions per 
minute that a wheel makes (running under normal conditions) depends 
solely upon two factors, viz., its diameter and the head of water. 

The choice of the diameter of a wheel is not therefore controlled by the 
power required but by the speed required when working under a given 
head. If a wheel has no load, and is not governed, it will speed up until 
the periphery is revolving at approximately the same velocity as the 
spouting velocity of the jet, but as soon as the wheel commences to de- 
velop power by driving machinery, etc., its velocity will drop. In a 
properly designed wheel the velocity of the rim in lineal feet per minute, 
at full load, will be from 48 to 50% of the spouting velocity of the jet. 

The diameter of pulley wheels on wheel shaft and countershafts of 
machinery should be so proportioned that the water wheel shall run at 
the speed given in the table. 

The width, area and curvature of buckets are designed to meet condi- 
tions of volume of flow under given heads. The higher the peripheral 
velocity of the wheel, the greater the volume of water that the buckets 
can handle, and consequently the same standard wheel can handle more 
water, the higher the head. 

Standard wheels can generally be adapted one size larger or one size 
smaller to meet conditions of a variation of speed or volume of flow 
under a given head. Wheels designed for a given horse-power can be 
used for smaller powers (within reasonable limits) with very little loss of 
efficiency, but an increase in the volume to be used requires a larger 
bucket. If, for the purpose of maintaining the same speed conditions, 
the same diameter of wheel is to be adhered to, then a special wheel 
must be built with either very large buckets or with two or more nozzles, 
or else a double or multiple unit must be adopted. 

It is advised to subdivide large streams between two, three or more 
runners, as this insures a greater freedom from breakdown and is often 
cheapest in the end. Single-nozzle, multiple runner units are easier to 
govern than multiple-nozzle, single runner units. When two or more 
nozzles are used in combination on one runner, the increased volume to 
be dealt with is divided between the different nozzles, which are so 
arranged that their respective jets impinge on different buckets at differ- 
ent parts of the periphery. Three-nozzle and five-nozzle wheels have 
many disadvantages, when governing is required, and should only be 
adopted for handling a very large volume of water when other designs 
cannot be used. 

Combined Heads. — When two or more water powers are available at 
the same site, but under different heads, it is possible to utilize them by 
mounting wheels of different diameters in parallel, or, when the difference 
of head and. volume is very great, it would even be possible to arrange 
for a turbine for the low head and a tangential wheel for the high head, 
although, in the latter case, it would probably be best to mount them 
independently and connect to the machinery through the medium of 
belts and countershafts. In either case, separate pipe lines must be 
employed. 

Reversible Wheels. — In the case of reversible wheels desired for use 
with hoists, cableways, etc., two wheels of proper dimensions and the 
same type may be mounted parallel on the same shaft, one of the wheels 
having the buckets and nozzles arranged to run in the opposite direction 
to the other. Suitable valves, levers and pipe connections can be arranged 
to cut the water off one wheel and turn it on to the other. 

Horizontal Wheels. — For electric generating stations, when it is de- 
sired to place the wheels below the floor of the generators, where vertical 
direct-connected equipments are used, tangential wheels may be mounted 
horizontally with vertical shafts and step bearings. 

Notes on Hydraulic Power Installations. (Joshua Hendy Iron 
Works.)— Apertures of screens must be slightly smaller than the diameter 
of the smallest nozzle used. 



750 WATER-POWER. 



When not in use, keep the pipe full by closing the valve at the lower 
end. There is less liability for trouble from expansion and contraction 
with a full pipe line. 

Equip the pipe line with air valves, approximately one for every 20 ft. 
of head. 

When operating under high heads, when no other precaution has been 
taken to avoid water ram during the process of governing, it is advisable 
to install relief valves between the lower end of the pipe line and the 
gates or controllers. 

When operating under even moderately high heads, if no safety device 
or by-pass has been installed, and a plain valve is to be used, sliding 
gates and butterfly valves should not be employed, but only screw gates, 
as the former would be too rapid in their action and might set up a 
dangerous water ram. 

The size of the nozzle that must be used on a wheel for maximum 
efficiency must be such as will just keep the pipe line full. If water 
overflows, put on a larger nozzle. If the pipe remains partly empty, put 
on a smaller nozzle, as otherwise the effective head is reduced, with con- 
siderable loss of efficiency. 

The nozzles may be placed either above or below the wheel, depending 
on the direction of rotation required. 

Control of Tangential Water-Wheels. — The methods of regulating 
tangential water-wheels may be classified under five heads: 

1. Permanently or semi-permanently altering the area of efflux of the 
nozzles, with water economy and without loss of efficiency. 

2. Reducing the volume of flow without altering the area of efflux, 
with water economy but with loss of efficiency. 

3. Variable alteration of the area of efflux without loss of efficiency 
and with water economy. 

4. Deflection of the jet, so that only a portion of its energy is trans- 
mitted to the wheel, without water economy. 

5. Combined regulation of 3 and 4, producing an effect whereby the 
energy of the jet is reduced rapidly without water ram and the area of 
efflux reduced slowly to effect water economy, or by a combination of 3 
with some form of by-pass. 

Governors. — Of the five methods of control enumerated above, the 
first cannot be done automatically; the other four, however, are suscep- 
tible to either hand regulation or automatic regulation by means of gov- 
ernors, the function of the governor being merely to automatically bring 
into action the particular controlling device with which the wheel has 
been equipped. There are two leading types of governors, the hydraulic 
and the mechanical. In the first, the mechanism of the water-wheel 
regulator is actuated by a hydraulically operated piston, the motive 
power being taken from a small branch pipe from the main water supply, 
or from an independent high-pressure oil-pumping system, the position 
of the piston in the cylinder and consequent relative position of the 
controlling mechanism being dependent upon the amount of fluid under 
pressure admitted to the cylinder at either end. This is controlled by a 
main valve, operated by a very sensitive relay valve which, in turn, is 
directly controlled by the centrifugal balls of the governor. 

The second type, or mechanically operated governor, consists of a 
device for automatically controlling and directing the transmission of 
the requisite amount of energy taken from the wheel shaft, to operate 
the water-regulating mechanism. The Lombard governor is a represen- 
tative of the first type, and the Lombard-Replogle governor of the 
second. 

The close regulation that can be obtained with the latter is remarkable. 
Any size will go into operation and make connection at so slight a devia- 
tion as one-tenth of one per cent from normal, and in installations which 
have been made they will not permit of a departure of more than five to 
eight per cent temporarily where there is an instantaneous drop from 
full load to practically no load. When there is sufficient fly-wheel effect, 
the deviation will not be over two per cent. The adoption of fly wheels 
greatly facilitates many problems of governing. 



TANGENTIAL OR IMPULSE WATER-WHEEL. 751 



Tangential Water-Wheel Table. (Joshua Hendy Iron Works.) 

P = horse-power, Q = cubic feet per minute, R = revs, per min. The 
smaller figures in the first column give the spouting velocity of the jet 
in feet per minute. (The table is greatly condensed from the original; 
6-in., 15-in., and 30-in. wheels are also listed. P and Q are the same, 
with any given head, for a 30 as for a 36-in. wheel, but R is 20% greater.) 



a. a 


P 

Q 
R 


12 

Inch. 


18 

Inch. 


24 

Inch. 


36 

Inch. 


48 

Inch. 


60 

Inch. 


72 

Inch. 


8 

Feet. 


10 

Feet. 


12 

Feet. 


20 ( 

2152 | 


.12 
3.91 

342 


.37 
11.72 

228 


.66 

20.83 

171 


1.50 

46.93 

114 


2.64 

83.32 

85 


4.18 

130.36 

70 


6.00 

187.72 

57 


10.64 

332.70 

43 


16.48 
515.04 

34 


23.80 

748.95 

29 


30 ( 

2636 j 


P 

Q 

R 


.23 
4.79 

418 


.69 

14.36 

279 


1.22 

25.51 

209 


2.76 

57.44 

139 


4.88 

102.04 

104 


7.69 

159.66 

83 


11.04 

229.76 

69 


19.53 

407.03 

52 


30.00 

630.00 

41 


43.80 

916.47 

35 


40 j 

3043 ( 


P 
Q 
R 


.35 
5.53 
484 


1.05 

16.59 

323 


1.89 

29.46 

242 


4.24 

66.36 

161 


7.58 

107.84 

121 


11.85 

184.36 

96 


16.96 

265.44 

80 


30.08 

470.27 
62 


46.60 

728.16 
49 


67.60 

1058.86 

40 


50 ( 
3403 J 


P 

Q 
R 


.49 
6.18 
541 


1.49 

18.54 

361 


2.65 

32.93 

270 


5.98 

74.17 

180 


10.60 

131.72 

135 


16.63 

206.13 

108 


23.93 

296.70 

90 


42.05 

525.90 
69 


65.00 

814.32 
55 


94.50 

1184.15 

46 


60 \ 
3727 ( 


P 
Q 
R 


.65 
6.77 
592 


1.96 

20.31 

395 


3.48 

36.08 

296 


7.84 

81.25 

197 


13.94 

144.32 

148 


21.77 

225.80 

118 


31.36 

325.00 

98 


55.20 

576.00 

75 


85.62 

892.00 
60 


124.50 

1297.00 

50 


70 S 

4026 ( 


P 


.82 
7.31 
640 


2.47 

21.94 

427 


4.39 

38.^7 

320 


9.88 
87.76 
2.13 


17.58 

155.88 
160 


27.51 

243.89 

130 


39.52 

351.04 

106 


70.00 

624.00 
81 


107.80 

966.24 

64 


157.50 

1405.17 

54 


80 S 

4304 ( 


P 
Q 
R 


1.00 

7.82 
684 


3.01 

23.46 

456 


5.36 

41.66 

342 


12.04 

93.84 
228 


21.44 

166.64 

171 


33.54 

260.73 

137 


48.16 

375.36 

114 


85.76 

666.56 

87 


134.16 

1042.92 
69 


192.64 

1501.44 

58 


90 j 

4565 ( 


P 

R 


1.20 

8.29 
726 


3.60 

24.88 

484 


6.39 

44.19 

363 


14.40 

99.52 

242 


25.59 

176.75 

181 


40.04 

276.55 
145 


57.60 

398.08 

121 


102.36 

707.00 
93 


160.16 

1106.20 

73 


230.40 

1592.32 

62 


100 i 

4812 ( 


P 
R 


1.40 

8.74 
765 


4.21 

26.22 

510 


7.49 

46.58 

382 


16.84 

104.88 

255 


29.93 

186.32 

191 


46.85 

291.51 

152 


67.36 

419.52 

127 


119.72 

745.28 
96 


187.40 
1166.04 

77 


269.44 

1678.08 

64 


120 \ 

5271 ( 


P 

Q 
R 


1.84 
9.57 
838 


5.54 

28.72 

559 


9.85 

51.02 

419 


22.18 

114.91 

279 


39.41 

204.10 
209 


61.66 

319.33 

167 


88.75 

459.64 

139 


157.64 

816.40 

105 


246.64 

1277.32 

83 


355.00 

1838.56 

70 


140 ( 

5694 j 


P 

1 


2.33 

10.34 

906 


6.99 

31.03 

604 


12.41 

55.11 

453 


27.96 

124.12 

302 


49.64 

220.44 

226 


77.71 

344.92 

181 


111.85 

496.43 
151 


198.56 

881.76 
114 


310.84 

1379.68 

90 


447.40 

1985.92 

75 


160 ( 

6087 ( 


P 
Q 
R 


2.84 

11.05 

969 


8.54 

33.17 

646 


15.17 

58.92 
484 


34.16 

132.68 

323 


60.68 

235.68 

242 


94.94 

368.73 
193 


136.65 

530.75 

161 


242.72 

942.72 

121 


377.76 

1474.92 

97 


546.60 

2123.00 

81 


180 ( 

6456 j 


P 
Q 
R 


3.39 
11.72 
1024 


10.19 

35.18 
683 


18.10 

62.49 

513 


40.77 

140.74 

342 


72.41 

249.97 

256 


113.30 

391.10 
206 


163.08 

562.96 

171 


289.64 

999.83 

128 


453.20 

1564.40 

103 


652.32 

2251.84 

86 


200$ 

6805 j 


P 
Q 
R 


3.97 
12.36 

1080 


11.93 

37.08 
720 


21.20 

65.87 

540 


47.75 

148.35 

360 


84.81 

263.49 

270 


132.70 

412.25 

216 


191.00 

593.40 
180 


339.24 

1053.96 

135 


530.80 

1649.00 

108 


764.00 

2373.60 

90 


225 ( 

7215 j 


P 

Q 
R 
P 
Q 
R 








56.99 

157.33 

382 

66.74 
165.86 
. 403 


101.20 
279.44 

287 
118.54 
294.59 

302 


158.38 
437.23 

229 
185.47 
460.91 

241 


227.96 
629.32 

191 
266.96 
663.45 

202 


404.80 
1117.76 
144 
474.16 
1178.36 
151 


633.52 
1748.92 
115 
741.88 
1843.64 
121 


911.84 








2517.28 








96 


250 ( 

7608 j 


5.56 

13.82 
1209 


16.68 

41.46 

806 


29.63 

73.64 

605 


1067.84 

2653.80 

101 



752 



WATER-POWER. 



Tangential Water- Wheel Table.— Continued. 





P 
Q 
R 


12 
Inch. 


18 
Inch. 


24 

Inch. 


36 

Inch. 


48 

Inch. 


60 

Inch. 


72 

Inch. 


8 

Feet. 


10 

Feet. 


12 

Feet. 


275 ( 

7975 j 






77.00 

173.94 

423 


136.76 

308.92 

317 


214.00 

483.39 

253 


308.00 

695.76 

211 


547.04 

1235.68 

159 


856.00 

1933.56 

127 


1232.00 

2783.04 

106 














300 ( 

8335 | 


P 
Q 
R 


7.31 
15.13 
1326 


21.93 

45.42 
884 


38.95 

80.67 

663 


87.73 

181.59 

442 


155.83 

322.71 

331 


243.82 

504.91 

265 


350.94 

726.76 

221 


623.32 

1290.84 

166 


975.28 

2019.64 

133 


1403.76 

2907.04 

111 


325 ( 

8672) 


P 
Q 
R 
P 

R 








98.93 
189.10 

460 
110.56 
196.25 

477 


175.68 
335.84 

344 
196.38 
348.57 

358 


274.94 
525.50 

276 
307.25 
545.36 

275 


395.72 
756.40 

230 
442.27 
785.00 

238 


702.72 
1343.36 
172 
785.52 
1394.28 
179 


1099.76 
2102.00 

138 
1229.00 
2181.44 

143 


1582.88 

3025.60 

115 














350 ( 

9002 | 


9.21 
16.35 

1432 


27.64 

49.06 

955 


49.09 

87.14 

716 


1769.08 

3140.00 

119 


400 j 

9624 j 


P 
Q 

R 


11.25 
17.48 
1531 


33.77 
52.45 
1021 


59.98 

93 16 

765 


135.08 

209.80 
510 


239.94 

372.64 

382 


375.40 

583.02 

306 


540.35 

839.20 

255 


959.76 

1490.56 

101 


1501.60 

2332.08 

153 


2161.40 

3356.80 

128 


450 ( 

10208 j 


P 

Q 
R 


13.43 

18.54 
1624 


40.79 
55.63 
1083 


71.57 

98.81 
812 


161.19 

222.52 
541 


286.31 

395.24 

406 


447.95 

618.38 

324 


644.78 

890.11 

270 


1145.24 

1580.96 

203 


1791.80 

2473.52 

162 


2579.12 

3560.44 

135 


500 ( 

10760 I 


P 


15.73 
19.54 
1713 


47.20 
58.64 
1142 


83.83 

104.15 

856 


188.80 

234.56 

571 


335.34 

416.62 

428 


524.66 

651.83 

342 


755.20 

938.25 

285 


1341.36 

1666.48 

214 


2098.64 

2607.02 

171 


3020.80 

3753.00 

143 


550 ( 

11279 J 


P 

R 
P 

R 








217.82 
246.00 

599 
248.16 
256.95 

625 


386.84 
436.92 

449 
440.77 
456.38 

469 


605.31 
683.62 

359 
689.63 
714.05 

375 


871.28 
984.00 

299 
992.65 
1027.80 

312 


1547.36 
1747.68 

225 
1763.08 
1825.52 

235 


2421 .24 
2734.48 

179 
2758.52 
2856.20 

188 


3485 12 








3936 00 








150 


600 ( 

11787) 


24.26 

25.12 

1876 


62.04 
64.24 
1251 


110.19 

114 09 

938 


3970.60 

4111.20 

156 


640 ( 


P 

R 
P 
Q 

R 








270.97 
264.63 

644 
312.73 
277.54 

675 


484.16 
466.12 

483 
555.46 
492.95 

506 


748.80 
731.59 

387 
869.06 
771.26 

405 


1083.88 
1058.52 

322 
1250.92 
1110.16 

337 


1936.64 
1864.48 

242 
2221.84 
1971.80 

253 


2995.20 
2926.36 

194 
3476.24 
3085.04 

203 


4335 52 








4234 08 










161 


700 ( 
12731 | 


30.57 
27.13 
2026 


78.18 
69.38 
1351 


138.86 

123.23 

1013 


5003.68 

4440.64 

169 


750 ( 

13178) 


P 

Q 
R 


33.91 

28.08 
2098 


86.70 
71.82 
1309 


154.00 

127.56 

1049 


346.83 

287.28 

699 


616.03 

510.25 

524 


963.82 

798.33 

419 


1387.34 

1149.13 

349 


2464.12 

2041.00 

262 


3855.28 

3193.32 

210 


5549.36 

4596.52 

175 


800 ( 

13610) 


P 

Q 

R 


37.35 
29.00 
2166 


95.52 
74.17 
1444 


169.66 

131.74 

1083 


382.09 

296.70 

722 


678.66 

526.99 

542 


1061.81 

824.51 

433 


1528.36 

1186.81 

361 


2714.64 

2107.96 

271 


4247.24 

3298.04 

217 


6113.44 

4747.24 

181 


900 ( 

14436 j 


P 

Q 

R 


44.57 
30.76 
2298 


113.98 
78.67 
1532 


202.45 

139.74 

1149 


455.94 

314.70 

766 


809.82 

558.96 

574 


1267.02 

874.53 

459 


1823.76 

1258.81 

383 


3239.28 

2235.84 

287 


5068.08 

3498.12 

229 


7295.04 

5035.24 

192 


1000 ( 

15217 J 


P 
Q 
R 


52.20 
32.42 
2420 


133.50 
82.93 
1615 


237.12 

147.30 

1210 


534.01 

331.72 

807 


948.48 

589.19 

605 


1483.97 
921.83 

484 


2136.04 

1326.91 

403 


3793.92 

2356.76 

303 


5935.88 

3687.32 

242 


8544.16 

5287.64 

202 



The above tables are compiled on the following ba,sis: 

The head (h) is the net effective head at the nozzle. Proper allowance 

must be made for all losses in the pipe line. 

The velocity of efflux (V) is the approximate spout ing velocity of the 

jet in feet per minute as it issues from the nozzle = V2 gh X 60 = 481.2 

VK. 

The discharge in cubic feet per minute = Q = V X a, where a equals 
the cross-section area of nozzle opening in sq. ft., no allowance being 
made for friction in the nozzle. 



TANGENTIAL OR IMPULSE WATER-WHEEL. 



753 



The weight of a cubic foot of water is taken at 39.2° Fahr. = 62.425 lbs. 

The theoretical horse-power = Q X 62.425 xft + 33.000 = 0.00189 Qh. 

The horse-power in the tables is based on 85% mechanical efficiency for 
the wheels. 

The diameter is the effective diameter at the line of the nozzle center, 
where the jet impinges on the center of the bucket. 

The number of revolutions is based on a peripheral speed for the effec- 
tive diameter, of half the velocity of efflux of the jet, and equals 7t2C, 
where C = the circumference (in feet) of the effective diameter. 

Small wheels, up to 24-in. diam., are commonly called motors. 

Amount of Water Required to Develop a Given Horse-Power, with 
a Given Available Effective Head. 



Horse-Power Based on 85% Efficiency of the Water Wheel. 



Flow in Cubic Feet of Water per Minute Required to 
Develop Power. 



250 


375 


500 


625 


750 


875 


1000 


1125 


208 


312 


416 


520 


624 


726 


830 


934 


177 


266 


355 


444 


532 


621 


709 


798 


155 


232 


311 


388 


466 


544 


622 


699 


140 


210 


280 


350 


420 


490 


560 


630 


125 


186 


248 


312 


372 


435 


498 


558 


118 


176 


234 


293 


350 


410 


467 


525 


104 


156 


208 


260 


312 


364 


415 


467 


96 


143 


192 


240 


287 


335 


385 


430 


89 


133 


178 


222 


266 


310 


355 


400 


83 


125 


166 


208 


250 


292 


332 


375 


78 


117 


155 


195 


233 


272 


312 


350 


73 


110 


146 


183 


220 


256 


293 


330 


69 


104 


138 


172 


207 


242 


276 


310 


65 


98 


132 


164 


198 


230 


262 


295 


62 


93 


124 


155 


186 


218 


248 


280 


59 


89 


118 


148 


177 


206 


236 


266 


57 


85 


113 


141 


169 


198 


225 


255 


54 


81 


108 


135 


162 


190 


216 


243 


52 


78 


104 


130 


155 


181 


207 


233 


50 


75 


100 


125 


149 


174 


199 


224 


48 


72 


96 


120 


144 


167 


191 


215 


46 


69 


92 


115 


138 


161 


184 


207 


45 


67 


89 


111 


133 


156 


178 


200 


43 


65 


86 


107 


129 


150 


172 


193 


42 


62 


83 


104 


124 


145 


166 


187 


41 


60 


80 


100 


120 


140 


160 


180 


40 


59 


78 


97 


117 


136 


156 


175 


38 


57 


76 


94 


113 


132 


151 


170 


37 


55 


74 


92 


110 


128 


146 


165 


36 


53 


71 


89 


106 


124 


142 


160 


35 


52 


69 


86 


102 


121 


138 


155 


34 


50 


67 


84 


100 


117 


134 


151 


33 


49 


66 


82 


98 


114 


130 


147 


32 


48 


64 


80 


96 


111 


127 


144 


31 


47 


63 


77 


94 


105 


124 


140 



1250 
1038 
886 
876 
700 
622 
585 
520 
478 
443 
416 
388 
365 
345 
326 
310 
295 
283 
270 
258 
248 
238 
230 
222 
215 
208 
200 
194 
188 
183 
178 
172 
168 
164 
160 
156 



Efficiency of the Doble Nozzle. — The nozzle tip is of brass, highly 
polished in the interior, with concave curves near the end. It contains 
a conical regulating needle, which is set at any desired distance from the 
opening to regulate the size of the opening and the diameter of the jet. 
A jet flowing from the nozzle has a clear, glassy appearance. Tests 



200 


300 


400 


500 


600 


700 


800 


0.20 


0.26 


0.27 


0.26 


0.22 


0.14 


0.03 


62 


75 


80 


77 


64 


41 


13 


0.36 


0.45 


0.51 


0.50 


0.42 


0.30 


0.12 


57 


- 75 


85 


85 


71 


50 


19 


0.41 


0.55 


0.63 


0.66 


0.60 


0.41 


0.20 


48 


64 


73 


76 


74 


66 


51 


0.48 


0.62 


0.70 


0.71 


0.64 


0.43 


0.19 


53 


70 


79 


81 


72 


50 


23 



754 WATER-POWER. 

by H. C. Crowell and G. C. D. Lenth, at Mass. Inst, of Tech., 1903, gave 
efficiencies under constant head from 96.4 to 99.3% for different settings 
of the needle, the coefficient of velocity being from 0.982 to 0.997. The 
efficiency of a jet is equal to the ratio of the velocity head in the jet to 
the total head at the entrance to the nozzle, and equal to the square of 
the coefficient of velocity. — Bulletin of the Abner Doble Co., No. 6, 1904 
Tests of a 12-in. Doble Laboratory Motor (Bulletin No. 12, 1908. 
Abner Doble Co.). — The tests were made by students at the University 
of Missouri. The available head was 46 ft. The needle valve was 
opened two, four, six and eight turns in the four series of tests, and with 
each opening different loads were applied by a Prony brake. The results 
were recorded and plotted in curves showing the relation of speed, load 
and efficiency, and from these curves the following approximate figures 
are taken: 

Speed, Revolutions per Minute. 

Valve open 200 

Two turns {ijg^J 
Four turns {i^/\\ 
Six turns {My*%. 
Eight turns {]^!J; P ^- 

Water-power Plants Operating under High Pressures. — The fol- 
lowing notes are contributed by the Pelton Water Wheel Co.: 

The Consolidated Virginia & Col. Mining Co., Virginia, Nev., has a 3-ft. 
steel-disk Pelton wheel operating under 2100 ft. fall, equal to 911 lbs. 
per sq. in. It runs at a peripheral velocity of 10,804 ft. per minute and 
has a capacity of over 100 H.P. The rigidity with which water under 
such a high pressure as this leaves the nozzle is shown in the fact that it 
is impossible to cut the stream with an axe, however heavy the blow, 
as it will rebound just as it would from a steel rod travelling at a high 
rate of speed. 

The London Hydraulic Power Co. has a large number of Pelton wheels 
from 12 to 18 in. diameter running under pressure of about 1000 lbs. per 
sq. in. from a system of pressure-mains. The 18-in. wheels weighing 
30 lbs. have a capacity of over 20 H.P. (See Blaine's "Hydraulic Ma- 
chinery.") 

Hydraulic Power-hoist of Milwaukee Mining Co., Idaho. — One cage 
travels up as the other descends; the maximum load of 5500 lbs. at a 
speed of 400 ft. per min. is carried by one of a pair of Pelton wheels (one 
for each cage). Wheels are started and stopped by opening and closing 
a small hydraulic valve at the engineer's stand which operates the larger 
valves by hydraulic pressure. An air-chamber takes up the shock that 
would otherwise occur on the pipe line under the pressure due to 850 ft. 
fall. 

The Mannesmann Cycle Tube Works, North Adams, Mass., are using 
four Pelton wheels, having a fly-wheel rim, under a pump pressure of 
600 lbs. per sq. in. These wheels are direct-connected to the rolls 
through which the ingots are passed for drawing out seamless tubing. 

The Alaska Gold Mining Co., Douglass Island, Alaska, has a 22- 
Pelton wheel on the shaft of a Riedler duplex compressor. It is used 
a fly-wheel as well, weighing 25,000 lbs., and develops 500 H.P. at 
revolutions. A valve connected to the pressure-chamber starts and 
stops the wheel automatically, thus maintaining the pressure in the 
air-receiver. 

At Pachuca in Mexico five Pelton wheels having a capacity of 600 
H.P. each under 800 ft. head are driving an electric transmission plant. 
These wheels weigh less than 500 lbs. each, showing over a horse-power 
per pound of metal. 

Formulae for Calculating the Power of Jet Water-wheels, such as 
the Pelton (F. K. Blue). —HP = horse-power delivered; .6 = 62.36 lbs. 
per cu. ft.; E = efficiency of turbine; q = quantity of water, cubic feet 
per minute; h = feet effective head: d = inches diameter of jet; v = 
pounds per square inch effective head; c = coefficient of discharge from 
nozzle, which may be ordinarily taken at 0.9, 



■ft, 
as 1 
75 



THE POWER OF OCEAN WAVES. 



755 



SEqh 
= 33000 



■-.001S9Eqh = .00436 Eqp = .00496P«/ 2 V/, 3 = .017 4Pcd 2 vV # 



- oft ^PP w „ //P 

</ = 529.2 -=t = 229 -= — = 
■Eh Ep 



■ 2.62 cd? ^h = 3.99 cd 2 Vp 



# = 201.6 



— — = 57.4 — = 0.381 7= — 0.25 — 



THE POWER OF OCEAN WAVES. 

Albert W. Stahl, U. S. N. {Trans. A. S. M. P., xiii. 438), gives the fol- 
lowing formulae and table, based upon a theoretical discussion of wave 
motion: 

The total energy of one whole wave-length of a wave H feet high, L feet 
long, and one foot in breadth, the length being the distance between suc- 
cessive crests, and the height the vertical distance between the crest and 

the trough, is E = 8 LIT 1 (l - 4.935 j^\ foot-pounds. 

The time required for each wave to travel through a distance equal to 

its own length is P = a/ seconds, and the number of waves passing 

any given point in one minute is N = 



^ 



Hence the total 

energy of an indefinite series of such waves, expressed in horse-power per 
foot of breadth, is 



EXN 
33,000 = 



Vl 



(l-4.935f:). 



By substituting various values for H -*- L, within the limits of such 
values actually occurring in nature, we obtain the following table of 



Total Energy of Deep-sea Waves in Terms of Horse-power per 
Foot of Breadth. 



Ratio of 






Len 


?th of Waves in Feet. 






Length to 


















Height of 


















Waves . 


25 


50 


75 


100 


150 


200 


300 


400 


50 


0.04 


0.23 


0.64 


1.31 


3.62 


7.43 


20.46 


42.01 


40 


0.06 


0.36 


1.00 


2.05 


5.65 


11.59 


31.95 


65.58 


30 


0.12 


0.64 


1.77 


3.64 


10.02 


20.57 


56.70 


116.38 


20 


0.25 


1.44 


3.96 


8.13 


21.79 


45.98 


120.70 


260.08 


15 


0.42 


2.83 


6.97 


14.31 


39.43 


80.94 


223.06 


457.89 


10 


0.98 


5.53 


15.24 


31.29 


86.22 


177.00 


487.75 


1001.25 


5 


3.30 


18.68 


51.48 


105.68 


291.20 


597.78 


1647.31 


3381.60 



The figures are correct for trochoidal deep-sea waves only, but they 
give a close approximation for any nearly regular series of waves in deep 
water and a fair approximation for waves in shallow water. 

The question of the practical utilization of the energy which exists in 
ocean waves divides itself into several parts: 

1. The various motions of the water which may be utilized for power 
purposes. 



756 WATER-POWER. 

2. The wave-motor proper. That is, the portion of the apparatus in 
direct contact with the water, and receiving and transmitting the energy 
thereof; together with the mechanism for transmitting this energy to the 
machinery for utilizing the same. 

3. Regulating devices, for obtaining a uniform motion from the irregu- 
lar and more or less spasmodic action of the waves, as well as for adjusting 
the apparatus to the state of the tide and condition of the sea. 

4. Storage arrangements for insuring a continuous and uniform output 
of power during a calm, or when the waves are comparatively small. 

The motions that may be utilized for power purposes are the following: 
1. Vertical rise and fall of particles at and near the surface. 2. Hori- 
zontal to-and-fro motion of particles at and near the surface. 3. Vary- 
ing slope of surface of wave. 4. Impetus of waves rolling up the beach 
in the form of breakers. 5. Motion of distorted verticals. All of these 
motions, except the last one mentioned, have at various times been 
proposed to be utilized for power purposes; and the last is proposed to 
be used in apparatus described by Mr. Stahl. 

The motion of distorted verticals is thus defined: A set of particles, 
originally in the same vertical straight line when the water is at rest, 
does not remain in a vertical line during the passage of the wave; so that 
the line connecting a set of such particles, while vertical and straight in 
still water, becomes distorted, as well as displaced, during the passage 
of the wave, its upper portion moving farther and more rapidly than its 
lower portion. 

Mr. Stahl's paper contains illustrations of several wave-motors designed 
upon various principles. His conclusion as to their practicability is as 
follows: "Possibly none of the methods described in this paper may ever 
prove commercially successful; indeed the problem may not be susceptible 
of a financially successful solution. My own investigations, however, so 
far as I have yet been able to carry them, incline me to the belief that 
wave-power can and will be utilized on a paying basis." 

Continuous Utilization of Tidal Power. (P. Decceur, Proc. Inst. 
C. E. 1890.) — ■ In connection with the training-walls to be constructed in 
the estuary of the Seine, it is proposed to construct large basins, by means 
of which the power available from the rise and fall of the tide could be 
utilized. The method proposed is to have two basins separated by a 
bank rising above high water, within which turbines would be placed. 
The upper basin would be in communication with the sea during the hie her 
one-third of the tidal range, rising, and the lower basin during the lower 
one-third of the tidal range, falling. If H be the range in feet, the 
level in the upper basin would never fall below 2/ 3 H measured from low 
water, and the level in the lower basin would never rise above 1/3 H. 
The available head varies between 0.53 H and 0.80 H, the mean value 
being 2/3 H. If $ square feet be the area of the lower basin, and the 
above conditions are fulfilled, a quantity 1/3 £# cu. ft. of water is deliv- 
ered through the turbines in the space of 91/4 hours. The mean flow is, 
therefore, SH -f- 99,900 cu. ft. per sec, and, the mean fall being Z.$H, 
the available gross horse-power is about 1/30 S'H 2 , where S' is measured 
in acres. This might be increased by about one-third if a variation of 
level in the basins amounting to 1/2 H were permitted. But to reach this 
end the number of turbines would have to be doubled, the mean head 
being reduced to 1/2 H, and it would be more difficult to transmit a con- 
stant power from the turbines. The turbine proposed is of an improved 
model designed to utilize a large flow with a moderate diameter. One 
has been designed to produce 300 horse-power, with a minimum head of 
5 ft. 3 in. at a speed of 15 revolutions per minute, the vanes having 13 ft. 
internal diameter. The speed would be maintained constant by regulat- 
ing sluices. 



PUMPS AND PUMPING ENGINES. 



757 



PUMPS AND PUMPING ENGINES. 



Theoretical Capacity of a Pump. — Let Q'=cu. ft. per min.; 

G' = U. S. gals, per min. = 7.4805 Q 7 ; d — diam. of pump in inches; 
I = stroke in inches ; N = number of single strokes per min. 

IN 



Capacity in cu. ft. per min. 

Capacity in U. S. gals, per min. 
Capacity in gals, per hour 



= Q' = ~. • rr7 ' rk = 0.0004545 N<Jl\ 



4 144 12 



Nffl, 

' 231 ' 



= 0.0034 N&l; 
= 0.204 NcPl. 



*- 46.9 Vf^^Vm- 



■ 4.95 



Vf- 



Diameter required for 
given capacity per min. J " ^"• c/ \Nl A '^" \ Nl 

If v = piston speed in feet per min., d = 13.54 \— 
If the piston speed is 100 feet per min.: 

Nl = 1200, and d = 1.354 Vq> = 0.495 >/(?'; G' = 4.08 d 2 per min! 
The actual capacity will be from 60% to 95% of the theoretical, accord- 
ing to the tightness of the piston, valves, suction-pipe, etc. 

Theoretical Horse-power Required to Raise Water to a Given 
Height. — Horse-power = 

Volume in cu. ft. per min. X pressure per sq. ft. _ Weight X height of lift 
33,000 ~ 33,000 

Q' = cu. ft. per min.; G' = gals, per min.; W = wt. in lbs.; P = 
pressure in lbs. per sq. ft.: p = pressure in lbs. per sq. in.; H = height of 
lift in ft.; W = 62.355 Q', P = 144 p, p = 0.433 H, H = 2.3094 p, (?'== 
7.4805 Q'. 

Q'P = Q'H X 144 X 0.433 = Q'H = G'H 
33,000 33,000 529.23 3958.9 

WH __ Q'X 62.355 X 2.3094 p = Q'p = G'p 
221 



HP. 



HP. = 



1. 0104 G' H 
4000 



33,000 33,000 229.17 1714.3 

For the actual horse-power required an allowance must be made for 
the friction, slips, etc., of engine, pump, valves, and passages. 

Depth of Suction. — Theoretically a perfect pump will draw water 
from a height of nearly 34 feet, or the height corresponding to a perfect 
vacuum (14.7 lbs. X 2.309 = 33.95 feet): but since a perfect vacuum 
cannot be obtained on account of valve-leakage, air contained in the 
water, and the vapor of the water itself, the actual height is generally 
less than 30 feet. When the water is warm the height to which it can be 
lifted by suction decreases, on account of the increased pressure of the 
vapor. In pumping hot water, therefore, the water must flow into the 
pump by gravity. The following table shows the theoretical maximum 



depth of suction for different temperatures, 


leakage not considered: 


Temp. 
Fahr. 


Absolute 
Pressure 
of Vapor, 

lbs. per 
sq. in. 


Vacuum 

in 
Inches of 
Mercury. 


Max. 
Depth 
of 
Suc- 
tion, 
feet. 


Temp. 
Fahr. 


Absolute 
Pressure 
of Vapor, 
lbs. per 
sq. in. 


Vacuum 

in 
Inches of 
Mercury. 


Max. 
Depth 
of 
Suc- 
tion, 
feet. 


102.1 
126.3 
141.6 
153.1 
162.3 
170.1 
176.9 


1 
2 
3 
4 
5 
6 
7 


27.88 
25.85 
23.83 
21.78 
19.74 
17.70 
15.67 


31.6 
29.3 
27.0 
24.7 
22.3 
20.0 
17.7 


182.9 
188.3 
193.2 
197.8 
202.0 
205.9 
209.6 


8 

9 . 
10 
11 
12 
13 
14 


13.63 
11.60 
9.56 
7.52 
5.49 
3.45 
1.41 


15.4 
13.1 
10.8 
8.5 
6.2 
3.9 
1.6 



758 



PUMPS AND PUMPING ENGINES. 



The Deane Single Boiler-feed or Pressure Pump. — Suitable for 
pumping clear liquids at a pressure not exceeding 150 lbs. 





Sizes. 




Capacity 
per min. 






Sizes of Pipes. 












CD 




















Speed. 


Xi 

a 


o 
,3 

CI 










c 


>» 


>> 




0) 

ft fl i 






el 




_^ 




0) 


1 

3 


3 a> 

P 

02 




fj 
5 


11 
o 

.07 




m 
150 


S 


"Si 
3 


x\ 


d 

o3 

m 


3 
o3 
,3 


3 

_o 

3 
GO 


o3 
-3 

Q 





3 


2 


10 


291/ ? 


7 


V? 


3/ 4 


U/4 


1 


1 


3V ? 


21/4 


3 


.09 


150 


13 


33 1/? 


•j v? 


Va 


»/4 


H/4 


1 


IV? 


4 


2 3/s 


3 


.10 


150 


15 


331/? 


71/?, 


i/?, 


3/4 


11/4 


1 


2 


4 


2 V?, 


!> 


.11 


150 


16 


331/? 


71/?, 


V? 


3/4 


H/4 


1 


21/?, 


43/ 4 


3 


3 


.13 


150 


22 


34 


81/-> 


V? 


3/ 4 


H/9, 


11/4 


3 


5 


31/4 


•J 


.23 


125 


31 


431/? 


91/4 


3/4 


1 


2 


U/2 


4 


31/? 


3 3/ 4 


7 


.a 


125 


42 


43 1/? 


91/4 


3/4 


1 


2 


11/?, 


4 V? 


7 


41/4 


8 


.49 


120 


58 


3ll/o 


12 




IV? 


3 


2 


5 


7 


41/-> 


10 


,69 


100 


69 


55 


12 




U/o 


3 


2 


6 


71/2 


5 


10 


85 


100 


85 


55 


12 




ll/o 


3 


2 


61/? 


8 


5 


12 


1.02 


100 


102 


63 


14 




IV? 


3 


21/?, 


7 


10 


6 


12 


1 47 


100 


147 


69 


19 


ll/o 


2 


4 


4 


8 


12 


7 


12 


2.00 


100 


200 


69 


19 


2 


21/o 


5 


4 


9 


14 


8 


12 


2.6! 


100 


261 


69 


21 


2 


21/? 


5 


5 



The Deane Single Tank 


or Light-service 


Pum 


3. — These pumps 
le water-cylinders. 


will all stand a constant working pressure of 75 lbs. on t 




Sizes. 






Capacity 
per min. 








Sizes of Pipes. 
































Speed. 


3 


-3 

J 
3 










1>> 


">> 


° 6 


»u 






.3 




j 




a3 


3 a 
1*3 
GO 




•8* 


3 o 


<D 


3 


X 


^ 


i 

03 

m 


3 


3 
O 


03 


*T3 




"o3^ 
O 


O 
GQ 


O 

"3 
O 


60 

3 


s 


X 

X 


3 


Q 


4 


4 


5 


.27 


130 


35 


33 


9 l/o 


V? 


3/4 


2 


U/2 


5 


4 


7 


.38 


125 


48 


43 1/? 


15 


3/4 


1 


3 


21/2 


M/? 


31/o 


7 


.72 


125 


90 


431/0 


15 


3/4 


1 


3 


21? 


71/?, 


71/? 


10 


1.91 


110 


210 


58 


17 


I 


IV? 


5 


4 


8 


6 


12 


1.46 


100 


146 


67 


20 1/2 


1 


ll/o 


4 


4 


6 


7 


12 


2.00 


100 


200 


66 


17 


3/4 


1 


4 


4 


8 


7 


12 


2.00 


100 


200 


67 


20 l/o 


1 


U/o 


5 


4 


8 


8 


12 


2.61 


100 


261 


68 


30 


1 


ll/o 


5 


5 


10 


8 


12 


2.61 


100 


261 


68I/2 


30 


11? 


2 


5 


5 


8 


10 


12 


4.08 


100 


408 


68 • 


201/2 


1 


U/o 


8 


8 


10 


10 


12 


4.08 


100 


408 


68I/2 


30 


1 1/2 


2 


8 


8 


12 


10 


12 


4.08 


100 


408 


64 


24 


2 


21/o 


8 


8 


10 


12 


12 


5.87 


100 


587 


68I/2 


30 


U/o 


2 


8 


8 


12 


12 


12 


5.87 


100 


587 


64 


28l/o 


2 


2 l/o 


8 


8 


10 


12 


18 


8.79 


70 


616 


95 


25 


ll/o 


2 


8 


8 


12 


12 


18 


8.79 


70 


616 


95 


28l/o 


2 


21/o 


8 


8 


12 


14 


18 


12.00 


70 


840 


95 


28l/o 


2 


21/o 


8 


8 


14 


16 


18 


15.66 


70 


1096 


95 


34 


2 


21/o 


12 


10 


16 


16 


18 


15.66 


70 


1096 


95 


34 


2 


2l/o 


12 


10 


18 


16 


18 


15.66 


70 


1096 


97 


34 


3 


3 l/o 


12 


10 


16 


18 


24 


26.42 


50 


1321 


115 


40 


2 


21/o 


14 


12 


18 


18 


24 


26.42 


50 


1321 


135 


40 


3 


31/2 


14 


12 



























PUMPS AND PUMPING ENGINES. 759 

Amount of Water raised by a Single-acting Lift-pump. — It is 

common to estimate that the quantity of water raised by a single-acting 
bucket-valve pump per minute is equal to the number of strokes in one 
direction per minute, multiplied by the volume traversed by the piston 
in a single stroke, on the theory that the water rises in the pump only 
when the piston or bucket ascends; but the fact is that the column of 
water does not cease flowing when the bucket descends, but flows on 
continuously through the valve in the bucket, so that the discharge of 
the pump, if it is operated at a high speed, may amount to considerably 
more than that calculated from the displacement multiplied by the num- 
ber of single strokes in one direction. 

Proportioning the Steam-cylinder of a Direct-acting Pump. — 

Let 

A = area of steam-cylinder; a = area of pump-cylinder; 

D = diameter of steam-cylinder; d = diameter of pump-cylinder; 

P = steam-pressure, lbs. per sq. in. ; p = resistance per sq. in. on pumps; 

II = head = 2.309 p; p = 0.433 H ; 

„ pc . . , . work done in pump-cvlinder 

E = efficiency of the pump = r - 5 c — ~ — , ,. „ • 

work done by the steam-cylinder 



,'*— y&'«-W-----*- 



p ' EA' 



V _ 
' EP EP 



E is commonly taken at 0.7 to 0.8 for ordinary direct-acting pumps. 
For the highest class of pumping-engines it may amount to 0.9. The 
steam-pressure P is the mean effective pressure, according to the indi- 
cator-diagram; the water-pressure p is the mean total pressure acting 
on the pump plunger or piston, including the suction, as could be shown 
by an indicator-diagram of the water-cylinder. The pressure on the 
pump-piston is frequently much greater than that due to the height of 
the lift, on account of the friction of the valves and passages, which 
increases rapidly with velocity of flow. 

Speed of Water through Pipes and Pump-passages. — The speed 
of the water is commonly from 100 to 200 feet per minute. If 200 feet 
per minute is exceeded, the loss from friction may be considerable. 



i ,. , , . . , . . __ / gallons per minute 

The diameter of pipe required is 4.95-%/- — - 



if velocity in feet per minute 



For a velocity of 200 feet per minute, diam. = 0.35 X v gallons per min. 

Sizes of Direct-acting Pumps. — The tables on pages 758 and 760 
are selected from catalogues of manufacturers, as representing the two 
common types of direct-acting pump, viz., the single-cylinder and the 
duplex. Both types are made by most of the leading manufacturers. 

Efficiency of Small Direct-acting Pumps. — Chas. E. Emery, in 
Reports of Judges of Philadelphia Exhibition, 1876, Group xx., says: 
"Experiments made with steam-pumps at the American Institute Exhibi- 
tion of 1867 showed that average-sized steam-pumps do not, on the aver- 
age, utilize more than 50 per cent of the indicated power in the steam- 
cylinders, the remainder being absorbed in the friction of the engine, but 
more particularly in the passage of the water through the pump. It 
may be safely stated that ordinary steam-pumps rarely require less than 
120 pounds of steam per hour for each horse-power utilized in raising 
water, equivalent to a duty of only 15,000,000 foot-pounds per 100 
pounds of coal. With larger steam-pumps, particularly when they are 
proportioned for the work to be done, the duty will be materially in- 
creased." 



760 



PUMPS AND PUMPING ENGINES. 



The Worthington Duplex Pump. 

Standard Sizes for Ordinary Service. 









u 


'S-S 


£a . 


.a ° ■ 




Sizes of Pipe 


3 for 








a 


05 £ . 


i°1 




Short Lengths. 


is 


.2 




w 


3 £ 


** 


.SSI 


To be increas 


3d as 


c 


bo 

a 

_2 




"3 bD 


B MS 
*=< >> 05 


.SI! 


sis 

Sag 




length 


increases. 


">> 












"a 




O B 


tn 03 a 














a 


03 


6 


3 


03 > 

a^ 

B 


a^» 

T3 ^ 


SB,, 










03 


c3 


^ 




m tToj 


03 to m 


3 — u 










"5 


03 

a; 





bO 

03 tw 

a ° 


r^ b0^ 

gflo 
£.3 £ 

03 03 "3 


03 03 S 

"S 3+? 


III 


03 
ft 
"ft 

£ 




03 

a 
'a 

■ 3 


03 
_ft 
"ft 

fl 

O 


a 
"a 

i 
bD 
03 


a 


| 




.2CQ 


g'S.a 

80^ 


-2 O 05 


III 


03 







5 


5 


h5 


Q 


(In 


o- 


5 


m 


w 


m 


s 


3 


2 


3 


.04 


100 to 250 


8 to 20 


2 7/ 8 


3/8 


1/2 


11/4 


1 


41/2 


23/4 


4 


.10 


100 to 200 


20 to 40 


4 


1/2 


3/ 4 


2 


11/2 


51/4 


31/2 


5 


.20 


100 to 200 


40 to 80 


5 


34 


U/4 


21/2 


11/2 


6 


4 


6 


.33 


100 to 150 


70 to 100 


5 5/8 


1 


I 1/2 


3 


2 


71/2 


41/2 


6 


.42 


100 to 150 


85 to 125 


63 8 


11/2 


2 


4 


3 


71/2 


5 


6 


.51 


100 to 150 


100 to 150 


7 


11/2 


2 


4 


3 


71,2 


41/2 


10 


.69 


75 to 125 


100 to 170 


6 3/s 


11/2 


2 


4 


3 


9 


51/4 


10 


.93 


75 to 125 


135 to 230 


71/2 


2 


21/2 


4 


3 


10 


6 


10 


1.22 


75 to 125 


180 to 300 


81/2 


2 


21/2 


5 


4 


10 


7 


10 


1.66 


75 to 125 


245 to 410 


9 7/s 


2 


21/2 


6 


5 


12 


7 


10 


1.66 


75 to 125 


245 to 410 


97/s 


21/2 


3 


6 


5 


14 


7 


10 


1.66 


75 to 125 


245 to 410 


9 7/s 


21/2 


3 


6 


5 


12 


81/2 


10 


2.45 


75 to 125 


365 to 610 


12 


21/2 


3 


6 


5 


14 


81/ 2 


10 


2.45 


75 to 125 


365 to 610 


12 


I ' : 


3 


6 


5 


16 


81/2 


10 


2.45 


75 to 125 


365 to 610 


12 




3 


6 


5 


181/2 


81/2 


10 


2.45 


75 to 125 


365 to 610 


12 


3 


31/2 


6 


5 


20 


81/2 


10 


2.45 


75 to 125 


365 to 610 


12 


4 


5 


6 


5 


12 


101/ 4 


10 


3.57 


75 to 125 


530 to 890 


141/4 


21/2 


3 


8 


7 


14 


IOI/4 


10 


3.57 


75 to 125 


530 to 890 


141/4 


21/2 


3 


8 


7 


16 


IOI/4 


10 


3.57 


75 to 125 


530 to 890 


141/4 


21/2 


3 


8 


7 


181/2 


101/4 


10 


3.57 


75 to 125 


530 to 890 


141/4 


3 


31/2 


8 


7 


20 


IOI/4 


10 


3.57 


75 to 125 


530 to 890 


HI/4 


4 


5 


8 


7 


14 


12 


10 


4.89 


75 to 125 


730 to 1220 


17 


21/2 


3 


10 


8 


16 


12 


10 


4.89 


75 to 125 


730 to 1220 


17 




3 


10 


8 


181/2 


12 


10 


4.89 


75 to 125 


730 to 1220 


17 


3 


31/2 


10 


8 


20 


12 


10 


4.89 


75 to 125 


730 to 1220 


17 


4 


5 


10 


8 


I8I/2 


14 


10 


6.66 


75 to 125 


990 to 1660 


19 3/ 4 


3 


31/2 


12 


10 


20 


14 


10 


6.66 


75 to 125 


990 to 1660 


193 4 


4 


5 


12 


10 


17 


10 


15 


5.10 


50 to 100 


510 to 1020 


14 


3 


31/2 


8 


7 


20 


12 


15 


7.34 


50 to 100 


730 to 1460 


17 


4 


5 


12 


10 


20 


15 
15 


15 
15 


11.47 
11.47 


50 to 100 
50 to 100 


1145 to 2290 
1145 to 2290 


21 
21 










25 





















Speed of Piston. — A piston speed of 100 feet per minute is commonly 
assumed as correct in practice, but for short-stroke pumps this gives too 
high a speed of rotation, requiring too frequent a reversal of the valves. 
For long-stroke pumps, 2 feet and upward, this speed may be consider- 
ably exceeded, if valves and passages are of ample area. 



PUMPS AND PUMPING ENGINES. 



761 



Number of Strokes Required to Attain a Piston Speed from 50 to 

135 Feet per Minute for Pumps Having Strokes 

from 3 to 18 Inches in Length. 





Length of Stroke in Inches. 


«1 


3 


< 


5 


• 


7 | . 


10 


12 


'» 


.. 












1 












Number 


of Strokes per 


Minute. 






50 


200 


150 


120 


100 


86 


75 


60 


50 


40 


33 


55 


220 


165 


132 


110 


94 


82.5 


66 


55 


44 


37 


60 


240 


180 


144 


120 


103 


90 


72 


60 


48 


40 


65 


260 


195 


156 


130 


111 


97.5 


78 


65 


52 


43 


70 


280 


210 


168 


140 


120 


105 


84 


70 


56 


47 


75 


300 


225 


180 


150 


128 


112.5 


90 


75 


60 


50 


80 


320 


240 


192 


160 


137 


120 


96 


80 


64 


53 


85 


340 


255 


204 


170 


146 


127.5 


102 


85 


68 


57 


90 


360 


270 


216 


180 


154 


135 


108 


90 


72 


m 


95 • 


380 


285 


228 


190 


163 


142.5 


114 


95 


76 


63 


100 


400 


300 


240 


200 


171 


150 


120 


100 


80 


67 


105 


420 


315 


252 


210 


180 


157.5 


126 


105 


84 


70 


110 


440 


330 


264 


220 


188 


165 


132 


110 


88 


73 


115 


460 


345 


276 


230 


197 


172.5 


138 


115 


92 


77 


120 


480 


360 


288 


240 


206 


180 


144 


120 


96 


80 


125 


500 


375 


300 


250 


214 


187.5 


150 


125 


100 


83 



Piston Speed of Pumping-engines. — (John Birkinbine, Trans. A. I. 
M. E., v. 459.) — In dealing with such a ponderous and unyielding sub- 
stance as water there are many difficulties to overcome in making a pump 
work with a high piston speed. The attainment of moderately high speed 
is, however, easily accomplished. Well-proportioned pumping-engines of 
large capacity, provided with ample water-ways and properly constructed 
valves, are operated successfully against heavy pressures at a speed of 
250 ft. per minute, without "thug," concussion, or injury to the appara- 
tus, and there is no doubt that the speed can be still further increased. 

Speed of Water through Valves. — If areas through valves and 
water passages are sufficient to give a velocity of 250 ft. per min. or less, 
thev are ample. The water should be carefully guided and not too 
abruptly deflected. (F. W. Dean, Eng. News, Aug. 10, 1893 ) 

Boiler-feed Pumps. — Practice has shown that 100 ft. of piston speed 
per minute is the limit, if excessive wear and tear is to be avoided. 

The velocity of water through the suction-pipe must not exceed 200 ft. 
per minute, else the resistance of the suction is too great. 

The approximate size of suction-pipe, where the length does not exceed 
25 ft. and there are not more than two elbows, may be found as follows: 

7/io of the diameter of the cylinder multiplied by Vioo of the piston 
speed in feet. For duplex pumps of small size, a pipe one size larger is 
usually employed. The velocity of flow in the discharge-pipe should not 
exceed 500 ft. per minute. The volume of discharge and length of pipe 
vary so greatly in different installations that where the water is to be 
forced more than 50 ft. the size of discharge-pipe should be calculated 
for the particular conditions, allowing no greater velocity than 500 ft. 
per minute. The size of discharge-pipe is calculated in single-cylinder 
pumps from 250 to 400 ft. per minute. Greater velocity is permitted in 
the larger pipes. 

In determining the proper size of pump for a steam-boiler, allowance 
must be made for a supply of water sufficient for the maximum capacity 
of the boiler when over driven, with an additional allowance for feeding 
water beyond this maximum capacity when the water level in the boiler 
becomes low. The average run of horizontal tubular boilers will evapor- 
ate from 2 to 3 lbs. of water per sq. ft. of heating-surface per hour, but 



762 PUMPS AND PUMPING ENGINES. 

may be driven up to 6 lbs. if the grate-surface is too large or the draught 
too great for economical working. 

Pump- Valves. — A. F. Nagle {Trans. A. S. M. E., x. 521) gives a 
number of designs with dimensions of double-beat or Cornish valves 
used in large pumping-engines, with a discussion of the theory of their 
proportions. Mr. Nagle says: There is one feature in which the Cornish 
valves are necessarily defective, namely, the lift must always be quite 
large, unless great power is sacrificed to reduce it. A small valve pre- 
sents proportionately a larger surface of discharge with the same lift than 
a larger valve, so that whatever the total area of valve-seat opening, its 
full contents can be discharged with less lift through numerous small valves 
than with one large one. See also Mr. Nagle's paper on Pump Valves and 
Valve Areas, Trans. A.S. M. E ., 1909. 

Henry R. Worthington was the first to use numerous small rubber 
valves in preference to the larger metal valves. These valves work well 
under all the conditions of a city pumping-engine. A volute spring is 
generally used to limit the rise of the valve. 

In the Leavitt high-duty sewerage-engine at Boston {Am. Machinist, 
May 31, 18S4), the valves are of rubber, 3/ 4 inch thick, the opening in 
valve-seat being 131/2 X 4. V2 inches. The valves have iron face and 
back-plates, and form their own hinges. 

The large pumping engines at the St. Louis water works have rub- 
ber valves 31/2 in. outside diam. There are seven valve cages in each 
of the suction and discharge diaphragms, each cage having 28 valves. 
The aggregate free area of 196 valves is 7.76 sq. ft., the area of one 
plunger being 6.26 sq. ft. The suction and discharge pipes are each 
36 in. diam., = 7.07 sq. ft. area. (Bull. No. 1609, Allis-Chalmers Co. 
Such liberal proportions of valves are found usually only in the highest 
grade of large high-duty engines. In small and medium sized pumps 
a valve area equal to one-third the plunger area is commonly used.) 



The Worthington "High-Duty" Pumping Engine dispenses with a 
fly-wheel, and substitutes for it a pair of oscillating hydraulic cylinders, 
which receive part of the energy exerted by the steam during the first 



half of the stroke, and give it out in the latter half. For description see 
catalogue of H. R. Worthington, New York. A test of a triple expan- 
sion condensing engine of this type is reported in Eng. News, Nov. 29, 

1904. Steam cylinders 13, 21, 34 ins.; plungers 30 in., stroke 25 in. 
Steam pressure, 124 lbs. Total head, 79 ft.; capacity, 14,267,000 gal. 
in 24 hrs. Duty per million B.T.U., 102,224,000 ft.-lbs. 

The d'Auria Pumping Engine substitutes for a fly-wheel a compen- 
sating cylinder in line with the plunger, with a piston which pushes water 
to and fro through a pipe connecting the ends of the cylinder. It is built 
by the Builders' Iron Foundrv, Providence, R. I. 

A 72,000,000-gallon Pumping Engine at the Calf Pasture Station of 
the Boston Main Drainage Works is described in Eng. News, July 6, 

1905. It has three cylinders, I8I/2, 33 and 523/ 4 ins., and two plungers, 
60-in. diam.; stroke of all, 10 ft. The piston-rods of the two smaller 
cylinders connect to one end of a walking beam and the rod of the third 
cylinder to the other. Steam pressure 185 lbs. gauge; revolutions per 
min., 17; static head 37 to 43 ft. Suction valves 128; ports, 4 X 16 1/4 in.; 
total port area 8576 sq. in. Delivery valves, 96; ports, 4 X 163/4 to 203/ 4 
in.; total port area 7215 sq. in. The valves are rectangular, rubber flaps, 
backed and faced with bronze and weighted with lead. They are set with 
their longest dimension horizontal, on ports which incline about 45° to the 
horizontal. At 17 r.p.m. the displacement is 72,000,000 gallons in 24 hours. 

The Screw Pumping Engine of the Kinnickinick Flushing Tunnel, 
Milwaukee, has a capacity of 30,000 cubic feet per minute ( = 323,000,000 
gal. in 24 hrs.) at 55 r.p.m. The head is 31/2 ft. The wheel 12.5 ft. 
diam., made of six blades, revolves in a casing set in the tunnel lining. 
A cone, 6 ft. diam. at the base, placed concentric with the wheel on 
the approach side diverts the water to the blades. A casing beyond 
the wheel contains stationary deflector blades which reduce the swirling 
motion of the water (Allis-Chalmers Co., Bulletin No. 1610). The two 
screw pumping engines of the Chicago sewerage system have wheels 
143/4 ft. diam., consisting of a hexagonal hub surmounted by six blades, 
and revolving in cylindrical casings 16 ft. long, allowing 1/4 in. clearance 
at the sides. The pumps are driven by vertical triple-expansion engines 
with cylinders 22, 38 and 62 in. diam., and 42 in, stroke. 



PUMPS AND PUMPING ENGINES. 



763 



Finance of Pumping Engine Economy. — A critical discussion of 
the results obtained by the Nordberg and other high-duty engines is 
printed in Eng. News, Sept. 27, 1900. It is shown that the practical 
question in most cases is not how great fuel economy can be reached, 
but how economical an engine it will pay to install, taking into consid- 
eration interest, depreciation, repairs, cost of labor and of fuel, etc. 
The following table is given, showing that with low cost of fuel and 
labor it does not pay to put in a very high duty engine. Accuracy is 
not claimed for the figures; they are given only to show the method 
of computation that should be used, and to show the influence of different 
factors on the final result. 

Tabular Statement of Total Annual Cost op Pumping with an 

800-H .P. Engine, as Influenced by Varying Duty of Engine, 

Varying Price of Fuel, and Varying Time of Operation. 



Duty per million B.T.U. 



First cost: 

Engine 

Engine, per H.P 

Boilers, economizers 

Engine and boilers . . 

Int. and depreciation: 

On engine, at 6% 

Boilers, 8% 

Total 

Labor per annum 

Fuel cost: 
4,000 hrs. per yr.: 

$3.00 per ton 

4.00 per ton 

5.00 per ton 

6,000 hrs. per yr.: 

$3.00 per ton 

4.00 per ton 

5.00 per ton 

Total annual cost: 
4,000 hrs. per yr.: 
Coal, $3 per ton 

4 per ton 

5 per ton. : . . . . 
6,000 hrs. per yr. 
Coal, $3 per ton 

4 per ton. ...... 

5 per ton 



50. 

$24,000 

30.00 

27,000 

51,000 


100. 

$48,000 
60.00 
13,500 
61,500 


120. 

$68,000 

85.00 

11,250 

79,250 


150. 

$118,000 

147.50 

9,000 

127,000 


180. 

$148,000 

185.00 

7,500 

155,500 


1,440 
2,160 
3,600 
6,022 


2,880 
1,080 
3,960 
6,022 


4,080 

900 

4,980 

7,655 


7,080 

720 

7,800 

9,307 


8,880 

600 

9,480 

10,220 


17,280 
23,040 
28,800 


8,640 
11,520 
14,400 


7,200 
9,600 
12,400 


5,760 
7,680 
9,600 


4,800 
6,400 
8,000 


25,920 
34,560 
43,200 


12,960 
17,280 
21,600 


10,800 
14,400 
18,600 


8,640 
11,520 
14,400 


7,200 
9,600 
12,000 


26,902 
32,662 
38,422 


18,622 
21,502 
24,382 


19,835 
22,235 
25,035 


22,867 
24,787 
26,707 


24,500 
25,100 
27,700 


35,522 
44,182 
52,822 


22,942 
27,262 
31,582 


23,435 
27,035 
31,235 


25,747 
28,627 
31,507 


26,900 
29,300 
31,700 



Cost of Electric Current for Pumping 1000 Gallons per Minute 

100 ft. High. (Theoretical H.P. with 100% efficiency = 

100,000 -^ 3958.9 = 25.259 H.P.) 

Assume cost of current = 1 cent per K.W. hour delivered to the motor; 
efficiency of motor = 90%; mechanical efficiency of triplex pumps = 
80%; of centrifugal pumps == 72%; combined efficiency, triplex pumps, 
72%: centrifugal, 64.8%. 1 K.W. = 1.34 electrical H.P. on wire. 

Triplex, 1.34 X 0.72 = 0.9648 pump H.P.; X 33,000= 31,838 ft.-lbs. 
per min. 

Centrifugal, 1.34 X 0.648 = 0.86382 pump H.P.; X 33,000 = 28,654 
ft.-lbs. per min. 

1000 gallons 100 ft. high = 833,400 ft.-lbs. per min. 

Triplex, 833,400 -s- 31,838 = 26.1763 K.W. X 8760 hours per year 
X $0.01 = $2293.04. 

Centrifugal, 833,400 + 28,655 = 29.0840 K.W. X 8760 hours per year 
X $0.01 = $2547.76. 

For 100% efficiency, $2293.04 X 0.72 = $1650.00. For any other effi- 
ciency, divide $1650.00 by the efficiency. For any other cost per K.W. 
hour, in cents, multiply by that cost. 



764 



PUMPS AND PUMPING ENGINES. 



Cost of Fuel per Year 


for Pumping 1,000 Gallons per Minute 






100 Ft. 


High by Steam 


Pumps. 






(») 


(2) 


(3) 


(4) 


(5) 


(6) 


(7) 




100% Effy 


. 90% 












10. 


198. 


178.2 


142.56 


0.5846 


0.42090 


153.63 


460.89 


11.88 


166.667 


150. 


120. 


0.6945 


0.50004 


182.51 


547.53 


14. 


141.433 


127.87 


101.83 


0.8184 


0.58926 


215.08 


645.24 


14.256 


138.889 


125. 


100. 


0.8334 


0.60005 


219.02 


657.06 


15. 


132. 


118.8 


95.04 


0.8769 


0.63125 


230.44 


691 .32 


16. 


123.75 


111.375 


89.10 


0.9354 


0.67344 


245.80 


737.40 


17.82 


111.111 


100. 


80. 


1.0417 


0.75006 


273.77 


821.31 


20. 


99. 


89.1 


71.28 


1.1692 


0.84180 


307.26 


921.78 


23.76 


83.333 


75. 


60. 


1.3890 


1.00008 


365.03 


1095.09 


30. 


66. 


59.4 


47.52 


1.7538 


1.26270 


460.89 


1382.67 


35.64 


55.556 


50. 


40. 


2.0835 


1.50012 


547.54 


1642.62 


40. 


49.5 


44.5 


35.64 


2.3384 


1.68360 


614.52 


1843.56 


47.52 


41.667 


37.5 


30. 


2.7780 


2.00016 


730.06 


2190.18 


50. 


39.6 


35.64 


28.51 


2.9230 


2.10450 


768.15 


2304.45 


a 


b 


c 


d 


e 


f 


g 


h 



(1) Lbs. steam per I.H.P. per hour. 

(2) Duty million ft.-lbs. per 1000 lbs. steam, b, 100% effy., c, 90%. 

(3) Duty per 100 lbs. coal, 90% effy., 8 lbs. steam per lb. coal. 

(4) Lbs. coal per min. for 1000 gals., 100 ft. high. 

(5) Tons, 2000 lbs. in 24 hours. 

(6) Tons per year, 365 days. 

(7) Cost of fuel per year at $3.00 per ton. 

Factors for calculation: 6 = 1980 + a; c = & X 0.9; d = c X 0.8; 
e = 8334 ^ 100 d\ f = e X 0.72; g = f X 365; h = g X 3. 

For any other cost of coal per ton, multiply the figures in the last 
column by the ratio of that cost to $3.00. 

Cost of Pumping 1000 Gallons per Minute 100 ft. High fey 
Gas Engines. 

Assume a gas engine supplied by an anthracite gas producer using 1.5 
lbs. of coal per brake H.P. hour, coal costing $3.00 per ton of 2000 lbs. 

Efficiency of triplex pump 80%, of centrifugal pump, 72%. 

1000 gals, per min. 100 ft. high = 833,400 ft.-lbs. per min. -h 33,000 
= 25.2545 H.P. 

Fuel cost per brake H.P. hour 1.5 lbs. X 300 cents +- 2000 = 0.225 
cent X 8760 hours per year= $19.71 per H.P. X 25.2545= $497,766 for 
100% efficiency. 

For 80% effy., $622.21 ; for 72% effy., $691.34; or the same as the cost 
with a steam pumping engine of 95,000,000 foot-pounds duty per 100 
lbs. of coal. 

Cost of Fuel for Electric Current. 

Based on 10 lbs. steam per I.H.P. hour, 8 lbs. steam per lb. coal, or 
1.25 lbs. coal per I.H.P. per hour. (Electric line loss not included.) 

Efficiency of engine 0.90, of generator 0.90, combined effy. 0.81. 

I.H.P. = 0.746 K.W., 0.746 X 0.81 = 0.6426 K.W. on wire for 10 lbs. 
steam. Reciprocal = 16.5492 lbs. steam per K.W. hour. 8 lbs. steam 
per lb. coal = 2.06865 lbs. coal, at $3.00 per ton of 2,000 lbs. = 0.3103 
cents per K.W. hour. 

Lbs. steam per I.H.P. hr. — 

12 14 16 18 20 30 40 

Fuel cost, cents per K.W. hr. — 

0.3724 0.4344 0.4965 0.5585 0.6206 0.9309 1.2412 

CENTRIFUGAL PUMPS. 

Theory of Centrifugal Pumps. — Bulletin No. 173 of the Univ. of 
Wisconsin, 1907, contains an investigation by C. B. Stewart of a 6-in. 
centrifugal pump which, gave a maximum efficiency, under the best 
conditions of load, of only 32%,, together with a discussion of the general 
theory of M. Combe, 1840, which has been followed by Weisbach, Ran-' 
kine, and Unwin. Mr. Stewart says that the theory of the centrifugal 



CENTRIFUGAL PUMPS. 765 

pump, at the times of these writers, seemed practically settled, but it 
was found later that the pump did not follow the theoretical laws de- 
rived, and the subject is still open for investigation. The theoretical 
head developed by the impeller can be stated for the condition of impend- 
ing delivery, but as soon as flow begins the ordinary theory does not 
seem to apply. Experiment shows that the main difficulty to be over- 
come in order to secure high efficiency with the centrifugal pump is in 
providing some means of transforming the portion of the energy which 
exists in the kinetic form, at the outlet of the impeller, to the pressure 
form, or of reducing the loss of head in the pump casing to a minimum. 
The theoretical head for impending delivery is V 2 +g, while experiment 
shows that the maximum actual head approaches V 2 -^ 2 g as a limit. 
As the flow commences each pound of water discharged will possess the 
kinetic energy V 2 +2g in addition to its pressure energy. To secure 
high efficiency some means must be found of utilizing this kinetic energy. 
The use of a 'free vortex or whirlpool, surrounding the impeller, and this 
surrounded by a suitable spiral discharge chamber, is practically accepted 
as one means of utilizing the energy of the velocity head. Guide vanes 
surrounding the impeller also provide a means of changing velocity head 
to pressure head, but the comparative advantage of these two means 
cannot be stated until more experimental data are obtained. 

The catalogue of the Alberger Pump Co., 1908, contains the following: 

It was not until the year 1901 that the centrifugal pump was shown to 
be nothing more or less than a water turbine reversed, and when designed 
on similar lines was capable of dealing with heads as great, and with 
efficiencies as good, as could be obtained with the turbines themselves. 
Since this date great progress has been made in both the theory and 
design, until now it is quite possible to build a pump for any reasonable 
conditions and to accurately estimate the efficiency and other charac- 
teristics to be expected during actual operation. 

The mechanical power delivered to the shaft of a centrifugal pump by 
the prime mover is transmitted to the water by means of a series of 
radial vanes mounted together to form a single member called the im- 
peller, and revolved by the shaft. The water is led to the inner ends of 
the impeller vanes, which gently pick it up and with a rapidly accelerat- 
ing motion cause it to flow radially between them so that upon reaching 
the outer circumference of the impeller the water, owing to the velocity 
and pressure acquired, has absorbed all the power transmitted to the 
pump shaft. The problem to be solved in impeller design is to obtain 
the required velocity and pressure with the minimum loss in shock and 
friction. Since the energy of the water on leaving the pump is required to 
be mostly in the form of pressure, the next problem is to transform into 
pressure the kinetic energy of the water due to its velocity on leaving the 
impeller and furthermore to accomplish this with the least possible loss. 

The next consideration in impeller design is the proportions of the 
vanes and the water passages, and to properly solve this problem an 
extensive use of intricate mathematical formulae is necessary in addition 
to a wide knowledge of the practical side of the question. It is possible 
to obtain the same results as to capacity and head with practically an 
infinite number of different shapes, each of which gives a different effi- 
ciency as well as other varied characteristics. The change from velocity 
to pressure is accomplished by slowing down the speed of the water in an 
annular diffusion space extending from the impeller to the volute casing 
itself and so designed that there is the least loss from eddies or shock. 
It is necessary that this change shall take place gradually and uniformly, 
as otherwise most of the velocity would be consumed in producing eddies. 
With a proper design of the diffusion space and volute it is possible to 
transform practically the whole of the velocity into pressure so that the 
loss from this source may be very small. 

It is necessary also to furnish a uniform supply of water to all parts of 
the inlet or suction opening of the impeller, for unless all the impeller 
vanes receive the same quantity of water at their inner edges, they 
cannot deliver an equal quantity at their outer edges, and this would 
seriously interfere with the continuity of the flow of water and the suc- 
cessful operation of the pump. 

Design of a Four-stage Turbine Pump. — C. W. Clifford, in Am. 
Mack., Oct. 17, 1907, describes the design of a four-stage pump of a 
capacity of 2300 gallons per minute = 5.124 cu. ft. per sec. Following 



766 PUMPS AND PUMPING ENGINES. 

is an abstract of the method adopted. The total head was 1000 ffe. 
Three sets of four-stage pumps were used at elevations of 16, 332 and 
666 ft., the discharge of the first being the suction of the second, and so on. 

The speed of the motor shaft is 850 r.p.m. This gives, for the diameter 
of the impeller, d — 12 X 60 X 75.05 -*- 850 v = 20.24 in. Circumfer- 
ence C = 63.6 in; h = head for eac h im peller, in ft. 

V — peripheral speed = 1.015 *^2gh = 75.05 ft. per sec, 1.015 being 
an assumed coefficient. The velocity V is divided into two parts by the 
formula V t =V - V 2 ; V* = 2 gh -*■ 2 V; whence V t = 38.65 ft. per sec. 
This is the tangential component of the actual velocity of the water as it 
leaves the vane of the impeller. The radial component, or the radial 
velocity, was taken approximately at 8 ft. per sec; 8 -s- 38.65 = tang, of 
11° 42', the calculated angle between the vane and a tangent at the 
periphery. Taking this at 12° gives tang. 12° X 38.65 = 8.215 ft. per sec. 
= radial velocity V. The outflow area at the impeller then is 5.124 X 
144 -5- (8.215 X 0.85) = 105 sq. in.; the 0.85 is an allowance for contrac- 
tion of area in the impeller. The thickness of the vane measured on the 
periphery is approximately 13/ 4 in.; taking this into account the width 
of the impeller was made 17/ 8 in. [105 + (63.6 - 6 X 13/4) = 1.98 in.]. 
The vanes were then plotted as shown in Fig. 148, keeping the distance 
between them nearly constant and of uniform section. Care was taken 
to increase the velocity as gradually as possible. 

The suction velocity was 9.37 ft. per sec, the diam. of the opening being 
10 in. This was increased to 11 ft. per sec at the opening of the im- 
peller, from which, after deducting the area of the shaft, the diameter, d, 
of the impeller inlet was found. Three long and three short vanes were 
used to reduce the shock. 

The diffusive vanes, Fig. 149, were then designed, the object being to 
change the direction of the water to a radial one, and to reduce the 
velocity gradually to 2 ft. per sec. at the discharge through the ports. 

Fig. 150 shows a cross-section of the pump. The pumps were thor- 
oughly tested, and the following figures are derived from a mean curve 
of the results: 

Gals, per min.. 500 1000 1500 2000 2200 2400 2500 3000 3500 
Efficiency, % 30 51 68 78 79 78 76 61 31 

Relation of the Peripheral Speed to the Head. — For constant speed 
the discharge of a centrifugal pump for any lift varies with the square 
root of the difference between the actual lift and the hydrostatic head 
created by the pump without discharge. If any centrifugal pump con- 
nected to a source of supply and to a discharge pipe of considerable 
height is put in revolution, it will be found that it is necessary to main- 
tain a certain peripheral runner speed to hold the water 1 ft. high without 
discharge, and that for any other height the requisite speed will be very 
nearly as the square of the velocity for 1 ft. 

Experiments prove that the peripheral speed in ft. per min. neces- 
sary to lift water to a given height with_yanes of different forms is approxj; 
imately as follows: a, 481 Vfc; b, 554 Vh; c, 610 Vh; d, 780 ^h\e, 394 "^h. 
a is a straight radial vane, & is a straight vane bent backward, c is a curved 
vane, its extremity making an angle of 27° with a tangent to the impeller, 
d is a curved vane with an angle of 18°, e is a vane curved in the reverse 
direction so that outer end is radial. _ 

Applying the above formula, speed ft. per min. =^coeff. X ^h, to the. 
design of Mr. Clifford, gives 60 X 75.05 = C X Vs5, whence C = 488. 
The vane angle was 12°. It is evident that the value of C depends on 
other things than the shape or angle of the vanes, such as smoothness of 
the vanes and other surfaces, shape and area of the diffusion vanes, and 
resistance due to eddies in the pump passages. 

The coefficient varies with the shape of the vanes; this means that 
different speeds are necessary to hold water to the same heights with 
these different forms of vanes, and for any constant speed or lift there 
must be a form of vane more suitable than any other. It would seem at 
first glance that the runner which creates a given hydrostatic head with 
the least peripheral velocity must be the most efficient, but practically 
it is apparent from tests that the curvature of the vanes can be designed 
to suit the speed and lift without materially lowering the efficiency. 
(L. A. Hicks, Eng. News, Aug. 9, 1900.) 



CENTRIFUGAL PUMPS. 



767 





768 



PUMPS AND PUMPING ENGINES. 



A Combination Single-stage and Two-stage Pump, for low and 

high heads, designed by Rateau, is described by J. B. Sperry in Power, 
July 13, 1909. It has two runners, one carried on the main driving- 
shaft, and the other on a hollow shaft, driven from the main shaft by a 
clutch. It has two discharge pipes, either one of which may be closed. 
When the hollow shaft is uncoupled, one runner only is used, and the 
pump is then a single-stage pump for low heads. When the shafts are 
coupled, the water passes through both runners, and may then be deliv- 
ered against a high head. 

Tests of De Laval Centrifugal Pumps. — The tables given below con- 
tain a condensed record of tests of three De Laval pumps made by Prof. 
J. E. Denton and the author in April, 1904. Two of the pumps were 
driven by De Laval steam turbines, and the other one by an electiic 
motor. In the two-stage pump the small wheel was coupled direct to 
the high-speed shaft of the turbine, running at about 20,500 r.p.m., and 
the large wheel was coupled to the low-speed shaft, which is driven by the 
first through gears of a ratio of 1 to 10. The water delivery and the 
duty were computed from weir measurements, Francis's formula being 
used, and this was checked by calibration of the weir at different heads 
by a tank, the error of the formula for the weir used being less than 1%. 
Pitot tube measurements of the water delivered through a nozzle were 
also made. 

One inch below the center of the nozzle was located one end of a thin 
half-inch brass tube, tapered so as to make an orifice of 3/ 32 inch diameter. 
The other end of this tube was connected to a vertical glass tube, fastened 
to the wall of the testing room, graduated in inches over a height of about 
30 ft. The stream of water issuing from the nozzle impinged upon the 
orifice of the brass tube, and thereby maintained a height of water in 
the glass tube. This height afforded a "Pitot Tube Basis" of measure- 
ment of the quantity of water flowing, the reliability of which was tested 
by the flow as determined from the weir. The Pitot tube gave the 
sa me result as the weir from the formula Qi= C X Area of Nozzle X 
v / 2gh with a value of C varying only between 0.953 and 0.977 for the 
large nozzle, and between 0.942 and 0.960 for the small nozzle. 

Test of Steam Turbine Centrifugal Pump, Rated at 1700 Gals. 
per Min., 100 Ft. Head. 





Steam 






Ol 




4-< 




M 

3 


"o3 
O 






Press, at 


a 

3 
3 

o3 
i> 

0> 

a 




& 




°o • 


£ 


-3 • 


s 








& • 

& Ol 

0"3 

a 


s & 


a- £ 


o 






3 


No. of 
Test. 


nor Valve. 
Lbs. per 
Sq. In. 


C.-2 

.2 3 

11 

> u 

tf a 


af 

c3 O 


:3 o ^ 
£ ° 


k 

o 
M 

Oi 


O Ol 

•eg 

C3.0 


73 . 

3 • 
u ft 






6 
> 



< 


o 


'3 




o> 
ffl 






« 




Qfa 


£ 


o 


£ 


W 


6 


190 


126 


251/4 


1,547 


47.7 


25.45 


37.43 


22.95 


45.97 


1,978 


0.481 


10 


190 


148 


251/9 


1,536 


56.65 


24.42 


50.44 


34.95 


70.75 


1,958 


0.617 


1 


188 


155.2 


25 


1,553 


59.6 


24.06 


61.50 


44.54 


94.9 


1,860 


0.747 


2 


188 


153.5 


251/ 4 


1,547 


58.9 


24.21 


61.86 


44.55 


100.37 


1,759 


0.756 


3 


188 


150.7 


251/4 


1,540 


57.7 


24.33 


61.47 


43.59 


106.94 


1,615 


0.755 


4 


188 


143.5 


251/9 


1,549 


54.8 


24.53 


60.00 


40.72 


115.46 


1,398 


0.743 


5 


188 


161 


253/ 8 


1,540 


47.5 


24.5 


54.47 


31.80 


125.85 


1,001 


0.676 


6A 


189.5 


170 


751/9 


1,565 


24.9 




Shut- 


off T. 


142.15 






\l 


189 
189 
189 


169.5 

169 

169.7 




1,537 
1,535 
1,538 






45.15 
45.12 
44.62 


43.85 
43.82 
42.93 


95.14 
99.05 
104.42 


1,826 
1,753 
1,629 










P 















* The brake H.P. and the steam per B.H.P. hour were calculated by a 
formula derived from Prony brake tests of the turbine. 
•f Non-condensing. 



CENTRIFUGAL PUMPS. 



769 



Test of Electric Motor Centrifugal Pump. Diam. of Pump Wheel 
89/32 In. Rated at 1200 Gals. Per Min. — 45 Ft. Head. 
2000 Revs.' Per Min. 



















u 

0> 


<u 


. 


a 

S 




0> 

H 

'o 
6 




O- 

a 
8 
< 




o> £ 

M o 

gPn 

« £ 
* o 

w 


1.2 

S> CD 

M ft 


° 8 

0> L..S 


o 
Ph 

o 

H 


En 

tS 

o 


a^ 

<^a 


Ph 

'o 
>> 

a 

& 


1 




242.5 

242.3 


55.2 

54.8 


17.94 

17.80 


15.07 

14.94 


2,006 
1,996 


3.158 
3.126 


10.25 
10.67 


28.52 
30.12 


1,417 

1,403 


0.680 


?, 




0.714 


3 




242 


59 


19.14 


16.22 


1,996 


2.885 


11.80 


36.1 


1,295 


0.728 


4 




242 


62.4 


20.24 


17.27 


2,005 


2.826 


12.18 


38.05 


1,268 


0.706f 


5 




241.8 


•62.9 


20.39 


17.41 


2,000 


2.525 


13.06 


45.66 


1,133 


0.750 


6 




240.8 


66 


21.30 


18.28 


2,005 


2.504 


13.40 


47.25 


1,124 


0.733t 


7 




241.4 


64 


20.71 


17.71 


2,003 


2.197 


13.12 


52.7 


986 


0.742 


8 




239.7 
240.9 


66.3 
63.2- 


21.30 
20.41 


18.28 
17.43 


1,997 
2,007 


2.179 
1.735 


13.15 
11.42 


53.28 
58.10 


978 
779 


720f 


9 




0.665f 


in 




242 


62 


20.11 


17.14 


2,003 


1.760 


11.71 


58.76 


790 


0.683 


ii 




248 


34 


11.30 


8.74 


2,040 


Shut-off 




68.39 







* Brake H.P. calculated from a formula derived from a brake test of 
the motor. 

t Tests marked f were made with the pump suction throttled so as to 
make the suction equal to about 22 ft. of water column. In the other 
tests the suction was from 5.6 to 10.9 ft. 



Test of Steam Turbine Two-Stage Centrifugal Pump. Rated at 

250 Gals, per Min. 700 Ft. Head. Large Pump Wheel, 

2050 R.P.M.; Small Wheel, 20,500 R.P.M. 



Steam 


g 




O 








u 


"3 . 


£ 




Press, at 




a 


ft 


Oi 




* 


O.3. 




K,3 


the Gover- 
nor Valve. 


£ .« 


& 


8 

3 ■/ 


c3 >> 

>^2 


o> . 


Ph 


.&£&. 




aw 


Lbs. per 
Sq. In. 




a 

1 


Z — 

O 

3 

03 


(3 


O D'S 

O 


3&H 

o 
H 




3* 

03 ft 


5 a 


a3 




3^ 


< 


0> 

pq 




m 








£ 


£ 


3 
P 




186 


120.7 


28.1 


25.25 


341 


2,104 


0.830 


135.76 


12.83 


373 


18.63 


106.2 


175 


138.3 
162.3 


27.5 
27.05 


24.4 
25.5 


385 


2,092 
2,074 


0.799 
0.790 


193.85 
288 


17.54 

25.78 


359 
354 






181 


28.73 


68.9 


178 


173.7 


26.2 


25.5 


316 


2,056 


0.775 


358.78 


31.50 


347 


32.9 


60.2 


180 


180.3 


26 


25.3 


m 


2,027 


1.750 


420.5 


35.60 


336 


36.00 


54.9 


181 


182 


25.3 


25.25 


V5 


•2,001 


0.731 


494.35 


40.92 


328 


41.55 


47.7 


180 


182 
188.3 


24.9 
25.5 


25.35 
26.3 


331 


1,962 
2,014 


0.697 
0.664 


585.06 
632.6 


46.19 
47.58 


312 

299 






186 


47.43 


41.77 


185 


185 


30 


25.3 


331 


2,012 


3.558 


756.38 


47.81 


251 


47.67 


41.5 


185 


184 


29 


26.5 


325 


2,029 


0.544 


781.4 


48.15 


244 


48.88 


40.50 



770 



PUMPS AND PUMPING ENGINES. 



A Test of a Lea-Deagan Two-Stage Pump, by Prof. J. E. Denton, 
is reported in Eng. Rec, Sept. 29, 1906. The pump had a 10-in. suction 
and discharge line, and impellers 24 in. diam., each with 8 blades. The 
following table shows the principal results, as taken from plotted curves 
of the tests. The pump was designed to give equal efficiency at different 
speeds. 
Gal. per min. 

400 800 1200 1600 2000 2400 2800 3000 3200 3400 3600 3800 
Efficiency. 

400 r.p.m. 42 61 69 75 77 77 70 

500 " 39 56 65 71 75 77 77.6 77 74 70 

600 " 35 50 62 68 71 74 76 77 78 78 76 54 
Head. 

400 r.p.m. 55 55 53 51 47 42 34 

500 " 63 86 84 82 78 73 67 63 58 51 

600 " 126 127 125 122 118 115 107 104 101 97 87 55 

The following results were obtained under conditions of maximum 
efficiency: 

400 r.p.m. 77.7% effy. 2296 gals, per min. 43.6 ft. lift 
500 " 77.6 " 2794 " " 67.4 

600 " 77.97 " 3235 " " 100.7 

A High-Duty Centrifugal Pump. — A 45,000,000 gal. centrifugal pump 
at the Deer Island sewage pumping station, Boston, Mass., was tested 
in 1896 and showed a duty of 95,867,476 ft.-lbs., based on coal fired to 
the boilers. — (Allis-Chalmers Co., Bulletin No. 1062.) 

Rotary Pumps. — Pumps with two parallel geared shafts carrying 
vanes or impellers which mesh with each other, and other forms of posi- 
tive driven apparatus, in which the water is pushed at a moderate veloc- 
ity, instead of being rotated at a high velocity as in centrifugal pumps, 
are known as rotary pumps. They have an advantage over recipro- 
cating pumps in being valveless, and over centrifugal pumps in working 
under variable heads. They are usually not economical, but when care- 
fully designed with the impellers of the correct cycloidal shape, like 
those used in positive rotary blowers, they give a moderately high 
efficiency. 

Tests of Centrifugal and Rotary Pumps. (W. B. Gregory, Bull. 
183, U. S. Dept. of Agriculture, 1907.) — These pumps are used for irri- 
gation and drainage in Louisiana. A few records of small pumps, giving 
very low efficiencies, are omitted. Oil was used as fuel in the boilers, 
except in the pump of the New Orleans drainage station No. 7 (figures in 
the last column), which was driven by a gas-engine. 



Actual lift 

Disch. cu. ft. per sec. 
Water horse-power. . . 

I.H.P 

Effy., engine, gearing 

and pumps 

Duty, per 1000 lbs. stea 
Duty, per million 

BT.U.infuel 

Therm, effy. from stea 
Kind of engine, and 

pump 



15.5 
72.6 
127.5 
155.6 


16.2 
157.0 
287.4 
671.2 


11.2 
116.0 
147.1 
229.8 


30.2 
93.2 
318.0 
648.0 


9.5 
71.4 
76.5 
137.7 


28.7 
68.7 
222.8 
503.9 


31.7 

85.6 
306.8 
452.3 


6.8 
130.5 
98.8 
193.6 


31.6 

152.9 
547.9 
657.7 


81.7 
72.1 


42.9 
34.3 


64.2 
40.7 


49.0 
33.8 


55,6 


44.3 
33.9 


67.9 
78.2 


51.0 
31.4 


83.3 
75.4 


37.8 
8.16 


18.3 
4.23 


20.7 
4.68 


24.2 
4.16 


22.1 


17.3 
4.09 


51.1 
9.70 


16.7 
3.93 


50.1 
9.61 


a,f 


b,g 


b,g 


b,g 


c, g 


b,g 


a, g 


d,g 


a, g 



13.4 
30.5 
46.2 
90.6 

51.0 



a, Tandem compound condensing Corliss; b, Simple condensing Cor- 
liss; c, Simple non-condensing Corliss; (/.Triple-expansion condensing, 
vertical; e, Three-cylinder vertical gas-engine, with gas-producer, 0.85 lb. 
coal per I.H.P. per hour; /, Rotary pump; g, Cycloidal rotary. 

The relatively low duty per million B.T.U. is due to the low efficiency 
of the boilers. The test whose figures are given in the next to the last 
column is reported by Prof. Gregory in Trans. A. S. M. E., to vol. xxviii. 



DUTY TRIALS OF PUMPING-ENGINES. 771 



DUTY TRIALS OF PUMPING-ENGINES. 

A committee of the A. S. M. E. (Trans., xii. 530) reported in 1891 on a 
standard method of conducting duty trials. Instead of the old unit of 
duty of foot-pounds of work per 100 lbs. of coal used, the committee recom- 
mend a new unit, foot-pounds of work per million heat-units furnished by 
the boiler. The variations in quantity of coal make the old standard unfit 
as a basis of duty ratings. The new unit is the precise equivalent of 100 
lbs. of coal in cases where each pound of coal imparts 10,000 heat-units to 
the water in the boiler, or where the evaporation is 10,000 -4-965.7 = 10.355 
lbs. of water from and at 212° per pound of fuel. This evaporative result 
is readily obtained from all grades of Cumberland or other semi-bitumi- 
nous coal used in horizontal return tubular boilers, and, in many cases, 
from the best grades of anthracite coal. 

The committee also recommends that the work done be determined by 
plunger displacement, after making a test for leakage, instead of by 
measurement of flow by weirs or other apparatus, but advises the use of 
such apparatus when practicable for obtaining additional data. The 
following extracts are taken from the report. When important tests are 
to be made the complete report should be consulted. 

The necessary data having been obtained, the duty of an engine, and 
other quantities relating to its performance, may be computed by the use 
of the following formulae: 

r> t — Foot-pounds of work done v 

l. Duty - Total number 0( h eat-units consumed X 1 > UUU ' UUU 
_ A(P± p + s)X LX N . 



H 



X 1,000,000 (foot-pounds). 



C X 144 

2. Percentage of leakage = X 100 (per cent). 

A. X Li X JS 

3. Capacity = number of gallons of water discharged in 24 hours 

iXLXiVX 7.4805 X24 AXLXNX 1.24675 . 



DX 144 
of tot 
I.H.P. - - 



- (gallons). 



Percentage of total frictions, 

A (P ± p + s) X L X N ' 
£> X 60 X 33,000 



I.H.P. 

_ A(P±p+s)XLXN l . 

A s X M.E.P. XL S X N s ] X iUU (peI Cent; ' 

or, in the usual case, where the length of the stroke and number of strokes 
of the plunger are the same as that of the steam-piston, this last formula 
becomes : 

Percentage of total frictions = |"l - \^ ^ p"^ 1 x 10 ° (P er cent -) 

In these f ormulae the letters refer to the following quantities : . 

A = Area, in square inches, of pump plunger or piston, corrected for 

area of piston rod or rods; 
P = Pressure,' in pounds per square inch, indicated by the gauge on the 

force main ; * 

* E. T. Sederholm, chief engineer of Fraser & Chalmers, in a letter to 
the author, Feb. 20, 1900, shows that the sum P ± p + s may lead to 
erroneous results unless the two gauges are placed below the levels of the 
water in the discharge and suction air chambers respectively, and the 
connecting pipes to the gauges run so they will always be full of water. 
He prefers to connect these gauges to the air spaces of the two air cham- 
bers, running the connecting pipes so they will be full of air only, and to 
add to the sum of the indications of the two gauges the difference in water 
level of the two chambers. 



772 PUMPS AND PUMPING ENGINES. 

p = Pressure, in pounds per square inch, corresponding to indication of 
the vacuum-gauge on suction-main (or pressure-gauge, if the 
suction-pipe is under a head). The indication of the vacuum- 
gauge, in inches of mercury, may be converted into pounds by 
dividing it by 2.035; 
* = Pressure, in pounds per square inch, corresponding to distance be- 
tween the centers of the. two gauges. The computation for this 
pressure is made by multiplying the distance, expressed in feet, 
by the weight of one cubic foot of water at the temperature of the 
pump-well, and dividing the product by 144; 
L = Average length of stroke of pump-plunger, in feet; 
N = Total number of single strokes of pump-plunger made during the 
trial ; 

As = Area of steam-cylinder, in square inches, corrected for area of piston- 
rod. The quantity As X M.E.P., in an engine having more than 
one cylinder, is the sum of the various quantities relating to the 
respective cylinders: 

L s = Average length of stroke of steam-piston, in feet; 

N s = Total number of single strokes of steam-piston during trial; 

M.E.P. = Average mean effective pressure, in pounds per square inch, 
measured from the indicator-diagrams taken from the steam- 
cylinder; 

I.H.P. = Indicated horse-power developed by the steam-cylinder; 
C = Total number of cubic feet of water which leaked by the pump- 
plunger during the trial, estimated from the results of the leak- 
age test; 
D = Duration of trial in hours ; 

H = Total number of heat-units (B.T.U.) consumed by engine = 
weight of water supplied to boiler by main feed-pump X total 
heat of steam of boiler pressure reckoned from temperature of 
main feed-water + weight of water supplied by jacket-pump X 
total heat of steam of boiler-pressure reckoned from temperature 
of jacket-water + weight of any other water supplied X total 
heat of steam reckoned from its temperature of supply. The 
total heat of the steam is corrected for the moisture or superheat 
which the steam may contain. No allowance is made for water 
added to the feed-water, which is derived from any source ex- 
cept the engine or some accessory of the engine. Heat added to 
the water by the use of a flue-heater at the boiler is not to be 
deducted. Should heat be abstracted from the flue by means of 
a steam reheater connected with the intermediate receiver of the 
engine, this heat must be included in the total quantity supplied 
by the boiler. 

Leakage Test of Pump. — The leakage of an inside plunger (the only 
tvpe which requires testing) is most satisfactorily determined by making 
the test with the cylinder-head removed. A wide board or plank may be 
temporarily bolted to the lower part of the end of the cylinder, so as to 
hold back the water in the manner of a dam, and an opening made in the 
temporary head thus provided for the reception of an overflow-pipe. 
The plunger is blocked at some intermediate point in the stroke (or, if 
this position is not practicable, at the end of the stroke), and the water 
from the force main is admitted at full pressure behind it. The leakage 
escapes through the overflow-pipe, and it is collected in barrels and 
measured. The test should be made, if possible, with the plunger in 
various positions. 

In the case of a pump so planned that it is difficult to remove the 
cylinder-head, it may be desirable to take the leakage from one of the 
openings which are provided for the inspection of the suction-valves, 
the head being allowed to remain in place. 

It is assumed that there is a practical absence of valve leakage. Exami- 
nation for such leakage should be made, and if it occurs, and it is found to 
be due to disordered valves, it should be remedied before making the 
plunger test. Leakage of the discharge valves will be shown by water 
passing down into the empty cylinder at either end when they are under 
pressure. Leakage of the suction-valves will be shown by the disappear- 
ance of water which covers them. 

If valve leakage is found which cannot be remedied the Quantity of 



DUTY TRIALS OF PUMPING-ENGINES. 773 

water thus lost should also be tested. One method is to measure the 
amount of water required to maintain a certain pressure in the pump 
cylinder when this is introduced through a pipe temporarily erected, no 
water being allowed to enter through the discharge valves of the pump. 

Table of Data and Results. — In order that uniformity may be se- 
cured, it is suggested that the data and results, worked out in accordance 
with the standard method, be tabulated in the manner indicated in the 
following scheme: 

DUTY TRIAL OF ENGINE. 

DIMENSIONS. 

1. Number of steam-cylinders 

2. Diameter of steam-cylinders ins. 

3. Diameter of piston-rods of steam-cylinders ins. 

4. Nominal stroke of steam-pistons . . * ft. 

5. Number of water-plungers 

6. Diameter of plungers ins. 

7. Diameter of piston-rods of water-cylinders ins. 

8. Nominal stroke of plungers ft. 

9. Net area of steam-pistons sq. ins. 

10. Net area of plungers sq. ins. 

11. Average length of stroke of steam-pistons during trial ft. 

12. Average length of stroke of plungers during trial ft. 

(Give also complete description of plant.) 

TEMPERATURES. 

13. Temperature of water in pump-well degs. 

14. Temp, of water supplied to boiler by main feed-pump degs. 

15. Temp, of water supplied to boiler from other sources degs. 

FEED- WATER. 

16. Weight of water supplied to boiler by main feed-pump . . . lbs. 

17. Weight of water supplied to boiler from other sources lbs. 

18. Total weight of feed-water supplied from all sources lbs 

PRESSURES. 

19. Boiler pressure indicated by gauge lbs. 

20. Pressure indicated by gauge on force main , lbs. 

21. Vacuum indicated by gauge on suction main ins. 

22. Pressure corresponding to vacuum given in preceding line lbs. 

23. Vertical distance between the centers; of the two gauges . . ins. 

24. Pressure equivalent to distance between the two gauges . . lbs. 

MISCELLANEOUS DATA. 

25. Duration of trial hrs. 

26. Total number of single strokes during trial 

27. Percentage of moisture in steam supplied to engine, or 

number of degrees of superheating % or deg„ 

28. Total leakage of pump during trial, determined from results 

of leakage test lbs. 

29. Mean effective pressure, measured from diagrams taken 

from steam-cylinders M.E.P. 

PRINCIPAL RESULTS. 

30. Duty ft.-lbs. 

31. Percentage of leakage % 

32. Capacity gals. 

33. Percentage of total friction .« . % 

ADDITIONAL RESULTS 

34. Number of double strokes of steam-piston per minute — 

35. Indicated horse-power developed by the various steam- 

cylinders ! I.H.P. 

36. Feed-water consumed by the plant per hour lbs. 

37. Feed-water consumed by the plant per indicated horse- 

power per hour, corrected for moisture in steam . .,.,., lbs. 



774 



PUMPS AND PUMPING ENGINES. 



38. Heat units consumed per I.H.P. per hour B.T.U. 

39. Heat units consumed per I.H.P. per minute B.T.U. 

40. Steam accounted for by indicator at cut-off and release in 

the various steam-cyiinders : . . . . lbs. 

41. Proportion which steam accounted for by indicator bears 

to the feed-water consumption 

42. Number of double strokes of pump per minute 

43. Mean effective pressure, measured from pump diagrams . M.E.P. 

44. Indicated horse-power exerted in pump-cylinders I.H.P. 

45. Work done (or duty) per 100 lbs. of coal ft.-lbs. 

SAMPLE DIAGRAM TAKEN FROM STEAM-CYLINDERS. 

(Also, if possible, full measurement of the diagrams, embracing pres- 
sures at the initial point, cut-off, release, and compression; also back 
pressure, and the proportions of the stroke completed at the various 
points noted.) 

SAMPLE DIAGRAM TAKEN FROM PUMP-CYLINDERS. 

These are not necessary to the main object, but it is desirable to give 
them. 

DATA AND RESULTS OF BOILER TEST. 

(In accordance with the scheme recommended by the Boiler-test Com- 
mittee of the Society.) 

Notable High-duty Pumping Engine Records. 



Date of test . 
Locality 



Capacity, mil. gal., 24 hrs. . . 
Diam. of steam cylinders, in 

Stroke, in 

No. and diam. of plungers. . . 
Piston speed, ft. per min. . . . 

Total head, ft 

Steam pressure 

Indicated Horse-power 

Friction, % 

Mechanical efficiency, % 

Dry steam per I.H.P. hr. . . 
B.T.U. per I.H.P. per min.. 

Duty, B.T.U. basis 

Duty per 1000 lbs. steam . . . 
Thermal efficiency, % 



(I) 

1899 

Wildwood, 

Pa. 



.19.5, 29,49.5 

57.5x42 

(2) 143/4 

256 

504 

200 

712 

6.95 

93.05 

12.26, 11.4 

186* 

162.9* 147 .5t 

150.2* 

22.81 



(2) 
1900 
St. 
Louis 
(10). 



(3) 
1900 
Boston 
Chest- 
nut Hill 



15 
34, 62,92 

X42 
(3)29^ 

292 

126 

801 

3.16 

96.84 

10.68 

202 

158.07 

179.45 

21.00 



30 
30, 56,87 
X66 
(3)42 
195 
140 
185 
801 
6.71 
93.29 
10.34 
196 
156 

178.49 
21.63 



(4) 

1901 

Boston, 

Spot 

Pond. 



(5) 

1906 

St, 
Louis 

(3), 
Bissell's 
Point. 



30 

22,41.5,62 

X60 

(3) 30.5 

244 

125 

151 

464 

3.47 

96.53 

11.09 

203 

156.59 

172.40 

20 



20 
34, 62,94 

72 
(3)337/ 8 
198 
238 
146 
859 
2.27 
97.73 



202.8 
158.85 
181.30 
20.92 



With reheaters. 



t Without reheaters. 



(1) (2). From Eng. News, Sept. 27, 1900. 
(4) Do. Nov. 4, 1901. (5) Allis-Clmlmers Co., 



(3) Do. Aug. 23, 1900. 

, Bulletin No. 1609. The 

Wildwood engine has double-acting plungers. 

The coal consumption of the. Chestnut Hill engine was 1.062 lbs. per 
I H.P. per hour, the lowest figure on record at that date, 1901. 

The Nordberg Pumping Engine at Wildwood, Pa. — Eng. News, 
May 4, 1899, Aug. 23, 1900, Trans. A. S. M. E., 1899. The peculiar 
feature of this engine is the method used in heating the feed-water. The 
engine is quadruple expansion, with four cylinders and three receivers. 
There are five feed-water heaters in series, a, b, c, d, e. The water is 
taken from the hot-well and passed in succession through a which is 
heated bv the exhaust steam on its passage to the condenser; b receives 
its heat from the fourth cylinder, and c, d and e respectively from the 



VACUUM PUMPS. 



775 



third, second and first receivers. An approach is made to the requirement 
of the Carnot thermodynamic cycle, i.e., that heat entering the system 
should be entered at the highest temperature; in this case the water 
receives the heat from the receivers at gradually increasing temperatures. 
The temperatures of the water leaving the several heaters were, on the' 
test, 105°, 136°, 193°, 260°, and 311° F. The economy obtained with this 
engine was the highest on record at the date (1900) viz., 162,948,824 ft. 
lbs. per million B.T.U., and it has not yet been exceeded (1909). 



VACUUM PUMPS. 

The Pulsometer. — In the pulsometer the water is raised by suction 
into the pump-chamber by the condensation of steam within it, and is 
then forced into the delivery-pipe by the pressure of a new quantity of 
steam on the surface of the water. Two chambers are used which work 
alternately, one raising while the other is discharging. 

Test of a Pulsometer. — A test of a pulsometer is described by De Volson 
Wood in Trans. A. S. M. E., xiii. It had a 3 1/2-inch suction-pipe, stood 
40 in. high, and weighed 695 lbs. 

The steam-pipe was 1 inch in diameter. A throttle was placed about 
2 feet from the pump, and pressure gauges placed on both sides of the 
throttle, and a mercury well and thermometer placed beyond the throttle. 
The wire drawing due to throttling caused superheating. 

The pounds of steam used were computed from the increase of the 
temperature of the water in passing through the pump. 

Pounds of steam X loss of heat — lbs. of water sucked in X increase of 
temp. 

The loss of heat in a pound of steam is the total heat in a pound of 
saturated steam as found from "steam tables" for the given pressure, 
plus the heat of superheating, minus the temperature of the discharged 
water; or 

_ . „ . lbs. water X increase of temp. 

Pounds of steam = H-048't - T ' 



The results for the four tests are given in 


the following table 




Data and Results. 


1 


2 


3 


4 




71 

114 

19 

270.4 

3.1 

1617 
404,786 

75.15 
4.47 

29.90 

12.26 

42.16 

32.8 
0.777 
0.012 
0.0093 
0.0065 

10,511,400 


60 

110 
30 
277 

3.4 
931 

186,362 
80.6 
5.5 
54.05 
12.26 
66.31 
57.80 
0.877 
0.0155 
0.0136 
0.0095 

13,391,000 


57 

127 

43.8 
309.0 

17.4 

1518 
228,425 

76.3 
7.49 

54.05 

19.67 

73.72 

66.6 
0.911 
0.0126 
0.0115 
0.0080 

11,059,000 


64 


Steam pressure in pipe before 


104.3 


Steam pressure after throttling.. 
Steam temp, after throttling, °F. . 


26.1 

270.1 

1.4 




1019.9 




248,053 


Water temp, before entering pump 

Water temperature, rise of 

Water head by gauge on lift, ft.. . . 
Water head by gauge on suction . . 
Water head by gauge, total (H) . . 
Water head by measure, total (h) 
Coeffi. of friction of plant, h/H 


70.25 
4.55 

29.90 

19.67 

49.57 

41.60 
0.839 
0.0138 


Eff y of plant exclusive of boiler 
Eff'y of plant if that of boiler be 0.7 
Duty, if 1 lb. evaporates 10 lbs. 
water 


0.0116 
0.0081 

12,036,300 



Of the two tests having the highest lift (54.05 ft.), that was more 
efficient which had the smaller suction (12.26 ft.), and this was also the 
most efficient of the four tests. But, on the other hand, the other two 
tests having the same lift (29.9 ft.), that was the more efficient which had 
the greater suction (19.67), so that no law in this regard was established. 
The pressures used, 19, 30, 43.8, 26.1, follow the order of magnitude of 



776 PUMPS AND PUMPING ENGINES. 



the total heads, but are not proportional thereto. No attempt was made 
to determine what pressure would give the best efficiency for any par- 
ticular head. The pressure used was intrusted to a practical runner, 
and he judged that when the pump was running regularly and well, the 
pressure then existing was the proper one. It is peculiar that, in the first 
test, a pressure of 19 lbs. of steam should produce a greater number of 
strokes and pump over 50% more water than 26.1 lbs., the lift being the 
same as in the fourth experiment. 

Chas. E. Emery in discussion of Prof. Wood's paper says, referring to 
tests made by himself and others at the Centennial Exhibition in 1876 
(see Report of the Judges, Group xx.), that a vacuum-pump tested by 
him in 1871 gave a duty of 4.7 millions; one tested by J. F. Flagg, at the 
Cincinnati Exposition in 1875, gave a maximum duty of 3.25 millions. 
Several vacuum and small steam-pumps, compared later on the same 
basis, were reported to have given duties of 10 to 11 millions, the steam- 
pumps doing no better than the vacuum-pumps. Injectors, when used 
for lifting water not Tequired to be heated, have an efficiency of 2 to 5 
millions; vacuum-pumps vary generally between 3 and 10; small steam- 
pumps between 8 and 15; larger steam-pumps, between 15 and 30, and 
pumping-engines between 30 and 140 millions. 

A very high record of test of a pulsometer is given in Eng'g, Nov. 24, 
1893, p. 639, viz.: Height of suction 11.27 ft.; total height of lift, 102.6 
ft.; horizontal length of delivery-pipe, 118 ft.; quantity delivered per 
hour, 26,188 British gallons. Weight of steam used per H. P. per hour, 
92.76 lbs.; work done per pound of steam 21,345 foot-pounds, equal to a 
duty of 21,345,000 foot-pounds per 100 lbs. of coal, if 10 lbs. of steam 
were generated per pound of coal. 

The Jet-pump. — This machine works by means of the tendency of a 
stream or jet of fluid to drive or carry contiguous particles of fluid along 
with it. The water-jet pump, in its present form, was invented by Prof. 
James Thomson, and first described in 1852. In some experiments on a 
small scale as to the efficiency of the jet-pump, the greatest efficiency was 
found to take place when the depth from which the water was drawn by 
the suction-pipe was about nine tenths of the height from which the 
water fell to form the jet ; the flow up the suction-pipe being in that case 
about one fifth of that of the jet, and the efficiency, consequently, 9/io X 
1/5 = 0.18. This is but a low efficiency; but it is probable that it may be 
increased by improvements in proportions of the machine. (Rankine, 
S. E.) 

The Injector when used as a pump has a very low efficiency. (See 
Injectors, under Steam-boilers.) 

PUMPING BY COMPRESSED AIR — THE AIR-LIFT PUMP. 

Air-lift Pump. — The air-lift pump consists of a vertical water-pipe 
with its lower end submerged in a well, and a smaller pipe delivering air 
into it at the bottom. The rising column in the pipe consists of air 
mingled with water, the air being in bubbles of various sizes, and is there- 
fore lighter than a column of water of the same height; consequently the 
water in the pipe is raised above the level of the surrounding water. 
This method of raising water was proposed as early as 1797, by Loescher, 
of Freiberg, and was mentioned by Collon in lectures in Paris in 1876, 
but its first practical application probably was by Werner Siemens in 
Berlin in 1885. Dr. J. G. Pohle experimented on the principle in Cali- 
fornia in 1886, and U. S. patents on apparatus involving it were granted 
to Pohle and Hill in the same year. A paper describing tests of the air- 
lift pump made by Randall, Browne and Behr was read before the Tech- 
nical Society of the Pacific Coast in Feb., 1890. 

The diameter of the pump-column was 3 in., of the air-pipe 0.9 in., and 
of the air-discharge nozzle 5/ 8 in. The air-pipe had four sharp bends and a 
length of 35 ft. plus the depth of submersion. 

The water was pumped from a closed pipe-well (55 ft. deep and 10 in. 
in diameter). The efficiency of the pump was based on the least work 
theoretically required to compress the air and deliver it to the receiver. 
If the efficiency of the compressor be taken at 70%, the efficiency of the 
pump and compressor together would be 70% of the efficiency found for 
the pump alone, 






PUMPING BY COMPRESSED AIR. 777 



For a given submersion (h) and lift (//), the ratio of the two being kept 
within reasonable limits, (//) being not much greater than (/?,), the effi- 
ciency was greatest when the pressure in the receiver did not greatly 
exceed the head due to the submersion. The smaller the ratio H ■*■ h, 
the higher was the efficiency. 

The pump, as erected, showed the following efficiencies: 

For H 4- h = 0.5 1.0 1.5 2.0 

Efficiency =50% 40% 30% 25% 

The fact that there are absolutely no moving parts makes the pump 
especially fitted for handling dirty or gritty water, sewage, mine water, 
and acid or alkali solutions in chemical or metallurgical works. 

In Newark, N. J., pumps of this type are at work having a total capacity 
of 1,000,000 gallons daily, lifting water from three 8-in. artesian wells. 
The Newark Chemical Works use an air-lift pump to raise sulphuric acid 
of 1.72° gravity. The Colorado Central Consolidated Mining Co., in one 
of its mines at Georgetown, Colo., lifts water in one case 250 ft., using a 
series of lifts. 

For a full account of the theory of the pump, and details of the tests 
above referred to, see Eng'g News, June 8, 1893. 

Air-Lifts for Deep Oil-Wells are described by E. M. Ivens, in Trans. 
A. S. M. E. 1909, p. 341. The following are soma results obtained in wells 
in Evangeline, La.: 

Cu. ft. free air per minute, displacement of 

compressor 650 442 702 536 

Cu. ft. oil pumped per minute 4.35 4.87 13.7 5.54 

Air pressure at well, lbs. per sq. in.. 155 200 202 252 

Pumping head, from oil level while pumping, ft. 1155 1081 1076 917 

Submergence, from oil level to air entrance, ft. 358 412 419 583 

Submergence h- total ft. of vertical pipe, %. . . 23.6 27.6 28 39 

Pumping efficiency, % 9.3 13.4 19.5 10.3 

Artesian Well Pumping by Compressed Air. — H. Tipper, Eng. News, 
Jan. 16, 1908, mentions cases where 1-in. air lines supplied air for 6-in. 
wells, with the inside air-pipe system; the length of the pipe was 300 ft. 
from the well top, and another 350 ft. to the compressor. The wells 
pumped 75 gals, per min., using 200 cu. ft. of air, the efficiency being 6V2%. 
Changing the pipes to 21/2 i^- above the well, and 2 in. in the well, and 
putting an air receiver near the compressor, raised the delivery to 180 
gals, per min., with a little less air, and the efficiency to 23%. A large 
receiver capacity, a large pipe above ground, a submergence of 55%, 
well piping proportioned for a friction loss of not over 5%, with lifts not 
over 200 ft., gave the best results, 1 gal. of water being raised per cu. ft. 
of air. The utmost net efficiency of the air-lift is not over 25 to 30%. 

Eng. News, June 18, 1908, contains an account of tests of eleven wells 
at Atlantic City. The Atlantic City wells were 10 in. diam., water. pipes, 
4 to 51/4 in., air pipes, 3/ 4 to 11/4 in. The maximum lift of the several 
wells ranged from 26 to 40 ft., the submergence, 37 to 49 ft., ratio of sub- 
mergence to lift, 0.9 to 1.8, submergence % of length of pipe, 53 to 64. 
Capacity test, 3,544,900 gals, in 24 hrs., mean lift, 26.88 ft., air pressure, 
31 lbs., duty of whole plant, 19,900,000 ft. lbs. per 1000 lbs. of steam used 
by the compressors. Two-thirds capacity test, delivery, 2,642,900 gals., 
mean lift, 25.43 ft., air pressure, 26 lbs., duty, 24,207,000. 

An article in The Engineer (Chicago), Aug. 15, 1904, gives the following 
formula and rules for the design of air-lifts of maximum efficiency. The 
authority is not given. . 

Ratio of area of air pipe to area of water pipe, 0.16. 

Submerged portion = 65% of total length of pipe. 

Economical range of submersion ratio, 55 to 80%. 

Velocity of air in air pipe, not over 4000 ft. per min. 

Volume of air to raise 1 cu. ft. of water, 3.9 to 4.5 cu. ft. 

C = cu. ft. of water raised per min., A = cu. ft. of air used, L = lift 
above water level, D = submergence, in feet. 

A = LC -5- 16.824; C = 8.24 AD h- L 2 . 

Where L exceeds 180 ft. it will be more economical to use two or more 
air-lifts in series. 



778 PUMPS AND PUMPING ENGINES. 



THE HYDRAULIC RAM. 

Efficiency. — The hydraulic ram is used where a considerable flow of 
water with a moderate fall is available, to raise a small portion of that flow 
to a height exceeding that of the fall. The following are rules given by 
Eytelwein as the results of his experiments (from Rankine) : 

Let Q be the whole supply of water in cubic feet per second, of which q 
is lifted to the height h above the pond, and Q — q runs to waste at the 
depth H below the pond; L, the length of the supply-pipe, from the pond 
to the waste-clack; D, its diameter in feet; then 



= V(1.63Q); L-,^,^^ : 



-0.2^, when | 



1.12 — 0.2 \\ — , when —does not exceed 20; 



'(Q-q)H 
1-5- (1 + h/10 H) nearly, when h/H does not exceed 12. 



hh) 



= 1.42 



Wi 



40 


100 200 


72 


44 14 


18 


4.4 0.7 


65.9 


41.4 13.4 



QH 

Clark, using five sixths of the values given by D'Aubuisson's formula, 
gives: 

Ratio of lift to fall. 4 6 8 10 12 14 16 18 20 22 24 26 
Efficiency per cent. 72 61 52 44 37 31 25 19 14 9 4 
The efficiency as calculated by the two formulae given above is nearly 
the same for high ratios of lift, but for low ratios there is considerable 
difference. For example: 

Let Q = 100, H = 10, II + h = 20 

Efficiency, D'Aubuisson's formula, % 80 

q w effy. X QH -*- (H + h)= 40 

Efficiency by Rankine's formula, % 662/ 
D'Aubuisson's formula is that of the machine itself, on the basis that 
the energy put into the machine is that of the whole column of water, 
Q, falling through the height h and that the energy delivered is that of q 
raised through the whole height above the ram, H + h; while Rankine's 
efficiency is that of the whole plant, assuming that the energy put in is 
only that of the water that runs to waste, and that the work done is 
lifting the quantity q not from the level of the ram but only from that of 
the supply pond. D'Aubuisson's formula is the one in harmony with 
the usual definition of efficiency. It also is applicable (as Rankine's is 
not) to the case of a ram which uses the quantity Q from one source of 
supply to pump water of different quality from a source at the level of 
the ram. 

An extensive mathematical investigation of the hydraulic ram, by 
L. F. Harza, is contained in Bulletin No. 205 of the University of Wiscon- 
sin, 1908, together with results of tests of a Rife "hydraulic engine," 
which appear to verify the theory. It was found both by theory and by 
experiment that the efficiency bears a relation to the velocity in the 
drive pipe. From plotted diagrams of the results the following figures 
(roughly approximate) are taken: Length of 2-in. drive pipe, 85.4 ft.; 
supply head, 8.2 ft. 

Max. vel. in drive pipe, ft. per sec. . . 1.5 2 3 4 5 6 
Efficiency of machine, %. 

Pumping head, ft. 



2.6 


60 


30 
60 


20 
45 


15 
33 


7 
18 





12.3 





23.2 


60 


65 


53 


40 


20 





43.5 


55 


60 


53 


42 


30 





63.1 




60 


55 


50 


28 






The author of the paper concludes that the comparison of experiment 
and theory has demonstrated the practicability of the logical design of 
a hydraulic ram for any given working conditions. 

An interesting historical account, with illustrations, of the develop- 
ment of the hydraulic ram, with a description of Pearsall's hydraulic 
engine, is given by J. Richards in Jour. Assn. Eng'g Societies, Jan., 1898. 
For a description of the Rife hydraulic engine see Eng. News, Dec. 31, 
1896. 



HYDRAULIC-PRESSURE TRANSMISSION. 



779 



The Columbia Steel Co., Portland, Ore., furnished the author in July, 
1908, records of tests of four hydraulic rams, from which the following 
is condensed, the efficiency, by D'Aubuisson's formula, being calculated 
from the data given. L = length in ft. and D = diam. in ins. of the 
drive pipe, I and d, length and diameter of the discharge pipe. 



Size of Ram.* 


H 


H 


Q* 


q* 


L 


D 


I 


d 


Effy. 

% 


Ins. 
3 


Ft. 

4 

5 

12 
37.6 


Ft. 

28 

45 

36.4 
144.1 


35 
100 
200 
6.26 


3.5 

8 

50.5 

1.15 


Ft. 

28 

40 

60 
192.5 


Ins. 
3 

41/2 
41/2 
6 


Ft. 

1008 
325 
945 

1785 


Ins. 
U/2 

"21/2 
I0f 


58.9 


41/., 


72.0 


6 


76.6 


6 


70.4 







; Q and q are in gallons per min., except the last line, which is in cu. 
ft. per sec. 

f Eleven rams discharge into one 10-in. jointed wood pipe. The loss 
of head in the drive pipe was 0.7 ft., and in the discharge pipe, 2.7 ft. On 
another test 1 cu. ft. per sec. was delivered with less than 5 cu. ft. enter- 
ing the drive pipe. Taking 5 cu. ft. gives 76.6% efficiency. 

A description and record of test of the Foster "impact engine" is given 
in Eng'g News, Aug. 3, 1905. Two engines are connected into one 8-in. 
delivery pipe. Using the same notation as before, the data of the tests 
of the two engines are as follows: Q, gal. per min., 582, 578; q, 232, 228; 
H 36.75, 37.25; H + h, 84, 84; strokes per min., 130, 130; Effy. (D'Aubu- 
isson), 91.23, 89.06%. 

Prof. R. C. Carpenter {Eng'g Mechanics, 1894) reports the results of 
four tests of a ram constructed by Rumsey & Co., Seneca Falls. The 
supply-pipe used was 11/2 inches in diameter, about 50 feet long, with 3 
elbows. Each run was made with a different stroke for the waste-valve, 
the supply and delivery head being constant; the object of the experi- 
ment was to find that stroke of clack-valve which would give the highest 
efficiency. 



Length of stroke, per cent 


100 


80 


60 


46 


Number of strokes per minute 


52 


56 


61 


66 


Supply head, feet of water 


5.67 


5.77 


5.58 


5.65 


Delivery head, feet of water 


19.75 


19.75 


19.75 


19.75 


Total water pumped, pounds 

Total water supplied, pounds 


297 


296 


301 


297.5 


1615 


1567 


1518 


1455.5 




64.1 


64.7 


70.2 


71.4 







The highest efficiency realized was obtained when the clack-valve trav- 
elled 60% of its full stroke, the full travel being l'Vie in. 



HYDRAULIC-PRESSURE TRANSMISSION. 

Water under high pressure (700 to 2000 lbs. per sq. in. and upwards) 
affords a satisfactory method of transmitting power to a distance, espe- 
cially for the movement of heavy loads at small velocities, as by cranes 
and elevators. The system consists usually of one or more pumps ca- 
pable of developing the required pressure; accumulators, which are vertical 
cylinders with heavily-weighted plungers passing through stuffing-boxes 
in the upper end, by which a quantity of water may be, accumulated at the 
pressure to which the plunger is weighted; the distributing-pipes; and the 
presses, cranes, or other machinery to be operated. 

The earliest important use of hydraulic pressure probably was in the 
Bramah hydraulic press, patented in 1796. Sir. W. G. Armstrong in 
1846 was one of the pioneers in the adaptation of the hydraulic system 
to cranes. The use of the accumulator by Armstrong led to the extended 
use of hydraulic machinery. Recent developments and applications of 
the system are largely due to Ralph Tweddell, of London, and Sir Joseph 
Whitworth. Sir Henry Bessemer, in his patent of May 13, 1S56, No. 



780 HYDRAULIC-PRESSURE TRANSMISSION. 

1292, first suggested the use of hydraulic pressure for compressing steel 
ingots while in the fluid state. 

The Gross Amount of Energy of the water under pressure stored in 
the accumulator, measured in foot-pounds, is its volume in cubic feet X 
its pressure in pounds per square foot: The horse-power of a given 
quantity steadily flowing is H.P. = 144 pQ/550 =0.2618 pQ, in which Q is 
the quantity flowing in cubic feet per second and p the pressure in pounds 
per square inch. 

The loss of energy due to velocity of flow in the pipe is calculated as 
follows (R. G. Blaine, Eng'g, May 22 and June 5, 1891): 

According to Darcy, every pound of water loses A4L/Z) times its kinetic 
energy, or energy due to its velocity, in passing along a straight pipe L 
feet in length and D feet diameter, where A is a variable coefficient. "For 

clean cast-iron pipes it may be taken as A =0.005 ( 1 +r^ I , or for di-' 

ameter in inches = d. 

d = 1/2 1 2 3 4 5 6 7 8 9 10 12 

A = .015 .01 .0075 .00667 .00625 .006 .00583 .00571 .00563 .00556 .0055 .00542 

The loss of energy per minute is 60 X 62.36 QX-r, 1 , and the 

..:•:.. • • ™ 0.6363A£(H.P.) 3 . , . . , 

horse-power wasted in the pipe is W = ^yrr — , in which A 

varies with the diameter as above, p = pressure at entrance in pounds 

per square inch. Values of 0.6363 A for different diameters of pipe in 
inches are: 

d = 1/2 1 2 3 45 6 7 8 

.00954 .00636 .00477 .00424 .00398 .00382 .00371 .00363 .00358 

9 10 12 

.00353 .00350 .00345 

Efficiency of Hydraulic Apparatus. — The useful effect of a direct 
hydraulic plunger or ram is usually taken at 93%. The following is 
given as the efficiency of a ram with chain-and-pulley multiplying gear 
properly proportioned and well lubricated: 

Gear 2 to 1 4 to 1 6 to 1 8 to 1 10 to 1 12 to 1 14 to 1 16 to 1 
Eff'y 0.80 0.76 0.72 0.67 0.63 0.59 0.54 0.50 

With large sheaves, small steel pins, and wire rope for multiplying 
gear the efficiency has been found as high as 66% for a multiplication of 
20 to 1. 

Henry Adams gives the following formula for effective pressure in! 
cranes and hoists: P = accumulator pressure in pounds per square inch; 
m = ratio of multiplying power; E = effective pressure in pounds per 
square inch, including all allowances for friction; 
E = P (0.84-0.02 m). 

J. E. Tuit (Eng'g, June 15, 1888) describes some experiments on the 
friction of hydraulic jacks from 3 1/4 to 135/g-inch diameter, fitted with 
cupped leather packings. The friction loss varied from 5.6% to 18.8% 
according to the condition of the leather, the distribution of the load on 
the ram, etc. The friction increased considerably with eccentric loads. 
With hemp packing a plunger, 14-inch diameter, showed a friction loss 
of from 11.4% to 3.4%, the load being central, and from 15.0% to 7.6% 
with eccentric load, the percentage of loss decreasing in both cases with 
increase of load. 

Thickness of Hydraulic Cylinders. — Sir W. G. Armstrong gives the 
following, for cast-iron cylinders, for a pressure of 1000 lbs. per sq. in.: 
Diam. of cylinder, inches — 

2 4 6 8 10 12 16 20 24 

Thickness, inches — 

0.832 1.146 1.552 1.875 2.222 2.578 3.19 3.69 4.11 

For any other pressure multiply by the ratio of that pressure to 1000. 
These figures correspond nearly to the formula t = 0.175 d + 0.48, in 
which t = thickness and d = diameter in inches, up to 16 inches diam- 
eter, but for 20 inches diameter the addition 0.48 is reduced to 0.19 and 
at 24 inches it disappears. For formulae for thick cylinders see page 316. 



HYDRAULIC-PRESSURE TRANSMISSION. 781 

Cast iron should not be used for pressures exceeding 2000 lbs. per 
square inch. For higher pressures steel castings or forged steel should 
be used. For working pressures of 750 lbs. per square inch the test 
pressure should be 2500 lbs. per square inch, and for 1500 lbs. the test 
pressure should not be less than 3500 lbs. 

Speed of Hoisting by Hydraulic Pressure. — The maximum allow- 
able speed for warehouse cranes is 6 feet per second; for platform cranes 
4 feet per second; for passenger and wagon hoists, heavy loads, 2 feet per 
second. The maximum speed under any circumstances should never 
exceed 10 feet per second. 

The Speed of Water Through Valves should never be greater than 
100 feet per second. 

Speed of Water Through Pipes. — Experiments on water at 1600 
lbs. pressure per square inch flowing into a flanging-machine ram, 20- 
inch diameter, through a 1/2-inch pipe contracted at one point to 1/4-inch, 
gave a velocity of 114 feet per second in the pipe, and 456 feet at the 
reduced section. Through a 1/2-inch pipe reduced to 3/ 8 _inch at one 
point the velocity was 213 feet per second in the pipe and 381 feet at the 
reduced section. In a 1/2-inch pipe without contraction the velocity 
was 355 feet per second. 

For many of the above notes the author is indebted to Mr. John Piatt, 
consulting engineer, of New York. 

High-pressure Hydraulic Presses in Iron-works are described bv 
IR. M. Daelen, of Germany, in Trans. A.I M. E., 1892. The following 
distinct arrangements used in different systems of high-pressure hydrau- 
lic work are discussed and illustrated: 

1. Steam-pump, with fly-wheel and accumulator. 

2. Steam-pump, without fly-wheel and with accumulator. 

3. Steam-pump, without fly-wheel and without accumulator. 

In these three systems the valve-motion of the working press is oper- 
ated in the high-pressure column. This is avoided in the following: 

4. Single-acting steam-intensifier without accumulator. 

5. Steam-pump with fly-wheel, without accumulator and with pipe- 
circuit. 

6. Steam-pump with fly-wheel, without accumulator and without 
pipe-circuit. 

The disadvantages of accumulators are thus stated: The weighted 
plungers which formerly served in most cases as accumulators, cause 
violent shocks in the pipe-line when changes take place in the move- 
ment of the water, so that in many places, in order to avoid bursting 
from this cause, the pipes are made exclusively of forged and bored steel. 
The seats and cones of the metallic valves are cut by the water (at high 
speed), and in such cases only the most careful maintenance can prevent 
great losses of power. 

Hydraulic Power in London. — The general principle involved is 
pumping water into mains laid in the streets, from which service-pipes 
are carried into the houses to work lifts or three-cylinder motors when 
rotary power is required. In some cases a small Pelton wheel has been 
tried, working under a pressure of over 700 lbs. on the square inch. 
Over 55 miles of hydraulic mains are at present laid (1892). 

The reservoir of power consists of capacious accumulators, loaded to 
800 lbs. per sq. in. 

The engine-house contains six sets of triple-expansion pumping en- 
gines. Each pump will deliver 300 gallons of water per minute. 

The water delivered from the main pumps passes into the accumu- 
lators. The rams are 20 inches in diameter, and have a stroke of 23 
feet. They are each loaded with 110 tons of slag, contained in a wrought- 
iron cylindrical box suspended from a cross-head on the top of the ram. 
One of the accumulators is loaded a little more heavily than the other, 
so that they rise and fall successively; the more heavily loaded actuates a 
stop-valve on the main steam-pipe. 

The mains in the public streets are so constructed and laid as to be per- 
fectly trustworthy and free from leakage. Every pipe and valve used 
throughout the system is tested to 2500 lbs. per sq. in. before being placed 
on the ground and again tested to a reduced pressure in the trenches to 
insure the perfect tightness of the joints. The jointing material used is 
gutta-percha. 



782 HYDRAULIC-PRESSURE TRANSMISSION. 



The average rate obtained by the company is about 3 shillings per 
thousand gallons. The principal use of the power is for intermittent 
work in cases where direct pressure can be employed, as, for instance, 
passenger elevators, cranes, presses, warehouse hoists, etc. 

An important use of the hydraulic power is its application to the 
extinguishing of fire by means of Greathead's injector hydrant. By the 
use of these hydrants a continuous fire-engine is available. 

Hydraulic Riveting-machines. — Hydraulic riveting was introduced 
in England by Mr. R. H. Tweddell. Fixed riveters were first used about 
1868. Portable riveting-machines were introduced in 1872. 

The riveting of the large steel plates in the Forth Bridge was done by 
small portable machines working with a pressure of 1000 lbs. per square 
inch. In exceptional cases 3 tons per inch were used. (Proc. Inst. M. E., 
May, 1889.) 

An application of hydraulic pressure invented by Andrew Higginson, 
of Liverpool, dispenses with the necessity of accumulators. It consists 
of a three-throw pump driven by shafting or worked by steam and 
depends partially upon the work accumulated in a heavy fly-wheel. 
The water in its passage from the pumps and back to them is in con- 
stant circulation at a very feeble pressure, requiring a minimum of 
power to preserve the tube of water ready for action at the desired 
moment, when by the use of a tap the current is stopped from going 
back to the pumps, and is thrown upon the piston of the tool to be set 
in motion. The water is now confined, and the driving-belt or steam- 
engine, supplemented by the momentum of the heavy fly-wheel, is 
employed in closing up the rivet, or bending or forging the object sub- 
jected to its operation. 

Hydraulic Forging-press. 

For a very complete illustrated account of the development of the 
hydraulic forging-press, see a paper by R. H. Tweddell in Proc. Inst. 
C. E., vol. cxvii. 1893-4. 

In the Allen forging-press the force-pump and the large or main cylinder 
of the press are in direct and constant communication. There are no 
intermediate valves of any kind, nor has the pump any clack-valves, 
but it simply forces its cylinder full of water direct into the cylinder of 
the press, and receives the same water, as it were, back again on the return 
stroke. Thus, when both cylinders and the pipe connecting them are 
full, the large ram of the press rises and falls simultaneously with each 
stroke of the pump, keeping up a continuous oscillating motion, the ram, 
of course, traveling the shorter distance, owing to the larger capacity of 
the press cylinder. (Journal Iron and Steel Institute, 1891. See also 
illustrated article in "Modern Mechanism," page 668.) 

A 2000-ton forging-press erected at the Couillet forges in Belgium is 
described in Eng. and M. Jour., Nov. 25, 1893. The press is composed 
essentially of two parts — the press itself and the compressor. The com- 
pressor is formed of a vertical steam-cylinder and a hydraulic cylinder. 
The piston-rod of the former forms the piston of the latter. The hy- 
draulic piston discharges the water into the press proper. The distribu- 
tion is made by a cylindrical balanced valve; as soon as the pressure is 
released the steam-piston falls automatically under the action of gravity. 
During its descent the steam passes to the other face of the piston to 
reheat the cylinder, and finally escapes from the upper end. 

When steam enters under the piston of the compressor-cylinder the 
piston rises, and its rod forces the water into the press proper. The 
pressure thus exerted on the piston of the latter is transmitted through a 
cross-head to the forging which is upon the anvil. To raise the cross- 
head two small single-acting steam-cylinders are used, their piston-rods 
being connected to the cross-head: steam acts only on the pistons of these 
cylinders from below. The admission of steam to the cylinders, which 
stand on top of the press frame, is regulated by the same lever which 
directs the motions of the compressor. The movement given to the dies 
is sufficient for all the ordinary purposes of forging. 

A speed of 30 blows per minute has been attained. A double press on 
the same system, having two compressors and giving a maximum pressure 
of 6000 tons, has been erected in the Krupp works, at Rssen. 



HYDRAULIC-PRESSURE TRANSMISSION. 783 

Hydraulic Engine driving an Air-compressor and a Forging- 
hammer. ( Iron Age, May 12, 1892.) — The great hammer in Terni, 
near Rome, is one of the largest in existence. Its falling weight amounts 
to 100 tons, and the foundation belonging to it consists of a block of cast 
iron of 1000 tons. The stroke is 16 feet 43/4 inches; the diameter of the 
cylinder 6 feet 3V2 inches; diameter of piston-rod 13 3/4 inches; total 
height of the hammer, 62 feet 4 inches. The power to work the hammer, 
as well as the two cranes of 100 and 150 tons respectively, and other 
auxiliary appliances belonging to it, is furnished by four air-compressors 
coupled together and driven directly by water-pressure engines, by 
means of which the air is compressed to 73.5 pounds per square inch. 
The cylinders of the water-pressure engines, which are provided with a 
bronze lining, have a 133/4-inch bore. The stroke is 473/4 inches, with a 
pressure of water on the piston amounting to 264.6 pounds per square 
inch. The compressors are bored out to 31 V2 inches diameter, and have 
47 3 '4-inch stroke. Each of the four cylinders requires a power equal to 
280 horse-power. The compressed aif is delivered into huge reservoirs, 
where a uniform pressure is kept up by means of a suitable water-column. 

The Hydraulic Forging Plant at Bethlehem, Pa., is described in a 
paper by R. W. Davenport, read before the Society of Naval Engineers 
and Marine Architects, 1893. It includes two hydraulic forsing-presses 
complete, with engines and pumps, one of 1500 and one of 4500 tons 
capacity, together with two Whitworth hydraulic traveling forging- 
cranes and other necessary appliances for each press; and a complete 
fluid-compression plant, including a press of 7000 tons capacity and a 
125-ton hydraulic traveling crane for serving it (the upper and lower 
heads of this press weighing respectively about 135 and 120 tons). 

A new forging-press designed by Mr. John Fritz, ior the Bethlehem 
Works, of 14,000 tons capacity, is run by engines and pumps of 15,000 
horse-power. The plant is served by four open-hearth steel furnaces of 
a united capacity of 120 tons of steel per heat. 

The Davy High-speed Steam-hydraulic Forging Press is described 
in the Iron Age, April 15, 1909. It is built in sizes ranging from 150 to 
12,000 tons capacity. In the four-column type, in which all but the 
smaller sizes are built, there is a central press operated by hydraulic 
pressure from a steam intensifier, and two steam balance cylinders 
carried on top of the entablature. A single lever controls the press. 
The operator admits steam to the balance cylinders, lifting the cross 
head and the main plunger, and forcing the water from the press cylinder 
into the water cylinder of the intensifier. Exhausting the steam from 
the balance cylinders, allows the plunger to descend and rest on the 
forging. To and fro motions of the lever, slow or fast as the operator 
desires, up to 120 a minute, then are made to reduce the forging. The 
smaller, or single frame, type has only one balance cylinder, immediately 
above the press cylinder. The Davy press is made in the United States 
by the United Engineering & Foundry Co., Pittsburgh. 

Some References on Hydraulic Transmission. — Reuleaux's "Con- 
structor;" "Hydraulic Motors, Turbines, and Pressure-engines," G. 
Bodmer, London, 1889; Robinson's "Hydraulic Power and Hydraulic 
Machinery," London, 1888: Colyer's "Hydraulic Steam, and Hand-power 
Lifting and Pressing Machinery " London, 1881, See also Engineering 
(London), Aug. 1, 1884, p. 99; March 13, 1885, p. 262; May 22 and June 
5, 1891, pp. 612, 665; Feb. 19, 1892, p. 25; Feb. 10, 1893, p. 170. 



784 



FUEL. 



FUEL. 



Theory of Combustion of Solid Fuel. (From Rankine, somewhat 
altered.) — The ingredients of every kind of fuel commonly used may be I 
thus classed: (1) Fixed or free carbon, which is left in the form of char- 
coal or coke after the volatile ingredients of the fuel have been distilled 
away. These ingredients burn either wholly in the solid state (C to CO2), 
or part in the solid state and part in the gaseous state (CO + O = CO2), 
the latter part being first dissolved by previously formed carbon dioxide 
by the reaction CO2 + C = 2 CO. Carbon monoxide, CO, is produced 
when the supply of air to the fire is insufficient. 

(2) Hydrocarbons, such as olefiant gas, pitch, tar, naphtha, etc., all of 
which must pass into the gaseous state before being burned. 

If mixed on their first issuing from amongst the burning carbon with a j 
large quantity of hot air, these inflammable gases are completely burned ! 
with a transparent blue flame, producing carbon dioxide and steam. 
When mixed with cold air they are apt to be chilled and pass off unburned. 
When raised to a red heat, or thereabouts, before being mixed with a 
sufficient quantity of air for perfect combustion, they disengage carbon 1 
in fine powder, and pass to the condition partly of marsh gas, CH 4 and 
partly of free hydrogen; and the higher the temperature, the greater is . 
the proportion of carbon thus disengaged. 

If the disengaged carbon is cooled below the temperature of ignition 
before coming in contact with oxygen, it constitutes, while floating in the 
gas, smoke, and when deposited on solid bodies, soot. 

But if the disengaged carbon is maintained at the temperature of igni- 
tion and supplied with oxygen sufficient for its combustion, it burns 
while floating in the inflammable gas, and forms red, yellow, or white 
flame. The flame from fuel is the larger the more slowly its combustion 
is effected. The flame itself is apt to be chilled by radiation, as into the 
heating surface of a steam-boiler, so that the combustion is not completed, 
and part of the gas and smoke pass off unburned. 

(3) Oxygen or hydrogen either actually forming water, or existing in 
combination with the other constituents in the proportions which form 
water. Such quantities of oxygen and hydrogen are to be left out of 
account in determining the heat generated by the combustion. If the 
quantity of water actually or virtually present in each pound of fuel is so 
great as to make its latent heat of evaporation worth considering, that 
heat is to be deducted from the total available heat of combustion of the 
fuel. 

(4) Nitrogen, either free or in combination with other constituents. 
This substance is simply inert. 

(5) Sulphide of iron, which exists in coal and is detrimental, as tending 
to cause spontaneous combustion. 

(6) Other mineral compounds of various kinds, which are also inert, 
and form the ash left after complete combustion of the fuel, and also the 
clinker or glassy material produced by fusion of the ash, which tends to 
choke the grate. 

Oxygen and Air Required for the Combustion of Carbon, Hydro- 
gen, etc. 













Gase- 


Heat of 






Lbs. O 


Lbs.N, 
= 3.32 


Air per 


ous 


Combus- 


Chemical Reaction. 


per lb. 


lb.= 


Prod- 


tion, 






Fuel. 


4.32 0. 


ucts 


B.T.U. 












per lb. 


per lb. 


C to CO2 


C+20=C0 2 


21/3 


8.85 


11.52 


12.52 


14,600 


CtoCO 


C + = CO 


11/3 


4.43 


5.76 


6.76 


4,450 


CO to CO2 


CO + O = CO2 


4 /7 


1.90 


2.47 


3.47 


10,150 


H to H2O 


2 H + = H2O 


8 


26.56 


34.56 


35.56 


62,000 


CH 4 to CO2 ) 


CH 4 + 40 












andH 2 J 


= C0 2 + 2H 2 


4 


13.28 


17.28 


18.28 


23,600 


S to SO2 


S + 20 = S0 2 


1 


3.32 


4.32 


5.32 


4,050 



For heat of combustion of various fuels see Heat, page 533, 



785 



The imperfect combustion of carbon, making carbon monoxide, pro- 
duces less than one-third of the heat which is yielded by the complete 
combustion, making carbon dioxide. 

The total heat of combustion of any compound of hydrogen and carbon 
is nearly the sum of the quantities of heat which the constituents would 
produce separately by their combustion. (Marsh-gas is an exception.) 

In computing the total heat of combustion of compounds containing 
oxygen as well as hydrogen and carbon, the following principle is to be 
observed: When hydrogen and oxygen exist in a compound in the proper 
proportion to form water (that is, by weight one part of hydrogen to 
eight of oxygen), these constituents have no effect on the total heat of 
combustion. If hydrogen exists in a greater proportion, only the surplus 
of hydrogen above that which is required by the oxygen is to be taken 
into account. 

The following is a general formula (Dulong's) for the total heat of com- 
bustion of any compound of carbon, hydrogen, and oxygen: 

Let C, H, and O be the fractions of one pound of the compound, which 
consists respectively of carbon, hydrogen, and oxygen, the remainder 
being nitrogen, ash, and other impurities. Let h be the total heat of 
combustion of one pound of the compound in British thermal units. 



Then 



h = 14,600 C + 62,000 (H - l/ 8 O). 



Analyses of Gases of Combustion. — The following are selected 
from a large number of analyses of gases from locomotive boilers, to s.how 
the range of composition under different circumstances (P. H. Dudley, 
Trans. A.I. M. E., iv. 250): 



No smoke visible. 

Old fire, escaping gas white, engine working 

hard. 
Fresh fire, much black gas, engine working 

hard. 
Old fire.damper closed, engine standing still. 
" " smoke white, engine working hard. 
New fire, engine not working hard. 
Smoke black, engine not working hard. 

dark, blower on, engine standingstill. 
" white, engine working hard. 



Test. 


C0 2 


CO 


O 


N 


I 


13.8 


2.5 


2.5 


81.6 


2 


1 1.5 




6 


82.5 


3 


8.5 




8 


83 


4 


2.3 




17.2 


80.5 


5 


5.7 




14.7 


79.6 


6 


8.4 


1.2 


8.4 


82 


7 


12 


1 


4.4 


82.6 


8 


3.4 




16.8 


76.8 


9 


6 




13.5 


81.5 



In analyses on the Cleveland and Pittsburgh road, in every instance 
when the smoke was the blackest, there was found the greatest percent- 
age of unconsumed oxygen in the product, showing that something 
besides the mere presence of oxygen is required to effect the combustion 
of the volatile carbon of fuels. (What is needed is thorough mixture of 
the oxygen with the volatile gases in a hot combustion chamber.) 

Temperature of the Fire. (Rankine, S. E., p. 283.) — By temper- 
ature of the fire is meant the temperature of the products of combustion 
at the instant that the combustion is complete. The elevation of that 
temperature above the temperature at which the air and the fuel are. 
supplied to the furnace may be computed by dividing the total heat of 
combustion of one lb. of fuel by the weight and by the mean specific 
heat of the whole products of combustion, and of the air employed for 
their dilution under constant pressure. 

Temperature of the Fire, the Fuel Containing Hydrogen and 
Water. — The following formula is developed in the author's " Steam- 
boiler Economy" on the assumptions that all the hydrogen and the 
water exist in the combustion chamber as superheated steam at the tem- 
perature of the fire, and that the specific heat of the gases is a constant, 
= 0.237. The last assumption is probably largely in error, since it is 
now known that the specific heat of gases increases with the tempera- 
ture. (See page 537.) The formula will give approximate results, how- 
ever, and is sufficiently accurate when relative figures only are desired. 

Let C, H, O, and W represent respectively the percentages of carbon, 
hydrogen, oxygen, and water in a fuel, and /the pounds of dry gas per 



786 



pound of fuel, = C0 2 + N + excess air, then the theoretical elevation of 

the temperature of the fire above the temperature of the atmosphere, 

616 C + 2200 H - 327 O - 44 W 

/+0.02 W +0.18// 

Example. — Required the maximum temperature obtainable by burn- 
ing moist wood of the composition C, 38; H, 5; O, 32; ash, 1; moisture 24; 
the dry gas being 15 lbs. per pound of wood, and the temperature of the 
atmosphere 62°. 



616 X 38 + 2220 X 5 - 327 X 32 - 44 X 24 
15 + 0.02 X 24+ 0.18 X 5 



= 1403, add 62° = 1465°. 



Rise of Temperature in Combustion of Gases. (Eng'g, March 
12 and April 2, 1886.) — It is found that the temperatures obtained by 
experiment fall short of those obtained by calculation. Three theories 
have been given to account for this: 1. The cooling effect of the sides of 
the containing vessel; 2. The retardation of the evolution of heat caused 
by dissociation; 3. The increase of the specific heat of the gases at very 
high temperatures. The calculated temperatures are obtainable only on 
the condition that the -gases shall combine instantaneously and simulta- 
neously throughout their whole mass. This condition is practically im- 
possible in experiments. The gases formed at the beginning of an explo- 
sion dilute the remaining combustible gases and tend to retard or check 
the combustion of the remainder. 

CLASSIFICATION OF SOLID FUELS. 

Gruner classifies solid fuels as follows (Eng'g and M'g Jour., July, 1874). 



Name of Fuel. 


Ratio tr-. 

O+N* 


Proportion of Coke or 
Charcoal yielded by 
the Dry Pure Fuel. 


Pure cellulose 

Wood (cellulose and encasing matter) . . 


8 

7 

6@ 5 

4@1 
1 @ 0.75 


0.28 @ 0.30 
.30 @ .35 
.35 @ .40 




.40@ .50 


Bituminous coals 

Anthracite 


.50® .90 
.90® .92 



* The nitrogen rarely exceeds 1 per cent of the weight of the fuel. 



Progressive Change from Wood to Graphite. 

(J. S. Newberry in Johnson's Cyclopedia.) 



Carbon . . . 
Hydrogen 
Oxygen . . . 



^3 
O 
O 


o 


1 





§ 2 "3 
~ z z 








^ 


^ 


3 


hi 


S 


h-! 


< 


rf 


49.1 


18.65 


30.45 


12.35 


18.10 


3.57 


14.53 


1.42 


6.3 


3.25 


3.05 


1.85 


1.20 


0.93 


0.27 


0.14 


44.6 


24.40 


20.20 


18.13 


2.07 


1.32 


0.65 


0.65 


100.0 


46.30 


53.70 


32.33 


21.37 


5.82 


15.45 


2.21 



13.11 

0.13 
0.00 



Classification of Coals. 

It is convenient to classify the several varieties of coal according to 
the relative percentages of carbon and volatile matter contained in their 
combustible portion as determined by proximate analysis. The follow- 
ing is the classification given in the author's "Steam-boiler Economy": 



CLASSIFICATION OF SOLID FUELS. 



787 





Classification 


of Coals. 
















Relative 










Heating 


Value of 






Fixed 


Volatile 


Value 


Combus- 






Carbon. 


Matter. 


per lb. of 
Combustible 


tible 

Semi-bit. 

= 100 




97 to 92.5 

92.5 to 87.5 


3 to 7.5 
7.5 to 12.5 


14600 to 14800 
14700 to 15500 


93 


Semi-anthracite 




96 






87.5 to 75 
75 to 60 


12.5 to 25 
25 to 40 


15500 to 16000 
14800 to 15500 


100 


Bituminous, Eastern. 




96 


Bituminous, Western 




65 to 50 


35 to 50 


13500 to 14800 


90 






under 50 


over 50 


11000 to 13500 


77 







The anthracites, with some unimportant exceptions, are confined to 
three small fields in eastern Pennsylvania. The semi-anthracites are 
found in a few small areas in the western part of the anthracite field. 
The semi-bituminous coals are found on the eastern border of the great 
Appalachian coal field, extending from north central Pennsylvania across 
the southern boundary of Virginia into Tennessee, a distance of over 300 
miles. They include the coals of Clearfield, Cambria, and Somerset 
counties, Pennsylvania, and the Cumberland, Md., the Pocahontas, Va., 
and the New River, W. Va., coals. 

It is a peculiarity of the semi-bituminous coals that their combustible 
portion is of remarkably uniform composition, the volatile matter usually 
ranging between 18 and 22% of the combustible, and approaching in its 
analysis marsh gas, CH 4 , with very little oxygen. They are usually low 
also in moisture, ash, and sulphur, and rank among the best steaming 
coals in the world. 

The eastern bituminous coals occupy the remainder of the Appala- 
chian coal field, from Pennsylvania and eastern Ohio to Alabama. They 
are higher in volatile matter, ranging from 25 to over 40%, the higheT 
figures in the western portion of the field. The volatile matter is of 
lower heating value, being higher in oxygen. The western bituminous 
coals are found in most of the states west of Ohio. They are higher in 
volatile matter and in oxygen and moisture than the bituminous coals 
of the Appalachian field, and usually give off a denser smoke when 
burned in ordinary furnaces. 

The U. S. Geological Survey classifies coals into six groups, as follows: 
(1) anthracite; (2) semi-anthracite; (3) semi-bituminous; (4) bitu- 
minous; (5) sub-bituminous, or black lignite; and (6) lignite. 

Classes 5 and 6 are described as follows: 

Sub-bituminous coal is commonly known as "lignite," "lignitic coal," 
"black lignite," "brown coal," etc. It is generally black and shining, 
closely resembling bituminous coal, but it weathers, more rapidly on 
exposure and lacks the prismatic structure of bituminous coal. Its 
calorific value is generally less than that of bituminous coal. The local- 
ities in which this sub-bituminous coal is found include Montana, Idaho, 
Washington, Oregon, California, Wyoming, Utah, Colorado, New Mexico, 
and Texas. 

Lignite is commonly known as "lignite," "brown lignite," or "brown 
coal." It usually has a woody structure and is distinctly brown in color, 
even on a fresh fracture. It carries a higher percentage of moisture than 
any other class of coals, its mine samples showing from 30 to 40% of 
moisture. The localities in which lignite is found are chiefly North 
Dakota, South Dakota, Texas, Arkansas, Louisiana, Mississippi, and 
Alabama. 

The following analyses of representative coals of the six classes are 
given by Prof. N. W. Lord: 

Class 1 — Anthracite Culm. Penna. 

Class 2 — Semi-anthracite. Arkansas. 

Class 3 — Semi-bituminous. W. Va. 

Class 4(a) — Bituminous coking. Connellsville, Pa. 

Class 4(6) — Bituminous non-coking. Hocking Valley, Ohio. 

Class 5 — Sub-bituminous. Wyoming, black lignite. 

Class 6 — Lignite, Texas, 



788 



Composition of Illustrative Coals — Car-Load Samples. 
Proximate Analysis of " Air-dried " Sample. 

Class 1 2 3 4a 46 5 6 

Moisture 2.08 1.28 0.65 0.97 7.55 8.68 9.88 

Vol. comb 7.27 12.82 18.80 29.09 34.03 41.31 36.17 

Fixed carbon 74.32 73.69 75.92 60.85 52.57 46.49 43.65 

Ash .16.33 12.2 1 4.63 9.09 5 . 85 3.52 10.30 

Loss on air-drying 3 . 40 1.10 1.10 4.20 Undet. 11.30 23.50 

Ultimate Analysis of Coal Dried at 105° C. 

Hydrogen 2.63 3.63 4.54 4.57 5.06 5.31 4.47 

Carbon 76.86 78.32 86.47 77.10 75.82 73.31 64.84 

Oxygen 2.27 2.25 2.68 6.67 10.47 15.72 16.52 

Nitrogen 0.82 1.41 1.08 1.58 1.50 1.21 1.30 

Sulphur 0.78 2.03 0.57 0.90 0.82 0.60 1.44 

Ash 16.64 12.36 4.66 9.18 6.33 3 ."85 11.43 

Results Calculated to an Ash and Moisture Free Basis. 

Volatile comb 8.91 14.82 19.85 32.34 39.30 47.05 45.31 

Fixed carbon 91.09 85.18 80.15 67.66 60.70 52.95 54.69 

Ultimate Analysis. 

Hydrogen 3.16 4.14 4.76 5.03 5.41 5.50 5.05 

Carbon 92.20 89.36 90.70 84.89 80.93 76.35 73.21 

Oxvgen 2.72 2.57 2.81 7.34 11.18 16.28 18.65 

Nitrogen 0.98 1.61 1.13 1.74 1.61 1.25 1.47 

Sulphur . 0.94 2.32 0.60 1.00 0.87 0.62 1.62 

Calorific Value in B.T.U. per lb., by Dulong's formula. 
Air-dried coal. 12,472 13,406- 15,190 13,951 12,510 11,620 10,288 
Combustible .. 15,286 15,496 16,037 15,511 14,446 13,235 12,889 

Caking and Non-caking Coals. — Bituminous coals are sometimes 
classified as caking and non-caking coals, according to their behavior 
when subjected to the process of coking. The former undergo an incipi- 
ent fusion or softening when heated, so that the fragments coalesce and 
yield a compact coke, while the latter (also called free-burning) preserve 
their form, producing a coke which is only serviceable when made from 
large pieces of coal, the smaller pieces being incoherent. The reason of 
this difference is not clearly understood, as non-caking coals are often of 
similar ultimate chemical composition to caking coals. Some coals 
which cannot be made into coke in a bee-hive oven are easily coked in 
gas-heated ovens. - 

Cannel Coals are coals that are higher in hydrogen than ordinary 
coals. They are valuable as enrichers in gas-making. The following are 
some ultimate analyses: 





C. 


H. 


O+N. 

7.25 
8.19 
4.93 


S. 


Ash. 


Combustible. 




C. 


H. 

11.24 
9.14 
10.99 


O+N. 


Boghead, Scotland 


63.10 

82.67 
79.34 


8.91 
9.14 
10.41 


0.96 


19.78 


79.61 

82.67 
83.80 


9.15 

8.19 


Tasmanite, Tasmania. . . 


5.32 




5.21 



Rhode Island Graphitic Anthracite. — A peculiar variety of coal is 
found in the central part of Rhode Island and in Eastern Massachusetts. 
It resembles both graphite and anthracite coal, and has about the follow- 
ing composition (A. E. Hunt, Trans. A. I. M. E., xvii. 678: Graphitic 
carbon, 78%; volatile matter, 2.60%; silica, 15.06%; phosphorus, .045%. 
It burns with extreme difficulty. 



ANALYSIS AND HEATING VALUE OP COALS. 789 



ANALYSIS AND HEATING VALUE OF COALS. 

Coal is composed of four different things, which may be separated by- 
proximate analysis, viz.: fixed carbon, volatile hydrocarbon, ash and 
moisture. In making a proximate analysis of a weighed quantity, such 
as a gram of coal, the moisture is first driven off by heating it to about 
250° F. then the volatile matter is driven off by heating it in a closed 
crucible to a red heat, then the carbon is burned out of the remaining 
coke at a white heat, with sufficient air supplied, until nothing is left 
but the ash. 

The fixed carbon has a constant heating value of about 14,600 B.T.U. 
per lb. The value of the volatile hydrocarbon depends on its composi- 
tion, and that depends chiefly on the district in which the coal is mined. 
It may be as high as 21,000 B.T.U. per lb., or about the heating value of 
marsh gas, in the best semi-bituminous coals, which contain very small 
percentages of oxygen, or as low as 12,000 B.T.U. per lb., as in those 
from some of the western states, which are high in oxygen. The ash has 
no heating value, and the moisture has in effect less than none, for its 
evaporation and the superheating of the steam made from it to the tem- 
perature of the chimney gases, absorb some of the heat generated by the 
combustion of the fixed carbon and volatile matter. 

The analysis of a coal may be reported in three different forms, as per- 
centages of the moist coal, of the dry coal or of the combustible, as in the 
following table. By "combustible" is always meant the sum of the 
fixed carbon and volatile matter, the moisture and ash being excluded, 
By some writers it is called "coal dry and free from ash" and by others 
"pure coal." 





Moist Coal. 


Dry Coal. 


Combus- 
tible. 




10 
30 
50 
10 








33.33 
55.56 
11.11 


37.50 




62.50 


Ash 










100 


100.00 


100.00 



The sulphur, commonly reported with a proximate analysis, is deter- 
mined separately. In the proximate analysis part of it escapes with the 
volatile matter and the rest of it is found in the ash as sulphide of iron. 
The sulphur should be given separately in the report of the analysis. 

The relation of the volatile matter and of the fixed carbon in the com- 
bustible portion of the coal enables us to judge the class to which the 
coal belongs, as anthracite, semi-anthracite, semi-bituminous, bituminous, 
or lignite. Coals containing less than 7.5 per cent volatile matter in the 
combustible, would be classed as anthracite, between 7.5 and 12.5 per 
cent as semi-anthracite, between 12.5 and 25 per cent as semi-bituminous, 
between 25 and 50 per cent as bituminous, and over 50 per cent as lig- 
nitic coals or lignites. In the classification of the U. S. Geological Sur- 
vey the sub-bituminous coals and lignites are distinguished by their 
structure and color rather than by analysis. 

The figures in the second column, representing the percentages in the 
dry coal, are useful in comparing different lots of coal of one class, and 
they are better for this purpose than the figures in the first column, for 
the moisture is a variable constituent, depending to a large extent on the 
weather to which the coal has been subjected since it was mined, on the 
amount of moisture in the atmosphere at the time when it is analyzed, 
and on the extent to which it may have accidentally been dried during 
the process of sampling. 

The heating value of a coal depends on its percentage of total combus- 
tible matter, and on the heating value per pound of that combustible. 
The latter differs in different districts and bears a relation to the per- 
centage of volatile matter. It is highest in the semi-bituminous coals, 
being nearly constant at about 15,750 B.T.U. per pound. It is between 
14,500 and 15,000 B.T.U. in anthracite, and ranges from 15,500 down to 



790 



FUEL. 



13,000 in the bituminous coals, decreasing usually as we go westward, 
and as the volatile matter contains an increasing percentage of oxygen. 
In some lignites it is as low as 10,000. 

In reporting the heating value of a coal, the B.T.U. per pound of com- 
bustible should always be stated, for convenient comparison with other 
reports. 

Proximate Analyses and Heating Values of American Coals. 

The accompanying table of proximate, analyses and heating values of 
American coals is condensed from one compiled by the author for the 
1898 edition of the Babcock & Wilcox Co. 's book, "Steam." The analyses 
are selected from various sources, and in general are averages of many 
samples. The heating values per pound of combustible are either ob- 
tained from direct caforimetric determinations or calculated from ulti- 
mate analyses, except those marked (?) which are estimated from the 
heating values of coals of similar composition. 

Table of Heating Value of Coals. 















oP. 


li 










<D 








i>H 


-^ o 


^ ■£ 








^ 


a 
o 

o 






^W 


.33 


HS53 




6 


3 




3 


%8 




>B 

$8 


leoretical 
ration frc 
at 212° p 
Combusti 




*o 


-S 


1 


-3 


3 


01 


53 §3 


1M 




§ 


> 


fe 


< 


w 


> 


w 


H 


Anthracite. 




















Northern Coal Field . . 


3 42 


4 38 


83 27 


8 20 


73 


13160 


5.00 


14900 


15.42 


East Middle Field .... 


3 71 


3.08 


86.40 


6 27. 


58 


13420 


3.44| 14900 


15.42 


West Middle Field.... 


3 16 


3 72 


81 59 


10 65 


50 


12840 


4.36 14900 


15.42 


Southern Coal Field . . 


3.09 


4.28 


83.81 


8.18 


0.64 


13220 


4.85 


14900 


15.42 


Semi-anthracite. 




















Loyalsock Field 


1.30 


8.10 


83.34 


6.23 


1.63 


13920 


8.86 


15500 


16.05 


Bernice Basin 


0.6!> 


9.40 


83.69 


3.34 


0.91 


13700 


10.98 


15500 


16.05 


Semi-bituminous. 




















Clearfield Co., Pa 


76 


22 52 


71 82 


3 99 


91 


14950 


24.60 


15700 


16.25 


Cambria Co., Pa 


94 


19 20 


71.12 


7 04 


1 70 


14450 


22.71! 15700 


16.25 


Somerset Co., Pa 


1 58 


16 42 


71 51 


8 62 


1 87 


14200 


20.37 


15800 


16.36 


Cumberland, Md 


1 09 


17.30 


73.12 


7.75 


74 


14400 


19.79 


15800 


16.36 


Pocahontas, Va 


1.00 


21.00 


74.39 


3.03 


58 


15070 


22.50 


15700 


16.25 


New River, W. Va 


0.85 


17.88 


77.64 


3.36 


0.27 


15220 


18.95 


15800 


16.36 


Bituminous. 




















Connellsville, Pa 


1 26 


30.12 


59.61 


8.23 


78 


14050 


34.03 


15300 


15.84 


Youghiogheny, Pa 


1.03 


36.50 


59.05 


2.61 


81 


14450 


38.73 


15000 


15.53 


Jefferson Co., Pa.. . . 


1 21 


32.53 


60.99 


4.27 


1.00 


14370 


35.47 


152C0 


15.74 


Brier Hill, Ohio 


4 80 


34 60 


56 30 


4 30 




13010 


38.20 


14300 


14.80 


Vanderpool, Ky 

Muhlenberg Co., Ky. . 


4 00 


34 10 


54.60 


7 30 




12770 


38.50 


14400 


14.91 


4 33 


33.65 


55.50 


4 95 


1 57 


13060 


38.86 


14400(?) 


14.91 


Scott Co., Tenn 


1 26 


35 76 


53 14 


8 02 


1 80 


13700 


34.17 


15100(?) 


15.63 


Jefferson Co., Ala 


1.55 


34.44 


59 77 


2.62 


1.42 


13770 


37.63 


14400(?) 


14.91 


Big Muddy, III 


7.50 


30.70 


53 80 


8.00 




12420 


36.30 


14700 


15.22 


Mt. Olive, 111 


11.00 


35.65 


37.10 


13.00 




10490 


47.00 


13800 


14.29 


Streator, 111 


12 00 


33.30 


40 70 


14 00 




10580 


45.00 


14300 


14.80 


Missouri 


6.44 


37.57 


47.94 


8.05 




12230 


43.94 


I4300(?) 


14.80 



The heating values per pound of combustible given in the table, except 
those marked (?) are probably within 3% of the average actual heating 
values of the combustible portion of the coals of the several districts. 
When the percentage of moisture and ash in any given lot of coal is known 



ANALYSIS AND HEATING VALUE OF COALS. 791 



the heating value per pound of coal may be found approximately by 
multiplying the heating value per pound of combustible of the average 
coal of the district by the difference between 100% and the sum of the 
percentages of moisture and ash. 

In 1890 the author deduced from Mahler's tests on European coals 
the following table of the approximate heating value of coals of different 
composition. 





Approximate Heating Values 


of Coals. 




Per Cent 
Fixed Car- 
bon in 
Coal Dry 
and Free 
from Ash. 


Heating 
Value, B.T.U. 
per lb. 
Combus- 
tible. 


Equivalent 

Water 
Evapora- 
tion from 
and at 212° 

per lb. 
Combus- 
tible. 


Per Cent 
Fixed Car- 
bon in 
Coal Dry 
and Free 
from Ash. 


Heating 
Value, B.T.U. 
per lb. 
Combus- 
tible . 


Equivalent 
Water 
Evapora- 
tion from 
and at 212° 

per lb. 
Combus- 
tible. 


100 
97 
94 
90 
87 
80 
72 


14,580 
14,940 
15,210 
15,480 
15,660 
15,840 
15,660 


15.09 
15.47 
15.75 
16.03 
16.21 
16.40 
16.21 


68 
63 
60 
57 
55 
53 
51 


15,480 
15,120 
14,760 
14,220 
13,860 
13,320 
12,420 


16.03 

15.65 

15.28 

14.72 

14.35 . 

13.79 

12.86 



The experiments of Lord and Haas on American coals (Trans. A.I. M. E., 
1897) practically confirm these figures for all coals in which the percent- 
age of fixed carbon is 60% and over of the combustible, but for coals 
containing less than 60% fixed carbon or more than 40% volatile matter 
in the combustible, they are liable to an error in either direction of about 
4%. It appears from these experiments that the coal of one seam in a 
given district has the same heating value per pound of combustible 
within one or two percent, [true only of some districts] but coals of the 
same proximate analysis, and containing over 40% volatile matter, but 
mined in different districts, may vary 6 or 8% in heating value. 

The coals containing from 72 to 87 per cent of fixed carbon in the com- 
bustible have practically the same heating value. This is confirmed by 
Lord and Haas's tests of Pocahontas coal. A study of these tests and of 
Mahler's indicates that the heating value of all the semi-bituminous coals, 
75 to 87.5% fixed carbon, is within H/ 2 % of 15,750 B.T.U. per pound. 

The heating value of any coal may also be calculated from its ultimate 
analysis, with a probable error not exceeding 2%, by Dulong's formula: 



Heating value per lb. = 146 C + 620 



(*-s> 



40 S, 



in which C, H, and O are respectively the percentages of carbon, hydro- 
gen and oxygen. Its approximate accuracy is proved by both Mahler's 
and Lord f nd Haas's experiments, and any deviation of the calorimetric 
determination of any coals (cannel coals and lignites excepted) more than 
2% from that calculated by the formula, is more likely to proceed from 
an error in either the calorimetric test or the analysis, than from an error 
in the formula. 

Tests of the U. S. Geological Survey, 1904-1906. — Coals were 
selected at the mines in different parts of the country for the purpose of 
testing their relative value in developing power through a steam boiler 
and engine and through a gas producer and gas engine. The full account 
of these tests will be found in Bulletins 261, 290 and 323, and Profes- 
sional Paper 48, of the U. S. Geological Survey. The following table 
shows approximately the range of heating values per pound of combus- 
tible, as determined by the Mahler calorimeter, and the range of percent- 
ages of fixed carbon in the combustible (total of fixed carbon and volatile 



792 



matter) in the coals from the several states. The extreme figures, 10,200 I 
and 15,950, fairly represent the whole range of heating values of the com- j 
bustible of the coals of the United States, but the figures for each state I 
do not nearly cover the range of values in that state, and in some cases, j 
as in Indiana and Illinois, the figures are much lower than the average j 
heating values of the coals of the states. 





Fixed C. %. 


B.T.U.perlb. 




89 
80 to 76.5 
84 to 77 

67 
67.5 to 55 

60 

55 to 50.5 
61.5 to 59 
62 to 53.5 

56 to 5) 
50.5 to 47 
59 to 47.5 

57 to 53.5 
49 

50.5 to 47 
48 to 41.5 

48.5 

46 
48.5 to 42.5 
44.5 to 34 


14,900 




15,950 to 15,650 




15,250 to 15,500 




15,500 




15,500 to 15,000 




15,000 




14,400 to 13,700 




14,800 to 14,200 




14,800 to 14,100 




14,600 to 13,100 




14,300 to 12,600 




13,700 to 12,400 




13,600 to 12,700 




13,300 




12,500 to 12,300 




13,300 to 10,900 




12,100 
11,500 






10,200 to 11,400 




10,900 to 11,000 







Average Results of Lord and Haas's Tests. - 

Economy," p. 104.) 



- (" Steam Boiler 



















■g 


d 


3*ri 


• 


Name of Coal. 


C, 


H 


O 


N 


S 




"S 


3 


73 


-*"s 


£ 














-C 


o 




X 


T^S 


H 














< 


Ui 


!> 


fe 


> 


W 


Pocahontas, Va.. 


84 87 


4 20 


2 84 


85 


59 


5.89 


76 


18 51 


74.84 


19.82 


15766 


Thacker, W. Va. 


78 65 


5 00 


6.01 


1 41 


1 28 


6.27 


1 38 


35.68 


56.67 


38.62 


15237 


Pittsburg, Pa.. . . 


75.24 


5.01 


7.04 


1 51 


1.79 


8.02 


1 37 


36.80 


53.81 


40.61 


14963 


Middle Kittan- 


























75.19 


4.91 


7.47 


1.46 


1.98 


7.18 


1.81 


36.32 


54.69 


39.91 


1480 


Upper Freeport, 




Pa. and O 


12 65 


4 82 


1 26 


1 iA 


2 89 


9.10 


1 9i 


M 35 


51.63 


41.98 


14/55 


Mahoning, O 


71 13 


4 56 


7.17 


1 23 


1 86 


10.90 


3 15 


35 00 


50.95 


40.72 


14728 


Jackson Co., O.. . 


70.72 


4.45 


10.82 


1.47 


1.13 


3.25 


8 17 


35.79 


52.78 


40.41 


14141 


Hocking Val- 
























ley, O 


68.03 


4.97 


9.87 


1.44 


1.59 


8.00 


6.59 


35.77 


49.64 


41.84 


14040 







* Per lb. of combustible, by the Mahler calorimeter. The average 
figures calculated from the ultimate analyses agreed within 0.5%, except 
in the case of the Jackson Co. coal in which the calorimetric result was 
1.6% higher than that computed from the analysis. 

Sizes of Anthracite Coal. — "When anthracite is mined it is crushed 
in a "breaker," and passed over screens separating it into different sizes, 
which are named as follows: 

Lump, passes over bars set 31/2 to 5 in. apart; steamboat, over 31/2 in. 
and out of screen; broken, through 31/2 in., over 23/4 in. ; egg, 23/4 to 2 in.; 
stove, 2 to 13/ 8 in.; chestnut, 13/ 8 to 3/ 4 in.; pea, 3/ 4 to 1/2 in.; buckwheat, 
1/2 to 3/g in.; rice, 3/ 8 to 3/ 16 in.; culm, through 3/ 16 in. 



ANALYSIS AND HEATING VALUE OF COALS. 793 



When coal is screened into sizes for shipment the purity of the different 
sizes as regards ash varies greatly. Samples from one mine gave results 
as follows: 





Screened. 


Analyses. 


Name of Coal. 


Through 
Inches. 


Over 
Inches. 


Fixed 
Carbon. 


Ash. 


Egg 


2.5 
1.75 
1.25 
0.75 
0.50 


1.75 
1.25 
0.75 
0.50 
0.25 


88.49 
83.67 
80.72 
79.05 
76.92 


5.66 


Stove 

Chestnut 

Pea 


10.17 
12.67 
14.66 


Buckwheat 


16.62 



Water. 


Vol. H.C. 


Fixed C. 


Ash. 


Sulphur. 


0.96 


3.56 


82.52 


3.27 


0.24 


to 


to 


to 


to 


to 


1.97 


8.56 


89.39 


9.34 


1.04 



Space Occupied by Anthracite Coal. (/. C. I. W., vol. iii.) — The cubic 
contents of 2240 lbs. of hard Lehigh coal is a little over 36 feet; an aver- 
age Schuylkill white-ash, 37 to 38 feet; Shamokin, 38 to 39 feet; Lorberry, 
nearly 41. 

According to measurements made with Wilkesbarre anthracite coal 
from the Wyoming Valley, it requires 32.2 cu. ft. of lump, 33.9 cu. ft. 
broken, 34.5 cu. ft. egg, 34.8 cu. ft. of stove, 35.7 cu. ft. of chestnut, and 

36.7 cu. ft. of pea, to make one ton cf coal of 2240 lbs.; while it requires 

28.8 cu. ft. of lump, 30.3 cu. ft. of broken, 30.8 cu. ft. of egg, 31.1 cu. ft. 
of stove, 31.9 cu. ft. of chestnut, and 32.8 cu. ft. of pea, to make one ton 
of 2000 lbs. 

Bernice Basin, Pa., Coals. 

Bernice Basin, Sullivan 

and Lycoming Cos.; 

range of 8 

This coal is on the dividing-line between the anthracites and semi- 
anthracites, and is similar to the coal of the Lykens Valley district. 

More recent analyses (Trans. A. I. M. E., xiv. 721) give: 

Water. Vol. H.C. Fixed Carb. Ash. Sulphur. 

Working seam 0.65 9.40 83.69 5.34 0.91 

60 ft. below seam 3.67 15.42 71.34 8.97 0.59 

The first is a semi-anthracite, the second a semi-bituminous. 

Connellsville Coal and Coke. (Trans. A.I. M. E., xiii. 332.) — The 
Connellsville coal-field, in the southwestern part of Pennsylvania, is a 
strip about 3 miles wide and 60 miles in length. The mine workings are 
confined to the Pittsburgh seam, which here has its best development as 
to size, and its quality best adapted to coke-making. It generally affords 
from 7 to 8 feet of coal. 

The following analyses by T. T. Morrell show about its range of com- 
position: 

Moisture. Vol. Mat. Fixed C. Ash. Sulphur. Phosph's. 

Herold Mine 1.26 28.83 60.79 8.44 0.67 0.013 

Kintz Mine 0.79 31.91 56.46 9.52 1.32 0.02 

In comparing the composition of coals across the Appalachian field, 
in the western section of Pennsylvania, it will be noted that the Con- 
nellsville variety occupies a peculiar position between the rather dry 
semi-bituminous coals eastward of it and the fat bituminous coals flank- 
ing it on the west. 

Beneath the Connellsville or Pittsburgh coal-bed occurs an interval of 
from 400 to 600 feet of "barren measures," separating it from the lower 
productive coal-measures of Western Pennsylvania. The following tables 
show the great similarity in composition in the coals of these upper and 
lower coal-measures in the same geographical belt or basin. 



794 



Analyses from the Upper 


Coal-measures in a Westward Order. 


Localities. 


Moisture. 


Vol. Mat. 


Fixed Carb. 


Ash. 


Sulphur. 




1.35 
0.89 
1.66 


3.45 
15.52 
22.35 
31.38 
33.50 
37.66 


89.06 

74.28 
68.77 
60.30 
61.34 
54.44 


5.81 
9.29 
5.96 
7.24 
3.28 
5.86 


30 


Cumberland, Md 

Salisbury, Pa 


0.71 
1.24 
1 09 


Greensburg, Pa 

Irwin's, Pa 


1.02 
1.41 


0.86 
0.64 



Analyses from the Lower 


Coal-measures in a 


Westward Order. 


Localities. 


Moisture. 


Vol. Mat. 


Fixed Carb. 


Ash. 


Sulphur. 




1.35 
0.77 
1.40 
1.18 
0.92 
0.96 


3.45 
18.18 
27.23 
16.54 
24.36 
38.20 


89.06 
73.34 
61.84 
74.46 
62.22 
52.03 


5.81 
6.69 
6.93 
5.96 
7.69 
5.14 


30 




1 02 


Bennington 

Johnstown 


2.60 
1.86 
4.92 


Armstrong Co 


3.66 



Analyses of Southern Coals. 



Fixed C. Ash 



Sul- 
phur. 



Virginia and Kentucky. 

Big Stone Gap Field,* 9 an- 
alyses, range 

Kentucky. 

Pulaski Co., 3 analyses, 
range 

Muhlenberg Co., 4 analyses, 
range 

Pike Co., Eastern Ky., 37 an- 
alyses, range 

Kentucky Cannel Coals, 5 

analyses, range 

Tennessee. 

Scott Co., range of several I. 

Roane Co., Rockwood 

Hamilton Co., Melville 

Marion Co., Etna 

Sewanee Co., Tracy City 

Kelly Co., Whiteside 

Georgia. 

Dade Co 

Alabama. 
Warren Field: 

Jefferson Co., Birmingham 

Jefferson Co., Black Creek. 

Tuscaloosa Co 

Cahaba Field, ) Helena Vein 

Bibb Co | Coke Vein.. 



[from 0.80 
I to 2.01 

[from 1.26 
[ to 1.32 
[from 3.60 
! to 7.06 
f from 1 
i to 1.60 
from 
. to 

from 0.70 
to 1.83 
1.75 
2.74 
0.94 
1.60 
1.30 



3.01 
0.12 
1.59 
2.00 
1.78 



31.44 
36.27 

35.15 
39.44 
30.60 
38.70 
26.80 
41.00 
40.20 f 
66.30 f 

32.33 
41.29 
26.62 
26.50 
23.72 
29.30 
21.80 



42.76 
26.11 
38.33 
32.90 
30.60 



54.80 
63.50 

60.85 

52.48 
58.80 
53.70 
67.60 
50 -.37 
59.80 coke 
33.70 coke 

46.61 
61.66 
60.11 
67.08 
63.94 
61.00 
74.20 



48.30 
71.64 
54.64 
53.08 
66.58 



1.73 

8.25 

1.23 
5.52 
3.40 
6.50 
3.80 
7.80 
8.81 
4.80 

16.94 
1.11 

11.52 
3.68 

11.40 
7.80 
2.70 



3.21 
2.03 
5.45 
11.34 
1.09 



0.56 
1.72 

0.40 
1.00 
0.79 
3.16 
0.97 
0.03 
0.96 
1.32 

3.37 
0.77 
1.49 
0.91 
1.19 



2.72 
0.10 
1.33 
0.68 
0.04 



* This field covers about 120 square miles in Virginia, and about 30 
square miles in Kentucky. 

t Volatile matter including moisture. 

t Single analyses from Morgan, Rhea, Anderson, and Roane counties 
fall within this range. 



ANALYSIS AND HEATING VALUE OF COALS. 795 



Analyses of Southern Coals — 


- Continued. 






Moisture. 


Vol. 

Mat. 


Fixed C. 


Ash. 


Sul- 
phur. 


Texas. 

Eagle Mine 

Sabinas Field, Vein I 

" II 

" III 

" IV 


3.54 
1.91 
1.37 
0.84 
0.45 


30.84 
20.04 
16.42 
29.35 
21.6 


50.69 

62.71 
68.18 
50.18 
45.75 


14.93 
15.35 
13.02 
19.63 
29.1 


i! 15 ' 



Indiana Coals. (J. S. Alexander, Trans. A. I. M. E., iv. 100.) — The 
typical block coal of the Brazil (Indiana) district differs in chemical com- 
position but little from the coking coals of Western Pennsylvania. The 
physical difference, however, is quite marked; the latter has a cuboid 
structure made up of bituminous particles lying against each other, so 
that under the action of heat fusion throughout the mass readily takes 
place, while block coal is formed of alternate layers of rich bituminous 
matter and a charcoal-like substance, which is not only very slow of 
combustion, but so retards the transmission of heat that agglutination 
is prevented, and the coal burns away layer by layer, retaining its form 
until consumed. 

An ultimate analysis of block coal from Sand Creek by E. T. Cox gave: 
C, 72.94; H, 4.50; O, 11.77; N, 1.79; ash, 4.50; moisture, 4.50. 

Analyses of other Indiana coals are given below. 





Moisture. 


Vol. 
Mat. 


Fixed C. 


Ash. 


Caking Coals. 


4.50 
2.35 
7.00 
3.50 

8.50 
2.50 
5.50 


45.50 
45.25 
39.70 
45.00 

31.00 
44.75 
36.00 


45.50 
51.60 
47.30 
46.00 

57.50 
51.25 
53.50 


4 50 


Sullivan Co 

Clay Co 


0.80 
6.00 


Spencer Co 

Block Coals. 
Clay Co 


2.50 
3 00 


Martin Co 

Daviess Co 


1.50 
5.00 



Illinois Coals. The Illinois coals are generally high in moisture, 
volatile matter, ash and sulphur, and the volatile matter is high in oxygen; 
consequently the coals are low in heating value. The range of quality is 
a wide one. The Big Muddy coal of Jackson Co., which has a high 
reputation as a steam coal in the St. Louis market, has about 36% of 
volatile matter in the combustible, while a coal from Staunton, Macou- 
pin Co., tested by the author in 1883 {Trans. A. S. M. E., v. 266) had 
68%. A boiler test with this coal gave only 6.19 lbs. of water evapo- 
rated from and at 212° per lb. of combustible, in the same boiler that had 
given 9.88 lbs. with Jackson, O., nut. 

Prof. S. W. Parr, in Bulletin No. 3 of the 111. State Geol. Survey, 1906, 
reports the analyses and calorimetric tests of 150 Illinois coals. The two 
having the lowest and the highest value per pound of combustible have 
the following analysis: 





Air-dried Coal. 


Pure Coal. 




Moist. 


Ash. 


Vol. 


Fixed 
C. 


S. 


Vol. 


Fixed 
C. 


B.T.U. 

per lb. 


Lowest . . 
Highest . 


9.90 
5.68 


5.02 
8.90 


40.75 
33.32 


44.33 
52.10 


2.00 
1.18 


47.90 
39.02 


52.10 
60.98 


12,162 
14,830 



796 



The poorest coal of the series had a heating value of only 8645 B.T.U. 
per lb., air dry; it contained 9.70 moisture and 31.18 ash, and the B.T.U. 
per lb. combustible was 14,623. The best coal had a heating value of 
13,303 per lb.; moisture 4.20, ash 5.50, B.T.U. per lb. combustible, 14,734. 

Of the 150 coals, 28 gave between 14,500 and 14,830 B.T.U. per lb. 
combustible; 82 between 14,000 and 14,500; 32 between 13,500 and 
14,000; 6 between 13,000 and 13,500; one 12,535 and one 12,162. The 
average is about 14,200. The volatile matter ranged from 36.24% to 
53.80% of the combustible; the sulphur from 0.62 to 4.96%; the ash 
from 2.32 to 31.18%, and the moisture from 3.28 to 12.74%, all calcu- 
lated from the air-dried samples. The moisture in the coal as mined is 
not stated, but was no doubt considerably higher. The author has 
found over 14% moisture in a lump of Illinois coal that was apparently 
dry, having been exposed to air, under cover, for more than a month. 

Colorado Coals. — The Colorado coals are of extremely variable com- 
position, ranging all the way from lignite to anthracite. G. C. Hewitt 
{Trans. A. I. M. E., xvii. 377) says: The coal seams, where unchanged 
by heat and flexure, carry a lignite containing from 5% to 20% of water. 
In the southeastern corner of the field the same have been metamor- 
phosed so that in four miles the same seams are an anthracite, coking, 
and dry coal. The dry seams also present wide chemical and physical 
changes in short distances. A soft and loosely bedded coal has in a 
hundred feet become compact and hard without the intervention of a 
fault. A couple of hundred feet has reduced the water of combination 
from 12% to 5%. 

Western Arkansas and Oklahoma, (formerly Indian Territory). 
(H. M. Chance, Trans. A. I. M. E., 1890.) — The western Arkansas coals 
are dry semi-bituminous or semi-anthracitic coals, mostly non-coking, 
or with quite feeble coking properties, ranging from 14% to 16% in 
volatile matter, the highest percentage yet found, according to Mr. Wins- 
low's Arkansas report, being 17.655. 

In the Mitchell basin, about 10 miles west from the Arkansas line, the 
coal shows 19% volatile matter; the Mayberry coal, about 8 miles farther 
west, contains 23%; and the Bryan Mine coal, about the same distance 
west, shows 26%. About 30 miles farther west, the coal shows from 
38% to 411/2% volatile matter, which is also about the percentage in 
coals of the McAlester and Lehigh districts. 

"Western Lignites. — The ultimate analyses of some lignites from 
Utah, Wyoming, Oregon and Alaska are reported by R. W. Raymond in 
Trans. A. I. M. E., vol. ii. 1873. The range of the analyses is as follows: 
C, 55.79 to 69.84; H, 3.26 to 5.08; O, 9.54 to 21.82; N, 0.42 to 1.93; S, 
0.63 to 3.92; moisture, 3.08 to 16.52; ash, 1.68 to 9.28. The heating 
value in B.T.U. per lb. combustible, calculated by Dulong's formula, 
ranges from 10,090 to 13,970. 

Analyses of Foreign Coals. (Selected from D. L. Barnes's paper on 
American Locomotive Practice, Trans. A. S. C. E., 1893.) 



Great, Britain: 

South- Wales 

South-Wales 

Lancashire, Eng 

Derbyshire, 

Durham, " * 

• Staffordshire, " 

Scotlandf 

Scotland! 

South America: 

Chili 



JK ^ 


"8 8 


r6 


li 


&s 


< 


8.5 


88.3 


3.2 


6.2 


92.3 


1.5 


17.2 


80.1 


2.7 


17.7 


79.9 


2.4 


15.05 


86.8 


1.1 


20.4 


78.6 


1.0 


17.1 


63.1 


19.8 


17.5 


80.1 


2.4 


21.93 


70.55 


7.52 



South America: 
Chili, Chiroqui. . 



Brazil 
Canada: 

Nova Scotia 

Cape Breton 

Australia. 

Lignite 

Sydney, N.S.W. 

Borneo 

Tasmania 



^ ^ 


n 






>% 


*£ 


24.11 


38.98 


24.35 


62.25 


40.5 


57.9 


26.8 


60.7 


26.9 


67.6 


15.8 


64.3 


14.98 


82.39 


26.5 


70.3 


6.16 


63.4 



36.91 
13.4 
1.6 

12.5 
5.5 

10.0 
2.04 
14.2 
30.45 



* Semi-bit. coking coal. f Boghead cannel gas coal. 

% Semi-bit. steam-coal. 



RELATIVE VALUE OF STEAM COALS. 797 

An analysis of Pictou, N. S., coal, in Trans. A. I. M. E., xiv. 560, is: 
vol., 29.63; carbon, 56.98; ash, 13.39; and one of Sydney, Cape Breton, 
coal is: vol., 34.07; carbon, 61.43; ash, 4.50. 

Sampling Coal for Analysis. — J. P. Kimball, Trans. A. I. M. E., 
xii. 317, says: The unsuitable sampling of a coal-seam, or the improper 
preparation of the sample in the laboratory, often gives rise to errors in 
determinations of the ash so wide in range as to vitiate the analysis for 
all practical purposes; every other single determination, excepting mois- 
ture, showing its relative part of the error. The determinations of sul- 
phur and ash are especially liable to error, as they are intimately asso- 
ciated in the slates. 

Wm. Forsyth, in his paper on The Heating Value of Western Coals 
{Eng'g News, Jan. 17, 1895), says: This trouble in getting a fairly average 
sample of anthracite coal has compelled the Reading R. R. Co., in getting 
its samples, to take as much as 300 lbs. for one sample, drawn direct 
from the chutes, as it stands ready for shipment. 

The directions for collecting samples of coal for analysis at the C, B. 
& Q. laboratory are as follows: 

Two samples should be taken, one marked "average," the other 
"select." Each sample should contain about 10 lbs., made up of lumps 
about the size of an orange taken from different parts of the dump or 
car, and so selected that they shall represent as nearly as possible, first, 
the average lot; second, the best coal. 

An example of the difference between an "average" and a "select" 
sample, taken from Mr. Forsyth's paper, is the following of an Illinois 
coal: 

Moisture. Vol. Mat. Fixed Carbon. Ash. 

Average 1.36 27.69 35.41 35.54 

Select 1.90 34.70 48.23 15.17 

The theoretical evaporative power of the former was 9.13 lbs. of water 
from and at 212° per lb. of coal, and that of the latter 11.44 lbs. 

RELATIVE VALUE OF STEAM COALS. 

The heating value of a coal may be determined, with more or less 
approximation to accuracy, by three different methods. 

1st, by chemical analysis; 2d, by combustion in a coal calorimeter; 
3d, by actual trial in a steam-boiler. 

The accuracy of the first two methods depends on the precision of the 
method of analysis or calorimetry adopted, and upon the care and skill 
of the operator. The results of the third method are subject to numer- 
ous sources of variation and error, and may be taken as approximately 
true only for the particular conditions under which the test is made. 
Analysis and calorimetry give with considerable accuracy the heating 
value which may be obtained under the conditions of perfect combus- 
tion and complete absorption of the heat produced. A boiler test gives 
the actual result under conditions of more or less imperfect combustion, 
and of numerous and variable wastes. It may give the highest practical 
heating value, if the conditions of grate-bars, draft, extent of heating 
surface, method of firing, etc., are the best possible for the particular 
coal tested, and it may give results far beneath the highest if these con- 
ditions are adverse or unsuitable to the coal. 

In a paper entitled Proposed Apparatus for Determining the Heating 
Power of Different Coals (Trans. A. I. M. E., xiv. 727) the author de- 
scribed and illustrated an apparatus designed to test fuel on a large 
scale, avoiding the errors of a steam-boiler test. It consists of a fire- 
brick furnace enclosed in a water casing, and two cylindrical shells con- 
taining a great number of tubes, which are surrounded by cooling water 
and through which the gases of combustion pass while being cooled. No 
steam is generated in the apparatus, but water is passed through it and 
allowed to escape at a temperature below 200° F. The product of the 
weight of the water passed through the apparatus by its increase in tem- 
perature is the measure of the heating value of the fuel. 

A study of M. Mahler's calorimetric tests shows that the maximum 
.difference between the results of these tests and the calculated heating 
power by Dulong's law in any single case is only a little over 3%, and 
the results of 31 tests show that Dulong's formula gives an average of 



798 FUEL. 

only 47 thermal units less than the calorimetric tests, the average total 
heating value being over 14,000 B.T.U., a difference of less than 0.4%.* 

The close agreement of the results of calorimetric tests when properly- 
conducted, and of the heating power calculated from the ultimate chemi- 
cal analysis, indicates that either the chemical or the calorimetric method 
may be accepted as correct enough for all practical purposes for deter- 
mining the total heating power of coal. The results obtained by either 
method may be taken as a standard by which the results of a boiler test 
are to be compared, and the difference between the total heating power 
and the result of the boiler test is a measure of the inefficiency of the 
boiler under the conditions of any particular test. 

The heating value that can be obtained in boiler practice from any 
given coal depends upon the efficiency of the boiler, and this largely 
upon the difficulty of thoroughly burning the volatile combustible matter 
in the boiler furnace. 

With the best anthracite coal, in which the combustible portion is, 
say, 97% fixed carbon and 3% volatile matter, the highest result that 
can be expected in a boiler-test with all conditions favorable is 12.2 lbs. 
of water evaporated from and at 212° per lb. of combustible, which is 
79% of 15.47 lbs., the theoretical heating-power. With the best semi- 
bituminous coals, such as Cumberland and Pocahontas, in which the 
fixed carbon is 80% of the total combustible, 12.5 lbs., or 76% of the 
theoretical 16.4 lbs., may be obtained. For Pittsburgh coal, with a 
fixed carbon ratio of 68%, 11 lbs., or 69% of the theoretical 16.03 lbs., is 
about the best practically obtainable with the best boilers when hand- 
fired, with ordinary furnaces. (The author has obtained 78% with an 
automatic stoker set in a "Dutch oven" furnace.) With some good 
Ohio Coals, with a fixed carbon ratio of 60%, 10 lbs., or 66% of the the- 
oretical 15.28 lbs., has been obtained, under favorable conditions, with a 
fire-brick arch over the furnace. With coals mined west of Ohio, with 
lower carbon ratios, the boiler efficiency is not apt to be as high as 60% 
unless a special furnace, adapted to the coal, is used. 

From these figures a table of probable maximum boiler-test results with 
ordinary furnaces from coals of different fixed carbon ratios may be 
constructed as follows: 

Fixed carbon ratio. . 97 80 68 60 54 50 

Evap. from and at 212° per lb. combustible, maximum in boiler-tests: 

12.2 12.5 11 10 8.3 7.0 

Boiler efficiency, per cent 80 76 69 66 60 55 

Loss, chimney, radiation, imperfect combustion, etc: 

20 24 31 34 40 45 

The difference between the loss of 20% with anthracite and the greater 
losses with the other coals is chiefly due to imperfect combustion of the 
bituminous coals, the more highly volatile coals sending up the chimney 
the greater quantity of smoke and unburned hydrocarbon gases. It is a 
measure of the inefficiency of the boiler furnace and of the inefficiency of 
heating-surface caused by the deposition of soot, the latter being pri- 
marily caused by the imperfection of the ordinary furnace and its unsuit- 
ability to the proper burning of bituminous coal. If in a boiler-test 
with an ordinary furnace lower results are obtained than those in the 
above table, it is an indication of unfavorable conditions, such as bad 
firing, wrong proportions of boiler, defective draft, a rate of driving 
beyond the capacity of the furnace, or beyond the capacity of the boiler 
to absorb the heat produced in the furnace. It is quite possible, however, 
with automatic stokers and fire-brick combustion chambers to obtain an 
efficiency of 70% with the highly volatile western coals. 

* Mahler gives Dulong's formula with Berthelot's figure for the heat- 
ing value of carbon, in British thermal units, 

Heating Power = 14,650 C + 62,025 (h - (° + N), - 1 \ 

The formula commonly used in the United States is 14,600 C + 62,000 
(H — 1/8 O) + 4050 S. For a description of the Mahler calorimeter and 
its method of operation see the author's "Steam Boiler Economy." Prof. 
S. W. Parr, of the University of Illinois, has put a calorimeter on the 
market which gives results practically equal to those obtained with 
Mahler's instrument. 



RELATIVE VALUE OF STEAM COALS. 



799 



Purchase of Coal under Specifications. — It is customary for large 
users of coal to purchase it under specifications of its analysis or heating 
value with a penalty attached for failure to meet the specifications. The 
following standards for a specification were given by the author in his 
"Steam Boiler Economy," 1901: 

Anthracite and Semi-anthracite. — The standard is a coal containing 
5% volatile matter, not over 2% moisture, and not over 10% ash. A 
premium of 1% on the price will be given for each per cent of volatile 
matter above 5% up to and including 15%, and a reduction of 2% on 
the price will be made for each 1% of moisture and ash above the 
standard. 

Semi-bituminous and Bituminous. — The standard is a semi-bituminous 
coal containing not over 20% volatile matter, 2% moisture, 6% ash. 
A reduction of 1 % in the price will be made for each 1 % of volatile mat- 
ter in excess of 25%, and of 2% for each 1% of ash and moisture in excess 
of the standard. 

For western coals in which the volatile matter differs greatly in its 
percentage of oxygen, the above specification based on proximate analy- 
sis may not be sufficiently accurate, and it is well to introduce either the 
heating value as determined by a calorimeter or the percentage of oxygen. 
The author has proposed the following for Illinois coal: 

The standard is one containing 14,500 B.T.U. per lb. of pure coal 
(coal free from moisture and ash), not over 6% moisture and 10% ash - 
in an air-dried sample. For lower heating value per lb. of pure coal, the 
price shall be reduced proportionately, and for every 1 % increase in ash 
or moisture above the specified figures, 2% on the price shall be deducted. 

Several departments of the U. S. government now purchase coal under 
specifications. See paper on the subject by D. T. Randall, Bulletin No. 
339, U. S. Geological Survey, 1908. 



Evaporative Power of Bituminous 


Coals 








(Tests with Babcock & Wilcox Boilers, Trans. A. S. M. E., iv. 


267.) 












*s 


0*0 


o3 


3 . 


















n c8 


O . 


r£0 










£ 


6 1 


6 


6 1 


® ii 

^4 


O 03 




^ 



a 




^ 


o 1 


of 


*S 


m . 


1*1 


3™ 


Z. 03 


1 


> 










w 




e3 C S 


Om 


P'S 





0> 


Name of Coal. 




a? 


3 


fefl 




O o3 P- 

6™§ 


a^ 

03 


3 S 
O c3 
P-g 

& ° 
a£ 


a 

O 

w 


1 


a 




'£ 


» 


_£ 




~ * 


^ 0^ 


sa 


u, a) 


TJ 


6 




3 


e3 
O 




fS 





d£ a 


£ 


■23 

o3 \£ 


1 



W 


1 . Welsh 


13l/ 2 hrs 
} IOI/4I1 


40 
60 


1679 

3126 


7.5 
8.8 


6.3 

17.6 


2.07 
4.32 


11.53 

11.32 


12.46 
12.42 


146 

272 


~ 96 


2. Anthracite scr's 1/5- 
Semi-bit. 4/5, 


448 


3. Pittsb'gh fine slack 


4 hrs 


33.7 


1679 


12.3 


21.9 


4.47 


8.12 


9.29 


146 


250 


" 3d Pool lump 


10 " 


43.5 


2760 


4.8 


27.5 


4.76 


10.47 


11.00 


240 


419 


4. Castle Shannon, nr. 


) 




















Pittsb'gh, 3/ 8 nut, 


\ 421/4 h 


69.1 


4784 


10.5 


27.9 


4.13 


10.00 


11.17 


416 


570 


5/8 lump, 


J 




















5. 111. " run of mine ". 


6 days 




1196 






1.41 


9.49 




104 


54 


" Ind. block 


3 days 
8 hrs. 


48" 


1196 
3358 






2.95 
4.11 


9.47 
8.93 


"9:88 


104 

292 


111 


6. Jackson, O., nut .... 


^6 


32J 


460 


" Staunton, 111., nut.. 


8 " ' 


60 


3358 


17.7 


25.1 


2.27 


5.09 


6.19 


292 


246 


7. Renton screenings . . 


5h50m 


21.2 


1564 


13.8 


31.5 


2.95 


6.88 


7.98 


136 


151 


" Wellington scr'gs . . . 


6h30m 


21.2 


1564 


18.3 


27 


2.93 


7.89 


9.66 


136 


150 


" Black Diam. scr'gs.. 


5h58m 


21.2 


1564 


19.3 


36.4 


3.11 


6.29 


7.80 


136 


"160 


" Seattle screenings . . 


6h24m 


21.2 


1564 


13.4 


31.3 


2.91 


6.86 


7.92 


136 


150 


" Wellington lump. . . . 


6hl9m 


21.2 


1564 


13.8 


28.2 


3.52 


9.02 


10.46 


136 


171 


" Cardiff lump. .. . 


6h47m 


21.2 


1564 


11.7 


26.7 


3.69 


10.07 


11.40 


136 


189 




7h23m 


21.2 


1564 


19.1 


25.6 


3.35 


9.62 


11.89 


136 


174 


" South Paine lump . . 


6h35m 


21.2 


1564 


13.9 


28.9 


3.53 


8,96 


10.41 


136 


182 


*' Seattle lump 


6h 5m 


21.2 


1564 


9.5 


34.1 


3.57 


7.68 


8.49 


136 


184 



800 



Place of Test: 1. London, England; 2. Peacedale, R. I.; 3. Cincinnati; 
4. Pittsburgh; 5. Chicago; 6. Springfield, O.; 7. San Francisco. 

In all the above tests the furnace was supplied with a fire-brick arch 
for preventing the radiation of heat from the coal directly to the boiler. 

Weathering of Coal. (I. P. Kimball, Trans. A. I. M. E., viii. 204.) — 
The effect of the weathering of coal, while sometimes increasing its 
weight, is to diminish the carbon and disposable hydrogen and to increase 
the oxygen and indisposable hydrogen. Hence a reduction in the calo- 
rific value. An excess of pyrites in coal tends to produce rapid oxida- 
tion and mechanical disintegration of the mass, with development of 
heat, loss of coking power, and spontaneous ignition. 

The only appreciable results of the weathering of anthracite are con- 
fined to the oxidation of its accessory pyrites. In coking coals, however, 
weathering reduces and finally destroys the coking power. 

Richters found that at a temperature of 158° to 180° Fahr., three coals 
lost in fourteen days an average of 3.6% of calorific power. It appears 
from the experiments of Richters and Reder that when there is no rise 
of temperature of coal piled in heaps and exposed to the air for nine to 
twelve months, it undergoes no sensible change, but when the coal 
becomes heated it suffers loss of C and H by oxidation and increases in 
weight by the fixation of oxygen. (See also paper by R. P. Rothwell, 
Trans. A. I. M. E., iv. 55.) 

Experiments by S. W. Parr and N. D. Hamilton (Bull. No. 17 of 
Univ'y of 111. Eng'g Experiment Station, 1907) on samples of about 
100 lbs. each, show that no appreciable change takes place in coal sub- 
merged in water. Their conclusions are: 

(a) Submerged coal does not lose appreciably in heat value. 

(b) Outdoor exposure results in a loss of heating value varying from 
2 to 10 per cent. 

(c) Dry storage has no advantage over storage in the open except 
with high sulphur coals, where the disintegrating effect of sulphur in the 
process of oxidation facilitates the escape or oxidation of the hydrocar- 
bons. 

(d) In most cases the losses in storage appear to be practically com- 
plete at the end of five months. From the seventh to the ninth month 
the loss is inappreciable. 

This paper contains also a historical review of the literature on weather- 
ing and on spontaneous combustion, with a summary of the opinions of 
various authorities. 

Later experiments on storing carload lots of Illinois coals (W. F. "Wheeler, 
Trans. A. I. M. E., 1908) confirm the above conclusions, except that 
4 per cent seems to be amply sufficient to cover the losses sustained by 
Illinois coals under regular storage-conditions, the larger losses indi- 
cated in the former series being probably due to the small size of the 
samples exposed. In these latter tests, the losses sustained by the sub- 
merged coal, though small in amount, are only slightly less than those 
indicated for the exposed coal. Screenings and 3-in. nut coal from three 
mines were stored outdoors, under cover and under water. The average 
loss in heating value at the end of one week was 0.8%, at the end of two 
months 1.3%, and at the end of six months 2.0%. Pillar coal exposed 
underground from 22 to 27 years showed less than 3% loss in heating 
value as compared with fresh face coal from the same mines. 

An extreme case of weathering was found in coal taken from near an 
outcrop that had been covered with soil and forest. The coal in this 
case had become so changed as to appear nearly like lignite, and the 
analysis shows a corresponding resemblance. The dry coal analysis of 
the outcrop coal, as compared with fresh face coal 300 ft. from the out- 
crop, is as follows: 

Ash. Vol. Mat. Fixed C. Sulphur. 

Outcrop 16.86 39.27 43.87 0.85 

Fresh coal 16.25 40.72 43.03 3.91 

The moisture in the outcrop coal was 29.81% and in the fresh coal 
13.86%. The heating value of the ash-, water- and sulphur-free coal 
from the outcrop was 11,164 B.T.U. and that of the fresh coal 14,618 
B.T U. 



801 



Pressed Fuel. (E. F. Loiseau, Trans. A, I. M. E., viii. 314.) — 

Pressed fuel has been made from anthracite dust by mixing the dust with 
ten per cent of its bulk of dry pitch, which is prepared by separating from 
tar at a temperature of 572° F. the volatile matter it contains. The 
mixture is kept heated by steam to 212°, at which temperature the pitch 
acquires its cementing properties, and is passed between two rollers, on 
the periphery of which are milled out a series of semi-oval cavities. The 
lumps of the mixture, about the size of an egg, drop out under the 
rollers on an endless belt which carries them to a screen in eight minutes, 
which time is sufficient to cool the lumps, and they are then ready for 
delivery. 

The enterprise of making the pressed fuel above described was not 
commercially successful, on account of the low price of other coal. In 
France, however, "briquettes" are regularly made of coal-dust (bitu- 
minous and semi-bituminous). 

Experiments with briquets for use in locomotives have been made 
by the Penna. R. R. Co., with favorable results, which were reported at 
the convention of the Am. Ry. Mast. Mechs. Assn. (Eng. News, July 2, 
1908). A rate of evaporation as high as 19 lbs. per sq. ft. of heating 
surface per hour was reached. The comparative economy of raw coal 
and of briquets was as follows: 

Evap. per sq.ft. heat. surf, per hr., lbs 8 10 12 14 16 

Evap. from and at I Lloydell coal . . . . 9.5 8.8 8.0 7.3 6.6 
212° per lb. of fuel J Briquetted coal. 10.7 10.2 9.7 9.2 8.7 

The fuel consumed per draw-bar horse-power with the locomotive 
running at 37.8 miles per hour and a cut-off of 25% was: with raw coal, 
4.48 lbs.; with round briquets, 3.65 lbs. 

Experiments on different binders for briquets are discussed by J. E. 
Mills in Bulletin No. 343 of the U. S. Geological -Survey, 1908. 

The experiments show that, in general, where it can be obtained, the 
cheapest binder will be the heavy residuum from petroleum, often known 
to the trade as asphalt. Four per cent of this binder being sufficient, 
its cost ranges from 45 to 60 cts. per ton of briquets produced. This 
binder is available in California, Texas, and adjacent territory. 

Second in order of importance comes water-gas tar pitch. Five to 
six per cent usually proving sufficient, the cost of this binder ranges 
from 50 to 60 cts. per ton of briquets. As water-gas pitch is also derived 
from petroleum, it will be available in oil-producing regions. 

Third in order is coal-tar pitch. This binder is very widely available, 
From 6.5 to 8% will usually be required, and the cost ranges from 65 to 
90 cts. per ton of briquets. " 

Other substances are also mentioned which may possibly be used for 
binders, such as asphalts and tars derived from wood distillation; pitch 
made from producer-gas tar; and magnesia. Starch and the waste sul- 
phite liquor from paper mills may also be used, but the briquets made 
with them are not waterproof. 

Briquetting tests made at the St. Louis exhibition, 1904, with descrip- 
tions of the machines used are reported in Bulletin No. 261 of the U. S. 
Geological Survey, 1905. See also paper on Coal Briquetting in the 
U. S., by E. W. Parker, Trans. A. I. M. E„ 1907. 

COKE. 

Coke is the solid material left after evaporating the volatile ingredi- 
ents of coal, either by means of partial combustion in furnaces called 
coke ovens, or by distillation in the retorts of gas-works. 

Coke made in ovens is preferred to gas coke as fuel. It is of a dark 
gray color, with slightly metallic luster, porous, brittle, and hard. 

The proportion of coke yielded by a given weight of coal is very differ- 
ent for different kinds of coal, ranging from 0.9 to 0.35. 

Being of a porous texture, it readily attracts and retains water from 
the atmosphere, and sometimes, if it is kept without proper shelter, 
from 0.15 to 0.20 of its gross weight consists of moisture. 



802 



FUEL. 



Analyses of Coke. 

(From report of John R. Procter, Kentucky Geological Survey.) 



Where Made. 


Fixed 
Carbon. 


Ash. 


Sul- 
phur. 


Connellsville, Pa. (Average of 3 samples) 

Chattanooga, Tenn. "4 

Birmingham, Ala. " "4 " 

Pocahontas, Va. "3 " 

New River, W.Va. " "8 " 

Big Stone Gap, Ky. " "7 " 


88.96 
80.51 
87.29 
92.53 
92.38 
93.23 


9.74 
16.34 
10.54 
5.74 
7.21 
5.69 


0.810 
1.595 
1.195 
0.597 
0.562 
0.749 



Experiments in Coking. Connellsville Region. 
(John Fulton, Amer. Mfr., Feb. 10, 1893.) 













M 


03 


Per cent of Yield. 






.a.d 


T3 
03 
M 

on 


03 

s 


03 

03 d 

.S 2 


o 


o 
O . 










■ 


03 


IS 




a, . 
, o 


fc 


H 


< 


p*. 


s 


H 


< 


fe 


s 


H 


Pn 




h. m. 


lb. 


lb. 


lb. 


lb. 


lb. 












1 


67 00 


12,420 


99 


385 


7,518 


7,903 


00.80 


3.10 


60.53 


63.63 


35.57 


2 


68 00 


11,090 


90 - 


359 


6,580 


6,939 


00.81 


3.24 


59.33 


62.57 


36.62 


3 


45 00 


9,120 


77 


272 


5,418 


5,690 


00.84 


2.98 


59.41 


62.39 


36.77 


4 


45 00 


9,020 


74 


349 


5,334 


5,683 


00.82 


3.87 


59.13 


63.00 


36.18 



These results show, in a general average, that Connellsville coal care- 
fully coked in a modern beehive oven will yield 66.17% of marketable 
coke, 2.30% of small coke or breeze, and 0.82% of ash. 

The total average loss in volatile matter expelled from the coal in coking 
amounts to 30.71%. 

The beehive coke oven is 12 feet in diameter and 7 feet high at crown 
of dome. It is used in making 48 and 72 hour coke. [The Belgian type 
of beehive oven is rectangular in shape.] 

In making these tests the coal was weighed as it was charged into the 
oven; the resultant marketable coke, small coke or breeze and ashes 
weighed dry as they were drawn from the oven. 

Coal Washing. — In making coke from coals that are high in ash and 
sulphur, it is advisable to crush and wash the coal before coking it. A 
coal-washing plant at Brookwood, Ala., has a capacity of 50 tons per hour. 
The average percentage of ash in the coal during ten days' run varied 
from 14% to 21%, in the washed coal from 4.8% to 8.1%, and in the 
coke from 6.1% to 10.5%. During three months the average reduction 
of ash was 60.9%. (Eng. and Mining Jour., March 25, 1893.) 

An experiment on washing Missouri No. 3 slack coal is described in 
Bulletin No. 3 of the Engineering Experiment Station of Iowa State Col- 
lege, 1905. The raw coal analyzed: moisture, 14.37; ash, 28.39; sulphur, 
4.30; and the washed coal, moisture, 23.90; ash, 7.59; sulphur, 2.89. 
Nearly 25% of the coal was lost in the operation. 

Recovery of By-products in Coke Manufacture. — In Germany 
considerable progress has been made in the recovery of by-products. 
The Hoffman-Otto oven has been most largely used, its principal feature 
being that it is connected with regenerators. In 1884 40 ovens on this 
system were, running, and in 1892 the number had increased to 1209. 

A Hoffman-Otto oven in Westphalia takes a charge of 61/4 tons of dry 
coal and converts it into coke in 48 hours. The product of an oven 
annually is 1025 tons in the Ruhr district, 1170 tons in Silesia, and 960 
tons in the Saar district. The yield from dry coal is 75% to 77% of 
coke, 2.5% to 3% of tar, and 1.1% to 1.2% of sulphate of ammonia in 



803 



the Ruhr district; 65% to 70% of coke, 4% to 4.5% of tar, and 1% to 
1.25% of sulphate of ammonia in the Upper Silesia region, and 68% to 
72% of coke, 4% to 4.3% of tar and 1.8% to 1.9% of sulphate of 
ammonia in the Saar district. A group of 60 Hoffman ovens, therefore, 
yields annually the following: 



District. 


Coke, 
tons. 


Tar, 
tons. 


Sulphate 
Ammo- 
nia, tons. 


Ruhr 


51,300 
48,000 
40,500 


1860 
3000 
2400 


780 


Upper Silesia 


840 

492 







An oven which has been introduced lately into Germany in connection 
with the recovery of by-products is the Semet-Solvay, which works hotter 
than the Hoffman-Otto, and for this reason 73% to 77% of gas coal can 
be mixed with 23% to 27% of coal low in volatile matter, and yet yield 
a good coke. Mixtures of this kind yield a larger percentage of coke, 
but, on the other hand, the amount of gas is lessened, and therefore the 
yield of tar and ammonia is not so great. 

The yield of coke by the beehive and the retort ovens respectively is 
given as follows in a pamphlet of the Solvay Process Co.: Connellsville 
coal: beehive, 66%, retort, 73%; Pocahontas: beehive, 62%, retort, 83%; 
Alabama: beehive, 60%, retort, 74%. (See article in Mineral Industry, 
vol. viii. 1900.) 

References: F. W. Luerman, Verein Deutscher Eisenhuettenleute 1891, 
Iron Age, March 31, 1892; Amer. Mfr., April 28, 1893. An excellent 
series of articles on the manufacture of coke, by John Fulton, of Johns- 
town, Pa., is published in the Colliery Engineer, beginning in January, 
1893. 

Since the above was written, great progress in the introduction of coke 
ovens with by-product attachments has been made in the United States, 
especially by the Semet-Solvay Co., Syracuse, N. Y. See paper on The 
Development of the Modern By-product Coke-oven, by C. G. Atwater, 
Trans. A. I. M. E., 1902. 

Generation of Steam from Waste Heat and Gases of Coke-ovens. 
(Erskine Ramsey, Amer. Mfr., Feb. 16, 1894.) — The gases from a num- 
ber of adjoining ovens of the beehive type are led into a long horizontal 
flue, and thence to a combustion-chamber under a battery of boilers. 
Two plants are in satisfactory operation at Tracy City, Tenn., and two 
at Pratt Mines, Ala. 

A Bushel of Coal. — The weight of a bushel of coal in Indiana is 70 
lbs.; in Penna., 76 lbs.; in Ala., Colo., Ga., 111., Ohio, Tenn., and W. Va., 
it is 80 lbs. 

A Bushel of Coke is almost uniformly 40 lbs., but in exceptional 
cases, when the coal is very light, 38, 36, and 33 lbs. are regarded as a 
bushel, in others from 42 to 50 lbs. are given as the weight of a bushel; 
in this case the coke would be quite heavy. 

Products of the Distillation of Coal. — S. P. Sadler's Handbook of 
Industrial Organic Chemistry gives a diagram showing over 50 chemical 
products that are derived from distillation of coal. The first derivatives 
are coal-gas, gas-liquor, coal-tar, and coke. From the gas-liquor are 
derived ammonia and sulphate, chloride and carbonate of ammonia. 
The coal-tar is split up into oils lighter than water or crude naphtha, 
oils heavier than water — otherwise dead oil or tar, commonly called 
creosote, — and pitch. From the two former are derived a variety of 
chemical products. 

From the coal-tar there comes an almost endless chain of known com- 
binations. The greatest industry based upon their use is the manufac- 
ture of dyes, and the enormous extent to which this has grown can be 
judged from the fact that there are over 600 different coal-tar colors in 
use, and many more which as yet are too expensive for this purpose. 
Many medicinal preparations come from the series, pitch for paving 



804 FUEL. 

purposes, and chemicals for the photographer, the rubber manufacturers 
and tanners, as well as for preserving timber and cloths. 

The composition of the hydrocarbons in a soft coal is uncertain and 
quite complex; but the ultimate analysis of the average coal shows that 
it approaches quite nearly to the composition of CH 4 (marsh-gas). (W. H. 
Biauvelt, Trans. A. I. M. E., xx. 625.) 

WOOD AS FUEL. 

Wood, when newly felled, contains a proportion of moisture which 
varies very much in different kinds and in different specimens, ranging be- 
tween 30% and 50%, and being on an average about 40%. After 8 or 
12 months' ordinary drying in the air 4he proportion of moisture is from 
20 to 25%. This degree of dryness, or almost perfect dryness if required, 
can be produced by a few days' drying in an oven supplied with air at 
about 240° F. When coal or coke is used as the fuel for that oven, 1 lb. 
of fuel suffices to expel about 3 lbs. of moisture from the wood. This is the 
result of experiments on a large scale by Mr. J. R. Napier. If air-dried 
wood were used as fuel for the oven, from 2 to 2V2 lbs. of wood would prob- 
ably be required to produce the same effect. 

The specific gravity of different kinds of wood ranges from 0.3 to 1.2. 

Perfectly dry wood contains about 50% of carbon, the remainder con- 
sisting almost entirely of oxygen and hydrogen in the proportions which 
form water. The coniferous family contain a small quantity of turpen- 
tine, which is a hydrocarbon. The proportion of ash in wood is from 
1% to 5%. The total heat of combustion of all kinds of wood, when dry, 
is almost exactly the same, and is that due to the 50% of carbon. 

The above is from Rankine; but according to the table by S. P. Sharp- 
less in Jour. C. I. W., iv. 36, the ash varies from 0.03% to 1.20% in 
American woods, and the fuel value, instead of being the same for all 
woods, ranges from 3667 (for white oak) to 5546 calories (for long-leaf 
pine) = 6600 to 9883 British thermal units for dry wood, the fuel value 
of 0.50 lb. carbon being 7272 B. T. U. 

Heating Value of Wood. — The following table is given in several 
books of reference, authority and quality of coal referred to not stated. 

The weight of one cord of different woods (thoroughly air-dried) is 
about as follows: 

lbs. lbs. 

Hickory or hard maple . . . 4500 equal to 1800 coal. (Others give 2000.) 

White oak 3850 " 1540 " ( " 1715.) 

Beech, red and black oak. .3250 " 1300 " ( " 1450.) 

Poplar, chestnut, and elm. 2350 " 940 " ( " 1050.) 

The average pine 2000 " 800 ( " 925.) 

Referring to the figures in the last column, it is said: 
From the above it is safe to assume that 21/4 lbs. of dry wood are equal 
to 1 lb. average quality of soft coal and that the full value of the same 
weight of different woods is very nearly the same — that is, a pound of 
hickory is worth no more for fuel than a pound of pine, assuming both to 
be dry. It is important that the wood be dry, as each 10% of water or 
moisture in wood will detract about 12% from its value as fuel. 

Taking an average wood of the analysis C 51%, H 6.5%, O 42.0%, ash 
0.5%, perfectly dry, its fuel value per pound, according to Dulong's 

formula, V = fl4,600 C + 62,OOo(h - ~\\ , is 8221 British thermal 



units. If the wood, as ordinarily dried in air, contains 25% of moisture, 
then the heating value of a pound of such wood is three quarters of 
8221 = 6165 heat-units, less the heat required to heat and evaporate the 
1/4 lb. of water from the atmospheric temperature, and to heat the steam 
made from this water to the temperature of the chimney gases, say 
150 heat-units per pound to heat the water to 212°, 970 units to evap- 
orate it at that temperature, and 100 heat-units to raise the temperature 
of the steam to 420° F., or 1220 in all = 305 for 1/4 lb., which subtracted 
from the 6165, leaves 5860-heat-units as the net fuel value of the wood 
per pound, or about 0.4 that of a pound of carbon. 



CHAKCOAL. 



805 



Composition of Wood. 

(Analysis of Woods, by M. Eugene Chevandier.) 



Woods. 


Carbon. 


Hydro- 
gen. 


Oxygen. 


Nitrogen. 


Ash. 




49.36% 

49.64 

50.20 

49.37 

49.96 


6.01% 

5.92 

6.20 

6.21 

5.96 


42.69% 

41.16 

41.62 

41.60 

39.56 


0.91% 

1.29 

1.15 

0.96 

0.96 


1.06% 
1.97 


Oak 


Birch 


0.81 




1.86 


Willow 


3.37 








49.70% 


6.06% 


41 .30% 


1 -05% 


1.80% 







The following table, prepared by M. Violette, shows the proportion of 
water expelled from wood at gradually increasing temperatures: 



Temperature. 


Water Expelled from 100 Parts of Wood. 


Oak. 


Ash. 


Elm. 


Walnut. 


257° Fahr 

302° Fahr 

347° Fahr 

392° Fahr 

437° Fahr 


15.26 
17.93 
32.13 
35.80 
44.31 


14.78 
16.19 
21.22 
27.51 
33.38 


15.32 
17.02 
36.94? 
33.38 
40.56 


15.55 

17.43 

21.00 

41.77? 

36.56 



The wood operated upon had been kept in store during two years. 
When wood which has been strongly dried by means of artificial heat is 
left exposed to the atmosphere, it reabsorbs about as much water as it 
contains in its air-dried state. 

A cord of wood = 4 X 4 X 8 = 128 cu. ft. About 56% solid wood and 
44% interstitial spaces. (Marcus Bull, Phila., 1829. J. C. I. W., vol. i., 
p. 293.) 

B. E. Fernow gives the per cent, of solid wood in a cord as determined 
officially in Prussia (J. C. I. W., vol. iii. p. 20): 

Timber cords, 74.07% = 80 cu. ft. per cord; 
Firewood cords (over 6" diam.), 69.44% = 75 cu. ft. per cord; 
"Billet" cords (over 3" diam.), 55.55% = 60 cu. ft. per cord; 
"Brush" woods less than 3" diam., 18.52%; Roots, 37.00%. 

CHARCOAL. 

Charcoal is made by evaporating the volatile constituents of wood and 
peat, either by a partial combustion of a conical heap of the material to be 
charred, covered with a layer of earth, or by the combustion of a separate 
portion of fuel in a furnace, in which are placed retorts containing the 
material to be charged. 

According to Peclet, 100 parts by weight of wood when charred in a 
heap yield from 17 to 22 parts by weight of charcoal, and when charred in 
a retort from 28 to 30 parts. 

This has reference to the ordinary condition of the wood used in char- 
coal-making, in which 25 parts in 100 consist of moisture. Of the re- 
maining 75 parts the carbon amounts to one half, or 37V2% of the gross 
weight of the wood. Hence it appears that on an average nearly half of 
the carbon in the wood is lost during the partial combustion in a heap, 
and about one quarter during the distillation in a retort. 

To char 100 parts by weight of wood in a retort, 12 1/2 parts of wood 
must be burned in the furnace. Hence in this process the whole expendi- 
ture of wood to produce from 28 to 30 parts of charcoal is II2V2 parts; 



806 



so that if the weight of charcoal obtained is compared with the whole 
weight of wood expended, its amount is from 25% to 27%; and the pro- 
portion lost is on an average 11 1/2 -J- 371/2 = 0.3, nearly. 

According to Peclet, good wood charcoal contains about 0.07 of its 
weight of ash. The proportion of ash in peat charcoal is very variable 
and is estimated on an average at about 0.18. (Rankine.) 

Much information concerning charcoal may be found in the Journal of 
the Charcoal-iron Workers' Assn., vols. i. to vi. From this source the 
following notes have been taken: 

Yield of Charcoal from a Cord of Wood. — From 45 to 50 bushels 
to the cord in the kiln, and from 30 to 35 in the meiler. Prof. Egleston 
in Trans. A. I. M, E., viii. 395, says the yield from kilns in the Lake 
Champlain region is often from 50 to 60 bushels for hard wood and 50 for 
soft wood; the average is about 50 bushels. 

The apparent yield per cord depends largely upon whether the cord is 
a full cord of 128 cu. ft. or not. 

In a four months' test of a kiln at Goodrich, Tenn., Dr. H. M. Pierce 
found results as follows: Dimensions of kiln — inside diameter of base, 
28 ft. 8 in.; diam. at spring of arch, 26 ft. 8 in.; height of walls, 8 ft.; rise 
of arch, 5 ft.; capacity, 30 cords. Highest yield of charcoal per cord of 
wood (measured) 59.27 bushels, lowest 50.14 bushels, average 53.65 
bushels. 

No. of charges 12, length of each turn or period from one charging to 
another 11 days. (J. C. I. W., vol. vi., p. 26.) 

Results from Different Methods of Charcoal-making. 





Character of Wood Used. 


Yield. 


i"3 

<» ag 

3 

m 




Coaling Methods. 


CD +a 


111 

a, 


.S«« 

3 
^pq g 

5*55.1 


Odelstjerna's experiments 
Mathieu's retorts, fuel ex- 


Birch dried at 230 F 




35.9 
28.3 

24.2 
27.7 
25.8 
24.7 

18.3 
22.0 

17.1 






(Air dry, av. good yel- ) 
\ low pine weighing > 
( abt. 28 lbs. per cu. ft. ) 

| Good dry fir and pine, ) 
\ mixed. 

( Poor wood, mixed fir ) 
{ and pine. J 
( Fir and white-pine ) 
] wood, mixed. Av. 25 > 
( lbs. per cu. ft. ) 
( Av. good yellow, pine ) 
\ weighing abt. 25 lbs. > 
( per cu. ft. ) 


77.0 
65.8 
81.0 

70,0 

72.2 

52.5 
54.7 

42.9 


63.4 

54.2 

66.7 

62.0 
59.5 

43.9 
45.0 

35.0 


15.7 


Mathieu's retorts, fuel in- 


15.7 


Swedish ovens, av. results 

Swedish ovens, av. results 
Swedish meilers excep- 


13.3 
13.3 
13.3 


Swedish meilers, av. results 
Amez-ican kilns, av. results 
American meilers, av. re- 
sults 


13.3 
17.5 
17.5 



Consumption of Charcoal in Blast-furnaces per Ton of Pig Iron; 

average consumption according to census of 1880, 1.14 tons charcoal per 
ton of pig. The consumption at the best furnaces is much below this 
average. As low as 0.853 ton, is recorded of the Morgan furnace; Bay 
furnace, 0.858; Elk Rapids, 0.884. (1892.) 

Absorption of Water and of Gases by Charcoal. — Svedlius, in his 
hand-book for charcoal-burners, prepared for the Swedish Government, 
says: Fresh charcoal, also reheated charcoal, contains scarcely any water, 
but when cool it absorbs it very rapidly, so that, after twenty-four hours, 
it may contain 4% to 8% of water. After the lapse of a few weeks the 
moisture of charcoal may not increase perceptibly, and may be esti- 
mated at 10% to 15%, or an average of 12%. A thoroughly charred 
piece of charcoal ought, then, to contain about 84 parts carbon, 12 parts 
water, 3 parts ash, and 1 part hydrogen. 



MISCELLANEOUS SOLID FUELS. 



807 



M. Saussure, operating with blocks of fine boxwood charcoal, freshly 
burnt, found that by simply placing such blocks in contact with certain 
gases they absorbed them in the following proportion: 



Volumes. 

Carbonic oxide 9 . 42 

Oxygen 9 . 25 

Nitrogen 6 . 50 

Carburetted hydrogen .... 5 . 00 
Hydrogen 1.75 



Volumes. 

Ammonia 90 . 00 

Hydrochloric-acid gas 85 . 00 

Sulphurous acid 65.00 

Sulphuretted hydrogen 55.00 

Nitrous oxide (laughing-gas) . 40 . 00 
Carbonic acid 35.00 

It is this enormous absorptive power that renders of so much value a 
comparatively slight sprinkling of charcoal over dead animal matter, as a 
preventive of the escape of odors arising from decomposition. 

In a box or case containing one cubic foot of charcoal may be stored 
without mechanical compression a little over nine cubic feet of oxygen, 
representing a mechanical pressure of one hundred and twenty-six pounds 
to the square inch. From the store thus preserved the oxygen can be 
drawn by a small hand-pump. 

Composition of Charcoal Produced at Various Temperatures. 

(By M. Violette.) 





Temperature of Car- 
bonization. 


Carbon. 


Hydro- 
gen. 


Oxygen. 


Nitro- 
gen and 
Loss. 


Ash. 


1 


150° Cent. 302° Fahr. 


47.51 


6.12 


46.29 


0.08 


47.51 


2 


200 392 


51.82 


3.99 


43.98 


0.23 


39.88 


3 


250 482 


65.59 


4.81 


28.97 


0.63 


32.98 


4 


300 592 


73.24 


4.25 


21.96 


0.57 


24.61 


■> 


350 662 


76.64 


4.14 


18.44 


0.61 


22.42 


6 


432 810 


81.64 


4.96 


15.24 


1.61 


15.40 


7 


1023 1873 


81.97 


2.30 


14.15 


1.60 


15.30 



The wood experimented on was that of black alder, or alder buck- 
thorn, which furnishes a charcoal suitable for gunpowder. It was pre- 
viously dried at 150 deg. C. = 302 deg. F. 

MISCELLANEOUS SOLID FUELS. 

Dust Fuel — Dust Explosions. — Dust when mixed in air burns with 
such extreme rapidity as in some cases to cause explosions. Explosions 
of flour-mills have been attributed to ignition of the dust in confined 
passages. Experiments in England in 1876 on the effect of coal-dust in 
carrying flame in mines showed that in a dusty passage the flame from a 
blown-out shot may travel 50 yards. Prof. F. A. Abel (Trans. A.I.M.E., 
xiii. 260) says that coal-dust in mines much promotes and extends 
explosions, and that it may readily be brought into operation as a fiercely 
burning agent which will carry flame rapidly as far as its mixture with 
air extends, and will operate as an explosive agent though the medium 
of a very small proportion of fire-damp in the air of the mine. The ex- 
plosive violence of the combustion of dust is largely due to the instan- 
taneous heating and consequent expansion of the air. (See also paper on 
"Coal Dust as an Explosive Agent," by Dr. R,. W.' Raymond, Trans. A. I. 
M. E., 1894.) Experiments made in Germany in 1893 show that pul- 
verized fuel may be burned without smoke, and with high economy. 
The fuel, instead of being introduced into the fire-box in the ordinary 
manner, is first reduced to a powder by pulverizers of any construction. 
In the place of the ordinary boiler fire-box there is a combustion chamber 
in the form of a closed furnace lined with fire-brick and provided with an 
air-injector. The nozzle throws a constant stream of fuel into the cham- 
ber, scattering: it throughout the whole space of the fire-box. When this 
■powder is once ignited, and it is very readily done by first raising the- 
Hnine to a hisrh temperature by an open fire, the combustion continues in 
an intense and regular manner under the action of the current of air 
which carries it in. (Mfrs. Record, April, 1893.) 



808 FUEL. 



Records of tests with the Wegener powdered-coal apparatus, which is 
now (1900) in use in Germany, are given in Eng. News, Sept. 16, 1897. 
An illustrated description is given in the author's Steam Boiler Economy, 
p. 183. Coal-dust fuel is now extensively used in the United States in 
rotary kilns for burning Portland cement. 

Powdered fuel was used in the Crompton rotary puddling-furnace at 
Woolwich Arsenal, England, in 1873. (Jour. I. & S. I., i. 1873, p. 91.) 
Numerous experiments on the use of powdered fuel for steam boilers 
were made in the U. S. between 1895 and 1905, but they were not com- 
mercially successful. 

Peat or Turf, as usually dried in the air, contains from 25% to 30% of 
water, which must be allowed for in estimating its heat of combustion. 
This water having been evaporated, the analysis of M. Regnault gives, in 
100 parts of perfectly dry peat of the best quality: C 58%, H 6%, O 31 %, 
Ash 5%. In some examples of peat the quantity of ash is greater, 
amounting to 7% and sometimes to 11%. 

The specific gravity of peat in its ordinary state is about 0.4 or 0.5. 
It can be compressed by machinery to a much greater density. (Rankine.) 

Clark (Steam-engine, i. 61) gives as the average composition of dried 
Irish peat: C 59%, H 6%, O 30 %, N 1.25%, Ash 4%. 

Applying Dulong's formula to this analysis, we obtain for the heating 
value of perfectly dry peat 10,260 heat-units per pound, and for air- 
dried peat containing 25% of moisture, after making allowance for 
evaporating the water, 7391 heat-units per pound. 

A paper on Peat in the U. S., by M. R. Campbell, will be found in Min- 
eral Resources of the U. S. (U. S. Geol. Survey) for 1905, p. 1319. 

Sawdust as Fuel. — The heating power of sawdust is naturally the 
same per pound as that of the wood from which it is derived, but if 
allowed to get wet it is more like spent tan (which see below). The 
conditions necessary for burning sawdust are that plenty of room should 
be given it in the furnace, and sufficient air supplied on the surface of 
the mass. The same applies to shavings, refuse lumber, etc. Sawdust 
is frequently burned in saw-mills, etc., by being blown into the furnace 
by a fan-blast. 

Wet Tan Bark as Fuel. — Tan, or oak bark, after having been used 
in the processes of tanning, is burned as fuel. The spent tan consists of 
the fibrous portion of the bark. Experiments by Prof. R. H. Thurston 
(Jour. Frank. Inst., 1874) gave with the Crockett furnace, the wet tan 
containing 59% of water, an evaporation from and at 212° F. of 4.24 lbs. 
of water per pound of the wet tan, and with the Thompson furnace an 
evaporation of 3.19 lbs. per pound of wet tan containing 55% of water. 
The Thompson furnace consisted of six fire-brick ovens, each 9 ft. X 4 ft. 
4 ins., containing 234 sq. ft. of grate in all, for three boilers with a total 
heating surface of 2000 sq. ft., a ratio of heating to grate surface of 9 to 1. 
The tan was fed through holes in the top. The Crockett furnace was an 
ordinary fire-brick furnace, 6X4 ft., built in front of the boiler, instead of 
under it, the ratio of heating surface to grate being 14.6 to 1. The con- 
ditions of success in burning wet fuel are the surrounding of the mass 
so completely with heated surfaces and with burning fuel that it may 
be rapidly dried, and then so arranging the apparatus that thorough 
combustion may be secured, and that the rapidity of combustion be 
precisely equal to and never exceed the rapidity of desiccation. Where 
this rapidity of combustion is exceeded the dry portion is consumed 
completely, leaving an uncovered mass of fuel which refuses to take fire. 

D. M. Myers (Trans. A.S.M.E., 1909) describes some experiments on 
tan as a boiler fuel. One hundred lbs. of air dried bark fed to the mill will 
produce 213 lbs. of spent tan containing 65% moisture. Taking 9500 
B.T.U. as the heating value per lb. of dry tan and 500° F. as the tempera- 
ture of the chimney gases, the available heat in 1 lb. of wet tan is 2665 
B.T.U. Based on this value as much as 71% efficiency has been obtained 
in a boiler test with a special iurnace, or 1.93 lbs. of water evaporated 
from and at 212° per lb. of wet tan. 

Straw as Fuel. (Eng'g Mechanics, Feb., 1893, p. 55.) — Experiments 
in Russia showed that winter-wheat straw, dried at 230° F., had the 
following composition: C, 46.1; H. 5.6; N, 0.42; O, 43.7; Ash, 4.1. Heat- 
ing value in British thermal units: dry straw, 6290; with 6% water, 
5770; with 10% water, 5448. With straws of other grains the heating 
value of dry straw ranged from 5590 for buckwheat to 6750 for flax. 



MISCELLANEOUS SOLID FUELS. 809 

Clark (S. E., vol. 1, p. 62) gives the mean composition of wheat and 
barley straw as C, 36; H, 5; O, 38; N, 0.50; Ash, 4.75; water, 15.75, the two 
straws varying less than 1%. The heating value of straw of this com- 
position, according to Dulong's formula, and deducting the heat lost in 
evaporating the water, is 5155 heat units. Clark erroneously gives it as 
8144 heat units. 

Bagasse as Fuel in Sugar Manufacture. — Bagasse is the name 
given to refuse sugar-cane, after the juice has been extracted. Prof. L. A. 
Becuel, in a paper read before the Louisiana Sugar Chemists' Associa- 
tion, in 1892, says: "With tropical cane containing 12.5% woody fibre, a 
juice containing 16.13% solids, and 83.87% water, bagasse of, say, 66% 
and 72% mill extraction would have the following percentage composi- 
tion: 

66% bagasse: Woody Fibre, 37; Combustible Salts, 10; Water, 53. 

72% bagasse: " " 45; " " 9; " 46. 

" Assuming that the woody fibre contains 51 % carbon, the sugar and 
other combustible matters an average of 42.1%, and that 12,906 units 
of heat are generated for every pound of carbon consumed, the 66% 
bagasse is capable of generating 297,834 heat-units per 100 lbs. as against 
345,200, or a difference of 47,366 units in favor of the 72% bagasse. 

"Assuming the temperature of the waste gases to be 450° F., that of 
the surrounding atmosphere and water in the bagasse at 86° F., and the 
quantity of air necessary for the combustion of one pound of carbon at 
24 lbs., the lost heat will be as follows: In the waste gases, heating air from 
86° to 450° F., and in vaporizing the moisture, etc., the 66% bagasse 
will require 112,546 heat units, and 116,150 for the 72% bagasse. 

"Subtracting these quantities from the above, we find that the 66% 
bagasse will produce 185,288 available heat-units per 100 lbs., or nearly 
24% less than the 72% bagasse, which gives 229,050 units. Accordingly, 
one ton of cane of 2000 lbs. at 66% mill extraction will produce 680 lbs. 
bagasse, equal to 1,259,958 available heat-units, while the same cane at 
72% extraction will produce 560 lbs. bagasse, equal to 1,282,680 units. 

"A similar calculation for the case of Louisiana cane containing 10% 
woody fibre, and 16% total solids in the juice, assuming 75% mill ex- 
traction, shows that bagasse from one ton of cane contains 1,573,956 
heat-units, from which 561,465 have to be deducted. 

"This would make such bagasse worth on an average nearly 92 lbs. 
coal per ton of cane ground. Under fairly good conditions, 1 lb. coal 
will evaporate 71/2 lbs. water, while the best boiler plants evaporate 10 
lbs. Therefore the bagasse from 1 ton of cane at 75% mill extraction 
should evaporate from 689 lbs. to 919 lbs. of water. The juice extracted 
from such cane would under these conditions contain 1260 lbs. of water. 
If we assume that the water added during the process of manufacture is 
10% (by weight) of the juice made, the total water handled is 1410 lbs. 
From the juice represented in this case, the commercial massecuite would 
be about 15% of the weight of the original mill juice, or, say, 225 lbs. 
Said mill juice 1500 lbs., plus 10%, equals 1650 lbs. liquor handled; and 
1650 lbs., minus 225 lbs., equals 1425 lbs., the quantity of water to be 
evaporated during the process of manufacture. To effect a 71/2-lb. evap- 
oration requires 190 lbs. of coal, and 142 1/2 lbs. for a 10-lb. evaporation. 

"To reduce 1650 lbs. of juice to syrup of, say, 27° Baume, requires 
the evaporation of 1170 lbs. of water, leaving 480 lbs. of syrup. If this 
work be accomplished in the open air, it will require about 156 lbs. of 
coal at 71/2 lbs. boiler evaporation, and 117 at 10 lbs. evaporation. 

"With a double effect the fuel required would be from 59 to 78 lbs., 
and with a triple effect, from 36 to 52 lbs. 

" To reduce the above 480 lbs. of syrup to the consistency of commer- 
cial massecuite means the further evaporation of 255 lbs. of water, 
requiring the expenditure of 34 lbs. coal at 71/2 lbs. boiler evaporation, 
and 251/2 lbs. with a 10-lb. evaporation. Hence, to manufacture one ton 
of cane into sugar and molasses, it will take from 145 to 190 lbs. addi- 
tional coal to do the work by the open evaporator process; from 85 to 
112 lbs. with a double effect, and only 71/2 lbs. evaporation in the boilers, 
while with 10 lbs. boiler evaporation the bagasse alone is capable of 
furnishing 8% more heat than is actually required to do the work. With 
triple-effect evaporation depending on the excellence of the boiler plant, 
the 1425 lbs. of water to be evaporated from the juice will require between 



810 



62 and 86 lbs. of coal. These vaiues show that from 6 to 30 lbs. of coal 
can be spared from the value of the bagasse to run engines, grind cane, etc. 

"It accordingly appears," says Prof. Becuel, "that with the best 
boiler plants, those taking up all the available heat generated, by using 
this heat economically the bagasse can be made to supply all the fuel 
required by our suerar-houses." 

E. W. Kerr, in Bulletin No. 117 of the Louisiana Agricultural Experi- 
ment Station, Baton Rouge, La., gives the results of a study of many 
different forms of bagasse furnaces. An equivalent evaporation of 21/4 lbs. 
of steam from and at 212° was obtained from 1 lb. of wet bagasse of a 
net calorific value of 3256 B.T.U. This net value is that calculated from 
the analysis by Dulong's formula, minus the heat required to evaporate 
the moisture and to heat the vapor to the temperature of the escaping 
chimney gases, 594° F. The approximate composition of bagasse of 75% 
extraction is given as 51% free moisture, and 28% of water combined 
with 21 % of carbon in the fibre and sugar. For the best results the bagasse 
should be burned at a high rate of combustion, at least 100 lbs. per sq. ft. 
of grate per hour. Not more than 1 .5 lbs. of bagasse per sq. ft. of heating 
surface per hour should be burned under ordinary conditions, and not less 
than 1.5 boiler horse- power should be provided per ton of coal per 24 
hours. 

LIQUID FUEL. 
Products of the Distillation of Crude Petroleum. 
Crude American petroleum of sp. gr. 0.800 may be split up by fractional 
distillation as follows (" Robinson's Gas and Petroleum Engines "): 



Temp, of 

Distillation 

Fahr. 


Distillate. 


Per- 
cent- 
ages. 


Specific 
Gravity. 


Flashing 

Point. 
Deg. F. 


113° 


Rhigolene. ) 


traces. 
1.5 
10. 
2.5 
2. 


.590 to .625 
.636 to .657 
.680 to .700 
.714 to .718 
.725 to .737 




140 to 158° 


Chymogene. j '" 

Gasoline (petroleum spirit) . . 

Benzine, naphtha C.benzolene 

( Benzine, naphtha B 

I Benzine, naphtha A 




158 to 248° 
248° 


14 


to 
347° 


32 


338° and ) 
upwards. J 

482° 


Kerosene (lamp-oil) 


50. 
15. 
2. 
16. 


.802 to .820 
.850 to .915 


100 to 122 
230 




Paraffine wax 



















Lima Petroleum, produced at Lima, Ohio, is of a dark green color, 
very fluid, and marks 48° Bailing at 15° C. (sp. gr., 0.792). 

The distillation in fifty parts, each part representing 2% by volume, 
gave the following results: 

Per Sp. Per Sp. Per Sp. Per Sp. Per Sp. Per Sp. 
cent. Gr. cent. Gr. cent. Gr. cent. Gr. cent. Gr. cent. Gr. 

0.815 
.815 



2 


0.680 


IS 


0.720 


34 


0.764 


50 


0.802 


68 


0.820 


88 


4 


.683 


20 


.728 


36 


.768 


52^ 




70 


.825 


90 


6 


.685 


22 


.730 


38 


.772 


to}- 


.806 


72 


.830 




8 


.690 


24 


.735 


40 


.778 


58 J 




73 


.830 


92") 


10 


.694 


:>tt 


.740 


42 


.782 


60 


.800 


76 


.810 


to >- 


12 


.698 


28 


.742 


44 


.788 


62 


.804 


7S 


.820 


100J 


14 


.700 


30 


.746 


46 


.792 


64 


.808 


82 


.818 




16 


.706 


32 


.760 


48 


.800 


66 


.812 


86 


.816 





RETURNS. 

16 per cent naphtha, 70° Baume. 6 per cent paraffine oil. 

68 per cent burning oil. 10 per cent residuum. 

The distillation started at 23° C, this being due to the large amount of 
naphtha present, and when 60% was reached, at a temperature of 310° C, 
the hydrocarbons remaining in the retort were dissociated, then gases 



LIQUID FUEL. 



811 



escaped, lighter distillates were obtained, and, as usual in such cases, the 
temperature decreased from 310° C. down gradually to 200° C, until 
75% of oil was obtained, and from this point the temperature remained 
constant until the end of the distillation. Therefore these hydrocarbons 
in statu moriendi absorbed much heat. (Jour. Am. Chem. Soc.) 

There is not a good agreement between the character of the materials 
designated gasoline, kerosene, etc., and the temperature of distillation 
and densities employed in different places. The following table shows 
one set of values that is probably as good as any. 



Boiling 
Point. 



Specific 
Gravity. 



Density at 
59° F. 



Petroleum ether. 

Gasoline 

Naphtha G- ; 

Naphtha B 

Naphtha A 

Kerosene. 



°F. 
104-158 
158-176 
176-212 
212-248 
248-302 
302-572 



0.650-0.660 
.660- .670 
.670- .707 
.707- .722 
.722- .737 
.753- .864 



3 Baume- 
85-80 
80-78 
78-^8 
68-64 
64-60 
56-32 



Gasoline is different from a simple substance with a fixed boiling point, 
and therefore theoretical calculations on the heat of combustion, air 
necessary, and conditions for vaporizing or carbureting air are of little 
value. (C. E. Lucke.) 

Value of Petroleum as Fuel. — Thos. Urquhart, of Russia (Proc. 
Inst. M. E., Jan., 1889), gives the following table of the theoretical evapo- 
rative power of petroleum in comparison with that of coal, as determined 
by Messrs. Favre and Silbermann: 



Fuel. 


Specific 
Gravity 

at 
32° F., 
Water 
= 1 .000 


Chem. Comp. 


Heating 
power, 
British 
Thermal 
Units. 


Theoret. 
Evap., 
lbs. 
Water per 
lb. Fuel, 
from and 
at 212°F. 




C. 


H. 


O. 


Penna. heavy crude oil. . . . 
Caucasian light crude oil . . 
Caucasian heavy crude oil. 

Petroleum refuse 

Good English Coal, Mean 


0.886 
0.884 
0.938 
0.928 

1.380 


84.9 
86.3 
86.6 
87.1 

80.0 


13.7 
13.6 
12.3 
11.7 

5.0 


1.4 
0.1 
1.1 
1.2 

8.0 


20,736 
22,027 
20,138 
19,832 

14,112 


21.48 
22.79 
20.85 
20.53 

14.61 







In experiments on Russian railways with petroleum as fuel Mr. Urquhart 
obtained an actual efficiency equal to 82% of the theoretical heating- 
value. The petroleum is fed to the furnace by means of a spray-injector 
driven by steam. An induced current of air is carried in around the 
injector-nozzle, and additional air is supplied at the bottom of the furnace. 

Beaumont, Texas, oil analyzed as follows (Eng. Neivs, Jan. 30, 1902): 
C, 84.60; H, 10.90; S, 1.63; O, 2.87. Sp. gr., 0.92; flash point, 142° F; 
burning point, 181° F.; heating value per lb., by oxygen calorimeter, 
19,060 B.T.U. A test of a horizontal tubular boiler with this oil, by J. E 
Denton gave an efficiency of 78.5%. As high as 82% has been reported 
for California oil. 

Bakersfield, Cal., oil: Sp. gr. 16° Baume; Moisture, 1%; Sulphur, 0.5%. 
B.T.U. per lb., 18,500. 

Redondo, Cal., oil, six lots: Moisture, 1.82 to 2.70%; Sulphur, 2.17 to 
2.60%: B.T.U. per lb., 17,717 to 17,966. Kilowatt-hours generated per 
barrel (334 lbs.) of oil in a 5000 K.W. plant, using water-tube boilers, and 
reciprocating engines and generators having a combined efficiency of 
90.2 to 94.75% (boiler economy and steam-rate of engine not stated). 
2000 K.W. load, 237.3; 3000 K.W., 256.7: 5000 K.W., 253.4; variable 
load, 24 hours, 243.8. (C. R. Weymouth, Trans. A.S.M.E., 1908.) 



812 



FUEL. 



The following table showing the relative values of petroleum and coal 
was given by the author in Power, Sept., 1902. It is based on the following 
assumed data: B.T.U. per lb. of oil 20,000; sp. gr., 0.885; =7.37 lbs. per 
gal.; 1 barrel = 41 gals. = 310 lbs. 



Coal, B.T.U. 


1 lb. coal 


1 barrel oil 


1 ton coal 


per lb. 


= lbs. oil. 


= lbs. coal. 


= barrels oil. 


10,000 


2. 


620 


3.23 


11,000 


1.818 


564 


3.55 


12,000 


1.667 


517 


3.87 


13,000 


1.538 


477 


4.19 


14,000 


1.429 


443 


4.52 


15,000 


1.333 


413 


4.84 



From this table we see that if coal of a heating value of only 10,000 
B.T.U. per lb. costs $3.23 per ton, and coal of 14,000 B.T.U. per lb. at 
$4.52 per ton, then the price of oil will have to be as low as $1 a barrel 
to compete with coal; or, if the poorer coal is $6.26 and the better coal 
$9.04 per ton, then oil will be the cheaper fuel if it is below $2 per barrel. 

Fuel Oil Burners. — A great variety of burners are on the market, 
most of them based on the principle of using a small jet of steam at the 
boiler pressure to inject the oil into the furnace, in the shape of finely 
divided spray, and at the same time to draw in the air supply and mix it 
intimately with the oil. So far as economy of oil is concerned these 
burners are all of about equal value, but their successful operation depends 
on the construction of the furnace. This should have a large combustion 
chamber, entirely surrounded with fire brick, and the jet should be so 
directed that it will strike a fire-brick surface and rebound before touch- 
ing the heating surface of the boiler. Burners using air at high pressure, 
40 lbs. per sq. in., without steam, have been used with advantage. Lower 
pressures have been found not sufficient to atomize the oil. 

When boilers are forced, with a combustion chamber too small to allow 
the oil spray to be completely burned in it before passing to the boiler 
surface, dense clouds of smoke result, with deposit of lampblack or soot. 

Oil vs. Coal as Fuel. {Iron Age, Nov. 2. 1893.) —Test by the Twin 
City Rapid Transit Company of Minneapolis and St. Paul. This test 
showed that with the ordinary Lima oil weighing 6.6 pounds per 
gallon, and costing 2 1/4 cents per gallon, and coal that gave an evapora- 
tion of 71/2 lbs. of water per pound of coal, the two fuels were equally 
economical when the price of coal was $3.85 per ton of 2000 lbs. With 
the same coal at $2.00 per ton, the coal was 37% more economical, and 
with the coal at $4.85 per ton, the coal was 20% more expensive than 
the oil. These results include the difference in the cost of handling the 
coal, ashes, and oil. 

In 1892 there were reported to the Engineers' Club of Philadelphia 
some comparative figures, from tests undertaken to ascertain the relative 
value of coal, petroleum, and gas. 

Lbs. Water, from 
and at 212° F. 

1 lb. anthracite coal evaporated 9. 70 

1 lb. bituminous coal 10.14 

1 lb. fuel oil, 36° gravity 16 . 48 

1 cubic foot gas, 20 C. P 1, 28 

The gas used was that obtained in the distillation of petroleum, having 
about the same fuel-value as natural or coal-gas of equal candle-power. 

Taking the efficiency of bituminous coal as a basis, the calorific energy 
of petroleum is more than 60% greater than that of coal; whereas, theo- 
retically, petroleum exceeds coal only about 45% — the one containing 
14,500 heat-units, and the other 21,000. 

Crude Petroleum vs. Indiana Block Coal for Steam-raising at 
the South Chicago Steel Works. (E. C. Potter, Trans. A. I. M. E., 
xvii, 807.) — With coal, 14 tubular boilers 16 ft. X 5 ft. required 25 men 
to operate them; with fuel oil, 6 men were required, a saving of 19 men at 
$2 per day, or $38 per day. 



ALCOHOL AS FUEL. 



813 



For one week's work 2731 barrels of oil were used, against 848 tons of 
coal required for the same work, showing 3.22 barrels of oil to be equiva- 
lent to 1 ton of coal. With oil at 60 cents per barrel and coal at $2.15 
per ton, the relative cost of oil to coal is as $1.93 to $2.15. No evapora- 
tion tests were made. 

Petroleum as a Metallurgical Fuel. — C. E. Felton (Trans. A. I. 
M. E., xvii, 809) reports a series of trials with oil as fuel in steel-heating 
and open-hearth steel-furnaces, and in raising steam, with results as 
follows: 1. In a run of six weeks the consumption of oil, partly refined 
(the paraffine and some of the naphtha being removed), in heating 14- 
inch ingots in Siemens furnaces was about 6V2 gallons per ton of blooms. 
2. In melting in a 30-ton open-hearth furnace 48 gallons of oil were used 
per ton of ingots. 3. In a six weeks' trial with Lima oil from 47 to 54 
gallons of oil were required per ton of ingots. 4. In a six months' trial 
with Siemens heating-furnaces the consumption of Lima oil was 6 gallons 
per ton of ingots. Under the most favorable circumstances, charging hot 
ingots and running full capacity, 41/2 to 5 gallons per ton were required. 
5. In raising steam in two 100-H.P. tubular boilers, the feed-water 
being supplied at 160° F., the average evaporation was about 12 pounds 
of water per pound of oil, the best 12 hours' work being 16 pounds. 

In all of the trials the oil was vaporized in the Archer producer, an 
apparatus for mixing the oil and superheated steam, and heating the 
mixture to a high temperature. From 0.5 lb. to 0.75 lb. of pea-coal was 
used per gallon of oil in the producer itself. 

ALCOHOL AS FUEL. 

Denatured alcohol is a grain or ethyl alcohol mixed with a denaturant 
in order to make it unfit for beverage or medicinal purposes. Under acts 
of Congress of June 7, 1906 and March 2, 1907, denatured alcohol became 
exempt from internal revenue taxation, when used in the industries. 

The Government formulas for completely denatured alcohol are: 

1. To every 100 gal. of ethyl or grain alcohol (of not less than 180% 
proof) there shall be added 10 gal. of approved methyl or wood alcohol 
and 1/2 gal. of approved benzine. (180% proof = 90% alcohol, 10% 
water, by volume.) 

2. To every 100 gal. of ethyl alcohol (of not less than 180% proof) 
there shall be added 2 gal. of approved methyl alcohol and 1/2 gal. of 
approved pyridin (a petroleum product) bases. 

Methyl alcohol, benzine and pyridin used as denaturants must con- 
form to specifications of the Internal Revenue Department. 

The alcohol which it is proposed to manufacture under the present 
law is ethyl alcohol, C2H5OH. This material is seldom, if ever, obtained 
pure, it being generally diluted with water and containing other alco- 
hols when used for engines. 

Specific Gravity of Ethyl Alcohol at 60° F. Compared with 
Water at 60°. (Smithsonian Tables.) 





Per cent Al- 




Per cent Al- 




Per cent Al- 




cohol. 




cohol. 




cohol. 


Sp. Gr. 




Sp.Gr. 




Sp. Gr. 


















Weight. 


Vol. 




Weight. 


Vol. 




Weight. 


Vol. 


0.834 


85.8 


90.0 


0.826 


88.9 


92.3 


0.818 


91.9 


94.5 


.832 


86.6 


90.6 


.824 


89.6 


92.9 


.816 


92.6 


95.0 


.830 


87.4 


91.2 


.822 


90.4 


93.4 


.814 


93.3 


95.5 


.828 


88.1 


91.8 


.820 


91.1 


94.0 


.812 


94.0 


96.0 



Tne heat of combustion of ethyl alcohol, 94% by volume, as deter- 
mined by the calorimeter, is 11,900 B.T.U. per lb. — a little more than 
half that of gasoline (Lucke). Favre and Silbermann obtained 12,913 
B.T.U. for absolute alcohol. 

The products of complete combustion of alcohol are H2O and CO2. 
Under certain conditions, with an insufficient supply of air, acetic acid is 



814 



formed, which causes rusting of the parts of an alcohol engine. This 
may be prevented by addition to the alcohol of benzol or acetylene. 

With any good small stationary engine as small a consumption as 0.70 
lb. of gasoline, or 1.16 lb. of alcohol per brake H.P. hour may reasonably 
be expected under favorable conditions (Lucke). 

References. — H. Diederichs, Intl. Marine Eng'g, July, 1906; Machy., 
Aug., 1906. C. E. Lucke and S. M. Woodward, Farmer's Bulletin, No. 
277, U. S. Dept. of Agriculture, 1907. Eng. Rec, Nov. 2, 1907. T. L. 
White, Eng. Mag., Sept., 1908. 

Vapor Pressure of Saturation for Various Liquids, in Mil- 
limeters of Mercury. 



(To convert into pounds per sq. in., 
inches of mercury, 


multiply by 0.01934; to convert into 
multiply by 0.03937.) 


Tem- 
pera- 
ture. 


Pure 
Ethyl 
Alco- 
hol. 


Pure 

Methyl 
Alco- 
hol. 


Water. 


Gaso- 
line. 


Tem- 
pera- 
ture. 


Pure 
Ethyl 
Alco- 
hol. 


Pure 
Methyl 
Alco- 
hol. 


Water. 


Gaso- 
line. 


°C 

5 

10 
15 

20 
25 
30 


F. 
32 
41 
50 
59 
68 
77 
86 


12 

17 
24 
32 
44 
59 
78 


30 
40 
54 
71 
94 
123 
159 


5 

7 
9 
13 
17 

24 
32 


99 
115 
133 
154 
179 
210 
251 


°C. 
35 

40 
45 
50 
55 
60 
65 


° F. 
95 
104 
113 
122 
131 
140 
149 


103 
134 
172 
220 
279 
350 
437 


204 
259 
327 
409 
508 
624 
761 


42 
55 
.71 
92 
117 
149 
187 


301 
360 
422 
493 
561 
648 
739 



Vapor Tension of Alcohol and Water 


, and Degree of Saturation 






of Air with these Vapors. 










1 Pound of Air Contains in Saturated 














Vapor Tension, Inches 
Mercury. 






Temp, 
degs. F. 










At 28.95 Inches. 


At 26.05 Inches. 




Alcohol 


Water 


Alcohol 


Water 


Alcohol 


Water. 




Vapor. 


Vapor. 


Vapor. 


Vapor. 


Vapor. 


Vapor. 


50 


0.950 


0.359 


0.055 


0.008 


0.061 


0.009 


59 


1.283 


0.500 


0.075 


0.011 


0.084 


0.013 


68 


1.733 


0.687 


0.104 


0.016 


0.117 


0.018 


77 


2.325 


0.925 


0.144 


0.022 


0.162 


0.025 


86 


3.090 


1.240 


0.200 


0.031 


0.227 


0.036 


104 


5.270 


2.162 


0.390 


0.063 


0.450 


0.072 


122 


8.660 


3.620 


0.827 


0.135 


1.002 


0.164 



FUEL GAS. 

The following notes are extracted from a paper by W. J. Taylor on 
"The Energy of Fuel" (Trans. A. I. M. E., xviii. 205): 

Carbon Gas. — In the old Siemens producer, practically all the heat 
of primary combustion — that is, the burning of solid carbon to carbon 
monoxide, or about 30% of the total carbon energy — was lost, as little 
or no steam was used in the producer, and nearly all the sensible heat of 
the gas was dissipated in its passage from the producer to the furnace, 
which was usually placed at a considerable distance. 

Modern practice has improved on this plan, by introducing steam 
with the air blown into the producer, and by utilizing the sensible heat of 
the gas in the combustion-furnace. It ought to be possible to oxidize 



FUEL GAS. 815 

one out of every four lbs. of carbon with oxygen derived from water- 
vapor. The thermic reactions in this operation are as follows: 

Heat-units. 
4 lbs. C burned to CO (3 lbs. gasified with air and 1 lb. with 

water) develop 17,600 

1.5 lbs. of water (which furnish 1.33 lbs. of oxygen to combine 

with 1 lb. of carbon) absorb by dissociation 10,333 

The gas, consisting of 9.333 lbs. CO, 0.167 lb. H, and 13.39 lbs. N, 

heated 600°, absorbs 3,748 

Leaving for radiation and loss 3,519 

17,600 
The steam which is blown into a producer with the air is almost all con- 
densed into finely-divided water before entering the fuel, and conse- 
quently is considered as water in these calculations. 

The 1.5 lbs. of water liberates 0.167 lb. of hydrogen, which is delivered 
to the gas, and yields in combustion the same heat that it absorbs in the 
producer by dissociation. According to this calculation, therefore, 60% 
of the heat of primary combustion is theoretically recovered by the dis- 
sociation of steam, and, even if all the sensible heat of the gas be counted, 
with radiation and other minor items, as loss, yet the gas must carry 
4 X 14,500 - (3748 + 3519) = 50,733 heat-units, or 87% of the calo- 
rific energy of the carbon. This estimate shows a loss in conversion of 
13%, without crediting the gas with its sensible heat, or charging it with 
the heat required for generating the necessary steam, or taking into 
account the loss due to oxidizing some of the carbon to CO2. In good 
producer-practice the proportion of CO2 in the gas represents from 4% 
to 7% of the C burned to CO2, but the extra heat of this combustion should 
be largely recovered in the dissociation of more water-vapor, and there- 
fore does not represent as much loss as it would indicate. As a con- 
veyer of energy, this gas has the advantage of carrying 4.46 lbs. less 
nitrogen than would be present if the fourth pound of coal had been 
gasified with air; and in practical working the use of steam reduces the 
amount of clinkering in the producer. 

Anthracite Gas. — In anthracite coal there is a volatile combustible 
varying in quantity from 1.5% to over 7%. The amount of energy 
derived from the coal is shown in the following theoretical gasification 
made with coal of assumed composition: Carbon, 85% ; vol. HC, 5%; ash, 
10%: 80 lbs. carbon assumed to be burned to CO; 5 lbs. carbon burned 
to CO2; three fourths of the necessary oxygen derived from air, and one 
fourth from water. 



-Products. - 



Process. Pounds. Cubic Feet. Anal, by Vol. 

80 lbs. C burned to CO 186.66 2529.24 33.4 

5 lbs. C burned to CO2 18.33 157.64 2.0 

5 lbs. vol. HC (distilled) 5.00 116.60 1.6 

120 lbs. oxygen are required, of 
which 30 lbs. from H 2 liber- 
ate H :.... 3.75 712.50 9.4 

90 lbs. from air are associated 

with N ..301.05 4064.17 53.6 



514.79 7580.15 

Energy in the above gas obtained from 100 lbs. anthracite: 

186.66 lbs. CO 807,304 heat-units. 

5.00 " CH 4 117,500 

3.75 " H 232,500 



1,157,304 

Total energy in gas per lb 2,248 " 

Total energy in 100 lbs. of coal. .. . 1,349,500 

Efficiency of the conversion 86%. 

The sum of CO and H exceeds the results obtained in practice. The 
sensible heat of the gas will probably account for this discrepancy and, 
therefore, it is safe to assume the possibility of delivering at least 82% 
of the energy of the anthracite. 



816 



Bituminous Gas. — A theoretical gasification of 100 lbs of coal, con- 
taining 55% of carbon and 32% of volatile combustible (which is above 
the average of Pittsburgh coal), is made in the following table. It is 
assume! that 50 lbs. of C are burned to CO and 5 lbs. to CO2; one fourth 
of the O is derived from steam and three fourths from air; the heat value 
of the volatile combustible is taken at 20,000 heat-units to the pound. 
In computing volumetric proportions all the volatile hydrocarbons, 
fixed as well as condensing, are classed as marsh-gas, since it is only by 
some such tentative assumption that even an approximate idea of the 
volumetric composition can be formed. The energy, however, is calcu- 
lated from weight: 

/ Products. \ 

Process. Pounds. Cubic Feet. Anal, by Vol. 

50 lbs. C burned to CO 116.66 1580.7 27.8 

5 lbs. C burned to CO2 18.33 157.6 2.7 

32 lbs. vol. HC (distilled) 32.00 746.2 13.2 

80 lbs. O are required, of which 20 
lbs., derived from H2O, liber- 
ate H 2.5 475.0 8.3 

60 lbs. O, derived from air, are as- 
sociated with N 200.70 2709.4 47.8 



370.19 5668.9 99.8 

Energy in 116.66 lbs. CO 504,554 heat-units. 

" 32.00 lbs. vol. HC 640,000 

2.50 lbs.. H 155,000 

1,299,554 

Energy in coal 1,437,500 

Per cent of energy delivered in gas 90.0 

Heat-units in 1 lb. of gas 3,484 

Water-gas. — Water-gas is made in an intermittent process, by blow- 
ing up the fuel-bed of the producer to a high state of incandescence (and 
in some cases utilizing the resulting gas, which is a lean producer-gas), 
then shutting off the air and forcing steam through the fuel, which dis- 
sociates the water into its elements of oxygen and hydrogen, the former 
combining with the carbon of the coal, and the latter being liberated. 

This gas can never play a very important part in the industrial field, 
owing to the large loss of energy entailed in its production, yet there are 
places and special purposes where it is desirable, even at a great excess 
in cost per unit of heat over producer-gas; for instance, in small high- 
temperature furnaces, where much regeneration is impracticable, or 
where the "blow-up" gas can be used for other purposes instead of being 
wasted. 

The reactions and energy required in the production of 1000 feet of 
water-gas, composed, theoretically, of equal volumes of CO and H, are as 
follows: 

500 cubic feet of H weigh 2. 635 lbs. 

500 cubic feet of CO weigh 36 . 89 " 

Total weight of 1000 cubic feet 39 . 525 lbs. 

Now, as CO is composed of 12 parts C to 16 of O, the weight of C in 
36.89 lbs. is 15.81 lbs. and of O 21.08 lbs. When this oxygen is derived 
from water it liberates, as above, 2.635 lbs. of hydrogen. The heat de- 
veloped and absorbed in these reactions (roughly, as we will not take 
into account the energy required to elevate the coal from the tempera- 
ture of the atmosphere to, say, 1800°) is as follows: 

Heat-units. 
2.635 lbs. H. absorb in dissociation from water 2.635 X 62,000 = 163,370 
15.81 lbs. C burned to CO develops 15.81 X 4400 = 69,564 

Excess of heat-absorption over heat-development = 93,806 

If this excess could be made up from C burnt to CO 2 without loss by 
radiation, we would only have to burn an additional 4.83 lbs. C to supply 
this heat, and we could then make 1000 feet of water-gas from 20.64 lbs. 



817 



of carbon (equal 24 lbs. of 85% coal). This would be the perfection of 
gas-making, as the gas would contain really the same energy as the coal; 
but instead, we require in practice more than double this amount of coal 
and do not deliver more than 50% of the energy of the fuel in the gas, 
because the supporting heat is obtained in an indirect way and with 
imperfect combustion. Besides this, it is not often that the sum of CO 
and H exceed 90%, the balance being CO2 and N. But water-gas should 
be made with much less loss of energy by burning the "blow-up" (pro- 
ducer) gas in brick regenerators, the stored-up heat of which can be 
returned to the producer by the air used in blowing-up. 

The following table shows what may be considered average volumetric 
analyses, and the weight and energy of 1000 cubic feet, of the four types 
of gases used for heating and illuminating purposes: 





Natural 
Gas. 


Coal- 
gas. 


Water- 
gas. 


Producer-gas. 


CO 


0.50 
2.18 
92.6 
0.31 
0.26 
3.61 
0.34 


6.0 

46.0 

40.0 

4.0 

0.5 

1.5 

0.5 

1.5 

32.0 

735,000 


45.0 
45.0 
2.0 


Anthra. 

27.0 

12.0 

1.2 


Bitu. 
27.0 


H 


12.0 


CH t . 


2.5 




0.4 


CO2 

N 

O 


4.0 
2.0 
0.5 
1.5 
45.6 
322,000 


2.5 
57.0 
0.3 


2.5 
56.2 
0.3 






Pounds in 1000 cubic feet 

Heat-units in 1000 cubic feet. . . . 


45.6 
1,100,000 


65.6 
137,455 


65.9 
156,917 



Natural Gas in Ohio and Indiana. 

(Eng. and M. J., April 21, 1894.) 





Fos- 

toria, 

O. 


Find- 
lay, 
O. 


St. 

Mary's, 

O. 


Muncie, 
Ind. 


Ander- 
son, 
Ind. 


Koko- 
mo, 
Ind. 


Mar- 
ion, 
Ind. 




1.89 
92.84 
.20 
.55 
.20 
.35 
3.82 
.15 


1.64 
93.35 
.35 
.41 
.25 
.39 
3.41 
.20 


1.94 
93.85 
.20 
.44 
.23 
.35 
2.98 
.21 


2.35 
92.67 
.25 
.45 
.25 
.35 
3.53 
.15 


1.86 
93.07 
.47 
.73 
.26 
.42 
3.02 
.15 


1.42 
94.16 
.30 
.55 
.29 
.30 
2.80 
.18 


1.20 




93.57 


Olefiant gas 

Carbon monoxide . 
Carbon dioxide .... 


.15 
.60 
.30 
.55 




3.42 


Hydrogen sulphide 


.20 



Natural Gas as a Fuel for Boilers. — J. M. Whitham {Trans. A. S. 
M. E., 1905) reports the results of several tests of water-tube boilers with 
natural gas. The following is a condensed statement of the results : 





Cook Vertical. 


Heine. 


Cahall Vert. 




Rated H.P. of boilers 


1500 


1500 


200 200 200 


300 


300 


H.P. developed 


1642 


1507 


155 218 258 


340 


260 


Temperature at chimney 


521 


494 


386 450 465 


406 


374 


Gas pressure at burners, oz. 


6.9 


6.4 




4.8 


7to30 


Cu. ft. of gas per boiler. . 












H.P.-hour 


44.9* 


41.0* 


46. Of 40. 7f 38. 3f 


42.3 


34 


Boiler efficiency, % 


72.7 




65.8 ... 74.9 







* Reduced to 4 oz. pressure and 62° F. 
t Reduced to atmos. press, and 32° F. 



818 



FUEL. 



Six tests by Daniel Ash worth on 2-flue horizontal boilers gave cu. ft. of 
gas per boiler H.B. hour, 58.0; 59.7; 67.0; 63.0; 74.0; 47.0. 

On the first Cook boiler test, the chimney gas, analyzed by the Orsat 
apparatus, showed 7.8 C0 2 ; 8.05 O; 0.0 CO; 84.15 N. This shows an 
excessive air supply. 

White versus Blue Flame. — Tests were made with the air supply throt- 
tled at the burners, so as to produce a white flame, and also unthrottled, 
producing a blue flame with the following results: 



Pressure of gas at burners, oz 

Kind of flame 

Boiler H. P. made per 250-H.P. boiler 
Cu. ft. of gas (at 4 oz. and 60° F.) per 

H.P. hour 

Chimney temperature 



White 
247 



Blue 
213 



White 
297 



41.6 
478 



Blue 
271 



37.9 
511 



White 
255 



40 
502 



Blue 
227 



43.1 
508 



Average of 6 tests,— White, 266 H.P., 43.6 cu. ft.; Blue, 237 H.P., 
43.8 cu. ft., showing that the economy is the same with each flame, but 
the capacity is greatest with the white flame. Mr. Whitham's principal 
conclusions from these tests are as follows: 

(1) There is but little advantage possessed by one burner over another. 

(2) As good economy is made with a blue as with a white or straw flame, 
and no better. 

(3) Greater capacity may be made with a straw-white than with a blue 
flame. 

(4) An efficiency as high as from 72 to 75 per cent in the use of gas is 
seldom obtained under the most expert conditions. 

(5) Fuel costs are the same under the best conditions with natural gas 
at 10 cents per 1000 cu. ft. and semi-bituminous coal at $2.87 per ton of 
2240 lbs. 

(6) Considering the saving of labor with natural gas, as compared with 
hand-firing of coal, in a plant of 1500 H.P., and coal at $2 per ton of 2240 
lbs., gas should sell for about 10 cents per 1000 cu. ft 

Analyses of Natural Gas. 

Illuminants 0.45 0.15 0.50 1.6 

Carbonic oxide 0.00 0.00 0.15 1.8 

Hydrogen 0.20 0.30 0.25 0.3 

Marsh gas 81.05 83.20 83.40 81.9 

Ethane 17.60 15.55 15.40 13.2 

Carbonic acid . 00 . 20 . 00 0.0 

Oxygen 0.15 0.10 0.00 0.4 

Nitrogen 0.55 0.50 0.30 0.8 

B.T.U. per cu. ft. at 60° F. and 

14.7 lbs. barometer 1030 1020 1026 1098 

The first three analyses are of the gas from nine wells in Lewis Co., 
W. Va.; the last is from a mixture from fields in three states supplying 
Pittsburg, Pa., used in the tests of the Cook boiler. 

Producer-gas from One Ton of Coal. 

(W. H. Blauvelt, Trans. A. I. M. E., xviii, 614.) 



Analysis by Vol . 


Per 
Cent. 


Cubic Feet. 


Lbs. 


Equal to — 


CO * 

H 

CIL 

C2H4 

CO2. 

N (by difference) 


25.3 
9.2 
3.1 
0.8 

3.4 
58.2 


33,213.84 
12,077.76 
4,069.68 
1,050.24 
4,463.52 
76,404.96 


2451.20 
63.56 
174.66 
77.78 
519.02 
5659.63 


1050.51 lbs.C + 1400.7 lbs. O. 
63.56 " H. 
174.66 " CH 4 . 
77.78 " C2H4. 
141.54 " C + 377. 44 lbs. O. 
7350.17 " Air. 




100~0 


131,280.00 


8945.85 





FUEL GAS. 819 

Calculated upon this basis, the 131,280 ft. of gas from the ton of coal 
contained 20,311,162 B.T.U., or 155 B.T.U. per cubic ft., or 2270 B. T.U. 
per lb. 

The composition of the coal from which this gas was made was as 
follows: Water, 1.26%; volatile matter, 36.22%; fixed carbon, 57.98%; 
sulphur, 0.70%; ash, 3.78%. One ton contains 1159.6 lbs. carbon and 
724.4 lbs. volatile combustible, the energy of which is 31,302,200 B.T.U. 
Hence, in the processes of gasification and purification there was a loss of 
35.2% of the energy of the coal. 

The composition of the hydrocarbons in a soft coal is uncertain and 
quite complex; but the ultimate analysis of the average coal shows that 
it approaches quite nearly to the composition of CH 4 (marsh-gas). 

Mr. Blauvelt emphasizes the following points as highly important in 
soft-coal producer-practice: 

First. That a large percentage of the energy of the coal is lost when the 
gas is made in the ordinary low producer and cooled to the temperature of 
the air before being used. To prevent these sources of loss, the producer 
should be placed so as to lose as little as possible of the sensible heat of 
the gas, and prevent condensation of the hydrocarbon vapors. A high 
fuel-bed should be carried, keeping the producer cool on top, thereby 
preventing the breaking-down of the hydrocarbons and the deposit of 
soot, as well as keeping the carbonic acid low. 

Second. That a producer should be blown with as much steam mixed 
with the air as will maintain incandescence. This reduces the percentage 
of nitrogen and increases the hydrogen, thereby greatly enriching the gas. 
The temperature of the producer is kept down, diminishing the loss of heat 
by radiation through the walls, and in a large measure preventing clinkers. 

The Combustion of Producer-gas. (H. H.Campbell, Trans. A. I. 
M. E., xix, 128.) — The combustion of the components of ordinary pro- 
ducer-gas may be represented by the following formulae: 

C2H4 +60 = 2C0 2 + 2H 2 0; 2H+0 = H 2 0; 
CH 4 +4.0= CO2+2H2O; CO + O = CO2. 

Average Composition by Volume of Producer-gas: A, made with 
Open Grates, no Steam in Blast; B, Open Grates, Steam-jet in 
Blast. 10 Samples of Each. 

; CO2. O. C2H4. CO. H. CH 4 . N. 

A min 3.6 0.4 0.2 20.0 5.3 3.0 58.7 

A max 5.6 0.4 0.4 24.8 8.5 5.2 64.4 

A average 4.84 0.4 0.34 22.1 6.8 3.74 61.78 

B min 4.6 0.4 0.2 20.8 6.9 2.2 57.2 

B max 6.0 0.8 0.4 24.0 9.8 3.4 62.0 

B average 5.3 0.54 0.36 22.74 8.37 2.56 60.13 

The coal used contained carbon 82%, hydrogen 4.7%. 
The following are analyses of products of combustion: 

CO2. O. CO. CH 4 . H. N. 

Minimum 15.2 0.2 trace. trace. trace. 80.1 

Maximum 17.2 1.6 2.0 0.6 2.0 83.6 

Average 16.3 0.8 0.4 0.1 0.2 82.2 

Proportions of Gas Producers and Scrubbers. (F. C. Tryon, Power, 
Dec. 1, 1908.) — Small inside diameter means excessive draft through the 
fire. If a fire is forced, as will be necessary with too small an inside diam- 
eter, the results will be clinkers and blow-holes or chimneys through the 
fire bed, with excess CO2 and weak gas; clinkers fused to the lining, and 
burning out of grates. If sufficient steam is used to keep down the ex- 
cessive heat, the result is likely to be too much hydrogen in the gas, with 
the attendant engine troubles. 

The lining should never be less than 9 in. thick even in the smaller sizes, 
and a 100-H.P., or larger, producer should have at least 12 in. of generator 
lining. The lining next to the fire bed should be of the best quality of 
refractory material. A good lining consists of a course of soft common 
bricks put in edgewise next to the steel shell of the generator, laid in 
Portland cement; then a good firebrick 6 in. thick laid inside to fit the 
circle, the bricks being dipped as laid in a fine grouting of ground firebrick. 

If we take 11/4 lbs. of coal per H.P.-hour as a fair average and 10 lbs. of 



820 



coal per hour per square foot of internal fuel-bed cross-section, with 9 in. 
of refractory lining up to 100 H.P. and at least 12 in. of lining on larger 
sizes, the generator will give good gas without forcing and without excess- 
ive heat in the zone of complete combustion. A 200-H.P. producer on 
this basis consumes 250 lbs. of coal at full load, and at 10 lbs. per sq. ft. 
internal area 25 sq. ft. will be necessary. With a 12-in. lining the outside 
diameter will be 92 in. 

Practice has shown that the depth of the fuel bed should never be less 
than the inside diameter up to 6 ft.; above this size the depth can be 
adjusted as experience indicates the best working results. Assuming for 
a 200-H.P. producer 18 in. for the ashpit below the grate, 12 in. for the 
thickness of the grate and the ashes to protect it, 68 in. depth of fuel bed, 
24 in. above the fuel to the gas outlet, the height will be 10 ft. 4 in. to the 
top of the generator; above this the coal-feeding hopper, say 32 in. high, 
is mounted; this makes the height over all 13 ft. 

The wet scrubber of a gas producer should be of ample size to cool the 
gas to atmospheric temperature and wash out most of the impurities. 
A good rule is to make its diameter three-fourths that of the inside diam- 
eter of the generator and the height one and one-half times the height of 
the generator shell. For a 100-H.P. producer, 4 ft. inside diam., the wet 
scrubber should be 3 ft. inside diam., and if the generator shell is 8 ft. 
6 in. high, the scrubber should be 12 ft. 9 in. high. When filled with the 
proper amount of baffling and scrubbing material (coke is commonly 
used), the scrubber will have space for about 30 cu. ft. of gas. A 100-H.P. 
gas engine using 12,000 B.T.TJ. per H.P.-hour will use 160 cu. ft. of 125- 
B.T.TJ. gas per minute. The wet scrubber will therefore be emptied 5 1/3 
times every minute, and would require about 8 1/3 gallons of water per 
minute; if the diameter of the scrubber were reduced one-third the vol- 
ume of water necessary to cool and scrub the gas would have to be doubled. 
Gas must be cooled below 90° F. to enable it to give up the impurities it 
carries in suspension, and even lower than this to condense its moisture. 

A separate dry scrubber with two compartments should always be pro- 
vided and the piping between the two scrubbers so arranged that the gas 
can be turned into either part of the dry scrubber at will. The dry 
scrubber should be equal in area to the inside of the generator, and the 
depth of each part should be sufficient to accommodate at least 2 cu. ft. 
of scrubbing material and give 1 cu. ft. of space next to the outlet. Oil- 
soaked excelsior is a good scrubbing material and should be packed as 
closely as possible. 

Taking as the standard the dimensions above stated for the different 
parts of a producer-gas plant, a list of dimensions for different horse-power 
capacities would be about as in the following table. 





Dimensions 


of Gas 


Producers and Scrubbers. 






Producers. 


Wet Scrub- 
bers. 


Dry Scrubbers. 


H.P. 




















Inside 
Diam. 


Out- 
side 
Diam. 


Height. 


Diam. 


Height. 




Diam. 


Height. 




in. 


in. 


ft. in. 


in. 


ft. in. 




in. 


ft. in. 


25 


24 


42 


6 6 


18 


9 9 


Single... 


24 


3 


35 


28 


46 


6 10 


21 


10 3 


...do.... 


28 


3 


50 


34 


52 


7 4 


26 


11 


Double. 


34 


6 


60 


37 


55 


7 7 


28 


11 5 


...do.... 


37 


6 


75 


42 


60 


8 


32 


12 


...do.... 


42 


6 


100 


48 


72 


8 6 


36 


12 9 


...do.... 


48 


7 


125 


54 


78 


9 6 


41 


14 3 


...do.... 


52 


7 


150 


58 


82 


9 10 


44 


14 9 


...do.... 


58 


7 6 


175 


63 


87 


10 3 


48 


15 5 


...do.... 


63 


7 6 


200 


68 


92 


10 8 


51 


16 


...do.... 


68 


7 6 



The inside diameter of the producers corresponds to the formula 
H.P. = 6.25d 2 . 



GAS PRODUCERS, 821 

Gas Producer Practice. — The following notes on gas producers are 
condensed from the catalogue of the Morgan Construction Co. 

The Morgan Continuous Gas Producer is made in the following sizes: 

Diana, inside of lining, ft 6 8 10 12 

Area of gas-making surface, sq. ft 28 50 78.5 113 

24-hour capacity with good coal, tons 4 7 10 15 

Diam. of outlet, in 20 27 33 40 

The best coal to buy for a producer in any locality is that which by 
analysis or calorimeter test shows the most heat units for a dollar. It 
rarely pays to buy gas coal unless it can be had at a moderate cost over the 
ordinary steam bituminous grade. For very high temperature melting 
operations a fairly high percentage of volatile matter is necessary to give a 
luminous flame and intensify the radiation from the roof of the furnace. 
Freely burning gas coals are the most easily gasified, and the capacity of 
the producer to handle these coals is twice as great as when a slaty, dirty 
coal, high in ash and sulphur, is used. It is usually best to use "run-of- 
mine" coal, crushed at the mine to pass a 4-in. ring. It never pays to use 
slack coal, for it cuts down the capacity by choking the blast, which has 
to be run at high pressure to get through the fire, overheating the gas and 
lowering the efficiency of the producer. 

There is always a certain amount of CO2 formed, even in the best practice; 
in fact, it is inevitable, and if kept within proper limits does not constitute 
a net loss of efficiency, especially with very short gas flues, because the 
energy of the fuel so burned is represented in the sensible heat or tem- 
perature of the gas, and results in delivering a hot gas to the furnace. 
The best result is at about 4% CO2, a gas temperature between 1100° and 
1200° F., and flues less than 100 ft. long. 

The amount of steam required to blow a gas producer is from 33% to 
40% of the weight of the fuel gasified. If 30 lbs. of steam is called a 
standard horse-power, we have therefore to provide about 1 H.P. of steam 
for every 80 lbs. of coal gasified per hour or for every ton of coal gasified in 
24 hours. 

In the original Siemens air-blown producer about 70% of the whole gas 
was inert and 30% combustible. Then with the advent of steam-blown 
producers the dilution was reduced to about 60%, with 40% combustible. 
Now, under the system of automatic, feed, uniform conditions, perfect 
distribution and adjustment of the steam blast here presented, we are able 
to reduce the nitrogen to 50% and sometimes less. 

In the best practice the volume of gas from the producer is now reduced 
to about 60 cu. ft. per pound of coal, of which 30 cu. ft. are nitrogen. 
These volumes are measured at 60° F. 

The temperature of the gas leaving the producer under best modern 
conditions is about 1200° F. It can be run cooler than this, but not much, 
except at a sacrifice of both quantity and quality. At this temperature, 
the sensible heat carried by the gas is 1200 X 0.35 (average specific heat) = 
420 B.T.U. per pound. As one pound of good gas is about 16 cu. ft. and 
carries about 16 X 180 = 2880 heat units at normal temperature, we see 
that the sensible heat carried away represents about one-seventh, or over 
14% of the combustive energy, which is much too large a percentage to lose 
whenever it can be utilized by using the gas at the temperature at which 
it is made. 

Capacity of Producers. — The capacity of a gas producer is a varying 
quantity, dependent upon the construction of the producer and upon the 
quality of the coal supplied to it. The point is, not to push the producer so 
hard as to burn up the gas within it; also to avoid blowing dust through 
into the flues. These two limitations in a well-constructed automatically 
fed gas producer occur at about the same rate of gasification, namely, 
at about 10 lbs. per sq. ft. of surface per hour with bituminous coal carry- 
ng 10% of ash and 1 1/2 % of sulphur. With gas coal, having high volatile 
percentage and low ash, this rate can be safely increased to 12 lbs. and in 
some cases to 15 lbs. per sq. ft. At 10 lbs. per sq. ft., the capacity of a 
gas producer 8 ft. internal diameter is 500 lbs. per hour, which with gas 
coals may be increased to a maximum of about 700 lbs. It frequently 
happens that the cheapest coal available is of such quality that neither 
of these figures can be reached, and the gasification per sq. ft. has to be cut 
down to 6 or 7 lbs. per hour to get the best results. 



822 FUEL 

Flues. — It is necessary to provide large flue capacity and to carry the 
full area right up to the furnace ports, which latter may be slightly reduced 
to give the gas a forward impetus. Generally speaking, the net area of a 
flue should not be less than Vi6 of the area of the gas-making surface in the 
producers supplying it. Or it may be stated thus: — The carrying capa- 
city of a hot gas flue is equivalent to 200 lbs. of coal per hour per sq. ft. of 
section. 

Loss of Energy in a Gas Producer. — The total loss from all sources in the 
gasification of fuel in a gas producer under fairly good conditions, when 
the gas is used cold or when its sensible heat is not utilized, ranges between 
20% and 25%, which under very bad conditions may be increased to 50%. 
The loss under favorable conditions, using the gas hot, is reduced to as 
low as 10%, which also includes the heat of the steam used in bloving. 

Test of a Morgan Producer. — The following is the record of a test made 
in Chicago by Robert W. Hunt & Co. The coal used was Illinois " New 
Kentucky" run-of-mine of the following analysis: — 

Fixed carbon, 50.87; volatile matter, 37.32; moisture, 5.08; ash (1.12 
sulphur) , 6.73. The average of all the gas analyses bv volumeis as follows : 

CO, 24.5; H, 17.8; CH 4 and C 2 H 4 , 6.8; total combustibles, 49.1%; C0 2 , 
3.7; O, 0.4; N, 46.8; total non-combustibles, 50.9%. 

Average depth of fuel bed, 3 ft. 4 in. Average pressure of steam on 
blower, 4.7 lbs. per sq. in. Analysis of ash: combustible, 4.66%; non- 
combustible, 95.34%. Percentage of fuel lost in the ash, 4.66 X 6.73 -*- 
100 = 0.3%. 

High Temperature Required for Production of CO. — In an ordinary 
coal fire, with an excess of air CO2 is produced, with a high temperature. 
When the thickness of the coal bed is increased so as to choke the air sup- 
ply CO is produced, with a decreased temperature. It appears, however, 
that if the temperature is greatly lowered, CO2 instead of CO will be pro- 
duced notwithstanding the diminished air supply. Herr Ernst (Eng'g, 
April 4, 1893) holds that the oxidation of C begins at 752° F., and that CO2 
is then formed as the main product, with only a small amount of CO, 
whether the air be admitted in large or in small quantities. When the 
rate of combustion is increased and the temperature rises to 1292° F. the 
chief product is CO2 even when the exhaust gases contain 20% by volume 
of CO2, which is practically the maximum limit, proving that all the 
oxygen has been consumed. Above 1292° F. the proportion of CO rapidly 
increases until 1823° F. is reached, when CO is exclusively produced. 

Experiments reported by J. K. Clement and H. A. Grine in Bulletin No. 
393 of the U. S. Geological Survey, 1909, show that with the rate of flow 
of gas and the depth of fuel bed which obtain in a gas producer a temper- 
ature of 1100° C. (2012° F.) or more is required for the formation of 90% 
CO gas from C0 2 and charcoal, and 1300° (2372° F.) for the same percen- 
tage from C0 2 and coke, and from C0 2 and anthracite coal. With a tem- 
perature 100° C. (180° F.) lower than these the resultant gas will contain 
about 50% CO. It follows that the temperature of the fuel bed of the gas 
producer must be at least 1300° C. in order to yield the highest possible 
percentage of CO. 

The Mond Gas Producer is described by H. A. Humphrey in Proc. Inst. 
C. E., vol. cxxix, 1897. The producer, which is combined with a by-prod- 
uct recovery plant, uses cheap bituminous fuel and recovers from it 90 
lbs. of sulphate of ammonia per ton, and yields a gas suitable for gas 
engines and all classes of furnace work. The producer is worked at a much 
lower temperature than usual, due to the large quantity of superheated 
steam introduced with the air, amounting to more than "twice the weight 
of the fuel. The gas containing the ammonia is passed through an absorb- 
ing apparatus, and treated so that 70% of the original nitrogen of the fuel 
is recovered. The result of a test showed that for every ton of fuel about 
2.5 tons of steam and 3 tons of air are blown through the grate, the mixture 
being at a temperature of about 480° F. The greater part of this steam 
passes through the producer undecomposed, its heat being used in a 
regenerator to furnish fresh steam for the producer. More than 0.5 ton 
of steam is decomposed in passing through the hot fuel, and nearly 4.5 tons 
of gas are produced from a ton of coal, equal to about 160,000 cu. ft. at 
ordinary atmospheric temperature. The gas has a calorific power of 81% 
of that of the original fuel. Mr. Humphrey gives the following table 
showing the relative value of different gases. 



FUEL GAS. 



823 



Volume per cent. 



fc4, 




8 c 


AS 




.1 


Hi 

«« O 


il 


sa . 

S «> S 
I °3 S 




A . 

O o3 

II 


a 

o a 


s 


co 


Q 


^ 


m 


O 


24.8 


8.6 


18.73 


20.0 


56.9 


48.0 


2.3 


2.4 


0.31 




22.6 


39.5 


nil 


nil 


0.31 


4.0(?) 


3.0 


3.8 


13.2 


24.4 


25.07 


21.0 


8.7 


7.5 


46.8 


59.4 


48.98 


49.5 


5.8 


0.5 


12.9 


5.2 


6.57 


5.0 


3.0 


nil 


100.0 


100.0 


100.0 


100.0 


100.0 


100.0 


40.3 


35.4 


44.42 


45.0 


91.2 


98.8 


112.4 


101.4 


113.2 


154.0 


410.0 


581.0 


85.9 


74.7 


88.9 


115.3 


284.0 


381.0 


154.6 


134.5 


160.0 


207.5 


511.2 


658.8 


1,374 


1,195 


1,432 


1,845 


4,544 


6,096 



Hydrogen (H) 

Marsh gas (CH 4 ) 

C n H 2n gases 

Carbonic oxide (CO) 

Nitrogen (N) 

Carbonic acid (CO2) 

Total volume 

Total combustible gases 

Theoretical. 
Air required for combustion . 
Calorific value per cu. ft., 

in lb. °C. units 

Do.,B.T.U. percu. ft 

Do., per litre, gram ° C. units 



22.0 
67.0 
6.0 
0.6 
3.0 
0.6 
100.0 
95.6 



806.0 

495.8 

892.4 
7,932 



Note. — Where the volume per cent does not add up to 100 the slight 
difference is due to the presence of oxygen. 

The following is the analysis of gas made in a Mond producer at the 
works of the Solvay Process" Co. in Detroit, Mich. (Mineral Industry, vol. 
viii, 1900): CO2, 14.1; O, 0.3; N, 42.9; H, 25.9; CH 4 , 4.1; CO, 12.7. Com- 
bustible, 42.7%. Calories per litre, 1540, = 173 B.T.U. per cu. ft. 

Relative Efficiencies of Different Coals in Gas Producer and 
Engine Tests. — The following is a condensed statement of the principal 
results obtained in the gas-producer tests of the U. S. Geological Survey 
at St. Louis in 1904. (R. H. Fernald, Trans. A. S. M. E., 1905.) 



Sample. 


B.t.u. 
per 
lb. 
com- 
bus- 
tible. 


Pounds per elec- 
trical H.P. hour 
at switchboard. 


Sample. 


B.t.u. 

per 

lb. 
com- 
bus- 
tible. 


Pounds per elec- 
trical H.P. hour 
at switchboard. 


Coal 

as 
fired. 


Dry 
coal. 


Com- 
bus- 
tible. 


Coal 

as 
fired. 


Dry 
coal. 


Com- 
bus- 
tible. 


Ala. No. 2.... 
Colo. No. 3... 

111. No. 3 

111. No. 4 

Ind.No. 1.... 
Ind.No. 2.... 
Okla.No. 1... 
Okla.No. 4... 
Iowa No. 2. . . 
Kan. No. 5. . . 


14820 
13210 
14560 
14344 
14720 
14500 
14800 
13890 
13950 
15200 


1.71 
2.14 
1.93 
2.01 
2.17 
1.68 
1.92 
1.57 
2.07 
1.69 


1.64 
1.71 
1.79 
1.76 
1.93 
1.55 
1.83 
1.43 
1.73 
1.62 


1.53 
1.58 
1.60 
1.57 
1.71 
1.39 
1.66 
1.17 
1.30 
1.43 


Ky.No. 3.. 

Mo. No. 2.. 
Mont. No. 1 
N.Dak.No.2 
Texas No. 1 
Texas No. 2 
W.Va.No.l 
W.Va.No.4 
W.Va.No.7 
Wyo. No. 2 


14650 
14280 
13580 
12600 
12945 
12450 
15350 
15600 
15800 
13820 


2.05 
1.94 
2.54 
3.80 
3.34 
2.58 
1.60 
1.32 
1.53 
2.28 


1.91 
1.71 
2.25 
2.29 
2.22 
1.71 
1.57 
1.29 
1.50 
2.07 


1.72 
1.43 
1.98 
2.05 
1.88 
1.52 
1.48 
1.17 
1.40 
1.60 



The gas was made in a Taylor pressure producer rated at 250 H.P. Its 
inside diam. was 7 ft., area of fuel bed 38.5 sq. ft., height of casing 15 ft.; 
rotative ash table; centrifugal tar extractor. The engine was a 3-cylinder 



824 FUEL. 

vertical Westinghouse, 19 in. diam., 22 in. stroke, 200 r.p.m., rated at 
235 B.H.P. Comparing the results of the W. Va. No. 7 coal, the best 
on the list, with the North Dakota coal, the one which gave the poorest 
results, the heat values per lb. combustible of the coals are as 1 to 0.808; 
reciprocal, 1 to 1.24; the lbs. combustible per E. H. P. hour as 1 to 1.75, 
and lbs. coal as fired per E. H. P. hour as 1 to 2.88. The relative thermal 
efficiencies of the engine with the two coals are as 2.05 to 1.17, or as 1 to 
0.578. The analyses by volume of the dry gas obtained from the two 
coals was : 

CO-2 O CO H CH 4 N Total 

combustible. 

N. Dak 10.16 0.24 15.82 11.16 3.74 58.88 40.06 

W. Va 8.69 0.23 20.90 14.33 4.85 51.02 30.72 

The dry-gas analysis shows the North Dakota gas to be by far the best; 
its much lower result in the engine test is due to the smaller quantity of 
gas produced per lb. of coal, which was 22.7 cu. ft. per lb. of coal as fired, 
as compared with 70.6 cu. ft. for the W. Va. coal, measured at 62° F. and 
14.7 lb. absolute pressure. 

Use of Steam in Producers and in Boiler-furnaces. (R. W. Ray- 
mond, Trans. A. I. M. E., xx, 635.) — No possible use of steam can cause 
a gain of heat. If steam be introduced into a bed of incandescent carbon 
it is decomposed into hydrogen and oxygen. 

The heat absorbed by the reduction of one pound of steam to hydrogen 
is much greater in amount than the heat generated by the union of the 
oxygen thus set free with carbon, forming either carbonic oxide or car- 
bonic acid. Consequently, the effect of steam alone upon a bed of incan- 
descent fuel is to chill it. In every water-gas apparatus, designed to 
produce by means of the decomposition of steam a fuel-gas relatively 
free from nitrogen, the loss of heat in the producer must be compensated 
by some reheating device. 

This loss may be recovered if the hydrogen of the steam is subsequently 
burned, to form steam again. Such a combustion of the hydrogen is 
contemplated, in the case of fuel-gas, as secured in the subsequent use of 
that gas. Assuming the oxidation of H to be complete, the use of steam 
will cause neither gain nor loss of heat, but a simple transference, the 
heat absorbed by steam decomposition being restored by hydrogen com- 
bustion. In practice, it may be doubted whether this restoration is ever 
complete. But it is certain that an excess of steam would defeat the 
reaction altogether, and that there must be a certain proportion of steam, 
which permits the realization of important advantages, without too great 
a net loss in heat. 

The advantage to be secured (in boiler furnaces using small sizes of 
anthracite) consists principally in the transfer of heat from the lower 
side of the fire, where it is not wanted, to the upper side, where it is 
wanted. The decomposition of the steam below cools the fuel and the 
grate-bars, whereas a blast of air alone would produce, at that point, 
intense combustion (forming at first CO2), to the injury of the grate, the 
fusion of part of the fuel, etc. 

Gas Analyses by Volume and by Weight. — To convert an analysis 
of a mixed gas by volume into analysis by weight: Multiply the percentage 
of each constituent gas by its relative density, viz: CO2 by 11, O by 8, 
CO and N each by 7, and divide each product by the sum of the products. 
Conversely, to convert analysis by weight into analysis by volume, divide 
the percentage by weight of each gas by its relative density, and divide 
each auotient by the sum of the quotients. 

Gas-fuel for Small Furnaces. — E. P. Reichhelm (Am. Mach., Jan. 
10, 1895) discusses the use of gaseous fuel for forge fires, for drop-forging, 
in annealing-ovens and furnaces for melting brass and copper, for case- 
hardening, muffle-furnaces, and kilns. Under ordinary conditions, in 
such furnaces he estimates that the loss by draught, radiation, and the 
heating of space not occupied by work is, with coal, 80%, with petro- 
leum 70%, and with gas above the grade of producer-gas 25%. He 
gives the following table of comparative cost of fuels, as used in these 
furnaces: 



ACETYLENE AND CALCIUM CARBIDE. 



825 



Kind of Gas. 



Natural gas 

Coal-gas, 20 candle-power 

Carburetted water-gas 

Gasolene gas, 20 candle-power 

Water-gas from coke 

Water-gas from bituminous coal. . . . 
Water-gas and producer-gas mixed . 

Producer-gas 

Naphtha-gas, fuel 2i/ 2 gals, per 1000 ft. 



M.2 3 

0i 



1,000,000 
675,000 
646,000 
690,000 
313,000 
377,000 
185,000 
150,000 
306,365 



3 3 CflN 



750,000 
506,250 
484,500 
517,500 
234,750 
282,750 
138,750 
112,500 
229,774 






$1.25 
1.00 
.90 
.40 
.45 
.20 
.15 
.15 



Coal, $4 per ton, per 1,000,000 heat-units utilized 

Crude petroleum, 3 cts. per gal., per 1,000,000 heat-units.. 



$2.46 

2.06 

1.73 

1.70 

1.59 

1.44 

1.33 

.65 

.73 

.73 



Mr. Reichhelm gives the following figures from practice in melting 
brass with coal and with naphtha converted into gas: 1800 lbs. of metal 
require 1080 lbs. of coal, at $4.65 per ton, equal to $2.51, or, say, 15 cents 
per 100 lbs. Mr. T.'s report: 2500 lbs. of metal require 47 gals, of naphtha, 
at 6 cents per gal., equal to $2.82, or. say, 11V4 cents per 100 lbs. 

Blast-Furnace Gas. — The waste-gases from iron blast furnaces 
were formerly utilized only for heating the blast in the hot-blast ovens and 
for raising steam for the blowing-engine pumps, hoists and other auxiliary 
apparatus. Since the introduction of gas engines for blowing and other 
purposes it has been found that there is a great amount of surplus gas 
available for other uses, so that a large power plant for furnishing electric 
current to outside consumers may easily be run by it. H. Freyn, in a 
paper presented before the Western Society of Engineers (Eng. Rec, 
Jan. 13, 1906), makes an elaborate calculation for the design of such a 
plant in connection with two blast furnaces of a capacity of 400 tons of 
pig iron each per day. Some of his figures are as follows: The two fur- 
naces would supply 4,350,000 cu. ft. of gas per hour, of 90 B.T.U. average 
heat value per cu. ft. The hot-blast stoves would require 30% of this, or 
1,305,000 cu. ft.; the gas-blowing engines 720,000 cu. ft.; pumps, hoists 
and lighting machinery, 120,000 cu. ft.; gas-cleaning machinery, 120,000 
cu. ft.; losses in piping, 48,000 cu. ft.; leaving available for outside uses, in 
round numbers, 2,000,000 cu. ft. per hour. At the rate of 100 cu. ft. of gas 
per brake H.P. hour this would supply engines of 20,000 H.P., but assum- 
ing that on account of irregular working of the furnaces only half this 
amount would be available for part of the time, a 10,000-H.P. plant could 
be run with the surplus gas of the two furnaces. Taking into account the 
cost of the plant, figured at $61.60 per B.H.P., interest, depreciation, 
labor, etc., the annual cost of producing one B.H.P., 24 hours a dayi is 
$17.88, no value being placed on the blast-furnace gas, and 1 K.W. hour 
would cost 0.295 cent, which is far below the lowest figure ever reached 
with a steam-engine power plant. 

Blast-furnace gas is composed of nitrogen, carbon dioxide and carbon 
monoxide, the latter being the combustible constituent. An analysis 
reported in Trans. A.I.M.E., xvii, 50, is, by volume, CO2, 7.08; CO, 27.80; 
O, 0.10; N, 65.02. The relative proportions of CO2 and CO vary con- 
siderably with the conditions of the furnace. 

ACETYLENE AND CALCIUM CARBIDE. 

Acetylene, C2H2, contains 12 parts C and 1 part H, or 92.3% C, 7.7% H 
It is described as follows in a paper on Calcium Carbide and Acetylene by 
J. B. Morehead (Am. Gas Light Jour., July 10, 1905): 

Acetylene is a colorless and tasteless gas. When pure it has a sweet, 
etheral odor, but in the commercial form it carries small percentages of 
phosphoreted and sulphureted hydrogen which give it a pungent odor. 
One cu. ft. requires 11.91 cu. ft. of air for its complete combustion. Its 



826 



specific gravity is 0.92, air being 1. It is the nearest approach to gaseous 
carbon, and it possesses a higher candle power than any other known sub- 
stance, or 240 candles for 5 cu. ft. It is soluble in its own volume of water, 
and in varying proportions in ether, alcohol, turpentine and acetone. It 
liquefies under a pressure of 700 lbs. per sq. in. at 70° F. The pressure 
necessary for liquefaction varies directly with the temperature up to 98°, 
which is its critical temperature, beyond which it is impossible to liquefy 
the gas at any pressure. 

When calcium carbide is brought into contact with water, the calcium 
robs the water of its oxygen and forms lime and thus frees the hydrogen, 
which combines with the carbon of the carbide to form acetylene. Sixty- 
four lbs. of calcium carbide combine with 36 lbs. of water and produce 
26 lbs. of acetylene and 17 lbs. of pure, slacked lime. [The chemical re- 
action is CaC 2 + 2H 2 = C2H2 + Ca(OH) 2 .] 

Chemically pure calcium carbide will yield at 70° F. and 30 in. mercury, 
5.83 cu. ft. acetylene per pound of carbide. Commercially pure carbide is 
guaranteed to yield 5 cu. ft. of acetylene per pound, and usually exceeds the 
guarantee by a few per cent. The reaction between calcium carbide and 
water, and the subsequent slacking of the calcium oxide produced, give rise 
to considerable heat. This heat from one pound of chemically pure cal- 
cium carbide amounts to sufficient to raise the temperature of 4.1 lbs. of 
water from the freezing to the boiling point. 

There are two types of generators; one in which a varying quantity of 
water is dropped on to the carbide, the other in which the carbide is 
dropped into a large excess of water. Owing to the large amount of heat 
generated by the reaction, and the susceptibility of the acetylene to heat, 
the first, or dry type, is confined to lamps and to small machines. 

Acetylene contains 1685 B.T.U. per cubic foot as compared with 1000 
for natural gas and 600 for coal or water gas. At the present state of 
development of the acetylene industry and the calcium carbide manu- 
facture, this gas will not compete with coal gas or water gas, or with 
electricity as supplied in our cities. Acetylene may be stored under pres- 
sure for railway and other portable lighting, and it may be absorbed in 
acetone and used for the same purpose. 

Calcium carbide was discovered on May 4, 1892, at the plant of the 
Willson Aluminum Co., in North Carolina. It is a crystalline body, hard, 
brittle and varying in color from almost black to brick red. Its specific 
gravity is 2.26. A cubic foot of crushed carbide weighs 138 lbs., and in 
weight, color and most of its physical characteristics is about like granite. 
If broken hot, the fracture shows a handsome, bluish purple iridescence and 
the crystals are apt to be quite large. 

Calcium carbide, CaC 2 , contains 62.5% Ca and'37.5% C. It is insoluble 
in most acids and in all alkalies, it is non-inflammable, infusible, non- 
explosive, unaffected by jars, concussions or time, and, except for the 
property of giving off acetylene when brought in contact with water, it is 
an inert and stable body. It is made by the reduction in an electric arc 
furnace of a mixture of finely pulverized and intimately mixed calcium 
oxide or quicklime and carbon in the shape of coke. [3C+ CaO = 
CaC 2 + CO.] The temperature is calculated to be from 5000 to 8000° F. 
The furnaces employ from 250 to 350 electric H.P. each and produce about 
one ton a day. The output is crushed to different sizes and it is sold for 
$70 per ton at the works. 

The entire use for calcium carbide is for the production of acetylene. 
[Wohler, in 1862, obtained calcium carbide by heating an alloy of calcium 
and zinc together with carbon to a very high temperature.] 

Acetylene Generators and Burners. — Lewes classifies acetylene 
generators under four types: (1) Those in which water drips or flows 
slowly on a mass of carbide: (2) those in which water rises, coming in 
contact with a mass of carbide; (3) those in which water rises, coming in 
contact with successive layers of carbide; (4) those in which the carbide is 
dropped or plunged into an excess of water. He shows that- the first two 
classes are dangerous: that some generators of the third class are good, but 
that those of the fourth are the best. 

Of the various burners used for acetylene, those of the Naphey type are 
among the most satisfactory. Two tubes leading from the base of the 
burner are so adjusted as to cause two jets of flame to impinge upon each 
other at some little distance from the nozzles, and mutually to splay each 
other out into a flat flame. The tips of the nozzles, usually of steatite, are 



ACETYLENE AND CALCIUM CARBIDE. 827 

formed on the principle of the Bunsen burner, insuring a thorough mixture 
of the acetylene with enough air to give the best illumination. (H. C. 
Biddle, Cal. Jour, of Tech., 1907.) 

Acetylene gas is an endothermic compound. In its formation heat is 
absorbed, and there resides in the acetylene molecule the power of spon- 
taneously decomposing and liberating this heat if it is subjected to a 
temperature or pressure bevond the capacity of its unstable nature to 
withstand. (Thos. L. White, Eng. Mag., Sept., 1908.) Mr. White 
recommends the use of acetylene for carbureting the alcohol used in alcohol 
motors for automobiles. 

The Acetylene Blowpipe. — (Machy., July, 1907.) — The acetylene is 
produced in a generator and stored in a tank at a pressure of 2.2 to 3 lbs. 
per sq. in. The oxygen is compressed in a tank at about 150 lbs. pressure. 
The acetylene is conveyed to the burner through a 1-in. pipe with one 
3/8-in. branch leading to each blowpipe connection. The oxygen is conveyed 
through 3/g-in. pipe withi/4-in. branches. The blowpipe is of brass, made on 
the injector principle. As acetylene is so rich in carbon — containing 
92.3 % —it is possible, when mixed with air in a Bunsen burner, to obtain 
3100° F., and when combined with oxygen, 6300° F., which is the hottest 
flame known as a product of combustion, and nearly equals the electric 
arc. This is about 1200° higher than the oxy-hydrogen blowpipe flame. 

In lighting the blowpipe, the acetylene is first turned on full; then the 
oxygen is added until the flame is only a single cone. At the apex of this 
cone is a temperature of 6300° F. In welding, this point is held from Vsto 
1/4 in. distant from the metal to be welded. Too much acetylene produces 
two cones and a white color; an excess of oxygen is indicated by a violet 
tint. 

Theoretically, 21/2 volumes of oxygen are required for complete com- 
bustion of 1 volume of acetylene. Practically, however, with the blow- 
pipe the best welding results are obtained with 1.7 volumes of oxygen to 
1 volume of acetylene. The acetylene is, therefore, not completely burned 
with the blowpipe, according to the reaction: 

2 C2H2 (4 vol.) + 5 2 (10 vol.) = 4 C0 2 4- 2 H2O, 
but it is incompletely burned according to the reaction: 
C2H2 (2 vol.) + O2 (2 vol.) = 2CO + H 2 . 

Making Oxygen for the Blowpipe. — The distinctive feature which has 
done the most to make the acetylene welding process of wide commercial 
value is the introduction of a means for producing oxygen. By combining 
a chemical product, known as "epurite," with water, pure oxygen is easily 
obtained. Epurite is composed of chloride of lime, sulphate of copper and 
sulphate of iron. The sulphate of copper is pulverized and mixed dry 
with the chloride of lime. In making oxygen, 50 lbs. of this dry mixture 
are dissolved in warm water. To this solution is added a solution of 
about 7 lbs. of sulphate of iron dissolved in one gallon of water. 

The oxygen-generating apparatus consists of two lead-lined chambers 
with a scrubber and settling chamber between. One generator is filled 
with lukewarm water to which one chemical charge is added. While this 
solution is being stirred with an agitator a solution of iron sulphate is 
added which acts as a catalyzer. The reaction is: 

6 Fe2S0 4 Aq + 7 CaOCl 2 Aq + CuS0 4 Aq = 2 Fe 2 3 S0 4 Aq + CuS0 4 Aq 

+ Fe 2 Cl 6 + 7 CaCl 2 + 3 CaS0 4 + 7 0. 

The oxygen, liberated, passes through a scrubber and a water-sealed trap 

into a gasometer; from which it is compressed to 10 atmospheres, with an 

air compressor, into a pressure storage tank. 

The Theory and Practice of Oxy-Acetylene Welding is described in an 
illustrated article by J. F. Springer in Indust. Eng'g., Oct., 1909. 

IGNITION TEMPERATURE OF GASES. 

Mayer and Munch (Berichte der deutscher Gesellschaft, xxvi, 2241) give 
the following: 

Marsh gas, C 2 H 4 , 667° C. 1233° F. 

Ethane, C 2 H 6 , 616 1141 

Propane, C 3 H 8 , 547 1017 

Acetylene, C 2 H 2 , 580 1076 

Propylene, C 3 H 6 , 504 939 



828 



ILLUMINATING-GAS. 



ILLUMINATING-GAS. 

Coal-gas is made by distilling bituminous coal in retorts. The retort 
is usually a long horizontal semi-cylindrical or o shaped chamber, holding 
from 160 to 300 lbs. of coal. The retorts are set in "benches" erf from 
3 to 9, heated by one fire, which is generally of coke. The vapors distilled 
from the coal are converted into a fixed gas by passing through the retort, 
which is heated almost to whiteness. 

The gas passes out of the retort through an "ascension-pipe" into a 
long horizontal pipe called the hydraulic main, where it deposits a por- 
tion of the tar it contains; thence it goes into a condenser, a series of iron 
tubes surrounded by cold water, where it is freed from condensable vapors, 
as ammonia-water, then into a washer, where it is exposed to jets of 
water, and into a scrubber, a large chamber partially filled with trays 
made of wood or iron, containing coke, fragments of brick or paving- 
stones, which are wet with a spray of water. By the washer and scrubber 
the gas is freed from the last portion of tar and ammonia and from some 
of the sulphur compounds. The gas is then finally purified from sulphur 
compounds by passing it through lime or oxide of iron. The gas is drawn 
from the hydraulic main and forced through the washer, scrubber, etc., 
by an exhauster or gas pump. 

The kind of coal used is generally caking bituminous, but as usually 
this coal is deficient in gases of high illuminating power, there is added to 
it a portion of cannel coal or other enricher. 

' The following table, abridged from one in Johnson's Cyclopedia, shows 
the analysis, candle-power, etc., of some gas-coals and enrichers: 



Gas-ooals, etc. 


> 


■s 


< 


Si . 


o 

8° 


Coke per 

ton of 2240 

lbs. 






lbs. 


bush. 


3 >>S 




36.76 
36.00 
37.50 
40.00 
43.00 
46.00 
53.50 


51.93 

58.00 
56.90 
53.30 
40.00 
41.00 
44.50 


7.07 
6.00 
5.60 
6.70 
17.00 
13.00 
2.00 












Westmoreland, Pa 

Sterling, 


10,642 
10,528 
10,765 
9,800 
13,200 
15,000 


16.62 
18.81 
20.41 
34.98 
42.79 
28.70 


1544 
1480 
1540 
1320 
1380 
1056 


40 
36 
36 
32 
32 
44 


6420 
3993 


Despard, W. Va 


2494 
2806 


Petonia, W. Va 


4510 


Grahamite, W. Va 





The products of the distillation of 100 lbs. of average gas-coal are about 
as follows. They vary according to the quality of coal and the tempera- 
ture of distillation. 

Coke, 64 to 65 lbs.; tar, 6.5 to 7.5 lbs.; ammonia liquor, 10 to 12 lbs.; 
purified gas, 15 to 12 lbs.; impurities and loss, 4.5% to 3.5%. 

The composition of the gas by volume ranges about as follows: Hydro- 
gen, 38% to 48%; carbonic oxide, 2% to 14%; marsh-gas (Methane, 
CH4), 43% to 31%; heavy hydrocarbons (CwH2», ethylene, propylene, 
benzole vapor, etc.), 7.5% to 4.5%; nitrogen, 1% to 3%. 

In the burning of the gas the nitrogen is inert ; the hydrogen and car- 
bonic oxide give heat but no light. The luminosity of the flame is due to 
the decomposition by heat of the heavy hydrocarbons into lighter hydro- 
carbons and carbon, the latter being separated in a state of extreme 
subdivision. By the heat of the flame this separated carbon is heated to 
intense whiteness, and the illuminating effect of the flame is due to the 
light of incandescence of the particles of carbon. 

The attainment of the highest degree of luminosity of the flame de- 
pends upon the proper adjustment of the proportion of the heavy hydro- 



ILLUMINATING-GAS. 829 

carbons (with due regard to their individual character) to the nature of 
the diluent mixed therewith. 

Investigations of Percy F. Frankland show that mixtures of ethylene 
and hydrogen cease to. have any luminous effect when the proportion of 
ethylene does not exceed 10% of the whole. Mixtures of ethylene and 
carbonic oxide cease to have any luminous effect when the proportion of 
the former does not exceed 20%, while all mixtures of ethylene and 
marsh-gas have more or less luminous effect. The luminosity of a mix- 
ture of 10% ethylene and 90% marsh-gas being equal to about 18 candles, 
and that of one of 20% ethylene and 80% marsh-gas about 25 candles. 
The illuminating effect of marsh-gas alone, when burned in an argand 
burner, is by no means inconsiderable. 

For further description, see the treatises on gas by King, Richards, 
and Hughes; also Appleton's Cyc. Mech., vol. i. p. 900. 

Water-gas. ■ — Water-gas is obtained by passing steam through a bed 
of coal, coke, or charcoal heated to redness or beyond. The steam is 
decomposed, its hydrogen being liberated and its oxygen burning the 
carbon of the fuel, producing carbonic-oxide gas. The chemical reaction 
is, C + H 2 = CO + 2 H, or 2 C + 2 H 2 = C + C0 2 + 4 H, followed 
by a splitting up of the CO2, making 2 CO + 4 H. By weight the normal 
gas CO + 2 H is composed of C + O + H = 28 parts CO and 2 parts H, 

12 + 16 + 2 
or 93.33% CO and 6.67% H; by volume it is composed of equal parts of 
carbonic oxide and hydrogen. Water-gas produced as above described 
has great heating-power, but no illuminating-power. It may, however, 
be used for lighting by causing it to heat to whiteness some solid sub- 
stance, as is done in the Welsbach incandescent light. 

An illuminating-gas is made from water-gas by adding to it hydro- 
carbon gases or vapors, which are usually obtained from petroleum or 
some of its products. A history of the development of modern illumi- 
nating water-gas processes, together with a description of the most recent 
forms of apparatus, is given by Alex. C. Humphreys, in a paper on " Water- 
gas in the United States," read before the Mechanical Section of the 
British Association for Advancement of Science, in 1889. After describ- 
ing many earlier patents, he states that success in the manufacture of 
water-gas may be said to date from 1874, when the process of T. S. C. 
Lowe was introduced. All the later most successful processes are the 
modifications of Lowe's, the essential features of which were " an apparatus 
consisting of a generator and superheater internally fired; the super- 
heater being heated by the secondary combustion from the generator, 
the heat so stored up in the loose brick of the superheater being used, in 
the second part of the process, in the fixing or rendering permanent of the 
hydrocarbon gases; the second part of the process consisting in the 
passing of steam through the generator fire, and the admission of oil or 
hydrocarbon at some point between the fire of the generator and the 
loose filling of the superheater." 

The water-gas process thus nas two periods: first the "blow," during 
which air is blown through the bed coal in the generator, and the par- 
tially burned gaseous products are completely burned in the superheater, 
giving up a great portion of their heat to the fire-brick work contained 
in it, and then pass out to a chimney; second, the "run" during which the 
air blast is stopped, the opening to the chimney closed, and steam is 
blown through the incandescent bed of fuel. The resulting water-gas 
passing into the carburetting chamber in the base of the superheater is 
there charged with hydrocarbon vapors, or spray (such as naphtha and 
other distillates or crude oil), and passes through the superheater, where 
the hydrocarbon vapors become converted into fixed illuminating gases. 
From the superheater the combined gases are passed, as in the coal-gas 
process, through washers, scrubbers, etc., to the gas-holder. In this 
case, however, there is no ammonia to be removed. 

The specific gravity of water-gas increases with the increase of the 
heavy hydrocarbons which give illuminating power. The following 
figures, taken from different authorities, are given by F. H. Shelton in a 
paper on "Water-gas," read before the Ohio Gas Light Association, in 
1894: 

Candle-power.... 19.5 20.22.5 24. 25.4 26.3 28.3 29.6 .30 to 31.9 
Sp. gr. (Air = l).. .571 .630 .589 .60 to .67 .64 .602 .70 .65 .65 to .71 



830 



ILLUMINATING-GAS. 



Analyses of Water-gas and Coal-gas Compared. 

The following analyses are taken from a report of Dr. Gideon E. Moore 
on the Granger Water-gas, 1885: 





Composition by Vol. 


Composition by Weight. 




Water-gas. 


Coal- 
gas. 
Heidel- 
berg. 


Water-gas. 


Coal- 




Wor- 
cester. 


Lake. 


Wor- 
cester. 


Lake. 


gas. 




2.64 
0.14 
0.06 
11.29 
0.00 
1.53 
28.26 
18.88 
37.20 


3.85 
0.30 
0.01 
12.80 
0.00 
2.63 
23.58 
20.95 
35.88 


2.15 
3.01 
0.65 
2.55 
1.21 
1.33 
8.88 
34.02 
46.20 


0.04402 
0.00365 
0.00114 
0.18759 


0.06175 
0.00753 
0.00018 
0.20454 


0.04559 




0.09992 




0.01569 


Ethylene 


0.05389 
0.03834 




0.07077 
0.46934 
0.17928 
0.04421 


0.11700 
0.37664 
0.19133 
0.04103 


0.07825 




0.18758 




0.41087 




0.06987 








100.00 


100.00 


100.00 


1.00000 


1.00000 


1.00000 




0.5825 
0.5915 


0.6057 
0.6018 


0.4580 


























B.T.U.fromlcu.ft.: 


650.1 
597.0 


688.7 
646.6 


642.0 
577.0 


























5311.2 


5281.1 


5202.9 


















22.06 


26.31 





















The heating-values (B.T.TJ.) of the gases are calculated from the analy- 
sis by weight, by using the multipliers given below (computed from 
results of J. Thomsen), and multiplying the result by the weight of 1 cu. 
ft. of the gas at 62° F., and atmospheric pressure. 

The flame-temperatures (theoretical) are calculated on the assumption 
of complete combustion of the gases in air, without excess of air. 

The candle-power was determined by photometric tests, using a pres- 
sure of 1/2-in. water-column, a candle consumption of 120 grains of sper- 
maceti per hour, and a meter rate of 5 cu. ft. per hour, the result being 
corrected for a temperature at 62° F. and a barometric pressure of 30 in. 
It appears that the candle-power may be regulated at the pleasure of the 
person in charge of the apparatus, the range of candle-power being from 
20 to 29 candles, according to the manipulation employed. 

Calorific Equivalents of Constituents of Illuminating-gas. 



Heat-units from 1 lb. 
Water Water 



Ethylene . 
Propylene . 



Liquid. 
. .21,524.4 
.21,222.0 



Benzole vapor .18,954.0 



Vapor. 
20,134.8 
19,834.2 
17,847.0 



Heat-units from 1 lb. 

Water Water 

Liquid. Vapor. 

Carbonic oxide . 4,395.6 4,395.6 

Marsh-gas 24,021.0 21,592.8 

Hydrogen 61 ,524.0 51 ,804.0 



Efficiency of a Water-gas Plant. — The practical efficiency of an 
illuminating water-gas setting is discussed in a paper by A. G. Glasgow 
(Proc. Am. Gartiqht Assn., 1890) from which the following is abridged: 

The results refer to 1000 cu. ft. of unpurified carburetted gas, reduced to 
60° F. The total anthracite charged per 1000 cu. ft. of gas was 33.4 lbs., 



ILLUMINATING-GAS. 



831 



ash and unconsumed coal removed 9.9 lbs., leaving total combustible 
consumed 23.5 lbs., which is taken to have a fuel-value of 14,500 B.T.U. 
per pound, or a total of 340,750 heat-units. 





Com- 
posi- 
tion by 
Vol. 


Weight 

per 
100 cu. 

ft. 


Com- 
posi- 
tion by 
W'ht. 


Specific 
Heat. 




C0 2 + H 2 S. 

C W H 2» 

CO 


3.8 
14.6 
28.0 
17.0 
35.6 

1.0 


.465842 
1 . 139968 
2.1868 
.75854 
.1991464 
.078596 


.09647 
.23607 
.45285 
.15710 
.04124 
.01627 


.02088 
.08720 
11226 


I. Carburetted Water-gas.. 


CH 4 

H 


.09314 
.14041 




N 


00397 












100.0 


4.8288924 


1.00000 


.45786 




f C0 2 

CO 


3.5 
43.4 
51.8 

1.3 


.429065 

3.389540 

.289821 

.102175 


.1019 
.8051 
.0688 
.0242 


.02205 
.19958 


II. Uncarburetted gas * 


H 


.23424 


N 


.00591 


. 










100.0 


4.210601 


1 .0000 


.46178 




r co 2 

0. 


17.4 
3.2 

79.4 


2.133066 

.2856096 

6.2405224 


.2464 
.0329 
.7207 


.05342 
.00718 


8 f 


N 


.17585 












100.0 


8.6591980 


1.0000 


.23645 


IV. Generator blast-gases.. -, 


r co 2 

CO 


9.7 
17.8 
72.5 


1.189123 
1.390180 
5.698210 


.1436 
.1680 
.6884 


.031075 
.041647 


N 


.167970 








I 




100.0 


8.277513 


1.0000 


.240692 



The heat-energy absorbed by the apparatus is 23.5 X 14,500 = 340,750 
heat-units = A. Its disposition is as follows: 

B, the energy of the CO produced; 

C, the energy absorbed in the decomposition of the steam; 

Z>, the difference between the sensible heat of the escaping illuminating- 
gases and that of the entering oil ; 

E, the heat carried off by; the escaping blast products ; 

F, the heat lost by radiation from the shells; 

G, the heat carried away from the shells by convection (air-currents) ; 
H, the heat rendered latent in the gasification of the oil; 

/, the sensible heat in the ash and unconsumed coal recovered from 
the generator. 

The heat equation is A=B+C+D+E+F+G+H+ I; A 

280 
being known. A comparison of the CO in Tables I and II show that -pr- . 

or 64.5% of the volume of carburetted gas, is pure water-gas, distributed 
thus: CO2, 2.3%; CO, 28.0%; H, 33.4%; N, 0.8%; = 64.5%. 1 lb. of CO 
at 60° F. = 13,531 cu. ft. CO per 1000 cu. ft. of gas = 280 -* 13.531 
= 20.694 lbs. Energy of the CO = 20.694 X 4395.6 = 91,043 heat- 
units == B. 1 lb. of H at 60° F. = 189.2 cu. ft. H per M of gas = 334 
-4- 189.2 = 1.7653 lbs. Energy of the H per lb. (according to Thomsen, 
considering the steam generated by its combustion to be condensed to 
water at 75° F.) = 61,524 B.T.U. In Mr. Glasgow's experiments the 
steam entered the generator at 331° F.; the heat required to raise the 
product of combustion of 1 lb. of H, viz., 8.98 lbs. H 2 0, from water at 75° 
to steam at 331° must therefore be deducted from Thomsen's figure, or 
61,524 - (8.98 X 1140.2) = 51,285 B.T.U. per lb. of H. Energy of 
the H, then, is 1.7653 X 51,285 = 90,533 heat-units = C. The heat 



832 ILLUMINATING-GAS. 

lost due to the sensible heat in the illuminating-gases, their temperature 
being 1450° F., and that of the entering oil 235° F., is 48.29 (weight) 
X. 45786 (sp. heat) X 1215 (rise of temperature) = 26,864 heat-units = D. 

(The specific heat of the entering oil is approximately that of the 
issuing gas.) 

The heat carried off in 1000 cu. ft. of the escaping blast products is 
86.592 (weight) X .23645 (sp. heat) X 1474° (rise of temp.) = 30,180 
heat-units: the temperature of the escaping blast gases being 1550° F., 
and that of the entering air 76° F. But the amount of the blast gases, 
by registration of an anemometer, checked by a calculation from the 
analyses of the blast gases, was 2457 cubic feet for every 1000 cubic feet 
of carburetted gas made. Hence the heat carried off per M. of carburetted 
gas is 30,180 X 2.457 = 74,152 heat-units = E. 

Experiments made by a radiometer covering four square feet of the 
shell of the apparatus gave figures for the amount of heat lost by radia- 
tion = 12,454 heat-units = F, and by convection = 15,696 heat-units 
= G. 

The heat rendered latent by the gasification of the oil was found by 
taking the difference between all the heat fed into the carburetter and 
superheater and the total heat dissipated therefrom to be 12,841 heat- 
units = H. The sensible heat in the ash and unconsumed coal is 9.9 lbs. 
X 1500° X .25 (sp. ht.) = 3712 heat-units = /. 

The sum of all the items B+C+D+E+F+G+H+I= 
327,295 heat-units, which subtracted from the heat-energy of the com- 
bustible consumed, 340,750 heat-units, leaves 13,455 heat-units, or 4 per 
cent unaccounted for. 

Of the total heat-energy of the coal consumed, or 340,750 heat-units, 
the energy wasted is the sum of items £>., E, F, G, and /, amounting to 
132,878 heat-units, or 39 per cent; the remainder, or 207,872 heat-units, 
or 61 per cent, being utilized. The efficiency of the apparatus as a heat 
machine is therefore 61 per cent. 

Five gallons, or 35 lbs. of crude petroleum, were fed into the carburetter 
per 1000 cu. ft. of gas made; deducting 5 lbs. of tar recovered, leaves 
30 lbs. X 20,000 = 600,000 heat-units as the net heating-value of the 
petroleum used. Adding this to the heating-value of the coal, 340,750 
B.T.U., gives 940,750 heat-units, of which there is found as heat-energy 
in the carburetted gas, as in the table below, 764,050 heat-units, or 81 
per cent, which is the commercial efficiency of the apparatus, i.e., the 
ratio of the energy contained in the finished product to the total energy 
of the coal and oil consumed. 



The heating-power per M. cu. ft. of 
the carburetted ga3 is 
C0 2 38.0 

C 3 H 6 *146.0x. 117220x21222.0=363200 
CO 280.0 x. 078100 x 4395.6= 96120 
CH 4 170.0x.044620x24021.0=182210 
H 356.0 x. 005594x61524.0 = 122520 
N 10.0 



1000.0 764050 



The heating-power per M. of the 
uncarburetted gas is 
C0 2 35.0 

CO 434.0x.078100x 4395.6=148991 
H 518.0X. 005594x61524.0= 178277 
N 13.0 



1000.0 327268 



The candle-power of the gas is 31, or 6.2 candle-power per gallon of oil 
used. The calculated specific gravity is .6355, air being 1. 

For description of the operation of a modern carburetted water-gas 
plant, see paper by J. Stelfox, Eng'g, July 20, 1894, p. 89. 

Space Required for a Water-gas Plant. — Mr. Shelton, taking 15 
modern plants of the form requiring the most floor-space, figures the 
average floor-space required per 1000 cubic feet of daily capacity as 
follows: 

Water-gas Plants of Capacity Require an Area of Floor-space for each 

in 24 hours of 1000 cu. ft. of about 

100,000 cubic feet 4 square feet. 

200,000 " " 3.5 

400,000 " " 2.75 " 

600,000 " " 2 to 2.5 sq. ft. 

7 to 10 million cubic feet 1.25 to 1.5 sq. ft. 

* The heating- value of the illuminants C n H 2n is assumed to equal that 
of C3H6. 



ILLUMINATING-GAS. 833 

These figures include scrubbing and condensing rooms, but not boiler 
and engine rooms. In coal-gas plants of the most modern and compact 
forms one with 16 benches of 9 retorts each, with a capacity of 1,500,000 
cubic feet per 24 hours, will require 4.8 sq. ft. of space per 1000 cu. ft. 
of gas, and one of 6 benches of 6 retorts each, with 300,000 cu. ft. capacity 
per 24 hours, will require 6 sq. ft. of space per 1000 cu. ft. The storage- 
room required for the gas-making materials is: for coal-gas, 1 cubic foot 
of room for every 232 cubic feet of gas made; for water-gas made from 
coke, 1 cubic foot of room for every 373 cu. ft. of gas made; and for 
water-gas made from anthracite, 1 cu. ft. of room for every 645 cu. ft. of 
gas made. 

The comparison is still more in favor of water-gas if the case is con- 
sidered of a water-gas plant added as an auxiliary to an existing coal- 
gas plant; for, instead of requiring further space for storage of coke, part 
of that already required for storage of coke produced and not at once 
sold can be cut off, by reason of the water-gas plant creating a constant 
demand for more or less of the coke so produced. 

Mr. Shelton gives a calculation showing that a water-gas of 0.625 sp. gr. 
would require gas-mains eight per cent greater in diameter than the same 
quantity coal-gas of 0.425 sp. gr. if the same pressure is maintained at the 
holder. The same quantity may be carried in pipes of the same diam- 
eter if the pressure is increased in proportion to the specific gravity. 
With the same pressure the increase of candle-power about balances the 
decrease of flow. With five feet of coal-gas, giving, say, eighteen candle- 
power, 1 cubic foot equals 3.6 candle-power; with water-gas of 23 candle- 
power, 1 cubic foot equals 4.6 candle-power, and 4 cubic feet gives 18.4 
candle-power, or more than is given by 5 cubic feet of coal-gas. Water- 
gas may be made from oven-coke or gas-house coke as well as from an- 
thracite coal. A water-gas plant may be conveniently run in connection 
with a coal-gas plant, the surplus retort coke of the latter being used as 
the fuel of the former. 

In coal-gas maldng it is impracticable to enrich the gas to over twenty 
candle-power without causing too great a tendency to smoke, but water- 
gas of as high as thirty candle-power is quite common. A mixture of 
coal-gas and water-gas of a higher C.P. than 20 can be advantageously 
distributed. 

Fuel- value of Illuminating-gas. — E. G. Love (Schocl of Mines 
Qtly, January, 1892) describes F. W. Hartley's calorimeter for determin- 
ing the calorific power of gases, and gives results obtained in tests of the 
carbureted water-gas made by the municipal branch of the Consoli- 
dated Co. of New York. The tests were made from time to time during 
the past two years, and the figures give the heat-units per cubic foot at 
60° F. and 30 inches pressure: 715, 692, 725, 732, 691, 738, 735, 703, 734, 
730, 731, 727. Average, 721 heat-units. Similar tests of mixtures of 
coal- and water-gases made by other branches of the same company give 
694, 715, 684, 692, 727, 665, 695, and 686 heat-units per foot, or an 
average of 694.7. The average of all these tests was 710.5 heat-units, 
and this we may fairly take as representing the calorific power of the 
illuminating gas of New York. One thousand feet of this gas, costing 
$1.25, would therefore vield 710,500 heat-units, which would be equiva- 
lent to 568,400 heat-units for $1.00. 

The common coal-gas of London, with an illuminating power of 16 to 
17 candles, has a* calorific power of about 668 units per foot, and costs 
from 60 to 70 cents per thousand. 

The product obtained by decomposing steam by incandescent carbon, 
as effected in the Motay process, consists of about 40% of CO, and a 
little over 50% of H. 

This mixture would have a heating-power of about 300 units per cubic 
foot, and if sold at 50 cents per 1000 cubic feet would furnish 600,000 units 
for $1.00, as compared with 568,400 units for $1.00 from illuminating gas 
at $1.25 per 1000 cubic feet. This illuminating-gas if sold at $1.15 per 
thousand would therefore be a more economical heating agent than the 
fuel-gas mentioned, at 50 cents per thousand, and be much more advan- 
tageous than the latter, in that one main, service, and meter could be used 
to furnish gas for both lighting and heating. 

A large number of fuel-gases tested by Mr. Love gave from 184 to 470 
heat-units per foot, with an average of 309 units. 

Taking the cost of heat from illuminating-gas at the lowest figure given 



834 



ILLUMINATING-GAS. 



by Mr. Love, viz., $1.00 for 600,000 heat-units, it is a very expensive fuel, 

equal to coal at $40 per ton of 2000 lbs., the coal having a calorific power 

of only 12,000 heat-units per pound, or about 83% of that of pure carbon: 

600,000: (12,000 X 2000) :: $1 : $40. 

FLOW OF GAS IN PIPES. 

The rate of flow of gases of different densities, the diameter of pipes 

required, etc., are given in King's Treatise on Coal Gas, vol. ii, 374, as 

follows: 

If d = diameter of pipe in inches, 
Q = quantity of gas in cu. ft. per 

hour, 
I = length of pipe in yards, 
h = pressure in inches of water, 
5 = specific gravity of gas, air 
being 1, 



Molesworth gives Q = 1000 



▼ si 



\f 



(1350)2/i 
CM 
(1350) 2 d^_ 

Q = 1350d2 V^ = 



Vf- 



J. P. Gill, Am. Gas-light Jour., 1894, gives Q = 1291 \ 



d*h 



s(l + d) 

This formula is said to be based on experimental data, and to make 
allowance for obstructions by tar, water, and other bodies tending to check 
the flow of gas through the pipe. 

King's formula translated into the form of the com mon formula for the 
flow of compressed air or steam in pipes, Q = c ^{Vi — P2) a b /wL, in 
which Q = cu. ft. per min., Pi — P2 = difference in pressure in lbs. per 
sq. in; w = density in lbs. per cu. ft., L = length in ft., d = diam. in ins., 
gives 56.6 for the value of the coefficient c, which is nearly the same as that 
commonly used (60) in calculations of the flow of air in pipes. For values 
of c based on Darcy's experiments on flow of water in pipes see Flow of 
Steam. 

An experiment made by Mr. Clegg, in London, with a 4-in. pipe, 6 miles 
long, pressure 3 in. of water, specific gravity of gas 0.398, gave a discharge 
into the atmosphere of 852 cu. ft. per hour, after a correction of 33 cu. ft. 
was made for leakage. 

Substituting this value, 852 cu. ft., for Q in the formula Q =C ^d^h -*- si, 
we find C, the coefficient, = 997, which corresponds nearly with the formula 
given by Molesworth. 

Wm. Cox (Am. Mach., Mar. 20, 1902) gives the following formula for 
flow of gas in long pi pes. 

q = 3000 sJ d 2^Bl 



-P2 2 ) 



= 41.3 



s/' 



</ 5 X(pi 2 -p^) 



I xu Y L 

Q= discharge in cu. ft. per hour at atmospheric pressure; d = diam. 
of pipe in ins.; p, = initial and pt = terminal absolute pressure, lbs. per 
sq. in.; I = length of pipe in feet, L = length in miles. For p x 2 — p 2 2 
may be substituted (p, + p 2 ) (p, — pi). The specific gravity of the 
gas is assumed to be 0.65, air being 1. For fluids of any other sp. gr., 
s, mult ply the coefficients 3000 or 41.3 by Vo.65/s. For air, s = 1, the 
coefficients become 2419 and 33.3. J. E. Johnson Jr.'s formula for air, 
page 596, translated into the same notation as Mr. Cox's, makes the coeffi- 
cients 2449 and 33.5. 

Services for Lamps. (Molesworth.) 



Lamps. 


Ft. from 
Main. 


Require 
Pipe-bore. 


Lamps. 


Ft. from 
Main. 


Require 
Pipe-bore. 


2 


40 
40 
50 
100 


3 '8 in. 

1/2 in. 
5/8 in. 
3/4 in. 


15 


130 
150 
180 
200 


1 in. 


4 


20 

25 

30 


1 1/4 in. 


6 


1 1/2 in. 


10 


13/4 in. 



(In cold climates no service less than 3/ 4 in. should be used.) 



FLOW OF GAS IN PIPES. 



835 



Maximum Supply of Gas through Pipes in cu. ft. per Hour, 
Specific Gravity being taken at 0.45, calculated from the 
Formula Q = 1000 V a h h -s- si. (Molesworth.) 
Length of Pipe = 10 Yards. 



Diameter of 




Pressure by the Water-gauge in Inches 






Pipe in 


























Inches. 


0.1 


0.2 


0.3 


0.4 


C.5 


0.6 


0.7 


0.8 


0.9 


1.0 


3/8 


13 


18 


22 


26 


29 


31 


34 


36 


38 


41 


V2 


26 


37 


46 


53 


59 


64 


70 


74 


79 


83 


3/4 


73 


103 


126 


145 


162 


187 


192 


205 


218 


230 


1 


149 


211 


258 


298 


333 


365 


394 


422 


447 


471 


H/4 


260 


368 


451 


521 


582 


638 


689 


737 


781 


823 


U/2 


411 


581 


711 


821 


918 


1006 


1082 


1162 


1232 


1299 


2 


843 


1192 


1460 


1686 


1886 


2066 


2231 


2385 


2530 


2667 



Length of Pipe = 100 Yards. 









Pressure by the Water-gauge in 


Inches 








0.1 

8 


0.2 


0.3 


0.4 


0.5 


0.75 


1.0 


1.25 


1.5 


2 


2.5 


1/2 


12 


14 


17 


19 


23 


26 


29 


32 


36 


42 


3/4 


23 


32 


42 


46 


51 


63 


73 


81 


89 


103 


115 


1 


47 


67 


82 


94 


105 


129 


149 


167 


183 


211 


236 


11/4 


82 


116 


143 


165 


184 


225 


260 


291 


319 


368 


412 


U/2 


130 


184 


225 


260 


290 


356 


411 


459 


503 


581 


649 


2 


267 


377 


462 


533 


596 


730 


843 


943 


1033 


1193 


1333 


21/2 


466 


659 


807 


932 


1042 


1276 


1473 


1647 


1804 


2083 


2329 


3 


735 


1039 


1270 


1470 


1643 


2012 


2323 


2598 


2846 


3286 


3674 


31/2 


1080 


1528 


1871 


2161 


2416 


2958 


3416 


3820 


4184 


4831 


5402 


4 


1508 


2133 


2613 


3017 


3373 


4131 


4770 


5333 


5842 


6746 


7542 



Length of Pipe = 1000 Yards. 





Pressure by the Water-gauge in Inches. 




0.5 


0.75 


1.0 


1.5 


2.0 


2.5 


3.0 


1 


33 


41 


47 


58 


67 


75 


82 


U/2 


92 


113 


130 


159 


• 184 


205 


226 


2 


189 


231 


267 


327 


377 


422 


462 


21/2 


329 


403 


466 


571 


659 


737 


807 


3 


520 


636 


735 


900 


1039 


1162 


1273 


4 


1067 


1306 


1508 


1847 


2133 


2385 


2613 


5 


1863 


2282 


2635 


3227 


3727 


4167 


4564 


6 


2939 


3600 


4157 


5091 


5879 


6573 


7200 



836 





Length of Pipe = 


= 5000 Yabds. 




Diameter of 
Pipe in 


Pressure by the Water-gauge in Inches. 












Inches. 


1.0 


1.5 


2.0 


2.5 


3.0 


2 


119 


146 


169 


189 


207 


3 


329 


402 


465 


520 


569 


4 


675 


826 


955 


1067 


1168 


5 


1179 


1443 


1667 


1863 


2041 


6 


1859 


2277 


2629 


2939 


3220 


7 


2733 


3347 


3865 


4321 


4734 


8 


3816 


4674 


5397 


6034 


6610 


9 


5123 


6274 


7245 


8100 


8873 


10 


6667 


8165 


9428 


10541 


11547 


12 


10516 


12880 


14872 


16628 


18215 



Mr. A. C. Humphreys says his experience goes to show that these tables 
give too small a flow, but it is difficult to accurately check the tables, on 
account of the extra friction introduced by rough pipes, bends, etc. For 
bends, one rule is to allow 1/42 of an inch pressure for each right-angle bend. 

Where there is apt to be trouble from frost it is well to use no service 
of less diameter than 3/4 in., no matter how short it may be. In extremely 
cold climates this is now often increased to 1 in., even for a single lamp. 
The best practice in the U. S. now condemns any service less than 3/ 4 in. 



STEAM. 

The Temperature of Steam in contact with water depends upon 
the pressure under which it is generated. At the ordinary atmospheric 
pressure (14.7 lbs. per sq. in.) its temperature is 212° F. As the pressure 
is increased, as by the steam being generated in a closed vessel, its tem- 
perature, and that of the water in its presence, increases. 

Saturated Steam is steam of the temperature due to its pressure — • 
not superheated. 

Superheated Steam is steam heated to a temperature above that due 
to its pressure. 

Dry Steam is steam which contains no moisture. It may be either 
saturated or superheated. 

Wet Steam is steam containing intermingled moisture, mist, or 
spray. It has the same temperature as dry saturated steam of the same 
pressure. 

Water introduced into the presence of superheated steam will flash into 
vapor until the temperature of the steam is reduced to that due its pres- 
sure. Water in the presence of saturated steam has the same temperature 
as the steam. Should cold water be introduced, lowering the temperature 
of the whole mass, some of the steam will be condensed, reducing the pres- 
sure and temperature of the remainder, until equilibrium is established. 

Total Heat of Saturated Steam (above 32° F.). — According to 
Marks and Davis, the formula for total heat of steam, based on researches 
by Henning, Knoblauch, Linde and Klebe, is H= 1150.3 + 0.3745 (t + 
212°) - 0.000550 it - 212) 2 , in which H is the total heat in B.T.U. above 
water at 32° F. and t is the temperature Fahrenheit. 

Latent Heat of Steam. — The latent heat, or heat of vaporization, is 
obtained by subtracting from the total heat at any given temperature the 
heat of the liquid, or total heat above 32° in water of the same temper- 
ature. 

The total heat in steam (above 32°) includes three elements: 

1st. The heat required to raise the temperature of the water to the tem- 
perature of the steam. 

2d. The heat required to evaporate the water at that temperature, 
called internal latent heat. 

3d. The latent heat of volume, or the external work done by the steam 
in making room for itself against the pressure of the superincumbent at- 
mosphere (or surrounding steam if inclosed in a vessel). 



STEAM. 



837 



The sum of the last two elements is called the latent heat of steam 
Heat required to Generate 1 lb. of Steam from water at 32° F. 



Sensible heat, to raise the water from 32° to 212° = 

Latent heat, 1, of the formation of steam at 212° = . 

2, of expansion against the atmospheric 

pressure, 2116.4 lbs. per sq. ft. X 

26.79 cu. ft. =55,786 foot-pounds -*■ 

778 = 



Heat-units. 

180.0 
. 897 . 6 



Total heat above 32° F 1150 . 4 

The Heat-Unit, or British Thermal Unit. — The old definition of 
the heat-unit (Rankine), viz., the quantity of heat required to raise the 
temperature of 1 lb. of water 1° F., at or near its temperature of maxi- 
mum density (39.1° F.), is now (1909) no longer used. Peabody defines 
it as the heat required to raise a pound of water from 62° to 63° F., and 
Marks and Davis as Vl80 of the heat required to raise 1 lb. of water from 
32° to 212° F. By Peabody's definition the heat required to raise 1 lb. of 
water from 32° to 212° is 180.3 instead of 180 units, and the heat of va- 
porization at 212° 969.7 instead of 970.4 units. 

Specific Heat of Saturated Steam. — -When a unit weight of saturated 
steam is increased in temperature and in pressure, the volume decreasing 
so as to just keep it saturated, the specific heat is negative, and decreases 
as temperature increases. (See Wood, Therm., p. 147; Peabody, Therm., 
p. 93.) 

Absolute Zero. — The value of the absolute zero has been variously 
given as from 459.2 to 460.66 degrees below the Fahrenheit zero. Marks 
and Davis, comparing the results of Berthelot (1903), Buckingham, 1907, 
and Ross-Innes, 1908, give as the most probable value — 459°. 64 F. The 
value — 460° is close enough for all engineering calculations. 

The Mechanical Equivalent of Heat. — The value generally accepted, 
based on Rowland's experiments, is 778 ft. -lbs. Marks and Davis give the 
value 777.52 standard ft. lbs., based on later experiments, and on the 
value of g = 980.665 cm. per sec. 2 , = 32.174 ft. per sec. 2 , fixed by inter- 
national agreement (1901). These values of the absolute zero and of the 
mechanical equivalent of heat have been used by Marks and Davis in the 
computation of their steam tables. In refined investigations involving 
the value of the mechanical equivalent of heat the value of g for the lati- 
tude in which the experiments are made must be considered. 

Pressure of Saturated Steam. — Holborn and Henning, Zeit. des 
Ver. deutscher Ingenieure, Feb. 20, 1909, report results of measurements of 
the pressures of saturated steam at temperatures ranging from 50° to 
200° C. (112° to 392° F.). Their values agree closely with those obtained 
in 1905 by Knoblauch, Linde and Klebe. From a table in the article 
giving pressures for each degree from 0° to 200° C, the following values have 
been transformed into English measurements (Eng. Digest April, 1909). 



Deg. F. 


Lbs. per sq. 
in. 


Deg. F. 


Lbs. per sq. 
in. 


Deg. F. 


Lbs. per sq. 
in. 


32 
68 
100 


0.0885 
0.3386 
0.9462 


150 
200 
250 


3.715 
11.527 
29.819 


300 
350 
400 


66.972 
134.508 
248.856 



Volume of Saturated Steam. — The values of specific volume of satu- 
rated steam are computed by Clapyron's equation (Marks and Davis's 
Tables) which gives results remarkably close to those found in the ex- 
periments of Knoblauch, Linde and Klebe. 

Volume of Superheated Steam. — Linde's equation (1905), 
/l 50, 300, 000 



pv = 0.5962 T-p (1 + 0.0014 2 



^3 



- 0.0833) 



in which p is in lbs. per sq. ft., v is in cu. ft. and T = t + 459.6 is the 
absolute temperature on the Fahrenheit scale, has been used in the com- 
putation of Marks and Davis's tables, 



838 



STEAM. 



The Specific Density of Gaseous Steam, that is, steam considerably 
superheated, is 0.622, that of air being 1. That is to say, the weight of a 
cubic foot of gaseous steam is about five-eighths of that of a cubic foot of 
air, of the same pressure and temperature. 

The density or weight of a cubic foot of gaseous steam is expressible by 
the same formula as that of air, except that the multiplier or coefficient is 
less in proportion to the less specific density. ThuSi 
2.7074pX.622 _ 1.684 p 
t + 461 t + 461 ' 

in which D is the weight of a cubic foot, p the total pressure per square inch 
and t the temperature Fahrenheit. (Clark's Steam-engine.) 

H. M. Prevost Murphy (Eng. News, June 18, 1908) shows that the 
specific density is not a constant, but varies with the temperature, and 

092 t 
that the correct value is 0.6113+ ' _ , • 

Properties of Superheated Steam. — See the table on page 843, con- 
densed from Marks and Davis's tables. 

Specific Heat of Superheated Steam. — Mean specific heats from the 
temperature of saturation to various temperatures at several pressures 
English and metric units. — Knoblauch and Jakob (from Peabody's Tables). 



Kg. per sq. 
























cm 


1 


2 


4 


6 


8 


10 


12 


14 


16 


18 


20 


Lbs. per sq. 
























in 


14.2 


28,4 


56 9 


85.3 


113.3 


142.2 


170.6 


199.1 


227.5 


256.0 


284.4 


Temp, sat., 
























°C 


99 


120 


143 


158 


169 


179 


187 


194 


200 


206 


211 


Temp, sat., 
























°F 


210 


248 


289 


316 


336 


350 


368 


381 


392 


403 


412 


°F. 


°C. 
























212 


100 
150 
200 
250 


0.463 
.462 
.462 
.463 






















302 


.478 
.475 
474 


.515 

.502 
495 


















392 


.530 
514 


.560 
.512 


.597 
.552 


.635 
.570 


.677 
.588 








482 


.609 


635 


.664 


572 


300 


.464 


475 


492 


505 


.517 


.530 


.541 


.550 


.561 


572 


.585 


662 


350 


.468 


477 


492 


.503 


.512 


.522 


.529 


.536 


.543 


.550 


.557 


752 


400 


.473 


.481 


.494 


.504 


.512 


.520 


.526 


.531 


.537 


.542 


.547 



The Rationalization of Regnault's Experiments on Steam. — 

(J. McFarlane Gray, Proc. Inst. M. E., July, 1889.) — The formulae con- 
structed by Regnault are strictly empirical, and were based entirely on 
his experiments. They are therefore not valid beyond the range of tem- 
peratures and pressures observed. 

Mr. Gray has made a most elaborate calculation, based not on experi- 
ments but on fundamental principles of thermodynamics, from which he 
deduces formulae for the pressure and total heat of steam, and presents 
tables calculated therefrom which show substantial agreement with 
Regnault's figures. He gives the following examples of steam-pressures 
calculated for temperatures beyond the range of Regnault's experiments. 



Temperature. 




Temperature. 






Pounds per 




Pounds in 






sq. in. 






sq. in. 


C. ■ 


Fahr. 




C. 


Fahr. 




230 


446 


406.9 


340 


644 


2156.2 


240 


464 


488.9 


360 


680 


2742.5 


250 


482 


579.9 


380 


716 


3448.1 


260 


500 


691.6 


400 


752 


4300.2 


280 


536 


940.0 


415 


779 


5017.1 


300 


572 


1261.8 


427 


800.6 


5659.9 


320 


608 


1661.9 









These pressures are higher than those obtained by Regnault's formula, 
which gives for 415° C. only 4067.1 lbs. per square inch. 



839 



Properties- of Saturated Steam. 

(Condensed from Marks and Davis's Steam Tables and Diagrams, 1909, 
by permission of the publishers, Longmans, Green & Co.) 



m 






Total Heat 


►44 


^<~ 




03 


a 

to 


1* 


3 1 -! 


- . 


above 32° F . 


S3 


to ° 


■5 


$! 




? j2 


a; oj 


1 i 


B-4 


ad 




'o 




< 




"B 1 


I i 






gifr, 


IS 


>, o 

a".n 


> 


H 


a K 


3 ^ 


i-l 


t> 


" 


to 


to 


29.74 


0.0886 


32 


0.00 


1073.4 


1073.4 


3294 


0.000304 


0.0000 


2.1832 


29.67 


0.1217 


40 


8.05 


.1076.9 


1068.9 


2438 


0.000410 


0.0162 


2.1394 


29.56 


0.1780 


50 


18.08 


1081.4 


1063.3 


1702 


0.000587 


0.0361 


2.0865 


29.40 


0.2562 


60 


28.08 


1085.9 


1057.8 


1208 


0.000828 


0.0555 


2.0358 


29.18 


0.3626 


70 


38.06 


1090.3 


1052.3 


871 


0.001148 


0.0745 


1.9868 


29.09 


0.505 


80 


48.03 


1094.8 


1046.7 


636.8 


0.001570 


0.0932 


1.9398 


28.50 


0.696 


90 


58.00 


1099.2 


1041.2 


469.3 


0.002131 


0.1114 


1.8944 


28.00 


0.946 


100 


67.97 


1103.6 


1035.6 


350.8 


0.002851 


0.1295 


1.8505 


27.88 


1 


101.83 


69.8 


1104.4 


1034.6 


333.0 


0.00300 


0.1327 


1.8427 


25.85 


2 


126.15 


94.0 


1115.0 


1021.0 


173.5 


0.00576 


0.1749 


1.7431 


23.81 


3 


141.52 


109.4 


1121.6 


1012.3 


118.5 


0.00845 


0.2008 


1.6840 


21.78 


4 


153.01 


120.9 


1126.5 


1005.7 


90.5 


0.01107 


0.2198 


1.6416 


19.74 


5 


162.28 


130.1 


1130.5 


1000.3 


73.33 


0.01364 


0.2348 


1.6084 


17.70 


6 


170.06 


137.9 


1133.7 


995.8 


61.89 


0.01616 


0.2471 


1.5814 


15.67 


7 


176.85 


144.7 


1136.5 


991.8 


53.56 


0.01867 


0.2579 


1.5582 


13.63 


8 


182.86 


150.8 


1139.0 


988.2 


47.27 


0.02115 


0.2673 


1.5380 


11.60 


9 


188.27 


156.2 


1141.1 


985.0 


42.36 


0.02361 


0.2756 


1.5202 


9.56 


10 


193.22 


161.1 


1143.1 


982.0 


38.38 


0.02606 


0.2832 


1.5042 


7.52 


11 


197.75 


165.7 


1144.9 


979.2 


35.10 


0.02849 


0.2902 


1.4895 


5.49 


12 


201.96 


169.9 


1146.5 


976.6 


32.36 


0.03090 


0.2967 


1 .4760 


3.45 


13 


205.87 


173.8 


1148.0 


974.2 


30.03 


0.03330 


"0.3025 


1.4639 


1.42 

lbs. 
gage. 


14 


209.55 


177.5 


1149.4 


971.9 


28.02 


0.03569 


0.3081 


1.4523 


14.70 


212 


180.0 


1150.4 


970.4 


26.79 


0.03732 


0.3118 


1.4447 


0.3 


15 


213.0 


18.1.0 


1150.7 


969.7 


26.27 


0.03806 


0.3133 


1.4416 


1.3 


16 


216.3 


184.4 


1152.0 


967.6 


24.79 


0.04042 


0.3183 


1.4311 


2.3 


17 


219.4 


187.5 


1153.1 


965.6 


23.38 


0.04277 


0.3229 


1.4215 


3.3 


18 


222.4 


190.5 


1154.2 


963.7 


22.16 


0.04512 


0.3273 


1.4127 


4.3 


19 


225.2 


193.4 


1155.2 


961.8 


21.07 


0.04746 


0.3315 


1.4045 


5.3 


20 


228.0 


196.1 


1156.2 


960.0 


20.08 


0.04980 


0.3355 


1.3965 


6.3 


21 


230.6 


198.8 


1157.1 


958.3 


19.18 


0.05213 


0.3393 


1.3887 


7.3 


22 


233.1 


201 .3 


1158.0 


956.7 


18.37 


0.05445 


0.3430 


1.3811 


8.3 


23 


235.5 


203.8 


1158.8 


955.1 


17.62 


0.05676 


0.3465 


1.3739 


9.3 


24 


237.8 


206.1 


1159.6 


953.5 


16.93 


0.05907 


0.3499 


1 .3670 


10.3 


25 


240.1 


208.4 


1160.4 


952.0 


16.30 


0.0614 


0.3532 


1 .3604 


11.3 


26 


242.2 


210.6 


1161.2 


950.6 


15.72 


0.0636 


0.3564 


1 .3542 


12.3 


27 


244.4 


212.7 


1161.9 


949.2 


15.18 


0.0659 


0.3594 


1.3483 


13.3 


28 


246.4 


214.8 


1162.6 


947.8 


14.67 


0.0682 


0.3623 


1 .3425 


14.3 


29 


248.4 


216.8 


1163.2 


946.4 


14.19 


0.0705 


0.3652 


1.3367 


15.3 


30 


250.3 


218.8 


1163.9 


945.1 


13.74 


0.0728 


0.3680 


1.3311 


16.3 


31 


252.2 


220.7 


1164.5 


943.8 


13.32 


0.0751 


0.3707 


1.3257 


17.3 


32 


254.1 


222.6 


1165.1 


942.5 


12.93 


0.0773 


0.3733 


1 .3205 


18.3 


33 


255.8 


224.4 


1165.7 


941.3 


12.57 


0.0795 


0.3759 


1.3155 


19.3 


34 


257.6 


226.2 


1166.3 


940.1 


12.22 


0.0818 


0.3784 


1.3107 


20.3 


35. 


259.3 


227.9 


1166.8 


938.9 


11.89 


0.0841 


0.3808 


1 .3060 


21.3 


36 


261.0 


229.6 


1167.3 


937.7 


11.58 


0.0863 


0.3832 


1.3014 


22.3 


37 


262.6 


231.3 


1167.8 


936.6 


11.29 


0.0886 


0.3855 


1.2969 


23.3 


38 


264.2 


232.9 


1168.4 


935.5 


11.01 


0.0908 


0.3877 


1.2925 


24.3 


39 


265.8 


234.5 


1168.9 


934.4 


10.74 


0.0931 


0.3899 


1.2882 


25.3 


40 


267.3 


236.1 


1169.4 


933.3 


10.49 


0.0953 


0.3920 


1.2841 


26.3 


41 


268.7 


237.6 


1169.8 


932.2 


10.25 


0.0976 


0.3941 


1 .2800 



840 



STEAM. 







Properties of Saturated Steam. (Continued.) 




go 


gfi 




Total Heat 


^ 




• • 


03 


a 


3 1- ? 


3 . 




above 32° F. 


„ e3 


fe'S 


Of-! 


J3 


> 




01 CQ 


af-J 






|W 


A* 


"B 


^ 


W 


o>0Q 


u ^ 


a « 


a 

33 


oi a 

13 


£1 

Ol S-< 


a "3 

1 1 


c3 £ 

-M 0> 


v a 


u 

■3.S0Q 


O a, 
a>fe 


£,01 

II 


ag 
go 





J3 


H 


a K 


£ K 


F-l ' 


> 


H 


m 


27.3 


42 


270.2 


239.1 


1170.3 


931.2 


10.02 


0.0998 


0.3962 


1.2759 


28.3 


43 


271.7 


240.5 


1170.7 


930.2 


9.80 


0.1020 


0.3982 


1.2720 


29.3 


44 


273.1 


242.0 


1171.2 


929.2 


9.59 


0.1043 


0.4002 


1.2681 


30.3 


45 


274.5 


243.4 


1171.6 


928.2 


9.39 


0.1065 


0.4021 


1.2644 


31.3 


46 


275.8 


244.8 


1172.0 


927.2 


9.20 


0.1087 


0.4040 


1.2607 


32.3 


47 


277.2 


246.1 


1172.4 


926.3 


9.02 


0.1109 


0.4059 


1.2571 


33.3 


48 


278.5 


247.5 


1172.8 


925.3 


8.84 


0.1131 


0.4077 


1.2536 


34.3 


49 


279.8 


248.8 


1173.2 


924.4 


8.67 


0.1153 


0.4095 


1.2502 


35.3 


50 


281.0 


250.1 


1173.6 


923.5 


8.51 


0.1175 


0.4113 


1.2468 


36.3 


51 


282.3 


251.4 


1174.0 


922.6 


8.35 


0.1197 


0.4130 


1.2432 


37.3 


52 


283.5 


252.6 


1174.3 


921.7 


8.20 


0.1219 


0.4147 


1.2405 


38.3 


53 


284.7 


253.9 


1174.7 


920.8 


8.05 


0.1241 


0.4164 


1.2370 


39.3 


54 


285.9 


255.1 


1175.0 


919.9 


7.91 


0.1263 


0.4180 


1.2339 


40.3 


55 


287.1 


256.3 


1175.4 


919.0 


7.78 


0.1285 


0.4196 


1.2309 


41.3 


56 


288.2 


257.5 


1175.7 


918.2 


7.65 


0.1307 


0.4212 


1.2278 


42.3 


57 


289.4 


258.7 


1176.0 


917.4 


7.52 


0.1329 


0.4227 


1.2248 


43.3 


58 


290.5 


259.8 


1176.4 


916.5 


7.40 


0.1350 


0.4242 


1.2218 


44.3 


59 


291.6 


261.0 


1176.7 


915.7 


7.28 


0.1372 


0.4257 


1.2189 


45.3 


60 


292.7 


262.1 


1177.0 


914.9 


7.17 


0.1394 


0.4272 


1.2160 


46.3 


61 


293.8 


263.2 


1177.3 


914.1 


7.06 


0.1416 


0.4287 


1.2132 


47.3 


62 


294.9 


264.3 


1177.6 


913.3 


6.95 


0.1438 


0.4302 


1.2104 


48.3 


63 


295.9 


265.4 


1177.9 


912.5 


6.85 


0.1460 


0.4316 


1.2077 


49.3 


64 


297.0 


266.4 


1178.2 


911.8 


6.75 


0.1482 


0.4330 


1.2050 


50.3 


65 


298.0 


267.5 


1178.5 


911.0 


6.65 


0.1503 


0.4344 


1.2024 


51.3 


66 


299.0 


268.5 


1178.8 


910.2 


6.56 


0.1525 


0.4358 


1 1998 


52.3 


67 


300.0 


269.6 


1179.0 


909.5 


6.47 


0.1547 


0.4371 


1.1972 


53.3 


68 


301.0 


270.6 


1179.3 


908.7 


6.38 


0.1569 


0.4385 


1.1946 


54.3 


69 


302.0 


271.6 


1179.6 


908.0 


6.29 


0.1590 


0.4398 


1.1921 


55.3 


70 


302.9 


272.6 


1179.8 


907.2 


6.20 


0.1612 


0.4411 


1.1896 


56.3 


71 


303.9 


273.6 


1180.1 


906.5 


6.12 


0.1634 


0.4424 


1.1872 


57.3 


72 


304.8 


274.5 


1180.4 


905.8 


6.04 


0.1656 


0.4437 


1.1848 


58.3 


73 


305.8 


275.5 


1180.6 


905.1 


5.96 


0.1678 


0.4449 


1.1825 


59.3 


74 


306.7 


276.5 


1180. 9 


904.4 


5.89 


0.1699 


0.4462 


1.1801 


60.3 


75 


307.6 


277.4 


1181.1 


903.7 


5.81 


0.1721 


0.4474 


1.1778 


61.3 


76 


308.5 


278.3 


1181.4 


903.0 


5.74 


0.1743 


0.4487 


1.1755 


62.3 


77 


309.4 


279.3 


1181.6 


902.3 


5.67 


0.1764 


0.4499 


1.1730 


63.3 


78 


310.3 


280.2 


1181.8 


901.7 


5.60 


0.1786 


0.4511 


1.1712 


64.3 


79 


311.2 


281.1 


1182.1 


901.0 


5.54 


0.1808 


0.4523 


1.1687 


65.3 


80 


312.0 


282.0 


1182.3 


900.3 


5.47 


0.1829 


0.4535 


1.1665 


66.3 


81 


312.9 


282.9 


1182.5 


899.7 


5.41 


0.1851 


0.4546 


1.1644 


67.3 


82 


313.8 


283.8 


1182.8 


899.0 


5.34 


0.1873 


0.4557 


1.1623 


68.3 


83 


314.6 


284.6 


1183.0 


898.4 


5.28 


0.1894 


0.4568 


1.1602 


69.3 


84 


315.4 


285.5 


1183.2 


897.7 


5.22 


0.1915 


0.4579 


1.1581 


70.3 


85 


316.3 


286.3 


1183. 4 


897.1 


5.16 


0.1937 


0.4590 


1.1561 


71.3 


86 


317.1 


287.2 


1183.6 


896.4 


5.10 


0.1959 


0.4601 


1.1540 


72.3 


87 


317.9 


288.0 


1183.8 


895.8 


5.05 


0.1980 


0.4612 


1 . 1520 


73.3 


88 


318.7 


288.9 


1184.0 


895.2 


5.00 


0.2001 


0.4623 


1.1500 


74.3 


89 


319.5 


289.7 


1184.2 


894.6 


4.94 


0.2023 


0.4633 


1.1481 


75.3 


90 


320.3 


290.5 


1184.4 


893.9 


4.89 


0.2044 


0.4644 


1.1461 


76.3 


91 


321.1 


291.3 


1184.6 


893.3 


4.84 


0.2065 


0.4654 


1.1442 


77.3 


92 


321.8 


292.1 


1184.8 


892.7 


4.79 


0.2087 


0.4664 


1.1423 


78.3 


93 


322.6 


292.9 


1185.0 


892.1 


4.74 


0.2109 


0.4674 


1.1404 


79.3 


94 


323.4 


293.7 


1185.2 


891.5 


4.69 


0.2130 


0.4684 


1 . 1385 


80.3' 


95 


324.1 


294.5 


1185.4 


890.9 


4.65 


0.2151 


0.4694 


1.1367 



841 



Properties of Saturated Steam. (Continued.) 



•d 


g*c 




Total Heat 


^■A 




d-Q 


<D 


a 


3M 


d 1- ? 




above 32° F. 


- d 


Ph"S 


Ohh 


"S 


> 




m C 


0»+a 






|w 


A* 


~B 


•H 


H 


CO d 1 
£02 


S-i £ 


a « 


a 

0) . 

Mm 

3.Q 


© a 

3 XD 

IS 


5Ji 

a.d 


1 1 


<s .13 

^§ 

,d a 




1 ! 


"8 g 

M+S 

"5 Eh 


° e3 
d^ 


d 5 


O 


£1 
< 


H 


a W 


£ W 


Hi 


> 


£ 


H 


W 


81.3 


96 


324.9 


295.3 


1185.6 


890.3 


4.60 


0.2172 


0.4704 


1.134f 


82.3 


97 


325.6 


296.1 


1185.8 


889.7 


4.56 


0.2193 


0.4714 


1 . 133C 


83.3 


98 


326.4 


296.8 


1186.0 


889.2 


4.51 


0.2215 


0.4724 


1.1312 


84.3 


99 


327.1 


297:6 


1186.2 


888.6 


4.47 


0.2237 


0.4733 


1.129! 


85.3 


100 


327.8 


298 .3 


1186.3 


888.0 


4.429 


0.2258 


0.4743 


1 . 127} 


87.3 


102 


329.3 


299.8 


1186.7 


886.9 


4.347 


0.2300 


0.4762 


1.1241 


89.3 


104 


330.7 


301.3 


1187.0 


885.8 


4.268 


0.2343 


0.4780 


1 . 120* 


91.3 


106 


332.0 


302.7 


1187.4 


884.7 


4.192 


0.2336 


0.4798 


1.1174 


93.3 


108 


333.4 


304.1 


1187.7 


883.6 


4.118 


0.2429 


0.4816 


1.1141 


95.3 


110 


334.8 


305.5 


1188.0 


882.5 


4.047 


0.2472 


0.4834 


1.1 10C 


97.3 


112 


336.1 


306.9 


1188.4 


881.4 


3.978 


0.2514 


0.4852 


1 . 1076 


99.3 


114 


337.4 


308.3 


1188.7 


880.4 


3.912 


0.2556 


0.4869 


1 . 1045 


101.3 


116 


338.7 


309.6 


1189.0 


879.3 


3.848 


0.2599 


0.4886 


1.10H 


103.3 


118 


340.0 


311.0 


1189.3 


878.3 


3.786 


0.2641 


0.4903 


1.0984 


105.3 


120 


341.3 


312.3 


1189.6 


877.2 


3.726 


0.2683 


0.4919 


1.0954 


107.3 


122 


342.5 


313.6 


1189.8 


876.2 


3.668 


0.2726 


0.4935 


1.0924 


109.3 


124 


343.8 


314.9 


1190.1 


875.2 


3.611 


0.2769 


0.4951 


1.0895 


111.3 


126 


345.0 


316.2 


1190.4 


874.2 


3.556 


0.2812 


0.4967 


1.0865 


113.3 


128 


346.2 


317.4 


1190.7 


873.3 


3.504 


0.2854 


0.4982 


1.0837 


115.3 


130 


347.4 


318.6 


1191.0 


872.3 


3.452 


0.2897 


0.4998 


1.0809 


117.3 


132 


348.5 


319.9 


1191.2 


871.3 


3.402 


0.2939 


0.5013 


1.0782 


119.3 


134 


349.7 


321.1 


1191.5 


870.4 


3.354 


0.2981 


0.5028 


1.0755 


121.3 


136 


350.8 


322.3 


1191.7 


869.4 


3.308 


0.3023 


0.5043 


1.0728 


123.3 


138 


352.0 


323.4 


1192.0 


868.5 


3.263 


0.3065 


0.5057 


1.0702 


125.3 


140 


353.1 


324.6 


1192.2 


867.6 


3.219 


0.3107 


0.5072 


1 .0675 


127.3 


142 


354.2 


325.8 


1192.5 


866.7 


3.175 


0.3150 


0.5086 


1.0649 


129.3 


144 


355.3 


326.9 


1192.7 


865.8 


3.133 


0.3192 


0.5100 


1 .0624 


131.3 


146 


356.3 


328.0 


1192.9 


864.9 


3.092 


0.3234 


0.5114 


1.0599 


133.3 


148 


357.4 


329.1 


1193.2 


864.0 


3.052 


0.3276 


0.5128 


1.0574 


135.3 


150 


358.5 


330.2 


1193.4 


863.2 


3.012 


0.3320 


0.5142 


1.0550 


137.3 


152 


359.5 


331.4 


1193.6 


862.3 


2.974 


0.3362 


0.5155 


1.0525 


139.3 


154 


360.5 


332.4 


1193.8 


861.4 


2.938 


0.3404 


0.5169 


1.0501 


141.3 


156 


361.6 


333.5 


1194.1 


860.6 


2.902 


0.3446 


0.5182 


1.0477 


143.3 


158 


362.6 


334.6 


1194.3 


859.7 


2.868 


0.3488 


0.5195 


1 .0454 


145.3 


160 


363.6 


335.6 


1194.5 


858.8 


2.834 


0.3529 


0.5208 


1.0431 


147.3 


162 


364.6 


336.7 


1194.7 


858.0 


2.801 


0.3570 


0.5220 


1 .0409 


149.3 


164 


365.6 


337.7 


1194.9 


857.2 


2.769 


0.3612 


0.5233 


1.0387 


151.3 


166 


366.5 


338.7 


1195.1 


856.4 


2.737 


0.3654 


0.5245 


1.0365 


153.3 


168 


367.5 


339.7 


1195.3 


855.5 


2.706 


0.3696 


0.5257 


1.0343 


155.3 


170 


368.5 


340.7 


1195.4 


854.7 


2.675 


0.3738 


0.5269 


1.0321 


157.3 


172 


369.4 


341.7 


1195.6 


853.9 


2.645 


0.3780 


0.5281 


1.0300 


159.3 


174 


370.4 


342.7 


1195.8 


853.1 


2.616 


0.3822 


0.5293 


1.0278 


161.3 


176 


371.3 


343.7 


1196.0 


852.3 


2.588 


0.3864 


0.5305 


1.0257 


163.3 


178 


372.2 


344.7 


1196.2 


851.5 


2.560 


0.3906 


0.5317 


1.0235 


165.3 


180 


373.1 


345.6 


1196.4 


850.8 


2.533 


0.3948 


0.5328 


1.0215 


167.3 


182 


374.0 


346.6 


1196.6 


850.0 


2.507 


0.3989 


0.5339 


1.0195 


169.3 


184 


374.9 


347.6 


1196.8 


849.2 


2.481 


0.4031 


0.5351 


1.0174 


171.3 


186 


375.8 


348.5 


1196.9 


848.4 


2.455 


0.4073 


0.5362 


1.0154 


173.3 


188 


376.7 


349.4 


1197.1 


847.7 


2.430 


0.4115 


0.5373 


1.0134 


175.3 


190 


377.6 


350.4 


1197.3 


846.9 


2.406 


0.4157 


0.5384 


1.0114 


177.3 


192 


378.5 


351.3 


1197.4 


846.1 


2.381 


0.4199 


0.5395 


1.0095 


179.3 


194 


379.3 


352.2 


1197.6 


845.4 


2.358 


0.4241 


0.5405 


1.0076 


181.3 


196 


380.2 


353.1 


1197.8 


844.7 


2.335 


0.4283 


0.5416 


1 .0056 


183.3 


198 


381.0 


354.0 


1197.9 


843.9 


2.312 


0.4325 


0.5426 


1 .0038 



842 







Properties of Saturated Steam. {Continued.) 




aT • 


Sa 




Total Heat 


q4. 




■ 


03 


a 


UA 


Id- 

St 

a 




above 32° F . 


► 03 

"JIM 

"T, 

m 


£o 


fs 


"S 


$ 


M 

03 

a 


b'o3 

S § 

03 u 


03 j£ 

d ft 

03 J, 

+* 03 


03^^ 

-U 03 


.03* g 

Id- 




'o 

ft03 


c o 


< 


H 


c tn 


a a 


.-I 


> 


H 


H 


185.3 


200 


381.9 


354.9 


1198.1 


843.2 


2.290 


0.437 


0.5437, 


1.0019 


190.3 


205 


384.0 


357.1 


1198.5 


841.4 


2.237 


0.447 


0.5463 


0.9973 


195.3 


210 


386.0 


359.2 


1198.8 


839.6 


2.187 


0.457 


0.5488 


0.9928 


200.3 


215 


388.0 


361.4 


1199.2 


837.9 


2.138 


0.468 


0.5513 


0.9885 


205.3 


220 


389.9 


363.4 


1199.6 


836.2 


2.091 


0.478 


0.5538 


0.9841 


210.3 


225 


391.9 


365.5 


1199.9 


834.4 


2.046 


0.489 


0.5562 


9799 


215.3 


230 


393.8 


367.5 


1200.2 


832.8 


2.004 


0.499 


0.5586 


9758 


220.3 


235 


395.6 


369.4 


1200.6 


831.1 


1.964 


0.509 


0.5610 


0.9717 


225.3 


240 


397.4 


371.4 


1209.9 


829.5 


1.924 


0.520 


0.5633 


0.9676 


230.3 


245 


399.3 


373.3 


1201.2 


827.9 


1.887 


0.530 


0.5655 


0.9638 


235.3 


250 


401.1 


375.2 


1201.5 


826.3 


1.850 


0.541 


0.5676 


0.9600 


245.3 


260 


404.5 


378.9 


1202.1 


823.1 


1.782 


0.561 


0.5719 


0.9525 


255.3 


270 


407.9 


382.5 


1202.6 


820.1 


1.718 


0.582 


0.5760 


0.9454 


265.3 


280 


411.2 


386.0 


1203.1 


817.1 


1.658 


0.603 


0.5800 


0.9385 


275.3 


290 


414.4 


389.4 


1203.6 


814.2 


1.602 


0.624 


0.5840 


0.9316 


285.3 


300 


417.5 


392.7 


1204.1 


811.3 


1.551 


0.645 


0.5878 


0.9251 


295.3 


310 


420.5 


395.9 


1204.5 


808.5 


1.502 


666 


0.5915 


0.9187 


305.3 


320 


423.4 


399.1 


1204.9 


805.8 


1.456 


0.687 


0.5951 


0.9125 


315.3 


330 


426.3 


402.2 


1205.3 


803.1 


1.413 


0.708 


0.5986 


0.9065 


325.3 


340 


429.1 


405.3 


1205.7 


800.4 


1.372 


0.729 


0.6020 


9006 


335.3 


350 


431.9 


408.2 


1206.1 


797.8 


1.334 


0.750 


0.6053 


8949 


345.3 


360 


434.6 


411.2 


1206.4 


795.3 


1.298 


0.770 


0.6085 


8894 


355.3 


370 


437.2 


414.0 


1206.8 


792.8 


1.264 


0.791 


0.6116 


0.8840 


365.3 


380 


439.8 


416.8 


1207.1 


790.3 


1.231 


0.812 


0.6147 


0.8788 


375.3 


390 


442.3 


419.5 


1207.4 


787.9 


1.200 


0.833 


0.6178 


0.8737 


385.3 


400 


444.8 


422 


1208 


786 


1.17 


0.86 


0.621 


0.868 


435.3 


450 


456.5 


435 


1209 


774 


1.04 


0.96 


0.635 


0.844 


485.3 


500 


467.3 


448 


1210 


762 


0.93 


1.08 


0.648 


0.822 


535.3 


550 


477.3 


459 


1210 


751 


0.83 


1.20 


0.659 


0.801 


585.3 


600 


486.6 


469 


1210 


741 


0.76 


1.32 


0.670 


0.783 



Available Energy in Expanding Steam. — Rankine Cycle. (J. B. 
Stanwood, Power, June 9, 1908.) — A simple formula for finding, with the 
aid of the steam and entropy tables, the available energy per pound of 
steam in B.T.U. when it is expanded adiabatically from" a higher to a 
lower pressure is: 

U = H - Hi + T CNi - N). 

U = available B.T.U. in 1 lb. of expanding steam; // and Hi total heat 
in 1 lb. steam at the two pressures; T = absolute temperature at the 
lower pressure; N — Ni, difference of entropy of 1 lb. of steam at the two 
pressures. 

Example. — Required the available B.T.U. in 1 lb. steam expanded 
from 100 lbs. to 14.7 lbs. absolute. H = 1186.3; Hi = 1150.4; T = 672; 
N = 1.602; Ni = 1.756. 35.9 + 103.5 = 138.4. 

Efficiency of the Cycle. — Let the steam be made from feed-water at 
212°. Heat required = 1186.3 - 180 = 1006.3; efficiency = 138.4 * 
1006.3 = 0.1375. 

Rankine Cycle. — This efficiency is that of the Rankine cycle, which 
assumes that the steam is expanded adiabatically to the lowest pressure 
and temperature, and that the feed-water from which the steam is made 
is introduced into the system at the same low temperature. 

Carnot Cycle. — The Carnot ideal cycle, which assumes that all the 
heat entering the system enters at the highest temperature, and in which 
the efficiency is (5"i - Tz) ■*- T ly gives (327.8- 212) -?- (327.8+ 460) = 
0.1470 and the available energy in B.T.U. = 0.1470 X 1006.3 = 147.9 B.T.U. 



843 



Properties of Superheated Steam. 

(Condensed from Marks and Davis's Steam Tables and Diagrams.) 
v = specific volume in cu. ft. per lb., h = total heat, from water at 
32° F. in B.T.U. per lb., n = entropy, from water at 32°. 



Jl. 




Degrees of Superheat. 


Oh 





20 


50 


100 


150 


200 


250 


300 


400 


500 


20 


228.0 


v 20.08 


20.73 


21.69 


23.25 


24.80 


26.33 


27.85 


29.37 


32.39 


35.40 






h 11562 


1165.7 


1179.9 


1203.5 


1227.1 


1250. t 


1274.1 


1297.6 


1344.8 


1392.2 






n 1.7320 


1.7456 


1.7652 


1.7961 


1.8251 


1.852* 


1.8781 


1.9026 


1.9479 


1.9893 


40 


267.3 


v 10.49 


10.83 


11.33 


12.13 


12.93 


13.70 


14.48 


15.25 


16.78 


18.30 






h 1169.4 


1179.3 


1194.0 


1218.4 


1242.4 


1266.4 


1290.3 


1314.1 


1361.6 


1409.3 






n 1.6761 


1.6895 


1.7089 


1.7392 


1.7674 


1.794C 


1.8189 


1.8427 


1.8867 


1.9271 


60 


292.7 


v7.17 


7.40 


7.75 


8.30 


8.84 


9.36 


9.89 


10.41 


11.43 


12.45 






h 1177.0 


1187.3 


1202.6 


1227.6 


1252.1 


1276.4 


1300.4 


1324.3 


1372.2 


1420.0 






n 1.6432 


1.6568 


1.6761 


1 . 7062 


1 . 7342 


1.7603 


1 . 7849 


1.8081 


1.8511 


1.8908 


80 


312.0 


v5.47 


5.65 


5.92 


6.34 


6.75 


7.17 


7.56 


7.95 


8.72 


9.49 






h 1182.3 


1193.0 


1208.8 


1234.3 


1259.0 


1283. t 


1307.8 


1331.9 


1379.8 


1427.9 






n 1.6200 


1.6338 


1.6532 


1.6833 


1.7110 


1.7366 


1.7612 


1 . 7840 


1.8265 


1.8658 


100 


327.8 


v4.43 


4.58 


4.79 


5.14 


5.47 


5.89 


6.12 


6.44 


7.07 


7.69 






h 1186.3 


1197.5 


1213.8 


1239.7 


1264.7 


1289.4 


1313.6 


1337.8 


1385.9 


1434.1 






n 1.6020 


1.6160 


1.6358 


1.6658 


1.6933 


1.7188 


1.7428 


1.7656 


1.8079 


1.8468 


120 


341.3 


v3.73 


3.85 


4.04 


4.33 


4.62 


4.89 


5.17 


5.44 


5.96 


6.48 






h 1189.6 


1201.1 


1217.9 


1244.1 


1269.3 


1294.1 


1318.4 


1342.7 


1391.0 


1439.4 






n 1.5873 


1.6016 


1.6216 


1.6517 


1.6789 


1.7041 


1.7280 


1 . 7505 


1.7924 


1.8311 


140 


353.1 


v3.22 


3.32 


3.49 


3.75 


4.00 


4.24 


4.48 


4.71 


5.16 


5.61 






h 1192.2 


1204.3 


1221.4 


1248.0 


1273.3 


1298.2 


1322.6 


1346.9 


1395.4 


1443.8 






n 1.5747 


1.5894 


1.6096 


1.6395 


1.6666 


1.6916 


1.7152 


1.7376 


1 . 7792 


1.8177 


160 


363.6 


v2.83 


2.93 


3.07 


3.30 


3.53 


3.74 


3.95 


4.15 


4.56 


4.95 






h 1194.5 


1207.0 


1224.5 


1251.3 


1276.8 


1301.7 


1326.2 


1350.6 


1399.3 


1447.9 






n 1.5639 


1.5789 


1.5993 


1.6292 


1.6561 


1.6810 


1.7043 


1.7266 


1.7680 


1.8063 


180 


373.1 


v2.53 


2.62 


2.75 


2.96 


3.16 


3.35 


3.54 


3.72 


4.09 


4.44 






h 1196.4 


1209.4 


1227.2 


1254.3 


1279.9 


1304.8 


1329.5 


1353.9 


1402.7 


1451.4 






n 1.5543 


1.5697 


1.5904 


1.6201 


1.6468 


1.6716 


1.6948 


1.7169 


1.7581 


1.7962 


200 


381.9 


v2.29 


2.37 


2.49 


2.68 


2.86 


3.04 


3.21 


3.38 


3.71 


4.03 






h 1198.1 


1211.6 


1229.8 


1257.1 


1282.6 


1307.7 


1332.4 


1357.0 


1405.9 


1454.7 






n 1.5456 


1.5614 


1.5823 


1.6120 


1.6385 


1.6632 


1.6862 


1 . 7082 


1 . 7493 


1.7872 


220 


389.9 


v2.09 


2.16 


2.28 


2.45 


2.62 


2.78 


2.94 


3.10 


3.40 


3.69 






h 1199.6 


1213.6 


1232.2 


1259.6 


1285.2 


1310.3 


1335.1 


1359.8 


1408.8 


1457.7 






n 1.5379 


1.5541 


1.5753 


1.6049 


1.6312 


1.6558 


1 .6787 


1.7005 


1.7415 


1.7792 


240 


397.4 


v 1.92 


1.99 


2.09 


2.26 


2.42 


2.57 


2.71 


2.85 


3.13 


3.40 






h 1200.9 


1215.4 


1234.3 


1261.9 


1287.6 


1312.8 


1337.6 


1362.3 


1411.5 


1460.5 






n 1.5309 


1.5476 


1.5690 


1.5985 


1.6246 


1.6492 


1.6720 


1.6937 


1.7344 


1.7721 


260 


404.5 


vl.78 


1.84 


1.94 


2.10 


2.24 


2.39 


2.52 


2.65 


2.91 


3.16 






h 1202.1 


1217.1 


1236.4 


1264.1 


1289.9 


1315.1 


1340.0 


L64.7 


1414.0 


1463.2 






n 1.5244 


1.5416 


1.5631 


1.5926 


1.6186 


1.6430 


1.6658 


1.6874 


1 . 7280 


1.7655 


280 


411.2 


v 1.66 


1.72 


1.81 


1.95 


2.09 


2.22 


2.35 


2.48 


2.72 


2.95 






h 1203.1 


1218.7 


1238.4 


1266.2 


1291.9 


1317.2 


1342.2 


1367.0 


1416.4 


1465.7 






n 1.5185 


1.5362 


1.5580 


1.5873 


1.6133 


1.6375 


1.6603 


1.6818 


1.7223 


1 7597 


300 


417.5 


vl.55 


1.60 


1.69 


1.83 


1.96 


2.09 


2 21 


2.33 


2.55 


2.77 






h 1204.1 


1220.2 


1240.3 


1268.2 


1294.0 


1319.3 


1344.3 


1369.2 


1418.6 


1468.0 






n 1.5129 


1.5310 


.5530 


1.5824 


1.6082 


1.6323 


1.6550 


1.6765 


1.7168 


1.7541 


350 


431.9 


vl.33 


1.38 


.46 


1.58 


1.70 


1.81 


1.92 


?.02 


2.22 


2.41 






h 1206.1 


1223.9 


244.6 


1272.7 


1298.7 


1324.1 


1349.3 


1374.3 


1424 


1473.7 






n 1.5002 


1.5199 


.5423 


1.5715 


1.5971 


1.62f0 


1.6436 


1.6650 


1 . 7052 


1.7422 


400 


444.8 


v 1.17 


1.21 


.28 


1.40 


1.50 


1.60 


1.70 , 


1.79 


1.97 


2.14 






h 1207.7 


1227.2 


248.6 


1276.9 


1303.0 


1328.6 


353.9 


1379.1 


1429.0 


1478.9 






n 1.4894 


1.5107 


.5336 


1.5625 


1.5880 


1.6117 


.6342 


1.6554 


1.6955 


1.7323 


450 


456.5 


v 1.04 


1.08 


.14 


1.25 


1.35 


1.44 


.53 


1.61 


1.77 


1.93 






h 1209 


1231 


252 


1281 


1307 


1333 


-1358 


383 


1434 


1484 






n 1.479 


1.502 


.526 


1.554 


1.580 


1.603 


1,626 


1.647 


1.687 


1.723 


500 


467.3 


v0.93 


0.97 


.03 


1.13 


1.22 


1.31 


1.39 


.47 


1.62 


.76 






h 1210 


1233 


256 


1285 


1311 


1337 


1362 


388 


1438 


489 






n 1.470 


1.496 


.519 


1.548 


1.573 


1.597 


1.619 


.640 


1.679 


.715 



844 



FLOW OF STEAM. 



Flow of Steam through a Nozzle. (From Clark on the Steam- 
engine.) — The flow of steam of a greater pressure into an atmosphere of a 
less pressure increases as the difference of pressure is increased, until the 
external pressure becomes only 58% of the absolute pressure in the boiler. 
The flow of steam is neither increased nor diminished by the fall of the ex- 
ternal pressure below 58%, or about 4/ 7 of the inside pressure, even to 
the extent of a perfect vacuum. In flowing through a nozzle of the best 
form, the steam expands to the external pressure, and to the volume aue to 
this pressure, so long as it is not less than 58% of the internal pressure. 
For an external pressure of 58%, and for lower percentages, the ratio of 
expansion is 1 to 1 .624. 

When steam of varying initial pressures is discharged into the atmos- 
phere — the atmospheric pressure being not more than 58% of the initial 
pressure — the velocity of outflow at constant density, that is, supposing the 
initial density to be maintained, is given by the formula V = 3.5953 "^h' 
V = velocity in feet per second, as for steam of the initial density; 
h = the height in feet of a column of steam of the given initial pressure, 
the weight of which is equal to the pressure on the unit of base. 

The lowest initial pressure to which the formula applies, when the steam 
is discharged into the atmosphere at 14.7 lbs. per sq. in., is (14.7 X 100/58) 
= 25.37 lbs. per sq. in. 

From the contents of the table below it appears that the velocity of out- 
flow into the atmosphere, of steam above 25 lbs. per sq. in. absolute pres- 
sure, increases very slowly with the pressure, because the density, and the 
weight to be moved, increase with the pressure. An average of 900 ft. per 
sec. may, for approximate calculations, be taken for the velocity of out- 
flow as for constant density, that is, taking the volume of the steam at the 
initial volume. For a fuller discussion of this subject see "Steam Tur- 
bines, page 1065. 

Outflow of Steam into the Atmosphere. — External pressure per 
square inch, 14.7 lbs. absolute. Ratio of expansion in nozzle, 1.624. 





, 


«4H 


tM 


03 • 




, 


<*H 


, 


• 






O 


rt 






d 


o 


d 


t<oJ 


"* u 


i3i 


£ 


I* ". i 

£ 1 , 03 

O oaSS a 


ik * • 


is$ 


>> 


, °S 


a£~ 


Mi 

3 so rt 


2ii 

' 3 fe ° 

-3« 55 


"3 A 

> O 03 

cO a 


ftJaS 

oj a 

SB a; a? 

lis 


9 £ 03 

O g g, 

,Ol-H m 


=4-1 <$ £ 

111 


> O 03 

oO a 


ischarge pei 
square inch 
Orifice per 
ute. 


£0° 

I'o ". £ 

a. cPh_§ 


< 


> 


< 


Q 


w 


< 


> 


< 


P 


w 


lbs. 


feet 
p. sec. 


feet 
per sec . 


lbs. 


H.P. 


lbs. 


feet 
p.sec. 


feet 
per sec. 


lbs. 


H.P. 


25.37 


863 


1401 


22.81 


45.6 


90 


895 


1454 


77.94 


155.9 


30 


867 


1408 


26.84 


53.7 


100 


898 


1459 


86.34 


172.7 


40 


874 


1419 


35.18 


70.4 


115 


902 


1466 


98.76 


197.5 


50 


880 


1429 


44.06 


88.1 


135 


906 


1472 


115.61 


231.2 


60 


885 


1437 


52.59 


105.2 


155 


910 


1478 


132.21 


264.4 


70 


889 


1444 


61.07 


122.1 


165 


912 


1481 


140.46 


280.9 


75 


891 


1447 


65.30 


130.6 


215 


919 


1493 


181.58 


363.2 



Bateau's Formula. — A. Rateau, in 1895-6, made experiments with 
converging nozzles 0.41, 0.59 and 0.95 in. diam., on steam of pressures from 
1.4 to 170 lbs. per sq. in. In his paper read at the Intl. Eng'g. Congress at 
Glasgow (Eng. Rec, Oct. 16, 1901) he gives the following formula, appli- 
cable when the final pressure, absolute, is less than 58% of the initial. 
Pounds per hour per sq. in. area of orifice = 3.6 P (16.3 — 0.96 log P). 
P = absolute pressure, lbs. per sq. in. 

Napier's Approximate Rule. — Flow in pounds per second = ab- 
solute pressure X area in square inches ■*■ 70. This rule gives results 



FLOW OF STEAM. 845 



which closely correspond with those in the above table, and with results 
computed by Rateau's formula, as shown below. 

Abs. press., lbs. 

persq. in 25.37 40 60 75 100 135 165 215 

Discharge per min., 

by table, lbs.... 22.81 35.18 52.59 65.30 86.34 115.61 140.46 181.58 

By Rateau's for- 
mula 22.76 35.43 52.49 65.25 86.28 115.47 140.28 181 39 

By Napier's rule 21.74 34.29 51.43 64.29 85.71 115.71 141.43 184.29 

Flow of Steam in Pipes. — A formula formerly used for velocity of 
flow of steam in pipes is the same as Downi ng's for the flow of water in 
smooth cast-iron pipes, viz., V= 50 ^HD/L, in which V= velocity in feet 
per second, L = length and D = diameter of pipe in feet, H = height in 
feet of a column of steam, of the pressure of the steam at the entrance, 
which would produce a pressure equal to the difference of pressures at the 
two ends of the pipe. (For derivation of the coefficient 50, see Briggs on 
"Warming Buildings by Steam," Proc. Inst. C. E., 1882.) 

If Q = quantity in cubic feet per minute, d = diameter in inches, L and 
H being in feet, the formula reduces to 

Q = 4.7233 Jj^dK # = 0.0448^, d = 0.5374 W '^ • 

These formulae are applicable to air and other gases as well as steam. 
They are not as accurate as later formulae (see below) in which the coeffi- 
cients vary with the diameter of the pipe. G. H. Babcock, in "Steam," 
gives the formula 



W = 87 * /- 



w(pi — gg) d 5 

(V+¥)' 



W=weight of steam flowing, in lbs. per minute, ■u? = density in lbs. per 
cu. ft. of the steam at the entrance to the pipe, Pi = pressure in lbs. per sq. 
in. at the entrance, p 2 =pressure at the exit, rf = diam. in inches, L=length 
in feet. This formula is apparently derived from Unwin's formula for flow 
of fluids in Ency. B rit., vol. xii, pp . 508, 516. Putting the formula in 
the form W =c ^w (pi — pz) d 5 /L, in which c will vary with the diam- 
eter of the pipe, we have, 

For diameter, inches. . . 1 2 3 4 6 9 12 

Value of c 40.7 52.1 58.8 63 68.8 73. 7 79.3 

One of t he m ost widely accepted formulae for flow of water is Darcy's, 

in which c has values ranging from 65 for a 1/2-inch pipe 

up to 11 1.5 for 24-inch. Using Darcy's coefficients, and modifying his 
formula to make it apply to steam, to the form 



Ihd 

V = C VL4' 



Q = c |/ (Pl -P ,)dt ; or W= c y ^<Pi -*>»>* , 
we obtain, 

For diameter, inches ..1/2I 2 34 5 6 7 8 

Value of c 36.8 45.3 52.7 56.1 57.8 58.4 59.5 60.1 60.7 

For diameter, inches . . 9 10 12 14 16 18 20 22 24 

Value of c 61.2 61.8 62.1 62.3 62.6 62.7 62.9 63.2 63.2 

In the absence of direct experiments these coefficients are probably as 
accurate as any that may be derived from formulae for flow of water. 
. .. . Q 2 wL W*L 

Loss of pressure in lbs. per sq. in. = p\— p%= = - 2 • 

For a comparison of different formulae for flow of steam see a paper 
by G. F. Gebhardt, in Power, June, 1907, 



846 



STEAM. 



(-^'" — V0T1 



Pi) d b 
(1 + 3.6/d)' 



Table of Flow of Steam in Pipes of Different Diameters and 
Different Drops in Pressure. (E. C. Sickles, Trans. A. S. M. E., xx 
354.) — The drop is calculated from the f ormula p\ — p 2 = 0.000131 

Pi and p2, initial and final 

pressures, lbs. per sq. in., d = diam. in ins., W = flow in pounds per 
minute, w = density of steam in lbs. per cu. ft., L = length of pipe in feet. 
The table is calculated on the basis of L = 1000 ft. For any other length 
the drop is proportional to the length -f* 1000. 

Example in Use of the Table. — Required the size of pipe to carry 
2500 lbs. per min. of steam of 150 lbs. absolute pressure. In the first table 
we find figures above 2500 lbs. per 'min. as follows: 2667, 13-in. pipe, line 
2; 2736, 14-in. pipe, line 4; 2527, 15-in. pipe, line 8; 2638, 16-in. pipe, line 
10; 2623, 18-in. pipe, line 14. In the table on the next page, under 150 
lbs., we find the corresponding drops per 1000 ft. as follows : line 2, 9.60 lbs.; 
line 4, 6.83 lbs.; line 8, 4.10 lbs.; line 10, 3.19 lbs.; line 14, 1.72 lbs. 



Steam Discharge in Pounds per Minute. 

Corresponding to Drop in Pressure in table on the next page, for Pipe 
Diameters in Inches in Top Line. 



Line 

No. 


24 


22 


20 


18 


16 


15 


14 


13 


12 


11 


10 


1 


14000 


11188 


8772 


6678 


4923 


4163 


3481 


2871 


2328 


1853 


1443 


2 


13000 


10392 


8144 


6203 


4573 


3867 


3233 


2667 


2165 


1721 


1341 


3 


12000 


9593 


7517 


5724 


4220 


3569 


2983 


2461 


1996 


1589 


1237 


4 


11000 


8804 


6891 


5247 


3868 


3271 


2736 


2256 


1830 


1456 


1134 


5 


10000 


7992 


6265 


4770 


3517 


2974 


2486 


2051 


1663 


1324 


1031 


6 


9500 


7705 


5947 


4532 


3341 


2825 


2362 


1940 


1580 


1258 


979 


7 


9000 


7205 


5638 


4293 


3165 


2676 


2237 


1846 


1497 


1192 


928 


8 


8500 


6905 


5321 


4054 


2989 


2527 


2113 


1743 


1414 


1125 


876 


9 


8000 


6506 


5012 


3816 


2814 


2379 


1989 


1640 


1331 


1059 


825 


10 


7500 


6106 


4695 


3577 


2638 


2230 


1865 


1538 


1248 


993 


873 


11 


7000 


5707 


4385 


3339 


2462 


2082 


1740 


1435 


1164 


927 


722 


12 


6500 


5307 


4069 


3100 


2286 


1933 


1616 


1333 


1081 


860 


670 


13 


6000 


4908 


j 758 


2862 


2110 


1784 


1492 


1230 


998 


794 


619 


14 


5500 


4508 


3443 


2623 


1934 


1635 


1368 


1128 


915 


728 


567 


15 


5000 


4108 


3132 


2385 


1758 


1487 


1243 


1025 


832 


662 


516 



Steam Discharge for Pipe Diameters in Inches, Continued. 



Line 
No. 


9 


8 

799 


7 

560 


6 

371 


5 


4 


31/2 


3 
55.9 


21/2 


2 


H/2 


1 


1093 


227 


123 


71.6 


28.8 


18.1 


6.81 


2 


1015 


747. 


521 


344 


210 


114.6 


68.6 


51.9 


27.6 


16.8 


6.52 


3 


937 


685 


481 


318 


194 


106.0 


65.6 


47.9 


26.4 


15.5 


6.24 


4 


859 


67,8 


441 


292 


178 


97.0 


62.7 


43.9 


25.2 


14.2 


5.95 


5 


781 


571 


401 


265 


162 


88.2 


59.7 


39.9 


24.0 


12.9 


5.67 


6 


742 


547, 


381 


252 


154 


83.8 


56.5 


37.9 


22.8 


12.3 


5.29 


7 


703 


514 


361 


239 


146 


79.4 


53.5 


35.9 


21.6 


11.6 


5.00 


8 


664 


485 


341 


226 


138 


75.0 


50.5 


33.9 


20.4 


10.9 


4.72 


9 


625 


457 


321 


212 


130 


70.6 


47.6 


31.9 


19.2 


10.3 


4.43 


10 


586 


478 


301 


199 


122 


66.2 


44.5 


23.9 


18.0 


9.68 


4.15 


11 


547 


400 


7.81 


186 


113 


61.7 


41.6 


27.9 


16.8 


9.03 


3.86 


12 


508 


371 


7.61 


172 


105 


57.3 


38.6 


25.9 


15.6 


8.38 


3.68 


13 


469 


343 


741 


159 


97.2 


52.9 


35.6 


23.9 


14.4 


7.74 


3.40 


14 


430 


314 


7.21 


146 


89.1 


48.5 


32.6 


21.9 


13.2 


7.10 


3.11 


15 


390 


286 


200 


132 


81.0 


44.1 


29.6 


20.0 


12.0 


6.45 


2.83 



2.52 
2.34 
2.16 
1.98 
1.80 
1.71 
1.62 
1.53 
1.44 
1.35 
1.26 
1.17 
1.08 
0.99 
0.90 



FLOW OF STEAM 



847 



Drop in Pressure in Pounds per Sq. In., per 1000 Ft. Length. 
Corresponding to Discharge in above Table. 



Density * 


0.208 


0.230 


0.273 


0.295 


0.316 


0.338 


0.401 


0.443 


0.485 


0.548 


Pressuref 


90 


100 


120 


130 


140 


150 


180 


200 


220 


250 


Line. 1 


18.10 


16.4 


13.8 


12.8 


11.9 


11.1 


9.39 


8.50 


7.76 


6.87 


2 


15.60 


14.1 


11.9 


11.0 


10.3 


9.60 


8.09 


7.33 


6.69 


5.92 


3 


13.3 


12.0 


10.1 


9.38 


8.75 


8.18 


6.90 


6.24 


5.70 


5.05 


4 


11.1 


10.0 


8.46 


7.83 


7.31 


6.83 


5.76 


5.21 


4.76 


4.21 


5 


9.25 


8.36 


7.5 


6.52 

5.87 


6.09 


5.69 


4.80 


4.34 


3.97 


3.51 


6 


8.33 


7.53 


6.35 


5.48 


5.13 


4.32 


3.91 


3.57 


3.16 


7 


7.48 


6.76 


5.70 


5.27 


4.92 


4.60 


3.88 


3.51 


3 21 


2.84 


8 


6.67 


6.03 


5.08 


4.70 


4.39 


4.10 


3.46 


3.13 


2.86 


2.53 


9 


5.91 


5.35 


4.50 


4.17 


3.89 


3.64 


3.07 


2.78 


2.53 


2.24 


10 


5.19 


4.69 


3.95 


3.66 


3.42 


3.19 


2.69 


2.44 


2 ?,3 


1.97 


11 


4.52 


4.09 


3.44 


3.19 


2.98 


2.78 


2.34 


2.12 


1.94 


1.72 


12 


3.90 


3.53 


2.97 


2.75 


2.57 


2.40 


2.02 


1.83 


1.67 


1.48 


13 


3.32 


3.00 


2.53 


2.34 


2.19 


2.04 


1.72 


1.56 


1.42 


1.26 


14 


2.79 


2.52 


2.13 


1.97 


1.84 


1.72 


1.45 


1.31 


1.20 


1.06 


15 


2.31 


2.09 


1.76 


1.63 


1.52 


1.42 


1.20 


1.C8 


0.991 


0.877 



* Density in lbs. per cu. ft. 



t Pressure, absolute, 



For Flow of Steam at low pressures, see Heating and Ventilation, 
page 670. 

Carrying Capacity of Extra Heavy Steam Pipes. 

(Power Speciality Co.) 





. 03 


200 


150 


100 


50 




, C3 ■ 


200 


150 


100 . 


50 


a o— 


.5 £,c 


lbs. 


lbs. 


lbs. 


lbs. 


co— 1 

1.3 & 


— . c3 ■ 

3 (U co 


lbs. 


lbs. 


lbs. 


lbs. 






Pounds of steam 
hour. 


per 


Pounds of steam per 
hour. 


i 


0.71 


1210 


872 


618 


362 


6 


25.93 


40800 


31600 


22600 


13210 


11 '4 


1.27 


2000 


1555 


1105 


646 


7 


34.47 


54600 


42250 


30000 


17600 


i*'2 


1.75 


2750 


2140 


1525 


894 


8 


44.18 


69500 


54000 


38400 


22450 


2 


2.93 


4610 


3590 


2550 


1525 


9 


58.42 


92000 


71500 


50800 


29800 


21/2 


4.20 


6610 


5150 


3660 


2140 


10 


74.66 


117300 


91500 


65000 


38100 


3 


6.56 


10300 


8050 


5720 


3450 


11 


90.76 


142800 


111500 


79200 


46300 


31/2 


8.85 


13900 


10820 


7720 


4520 


12 


1 08.45 


170500 


133000 


94750 


55400 


4 


11.44 


18000 


14000 


10000 


5850 


14 


153.94 


242000 


1 88200 


133900 


78600 


41/2 


14.18 


22300 


17350 


12320 


7230 


16 


176.71 


277500 


216200 


153800 


90500 


5 


18.19 


28610 


22250 


15800 


9300 


18 


226.98 


357000 


278000 


197500 


115700 



The pounds per hour in the above table are figured for the velocities 
given below: 



Steam superheated degrees F. . . 
Velocity, ft. per min 8000 



50 
8500 



100 
8950 



150" 
9450 



200 250 
9900 10450 



Flow of Steam in Long Pipes. Ledoux's Formula. — In the flow 
of steam or other gases in long pipes, the volume and the velocity are 
increased as the drop in pressure increases. Taking this into account a 
correct form ula for flow would be an exponential one. Ledoux gives 

notation being reduced to English meas- 
ures. (Annates des Mines, 1892; Trans. A. S. M. E., xx., 365; Power, June, 
1907.) See Johnson's formula for flow of air, page 596. 



4 / W 2 L 
d = 0.699 y pil . 94 _ p2l . 94 , his 



848 STEAM. 

Resistance to Flow by Bends, Valves, etc. (From Briggs on 
Warming Buildings by Steam.) — The resistance at the entrance to a 
tube when no special bell-mouth is given consists of two parts. The 
head v 2 -4- 2g is expended in giving the velocity of flow; and the head 
0.505 v 2 -h2# in overcoming the resistance of the mouth of the tube. 
Hence the whole loss of head at the entrance is 1.505 v 2 ■+ 2g. This resist- 
ance is equal to the resistance of a straight tube of a length equal to about 
60 times its diameter. 

The loss at each sharp right-angled elbow is the same as in flowing 
through a length of straight tube equal to about 40 times its diameter. 
For a globe steam stop- valve the resistance is taken to be 1 1/2 times that 
of the right-angled elbow. 

Sizes of Steam-pipes for Stationary Engines. — An old common 
rule is that steam-pipes supplying engines should be of such size that the 
mean velocity of steam in them does not exceed 6000 feet per minute, in 
order that the loss of pressure due to friction may not be excessive. The 
velocity is calculated on the assumption that the cylinder is filled at each 
stroke. In modern practice with large engines and high pressures, this 
rule gives unnecessarily large and costly pipes. For such engines the 
allowable drop in steam pressure should be assumed and the diameter 
calculated by means of the formulae given above. 

An article in Power, May, 1893, on proper area of supply-pipes for 
engines gives a table showing the practice of leading builders. To facili- 
tate comparison, all the engines have been rated in horse-power at 40 
pounds mean effective pressure. The table contains all the varieties of 
simple engines, from the slide-valve to the Corliss, and it appears that 
there is no general difference in the sizes of pipe used in the different types. 

The averages selected from this table are as follows: 

Diameters of Cylinders corresponding to Various Sizes of Steam- 
pipes based on Piston-speed of Engine of 600 ft. per Minute, 
and Allowable Mean Velocity of Steam in Pipe of 4000, 6000, 
and 8000 ft. per mln. (steam assumed to be admitted during 
Full Stroke.) 

Diam. of pipe, inches 2 21/2 3 31/2 4 41/2 5 6 

Vel. 4000 5.2 6.5 7.7 9.010.311.612.915.5 

Vel. 6000 6.3 7.9 9.511.112.614.215.819.0 

Vel. 8000 7.3 9.110.9 12.8 14.6 16.4 18.3 21.9 

Horse-power, approx 20 31 45 62 80 100 125 180 

Diam. of pipes, inches ... 7 8 9 10 11 12 13 14 

Vel. 4000 18.1 20.7 23.2 25.8 28.4 31.0 33.6 36.1 

Vel. 6000 22.1 25.3 28.5 31.6 34.8 37.9 41.1 44.3 

Vel. 8000 25.6 29.2 32.9 36.5 40.2 43.8 47.5 51 1 

Horse-power, approx 245 320 406 500 606 718 845 981 

_, , „ . Area of cylinder X piston-speed 

Formula. Area of pipe = r^-rr t— - : — —. — • 

mean velocity of steam in pipe 

For piston-speed of 600 ft. per min. and velocity in pipe of 4000, 6000, 
and 8000 ft. per min., area of pipe = respectively 0.15, 0.10, and 0.075 X 
area of cylinder. Diam. of pipe = respectively 0.3873, 0.3162, and 0.2739 X 
diam. of cylinder. Reciprocals of these figures are 2.582, 3.162, and 
3.651. 

The first line in the above table may be used for proportioning exhaust 
pipes, in which a velocity not exceeding 4000 ft. per minute is advisable. 
The last line, approx. H.P. of engine, is based on the velocity of 6000 ft. 
per min. in the pi pe, using the correspond ing diameter of piston, and 
taking H.P. = 1/2 (diam. of piston in inches) 2 . 

Sizes of Steam-pipes for Marine Engines. — In marine-engine 
practice the steam-pipes are generally not as large as in stationary practice 
for the same sizes of cylinder. Seaton gives the following rules: 

Main Steam-vives should be of such size that the mean velocity of flow 
does not exceed 8000 ft. per min. 

In large engines, 1000 to 2000 H.P., cutting off at less than half stroke, 
the steam-pipe may be designed for a mean velocity of 9000 ft., and 
10,000 ft. for still larger engines. 



FLOW OF STEAM. 



849 



In small engines and engines cutting off later than half stroke, a velocity 
of less than 8000 ft. per minute is desirable. 

Taking 8100 ft. per min. as the mean velocity, S speed of piston in feet 
per min., and D the diameter of the cylinder, 

Diam. of main steam-pipe = >/D 2 S -*- 8100 = D Vs -4- 90. 

Stop and Throttle Valves should have a greater area of passages than the 
area of the main steam-pipe, on account of the friction through the cir- 
cuitous passages. The shape of the passages should be designed so as to 
avoid abrupt changes of direction and of velocity of flow as far as possible. 

Area of Steam Ports and Passages = 

Area of piston X speed of piston in ft. per min. _ (Diam.) 2 X speed 
6000 ~ 7639 

Opening of Port to Steam. — To avoid wire-drawing during admission 
the area of opening to steam should be such that the mean velocity of 
flow does not exceed 10,000 ft. per min. To avoid excessive clearance 
the width of port should be as short as possible, the necessary area being 
obtained by length (measured at right angles to the line of travel of the 
valve). In practice this length is usually 0.6 to 0.8 of the diameter of 
the cylinder, but in long-stroke engines it may equal or even exceed the 
diameter. 

Exhaust Passages and Pipes. — The area should be such that the mean 
velocity of the steam should not exceed 6000 ft. per min., and the area 
should be greater if the length of the exhaust-pipe is comparatively long. 
The area of passages from cylinders to receivers should be such that the 
velocity will not exceed 5000 ft. per min. 

The following table is computed on the basis of a mean velocity of flow 
of 8000 ft. per min. for the main steam-pipe, 10,000 for opening to steam, 
and 6000 for exhaust. A = area of piston, D its diameter. 





Steam and Exhaust Openings. 




Piston- 


Diam. of 


Area of 


Diam. of 


Area of 




speed, 


Steam-pipe 


Steam-pipe 


Exhaust 


Exhaust 


to Steam 


ft. per min. 


+ D. 


-h .4. 


h- D. 


+ A. 


h- A. 


300 


0.194 


0.0375 


0.223 


0.0500 


0.03 


400 


0.224 


0.0500 


0.258 


0.0667 


0.04 


500 


0.250 


0.0625 


0.288 


0.0833 


0.05 


600 


0.274 


0.0750 


0.316 


0.1000 


0.06 


700 


0.296 


0.0875 


0.341 


0.1167 


0.07 


800 


0.316 


0.1000 


0.365 


0.1333 


0.08 


900 


0.335 


0.1125 


0.387 


0.1500 


0.09 


1000 


0.353 


0.1250 


0.400 


0.1667 


0.10 



Proportioning Steam-Pipes for Minimum Total Loss by Radiation 
and Friction. — For a given size of pipe and quantity of steam to be 
carried the loss of pressure due to friction is calculated by formulae given 
above, or taken from the tables. The work of friction, being converted 
into heat, tends to dry or superheat the steam, but its influence is usually 
so small that it may be neglected. The loss of heat by radiation tends to 
destroy the superheat and condense some of the steam into water. For 
well-covered steam-pipes this loss may be estimated at about 0.3 lb. per sq. 
ft. of external surface of the pipe per hour per degree of difference of 
temperature between that of the steam and that of the surrounding 
atmosphere (see Steam-pipe Coverings, p. 558). 

A practical problem in power-plant design is to find the diameter of 
pipe to carry a given quantity of steam with a minimum total loss of 
available energy due to both radiation and friction, considering also the 
money loss due to interest and depreciation on the value of the pipe 
and covering as erected. Each case requires a separate arithmetical 
computation, no formula yet being constructed to fit the general case. 
An approximate method of solution, neglecting the slight gain of heat by 



850 



the steam from the work of friction, and assuming that the water con- 
densed by radiation of heat is removed by a separator and lost, is as fol- 
lows: Calculate the amount of steam required. by the engine, in pounds 
per minute. From a steam pipe formula or table find the several drops 
of pressure, in lbs. per sq. in., in pipes of different assumed diameters, for 
the given quantity of steam and the given length of pipe. Compute from 
a theoretical indicator diagram of steam expanding in the engine the loss 
of available work done by 1 lb. of steam, due to the several drops already 
found, and the corresponding fraction of 1 lb. of steam that will have to 
be supplied to make up for this loss of work. State this loss as equiva- 
lent to so many pounds of steam per 1000 lbs. of steam carried. Calcu- 
late the loss in lbs. of steam condensed by radiation in the pipes of the 
different diameters, per 1000 lbs. carried. Add the two losses together 
for each assumed size of pipe, and by inspection find which pipe gives the 
lowest total loss. The money loss due to cost and depreciation may also 
be figured approximately in the same unit of lbs. of steam lost per 1000 
lbs. carried, by taking the cost of the covered pipe, assuming a rate of 
interest and depreciation, finding the annual loss in cents, then from the 
calculated value of steam, which depends on the cost of fuel, find the 
equivalent quantity of steam which represents this money loss, and 
the equivalent lbs. of steam per 1000 lbs. carried. This is to be added to 
the sum of the losses due to friction and radiation, and it will be found to 
modify somewhat the conclusion as to the diameter of pipe and the drop 
which corresponds to a minimum total loss. 

Instead of determining the loss of available work per pound of steam 
from theoretical indicator diagrams, it may be computed approximately 
on the assumption, based on the known characteristics of the engine, 
that its efficiency is a certain fraction of that of an engine working between 
the same limits of temperature on the ideal Carnot cycle, as shown in 
the table below, and from the efficiency thus found, compared with the 
efficiency at the given initial pressure less the drop, the loss of work may 
be calculated. 



Available Maximum Thermal Efficiency of Steam Expanded 
between the glven pressures and 1 lb. absolute, based on 
the Carnot Cycle. E = (Ti - T 2 ) -*■ Tu 





Maximum Initial Absolute Pressures. 


Initial Pressure 
less than Maxi- 
mum. 


100 


125 


150 


175 


200 


225 


250 


275 


300 




Maximum Thermal Efficiency. 


lbs. 



0.287 
.286 
.284 
.280 
.272 


0.302 
.301 
.299 
.296 
.290 


0.314 
.313 
.312 
.309 
.304 


0.324 
.323 
.322 
.320 
.316 


0.333 
.332 
.331 
.329 

.326 


0.341 
.340 
.339 
.337 
.335 


0.348 
.347. 
.346 
.345 

.342 


0.354 
.354 
.353 
.352 
.349 


0.360 


2 


.359 


5 


.359 


10 


.358 


20 


.356 







This table shows that if the initial steam pressure is lowered from 
100 lbs. to 80 lbs., the efficiency of the Carnot cycle is reduced from 
0.237 to 0.272, or over 5%, but if steam of 300 lbs. is lowered to 280 lbs. 
the efficiency is reduced only from 0.360 to 0.356 or 1.1%. Witn high- 
pressure steam, therefore, much greater loss of pressure by friction of 
steam pipes, valves and ports is allowable than with steam of low pressure. 

Theoretically the loss of efficiency due to drop in pressure on account 
of friction of pipes should be less than that indicated in the above table, 
since the work of friction tends to superheat the steam, but practically 
most, if not all. of the superheating is lost by radiation. 

By a method of calculation somewhat similar to that above outlined, 
the following figures were found, in a certain case, of the cost per day of 
the transmission of 50,000 lbs. of steam per hour a distance of 1000 feet, 
with 100 lbs. initial pressure. 



STEAM PIPES. 



851 



Diameter of Pipe. 


6 in. 


7 in. 


8 in. 


10 in. 


12 in. 


I. Interest, etc., 12% per annum. . 


$0.39 
1.51 
0.86 


$0.46 
1.76 
0.38 


$0.53 
2.01 
0.19 


$0.66 
2.51 
0.06 


$0.84 
3 02 




02 






Total per day 


$2.76 


$2.60 


$2.73 


$3.23 


$3.88 



STEAM PIPES. 

Bursting-tests of Copper Steam-pipes. (From Report of Chief 
Engineer Melville, U. S. N., for 1892.) — Some tests were made at the 
New York Navy Yard which show the unreliability of brazed seams in 
copper pipes. Each pipe was 8 in. diameter inside and 3 ft. 1 5/ 8 in. long. 
Both ends were closed by ribbed heads and the pipe was subjected to a 
hot-water pressure, the temperature being maintained constant at 371° F. 
Three of the pipes were made of No. 4 sheet copper (Stubs gauge) and the 
fourth was made of No. 3 sheet. 

The following were the results, in lbs. per sq. in., of bursting-pressure: 

Pipe number 1 2 3 4 4' 

Actual bursting-strength . . 835 785 950 1225 1275 

Calculated " V 1336 1336 1569 1568 1568 

Difference 501 551 619 343 293 

The tests of specimens cut from the ruptured pipes show the injurious 
action of heat upon copper sheets; and that, while a white heat does not 
change the character of the metal, a heat of only slightly gi eater degree 
causes it to lose the fibrous nature that it has acquired in rolling, and a 
serious reduction in its tensile strength and ductility results. 

A Failure of a Brazed Copper Steam-pipe on the British steamer 
Prodano was investigated by Prof. J. O. Arnold. He found that the 
brazing was originally sound, but that it had deteriorated by oxidation 
of the zinc in the brazing alloy by electrolysis, which was due to the 
presence of fatty acids produced by decomposition of the oil used in the 
engines. A full account of the investigation is given in The Engineer, 
April 15, 1898. 

Reinforcing Steam-pipes. (Eng., Aug. 11, 1893.) — In the Italian 
Navy copper pipes above 8 in. diam. are reinforced by wrapping them with 
a close spiral of copper or Delta-metal wire. Two or three independent 
spirals are used for safety in case one wire breaks. They are wound at a 
tension of about 11/2 tons per sq. in. 

Materials for Pipes and Valves for Superheated Steam. (M. W. 
Kellogg, Trans. A. S. M. E., 1907.) — The latest practice is to do away 
with fittings entirely on high-pressure steam lines and put what are known 
as "nozzles" on the piping itself. This is accomplished by welding 
wrought-steel pipe on the side of another section, so as to accomplish 
the same result as a fitting. In this way rolled or cast steel flanges and a 
Rockwood or welded joint can be used. This method has three distinct 
advantages: 1. The quality of the metal used. 2. The lightening of the 
entire work. 3. The doing away with a great many joints. 

As a general average, at least 50% of the joints can be left out; some- 
times the proportion runs up as high as 70%. 

Above 575° F. the limit of elasticity in cast .iron is reached with a 
pressure varying from 140 to 175 pounds. Under such conditions the 
material is strained and does not resume its former shape, eventually 
showing surface cracks which increase until the pipe breaks. 

It would seem that iron castings are unsuitable for both fittings and 
valves to be used in any superheated steam work. The only adaptable 
metal seems to be cast steel. Tests by Bach on this metal show that at 
572° F. the reduction in breaking strength amounts only to 1.1% and at 
752° F. to about 8%. 

The effect of temperature on nickel is similar to that on cast steel and 
in consequence this material is very suitable for use in connection with 



852 



highly superheated steam. Bach recommends that bronze alloys be 
done away with for use on steam lines above a temperature of about 
390° F. 

The old-fashioned screwed joint, no matter how well made, is not 
suitable for superheated steam work. 

In making up a joint, the face of all flanges or pipe where a joint is made 
should be given a fine tool finish and a plane surface, and a gasket should 
be used. The best results have been obtained with a corrugated soft 
Swedish steel gasket with "Smooth-on" applied, and with the McKim 
gasket, which is of copper or bronze surrounding asbestos. On super- 
heated steam lines a corrugated copper gasket will in time pit out in 
some part of the flange nearly through the entire gasket. 

Specifications for pipes and fittings for superheated steam service were 
published by Crane Co., Chicago, in the Valve World, 1907. 

Riveted Steel Steam-pipes have been used for high pressures. See 
paper on A Method of Manufacture of Large Steam-pipes, by Chas. H. 
Manning, Trans. A. S. M. E., vol. xv. 

Valves in Steam-pipes. — ■ Should a globe- valve on a steam-pipe have 
the steam-pressure on top or underneath the valve is a disputed question. 
With the steam-pressure on top, the stuffing-box around the valve-stem 
cannot be repacked without shutting off steam from the whole line of 
pipe; on the other hand, if the steam-pressure is on the bottom of the 
valve it all has to be sustained by the screw-thread on the valve-stem, 
and there is danger of stripping the thread. 

A correspondent of the American Machinist, 1892, says that it is a very 
uncommon thing in the ordinary globe-valve to have the thread give out, 
but by water-hammer and merciless screwing the seat will be crushed 
down quite frequently. Therefore with plants where only one boiler is 
used he advises placing the valve with the boiler-pressure underneath it. 
On plants where several boilers are connected to one main steam-pipe 
he would reverse the position of the valve, then when one of the valves 
needs repacking the valve can be closed and the pressure in the boiler 
whose pipe it controls can be reduced to atmospheric by lifting the safety- 
valve. The repacking can then be done without interfering with the 
operation of the other boilers of the plant. 

He proposes also the following other rules for locating valves: Place 
valves with the stems horizontal to avoid the formation of a water-pocket. 
Never put the junction-valve close to the boiler if the main pipe is above 
the boiler, but put it on the highest point of the junction-pipe. If the other 
plan is followed, the pipe fills with water whenever this boiler is stopped 
and the others are running, and breakage of the pipe may cause serious 
results. Never let a junction-pipe run into the bottom of the main pipe, 
but into the side or top. Always use an angle- valve where convenient, 
as there is more room in them. Never use a gate valve under high pressure 
unless a by-pass is used with it. Never open a blow-off valve on a boiler 
a little and then shut it; it is sure to catch the sediment and ruin the 
valve; throw it well open before closing. Never use a globe-valve on an 
indicator-pipe. For water, always use gate or angle valves or stop-cocks 
to obtain a clear passage. Buy if possible valves with renewable disks. 
Lastly, never let a man go inside a boiler to work, especially if he is to 
hammer on it, unless you break the joint between the boiler and the 
valve and put a plate of steel between the flanges. 

The " Steam-Loop " is a system of piping by which water of con- 
densation in steam-pipes is automatically returned to the boiler. In its 
simplest form it consists of three pipes, which are called the riser, the 
horizontal, and the drop-leg. When the steam-loop is used for returning 
to the boiler the water of condensation and entrainment from the steam- 
pipe through which the steam flows to the cylinder of an engine, the riser 
is generally attached to a separator; this riser empties at a suitable 
height into the horizontal, and from thence the water of condensation is 
led into the drop-leg, which is connected to the boiler, into which the 
water of condensation is fed as soon as the hydrostatic pressure in the 
drop-leg in connection with the steam-pressure in the pipes is sufficient to 
overcome the boiler-pressure. The action of the device depends on the 
following principles: Difference of pressure may be balanced by a water- 
column; vapors or liquids tend to flow to the point of lowest pressure; 
rate of flow depends on difference of pressure and mass; decrease of static 
pressure in a steam-pipe or chamber is proportional to rate of conden- 



STEAM PIPES. 853 

sation; in a steanvcurrent water will be carried or swept along rapidly 
by friction. (Illustrated in Modern Mechanism, p. 807. Patented by 
J. H. Blessing, Feb. 13, 1872, Dec. 28, 1883.) Mr. Blessing thus describes 
the operation of the loop in Eng. Review, Sept., 1907. 

The heating system is so arranged that the water of condensation from 
the radiators gravitates towards some low point and thence is led into the 
top of a receiver. After this is done it is found that owing to friction 
caused by the velocity of the steam passing through the different pipes 
and condensation due to radiation, the steam pressure in the small drip 
receiver is much less than that in the boiler. This difference will deter- 
mine the height, or the length of the loop, that must be employed so that 
the water will gravitate through it into the boiler; that is to say, if there is 
10 lbs. difference in pressure, the descending leg of the loop should extend 
about 30 feet above the water-level in the boiler, since a column of water 
2.3 ft. is equal to 1 lb. pressure, and a difference in pressure of 10 lbs. 
would require a column 23 ft. high. If we make the loop 30 feet high 
we shall have an additional length of 7 ft. with which to overcome fric- 
tion. The water, after it reaches the top of the loop, composed of a 
larger section of pipe, will flow into the boiler through the descending 
leg with a velocity due to the extra 7 ft. added to the discharging leg. 

Loss from an Uncovered Steam-pipe. (Bjorling on Pumping- 
engines.) — The amount of loss by condensation in a steam-pipe carried 
down a deep mine-shaft has been ascertained by actual practice at the 
Clay Cross Colliery, near Chesterfield, where there is a pipe 71/2 in. internal 
diam., 1100 ft. long. The loss of steam by condensation was ascertained 
by direct measurement of the water deposited in a receiver, and was found 
to be equivalent to about 1 lb. of coal per I.H.P. per hour for every 100 ft. 
of steam-pipe; but there is no doubt that if the pipes had been in the up- 
cast shaft, and well covered with a good non-conducting material, the loss 
would have been less. (For Steam-pipe Coverings, see p. 558, ante.) 

Condensation in an Underground Pipe Line. (W. W. Christie, 
Eng. Rec, 1904.) — A length of 300 ft. of 4-in. pipe, enclosed in a box 
of 11/4-in. planks, 10 ins. square inside, and packed with mineral wool, 
was laid in a trench, the upper end being 1 ft. and the lower end 5 ft. below 
the surface. With 80 lbs. gauge pressure in the pipe the condensation 
was equivalent to 0.275 B.T.U. per minute per sq. ft. of pipe surface 
when the outside temperature was 31° F., and 0.222 per min. when the 
temperature was 62° F. 

Steam Receivers on Pipe Lines. (W. Andrews, Steam Eng'g, Dec. 
10, 1902.) — In the four large power houses in New York City, with 
an ultimate capacity of 60,000 to 100,000 H.P. each, the largest steam 
mains are not over 20 ins. in diameter. Some of the best plants have 
pipes which run from the header to the engine two sizes smaller than that 
called for by the engine builders. These pipes before reaching the engine 
are carried into a steel receiver, which acts also as a separator. This 
receiver has a cubical capacity of three times that of the high-pressure 
cylinder and is placed as close as possible to the cylinder. The pipe from 
the receiver to the cylinder is of the full size called for by the engine 
builder. The objects of this arrangement are: First, to have a full supply 
of steam to the throttle; second, to provide a cushion near the engine on 
which the cut-off in the steam chest may be spent, thereby preventing 
vibrations from being transmitted through the piping system; and 
third, to produce a steady and rapid flow of steam in one direction only, 
by having a small pipe leading into the receiver. The steam flows 
rapidly enough to make good the loss caused during the first quarter of 
the stroke. Plants fitted up in this way are successfully running where 
the drop in steam pressure is not greater than 4 lbs., although the engines 
are 500 ft. away from the boilers. 

Equation of Pipes. — For determining the number of small sized 
pipes that are equal in carrying capacity to one of greater size the table 
given under Flo w of Air, page 597, is commonly used. It is based on the 
equation N = ^d^-^di 5 , in which N is the number of smaller pipes of 
diameter di equal in capacity to one pipe of diameter d. A more 
accu rate equ ation, based on Unwin's formula for flow of fluids, is N = 

- — f 1+ °' 6 ; (d and di in inches). For d= 2 d\, the first formula gives 
di 3 Vd + 3.6 



854 



THE STEAM-BOILER. 



N = 5.7, and the second N = 6.15, an unimportant difference, but for 
d == 8 c/i, the first gives N = 181 and the second N = 274, a considerable 
difference. (G. F. Gebhardt, Power, June, 1907). 

Identification of Power House Piping by Different Colors. (W. 

H. Bryan, Trans. A. S. M. E., 1908.) — In large power plants the multi- 
plicity of pipe lines carrying different fluids causes confusion and may 
lead to danger by an operator opening a wrong valve. It has therefore 
become customary to paint the different lines of different colors. The 
paper gives several tables showing color schemes that have been adopted 
in different plants. The following scheme, adopted at the New York 
Edison Co.'s Waterside Station, is selected as an example. 



Pipe Lines. 



Steam, high pressure to engines, boiler 

cross-overs, leaders and headers 

All other steam lines 

Steam, exhaust 

Steam, drips including traps 

Steam trap discharge 

Blow-offs, drips from water columns 

and low-pressure drips 

Drains from crank pits 

Cold water to primary heaters and 

jacket pumps 

Feed-water, pumps to boilers 

Hot-water mains, primary heaters to 

pumps, and cooling-water returns .... 

Air pump discharge to hot well 

Cooling water, pumps to engines 

Fire lines 

Cylinder oil, high pressure 

Cylinder oil, low pressure 

Engine oil 

Pneumatic system 





Bands, Cou- 


Colors of Pipe. 


plings, Valves, 




etc. 


Black 


Brass 


Buff 


Black 


Orange 


Red 


Orange 


Black 


Green 


Black 


Slate 


Red 


Dark Brown 


Blue 


Blue 


Red 


Maroon 


Same 


Green 


Red 


Slate 


Black 


Blue 


Black 


Vermilion 


Same 


Brown 


Black 


Brown 


Green 


Brown 


Red 


Black 


Same 



THE STEAM-BOILER. 

The Horse-power of a Steam-boiler. — The term horse-power has 
two meanings in engineering: First, an absolute unit or measure of the rate 
of work, that is, of the work done in a certain definite period of time, by 
a source of energy, as a steam-boiler, a waterfall, a current of air or water, 
or by a prime mover, as a steam-engine, a water-wheel, or a wind-mill. 
The value of this unit, whenever it can be expressed in foot-pounds of 
energy, as in the case of steam-engines, water-wheels, and waterfalls, is 
33,000 foot-pounds per minute. In the case of boilers, where the work 
done, the conversion of water into steam, cannot be expressed in foot- 
pounds of available energy, the usual value given to the term horse-power 
is the evaporation of 30 lbs. of water of a temperature of 100° F. into 
steam at 70 lbs. pressure above the atmosphere. Both of these units are 
arbitrary; the first, 33,000 foot-pounds per minute, first adopted by James 
Watt, being considered equivalent to the power exerted by a good London 
draught-horse, and the 30 lbs. of water evaporated per hour being con- 
sidered to be the steam requirement per indicated horse-power of an 
average engine. 

The second definition of the term horse-power is an approximate measure 
of the size, capacity, value, or "rating" of a boiler, engine, water-wheel, or 
other source or conveyer of energy, by which measure it may be described, 
bought and sold, advertised, etc. No definite value can be given to this 
measure, which varies largely with local custom or individual opinion of 
makers and users of machinery. The nearest approach to uniformity 
which can be arrived at in the term "horse-power," used in this sense, is 
to say that a boiler, engine, water-wheel, or 'other machine, "rated" at a 



STEAM-BOILER PROPORTIONS. 855 

certain horse-power, should be capable of steadily developing that horse- 
power for a long period of time under ordinary conditions of use and 
practice, leaving to local custom, to the judgment of the buyer and seller, 
to written contracts of purchase and sale, or to legal decisions upon such 
contracts, the interpretation of what is meant by the term "ordinary 
conditions of use and practice." (Trans. A. S. M. E., vol. vii, p. 226.) 

The Committee of Judges of the Centennial Exhibition, 1876, in report- 
ing the trials of competing boilers at that exhibition adopted the unit, 
30 lbs. of water evaporated into dry steam per hour from feed-water at 
100° F., and under a pressure of 70 lbs. per square inch above the atmos* 
phere, these conditions being considered by them to represent fairly 
average practice. 

The A. S. M. E. Committee on Boiler Tests, 1884, accepted the same 
unit, and defined it as equivalent to 34.5 lbs. evaporated per hour from a 
feed-water temperature of 212° into steam at the same temperature; 
The committee of 1899 adopted this definition, 34.5 lbs. per hour, from 
and at 212°, as the unit of commercial horse-power. Using the figures 
for total heat of steam given in Marks and Davis's steam tables (1909), 
34V2 lbs. from and at 212°, is equivalent to 33,479 B.T.U. per hour, or to 
an evaporation of 30.018 lbs. from 100° feed-water temperature into 
steam at 70 lbs. pressure. 

The Committee of 1899 says: A boiler rated at any stated capacity 
should develop that capacity when using the best coal ordinarily sold in 
the market where the boiler is located, when fired by an ordinary fireman, 
without forcing the fires, while exhibiting good economy; and further, the 
boiler should develop at least one-third more than the stated capacity 
when using the same fuel and operated by the same fireman,. the full 
draught being employed and the fires being crowded; the available draught 
at the damper, unless otherwise understood, being not less than 1/2 inch 
water column. 

Unit of Evaporation. (Abbreviation, U. E.) — It is the custom to 
reduce results of boiler-tests to the common standard of the equivalent 
evaporation from and at the boiling-point at atmospheric pressure, or 
" from and at 212° F." This unit of evaporation, or one pound of water 
evaporated from and at 212°, is equivalent to 970.4 British thermal 
units. 1 B.T.U. = the mean quantity of heat required to raise 1 lb. of 
water 1° F. between 32° and 212°. 

Measures for Comparing the Duty of Boilers. — The measure of 
the efficiency of a boiler is the number of pounds of water evaporated per 
pound of combustible (coal less moisture and ash), the evaporation being 
reduced to the standard of "from and at 212°." 

The measure of the capacity of a boiler, is the amount of " boiler horse- 
power " developed, a horse-power being defined as the evaporation oi 341/2 
lbs. per hour from and at 212° 

The measure of relative rapidity of steaming of boilers is the number of 
pounds of water evaporated from and at 212° per hour per square foot 
of water-heating surface. 

The measure of relative rapidity of combustion of fuel in boiler-furnaces 
is the number of pounds of coal burned per hour per square foot of grate- 
surface. 

STEAM-BOELER PROPORTIONS. 

Proportions of Grate and Heating Surface required for a given 
Horse-power. — The term horse-power here means capacity to evap- 
orate 34.5 lbs. of water from and at 212° F. 

Average proportions for maximum economy for land boilers fired with 
good anthracite coal: 

Heating surface per horse-power 11.5 sq. ft. 

Grate surface per horse-power 1/3 

Ratio of heating to grate surface 34.5 " 

Water evap'd from and at 212° per sq. ft. H.S. per hr. 3 lbs. 

Combustible burned per H.P. per hour 3 

Coal with 1/6 refuse, lbs. per H.P. per hour 3.6 " 

Combustible burned per sq. ft. grate per hour 9 

Coal with i/e refuse, lbs. per sq. ft. grate per hour 10.8 " 

Water evap'd from and at 212° per lb. combustible ... 11.5 " 
Water evap'd from and at 212° per lb. coal (1/6 refuse) 9.6 " 



856 THE STEAM-BOILER. 

Heating-surface. — For maximum economy with any kind of fuel a 
boiler should be proportioned so that at least one square foot of heating- 
surface should be given for every 3 lbs. of water to be evaporated from 
and at 212° F. per hour. Still more liberal proportions are required if a 
portion of the heating-surface has its efficiency reduced by: 1. Tendency 
of the heated gases to short-circuit, that is, to select passages of least 
resistance and flow through them with high velocity, to the neglect of 
other passages. 2. Deposition of soot from smoky fuel. 3. Incrusta- 
tion. If the heating-surfaces are clean, and the heated gases pass over 
it uniformly, little if any increase in economy can be obtained by increasing 
the heating-surface beyond the proportion of 1 sq. ft. to every 3 lbs. of 
water to be evaporated, and with all conditions favorable but little 
decrease of economy will take place if the proportion is 1 sq. ft. to every 
4 lbs. evaporated; but in order to provide for driving of the boiler beyond 
its rated capacity, and for possible decrease of efficiency due to the causes 
above named, it is better to adopt 1 sq. ft. to 3 lbs. evaporation per hour 
as the minimum standard proportion. 

Where economy may be sacrified to capacity, as where fuel is very 
cheap, it is customary to proportion the heating-surface much less liber- 
ally. The following table shows approximately the relative results that 
may be expected with different rates of evaporation, with anthracite coal. 

Lbs. water evapor 'd from and at 21 2° per sq . f t . heating-surface per hour : 
2 2.5 3 3.5 4 5 6 7 8 9 10 

Sq. ft. heating-surface required per horse-power: 
17.3 13.8 11.5 9.8 8.6 6.8 5.8 4.9 4.3 3.8 3.5 

Ratio of heating to grate surface if 1/3 sq. ft. of G.S. is required per H.P.: 
52 41.4 34.5 29.4 25.8 20.4 17.4 13.7 12.9 11.4 10.5 

Probable relative economy: 
100 100 100 95 90 85 80 75 70 65 60 

Probable temperature of chimney gases, degrees F.: 
450 450 450 518 585 652 720 787 855 922 • 990 

The relative economy will vary not only with the amount of heating- 
surface per horse-power, but with the efficiency of that heating-surface as 
regards its capacity for transfer of heat from the heated gases to the water, 
which will depend on its freedom from soot and incrustation, and upon the 
circulation of the water and the heated gases. 

With bituminous coal the efficiency will largely depend upon the 
thoroughness with which the combustion is effected in the furnace. 

The efficiency with any kind of fuel will greatly depend upon the amount 
of air supplied to the furnace in excess of that required to support com- 
bustion. With strong draught and thin fires this excess may be very 
great, causing a serious loss of economy. This subject is further discussed 
below. 

Measurement of Heating-surface. — The usual rule is to consider 
as heating-surface all the surfaces that are surrounded by water on one 
side and by flame or heated gases on the other, using the external instead 
of the internal diameter of tubes, for greater convenience in calculation, 
the external diameter of boiler-tubes usually being made in even inches or 
half inches. This method, however, is inaccurate, for the true heating- 
surface of a tube is the side exposed to the hot gases, the inner surface in a 
fire-tube boiler and the outer surface in a water-tube boiler. The re- 
sistance to the passage of heat from the hot gases on one side of a tube or 
plate to the water on the other consists almost entirely of the resistance to 
the passage of the heat from the gases into the metal, the resistance of the 
metal itself and that of the wetted surface being practically nothing. 
See paper by C. W. Baker, Trans. A. S. M. E., vol. xix. 

Rule for finding the heating-surface of vertical tubular boilers : Multiply 
the circumference of the fire-box (in inches) by its height above the grate; 
multiply the combined circumference of all the tubes by their length, and 
to these two products add the area of the lower tube-sheet; from this sum 
subtract the area of all the tubes, and divide by 144: the quotient is the 
number of square feet of heating-surface. 

Rule for finding the heating-surface of hozizontal tubular boilers: Take 
the dimensions in inches. Multiply two-thirds of the circumference of the 
shell by its length; multiply the sum of the circumferences of all the tubes 



STEAM-BOILER PROPORTIONS. 



857 



by their common length; to the sum of these products add two thirds of 
the area of both tube-sheets; from this sum subtract twice the combined 
area of all the tubes; divide the remainder by 144 to obtain the result in 
square feet. 

Rule for finding the square feet of heating-surface in tubes: Multiply 
the number of tubes by the diameter of a tube in inches, by its length in 
feet, and by 0.2618. 

Horse-power, Builder's Bating. Heating-surface per Horse- 
power. — It is a general practice among builders to furnish about 10 
square feet of heating-surface per horse-power, but as the practice is not 
uniform, bids and contracts should always specify the amount of heating- 
surface to be furnished. Not less than one-third square foot of grate-sur- 
face should be furnished per horse-power with ordinary chimney draught, 
not exceeding 0.3 in. of water column at the damper, for anthracite coal, 
and for poor varieties of soft coal high in ash, with ordinary furnaces. A 
smaller ratio of grate surface may be allowed for high grade soft coal and 
for forced draught. 

Horse-power of Marine and Locomotive Boilers. — The term horse- 
power is not generally used in connection with boilers in marine practice, 
or with locomotives. The boilers are designed to suit the engines, and 
are rated by extent of grate and heating-surface only. 

Grate-surface. — The amount of grate-surface required per horse- 
power, and the proper ratio of heating-surface to grate-surface are ex- 
tremely variable, depending chiefly upon the character of the coal and 
upon the rate of draught. With good coal, low in ash, approximately 
equal results may be obtained with large grate-surface and light draught 
and with small grate-surface and strong draught, the total amount of coal 
burned per hour being the same in both cases. With good bituminous 
coal, like Pittsburgh, low in ash, the best results apparently are obtained 
with strong draught and high rates of combustion, provided the grate- 
surfaces are cut down so that the total coal burned per hour is not too great 
for the capacity of the heating-surface to absorb the heat produced. 

With coals high in ash, especially if the ash is easily fusible, tending to 
choke the grates, large grate-surface and a slow rate of combustion are 
required, unless means, such as shaking grates, are provided to get rid of 
the ash as fast as it is made. 

The amount of grate-surface required per horse-power under various 
conditions may be estimated from the following table: 





a!" 




Pounds of Coal burned per square 




■** s 


— < P-* 3 


foot of Grate per hour. 






|«i 






8 


10 12 1 15 20 25 I 30 | 35 1 40 






aj 4> ® 




1 1 1 1 1 1 1 








A 


y! 


Sq. Ft. Grate per H. P. 


Good coal and 


no 


3.45 


.43 


.35 


.28 


.23 


.17 


.14 


.11 


.10 


.09 


boiler, 


1 9 


3.83 


.48 


.38 


.32 


.25 


.19 


.15 


.13 


.11 


.10 




( 8.61 


4. 


.50 


.40 


.33 


.26 


.20 


.16 


.13 


.12 


.10 


Fair coal or boiler, 


8 


4.31 


.54 


.43 


.36 


.29 


.22 


.17 


.14 


.13 


.11 




I 7 


4.93 


.62 


.49 


.4! 


.33 


.24 


.20 


.17 


.14 


.12 




( 6.9 


5. 


.63 


.50 


.42 


.34 


.25 


.20 


.17 


.15 


.13 


Poor coal or boiler, 


6 


5.75 


.72 


.58 


.48 


.38 


.29 


.23 


.19 


.17 


.14 




( 5 


6.9 


.86 


.69 


.58 


.46 


.35 


.28 


.23 


.22 


.17 


Lignite and poor 
boiler, 


1 345 


10. 


1.25 


1.00 


.83 


.67 


.50 


.40 


.33 


.29 


.25 



In designing a boiler for a given set of conditions, the grate-surface 
should be made as liberal as possible, say sufficient for a rate of combus- 
tion of 10 lbs. per square foot of grate for anthracite, and 15 lbs. per square 
foot for bituminous coal, and in practice a portion of the grate-surface 
may be bricked over if it is found that the draught, fuel, or other condi- 
tions render it advisable. 



858 THE STEAM-BOILER, 



Proportions of Areas of Flues and other Gas-passages. — Rules 
are usually given making the area of gas-passages bear a certain ratio to 
the area of the grate-surface; thus a common rule for horizontal tubular 
boilers is to make the area over the bridge wall 1/7 of the grates-surface, 
the flue area 1/8, and the chimney area 1/9. 

For average conditions with anthracite coal and moderate draught, say 
a rate of combustion of 12 lbs. coal per square foot of grate per hour, and a 
ratio of heating to grate surface of 30 to 1, this rule is as good as any, but 
it is evident that if the draught were increased so as to cause a rate of com- 
bustion of 24 lbs., requiring the grate-surface to be cut down to a ratio of 
60 to 1, the areas of gas-passages should not be reduced in proportion. 
The amount of coal burned per hour being the same under the changed 
conditions, and there being no reason why the gases should travel at a 
higher velocity, the actual areas of the passages should remain as before, 
but the ratio of the area to the grate-surface would in that case be 
doubled. 

Mr. Barrus states that the highest efficiency with anthracite coal is 
obtained when the tube area is 1/9 to 1/10 of the grate-surface, and with 
bituminous coal when it is 1/6 to 1/7, for the conditions of medium rates of 
combustion, such as 10 to 12 lbs. per square foot of grate per hour, and 12 
square feet of heating-surface allowed to the horse-power. 

The tube area should be made large enough not to choke the draught 
and so lessen the capacity of the boiler; if made too large the gases are apt 
to select the passages of least resistance and escape from them at a high 
velocity and high temperature. 

This condition is very commonly found in horizontal tubular boilers 
where the gases go chiefly through the upper rows of tubes; sometimes 
also in vertical tubular boilers, where the gases are apt to pass most rapidly 
through the tubes nearest to the center. It may to some extent be 
remedied by placing retarders in those tubes in which the gases travel the 
quickest. 

Air-passages through Grate-bars. — The usual practice is, air- 
opening = 30% to 50% of area of the grate; the larger the better, to avoid 
stoppage of the air-supply by clinker; but with coal free from clinker much 
smaller air-space may be used without detriment. See paper by F. A. 
Scheffler, Trans. A. S. M.E., vol. xv, p. 503. 



PERFORMANCE OF BOILERS. 

The performance of a steam-boiler comprises both its capacity for gener- 
ating steam and its economy of fuel. Capacity depends upon size, both of 
grate-surface and of heating-surface, upon the kind of coal burned, upon the 
draught, and also upon the economy. Economy of fuel depends upon the 
completeness with which the coal is burned in the furnace, on the proper 
regulation of the air-supply to the amount of coal burned, and upon the 
thoroughness with which the boiler absorbs the heat generated in the 
furnace. The absorption of heat depends on the extent of heating-sur- 
face in relation to the amount of coal burned or of water evaporated, upon 
the arrangement of the gas-passages, and upon the cleanness of the sur- 
faces. The capacity of a boiler may increase with increase of economy 
when this is due to more thorough combustion of the coal or to better regu- 
lation of the air-supply, or it may increase at the expense of economy 
when the increased capacity is due to overdriving, causing an increased 
loss of heat in the chimney gases. The relation of capacity to economy 
is therefore a complex one, depending on many variable conditions. 

A formula expressing the relation between capacity, rate of driving, or 
evaporation per square foot of heating-surface, to the economy, or evapo- 
ration per pound of combustible is given on page 865. 

Selecting the highest results obtained at different rates of driving with 
anthracite coal in the Centennial tests (see p. 867), and the highest results 
with anthracite reported by Mr. Barrus in his book on Boiler Tests, the 
author has plotted two curves showing the maximum results which may 
be expected with anthracite coal, the first under exceptional conditions 
such as obtained in the Centennial tests, and the second under the best 
conditions of ordinary practice. {Trans. A. S. M, E., xviii, 354.) From 
these curves the following figures are obtained, 



PERFORMANCE OF BOILERS. 859 

Lbs. water evaporated from and at 212° per sq. ft. heating-surface per 
hour: 

1.6 1.7 2 2.6 3 3.5 4 4.5 5 6 7 S 

Lbs. water evaporated from and at 212° per lb. combustible: 

Centennial. 11.8 11.9 12.0 12.1.12.05 12 11.85 11.7 11.5 10.85 9.8 8.5 

Barrus 11.4 11.5 11.55 11.6 11.6 11.5 11.2 10.9 10.6 9.9 9.2 8.5 

Avg. Cent'l 12.0 11.6 11.2 10.8 10.4 10.0 9.6 8.8 8.0 7.2 

The figures in the last line are taken from a straight line drawn as nearly 
as possible through the average of the plotting of all the Centennial tests. 
The poorest results are far below these figures. It is evident that no for- 
mula can be constructed that will express the relation of economy to rate of 
driving as well as do the three lines of figures given above. 

For semi-bituminous and bituminous coals the relation of economy to 
the rate of driving no doubt follows the same general law that it does with 
anthracite, i.e., that beyond a rate of evaporation of 3 or 4 lbs. per sq. ft. of 
heating-surface per hour there is a decrease of economy, but the figures 
obtained in different tests will show a wider range between maximum and 
average results on account of the fact that it is more difficult with bitumi- 
nous than with anthracite coal to secure complete combustion in the 
furnace. 

The amount of the decrease in economy due to driving at rates exceeding 
4 lbs. of water evaporated per square foot of heating-surface per hour 
differs greatly with different boilers, and with the same boiler it may differ 
with different settings and with different coal. The arrangement and size 
of the gas-passages seem to have an important effect upon the relation of 
economy to rate of driving. 

A comparison of results obtained from different types of boilers leads to 
the general conclusion that the economy with which different types of 
boilers operate depends much more upon their proportions and the con- 
ditions under which they work, than upon their type; and, moreover, 
that when the proportions are correct , and when the conditions are favor- 
able, the various types of boilers give substantially the same economic 
result. 

Conditions of Fuel Economy in Steam-boilers. — 1. That the boiler 
has sufficient heating surface to absorb from 75 to 80% of all the heat 
generated by the fuel. 2. That this surface is so placed, and the gas pas- 
sages so controlled by baffles, that the hot gases are forced to pass uni- 
formly over the surface, not being short-circuited. 3. That the furnace is 
of such a kind, and operated in such a manner, that the fuel is completely 
burned in it, and that no unburned gases reach the heating surface of the 
boiler. 4. That the fuel is burned with the minimum supply of air re- 
quired to insure complete combustion, thereby avoiding the carrying of an 
excessive quantity of heated air out of the chimney. 

There are two indices of high economy. 1. High temperature, ap- 
proaching 3000° F. in the furnace, combined with low temperature, below 
600° F., in the flue. 2. Analysis of the flue gases showing between 5 and 
8% of free oxygen. Unfortunately neither of these indices is available 
to the ordinary fireman; he cannot distinguish by the eye any temperature 
above 2000°, and he cannot know whether or not an excessive amount of 
oxygen is passing through the fuel. The ordinary haphazard way of firing 
therefore gives an average of about 10% lower economy than can be 
obtained when the firing is controlled, as it is in many large plants, by re- 
cording furnace pyrometers, or by continuous gas analysis, or by both. 
Low CO2 in the flue gases may indicate either excessive air supply in the 
furnace, or leaks of air into the setting, or deficient air supply with the 
presence of CO, and therefore imperfect combustion. The latter, if exces- 
sive, is indicated by low furnace temperature. The analysis for C0 2 should 
be made both of the gas sampled just beyond the furnace and of the gas 
sampled at the flue. Diminished CO2 in the latter indicates air-leakage. 

Less than 5% of free oxygen in the gases is usually accompanied with 
CO, and it therefore indicates imperfect combustion from deficient air 
supply. More than 8% means excessive air supply and corresponding 
waste of heat. 

Air Leakage or infiltration of air through the firebrick setting is a 
common cause of poor economy. It may be detected by analysis as above 



860 THE STEAM-BOILER. 

stated, and should be p. evented by stopping all visible cracks in the brick- 
work, and by covering it with a coating impervious to air. 

Autographic C0 2 Recorders are used in many large boiler plants for 
the continuous recording of the percentage of carbon dioxide in the gases. 
When the percentage of C0 2 is between 12 and 16, it indicates good fur- 
nace conditions, when below 12 the reverse. 

Efficiency of a Steam-boiler. — The efficiency of a boiler is the 
percentage of the total heat generated by the comoustion of the fuel 
which is utilized in heating the water and in raising steam. With anthra- 
cite coal the heating-value of the combustible portion is very nearly 
14,800 B.T.U. per lb., equal to an evaporation from and at 212° of 14,800 
-5- 970 = 15.26 lbs. of water. A boiler which when tested with anthra- 
cite coal shows an evaporation of 12 lbs. of water per lb. of combustible, 
has an efficiency of 12 -*- 15.26 = 78. 6%,. a figure which is approximated, 
•but scarcely ever quite reached, in the best practice. With bituminous 
coal it is necessary to have a determination of its heating-power made 
by a coal calorimeter before the efficiency' of the boiler using it can be 
determined, but a close estimate may be made from the chemical analysis 
of the coal. (See Coal.) 

The difference between the efficiency obtained by test and 100% is 
the sum of the numerous wastes of heat, the chief of which is the necessary 
loss due to the temperature of the chimney-gases. If we have an analysis 
and a calorimetric determination of the heating-power of the coal (properly 
sampled), and an average analysis of the chimney-gases, the amounts 
of the several losses may be determined with approximate accuracy by 
the method described below. 

Data given: 

1. Analysis of the Coal. 2. Analysis of the Dry Chimney- 
Cumberland Semi-bituminous. gases, by Weight. 

Carbon 80.55 

Hydrogen 4 . 50 

Oxygen 2.70 

Nitrogen 1.08 

Moisture 2.92 

Ash 8.25 



c. 


O. 


C0 2 = 13.6 = 3.71 


9.89 


CO = 0.2 = 0.09 


0.11 


O = 11.2 = 


11.20 


N = 75.0 = 





100.00 



21.20 75.00 



Heating-value of the coal by Dulong's formula, 14,243 heat-units. 
The gases being collected over water, the moisture in them is not deter- 
mined. ♦ 

3. Ash and refuse as determined by boiler-test, 10.25, or 2% more than 
that found by analysis, the difference representing carbon in the ashes 
obtained in the boiler-test. 

4. Temperature of external atmosphere, 60° F. 

. 5. Relative humidity of air, 60%, corresponding (see air- tables) to 
0.007 lb. of vapor in each lb. of air. 

6. Temperature of chimney-gases, 560° F. 

Calculated results: 

The carbon in the chimney-gases being 3.8% of their weight, the total 
weight of dry gases per lb. of carbon burned is 100 -h 3.8 = 26.32 lbs. 
Since the carbon burned is 80.55 — 2 = 78.55%, of the weight of the coal, 
the weight of the dry gases per lb. of coal is 26.32 X 7S.55 -s- 100 = 20.67 
lbs. 

Each pound of coal furnishes to the dry chimney-gases 0.7855 lb. C, 

0.0108 N, and (2.70- ^p) -*■ 100 = 0.0214 lb. O; a total of 0.8177, say 

0.82 lb. This subtracted from 20.67 lbs. leaves 19.85 lbs. as the quantity 
of dry air (not including moisture) which enters the furnace per pound 
of coal, not counting the air required to burn the available hydrogen, 
that is, the hydrogen minus one-eighth of the oxygen chemically combined 
in the coal. Each lb. of coal burned contained 0.045 lb. H, which requires 
0.045 X 8 = 0.36 lb. O for its combustion. Of this, 0.027 lb. is furnished 
by the coal itself, leaving 0.333 lb. to Come from the air. The quantity 
of air needed to supply this oxygen (air containing 23% bv weight of 
oxygen) is 0,333 -s- 0.23 = 1.45 lb., which added to the 19.85 lbs. already 



PERFORMANCE OF BOILERS. 861 

found gives 21.30 lbs. as the quantity of dry air supplied to the furnace 
per lb. of coal burned. 

The air carried in as vapor is 0.0071 lb. for each lb. of dry air, or 21.3 X 
0.0071= 0.151b. for each lb. of coal. Eacli lb. of coal contained 0.029 lb. 
of moisture, which was evaporated and carried into the chimney-gases. 
The 0.045 lb. of H per lb. of coal when burned formed 0.045 X 9 = 
0.405 1b. of H 2 0. 

From the analysis of the chimney-gas it appears that 0.09. -f- 3.80 = 
2.37% of the carbon in the coal was burned to CO instead of to CO2. 

We now have the data for calculating -the various losses of heat, as 
follows, for each pound of coal burned: 



20.67 lbs. dry gas X (560° - 60°) X sp. heat 0.24 = 
. 0.15 lb. vapor in air X (560° - 60°) X sp. ht. 0.4S -■ 
. 029 lb. moist, in coal heated from 60° to 212° = 
0.0291b. evap. from and at 212°; 0.029 X 966 
. 029 lb. steam (heated 212° to 560°) X348 X 0.48 = 
0.405 lb. H2O from H in coal X (152 + 966 + 

348 X 0.48) 
0.0237 lb. C burned to CO; loss by incomplete 

combustion, 0.0237 X (14544- 4451) 
0.02 lb. coal lost in ashes: 0.02 X 14544 
Radiation and unaccounted for, by difference 



Utilized in making steam, equivalent evapora- 
tion 10.37 lbs. from and at 212° per lb. of coal ■ 



Heat- 
units. 


Per cent of 
Heat -value 
of the Coal. 


2480 . 4 
36.0 

4.4 
28.0 

4.8 


17.41 
0.25 
0.03 
0.20 
0.03 


520.4 


3.65 


239.2 
290.9 
624.0 


1.68 
2.04 
4.38 


4228.1 


29.69 


10,014.9 


70.31 


14,243.0 


100.00 



The heat lost by radiation from the boiler and furnace is not easily 
determined directly, especially if the boiler is enclosed in brickwork, or is 
protected by non-conducting covering. It is customary to estimate the 
heat lost by radiation by difference, that is, to charge radiation with all 
the heat lost which is not otherwise accounted for. 

One method of determining the loss by radiation is to block off a portion 
of the grate-surface and build a small fire on the remainder, and drive this 
fire with just enough draught to keep up the steam-pressure and supply the 
heat lost by radiation without allowing any steam to be discharged, 
weighing the coal consumed for this purpose during a test of several hours' 
duration. 

Estimates of radiation by difference are apt to be greatly in error, as in 
this difference are accumulated all the errors of the analyses of the coal 
and of the. gases. An average value of the heat lost by radiation from a 
boiler set in brickwork is about 4 per cent. When several boilers are in a 
battery and enclosed in a boiler-house the loss by radiation may be very 
much less, since much of the heat radiated from the boiler is returned to it 
in the air supplied to the furnace, which is taken from the boiler-room. 

An important source of error in making a "heat balance" such as the 
one above given, especially when highly bituminous coal is used, may be 
due to the non-combustion of part of the hydrocarbon gases distilled from 
the coal immediately after firing, when the temperature of the furnace may 
be reduced below the point of ignition of the gases. Each pound of hydro- 
gen which escapes burning is equivalent to a loss of heat in the furnace of 
62,000 heat-units. Another sourceof error, especiall v with bituminous slack 
coal hi°:h in moisture, is due to the formation of water-gas, CO - 1 - H, by the 
decomposition of the water, end the consequent absorption of heat, this 
water-gas ecaping unbumed on account of the choking of the air supply 
when fine fresh coal is supplied to the fire. 

In analyzing the chimney-gases by the usual method the percentages of 
the constituent gases are obtained by volume instead of by weight. To 
reduce percentages by volume to percentages by weight, multiply the per- 
centage by volume of each gas by its specific gravity as compared with air, 
and divide each product by the sum of the products. 

Instead of using the percentages by weight of the gases, the percentage 



862 THE STEAM-BOILER. 

by volume may be used directly to find the weight of gas per pound of 
carbon by the formula given below. 

If O, CO, CO2, and N represent the percentages by volume of oxygen, 
carbonic oxide, carbonic acid, and nitrogen, respectively, in the gases 01 
combustion: 

Lbs. of air required to burn) _ 3.032 N 
one pound of carbon J CO2 + CO 

N 
Ratio of total air to the theoretical requirement =- 



N- 3.782 O 

Lbs. of air per pound ) _ J Lbs. of air per pound \ y I Per cent of carbon 
of coal J 1 of carbon J I in coal 

TU , , , , , HC0 2 +80 + 7(CO + N) 

Lbs. dry gas produced per pound of carbon = „ ,-„ — , ~' ■ 

6 (OU2 -r OUJ 

Relation of Boiler Efficiency to the Rate of Driving, Air Supply, 
etc. — ■ In the author's Steam Boiler Economy (p. 205) a formula is 
developed showing the efficiency that may be expected, when the com- 
bustion of the coal is complete, under different conditions. The formula is 

E a K - tcf 970 ac*f* W_ 

E p ~ K (1 + RS/W) K (K - tcf) S ' 

K = heating value per lb. of combustible; E a = actual evaporation from 
and at 212° per lb. of combustible; E p = possible evaporation = K -f- 
970; t = elevation of the temperature of the water in the boiler above 
the atmospheric temperature; c = specific heat of the chimney gases, 
taken at 0.24; / = weight of flue gases per lb. of combustible; S = square 
feet of heating surface; W = pounds of water evaporated per hour; 
W/S = rate of driving; R = radiation loss, in units of evaporation per 
sq. ft. of heating-surface per hour; a is a coefficient found by experiment; 
it may be called a coefficient of inefficiency of the boiler, and it depends 
on and increases with the resistance to the passage of heat through the 
metal, soot or scale on the metal, imperfect combustion, short-circuiting, 
air leakage, or any other defective condition, not expressed in terms in 
the formula, which may tend to lower the efficiency. Its value is between 
200 and 400 when records of tests show high efficiency, and above 400 for 
lower efficiencies. 

The coefficient a is a criterion of performance of a boiler when all the 
other terms of the formula are known as the results of a test. By trans- 
position its value is 

K- tcf 1 . c*P W 

L970 (1 + RS/W) a \ ' {K- tcf) S ' 

On the diagram below (Fig. 148), with abscissas representing rates of 
driving and ordinates representing efficiencies are plotted curves showing 
the relation of the efficiency to rate of driving: for values of a= 100 to 
400 and values of / from 20 to 35 together with a broken line showing 
the maximum efficiencies obtained by six boilers at the Centennial Exhi- 
bition, and other lines showing the poor results obtained from five other 
boilers. The curves are also based on the following values, K = 14.800; 
(C = 0.24; t= 300 (except one curve, t = 250); R = 0.1. 

An inspection of the curves shows the following. 1. The maximum 
Centennial results all lie below the curve / = 20, a = 200, by 2 to 4%, 
but they follow the general direction of the curve. This curve may 
therefore be taken as representing the maximum possible boiler per- 
formance with anthracite coal, as the results obtained in 1876 have never 
been exceeded with anthracite. 

2. With/ = 20 and a = 200 the efnciencv for maximum performance, 
according to the curve, is a little less than 82% at 2 lbs. evaporation per 
sq. ft. of heating-surface per hour, but it decreases very slowly at higher 
rates, so that it is 80% at 31/2 lbs., and 76% at 53/ 4 lbs. 

With a = 200 and / greater than 20, the efficiency has a lower maxi- 
mum, reaches the maximum at a lower rate of driving, and falls off 
rapidly as the rate increases, the more rapidly the higher the value of /. 
Excessive air supply is thus shown to be a most potent cause of low 
.economy. 



«=[«- 



PERFORMANCE OF BOILERS. 



863 



3. An increase in the value of a from 200 to 400 with / = 20 is much 
less detrimental to efficiency than an increase in/ from 20 to 30. 

In the diagram, Fig. 152, are plotted, together with the curve for /=20, 
a= 200, £=300, and K = 15,750, marked R= 0.1, a straight line, R = 0, 
showing the theoretical maximum efficiency when there is no loss by 



84 


















'+" 



























_£_ 


-300 


Jfi-20 


2 






80 

78 
76 
74 
































-. 










1 












, 


, 








# 








fT 














~s~ 










- 


--£% 
























*s< 








-i. 


^-L. 






'~- 


-^ 




s 












-^ 






'-c 




*y^ 








't 


/ 






























... 


















/ 






















■> 




































J 


72 
70 
68 
66 




































^ 


"-C 




























































4\ 




^ 


































/ 


































**« 


^ 








M. 


ercjj - ^ 


<f 








64 
62 

£60 


















N, 


k 












-> 


Vj 


tog 


ei 


3 &\ 


RJ 


1 ;- 






■«S 


^ 


A 






















































v ~ 




^ 


^ 


*o 


*"> 




sQ 




0o 














































«* 
















^56 

P.54 

£52 

fl 50 

•§48 

6 46 

W 44 

42 

40 

38 

36 

34 

32 

30 

28 

26 

24 

22 

20 
















































<>■ 










^^> 


fb 






























































































































•* 


















































x 


:j 




































































































































y ■ 


^ 






























































" 














F 


= 


F 


i - 


iei 


ic 


l 




















































L 


== 


Low 


e 
























































R 


~ 


lioot 
























































B 


= 


Babcoc 


k( 


fcl 


Vi 


co 


i 














































S 


= 


Smith 
























































G( 




- Gallon 


"' 






































































































































































^ 


































































& 







































































































































































































1 2 3 4 5 6 '7-8 

Lbs. of Water Evaporated from and at 212° F. per sq. ft. of Heating Surface per Hour 



' — ^ 


























*-. 




£w„- 
























„, " 




Jin 
























^^ 


e^?«< 


■Or 


















s'' 




^.r 


-<{«* 




























<iJSj j 


J <°v 
















**t p c 










■<5r* 


















utG *v 


>-^ 


o-iK 








,.., 
















2e s 


^r*" 1 


"^O 


-^ 




^%e 


-0 












lornyc 


oftrTe 






^ "~~ 




■^-~~c 


&L; 
















""v^ 


34 




^r^ter 






o- 


— oJJ 


abcock & Wi 


coxTc 


sts 




^x 


6 


1 ^ 




„ 






1 1 1 








1 




ko' 



1 2 3 4 5 6 7 8 9 10 11 12 13 14 

Lbs. of Water Evaporated from and at 212° F, per sq. ft-, of Heating Surface per Hour 



radiation, and the plottings of the results of two series of tests, one of a 
Thornycroft boiler, with W/S from 1.24 to 8.5, and the other of a Babcock 
& Wilcox marine boiler with W/S from 5.18 to 13.67, together with the 



864 



THE STEAM-BOILER. 



maximum Centennial tests. The calculated value of a in all these tests 
except one ranged from 191 to 454, the highest values being those showing 
the largest departure from the curve R= 0.1. The one exception is the 
Thornycroft test showing over 86% efficiency; this gives a value of a = 
57, which indicates an error in the test, as such a low value is far below 
the lowest recorded in any other test. 

TESTS OF STEAM-BOILERS. 

Boiler-tests at the Centennial Exhibition, Philadelphia, 1876. — 

(See Reports and Awards Group XX, International Exhibition, Phila., 
1376; also, Clark on the Steam-engine, vol. i, page 253.) 

Competitive tests were made of fourteen boilers, using good anthracite 
coal, one boiler, the Galloway, being tested with both anthracite and semi- 
bituminous coal. Two tests were made with each boiler: one called the 
capacity trial, to determine the economy and capacity at a rapid rate of 
driving; and the other called the economy trial, to determine the economy 
when driven at a rate supposed to be near that of maximum economy and 
rated capacity. The following table gives the principal results obtained 
in the economy trial, together with the capacity and economy figures of 
the capacity trial for comparison. 





Economy Tests. 


Capacity 

Tests. 




3 O 


£ 


03 
3 




Is* 


i 




d 






1 = 


Name of Boiler. 


• - ~ 
7 ^ 


o 1 

u ^ 

7"f 


(8 
.3 


-x 
ft x 

03 • 


Si? « 

m 


s 

.5 

3 


1 


1 

SB 




% 


So 

o 
$1 




o3 - 






> ft 


>~ o3 






c3 






> S 




- 1 

'" 03 

-. •-„ 


o3 

o 


P4 






ft 

s 

03 


3 

"o 


03 


ft 
A 

o 

W 


ft 
4 

o 
W 


Sal 






lbs. 


% 


lbs. 


lbs. 


,!f>"' 


% 


iles- 


H.P. 


H.P. 


lbs. 




H4 6 


9 1 


10 i 


; ->S 


12.094 


-i'4H 




4! 4 


119 8 








64 3 


Y' n 


10 ,1 


1 fifi 


11.988 


415 




3? 6 


57 8 




11 064 




30 6 


6 8 


1 1 3 


1 87 


11.923 


333 




9 4 


47 




11 163 


Smith 


45.8 


17 1 


11.1 


> 4 ;> 


11.906 


411 


1 3 




99 8 


125 


11 925 


Babcock & Wilcox . 


37.7 10.0 


11.0 2.43 


11.822 


296 


2 7 




135.6 


186.6 


10.330 




n 7 


M 6 


11 1 


=1 63 


1 1 . 583 


'403 




1 4 


103 3 


133 8 


11 216 


Do. semi-bit. coal. 


23.7 


7.9 


8 8 


3 20 


12.125 


325 


3 




<0.9 


125.1 


11.609 


Andrews 


15 6 


« n 


10 3 


? 3? 


11.039 


4WI 




71 7 


42 6 


58 7 


9.745 


Harrison 


27.3 


12.4 


8 5 


2 75 


10.930 


517 


9 




82.4 


108.4 


9.889 




30 7 


1? s 


o >i 


3 30 


10 834 


5?4 




^0 5 


147 5 


162 8 


9 145 


Anderson 


17 5 


9 7 


9 3 


?, 64 


10.618 


417 




15 7 


98 


132 8 


9.568 


Kelly 


?o 9 


10 8 


Q 


3 8? 


10 312 




5 6 




81 


99 9 


8 397 


Exeter. , 


33 5 


9 3 


11 4 


1 38 


10.041 


430 


4 7 




72.1 


108.0 


9.974 


Pierce 


14 o 


8 n 


11 


4 44 


10.021 


374 


5 ? 




51.7 


67.8 


9.865 


Rogers & Black. . . . 


19.0 


8.6 


9.9 


3.43 


9.613 


572 


2.1 




45.7 


67.2 


9.429 


Averages 








2.77 


11.123 








85.0 


110.8 


10.251 



The comparison of the economy and capacity trials shows that an 
average increase in capacity of 30 per cent was attended by a decrease in 
economy of 8 per cent, but the relation of economy to rate of driving 
varied greatly in the different boilers. In the Kelly boiler an increase in 
capacity of 22 per cent was attended by a decrease in economy of -over 
18 per cent, while the Smith boiler with an increase of 25 per cent in capac- 
ity showed a slight increase in economy. 

One of the most important lessons gained from the above tests is that 
there is no necessary relation between the type of a boiler and economy, 



TESTS OF STEAM-BOILEES. 865 

Of the five boilers that gave the best results, the total range of variation 
between the highest and lowest of the five being only 2.3%, three were 
water-tube boilers, one was a horizontal tubular boiler, and the fifth was 
a combination of the two types. The next boiler on the list, the Gallo- 
way, was an internally fired boiler, all of the others being externally 
fired. 

Some High Rates of Evaporation. — Eng'g, May 9, 1884, p. 415. 

Locomotive. Torpedo-boat. 

Water evap. per sq. ft. H.S. per hour 12.57 13.73 12.54 20.74 

Water evap. per lb. fuel from and at 212° 8.22 8.94 8.37 7.04 
Thermal units transfd per sq. ft. of H.S..12,142 13,263 12,113 20,034 
Efficiency 0.586 0.637 0.542 0.468 

It is doubtful if these figures were corrected for priming. 

Economy Effected by Heating the Air Supplied to Boiler-furnaces. 

— An extensive series of experiments was made by J. C. Hoadley (Trans. 
A. S. M. E., vi, 676) on a "Warm-blast Apparatus," for utilizing the heat 
of the waste gases in heating the air supplied to the furnace. The appara- 
tus, as applied to an ordinary horizontal tubular boiler 60 in. diameter, 
21 ft. long, with 65 3V2-in. tubes, consisted of 240 2-in. tubes, 18 ft. long, 
through which the hot gases passed while the air circulated around them. 
The net saving of fuel effected by the warm blast was from 10.7% to 15.5% 
of the fuel used with cold blast. The comparative temperatures averaged 
as follows, in degrees F.: 



Cold-blast Warm-blast 



In heat of fire 

At bridge wall 

In smoke box 

Air admitted to furnace . . . 
Steam and water in boiler . 
Gases escaping to chimney . 
External air 



Boiler. 


Boiler. 


Difference. 


2493 


2793 


300 


1340 


1600 


260 


373 


375 


2 


32 


332 


300 


300 


300 





373 


162 


211 


32 


32 






With anthracite coal the evaporation from and at 212° per lb. combus- 
tible was, for the cold-blast boiler, days 10.85 lbs., days and nights 10.51; 
and for the warm-blast boiler, days 11.83, days and nights 11.03. 

Maximum Boiler Efficiency with Cumberland Coal. — About 12.5 
lbs. of water per lb. combustible from and at 212° is about the highest 
evaporation that can be obtained from the best steam fuels in the United 
States, such as Cumberland, Pocahontas, and Clearfield. In exceptional 
cases 13 lbs. has been reached, and one test is on record (F. W. Dean, 
Eng'g News, Feb. 1, 1894) giving 13.23 lbs. The boiler was internally 
fired, of the Belpaire type, 82 inches diameter, 31 feet long, with 160 3-inch 
tubes 121/2 feet long. Heating-surface, 1998 square feet; grate-surface, 
45 square feet, reduced during the test to 30 1/2 square feet. Double fur- 
nace, with fire-brick arches and a long combustion-chamber. Feed- 
water heater in smoke-box. The following are the principal results: 

1st Test. 2d Test. 
Dry coal burned per sq. ft. of grate per hour, lbs.. . . 8.85 16.06 
Water evap. per sq.ft. of heating-surface per hour, lbs. 1.63 3.00 
Water evap. from and at 212° per lb. combustible, in- 
cluding feed-water heater 13.17 13.23 

Water evaporated, excluding feed-water heater 12.88 12.90 

Temperature of gases after leaving heater, F 360° 469° 

BOILERS USING WASTE GASES. 

Water-tube Boilers using Blast-furnace Gases. — D. S. Jacobus 
(Trans. A. I. M. E., xvii, 50) reports a test of a water-tube boiler using 
blast-furnace gas as fuel. The heating-surface was 2535 sq. ft. It 
developed 328 H.P., or 5.01 lbs. of water from and at 212° per sq. ft. of 
heating-surface per hour. Some of the principal data obtained were as 
follows: Calorific value of 1 lb. of the gas, 1413 B.T.U., including the effect 



866 



THE STEAM-BOILER. 



of its initial temperature, which was 650° F. Amount of air used to bum 
1 lb. of the gas = 0.9 lb. Chimney draught, 1 V.3 in. of water. Area of 
gas inlet, 300 sq.in.; of air inlet, 100 sq.in. Temperature of the chimney 
gases, 775° F. Efficiency of the boiler calculated from the temperatures 
and analyses of the gases at exit and entrance, 61 % „ The average analyses 
were as follows, hydrocarbons being included in the nitrogen: 





By Weight. 


By Volume. 




At Entrance. 


At Exit. 


At Entrance. 


At Exit. 


co 2 ...... 


10.69 
.11 
26.71 
62.48 
2.92 
11.45 
14.37 


26.37 
3.05 
1.78 

68.ro 

7.19 
0.76 
7.95 


7.08 
0.10 
27.80 
65.02 


18 64 


o 


2 96 


CO 


1.98 




76 42 


CinC0 2 




C in CO . „ 






Total C 













Steam-boilers Fired with Waste Gases from Puddling and Heat- 
ing-Furnaces. — The Iron Age, April 6, 1893, contains a report of a 
number of tests of steam-boilers utilizing the waste heat from puddling 
and heating-furnaces in rolling-mills. The following principal data are 
selected: in Nos. 1, 2, and 4 the boiler is a Babcock & Wilcox water-tube 
boiler, and in No. 3 it is a plain cylinder boiler, 42 in. diam. and 26 ft. long. 
No. 4 boiler was connected with a heating-furnace, the others with puddling 
furnaces. 

No. 1. No. 2. No. 3. No. 4. 

Heating-surface, sq. ft . 1026 1196 143 1380 

Grate-surface, sq. ft 19.9 13.6 13.6 16.7 

Ratio H.S. to G.S 52 87.2 10.5 82.8 

Water evap. per hour, lbs 3358 2159 1812 3055 

Water evap. per sq. ft. H.S. per hr., lbs 3.3 1.8 12.7 2.2 

Water evap. per lb. coal from and at 212° . . . 5.9 6.24 3.76 6.34 
Water evap. per lb. comb, from and a t 212° 7.20 4.31 8.34 

In No. 2, 1.38 lbs. of iron were puddled per lb. of coal. 
In No. 3, 1.14 lbs. of iron were puddled per lb. of coal. 
No. 3 shows that an insufficient amount of heating-surface was provided 
for the amount of waste heat available. 



RULES FOR CONDUCTING BOILER-TESTS. 

Code of 1899. 

(Reported by the Committee on Boiler Trials, Am. Soc. M. E.*) 

I. Determine at the outset the specific object of the proposed trial, 
whether it be to ascertain the capacity of the boiler, its efficiency as a 
steam-generator, its efficiency and its defects under usual working condi- 
tions, the economy of some particular kind of fuel, or the effect of changes 
of design, proportion, or operation; and prepare for the trial accordingly. 

II. Examine the boiler, both outside and inside; ascertain the dimensions 
of grates, heating surfaces, and all important parts; and make a full 
record, desrribin? the same, and illustrating special features by sketches. 

III. Notice the general condition of the boiier and its equipment, and 
record such facts in relation thereto as bear upon the objects in view. 

* The code is here slightly abridged. The complete report of the 
Committee may be obtained in pamphlet form from the Secretary of the 
American Society of Mechanical Engineers, 29 West 39th St., New York. 



RULES FOR CONDUCTING BOILER-TESTS. 867 

If the object of the trial is to ascertain the maximum economy or capac- 
ity of the boiler as a steam-generator, the boiler and all its appurtenances 
should be put in first-class condition. Clean the heating surface inside 
and outside, remove clinkers from the grates and from the sides of the 
furnace. Remove all dust, soot, and ashes from the chambers, smoke- 
connections and flues. Close air-leaks in the masonry and poorly fitted 
cleaning-doors. See that the damper will open wide and close tight. 
Test for air-leaks by firing a few shovels of smoky fuel and immediately 
closing the damper, observing the escape of smoke through the crevices; 
or by passing the flame of a candle over cracks in the brickwork. 

IV. Determine the character of the coal to be used. For tests of the 
efficiency or capacity of the boiler for comparison with other boilers the 
coal should, if possible, be of some kind which is commercially regarded 
as a standard. For New England and that portion of the country east 
of the Allegheny Mountains, good anthracite egg coal, containing not 
over 10 per cent of ash, and semi-bituminous Clearfield (Pa.), Cumberland 
(Md.), and Pocahontas (Va.) coals are thus regarded. West of the Alle- 
gheny Mountains, Pocahontas (Va.) and New River (W. Va.) semi-bitu- 
minous, and Youghiogheny or Pittsburg bituminous coals are recognized 
as standards.* 

For tests made to determine the performance of a boiler with a partic- 
ular kind of coal, such as may be specified in a contract for the sale of a 
boiler, the coal used should not be higher in ash and in moisture than that 
specified, since increase in ash and moisture above a stated amount is 
apt to cause a falling off of both capacity and economy in greater propor- 
tion than the proportion of such increase. 

V. Establish the correctness of all apparatus used in the test for weighing 
and measuring. These are: 

1. Scales for weighing coal, ashes, and water. 

2. Tanks or water-meters for measuring water. Water-meters, as a 
rule, should only be used as a check on other measurements. For accu- 
rate work the water should be weighed or measured in a tank. 

3. Thermometers and pyrometers for taking temperatures of air, steam, 
feed-water, waste gases, etc. 

4. Pressure-gauges, draught-gauges, etc. 

VI. See that the boiler is thoroughly heated before the trial to its usual 
working temperature. If the boiler is new and of a form provided with a 
brick setting, it should be in regular use at least a week before the trial, 
so as to dry and heat the walls. If it has been laid off and become cold, 
it should be worked before the trial until the walls are well heated. 

VII. The boiler and connections should be proved to be free from leaks 
before beginning a test, and all water connections, including blow and 
extra feed-pipes, should be disconnected, stopped with blank flanges, or 
bled through special openings beyond the valves, except the particular 
pipe through which water is to be fed to the boiler during the trial. During 
the test the blow-off and feed pipes should remain exposed to view. 

If an injector is used, it should receive steam directly through a felted 
pipe from the boiler being tested.! 

If the water is metered after it passes the injector, its temperature 
should be taken at the point where it leaves the injector. If the quan- 
tity is determined before it goes to the injector, the temperature should 
be determined on the suction side of the injector, and if no change of 

* These coals are selected because they are about the only coals which 
possess the essentials of excellence of quality, adaptability to various 
kinds of furnaces, grates, boilers, and methods of firing, and wide distribu- 
tion and general accessibility in the markets. 

t In feeding a boiler undergoing test with an injector taking steam from 
another boiler, or from the main steam-pipe from several boilers, the evap- 
orative results may be modified by a difference in the quality of the steam ■ 
from such source compared with that supplied by the boiler being tested, 
and in some cases the connection to the injector may act as a drip for the 
main steam-pipe. If it is known that the steam from the main pipe is of 
the same pressure and quality as that furnished by the boiler undergoing 
the test, the steam may be taken from such main pipe. 



868 THE STEAM-BOILER. 



temperature occurs other than that due to the injector, the temperature 
thus determined is properly that of the feed-water. When the temper- 
ature changes between the injector and the boiler, as by the use of a 
heater or by radiation, the temperature at which the water enters and 
leaves the injector and that at which it enters the boiler should all t>^ taken. 
In that case the weight to be used is tnat of the water leaving theu.jector, 
computed from the heat units if not directly measured; and the tem- 
perature, that of the water entering the boiler. 

Let w = weight of water entering the injector; 
x = weight of steam entering the injector; 
hi= heat-units per pound of water entering injector; 
h2= heat-units per pound of steam entering injector; 
hz = heat-units per pound of water leaving injector. 

Then w + x = weight of water leaving injector; 

_ hi — hi 
hi — h% 

See that the steam-main is so arranged that water of condensation 
cannot run back into the boiler. 

VIII. Duration of the Test. — For tests made to ascertain either the 
maximum economy or the maximum capacity of a boiler, irrespective of 
the particular class of service for which it is regularly used, the duration 
should be at least ten hours of continuous running. If the rate of com- 
bustion exceeds 25 pounds of coal per square foot of grate-surface per 
hour, it may be stopped when a total of 250 pounds of coal has been 
burned per square foot of grate. 

IX. Starting and Stopping a Test. — The conditions of the boiler and 
furnace in all respects should be, as nearly as possible, the same at the end 
as at the beginning of the test. The steam-pressure should be the 
same; the water-level the same; the fire upon the grates should be the 
same in quantity and condition; and the walls, flues, etc., should be of 
the same temperature. Two methods of obtaining the desired equality 
of conditions of the fire may be used, viz., those which were called in the 
Code of 1885 "the standard method" and "the alternate method," the 
latter being employed where it is inconvenient to make use of the stand- 
ard method.* 

X. Standard Method of Starting and Stopping a Test. — Steam being 
raised to the working pressure, remove rapidly all the fire from the grate, 
close the damper, clean the ash-pit, and as quickly as possible start a new 
fire with weighed wood and coal, noting the time and the water-level, 
while the water is in a quiescent state, just before lighting the fire.f 

At the end of the test remove the whole fire, which has been burned low, 
clean the grates and ash-pit, and note the water-level when the water is 
in a quiescent state, and record the time of hauling the fire. The water- 
level should be as nearly as possible the same as at the beginning of the 
test. If it is not the same, a correction should be made by computation, 
and not by operating the pump after the test is completed. 

XI. Alternate Method of Starting and Stopping a Test. — The boiler 
being thoroughly heated by a preliminary run, the fires are to be burned 
low and well cleaned. Note the amount of coal left on the grate as nearly 
as it can be estimated; note the pressure of steam and the water-level. 
Note the time, and record it as the starting-time. Fresh coal which has 

* The Committee concludes that it is best to retain the designations 
"standard" and "alternate," since they have become widely known and 
established in the minds of engineers and in the reprints in the Code of 
1885. Many engineers prefer the "alternate" to the "standard" method 
on account of its being less liable to error due to cooling of the boiler at the 
. beginning and end of a test. 

t The gauge-glass should not be blown out within an hour before the 
water-level is taken at the beginning and end of a test, otherwise an 
error in the reading of the water-level may be caused by a change in the 
temperature and density of the water in the pipe leading from the bottom 
of the glass into the boiler. 



RULES FOR CONDUCTING BOILER-TESTS. 869 

been weighed should now be fired. The ash-pits should be thoroughly 
cleaned at once after starting. Before the end of the test the fires should 
be burned low, just as before the start, and the fires cleaned in such a 
manner as to leave a bed of coal on the grates of the same depth, and in 
the same condition, as at the start. When this stage is reached, note the 
time and record it as the stopping-time. The water-level and steam- 
pressures should previously be brought as nearly as possible to the same 
point as at the start. If the water-level is not the same as at the start, a 
correction should be made by computation, and not by operating the 
pump after the test is completed. 

XII. Uniformity of Conditions. — In all trials made to ascertain max- 
imum economy or capacity the conditions should be maintained uni- 
formly constant. Arrangements should be made to dispose of the steam 
so that the rate of evaporation may be kept the same from beginning to 
end. 

XIII. Keeping the Records. — Take note of every event connected with 
the progress of the trial, however unimportant it may appear. Record 
the time of every occurrence and the time of taking every weight and 
every observation. 

The coal should be weighed and delivered to the fireman in equal propor- 
tions, each sufficient for not more than one hour's run, and a fresh portion 
should not be delivered until the previous one has all been fired. The 
time required to consume each portion should be noted, the time being 
recorded at the instant of firing the last of each portion. It is desirable 
that at the same time the amount of water fed into the boiler should be 
accurately noted and recorded, including the height of the water in the 
boiler, and the average pressure of steam and temperature of feed during 
the time. By thus recording the amount of water evaporated by succes- 
sive portions of coal, the test may be divided into several periods if desired, 
and the degree of uniformity of combustion, evaporation, and economy 
analyzed for each period. In addition to these records of the coal and 
the feed-water, half-hourly observations should be made of the tem- 
perature of the feed-water, of the flue-gases, of the external air in the 
boiler-room, of the temperature of the furnace when a furnace-pyrometer 
is used, also of the pressure of steam, and of the readings of the instru- 
ments for determining the moisture in the steam. A log should be kept 
on properly prepared blanks containing columns for record of the various 
observations. 

XIV. Quality of Steam. — The percentage of moisture in the steam 
should be determined by the use of either a throttling or a separating 
steam-calorimeter. The sampling-nozzle should be placed in the vertical 
steam-pipe rising from the boiler. It should be made of 1/2-inch pipe, 
and should extend across the diameter of the steam-pipe to within half 
an inch of the opposite side, being closed at the end and perforated with 
not less than twenty 1/8-inch holes equally distributed along and aroun-l 
its cylindrical surface, but none of these holes should be nearer than 1/2 inch 
to the inner side of the steam-pipe. The calorimeter and the pipe leading 
to it should be well covered with felting. Whenever the indications of the 
throttling or separating calorimeter show that the percentage of moisture 
is irregular, or occasionally in excess of three per cent, the results should 
be checked by a steam-separator placed in the steam-pipe as close to the' 
boiler as convenient, with a calorimeter in the steam-pipe just beyond 
the outlet from the separator. The drip from the separator should be 
caught and weighed, and the percentage of moisture computed therefrom 
added to that shown by the calorimeter. 

Superheating should be determined by means of a thermometer placed 
• in a mercury-weil inserted in the steam-pipe. The degree of superheating 
should be taken as the difference between the reading of the thermometer 
for superheated steam and the readings of the same thermometer for 
saturated steam at the same pressure as determined by a special experi- 
ment, and not by reference to steam-tables. 

XV. Sampling the Coal and Determining its Moisture. — As each 
barrow-load or fresh portion of coal is taken from the coal-pile, a repre- 
sentative shovelful is selected from it and placed in a barrel or box in a 
cool place and kept until the end of the trial. The samples are then mixed 
and broken into pieces not exceeding one inch in diameter, and reduced 
by the process of repeated quartering and crushing until a final sample 



870 THE STEAM-BOILER. 

weighing about five pounds is obtained, and the size of the larger pieces 
is such that they will pass through a sieve with 1/4-inch meshes. From 
this sample two one-quart, air-tight glass preserving-jars, or other air-tight 
vessels which will prevent the 'escape of moisture from the sample, are 
to be promptly filled, and these samples are to be kept for subsequent 
determinations of moisture and of heating value and for chemical analyses. 
During the process of quartering, when the sample has been reduced to 
about 100 pounds, a quarter to a half of it may be taken for an approxi- 
mate determination of moisture. This may be made by placing it in a 
shallow iron pan, not over three inches deep, carefully weighing it, and 
setting the pan in the hottest place that can be found on the brickwork 
of the boiler-setting or flues, keeping it there for at least 12 hours, and 
then weighing it. The determination of moisture thus made is believed 
to be approximately accurate for anthracite and semi-bituminous coals, 
and also for Pittsburg or Youghiogheny coal; but it cannot be relied upon 
for coals mined west of Pittsburg, or for other coals containing inherent 
moisture. For these latter coals it is important that a more accurate 
method be adopted. The method recommended by the Committee for 
all accurate tests, whatever the character of the coal, is described as 
follows: 

Take one of the samples contained in the glass jars, and subject it to a 
thorough air-drying, by spreading it in a thin layer and exposing it for 
several hours to the atmosphere of a warm room, weighing it before and 
after, thereby determining the quantity of surface moisture it contains. 
Then crush the whole of it by running it through an ordinary coffee-mill 
adjusted so as to produce somewhat coarse grains (less than Vie inch), 
thoroughly mix the crushed sample, select from it a portion of from 10 to 
50 grams, weigh it in a balance which will easily show a variation as small 
as 1 part in 1000, and dry it in an air- or sand-bath at a temperature 
between 240 and 280 degrees Fahr. for one hour. Weigh it and record 
the loss, then heat and weigh it again repeatedly, at intervals of an hour 
or less, until the minimum weight has been reached and the weight begins 
to increase by oxidation of a portion of the coal. The difference between 
the original and the minimum weight is taken as the moisture in the air- 
dried coal. This moisture test should preferably be made on duplicate 
samples, and the results should agree within 0.3 to 0.4 of one per cent, 
the mean of the two determinations being taken as the correct result. 
The sum of the percentage of moisture thus found and the percentage of 
surface moisture previously determined is the total moisture. 

XVI. Treatment of Ashes and Refuse. — The ashes and refuse are to be 
weighed in a dry state. If it is found desirable to show the principal 
characteristics of the ash, a sample should be subjected to a proximate 
analysis and the actual amount of incombustible material determined. 
For elaborate trials a complete analysis of the ash and refuse should be 
made. 

XVII. Calorific Tests and Analysis of Coal. — The quality of the fuel 
should be determined either by heat test or by analysis, or by both. 

The rational method of determining the total heat of combustion is to 
burn the sample of coal in an atmosphere of oxygen gas, the coal to be 
sampled as directed in Article XV of this code. 

The chemical analysis of the coal should be made only by an expert 
chemist. The total heat of combustion computed from the results of 
the ultimate analysis may be obtained by the use of Dulong's formula 
(with constants modified by recent determinations), viz., 



14,600 0+62,000 



(-*)- 



in which C, H, O, and S refer to the proportions of carbon, hydrogen, 
oxygen, and sulphur respectively, as determined by the ultimate analysis.* 
It is desirable that a proximate analysis should be made, thereby deter- 
mining the relative proportions of volatile matter and fixed carbon. 
These proportions furnish an indication of the leading characteristics of 
the fuel, and serve to fix the class to which it belongs. 

* Favre and Silbermann give 14,544 BT.TT. per pound carbon; Berthe- 
lot, 14.647 B.T.U. Favre and Silbermann give 62,032 B.T.U. per pound 
hydrogen; Thomsen, 61,816 B.T.U. 



RULES FOR CONDUCTING BOILER-TESTS. 871 

XVIII. Analysis of Flue-gases. — The analysis of the flue-gases is an 
especially valuable method of determining the relative value of different 
methods' of firing or of different kinds of furnaces. In making these 
analyses great care should be taken to procure average samples, since the 
composition is apt to vary at different points of the flue. The composition 
is also apt to vary from minute to minute, and for this reason the drawings 
of gas should last a considerable period of time. Where complete deter- 
minations are desired, the analyses should be intrusted to an expert 
chemist. For approximate determinations the Orsat or the Hempel 
apparatus may be used by the engineer. 

For the continuous indication of the amount of carbonic acid present 
in the flue-gases an instrument may be employed which shows the weight 
of CO2 in the sample of gas passing through it. 

XIX. Smoke Observations. — It is desirable to have a uniform system 
of determining and recording the quantity of smoke produced where 
bituminous coal is used. The system commonly employed is to express 
the degree of smokiness by means of percentages dependent upon the 
judgment of the observer. The actual measurement of a sample of soot 
and smoke by some form of meter is to be preferred. 

XX. Miscellaneoiis. — In tests for purposes of scientific research, in 
which the determination of all the variables entering into the test is 
desired, certain observations should be made which are in general unneces- 
sary for ordinary tests. As these determinations are rarely undertaken, 
it is not deemed advisable to give directions for making them. 

XXI. Calculations of Efficiency. — Two methods of defining and calcu- 
lating the efficiency of a boiler are recommended. They are: 

- r, ffi • * x, 1, -i Heat absorbed per lb. combustible 

1. Efficiency of the boiler- Calorific value of ! ib , combustibIe - 

n t^ • .,, , ., , Heat absorbed per ib. coal 

2. Efficiency of the boiler and grate- Calorific vaIue f l lb. coal ' 

The first of these is sometimes called the efficiency based on combusti- 
ble, and the second the efficiency based on coal. The first is recommended 
as a standard of comparison for all tests, and this is the one which is under- 
stood to be referred to when the word "efficiency" alone is used without 
qualification. The second, however, should be included in a report of a 
test, together with the first, whenever the object of the test is to determine 
the efficiency of the boiler and furnace together with the grate (or mechan- 
ical stoker), or to compare different furnaces, grates, fuels, or methods of 
firing. 

The heat absorbed per pound of combustible (or per pound coal) is to 
be calculated by multiplying the equivalent evaporation from and at 212 
degrees per pound combustible (or coal) by 965.7. 

XXII. The Heat Balance. — An approximate "heat balance " may be 
included in the report of a test when analyses of the fuel and of the chim- 
ney-gases have been made. It should be reported in the following form: 
[see next page.] 

XXIII. Report of the Trial. — The data and results should be reported 
in the manner given in either one of the two following tables [only the 
"Short Form" of table is given here], omitting lines where the tests have 
not been made as elaborately as provided for in such tables. Additional 
lines may be added for data relating to the specific object of the test. 
The Short Form of Report, Table No. 2, is recommended for commercial 
tests and as a convenient form of abridging- the longer form for publication 
when saving of space is desirable. For elaborate trials it is recommended 
that the full log of the trial be shown graphically, by means of a chart. 



872 



THE STEAM-BOILER. 



Heat Balance, or Distribution of the Heating Value op the Com- 
, bustible. 

Total Heat Value of 1 lb of Combustible B.T.U. 



Per 

Cent. 



1 - Heat absorbed by the boiler = evaporation from and at 
212 degrees per pound of combustible X 965.7 * 

2. Loss due to moisture in coal = per cent of moisture 
referred to combustible -h 100 X [(212 - t) + 966 + 
48 (T — 212)] (t = temperature of air in the boiler- 
room, T = that of the flue-gases) 

? Loss due to moisture formed by the burning of hydro- 
gen = per cent of hydrogen to combustible •*■ 100 x 9 
X [(212 - t) + 966 + 0.48 (T - 212)] 

4. t Loss due to heat carried away in the dry chimney-gases 

= weight of gas per pound of combustible x 0.24 x 
(T-t). 

5. % Loss due to incomplete combustion of carbon 

CO per cent C in combustible , n ,__ 
= COTTCO X_ 100 x 10,150 

6. Loss due to unconsumed hydrogen and hydrocarbons, 

to heating the moisture in the air, to radiation, and 
unaccounted for. (Some of these losses may be sepa- 
rately itemized if data are obtained from which they 

may be calculated) 

Totals 




* [The figure 965.7 (or 966) is taken from the old steam tables. If 
Peabody's new table (1909) is used it should be changed to 969.7, or if 
Marks & Davis's table is used, to 970.4.] 

t The weight of gas per pound of carbon burned may be calculated 
from the gas analyses as follows: 

11 C0 2 +80+7(CO+ N) . ■' ■-. ^ A 

Dry gas per pound carbon = _ .„,_ — , „;,. , in which COi, 

o (OU2 + LUJ 
CO, O, and N are the percentages by volume of the several gases. As the 
sampling and analyses of the gases in the present state of the art are 
liable to considerable errors, the result of this calculation is usually only 
an approximate one. The heat balance itself is also only approximate 
for this reason, as well as for the fact that it is not possible to determine 
accurately the percentage of unburned hydrogen or hydrocarbons in the 
flue-gases. 

The weight of dry gas per pound of combustible is found by multiply- 
ing the dry gas per pound of carbon by the percentage of carbon in the 
combustible, and dividing by 100. 

t CO2 and CO are respectively the percentage by volume of carbonic 
^cid and carbonic oxide in the flue-gases. The quantity 10,150 = num- 
oer of heat-units generated by burning to carbonic acid one pound of car- 
bon contained in carbonic oxide. 



RULES FOR CONDUCTING BOILER-TESTS. 



873 



TABLE NO. 2. 

Data and Results of Evaporative Test. 

Arranged in accordance with the Short Form advised by the Boiler Test 

Committee of the American Society of Mechanical Engineers. 

Code of 1899. 

Made by .on boiler, at 

to determine 

Kind of fuel 

Kind of furnace 



Method of starting and stopping the test (" standard ' : 

or " alternate," Arts. X and XI, Code) 

Grate surface 

Water-heating surface 

Superheating surface. 



total quantities. 

1 . Date of trial 

2. Duration of trial 

3. Weight of coal as fired * 

4. Percentage of moisture in coal f •• 

5. Total weight of dry coal consumed 

6. Total ash and refuse 

7. Percentage of ash and refuse in dry coal 

8. Total weight of water fed to the boiler J 

9. Water actually evaporated, corrected for moisture 

or superheat in steam 

9a. Factor of evaporation § 

10. Equivalent water evaporated into dry steam from 
and at 212 degrees. || (Item 9 x Item 9a.) , 



HOURLY QUANTITIES. 

1 1 . Dry coal consumed per hour 

12. Dry coal per square foot of grate surface per hour 

13. Water evaporated per hour corrected for quality of 

steam 

14. Equivalent evaporation per hour from and at 212 de- 



15. Equivalent evaporation per hour from and at 212 de- 
grees per square foot of water-heating surface || 



sq.ft. 



hours 

lbs. 

per cent 

lbs. 

per cent 
lbs. 



* Including equivalent of wood used in lighting the fire, not including 
unburned coal withdrawn from furnace at times of cleaning and at end of 
test. One pound of wood is taken to be equal to 0.4 pound of coal, or, in 
case greater accuracy is desired, as having a heat value equivalent to the 
evaporation of 6 pounds of water from and at 212 degrees per pound. 
(6 X 965.7 = 5794 B.T.U.) The term "as fired" means in its actual 
condition, including moisture. 

t This is the total moisture in the coal as found by drying it artificially, 
as described in Art. XV of Code. 

X Corrected for inequality of water-level and of steam-pressure at 
beginning and end of test. 

§ Factor of evaporation = .__ ■, in which H and h are respectively 
yoo.7 
the total heat in steam of the average observed pressure, and in water of 
the average observed temperature of the feed. 

H The symbol "U.E.," meaning "units of evaporation," may be con- 
veniently substituted for the expression "Equivalent water evaporated 
into dry steam from and at 212 degrees," its definition being given in a 
foot-note. 



874 



THE STEAM-BOILER. 



TABLE NO. 2 — Continued. 
Data and Results of Evaporative Test. 



AVERAGE PRESSURES, TEMPERATURES, ETC 

16. Steam pressure by gauge 

17. Temperature of feed-water entering boiler 

18. Temperature of escaping gases from boiler 

19. Force of draught between damper and boiler 

20. Percentage of moisture in steam, or number of de- 
• grees of superheating 

HORSE-POWER. 

2! . Horse-power developed. (Item 14 -s- 341/2.)* 

22. Builders' rated horse-power 

23. Percentage of builders' rated horse-power developed. 

ECONOMIC RESULTS- 

24. Water apparently evaporated under actual condi- 

tions per pound of coal as fired. (Item 8H-Item3.) 

25. Equivalent evaporation from and at 212 degrees per 

pound of coal as fired. || (Item 10 -=- Item 3.) 

26. Equivalent evaporation from and at 212 degrees per 

pound of dry coal.|| (Item 10 -f- Item 5.) 

27. Equivalent evaporation from and at 212 degrees per 

pound of combustible. [Item 10- -r (Item 5 — 

Item 6) .] 

(If Items 25, 26, and 27 are not corrected for quality 
of steam, the fact should be stated.) 

EFFICIENCY. 

28. Calorific value of the dry coal per pound 

29. Calorific value of the combustible per pound 

30. Efficiency of boiler (based on combustible) f 

31. Efficiency of boiler, including grate (based on dry 

coal) 

COST OF EVAPORATION. 

32. Cost of coal per ton of lbs. delivered in boiler- 

room 

33. Cost of coal required for evaporating 1000 pounds of 

water from and at 212 degrees 



lbs.p.sq.in, 
deg. 

ins. of water 

% or deg. 

H.P. 
per cent 



B.T.U. 

per cent 



* Held to be the equivalent of 30 lbs. of water evaporated from 100 
degrees Fahr. into dry steam at 70 lbs. gauge-pressure. 

t In all cases where the word "combustible" is used, it means the 
coal without moisture and ash, but including all other constituents. It 
is the same as what is called in Europe "coal dry and free from ash." 

II See foot-note on the preceding page. ' 



FACTORS OF EVAPORATION. 

The figures in the table on the next four pages are calculated from the 
formula F =(H — h) h- 970.4, in which H is the total heat above 32° of 
1 lb. of steam of the observed pressure, h the total heat above 32° of the 
feed water, and 970.4 the heat of vaporization, or latent heat, of steam at 
212° F. The values of these total heats and of the latent heat are those' 
given in Marks and Davis's steam tables. 

The factors are given for every 3° of feed water temperature between 
32° and 212°, and for every 5 or 10 lbs. steam pressure within the ordinary 
working limits of pressure. Intermediate values correct to the third 
decimal place may easily be found by interpolation. 



FACTORS OF EVAPORATION 



875 





Lbs 




















Gauge press. . 0.3 


10.3 


20.3 


30.3 


40.3 


50.3 


60.3 


70.3 


80.3 


85.3 


Abs. press. . . .15. 


25. 


35. 


45. 


55. 


65. 


75. 


85. 


95. 


100. 


Feed 
water. 


Factors of Evaporation. 


212° F. 


1.0003 


1.0103 


1.0169 


1.0218 


1.0258 


1.0290 


1.0316 


1 .0340 


1.0361 


1.03/0 


209 


34 


34 


1.0200 


50 


89 


1.0321 


47 


71 


92 


1.0401 


206 


65 


65 


31 


81 


1.0320 


52 


79 


1.0402 


1.0423 


32 


203 


96 


96 


62 


1.0312 


51 


83 


1.0410 


33 


54 


63 


200 


1.0127 


1.0227 


93 


43 


82 


1.0414 


41 


64 


85 


94 


197 


58 


58 


1.0324 


74 


1.0413 


45 


72 


95 


1.0516 


1 .0525 


194 


89 


89 


55 


1.0405 


44 


76 


1.0503 


1.0526 


47 


56 


191 


1.0220 


1.0320 


86 


36 


75 


1.0507 


34 


57 


78 


87 


188 


51 


51 


1.0417 


67 


1 .0506 


38 


65 


88 


1.0609 


1.0618 


185 


82 


82 


48 


98 


37 


69 


96 


1.0619 


40 


49 


182 


1.0313 


1.0413 


79 


1.0529 


68 


1.0600 


1 .0627 


50 


71 


80 


179 


44 


44 


1.0510 


60 


99 


31 


58 


81 


1.0702 


1.0711 


176 


75 


» 75 


41 


91 


1.0630 


62 


89 


1.0712 


33 


42 


173 


1.0406 


1.0505 


72 


1.0622 


61 


93 


1.0720 


43 


64 


73 


170 


37 


37 


1.0603 


53 


92 


1 .0724 


51 


74 


95 


1.0804 


167 


68 


68 


34 


84 


1.0723 


55 


82 


1 .0805 


1 .0826 


35 


164 


99 


99 


65 


1.0715 


54 


86 


1.0812 


36 


57 


66 


161 


1.0530 


1.0630 


96 


45 


85 


1.0817 


43 


67 


88 


97 


158 


61 


61 


1.0727 


76 


1.0816 


47 


74 


98 


1.0919 


1 .0928 


155 


92 


92 


58 


1.0807 


46 


78 


1.0905 


1.0929 


50 


59 


152 


1 .0623 


1 .0723 


89 


38 


77 


1.0909 


36 


60 


80 


90 


149 


54 


54 


1 .0820 


69 


1 .0908 


40 


67 


91 


1.1011 


1.1021 


146 


85 


85 


51 


1 .0900 


39 


71 


98 


1.1022 


42 


52 


143 


1.0715 


1.0815 


81 


31 


70 


1.1002 


1.1029 


52 


73 


82 


140 


46 


46 


1.0912 


62 


1.1001 


33 


60 


83 


1.1104 


1.1113 


137 


77 


77 


43 


93 


32 


64 


91 


1.1114 


35 


» 44 


134 


1.0808 


1.0908 


74 


1.1023 


63 


95 


1.1121 


45 


66 


75 


131 


39 


39 


1.1005 


54 


93 


1.1125 


52 


76 


97 


1.1206 


128 


70 


70 


36 


85 


1.1124 


56 


83 


1.1207 


1.1227 


37 


125 


1.0901 


1.1001 


67 


1.1116 


55 


87 


1.1214 


38 


58 


68 


122 


31 


31 


97 


47 


86 


1.1218 


45 


69 


89 


98 


119 


62 


62 


1.1128 


78 


1.1217 


49 


76 


99 


1.1320 


1.1329 


116 


93 


93 


59 


1.1209 


48 


80 


1.1306 


1 . 1330 


51 


60 


113 


1.1024 


1.1124 


90 


39 


79 


1.1310 


37 


61 


82 


91 


110 


55 


55 


1.1221 


70 


1 . 1309 


41 


68 


92 


1.1412 


1.1422 


107 


86 


86 


52 


1.1301 


40 


72 


99 


1.1423 


43 


53 


104 


1.1116 


1.1216 


82 


32 


71 


1.1403 


1.1430 


53 


74 


83 


101 


47 


47 


1.1313 


63 


1.1402 


34 


61 


84 


1.1505 


1.1514 


98 


78 


78 


44 


93 


33 


65 


91 


1.1515 


36 


45 


95 


1.1209 


1.1309 


75 


1.1424 


63 


95 


1.1522 


46 


66 


76 


92 


40 


40 


1.1406 


55 


94 


1.1526 


53 


77 


97 


1.1607 


89 


71 


71 


37 


86 


1.1525 


57 


84 


1.1608 


1.1628 


37 


86 


1.1301 


1.1401 


67 


1.1518 


56 


88 


1.1615 


38 


59 


68 


83 


32 


32 


98 


48 


87 


1.1619 


46 


69 


90 


99 


80 


63 


63 


1.1529 


78 


1.1618 


50 


76 


1.1700 


1.1721 


1.1730 


77 


94 


94 


60 


1.1609 


48 


80 


1.1707 


31 


51 


61 


74 


1.1425 


1.1525 


91 


40 


79 


1.1711 


38 


62 


82 


92 


71 


55 


55 


1.1621 


71 


1.1710 


42 


69 


92 


1.1813 


1.1822 


68 


86 


86 


52 


1.1702 


41 


73 


1.1800 


1.1823 


44 


53 


65 


1.1517 


1.1617 


83 


33 


72 


1.1804 


30 


54 


75 


84 


62 


48 


48 


1.1714 


63 


1.1803 


35 


61 


85 


1.1906 


1.1915 


59 


79 


79 


45 


94 


33 


65 


92 


1.1916 


37 


46 


56 


1.1610 


1.1710 


76 


1.1825 


64 


96 


1 . 1923 


47 


67 


77 


53 


41 


41 


1.1807 


56 


95 


1.1927 


54 


78 


98 


1.2008 


50 


72 


72 


38 


87 


1.1926 


58 


85 


1.2009 


1.2029 


39 


47 


1.1703 


1.1803 


69 


1.1918 


57 


89 


1.2016 


40 


60 


70 


44 


34 


34 


1.1900 


49 


88 


1.2020 


47 


71 


91 


1. 2101 


41 


65 


65 


31 


80 


1.2019 


51 


78 


1.2102 


1.2122 


32 


38 


96 


95 


62 


1.2011 


50 


82 


1.2109 


33 


53 


63 


35 


1.1827 


1 . 1927 


93 


42 


81 


1.2113 


40 


64 


84 


94 


32 


58 


58 


1.2024 


73 


1.2113 


44 


71 


95 


1.2216 


1.2225 



THE STEAM-BOILER. 



Lbs. 
Gauge press. 90.3 
Abs. press. .105. 



95.3 100.3 105.3 110.3 115.3 120.3 125.3 130.3 135.3 140.3 
110. 115. 120. 125. 130. 135. 140. 145: 150. 155. 



Feed 
water. 








Factors of Evaporation. 








212° F. 


1.0379 


1.0387 


1.0396 


1.0404 


1.0411 


1.0418 


1.0425 


1.0431 


1 .0437 


1.0443 


1.0449 


209 


1.0410 


1.0419 


1.0427 


35 


42 


49 


56 


62 


68 


74 


80 


206 


41 


50 


58 


66 


73 


81 


87 


93 


99 


1.0505 


1.0511 


'.03 


72 


81 


89 


97 


1.0504 


1.0512 


1.0518 


1 .0524 


1 .0530 


36 


43 


200 


1 .0504 


1.0512 


1.0520 


1.0528 


35 


43 


49 


55 


61 


67 


74 


197 


35 


43 


51 


59 


66 


74 


80 


86 


92 


98 


1.0605 


194 


66 


74 


82 


90 


97 


1.0605 


1.0611 


1.0617 


1 .0623 


1.0629 


36 


191 


97 


1.0605 


1.0613 


1 .0621 


1.0629 


36 


42 


48 


54 


60 


67 


188 


1.0628 


36 


44 


52 


60 


67 


73 


79 


85 


91 


98 


185 


59 


67 


75 


83 


91 


98 


1.0704 


1.0710 


1.0716 


1.0722 


1.0729 


182 


90 


98 


1.0706 


1.0714 


1.0721 


1.0729 


35 


41 


47 


53 


60 


179 


1 .0721 


1.0729 


37 


45 


52 


60 


66 


72 


78 


84 


91 


176 


52 


60 


68 


76 


83 


91 


97 


1 .0803 


1.0809 


1.0815 


1 .0822 


173 


82 


91 


99 


1 .0807 


1.0814 


1.0822 


1.0828 


34 


40 


46 


53 


170 


1.0813 


1.0822 


1.0830 


38 


45 


53 


59 


65 


71 


77 


83 


167 


44 


53 


61 


69 


76 


84 


90 


96. 


1.0902 


1.0908 


1.0914 


164 


75 


84 


92 


1 .0900 


1 .0907 


1.0914 


1.0921 


1.0927 


33 


39 


45 


161 


1 .0906 


1.0914 


1.0923 


31 


38 


45 


52 


58 


64 


70 


76 


158 


37 


45 


54 


62 


69 


76 


82 


89 


95 


1.1001 


1.1007 


155 


68 


76 


85 


93 


1.1000 


1.1007 


1.1013 


1.1020 


1.1026 


32 


38 


152 


99 


1.1007 


1.1015 


1.1024 


31 


38 


44 


51 


57 


63 


69 


149 


1.1030 


38 


46 


55 


62 


69 


75 


81 


88 


94 


1.1100 


146 


61 


69 


77 


86 


93 


1.1100 


1.1106 


1.1112 


1.1119 


1.1125 


31 


143 


92 


1.1100 


1.1108 


1.1116 


1.1124 


31 


37 


43 


49 


55 


62 


140 


1.1123 


31 


39 


47 


54 


62 


68 


74 


80 


86 


93 


137 , 


53 


62 


70 


78 


85 


93 


99 


1.1205 


1.1211 


1.1217 


1.1224 


134 


84 


93 


1.1201 


1.1209 


1.1216 


1.1223 


1.1230 


36 


42 


48 


54 


131 


1.1215 


1.1223 


32 


40 


47 


54 


60 


67 


73 


79 


85 


128 


46 


54 


62 


71 


78 


85 


91 


98 


1.1304 


1.1310 


1.1316 


125 


77 


85 


93 


1.1302 


1.1309 


1.1316 


1.1322 


1 . 1328 


35 


41 


47 


122 


1 . 1308 


1.1316 


1.1324 


32 


40 


47 


53 


59 


65 


71 


78 


119 


39 


47 


55 


63 


70 


78 


84 


90 


96 


1.1402 


1.1409 


116 


69 


78 


86 


94 


1.1401 


1.1408 


1.1415 


1.1421 


1.1427 


33 


39 


113 


1.1400 


1.1408 


1.1417 


1.1425 


32 


39 


45 


52 


58 


64 


70 


110 


31 


39 


47 


56 


63 


70 


76 


82 


89 


95 


1.1501 


107 


62 


70 


78 


87 


94 


1.1501 


1.1507 


1.1513 


1.1519 


1.1526 


32 


104 


92 


1.1501 


1.1509 


1.1517 


1.1525 


32 


38 


44 


50 


56 


63 


101 


1.1523 


32 


40 


48 


55 


63 


69 


75 


81 


87 


93 


98 


54 


62 


71 


79 


86 


93 


1.1600 


1.1606 


1.1612 


1.1618 


1.1624 


95 


85 


93 


1.1602 


1.1610 


1.1617 


1.1624 


30 


37 


43 


49 


55 


92 


1.1616 


1.1624 


32 


41 


48 


55 


61 


67 


74 


80 


86 


89 


47 


55 


63 


71 


79 


85 


92 


98 


1.1704 


1.1711 


1.1717 


86 


78 


86 


94 


1.1702 


1.1710 


1.1717 


1.1723 


1.1729 


35 


41 


48 


83 


1.1708 


1.1717 


1.1725 


33 


40 


48 


54 


60 


66 


72 


78 


80 


39 


47 


56 


64 


71 


78 


85 


91 


97 


1.1803 


1.1809 


77 


70 


78 


86 


95 


1.1802 


1.1809 


1.1815 


1.1822 


1.1828 


34 


40 


74 


1.1801 


1.1809 


1.1817 


1.1826 


33 


40 


46 


52 


59 


65 


71 


71 


32 


40 


48 


56 


64 


71 


77 


83 


89 


96 


1.1902 


68 


62 


71 


79 


87 


94 


1.1902 


1.1908 


1.1914 


1.1920 


1.1926 


33 


65 


93 


1.1902 


1.1910 


1.1918 


1.1925 


33 


39 


45 


51 


57 


63 


62 


1.1924 


32 


41 


49 


56 


63 


70 


76 


82 


88 


94 


59 


55 


63 


72 


80 


87 


94 


1.2000 


1.2007 


1.2013 


1.2019 


1.2025 


56 


86 


94 


1.2002 


1.2011 


1.2018 


1.2025 


31 


38 


44 


50 


56 


53 


1.2017 


1.2025 


33 


42 


49 


56 


62 


68 


75 


81 


87 


50 


48 


56 


64 


73 


80 


87 


93 


99 


1.2106 


1.2112 


1.2118 


47 


79 


87 


95 


1.2104 


1.2111 


1.2118 


1.2124 


1.2130 


37 


43 


49 


44 


1.2110 


1.2118 


1.2126 


35 


42 


49 


55 


61 


68 


74 


80 


41 


41 


49 


57 


66 


73 


80 


86 


92 


99 


1.2205 


1.2211 


38 


72 


80 


88 


97 


1.2204 


1.2211 


1.2217 


1.2223 


1.2230 


36 


42 


35 


1.2203 


1.2211 


1.2219 


1.2228 


35 


42 


48 


55 


61 


67 


73 


32 


34 


42 


51 


59 


66 


73 


79 


86 


92 


98 


1.2304 



FACTORS OF EVAPORATION. 



877 



150.3 155.3 160.3 165.3 170.3 175.3 
165. 170. 175. 180. 185. 190. 



180.3 185.3 190.3 195.3 
195. 200. 205. 210 



Feed 
water. 








Factors of Evap 


oration. 








212° F. 


1.0454 


1.0460 


1.0464 


1.0469 


1 .0474 


1.0478 


1 .0483 


1 .0487 


1 .0492 


1.0496 


1 .0499 


209 


86 


91 


95 


1 .0500 


1.0505 


1 .0509 


1.0514 


1.0519 


1 .0523 


1 .0527 


1 .0530 


206 


1.0517 


1 .0522 


1 .0526 


31 


36 


40 


45 


50 


54 


58 


61 


203 


48 


53 


57 


62 


67 


71 


77 


81 


85 


89 


92 


200 


79 


84 


88 


93 


98 


1.0602 


1 .0608 


1.0612 


1.0616 


1.0620 


1.0623 


197 


1.0610 


1.0615 


1.0619 


1.0624 


1.0629 


33 


39 


43 


47 


51 


54 


194 


41 


46 


50 


55 


60 


64 


70 


74 


78 


82 


85 


191 


72 


77 


81 


86 


91 


95 


1.0701 


1.0705 


1.0709 


1.0713 


1.0716 


188 


1.0703 


1 .0708 


1.0712 


1.0717 


1.0722 


1 .0727 


32 


36 


40 


44 


47 


185 


34 


39 


43 


48 


53 


58 


63 


67 


71 


75 


78 


182 


65 


70 


74 


79 


84 


88 


94 


98 


1.0802 


1.0806 


1 .0809 


179 


96 


1.0801 


1.0805 


1.0810 


1.0815 


1.0819 


1.0825 


1 .0829 


33 


37 


40 


176 


1.0827 


32 


36 


41 


46 


50 


56 


60 


64 


68 


71 


173 


58 


■ 63 


67 


72 


77 


8"1 


87 


91 


95 


99 


1 .0902 


170 


89 


94 


98 


1 .0903 


1.0908 


1.0912 


1.0917 


1 0922 


1.0926 


1.0930 


33 


167 


1.0920 


1 .0925 


1 .0929 


34 


39 


43 


48 


53 


57 


61 


64 


164 


51 


56 


60 


65 


70 


74 


79 


84 


88 


92 


95 


161 


81 


87 


91 


96 


1.1001 


1.1005 


1.1010 


1 1014 


1.1019 


1 . 1023 


1.1026 


158 


1.1012 


1.1018 


1.1022 


1.1027 


32 


36 


41 


45 


49 


54 


57 


155 


43 


48 


53 


58 


63 


67 


72 


76 


80 


85 


88 


152 


74 


79 


83 


89 


94 


98 


1.1103 


1.1107 


1.1111 


1.1115 


1.1119 


149 


1.1105 


1.1110 


1.1114 


1.1120 


1.1125 


1.1129 


34 


38 


42 


46 


49 


146 


36 


41 


45 


50 


56 


60 


65 


69 


73 


77 


80 


143 


67 


72 


76 


81 


86 


91 


96 


1.1200 


1.1204 


1 . 1208 


1.2111 


140 


98 


1.1203 


1.1207 


1.1212 


1.1217 


1.1221 


1.1227 


31 


35 


39 


42 


137 


1.1229 


34 


38 


43 


48 


52 


58 


62 


66 


70 


73 


134 


59 


65 


69 


74 


79 


83 


88 


92 


97 


1 . 1301 


1.1304 


131 


90 


95 


1.1300 


1.1305 


1.1310 


1.1314 


1.1319 


1.1323 


1 . 1327 


32 


35 


128 


1.1321 


1.1326 


30 


36 


41 


45 


50 


54 


58 


62 


66 


125 


52 


57 


61 


66 


72 


76 


81 


85 


89 


93 


96 


122 


83 


88 


92 


97 


1.1402 


1.1407 


1.1412 


1.1416 


1.1420 


1.1424 


1.1427 


119 


1.1414 


1.1419 


1.1423 


1.1428 


33 


37 


43 


47 


51 


55 


58 


116 


45 


50 


54 


59 


64 


68 


73 


78 


82 


86 


89 


113 


75 


81 


85 


90 


95 


99 


1.1504 


1.1508 


1.1512 


1.0515 


1.1520 


110 


1.1506 


1.1511 


1.1515 


1.1521 


1.1526 


1.1530 


35 


39 


43 


47 


50 


107 


37 


42 


46 


51 


57 


61 


66 


70 


74 


78 


81 


104 


68 


73 


77 


82 


87 


92 


97 


1.1601 


1.1605 


1 . 1609 


1.1612 


101 


99 


1.1604 


1.1608 


1.1613 


1.1618 


1.1622 


1.1627 


32 


36 


40 


43 


98 


1.1629 


35 


39 


44 


49 


53 


53 


62 


67 


71 


74 


95 


60 


65 


70 


75 


80 


84 


89 


93 


97 


1.1701 


1.1705 


92 


91 


96 


1.1700 


1.1705 


1.1711 


1.1715 


1.1720 


1.1724 


1.1728 


32 


35 


89 


1.1722 


1.1727 


31 


35 


42 


46 


51 


55 


59 


63 


66 


86 


53 


58 


62 


67 


72 


76 


82 


86 


90 


94 


97 


83 


84 


89 


' 93 


98 


1.1803 


1.1807 


1.1812 


1.1817 


1 . 1821 


1.1825 


1.1828 


80 


1.1814 


1.1820 


1.1824 


1.182? 


34 


38 


43 


47 


52 


56 


59 


77 


45 


50 


54 


60 


65 


69 


74 


78 


82 


86 


90 


74 


76 


81 


85 


90 


96 


1.1900 


1.1905 


1.1909 


1.1913 


1.1917 


1.1920 


71 


1.1907 


1.1912 


1.1916 


1.1921 


1.1926 


31 


36 


40 


44 


48 


51 


68 


38 


43 


47 


52 


57 


61 


67 


71 


75 


79 


82 


65 


69 


74 


78 


83 


88 


92 


97 


1.2002 


1 . 2006 


1.2010 


1.2013 


62 


99 


1.2005 


1 .2009 


1.2014 


1.2019 


1.2023 


1.2028 


32 


36 


41 


44 


59 


1.2030 


35 


40 


45 


50 


54 


59 


63 


67 


72 


75 


56 


61 


66 


70 


76 


81 


85 


90 


94 


98 


1.2102 


1.2106 


53 


92 


97 


1.2101 


1.2107 


1.2112 


1.2116 


1.2121 


1.2125 


1.2129 


33 


36 


50 


1.2123 


1.2128 


32 


37 


43 


47 


52 


56 


60 


64 


67 


47 


54 


59 


63 


68 


74 


78 


83 


87 


91 


95 


98 


44 


85 


90 


94 


1.2200 


1 .2205 


1.2209 


1.2214 


1.2218 


1.2222 


1.2226 


1.2229 


41 


1.2216 


1 .2221 


1.2225 


31 


36 


40 


45 


49 


53 


57 


60 


38 


47 


52 


56 


62 


67 


71 


76 


80 


84 


88 


91 


35 


78 


83 


88 


93 


98 


1.2302 


1.2307 


1.2311 


1.2315 


1.2320 


1.2323 


32 


1.2309 


1.2315 


1.2319 


1.2324 


1.2329 


33 


38 


42 


46 


51 


54 



THE STEAM-BOILER. 





Lbs. 






















Gauge press. 2J0.3 


255.3 210,3 215.3 220.3 225.3 230.3 235.: 


240.3 245.: 


250.. 


Abs. press. . .215. 


220. 


225. 


230. 


235. 


240. 


245. 


250. 


255.. 


260. 


265. 


Feed . 
water. 


Factors of Evaporation. 


212° F. 


1 .0503 


1.0507 


1.051C 


1.0513 


1.0517 


1.052C 


1.0523 


1.0527 


1.0525 


1 . 053 J 


1.053! 


209 


. 34 


3£ 


41 


44 


4£ 


52 


55 


56 


6C 


64 


6i 


206 


65 


69 


72 


75 


79 


83 


86 


89 


91 


95 


9! 


203 


96 


1.0600 


1.0603 


1.0606 


1.061 


1.0614 


1.0617 


1.0620 


1.0622 


1.0626 


1.062* 


200 


1.0627 


31 


34 


37 


42 


45 


48 


51 


53 


57 


6i 


197 


58 


62 


65 


6S 


73 


76 


79 


82 


84 


88 


9 


194 


89 


93 


96 


1.0700 


1.0704 


1.0707 


1.0710 


I .0713 


1.0715 


1.0719 


1.072. 


191 


1.0720 


1.0724 


1 .0727 


31 


35 


33 


41 


44 


46 


50 


5: 


188 


51 


55 


58 


62 


66 


69 


72 


75 


78 


81 


8- 


185 


82 


86 


89 


93 


97 


1.0800 


1.0803 


1.0806 


1.0809 


1.0812 


1.081! 


182 


1.0813 


1.0817 


1.0820 


1 .0823 


1.0828 


31 


34 


37 


39 


43 


4( 


179 


44 


48 


51 


54 


59 


62 


65 


68 


70 


74 


7; 


176 


75 


79 


82 


86 


90 


93 


96 


99 


1 .0901 


1 .0905 


I.090> 


173 


1 .0906 


1,0910 


1.0913 


1.0916 


1.0921 


1.0924 


1.0927 


1 .0930 


32 


36 


3< 


170 


37 


41 


44 


47 


51 


55 


58 


61 


63 


67 


6< 


167 


68 


72 


75 


78 


82 


86 


89 


92 


94 


98 


1.1001 


164 


99 


1.1003 


1.1005 


1.1009 


1.1013 


1.1016 


1.1019 


1.1023 


1.1025 


1.1029 


31 


•161 


1.1030 


34 


37 


40 


44 


47 


50 


54 


56 


60 


6: 


158 


61 


65 


68 


71 


75 


78 


81 


85 


87 


91 


91 


155 


92 


96 


99 


1.1102 


1.1106 


1.1109 


1.1112 


1.1115 


1.1118 


1.1122 


1.112' 


152 


1.U23 


1.1127 


1.1130 


33 


37 


40 


43 


46 


49 


53 


5.' 


149 


54 


58 


6) 


64 


68 


71 


74 


77 


80 


83 


8( 


146 


84 


89 


92 


95 


99 


1.1202 


1.1205 


1.1258 


1.1211 


1.1214 


1.121; 


143 


1.1215 


1.1219 


1.1223 


1.1226 


1 . 1230 


33 


36 


39 


42 


45 


41 


14Q 


46 


50 


53 


56 


61 


64 


67 


70 


72 


76 


7< 


137 


77 


81 


84 


87 


92 


95 


98 


1.1301 


1.1303 


1.1307 


1.1311 


134 


1.1308 


1.1312 


1.1315 


1.1318 


1 . 1322 


1.1326 


1.1329 


32 


34 


38 


4 


131 


39 


43 


46 


49 


53 


56 


59 


62 


65 


69 


71 


128 


70 


74 


77 


80 


84 


87 


90 


93 


96 


1.1400 


1.140; 


125 


1.1400 


1.1405 


1.1408 


1.1411 


1.1415 


1.1418 


1.1421 


1.1424 


1.1427 


30 


3. 


122 


31 


35 


39 


42 


46 


49 


52 


55 


58 


61 


6 


119 


62 


66 


69 


72 


77 


80 


83 


86 


88 


92 


9: 


116 


93 


97 


1.1500 


1.1503 


1.1507 


1.1511 


1.1514 


1.1517 


1.1519 


1.1523 


1.152! 


113 


1.1524 


1.1528 


31 


34 


38 


41 


44 


48 


50 


54 


5( 


110 


55 


59 


62 


65 


69 


72 


75 


76 


81 


85 


8; 


107 


85 


90 


93 


96 


1.1600 


1.1603 


1.1606 


1.1609 


1.1612 


1.1615 


1.1611 


104 


1.1616 


1.1620 


1.1624 


1.1627 


31 


34 


37 


40 


43 


46 


4« 


101 


47 


51 


54 


57 


61 


65 


68 


71 


73 


77 


8( 


98 


78 


82 


85 


88 


92 


95 


98 


1.1702 


1.1704 


1.1708 


1.1711 


95 


1.1709 


1.1713 


1.1716 


1.1719 


1.1723 


1.1726 


1.1729 


32 


35 


39 


4 


92 


39 


44 


47 


50 


54 


57 


60 


63 


66 


69 


7; 


89 


70 


75 


78 


81 


85 


88 


91 


94 


97 


1.1800 


1.180. 


86 


1.1801 


1.1805 


1.1808 


1.1812 


1.1816 


1.1819 


1.1822 


1.1825 


1.1827 


31 


3. 


83 


32 


36 


39 


42 


46 


50 


53 


56 


58 


62 


6 


80 


63 


67 


70 


73 


77 


80 


83 


87 


89 


93 


9: 


77 


94 


98 


1.1901 


1.1904 


1.1908 


1.1911 


1.1914 


1.1917 


1.1920 


1.1924 


1.192 


74 


1.1924 


1 . 1929 


32 


35 


39 


42 


45 


48 


51 


54 


5 


71 


55 


59 


63 


66 


70 


73 


76 


79 


82 


85 


8 


68 


86 


90 


93 


96 


1.2001 


1.2004 


1.2007 


1.2010 


1.2012 


1.2016 


1.201' 


65 


1.2017 


1.2021 


1.2024 


1.2027 


31 


35 


38 


41 


43 


47 


I 


62 


48 


52 


55 


58 


62 


65 


68 


72 


74 


78 


8 


59 


79 


83 


86 


89 


93 


96 


99 


1.2102 


1.2105 


1.2109 


1.211 


56 


1.2110 


1.2114 


1.2117 


1.2120 


1.2124 


1.2127 


1.2130 


33 


36 


40 


4 


53 


41 


45 


48 


51 


55 


58 


61 


64 


67 


70 


7 


50 


71 


76 


79 


82 


86 


89 


92 


95 


98 


1.2201 


1.220 


47 


1.2202 


1.2207 


1.2210 


1.2213 


1.2217 


1.2220 


1.2223 


1.2226 


1.2229 


32 


3 


44 


34 


38 


41 


44 


48 


51 


54 


57 


60 


63 


6 


41 


65 


69 


72 


75 


79 


82 


85 


88 


91 


94 


9 


38 


96 


1.2300 


1.2303 


1.2306 


1.2310 


1.2313 


1.2316 


1.2319 


1.2322 


1.2325 


1.232 


35 


1.2327 


31 


34 


37 


41 


44 


47 


50 


53 


57 


5 


32 


58 


62 


65 


68 


72 /5 


78 


82 


84 


88 


9< 



STRENGTH OF STEAM-BOILERS. 870 



STRENGTH OF STEAM-BOILERS. VARIOUS RULES FOR 
CONSTRUCTION.* 

There is a great lack of uniformity in the rules prescribed by different 
writers and by legislation governing the construction of steam-boilers. 
In the United States, boilers for merchant vessels must be constructed 
according to the rules and regulations prescribed by the Board of Super- 
vising Inspectors of Steam Vessels; in the U. S. Navy, according to rules 
of the Navy Department, and in some cases according to special acts of 
Congress. On land, in some places, as in Philadelphia, the construc- 
tion of boilers is governed by local laws; but generally there are no laws 
upon the subject, and boilers are constructed according to the idea of 
individual engineers and boiler-makers. In Europe the construction is 
generally regulated by stringent inspection laws. The rules of the U. S. 
Supervising Inspectors of Steam-vessels, the British Lloyd's and Board of 
Trade, the French Bureau Veritas, and the German Lloyd's are ably 
reviewed in a paper by Nelson Foley, M. Inst. Naval Architects, etc., 
read at the Chicago Engineering Congress, 1893, Division of Marine and 
Naval Engineering. From this paper the following notes are taken, 
chiefly with reference to the U. S. and British rules: 

(Abbreviations. — T. S., for tensile strength; el., elongation; contr., 
contraction of area.) 

Hydraulic Tests. — Board of Trade, Lloyd's, and Bureau Veritas. — 
Twice the working pressure. 

United States Statutes. ■ — One. and a half times the working pressure. 

Mr. Foley proposes that the proof pressure should be 11/2 times the 
working pressure + one atmosphere. 

Established Nominal Factors of Safety. — Board of Trade, — 4.5 for 
a boiler of moderate length and of the best construction and workman- 
ship. 

Lloyd's. — Not very apparent, but appears to lie between 4 and 5. 

United States Statutes. — Indefinite, because the strength of the joint 
is not considered, except by the broad distinction between single and 
double riveting. 

Bureau Veritas: 4.4. 

German Lloyd's: 5 to 4.65, according to the thickness of the plates. 

Material for Riveting. — Board of Trade. — Tensile strength of rivet 
bars between 26 and 30 tons, el. in 10 in. not less than 25%, and contr. of 
area not less than 50%. (Tons of 2240 lbs.) 

Lloyd's. — T. S., 26 to 30 tons; el. not less than 20% in 8 in. The mate- 
rial must stand bending to a curve, the inner radius of which is not greater 
than H 2 times the thickness of the plate, after having been uniformly 
heated to a low cherry-red, and quenched in water at 82° F. 

United States Statutes. — • No special provision. 

Rules Connected with Riveting. — Board of Trade. — The shearing 
resistance of the rivet steel to be taken at 23 tons per square inch, 5 to 
be used for the factor of safety independently of any addition to this factor 
for the plating. Rivets in double shear to have only 1.75 times the single 
section taken in the calculation instead of 2. The diameter must not be 
less than the thickness of the plate and the pitch never greater than 8 1/2". 
The thickness of double butt-straps (each) not to be less than 5/8 the thick- 
ness of the plate; single butt-straps not less than 9/s. 

Distance from center of rivet to edge of plate = diam. of rivet X IV2. 

Distance between rows of rivets 

= 2 X diam. of rivet or = [(diam. X 4) + 1] -5- 2, if chain, and 

_ v'Kpitch X 11) + (diam . X 4) ] X (pitch + diam. X 4) ., . ' ow 
— — 11 zigzag. 

Diagonal pitch= (pitch X 6+ diam. X4)* 10. 

Lloyd's. — Rivets in double shear to have only 1.75 times the single 
section taken in the calculation instead of 2. The shearing strength of 
rivet steel to be taken at 85% of the T. S. of the material of shell plates, 
In any case where the strength of the longitudinal joint is satisfactorily 

* For specifications for steel for boilers, see p. 483. For riveted joints, 
see page 401. 



880 THE STEAM-BOILER. 

shown by experiment to be greater than given by the formula, the actual 
strength may be taken in the calculation. 

United Stales Statutes. — No rules. [The rules in 1909 give formulas 
equivalent to those of the British Board of Trade and tables taken from 
T. W. Traill's "Boilers, Marine and Land."] 

Material for Cylindrical Shells Subject to Internal Pressure. — 
Board of Trade. — T. S. between 27 and 32 tons. In the normal condition, 
el. not less than 18% in 10 in., but should be about 25%; if annealed, not 
less than 20%. Strips 2 in. wide should stand bending until the sides are 
parallel at a distance from each other of not more than three times the 
plate's thickness. 

Lloyd's. — T. S. between the limits of 26 and 30 tons per square inch. 
El. not less than 20% in 8 in. Test strips heated to a low cherry-red and 
plunged into water at 82° F. must stand bending to a curve, the inner 
radius of which is not greater than 11/2 times the plate's thickness. 

U. S. Statutes. — Plates 1/2 in. thick and under shall show a contr. of 
not less than 50%; when over 1/2 in. and up to3/ 4 m. f not less than 45%; 
when over 3/ 4 in., not less than 40%. 

Mr. Foley's comments: The Board of Trade rules seem to indicate a 
steel of too high T. S. when a lower and more ductile one can be got: the 
lower tensile limit should be reduced, and the bending test might with 
advantage be made after tempering, and made to a smaller radius. 
Lloyd's rule for quality seems more satisfactory, but the temper test is 
not severe. The United States Statutes are not sufficiently stringent to 
insure an entirely satisfactory material. 

Mr. Foley suggests a material which would meet the following; 25 tons 
lower limit in tension; 25% in 8 in. minimum elongation; radius for bend- 
ing test after tempering = the plate's thickness. 

Shell-plate Formulae. — Board of Trade: P = TX J?** X2 - 

U X r 
D = diameter of boiler in inches; 
P = working-pressure in lbs. per square inch; 
t = thickness in inches; 

B = percentage of strength of joint compared to solid plate; 
T = tensile strength allowed for the material in lbs. per square inch; 
F = a factor of safety, being 4.5, with certain additions depending on 
method of construction. 

t = thickness of plate in sixteenths; B and D as before; C — a constant 
depending on the kind of joint. 

When longitudinal seams have double butt-straps, C = 20. When 
longitudinal seams have double butt-straps of unequal width, only 
covering on one side the reduced section of plate at the outer line of rivets, 
C = 19.5. 

When the longitudinal seams are lap-jointed, C = 18.5. 

U. S. Statutes. — Using same notation as for Board of Trade, 

P= D " „ ■ for single-riveting; add 20% for double-riveting; 

where T is the lowest T.S. stamped on any plate. 

Mr. Foley criticises the rule of the United States Statutes as follows: 
The rule ignores the riveting, except that it distinguishes between single 
and double, giving the latter 20% advantage; the circumferential riveting 
or class of seam is altogether ignored. The rule takes no account of 
workmanship or method adopted of constructing the joints. The factor, 
one sixth, simply covers the actual nominal factor of safety as well as 
the loss of strength at the joint, no matter what its percentage; we may 
therefore dismiss it as unsatisfactory. 

Rules for Flat Plates. — Board of Trade: P = C( c f + i )2 - 

O — D 

P = working-pressure in lbs. per square inch; 
S = surface supported in square inches; 
t = thickness in sixteenths of an inch; 
C = a constant as per following table: 



STRENGTH OF STEAM-BOILERS. 881 

C = 125 for plates not exposed to heat or flame, the stays fitted with nuts 

and washers, the latter at least three times the diameter of the 

stay and 2/3 the thickness of the plate; 
C = 1S7.5 for the same condition, but the washers 2/3 the pitch of stays 

in diameter, and thickness not less than plate; 
C = 200 for the same condition, but doubling plates in place of washers, 

the width of which is 2/3 the pitch and thickness the same as the 

plate; 
C = 112.5 for the same condition, but the stays with nuts only; 
C == 75 when exposed to impact of heat or flame and steam in contact 

with the plates, and the stays fitted with nuts and washers three 

times the diameter of the stay and 2/3 the plate's thickness; 
C = 67.5 for the same condition, but stays fitted with nuts only; 
C == 100 when exposed to heat or flame, and water in contact with the 

plates, and stays screwed into the plates and fitted with nuts; 
C = 66 for the same condition, but stays with riveted heads. 
U. S. Statutes. — Using same notation as for Board of Trade. 

C x t 2 
P= — , where p= greatest pitch in inches, P and t as above; 

C = 112 to 200 according to various specified conditions. [Rules of 1909.] 
Certain experiments were carried out by the Board of Trade which 
showed that the resistance to bulging does not vary as the square of the 
plate's thickness. There seems also good reason to believe that it is not 
inversely as the square of the greatest pitch. Bearing in mind, says Mr. 
Foley, that mathematicians have signally failed to give us true theoretical 
foundations for calculating the resistance of bodies subject to the simplest 
forms of stresses, we therefore cannot expect much from their assistance 
in the matter of flat plates. 

The Board of Trade rules for flat surfaces, being based on actual experi- 
ment, are especially worthy of respect; sound judgment appears also to 
have been used in framing them. 

Furnace Formulae. — Board of Trade. — Long Furnaces. — 
CXi 2 
P = , T .. n , but not where L is shorter than (11.5 t — 1), at which 

length the rule for short furnaces comes into play. 

P = working-pressure in pounds per square inch; t = thickness in 

inches; 
D = outside diameter in inches ; L = length of furnace in feet up to 10 ft. ; 
C = a constant, as per following table, for drilled holes: 

C = 99,000 for welded or butt-jointed with single straps, double- 
riveted ; 

C = 88,000 for butts with single straps, single-riveted; 

C = 99,000 for butts with double straps, single-riveted. 

Provided always that the pressure so found does not exceed that given 
by the following formulae, which apply also to short furnaces: 

C X t 

" for all the patent furnaces named; 

kdV^ erHa) when ™ th Adamson rin ^ s - 

C= 8,800 for plain furnaces; 

C— 14,000 for Fox; minimum thickness 5/ 16 in., greatest 5/sin.; plain 

part not to exceed 6 in. in length; 
C= 13,500 for Morison; minimum thickness s/jein., greatest 5/ 8 in.; 

plain part not to exceed 6 in. in length; 
C= 14,000 for Puryes-Brown; limits of thickness 7/ 16 in. and5/gin., 

plain part 9 in. in length; 
Cj= 8,800 for Adamson rings; radius of flange next fire 1 1/2 in. 
U. S. Statutes. — Long Furnaces. — Same notation. 

89 600 X £ 2 
P= — T n , but L not to exceed 8 ft. [New rules are given in 

1909; see page 884.] 



882 THE STEAM-BOILER. 

Mr. Foley comments on the rules for long furnaces as follows: The 
Board of Trade general formula, where the length is a factor, has a very 
limited range indeed, viz., 10 ft. as the extreme length, and 135 thicknesses 

C X t 2 
— 12 in., as the short limit. The original formula, P= _ , is that of 

Sir W. Fairbairn, and was, I believe, never intended by him to apply to 
short furnaces. On the very face of it, it js apparent, on the other hand, 
that if it is true for moderately long furnaces, it cannot be so for very long 
ones. We are therefore driven to the conclusion that any formula which 
includes simple L as a factor must be founded on a wrong basis. 

With Mr. Traill's form of the formula, namely, substituting (L + 1) 
for L, the results appear sufficiently satisfactory for practical purposes, 
and indeed, as far as can be judged, tally with the results obtained from 
experiment as nearly as could be expected. The experiments to which 
I refer were six in number, and" of great variety of length to diameter; 
the actual factors of safety ranged from 4.4 to 6.2, the mean being 4.78, 
or practically 5. It seems to me, therefore, that, within the limits pre- 
scribed, the Board of Trade formula may be accepted as suitable for our 
requirements. 

Material for Stays. — The qualities of material prescribed are as 
follows: 

Board of Trade. — The tensile strength to lie between the limits of 27 and 
32 tons per sq. in., and to have an elongation of not less than 20% in 
10 in. Steel stays which have been welded or worked in the fire should 
not be used. [Tons of 2240 lbs.] 

Lloyd's. — 26 to 30 ton steel, with elongation not less than 20% in 8 in. 

U . S. Statutes. — The only condition is that the reduction of area must 
not be less than 40% if the test bar is over 3/ 4 in. diameter. 

Loads allowed on Stays. — Board of Trade. — 9000 lbs. per square 
inch is allowed on the net section, provided the tensile strength ranges from 
27 to 32 tons. Steel stays are not to be welded or worked in the fire. 

Lloyd's. — For screwed and other stays, not exceeding 1 1/2 in. diameter 
effective, 8000 lbs. per square inch is allowed; for stays above IV2 in., 
9000 lbs. No stays are to be welded. 

U. S. Statutes. — Braces and stays shall not be subjected to a greater 
stress than 6000 lbs. per sq. in. [As high as 9000 lbs. is allowed in some 
cases in the rules of 1909.] 

[Rankine, S. E., p. 459, says: "The iron of the stays ought not to be 
exposed to a greater working tension than 3000 lbs. on the square inch, 
in order to provide against their being weakened by corrosion. This 
amounts to making the factor of safety for the working pressure about 
20." It is evident, however, that an allowance in the factor of safety 
for corrosion may reasonably be decreased with increase of diameter. 
W.K.] 

A discussion of various rules and formulae for stay bolts, braces and 
flat surfaces will be found in a paper bv R. S. Hale, Trans. A. S. M. E., 
1904. 

C Xd 2 X t 
Girders. — Board of Trade. P = _ — • P = working pressure 

in lbs. per sq. in.; W = width of flame-box; L = length of girder; p = 
pitch of bolts; D = distance between girders from center to center; d = 
depth of girder; t = thickness of sum -of same; C = a constant = 6600 for 
1 bolt, 9900 for 2 or 3 bolts, and 11,220 for 4 bolts. All dimensions in 
inches. 

Lloyd's. — The same formula and constants, except that C = 11,000 
for 4 or 5 bolts, 11,550 for 6 or 7, and 11,880 for 8 or more. 

U. S. Statutes. — [The rules in 1909 are the same as Lloyd's.] 

Tube-Plates. — Board of Trade. P= l (D ~J \ x 20 ' 0Q0 . jy = least 

W X D 
horizontal distance between centers of tubes in inches ; d = inside diameter 
of ordinary tubes; t = thickness of tube-plate in inches; W = extreme 
width of combustion-box in inches from front tube-plate to back of fire- 
box, or distance between combustion-box tube-plates when the boiler is 
double-ended and the box common to both ends. 

The crushing stress on tube-plates caused by the pressure on the flame- 
box top is to be limited to 10,000 lbs. per square inch, 



STRENGTH OF STEAM-BOILERS. 883 

Material for Tubes. — Mr. Foley proposes the following: If iron, the 
quality to be such as to give at least 22 tons per square inch as the mini- 
mum tensile strength, with an elongation of not less than 15% in 8 ins. 
If steel, the elongation to be not less than 26% in ins. for the material 
before being rolled into strips; and after tempering, the test bar to 
stand completely closing together. Provided the steel welds well, there 
does not seem to be any object in providing tensile limits. The ends should 
be annealed after manufacture, and stay-tube ends should be annealed 
before screwing. 

Holding-power of Boiler-tubes. (See also page 342.) — In Messrs. 
Yarrow's experiments on iron and steel tubes of 2 in. to 2i'4in. diameter 
the first 5 tubes gave way on an average of 23,740 lbs., which would ap- 
pear to be about 2/3 the ultimate strength of the tubes themselves. In all 
these cases the hole through the tube-plate was parallel with a sharp edge 
to it. and a ferrule was driven into the tube. 

Tests of the next 5 tubes were made under the same conditions as the 
first 5, with the exception that in this case the ferrule was omitted, the 
tubes being simply expanded into the plates. The mean pull required 
was 15,270 lbs., or considerably less than half the ultimate strength of the 
tubes. 

Effect of beading the tubes, the holes through the plate being parallel and 
ferrules omitted. The mean of the first 3, which are tubes of the same 
kind, gives 26,876 lbs. as their holding-power, under these conditions, as 
compared with 23,740 lbs. for the tubes fitted with ferrules only. This 
high figure is, however, mainly due to an exceptional case where the 
holding-power is greater than the average strength of the tubes them- 
selves. 

It is disadvantageous to cone the hole through the tube-plate unless its 
sharp edge is removed, as the results are much worse than those obtained 
with parallel holes, the mean pull being but 16.031 lbs., the experiments 
being made with tubes expanded and ferruled but not beaded over. 

In experiments on tubes expanded into tapered holes, beaded over and 
fitted with ferrules, the net result is that the holding-power is, for the 
size experimented on, about 3/ 4 of the tensile strength of the tube, the 
mean pull being 28,797 lbs. With tubes expanded into tapered holes 
and simply beaded over, better results were obtained than with ferrules; 
in these cases, however, the sharp edge of the hole was rounded off, which 
appears in general to have a good effect. 

In one particular the experiments are incomplete, as it is impossible to 
reproduce on a machine the racking the tubes get by the expansion of a 
boiler as it is heated up and cooled down again, and it is quite possible, 
therefore, that the fastening giving the best results on the testing-machine 
may not prove so efficient in practice. 

N.B. — It should be noted that the experiments were all made under 
the cold condition, so that reference should be made with caution, the 
circumstances in practice being very different, especially when there is 
scale on the tube-plates, or when the tube-plates are thick and subject 
to intense heat. 

Iron versus Steel Boiler-tubes. (Foley.) — Mr. Blechynden prefers 
iron tubes to those of steel, but how far he would go in attributing the 
leaky-tube defect to the use of steel tubes we are not aware. It appears, 
however, that the results of his experiments would warrant him in going 
a considerable distance in this direction. The test consisted of heating 
and cooling two tubes, one of wrought iron and the other of steel. Both 
tubes were 23/4 in. in diameter and 0.16 in. thickness of metal. The tubes 
were put in the same furnace, made red-hot, and then dipped in water. 
The length was gauged at a temperature of 46° F. 

This operation was twice repeated, with results as follows: 

Steel. Iron: 

Original length 55 . 495 in. 55.495 in. 

Heated to 186° F.; increase 0.052 in. 0.048 in. 

Coefficient of expansion per degree F 0000067 .0000062 

Heated red-hot and dipped in water; decrease .007 in. .003 in. 

Second heating and cooling, decrease .031 in. .004 in. 

Third heating and cooling, decrease .017 in. .006 in. 

Total contraction .055 in. .013 in. 



884 THE STEAM-BOILER. 



Mr. A. C. Kirk writes: That overheating of tube ends is the cause of the 
leakage of the tubes in boilers is proved by the fact that the ferrules at 
present used by the Admiralty prevent it. These act by shielding the tube 
ends from the action of the fiame, and consequently reducing evaporation, 
and so allowing free access of the water to keep them cool. 

Although many causes contribute, there seems no doubt that thick 
tube-plates must bear a share of causing the mischief. 

Rules for Construction of Boilers in Merchant Vessels in the 
United States. 

(Extracts from General Rules and Regulations of the Board of Supervis- 
ing Inspectors, Steamboat Inspection Service (as amended Jan., 1909).) 

Tensile Strength of Plate. — From each plate as rolled there shall 
be taken two test pieces, one for tensile test and one for bending test. 
The piece for tensile test shall be taken from the side of the plate at 
about one-third of its length from the top of the plate, and the piece for 
bending test shall be taken transversely from the top of the plate near the 
center. 

All the pieces shall be prepared so that the skin shall not be removed, 
the edges only planed or shaped. 

In no case shall test pieces be prepared by annealing or reduced in size 
by hammering. 

Tensile-test pieces shall be at least 16 ins. in length, from l J /2 to 31/2 
ins. in width at the ends, which ends shall join by an easy fillet, a straight 
part in the center of at least 9 ins. in length and 11/2 ins. in width, . . . 
marked with light prick punch marks at distances 1 inch apart, spaced 
so as to give 8 inches in length. 

Only steel plates manufactured by what is known as the basic or acid 
open-hearth processes will be allowed to be used in the construction or 
repairs of boilers for marine purposes. 

No plate made by the acid process shall contain more than 0.06 % of 
phosphorus and 0.04% of sulphur, and no plate made by the basic process 
shall contain more than 0.04% of phosphorus and 0.04% of sulphur. 

For steel plates the sample must show, when tested, a tensile strength 
not lower than 50,000 lbs. and not higher than 75,000 lbs. per sq. in. of 
section, and no such plate shall be stamped with a higher tensile strength 
than 70,000 lbs.: Provided, however, that for steel plates exceeding a 
thickness of 0.3125 in. intended for use in externally fired boilers, the 
sample must show, when tested, a tensile strength not lower than 54,000 
lbs. and not higher than 67,000 lbs. per sq. in. of section, and no plate 
exceeding a thickness of 0.3125 in. intended for use in externally fired 
boilers shall be stamped with a higher tensile strength than 62,000 lbs. 
Such sample must also show an elongation of at least 25% in a length of 
2 ins. for thickness up to 1/4 in., inclusive; in a length of 4 ins. for over 
1'4 to 7/ 16 in., inclusive; in a length of 6 ins. for all plates over 7/ 16 in. The 
sample must also show a reduction of sectional area as follows: 

At least 50% for thickness up to 1/2 in., inclusive; 45% for thickness 
over 1/2 to 3/4 in., inclusive, and 40% for thickness over 3/ 4 in. 

Quenching and bending test. — Quenching and bending test pieces shall 
be at least 12 ins. in length and from 1 to 31/2 ins. in width. The side 
where sheared or planed must not be rounded, but the edges may have 
the sharpness taken off with a fine file. The test piece shall be heated 
to a cherry red (as seen in a dark place) and then plunged into wafer at a 
temperature of about 82° F. Thus prepared, the sample shall be bent to a 
curve, the inner radius of which is not greater than 11 '2 times the thick- 
ness of the sample, without cracks or flaws. The ends must be parallel 
after bending. 

Cylindrical Shells. — The working steam pressure allowable on 
cylindrical shells of boilers constructed of plates inspected as required 
by these rules, when single riveted, shall not produce a strain to exceed 
one-sixth of the tensile strength of the iron or steel plates of which such 
boilers are constructed ; but where the longitudinal laps of the cvlindrical 
parts of such boilers are double riveted, and the rivet holes' for such 
boilers have been fairly drilled, an addition of 20 per cent to the working 
pressure provided for single riveting will be allowed. >. 



STRENGTH OF STEAM-BOILERS. 885 

The pressure for any dimension of boilers must be ascertained by the 
following rule, viz.: 

Multiply one-sixth of the lowest tensile strength found stamped on the 
plates in the cylindrical shell by the thickness — expressed in inches or 
part of an inch — and divide by the radius or half diameter — also 
expressed in inches — and the result will be the pressure allowable per 
square inch of surface for single riveting, to which add 20% for double 
riveting, when all the rivet boles in the shell of such boiler have been 
"fairly drilled ' and no part of such holes has been punched. The 
pressure allowed shall be based on the plate whose tensile strength multi- 
plied by its thickness gives the lowest product. 

Cylindrical Shells of Water-tube or Coil Boilers. — The working 
pressure allowable, when such shells have a row or rows of pipes or tubes 
inserted therein, shall be determined by the formula: 

P = (D - d)X TXS + (DX R), 

where P= working pressure allowable in pounds; D= distance in inches 
between the tube or pipe centers in a line from head to head; d= dia- 
meter of hole in inches; T= thickness of plate in inches; S= one-sixth 
of the tensile strength of the plate; R = radius of shell in inches. 

Convex Heads. — Plates used as heads, when new and made to 
practically true circles, shall be allowed a steam pressure in accordance 
with the formula: P = T X S -h R, where P = steam pressure allowable 
in lbs. per sq. in. ; 7" = thickness of plate in ins.; S = one-sixth of the tensile 
strength; R = one-half of the radius to which the head is bumped. 

Add 20% when the head is double riveted to the shell and the holes 
are fairly drilled. 

Bumped heads may contain a manhole opening flanged inwardly, 
when such flange is turned to a depth of three times the thickness of 
material in the head. 

Concave Heads. — For concave heads the pressure allowable will be 
0.6 times the pressure allowable for convex heads. 

Flat Heads. — Where flat heads do not exceed 20 ins. diameter they 
may be used without being stayed, and the steam pressure allowable 
shall be determined by the formula: P= CX T 2 -t- A, where P= steam 
pressure allowable in pounds; T— thickness of material in sixteenths of 
an inch; A = one-half the area of head in inches; C = 112 for plates 7/jg in. 
and under; C = 120 for plates over 7/ 16 in. Provided, the flanges are made 
to an inside radius of at least 1 1/2 inches. 

Flat Surfaces. — The maximum stress allowable on flat plates sup- 
ported by stays shall be determined by the following formula: 

All stayed surfaces formed to a curve the radius of which is over 21 ins. 
excepting surfaces otherwise provided for, shall be deemed flat surfaces. 

Working pressure = C X T* -s- P 2 , 

where T = thickness of plates in 16ths of an inch; P = greatest pitch 
of stays in ins.; C = 112 for screw stays with riveted heads, plates 
7/i6 thick and under; C= 120 for screw stays with riveted heads, plates 
above 7/ 16 in. thick; C = 120 for screw stays with nuts, plates 7/ 16 in. 
thick and under; C = 125 for screw stays with nuts, plates above 
7/ 16 in. thick and under 9/ 16 in.; C — 135 for screw stays with nuts, 
plates 9/i6 in. thick and above; C = 175 for stays with double nuts 
having one nut on the inside and one nut on the outside of plate, without 
washers or doubling plates; C = 160 for stays fitted with washers or 
doubling strips which have a thickness of at least 0.5 of the thickness of 
the plate and a diameter of at least 0.5 of the greatest pitch of the stay, 
riveted to the outside of the plates, and stays having one nut inside of 
the plate, and one nut outside of the washer or doubling strip. For T 
take 72% of the combined thickness of the plate and washer or plate and 
doubling strip. C = 200 for stays fitted with doubling strips which 
have a thickness equal to at least 0.5 of the thickness of the plate reen- 
forced, and covering the full area braced (up to the curvature of the 
flange, if any), riveted to either the inside or outside of the plate, and 
stays having one nut outside and one inside of the plates. Washers 
or doubling plates to be substantially riveted. For T take 72% of the 
combined thickness of the two plates. C = 200 for stays with plates 



886 THE STEAM-BOILER. 

stiffened with tees or angle bars having a thickness of at least 2/ 3 the 
thickness of plate and depth of webs at least 1/4 of the greatest pitch of 
the stays, and substantially riveted on the inside of the plates, and stays 
having one nut inside, bearing on washers fitted to the edges of the webs 
that are at right angles to the plate. For T take 72% of the combined 
thickness of web and plate. 

No such flat plates or surfaces shall be unsupported a greater distance 
than 18 inches. 

Stays. — The maximum stress in pounds allowable per square inch 
of cross-sectional area for stays used in the construction of marine boilers, 
when they are accurately fitted and properly secured, shall be ascertained 
by the following formula: 

P=iXC + a, where P = working pressure in lbs. per sq. in.; A = least 
cross-sectional area of stay in inches; a = area of surface supported by one 
stay, in inches; C = 9000 for tested steel stays exceeding 2V2 ins. diam.; 
C = 8000 for tested steel stays 11/4 ins. and not exceeding 21/2 ins. diam., 
when such stays are not forged or welded. The ends, however, may be 
upset to a sufficient diameter to allow for the depth of the thread. The 
diameter shall be taken at the bottom of the thread, provided it is the 
least diameter of the stay. All such stays after being upset shall be 
thoroughly annealed. C = 8000 for a tested Huston or similar type of 
brace, the cross-sectional area of which exceeds 5 sq. ins.; C = 7000 for 
such tested braces when the cross-sectional area is not less than 1.227 and 
not more than 5 sq. ins., provided such braces are prepared at one heat 
from a solid piece of plate without welds; C = 6000 for all stays not other- 
wise provided for. 

Flues subjected to External Pressure only. — Plain lap-welded steel 
flues 7 to 13 ins. diameter. D = outside diam., ins.; T = thickness, ins.; 
P = working pressure, lbs. per sq. in.; F = factor of safety. 

T = [(F X ^Lt^ 1386] D . This formula is applicable to lengths 
86670 
greater than six diameters of flue, to working pressures greater than 100 
lbs. per sq. in., and to temperatures less than 650° F. 

Riveted flues, made in sections riveted together, 6 to 9 ins. diam., 
maximum length of sections 60 ins.; over 9 and not over 13 ins. diam., 
maximum length 42 ins.: P = 8100 X T -4- D. 

Riveted or lap-welded flues, over 13 and not over 28 ins. diam., lengths 
not to exceed 31/2 times the diam.: 

P = ^~ [(18.75 X T) - (L X 1.03)]. 

(L = length of flue in inches; T = thickness in 16ths of an inch.) 

Furnaces. — The tensile strength of steel used in the construction of 
corrugated or ribbed furnaces shall not exceed 87,000, and be not less 
than 54,000 lbs.; and in all other furnaces the minimum tensile strength 
shall not be less than 58,000, and the maximum not more than 67,000 
lbs. The minimum elongation in 8 inches shall be 20%. 

All corrugated furnaces having plain parts at the ends not exceeding 
9 inches in length (except flues especially provided for), when new, and 
made to practically true circles, shall be allowed a steam pressure in 
accordance with the formula: P = C X T -4- D. 

P = pressure in lbs. per sq. in., T = thickness in inches, C = a con- 
stant, as below. 

Leeds suspension bulb furnace C = 17,000, T not less than 5/ 16 in. 

Morison corrugated type C = 15,600, T not less than 5/ 16 in. 

Fox corrugated type C = 14,000, T not less than 5/iein. 

Purves type, rib projections C = 14,000, T not less than 7/ 16 in. 

Brown corrugated type C = 14,000, T not less than 5/ 16 in. 

Type having sections 18 ins. long. . . . C = 10,000, T not less than 7/ 16 in. 

Limiting dimensions from center to center of the corrugations or pro- 
jecting ribs, and of their depth, are given for each furnace. 

Tubes. — Lap-welded tubes are allowed a working pressure of 225 lbs. 
per sq. in., if of the thicknesses given below, " provided they are deemed 
safe bv the inspectors." 

1 and 11/4 ins. diam., 0.072 in. thick; 1 1/2 ins., 0.083; 13/ 4 , 2 and 21/4 ins., 
0.095; 21/2, 23/4 and 3 ins., 0.109; 31/4, 31/2 and 33/4ins., 0.120; 4 and 41/2 
ins., 0.134; 5 ins., 0.148; 6 ins., 0.165. 



STRENGTH OF STEAM-BOILERS. 



887 



Safe Working Pressure in Cylindrical Shells. — The author desires 
to express his condemnation of the rule of the U. S. Statutes, as giving 
too low a factor of safety. (See also criticism by Mr. Foley, page 880, ante.) 

If Pb = bursting-pressure, t = thickness, T = tensile strength, c = 
coefficient of strength of riveted joint, that is, ratio of strength of the 
joint to that of the solid plate, d = diameter, Pb = 2tTc + d, or if c be taken 
for double-riveting at 0.7, then P b = lAtT + d. 

By the U. S. rule the allowable pressure P a = ~^ X 1.20 = ^^ ; 

whence Pb = 3.5P a ; that is, the factor of safety is only 3.5, provided the 
" tensile strength found stamped in the plate " is the real tensile strength 
of the material. 

The author's formula for safe working-pressure of externally fired 

14,000 1 Pd 



boilers with longitudinal seams double-riveted, is P 



d ' 14,000' 
thickness and d = diam. in 



P = gauge-pressure in lbs. per sq. in.; t = 
inches. 

2tTc 
This is derived from the formula P= —t-t- , taking c at 0.7 and /= 5 

for steel of 50,000 lbs. T.S., or 6 for 60,000 lbs. T.S.; the factor of safety 
being increased in the ratio of the T.S., since with the higher T.S. there 
is greater danger of cracking at the rivet-holes from the effect of punching 
and riveting and of expansion and contraction caused by variations of 
temperature. For external shells of internally fired boilers, these shells 
not being exposed to the fire, with rivet-holes drilled or reamed after 
punching, a lower factor of safety and steel of a higher T.S. may be allow- 
able. 

If the T.S. is 60,000, a working pressure P = 16,000 t -^- d would give a 
factor of safety of 5.25. 

The following table gives safe working pressures for different diameters 
of shell and thicknesses of plate calculated from the author's formula. 



Safe Working Pressures in Cylindrical Shells of Boilers, Tanks, 
Pipes, etc., in Pounds per Square Inch. 



Longitudinal seams double-riveted. 
(Calculated from formula P = 14,000 X thickness ■ 



diameter.) 



CD mA 






Diameter in Inches 








S^c 




















24 


30 


36 


38 


40 


42 


44 


46 


48 


50 


52 


1 


36.5 


29.2 


24.3 


23.0 


21.9 


20.8 


19.9 


19.0 


18.2 


17.5 


16.8 


2 


72.9 


58.3 


48.6 


46.1 


43.8 


41.7 


39.8 


38.0 


36.5 


35.0 


33.7 


3 


109.4 


87.5 


72.9 


69.1 


65.6 


62.5 


59.7 


57.1 


54.7 


52.5 


50.5 


4 


145.8 


116.7 


97.2 


92.1 


87.5 


83.3 


79.5 


76.1 


72.9 


70.0 


67.3 


5 


182.3 


145.8 


121.5 


115.1 


109.4 


104.2 


99.4 


95.1 


91.1 


87.5 


84.1 


6 


218.7 


175.0 


145.8 


138.2 


131.3 


125.0 


119.3 


114.1 


109.4 


105.0 


101.0 


7 


255.2 


204.1 


170.1 


161.2 


153.1 


145.9 


139.2 


133.2 


127.6 


122.5 


117.8 


8 


291.7 


233.3 


194.4 


184.2 


175.0 


166.7 


159.1 


152.2 


145.8 


140.0 


134.6 


9 


328.1 


262.5 


218.8 


207.2 


196.9 


187.5 


179.0 


171.2 


164.1 


157.5 


151.4 


10 


364.6 


291.7 


243.1 


230.3 


218.8 


208.3 


198.9 


190.2 


182.3 


175.0 


168.3 


11 


401.0 


320.8 


267.4 


253.3 


240.6 


229.2 


218.7 


209.2 


200.5 


192.5 


185.1 


12 


437.5 


350.0 


291.7 


276.3 


262.5 


250.0 


238.6 


228.3 


218.7 


210.0 


201.9 


13 


473.9 


379.2 


316.0 


299.3 


284.4 


270.9 


258.5 


247.3 


337.0 


227.5 


218.8 


14 


410.4 


408.3 


340.3 


322.4 


306.3 


291.7 


278.4 


266.3 


255.2 


245.0 


235.6 


15 


546.9 


437.5 


364.6 


345.4 


328.1 


312.5 


298.3 


285.3 


273.4 


266.5 


252.4 


16 


583.3 


466.7 


388.9 


368.4 


350.0 


333.3 


318.2 


304.4 


291.7 


280.0 


269.2 



888 



THE STEAM-BOILER. 





Safe Working Pressures in Cylindrical Shells - 


— Continued 




§"2 a 


, Diameter in Inches. 




54 


60 


66 


72 


78 


84 


90 


96 


102 


108 


114 


120 


1 


16.2 


14.6 


13.3 


12.2 


11.2 


10.4 


9.7 


9.1 


8.6 


8.1 


7.7 


7.3 


2 


32.4 


29.2 


25.5 


24.3 


22.4 


20.8 


19.4 


18.2 


17.2 


16.2 


15.4 


14.6 


3 


48 6 


43 7 


39 8 


36,5 


33 7 


31,3 


29.2 


27.3 


25.7 


24.3 


23.0 


21.9 


4 


64 8 


58 3 


53,0 


48,6 


44 9 


41,7 


38.9 


36.5 


34.3 


32.4 


30.7 


29.2 


5 


81 


72 9 


66 3 


60,8 


56 1 


52 1 


48.6 


45.6 


42.9 


40.5 


3d.4 


36.5 


6 


97 2 


87 5 


79 5 


72 9 


67,3 


62 5 


58.3 


54.7 


51.5 


48.6 


46.1 


43.8 


7 


113 4 


102 1 


92,8 


85.1 


78,5 


72 9 


68.1 


63.8 


60.0 


56.7 


53.7 


51.0 


8 


17.9 6 


116 7 


106.1 


97.2 


89.7 


83 3 


77.8 


72.9 


68.6 


64.8 


61.4 


58.3 


9 


145 8 


131 2 


119.3 


109,4 


101.0 


93.8 


87.5 


82.0 


77.2 


72.9 


69.1 


65.6 


10 


167, 


145 8 


132 6 


121.5 


112.3 


104,2 


97.2 


91.1 


85.8 


81.0 


76.8 


72.9 


11 


178 2 


160 4 


145 8 


133.7 


123.4 


114.6 


106.9 


100.3 


94.4 


89.1 


84.4 


80.2 


12 


194 4 


175 


159 1 


145,8 


134.6 


125.0 


116.7 


109.4 


102.9 


97.2 


92.1 


87.5 


13 


210 7 


189 6 


172 4 


158,0 


145.8 


135.4 


126.4 


118.5 


111.5 


105.3 


99.8 


94.8 


14 


226 9 


204 2 


185 6 


170.1 


157.1 


145,8 


136.1 


127.6 


120.1 


113.4 


107.5 


102.1 


15 


243 1 


218 7 


198 9 


182.3 


168.3 


156.3 


145.8 


136.7 


128.7 


121.5 


115.1 


109.4 


16 


259.3 


233.3 


212.1 


194.4 


179.5 


166.7 


155.6 


145.8 


137.3 


129.6 


122.8 


116.7 



Flat Stayed Surfaces in Steam-boilers. — Clark, in his treatise on the 
Steam-engine, also in his Pocket-hook, gives the following formula: p = 
407 ts -s- d, in which p is the internal pressure in pounds per square inch 
that will strain the plates to their elastic limit, t is the thickness of the 
plate in inches, d is the distance between two rows of stay-bolts in the 
clear, and s is the tensile stress in the plate, in tons of 2240 lbs., per 
square inch, at the elastic limit. Substituting values of s for iron, steel, 
and copper, 12, 14, and 8 tons respectively, we have the following: 

Formulae fob Ultimate Elastic Strength of Flat Stayed Surfaces. 





Iron. 


■ Steel. 


Copper. 




p = 5000J 
pxd 
5000 
5000 1 

V 


p = 5700 3 

d 

pxd 

1 ~ 5700 

,5700 t 

V 


p = 3300J 
pxd 

1 3300 
3300 f 


Thickness of plate 




V 



For Diameter of the Stay-bolts, Clark gives d' = 0.0024 \ — — , 

in which d' = diameter of screwed bolt at bottom of thread, P = longitudi- 
nal and P' transverse pitch of stay-bolts between centers, p = internal 
pressure in lbs. per sq. in. that will strain the plate to its elastic limit, s = 
elastic strength of the stay-bolts, in lbs. per sq. in. Taking s = 12, 14, 
and 8 tons, respectively, for iron, steel, and copper, we have 

For iron, d' = 0.00069 ^ PP'p , or if P = P' , d' = 0.00069 P vj- 
For steel, d' = 0.00064 y /pP'p , or it P = P' ', d' = 0.00064 P v^ ; 
For copper, d' = 0.00084 VpP'p, or if P = P', d' = 0.00084 P \/p. 

In using formulae for stays a large factor of safety should be taken to 
allow for reduction of size by corrosion. Thurston's Manual of Steam- 
boilers, p. 144, recommends that the factor be as large as 15 or 20. The 
Hartford Steam Boiler Insp. & Ins. Co. recommends not less than 10. 

Strength of Stays. — A. F. Yarrow (Engr., March 20, 1891) gives the 
following results of experiments to ascertain the strength of water-space , 
stays; 



IMPROVED METHODS OF FEEDING COAL. 



Description. 



Hollow stays screwed into f 
plates and hole expanded! 

Solid stays screwed into/ 
plates and riveted over. \ 



Length 
between 
Plates. 



4.75 in. 
4.64 in. 
4.80 in. 
4.80 in. 



Diameter of Stay over 
Threads. 



I in. (hole7/i6in. and 5/ 16 in.) 
1 in. (hole 9, 16 in. and 7/ie in.) 

7/8 in. 

7/8 in. 



Ulti- 
mate 

Stress. 



lbs. 
25,457 
20,992 
22,008 
22,070 



The above are taken as a fair average of numerous tests. 

Fusible plugs. — Fusible plugs should be put in that portion of the 
heating-surface which first becomes exposed from lack of water. The 
rules of the U. S. Supervising Inspectors specify Banca tin for the purpose. 
Its melting-point is about 445° F. The rule says: Every boiler, other than 
boilers of the water-tube type, shall have at least one fusible plug made 
of a bronze casing filled with good Banca tin from end to end. Fusible 
plugs, except as otherwise provided for, shall have an external diameter 
of not less than 3/4 in. pipe tap, and the Banca tin shall be at least 1/2 in. 
in diameter at the smallest end and shall have a larger diameter at the 
center or at the opposite end of the plug; smaller plugs are allowed for 
pressures above 150 lbs., also for upright boilers. Cylinder-boilers with 
flues shall have one plug inserted in one flue of each boiler; and also one 
plug inserted in the shell of each boiler from the inside, immediately 
below the fire line and not less than 4 ft. from the front end. Other shell 
boilers shall have one plug inserted in the crown of the back connection. 
Upright tubular boilers shall have a fusible plug inserted in one of the 
tubes at a point at least 2 in. below the lowest gauge-cock, but in boilers 
having a cone top it shall be inserted in the upper tube sheet. All tubes 
are to be inserted so that the small end of the tin shall be exposed to the 
fire. 

Steam-domes. — ■ Steam-domes or drums were formerly almost uni- 
versally used on horizontal boilers, but their use is now generally discon- 
tinued, as they are considered a useless appendage to a steam-boiler, and 
unless properly designed and constructed are an element of weakness. 

Height of Furnace. — Recent practice in the United States makes 
the height of furnace much greater than it was formerly. With large sizes 
of anthracite there is no serious objection to having the furnace as low as 
18 in., measured from the surface of the grate to the nearest portion of 
the heating surface of the boiler, but with coal containing much volatile 
matter and moisture a much greater distance is desirable. With very 
volatile coals the distance may be as great as 5 ft. or even 10 ft. Rankine 
(S. E., p. 457) says: The clear height of the "crown" or roof of the furnace 
above the grate-bars is seldom less than about 18 in., and often con- 
siderably more. In the fire-boxes of locomotives it is on an average 
about 4 ft. -The height of 18 in. is suitable where the crown of the fur- 
nace is a brick arch. Where the crown of the furnace, on the other hand, 
forms part of the heating-surface of the boiler, a greater height is desirable 
in every case in which it can be obtained; for the temperature of the 
boiler-plates, being much lower than that of the flame, tends to check the 
combustion of the inflammable gases which rise from the fuel. As a 
general principle a high furnace is favorable to complete combustion. 



IMPROVED METHODS OF FEEDING COAL. 

Mechanical Stokers. (William R. Roney, Trans. A. S. M. E., vol. 
xii.) — Mechanical stokers have been used in England to a limited extent 
since 1785. In that year one was patented by James Watt. (See D. K. 
Clark's Treatise on the Steam-engine.) 

After 1840 many styles of mechanical stokers were patented in England, 
but nearly all were variations and modifications of the two forms of 
stokers patented by John Jukes in 1841, and by E. Henderson in 1843. 

The Jukes stoker consisted of longitudinal fire-bars, connected by links, 
so as to form an endless chain. The small coal was delivered from a 
hopper on the front of the boiler, on to the grate, which slowly moving 



890 THE STEAM-BOILER. 



from front to rear, gradually advanced the fuel into the furnace and dis- 
charged the ash and clinker at the back. 

The Henderson stoker consists primarily of two horizontal fans revolv- 
ing on vertical spindles, which scatter the coal over the fire. 

The first American stoker was the Murphy stoker, brought out in 1878. 
It consists of two coal magazines placed in the side walls of the boiler 
furnace, and extending back from the boiler front 6 or 7 feet. In the 
bottom of these magazines are rectangular iron boxes, which are moved 
from side to side by means of a rack and pinion, and serve to push the coal 
upon the grates, which incline at an angle of about 35° from the inner edge 
of the coal magazines, forming a V-shaped receptacle for the burning coal. 
The grates are composed of narrow parallel bars, so arranged that each 
alternate bar lifts about an inch at the lower end, while at the bottom 
of the V, and filling the space between the ends of the grate-bars, is placed 
a cast-iron toothed bar, arranged to be turned by a crank. The purpose 
of this bar is to grind the clinker coming in contact with it. Over this 
V-shaped receptacle is sprung a fire-brick arch. 

In the Roney mechanical stoker the fuel to be burned is dumped into a 
hopper on the boiler front. Set in the lower part of the hopper is a 
"pusher" which, by a vibratory motion, gradually forces the fuel over the 
"dead-plate" and on the grate. The grate-bars in their normal con- 
dition form a series of steps. Each bar is capable of a rocking motion 
through an adjustable angle. All the grate-bars are coupled together by 
a "rocker-bar." A variable back-and-forth motion being given to the 
"rocker-bar," through a connecting-rod, the grate-bars rock in unison, 
now forming a series of steps, and now approximating to an inclined 
plane, with the grates partly overlapping, like shingles on a roof. When 
the grate-bars rock forward the fire will tend to work down in a body. 
But before the coal can move too far the bars rock back to the stepped 
position, checking the downward motion. The rocking motion is slow, 
being from 7 to 10 strokes per minute, according to the kind of coal. 
This alternate starting and checking motion is continuous, and finally 
lands the cinder and ash on the dumping-grate below. 

The Hawley Down-draught Furnace. — A foot or more above the 
ordinary grate there is carried a second grate composed of a series of 
water-tubes, opening at both ends into steel drums or headers, through 
which water is circulated. The coal is fed on this upper grate, and as it 
is partially consumed falls through it upon the lower grate, where the com- 
bustion is completed in the ordinary manner. The draught through the 
coal on the upper grate is downward through the coal and the grate. The 
volatile gases are therefore carried down through the bed of coal, where 
they are thoroughly heated, and are burned in the space beneath, where 
they meet the excess of hot air drawn through the fire on the lower grate. 
In tests in Chicago, from 30 to 45. lbs. of coal were burned per square foot 
of grate upon this system, with good economical results. (See catalogue 
Of the Hawley Down-draught Furnace Co., Chicago.) 

The Chain Grate Stoker, made by Jukes in 1841, is now (1909) widely 
used in the United States. It is made by the Babcock & Wilcox Co. 
and others. 

Under-feed Stokers. — Results similar to those that may be obtained 
with downward draught are obtained by feeding the coal at the bottom 
of the bed, pushing upward the coal already on the bed which has had its 
volatile matter distilled from it. The volatile matter of the freshly fired 
coal then has to pass through a body of ignited coke, where it meets a 
supply of hot air.. (See circular of The Underfeed Stoker Co., Chicago.) 

The Taylor Gravity Stoker, made by the Amer. Ship Windlass Co., 
Providence, R. I., is a combination of an underfeed stoker containing two 
horizontal rows of pushers with an inclined or step grate through which 
air is blown by a fan. 

SMOKE PREVENTION. 

The following article was contributed by the author to a " Report on 
Smoke Abatement," presented by a Committee to the Syracuse Chamber 
of Commerce, published by the Chamber in 1907. 

Smoke may be made in two ways: (1) By direct distillation of tarry 
condensible vapors from coal without burning; (2) By the partial burning 
or splitting up of hydrocarbon gases, the hydrogen burning and the 



SMOKE PREVENTION. 891 

carbon being left unburned as smoke or soot. These causes usually act 
conjointly. 

The direct cause of smoke is that the gases distilled from the coal are 
not completely burned in the furnace before coming in contact with the 
surface of the boiler, which chills them below the temperature of ignition. 

The amount and quality of smoke discharged from a chimney may 
vary all the way from a dense cloud of jet-black smoke, which may be 
carried by a light wind for a distance of a mile or more before it is finally 
dispersed into the atmosphere, to a thin cloud, which becomes invisible 
a few feet from the chimney. Often the same chimney will for a few 
minutes immediately after firing give off a dense black cloud and then a 
few minutes later the smoke will have entirely disappeared. 

The quantity and density of smoke depend upon many variable causes. 
Anthracite coal produces no smoke under any conditions of furnace. Semi- 
bituminous, containing 12.5 to 25% of volatile matter in the combustible 
part of the coal, will give off more or less smoke, depending on the con- 
ditions under which it is burned, and bituminous coal, containing from 
25 to 50% of volatile matter, will give off great quantities of smoke with 
all of the usual old-style furnaces, even with skillful firing, and this smoke 
can only be prevented by the use of special devices, together with proper 
methods of firing the fuel and of admission of air. 

Practically the whole theory of smoke production and prevention may 
be illustrated by the flame of an ordinary gas burner or gas stove. 
When the gas is turned down very low every particle of gas, as it emerges 
from the burner, is brought in contact with a sufficient supply of hot air to 
effect its complete and instantaneous combustion, with a pale blue or 
almost invisible flame. Turn on the gas a little more and a white flame 
appears. The gas is imperfectly burned in the center of the flame. Par- 
ticles of carbon have been separated which are heated to a white heat. 
If a cold plate is brought in contact with the white flame, these carbon 
particles are deposited as soot. Turn on the gas still higher, and it burns 
with a dull, smoky flame, although it is surrounded with an unlimited 
quantity of air.* Now, carry this smoky flame into a hot fire-brick or 
porcelain chamber, where it is brought in contact with very hot air, and 
it will be made smokeless by the complete burning of the particles. 

We thus see: (1) That smoke may be prevented from forming if each 
particle of gas, as it is made by distillation from coal, is immediately 
mixed thoroughly with hot air, and (2) That even if smoke is formed 
by the absence of conditions for preventing it, it may afterwards be 
burned if it is thoroughly mixed with air at a sufficiently high temperature. 
It is easy to burn smoke when it is made in small quantities, but when 
made in great volumes it is difficult to get the hot air mixed with it unless 
special apparatus is used. In boiler firing the formation of smoke must 
be prevented, as the conditions do not usually permit of its being burnea. 
The essential conditions for preventing smoke in boiler fires may be 
enumerated as follows: 

1. The gases must be distilled from the coal at a uniform rate. 

2. The gases, when distilled, must be brought into intimate mixture 
with sufficient hot air to burn them completely. 

3. The mixing should be done in a fire-brick chamber. 

4. The gases should not be allowed to touch the comparatively cold 
surfaces of the boiler until they are completely burned. This means that 
the gases shall have sufficient space and time in which to burn before they 
are allowed to come in contact with the boiler surface. 

Every one of these four conditions is violated in the ordinary method 
of burning coal under a steam boiler. (1) The coal is fired intermittently 
and often in large quantities at a time, and the distillation proceeds at so 
rapid a rate that enough air cannot be introduced into the furnace to burn 
the gas. (2) The piling of fresh coal on the grate in itself chokes the air 
supply. (3) The roof of the furnace is the cold shell, or tubes, of the 
boiler, instead of a fire-brick arch, as it should be, and the furnace is not of 
a sufficient size to allow the gases time and space in which to be thoroughly 
mixed with the air supply. 

In order to obtain the conditions for preventing smoke it is necessary: 
(1) That the coal be delivered into the furnace in small quantities at a 
time. (2) That the draught be sufficient to carrv enough air into the 
furnace to burn the gases as fast as they are distilled. (3) That the air 



892 THE STEAM-BOILER. 

itself be thoroughly heated either by passing through a bed of white-hot 
coke or by passing through channels in hot brickwork, or by contact with 
hot fire-brick surfaces. (4) That the gas and the air be brought into 
the most complete and intimate mixture, so that each particle of carbon 
in the gas meets, before it escapes from the furnace, its necessary supply 
of air. (5) That the name produced by the burning shall be completely 
extinguished by the burning of every particle of the carbon into invisible 
carbon dioxide. 

If a white flame touches the surface of a boiler, it is apt to deposit 
soot and to produce smoke. A white flame itself is the visible evidence 
of incomplete combustion. 

The first remedy for smoke is to obtain anthracite coal. If this is not 
commercially practicable, then obtain, if possible, coal with the smallest 
amount of volatile matter. Coal of from 15 to 25% of volatile matter 
makes much less smoke than coals containing higher percentages. Pro- 
vide a proper furnace for burning coal. Any furnace is a proper furnace 
which secures the conditions named in the preceding paragraphs. Next, 
compel the firemen to follow instructions concerning the method of 
firing. 

It is impossible with coal containing over 30% of volatile matter and 
with a water-tube boiler, with tubes set close to the grate and vertical 
gas passages, as in an anthracite setting, to prevent smoke even by the 
most skillful firing. This style of setting for a water-tube boiler should 
be absolutely condemned. A Dutch oven setting, or a longitudinal 
setting with fire-brick baffle walls, is highly recommended as a smoke- 
preventing furnace, but with such a furnace it is necessary to use con- 
siderable skill in firing. 

Mechanical mixing of the gases and the air by steam jets is sometimes 
successful in preventing smoke, but it is not a universal preventive, 
especially when the coal is very high in volatile matter, when the firing 
is done unskillfully, or when the boiler is being driven beyond its normal 
capacity. It is essential to have sufficient draught to burn the coal prop- 
erly and this draught may be obtained either from a chimney or a fan. 
There is no especial merit in forced draught, except that it enables a larger 
quantity of coal to be burned and the boiler to be driven harder in case 
of emergency, and usually the harder the boiler is driven, the more 
difficult it is to suppress smoke. 

Down-draught furnaces and mechanical stokers of many different kinds 
are successfully used for smoke prevention, and when properly designed 
and installed and handled skillfully, and usually at a rate not beyond 
that for which they are designed, prevent all smoke. If these appliances 
are found giving smoke, it is always due either to overdriving or to un- 
skillful handling. It is necessary, however, that the design of these 
stokers be suited to the quality of the coal and the quantity to be burned, 
and great care should be taken to provide a sufficient size of furnace with 
a fire-brick roof and means of introducing air to make them completely 
successful. 

Burning Illinois Coal without Smoke. (L. P. Breckenridge, 
Bulletin No. 15 of the Univ. of 111. Eng'g Experiment Station, 1907.) 
■ — Any fuel may be burned economically and without smoke if it is 
mixed with the proper amount of air at a proper temperature. The 
boiler plant of the University of Illinois consists of nine units aggregating 
2000 H.P. Over 200 separate tests have been made. The following is a 
condensed statement of the results in regard to smoke prevention. 

Boilers Nos. 1 and 2. Babcock & Wilcox. Chain-grate stoker. Usual 
vertical baffling. Can be run without smoke at from 50 to 120% of rated 
capacity. 

No. 3. Stirling boiler. Chain-grate stoker. Usual baffling and com- 
bustion arches. Can be run without smoke at capacities of 50 to 140%. 

No. 4. National water-tube. Chain-grate stoker. Vertical baffling.. 
No smoke at capacities of 50 to 120%. With the Murphy furnace it was 
smokeless except when cleaning fires. 

No. 5. Babcock & Wilcox. Roney stoker. Vertical baffling. Nearly 
smokeless (maximum No. 2 on a chart in which 5 represents black smoke) 
up to 100% of rating, but cannot be run above 100% without objection- 
able smoke. 



SMOKE PREVENTION. 893 

No. 6. Babcock & Wilcox. Roney stoker. Horizontal tile-roof baf- 
fling. Can be run without smoke at capacities of 50 to 100% of rating. 

Nos. 7 and 8. Stirling, equipped with Stirling bar-grate stoker. Usual 
baffling and combustion arches. Can be run without smoke at 50 to 
140% of rating. 

No. 9. Heine boiler. Chain-grate stoker. Combustion arch and tile- 
roof furnace. Can be run without smoke at capacities of 50 to 140%. 
It is almost impossible to make smoke with this setting under any con- 
dition of operation. As much as 46 lbs. of coal per sq. ft. of grate surface 
has been burned without smoke. 

Conditions of Smoke Prevention. — Bulletin No. 373 of the U. S. 
Geological Survey, 1909 (188 pages), contains a report of an extensive 
research by D. T. Randall and J. T. Weeks on The Smokeless Combustion 
of Coal in Boiler Plants. A brief summary of the conclusions reached is 
as follows: 

Smoke prevention is both possible and economical. There are many 
types of furnaces and stokers that are operated smokelessly. 

Stokers or furnaces must be set so that combustion will be complete 
before the gases strike the heating surfaces of the boiler. When partly 
burned gases at a temperature of say 2500° F. strike the tubes of a 
boiler at say 350° F., combustion may be entirely arrested. 

The most economical hand-fired plants are those that approach most 
nearly to the continuous feed of the mechanical stoker. The fireman is 
so variable a factor that the ultimate solution of the problem depends on 
the mechanical stoker — in other words, the personal element must be 
eliminated. 

A well designed and operated furnace will burn many coals without 
smoke up to a certain number of pounds per hour, the rate varying with 
different coals. If more than this amount is burned, the efficiency will 
decrease and smoke will be made, owing to the lack of furnace capacity 
to supply air and mix gases. 

High volatile matter in the coal gives low efficiency, and vice versa. 
When the furnace was forced the efficiency decreased. 

With a hand-fired furnace the best results were obtained when firing 
was done most frequently, with the smallest charge. 

Small sizes of coal burned with less smoke than large sizes, but developed 
lower capacities. 

Peat, lignite, and sub-bituminous coal burned readily in the tile-roofed 
furnace and developed the rated capacity, with practically no smoke. 

Coals which smoked badly gave efficiencies three to five per cent lower 
than the coals burning with little smoke. 

Briquets were found to be an excellent form for using slack coal in a 
hand-fired plant. 

In the average hand-fired furnace washed coal burns with lower effi- 
ciency and makes more smoke than raw coal. Moreover, washed coal 
offers a means of running at high capacity, with good efficiency, in a 
well-designed furnace. 

Forced draught did not burn coal any more efficiently than natural 
draught. It supplied enough air for high rates of combustion, but as the 
capacity of the boiler increased, the efficiency decreased and the per- 
centage of black smoke increased. 

Fire-brick furnaces of sufficient length and a continuous, or nearly 
continuous, supply of coal and air to the fire make it possible to burn 
most coals efficiently and without smoke. 

Coals containing a large percentage of tar and heavy hydrocarbons 
are difficult to burn without smoke and require special furnaces and more 
than ordinary care in firing. 



894 THE STEAM-BOILER. 



FORCED COMBUSTION IN STEAM-BOILERS. 

For the purpose of increasing the amount of steam that can be gener- 
ated by a boiler of a given size, forced draught is of great importance. 
It is universally used in the locomotive, the draught being obtained by a 
steam-jet in the smoke-stack. It is now largely used in ocean steamers, 
especially in ships of war, and to a small extent in stationary boilers. 
Economy of fuel is generally not attained by its use, its advantages being 
confined to the securing of increased capacity from a boiler of a given 
bulk, weight, or cost. 

There are three different modes of using the fan for promoting com- 
bustion: 1, blowing direct into a closed ash-pit; 2, exhausting the gases 
by the suction of the fan; 3, forcing air into an air-tight boiler-room 
or stoke-hold. Each of these three methods has its advantages and dis- 
advantages. 

In the use of the closed ash-pit the blast-pressure frequently forces 
the gases of combustion from the joint around the furnace doors in so 
great a quantity as to affect both the efficiency of the boiler and the 
health of the firemen. 

The chief defect of the second plan is the great size of the fan required 
to produce the necessary exhaustion, on account of the higher exit tem- 
perature enlarging the volume of the waste gases. 

The third method, that of forcing cold air by the fan into an air-tight 
boiler-room — the closed stoke-hold system — though it overcame the 
difficulties in working belonging to the two forms first tried, has serious 
defects of its own, as it cannot be worked, even with modern high-class 
boiler-construction, much, if at all, above the power of a good chimney 
draught, in most boilers, without damaging them. (J. Howden, Proc. 
Eng'g Congress at Chicago, in 1893.) 

In 1880 Mr. Howden designed an arrangement intended to overcome 
the defects of both the closed ash-pit and the closed stoke-hold systems. 

An air-tight chamber is placed on the front end of the boiler and sur- 
rounding the furnaces. This reservoir, which projects from 8 to 10 
inches from the end of the boiler, receives the air under pressure, which 
is passed by valves into the ash-pits and over the fires in proportions 
suited to the kind of fuel and the rate of combustion. The air used above 
the fires is admitted to a space between the outer and inner furnace- 
doors, the inner having perforations and an air-distributing box through 
which the air passes under pressure. By means of the balance of pressure 
above and below the fires all tendency of the fire to blow out at the door 
is removed. 

A feature of the system is the combination of the heating of the air of 
combustion by the waste gases with the controlled and regulated admis- 
sion of air to the furnaces. This arrangement is effected most conven- 
iently by passing the hot fire-gases after they leave the boiler through 
stacks of vertical tubes enclosed in the uptake, their lower ends being 
immediately above the smoke-box doors. Installations on Howden's 
system have been arranged for a rate of combustion to give an average 
of from 18 to 22 I H.P. per square foot oi fire-grate with fire-bars from 
5 to 51/2 ft. in length. It is believed that with suitable arrangement of 
proportions even 30 I. H.P. per square foot can be obtained. 

For an account of uses of exhaust-fans for increasing draught, see 
paper by W. R. Roney, Trans. A. S. M. E., vol. xv. 

FUEL ECONOMIZERS. 

Economizers for boiler plants are usually made of vertical cast-iron 
tubes contained in a long rectangular chamber of brickwork. The feed- 
water enters the bank of tubes at one end, while the hot gases enter the 
chamber at the other end and travel in the opposite direction to the 
water. The tubes are made of cast iron because it is more non-corrosive 
than wrought iron or steel when exposed to gases of combustion at low 
temperatures. An automatic scraping device is usually provided for 
the purpose of removing dust from the outer surface of the tubes. 

The amount of saving of fuel that may be made by an economizer varies 
greatly according to the conditions of operation. With a given quan- 
tity of "chimney gases to be passed through it, its economy will be greater 



FUEL ECONOMIZERS. 



895 



(1) the higher the temperature of these gases; (2) the lower the tem- 
perature of the water fed into it; and (3) the greater the amount of its 
heating surface. From (1) it is seen that an economizer will save more 
fuel if added to a boiler that is overdriven than if added to one driven at 
a nominal rate. From (2) it appears that less saving can be expected 
from an economizer in a power plant in which the feed-water is heated by- 
exhaust steam from auxiliary engines than when the feed-water entering 
it is taken directly from the condenser hot-well. The amount of heating 
surface that should be used in any given case depends not only on the 
saving of fuel that may be made, but also on the cost of coal, and on the 
annual costs of maintenance, including interest, depreciation, etc. 

The following table shows the theoretical results possibly attainable 
from economizers under the conditions specified. It is assumed that the 
coal has a heating value of 15,000 B.T.U. per lb. of combustible; that it 
is completely burned in the furnace at a temperature of 2500° F.; that 
the boiler gives efficiencies ranging from 60 to 75% according to the rate 
of driving; and that sufficient economizer surface is provided to reduce 
the temperature of the gases in all cases to 300° F. Assuming the specific 
heat of the gases to be constant, and neglecting the loss of heat by radi- 
ation, the temperature of the gases leaving the bciler and entering the 
economizer is directly proportional to (100-% of boiler efficiency), and 
the combined efficiency of boiler and economizer is (2500 - 300) -*- 2500 
= 88%, which corresponds to an evaporation of (15,000 -*- 970) X 0.88 = 
13.608 lbs. from and at 212° per lb. of combustible; or assuming the feed- 
water enters the economizer at 100° F. and the boiler makes steam of 
150 lbs. absolute pressure, to an evaporation of 11.729 lbs. under these 
conditions. Dividing this figure into the number of heat units utilized 
by the economizer per lb. of combustible gives the heat units added to 
the water, from which, by reference to a steam table, the temperature 
may be found. With these data we obtain the results given in the table 
below. 



Boiler Efficiency, %. 



60 


65 


70 


9000 


9750 


10500 


6000 


5250 


4500 


1000° 


875° 


750° 


300° 


300° 


300° 


4200 


3450 


2700 


28 


23 


18 


9.278 


10.051 


10.824 


4.330 


3.557 


2.884 


448° 


389° 


327° 


70 


65.7 


60 



B.T.U. absorbed by boiler per lb. combustible. . . 

B.T.U. in chimney gases leaving boiler 

Estimated temp, of gases leaving boiler 

Estimated temp, of gases leaving economizer.:.. 

B.T.U. saved by economizer 

Efficiency gained by economizer, % 

Equivalent water evap. per lb. comb, in boiler. . . 
B.T.U. saved by econ. equivalent to evap. of lbs 

Temp, of water leaving economizer 

Efficiency of the economizer, % 



11250 

3750 

625° 

300° 

1950 

13 

! 1.598 

2.010 

265° 

52 



Amount of Heating Surface. — The Fuel Economizer Co. says: 
We have found in practice that by allowing 4 sq. ft. of heating surface 
per boiler H.P. (34 1/2 lbs. evap. from and at 212° = 1 H.P.) we are able 
to raise the feed-water 60° F. for every 100° reduction in the temperature, 
the gases entering the economizer at 450° to 600°. With gases at 600° 
to 700° we have allowed a heating surface of 41/2 to 5 sq. ft. per H.P., 
and for every 100° reduction in temperature of the gases we have 
obtained about 65° rise in temperature of the water; the feed-water 
entering at 60 to 120°. With 5000 sq. ft. of boiler-heating surface (plain 
cylinder boilers) developing 1000 H.P. we should recommend 5 sq. ft. of 
economizer surface per boiler H.P. developed, or an economizer of about 
500 tubes, and it should heat the feed-water about 300°. 

Heat Transmission in Economizers. (Carl S. Dow, Indust. Eng'g, 
April, 1909.) — The rate of heat transmission (C) per sq. ft. per hour per 
degree of difference between the average temperatures of the gases and 
the water passing through the economizer varies with the mean tem- 
perature of the gas about as follows: Gas, 600°, C — 3.25; gas 500°, C = 3; 
gas 400°, C = 2.75; gas 300°, C = 2.25. 



THE STEAM-BOILER. 



Calculation of the Saving made by an Economizer. — The usual 
method of calculating the saving of fuel by an economizer when the boiler 
and the economizer are tested together as a unit is by the formula (Hi - h) 
-s- (Hi — h), in which h is the total heat above 32° of 1 lb. of water enter- 
ing, Hi the total heat of 1 lb. of water leaving the economizer, and Hi the 
total heat above 32° of 1 lb. of steam at the boiler pressure. If h = 100, 
Hi = 210, Hi = 1200, then the saving according to the formula is (210 — 
100) + 1100 = 10%. This is correct if the saving is defined as the ratio of 
the heat absorbed by the economizer to the total beat absorbed by the 
boiler and economizer together, but it is not correct if the saving is defined 
as the saving of fuel made by running the combined unit as compared with 
running the boiler alone making the same quantity of steam from feed- 
water at the low temperature, so as to cause the boiler to furnish Hi — h 
heat units per lb. instead of Hi — Hi. In this case the boiler is called 
on to do more work, and in doing it it may be overdriven and work 
with lower efficiency. 

In a test made by F. G. Gasche, in Kansas City in 1S97, using Missouri 
coal analyzing moisture 7.58; volatile matter, 36.69; fixed carbon. 35.02; 
ash, 15.69; sulphur, 5.12, he obtained an evaporation of 5.17 lbs. from 
and at 212° per lb. of coal with the boiler alone, and when the boiler 
and economizer were tested together the equivalent evaporation credited 
to the boiler was 5.55, to the economizer 0.72, and to the combined unit 
6.27, the saving by the combined unit as compared with the boiler alone 
being (6.27 - 5.17) -4- 6.27 = 17.5%, while the saving of heat shown by 
the economizer in the combined test is only (6.27 — 5.55) ■*- 6.27 = 
11.5%, or as calculated by Mr. Gasche from the formula (Hi — h) -*- 
(Hi - h), (172.1 - 39.3) -h (1181.8 -h 39.3) = 11.6%. 

The maximum saving of fuel which may be made by the use of an econo- 
mizer when attached to boilers that are working with reasonable economy 
is about 15%. Take the case of a condensing engine using steam of 125 
lbs. gauge pressure, and with a hot-well or feed-water temperature of 
100° F. The economizer may be expected under the best conditions to 
raise this temperature about 170°, or to 270°. Then h = 68, Hi = 239, 
Hi - 1190. (Hi - h) -4- (Hi - h) = 171 -J- 15.24%. 

If the boilers are not working with fair economy on account of being 
overdriven, then the saving made by the addition of an economizer may 
be much greater. 

Test of a Large Economizer. (R. D. Tomlinson, Power, Feb., 1904.) 
— Two tests were made of one of the sixteen Green economizers at the 
74th St. Station of the Rapid Transit Railway, New York City. Four 
520-H.P. B. & W. boilers were connected to the economizer. It had 512 
tubes, 10 ft. long, 49/i6 in. external diam.; total heating surface 6760 sq. 
ft., or 3.25 sq. ft. per rated H.P. of the boilers. Draught area through 
econ., 3 sq. in. per H.P. The stack for each 16 boilers and four econo- 
mizers was 280 ft. high, 17 ft. internal diam. The first test was made 
with the boilers driven at 94% of rating, the second at 113%. The 
results are given below, the figures of the second test being in parentheses. 

Water entering econ. 96° (93.5°); leaving 200° (203.8°); rise 104 (110.3). 

Gases entering econ. 548° (603°); leaving 295 (325); drop 253 (278). 

Steam, gauge pressure, 166 (165). Total B.T.U. per lb. from feed 
temp. 1132 (1134). 

Saving of heat by economizer, %, 9.17 (9.73). 

Reduction of draught in passing through econ., in. of water, 0.16 (0.23). 

Results from Seven Tests of Sturtevant Economizers (Catalogue of 
B. F. Sturtevant Co.) 



Plants 
Tested. 


Gases En- 


Gases 


Water En- 


Water 


Increase in 


tering. 


Leaving. 


tering. 


Leaving. 


Tempera- 


Deg. F. 


Deg. F. 


Deg. F. 


Deg. F. 


ture. 


1 


650 


275 


180 


340 


160 


2 


575 


290 


160 


320 


160 


3 


470 


230 


130 


260 


130 


4 


500 


240 


110 


230 


120 


5 


460 


200 


90 


230 


140 


6 


440 


220 


120 


236 


116 


7 


525 


225 


180 


320 


140 



INCRUSTATION AND CORROSION. 897 



THERMAL STORAGE. 

In Druitt Halpin's steam storage system (Industries and Iron, Mar. 22, 
1895) he employs only sufficient boilers to supply tile mean demand, and 
storage tanks sufficient to supply the maximum demand. These latter 
not being subjected to the fire suffer but little deterioration. The boilers 
working continuously at their most economical rate have their excess of 
energy during light load stored up in the water of the tank, from which 
it may be drawn at will during heavy load. He proposes that the boilers 
and tanks shall work under a pressure of 265 lbs. per square inch when 
fully charged, which corresponds to a temperature of 406° F., and that 
the engines be worked at 130 lbs. per square inch, which corresponds to 
347° F. The total available heat stored when the reservoirs are charged 
is that due to a range of 59°. The falling in temperature of 14V4 lbs. of 
water from 407° to 347° will yield 1 lb. of steam. To allow for radia- 
tion of loss and imperfect working, this may be taken at 16 lbs. of water 
per pound of steam. The steam consumption per effective H.P. maybe 
taken at 18 lbs. per hour in condensing and 25 lbs. per hour in non-con- 
densing engines. The storage-room per effective H.P. by this method 
would, therefore, be (16 X 18) -^ 62.5= 4.06 cu. ft. for condensing and 
(16 X 25) ■*■ 62.5 = 6.4 cu. ft. for non-condensing engines. 

Gas storage, assuming that illuminating gas is used, would require 
about 20 cu. ft. of storage room per effective H.P. hour stored, and if 
ordinary fuel gas were stored it would require about four times this 
capacity. In water storage 317 cu. ft. would be required at an elevation 
of 100 ft. to store one H.P. hour, so that of the three methods of storing 
energy the thermal method is by far the most economical of space. 

In the steam storage method the boiler is completely filled with water 
and the storage tank nearly so. The two are in free communication by 
means of pipes, and a constant circulation of water is maintained between 
the two, but the steam for the engines is taken only from the top of the 
storage tank through a reducing valve. 

In the feed storage system, the excess of energy during light load is 
stored in the tank as before, but the boilers are not completely filled. In 
this system the steam is taken exclusively from the boilers, the super- 
heated water of the storage tanks being used during heavy load as feed- 
water to the boilers. 

A third method is a combination of these two. In the "combined" 
feed and steam storage system the pressure in boiler and storage tank is 
equalized by connecting the steam spaces in both by pipe, and the steam 
for the engines is, therefore, taken from both. In other words they work 
in parallel. 

INCRUSTATION AND CORROSION. 

Incrustation or Scale. — Incrustation (as distinguished from mere 
sediments due to dirty water, which are easily blown out, or gathered 
up, by means of sediment-collectors) is due to the presence of salts in the 
feed-water (carbonates and sulphates of lime and magnesia for the most 
part), which are precipitated when the water is heated, and form hard 
deposits upon the boiler-plates. (See Impurities in Water, p. 691, ante.) 

Where the quantity of these salts is not very large (12 grains per 
gallon, say) scale preventives may be found effective. The chemical 
preventives either form with the salts other salts soluble in hot water; 
or precipitate them in the form of spft mud, which does not adhere to 
the plates, and can be washed out from time to time. The selection of 
the chemical must depend upon the composition of the water, and it 
should be introduced regularly with the feed. 

Examples. — Sulphate-of-lime scale prevented by carbonate of soda: 
The sulphate of soda produced is soluble in water; and the carbonate of 
lime falls down in grains, does not adhere to the plates, and may there- 
fore be blown out or gathered into sediment-collectors. The chemical 
reaction is: 

Sulphate of lime + Carbonate of soda = Sulphate of soda + Carbonate of lime 
CaS0 4 Na 2 C0 3 Na 2 S0 4 CaC0 3 

Where the quantity of salts is large, scale preventives are not of much 
use. Some other source of supply must be sought, or the bad water 



THE STEAM-BOILER. 



purified before it is allowed to enter the boilers. The damage done to 
boilers by unsuitable water is enormous. 

Pure water may be obtained by collecting rain, or condensing steam by 
means of surface condensers. The water thus obtained should be mixed 
with a little bad water, or treated with a little alkali, as undiluted, pure 
water corrodes iron; or, after each periodic cleaning, the bad water may 
be used for a day or two to put a skin upon the plates. 

Carbonate of lime and magnesia may be precipitated either by heating 
the water or by mixing milk of lime (Porter-Clark process) with it, the 
water being then filtered. 

Corrosion may be produced by the use of pure water, or by the presence 
of acids in the water, caused perhaps in the engine-cylinder by the action 
of high-pressure steam upon the grease, resulting in the production of 
fatty acids. Acid water may be neutralized by the addition of lime. 

Amount of Sediment which may collect in a 100-H.P. steam-boiler, 
evaporating 3000 lbs. of water per hour, the water containing different 
amounts of impurity in solution, provided that no water is blown off: 

Grams of solid impurities per U. S. gallon; 

5 10 20 30 40 50 60 70 80 90 100 

Equivalent parts per 100,000: 

8.57 17.14 34.28 51.42 68.56 85.71 102.85 120 137.1 154.3 171.4 
Sediment deposited in 1 hour, pounds: 

0.257 0.514 1.028 1.542 2.056 2.571 3.085 3.6 4.11 4.63 5.14 
In one day of 10 hours, pounds: 

2.57 5.14 10.28 15.42 20.56 25.71 30.85 36.0 41.1 46.3 51.4 
In one week of 6 days, pounds: 
15.43 30.85 61.7 92.55 123.4 154.3 185.1 216.0 246.8 277.6 308.5 

If a 100-H.P. boiler has 1200 sq. ft. heating-surface, one week's running 
without blowing off, with water containing 100 grains of solid matter per 
gallon in solution, would make a scale nearly 0.02 in. thick, if evenly depos- 
ited all over the heating-surface, assuming the scale to have a sp. gr. of 
2.5 = 156 lbs. per cu. ft.; 0.02 X 1200 X 156 X V12 = 312 lbs. 

Boiler-scale Compounds. — The Bavarian Steam-boiler Inspection 
Assn. in 1885 reported as follows: 

Generally the unusual substances in water can be retained in soluble 
form or precipitated as mud by adding caustic soda or lime. This is 
especially desirable when the boilers have small interior spaces. 

It is necessary to have a chemical analysis of the water in order to fully 
determine the kind and quantity of the" preparation to be used for the 
above purpose. 

All secret compounds for removing boiler-scale should be avoided. 
(A list of 27 such compounds manufactured and sold by German firms is 
then given which have been analyzed by the association.) 

Such secret preparations are either nonsensical or fraudulent, or 
contain either one of the two substances recommended by the association 
for removing scale, generally soda, which is colored to conceal its presence, 
and sometimes adulterated with useless or even injurious matter. 

These additions as well as giving the compound some strange, fanciful 
name, are meant simply to deceive the boiler owner and conceal from him 
the fact that he is buying colored soda or similar substances, for which 
he is paying an exorbitant price. 

Effect of Scale on Boiler Efficiency. — The following statement, 
or a similar one, has been published and republished for 40 years or more 
by makers of "boiler compounds," feed-water heaters and water-puri- 
fying apparatus, but the author has not been able to trace it to its original 
source:* 

" It has been estimated that scale i/so of an inch thick requires the 
burning of 5 per cent of additional fuel; scale 1/25 of an inch thick 

* A committee of the Am. Ry. Mast. Mechs. Assn. in 1872 quoted 
from a paper by Dr. Jos. G. Rodgers before the Am. Assn. for Adv. of 
Science (date not stated): "It has been demonstrated [how and by 
whom not stated] that a scale i'i6 in. thick requires the expenditure of 
15% more fuel. As the scale thickens the ratio increases; thus when it 
is 1/4 in. thick, 60% more is required." 



INCRUSTATION AND CORROSION. 899 



requires 10 per cent more fuel; i,'i6 of an inch of scale requires 15 per 
cent additional fuel; Vs of an inch. 30 per cent., and 1/4 of an inch, 66 per 
cent." 

The absurdity of the last statement may be shown by a simple calcu- 
lation. Suppose a clean boiler is giving 75% efficiency with a furnace 
temperature of 2400° F. above the atmospheric temperature, Neglecting 
the radiation and assuming a constant specific heat for the gases, the 
temperature of the chimney gases will be 600°. A certain amount of 
fuel and air supply will furnish 100 lbs. of gas. In the boiler with 1/4 in. 
scale 66% more fuel will make 66 lbs. more gas. As the extra fuel does 
no work in evaporating water, its heat must all go into the chimney 
gas. We have then in the chimney gases 

100 lbs. at 600° F., product 60,000 
66 lbs. at 2400° F., product 158,400 nio , nn 
21o,4UU 

which divided by 166 gives 1370° above atmosphere as the temperature 
of the chimney gas, or more than enough to make the flue connection and 
damper red hot. (Makers of boiler compounds, etc., please copy.) 

Another writer says: "Scale of Vi6 inch thickness will reduce boiler 
efficiency Vs, and the reduction of efficiency increases as the square of 
the thickness of the scale." 

This is still more absurd, for according to it if Vie in. scale reduces the 
efficiency 1/8, then 3/ 16 in. will reduce it 9/ 8 , or to below zero. 

From a series of tests of locomotive tubes covered with different thick- 
nesses of scale up to Vs in. Prof. E. C. Schmidt (Bull. No. 11 Univ. of 
111. Experiment Station, 1907) draws the following conclusions: 

1. Considering scale of ordinary thickness, say varying up to Vs inch, 
the loss in heat transmission due to scale may vary in individual cases 
from insignificant amounts to as much as 10 or 12 per cent. 

2. The loss increases somewhat with the thickness of the scale. 

3. The mechanical structure of the scale is of as much or more impor- 
tance than the thickness in producing this loss. 

4. Chemical composition, except in so far as it affects the structure 
of the scale, has no direct influence on its heat-transmitting qualities. 

In 1896 the author made a test of a water-tube boiler at Aurora, 111., 
which had a coating of scale about 1/4 in. thick throughout its whole 
heating surface, and obtained practically the same evaporation as in 
another test, a few days later, after the boiler had been cleaned. This 
is only one case, but the result is not unreasonable when it is known 
that the scale was very soft and porous, and was easily removed from the 
tubes by scraping. 

Prof. R. C. Carpenter (Am. Electrician, Aug., 1900) says: So far as I am 
able to determine by tests, a lime scale, even of great thickness, has no 
appreciable effect on the efficiency of a boiler, as in a test which was 
conducted by myself the results were practically as good when the boiler 
was thickly covered with lime scale as when perfectly clean. ... Ob- 
servations and experiments have shown that any scale porous to water 
has little or no detrimental effect on economy of the boiler. There 
is, I think, good philosophy for this statement; the heating capacity is 
affected principally by the rapidity with which the heated gases will 
surrender heat, as "the water and the metal have capacities for absorbing 
heat more than a hundred times faster than the air will surrender heat. 

A thin film of grease, being impermeable to water, keeps the latter 
from contact with the metal and generally produces disastrous results. 
It is much more harmful than a very thick scale of carbonate of lime. 

Kerosene and other Petroleum Oils; Foaming. — Kerosene has 
been recommended as a scale preventive. See paper by L. F. Lyne 
(Trans. A. S. M. E., ix. 247). The Am. Mach., May 22, 1890, says: 
Kerosene used in moderate quantities will not make the boiler foam; 
it is recommended and used for loosening the scale and for preventing the 
formation of scale. The presence of oil in combination with other im- 
purities increases the tendency of many boilers to foam, as the oil with the 
impurities impedes the free escape of steam from the water surface. 
The use of common oil not only tends to cause foaming, but is dangerous 
otherwise. The grease appears to combine with the impurities of the 
water, and when the boiler is at rest this compound sinks to the plates 



900 TOE STEAM-BOILER. 

and clings to them in a loose, spongy mass, preventing the water from 
coming in contact with the plates, and thereby producing overheating, 
which may lead to an explosion. Foaming may also be caused by forcing 
the fire, or by taking the steam from a point over the furnace or where 
the ebullition is violent ; the greasy and dirty state of new boilers is another 
good cause for foaming. Kerosene should be used at first in small quan- 
tities, the effect carefully noted, and the quantity increased if necessary 
for obtaining the desired results. 

R. C. Carpenter (Trans. A. S. M. E., vol. xi) says: The boilers of the 
State Argicultural College at Lansing, Mich., were badly incrusted with 
a hard scale. It was fully 3/ 8 in. thick in many places. The first appli- 
cation of the oil was made while the boilers were being but little used, 
by inserting a gallon of oil, filling with water, heating to the boiling-point 
and allowing the water to stand in the boiler two or three weeks before 
removal. By this method fully one-half the scale was removed during 
the warm season and before the boilers were needed for heavy firing. 
The oil was then added in small quantities when the boiler was in actual 
use. For boilers 4 ft. in diam. and 12 ft. long the best results were 
obtained by the use of 2 qts. for each boiler per week, and for each boiler 
5 ft. in diam. 3 qts. per week. The water used in the boilers has the fol- 
lowing analysis: CaC0 3 , 206 parts in a million; MgCCh, 78 parts; F62C03, 
22 parts; traces of sulphates and chlorides of potash and soda. Total 
solids, 325 parts in 1,000,000. 

Petroleum Oils heavier than kerosene have been used with good re- 
sults. Crude oil should never be used. The more volatile cils it contains 
make explosive gases, and its tarry constituents are apt to form a spongy 
incrustation. 

Removal of Hard Scale. — When boilers are coated with a hard scale 
difficult to remove the addition of 1/4 lb. caustic soda per horse-power, 
and steaming for some hours, according to the thickness of the scale, just 
before cleaning, will greatly facilitate that operation, rendering the scale 
soft and loose. Tins should be done, if possible, when the boilers are not 
otherwise in use. (Steam.) 

Corrosion in Marine Boilers. (Proc. Inst. M. E., Aug., 1884.) — 
The investigations of the Committee on Boilers served to show that the 
internal corrosion of boilers is greatly due to the combined action of air 
and sea-water when under steam, and when not under steam to the com- 
bined action of air and moisture upon the unprotected surfaces of the 
metal. There are other deleterious influences at work, such as the corro- 
sive action of fatty acids, the galvanic action of copper and brass, and the 
inequalities of temperature; these latter, however, are considered to be of 
minor importance. 

Of the several methods recommended for protecting the internal sur- 
faces of boilers, the three found most effectual are: First, the formation 
of a thin layer of hard scale, deposited by working the boiler with sea- 
water; second, the coating of the surfaces with a thin wash of Portland 
cement, particularly wherever there are signs of decay; third, the use of 
zinc slabs suspended in the water and «team spaces. 

As to general treatment for the preservation of boilers when laid up 
in the reserve, either of the two following methods is adopted. First, 
the boilers are dried as much as possible by airing-stoves, after which 
2 to 3 cwt. of quicklime is placed on trays at the bottom of the boiler and 
on the tubes. The boiler is then closed and made as air-tight as possible. 
Inspection is made every six months, when if the lime be found slacked 
it is renewed. Second, the boilers are filled with sea or fresh water, 
having added soda to it in the proportion of 1 lb. to every 100 or 120 lbs. 
of water. The sufficiency of the saturation can be tested by introducing 
a piece of clean new iron and leaving it in the boiler for ten or twelve 
hours: if it shows signs of rusting, more soda should be added. It is 
essential that the boilers be entirely filled, to the complete exclusion of 
air. 

Mineral oil has for many years been exclusively used for internal 
lubrication of engines, with the view of avoiding the effects of fatty acid, 
as this oil does not readily decompose and possesses no acid properties. 

Of all the preservative methods adopted in the British service, the use 
of zinc properly distributed and fixed has been found the most effectual 



INCRUSTATION AND CORROSION. 901 

In saving the iron and steel surfaces from corrosion, and also in neutral- 
izing by its own deterioration the hurtful influences met with in water as 
ordinarily supplied to boilers. The zinc slabs now used .in the navy 
boilers are 12 in. long, 6 ins. wide, and 1/2 in. thick; this size being found 
convenient for general application. The amount of zinc used in new 
boilers at present is one slab of the above size for every 20 I.H.P., or 
about 1 sq. ft. of zinc surface to 2 sq. ft. of grate surface. Rolled zinc is 
found the most suitable for the purpose. Especial care must be taken 
to insure perfect metallic contact between the slabs and the stays or 
plates to which they are attached. The slabs should be placed in such 
positions that all the surfaces in the boiler are protected. Each slab 
should be periodically examined to see that its connection remains per- 
fect, and to renew any that may have decayed; this examination is 
usually made at intervals not exceeding three months. Under ordinary 
circumstances of working these zinc slabs may be expected to last in fit 
condition from 60 to 90 days, immersed in hot sea-water; but in new 
boilers they at first decay more rapidly. The slabs are generally secured 
by means of iron straps 2 in. X 3/g in., and long enough to reach the 
nearest stay, to which the strap is attached by screw-bolts. 

To promote the proper care of boilers when not in use the following 
order has been issued to the French Navy by the Government: On board 
all ships in the reserve, as well as those which are laid up, the boilers will 
be completely filled with fresh water. In the case of large boilers with 
large tubes there will be added to the water a certain amount of milk of 
lime, or a solution of soda. In the case of tubulous boilers with small 
tubes milk of lime or soda may be added, but the solution will not be 
so strong as in the case of the larger tube, so as to avoid any danger of 
contracting the effective area by deposit from the solution; but the 
strength of the solution will be just sufficient to neutralize any acidity of 
the water. {Iron Age, Nov. 2, 1893.) 

Use of Zinc. — Zinc is often used in boilers to prevent the corrosive 
action of water on the metal. The action appears to be an electrical 
one, the iron being one pole of the battery and the zinc being the other. 
The hydrogen goes to the iron shell and escapes as a gas into the steam. 
The oxygen goes to the zinc. 

On account of this action it is generally believed that zinc will always 
prevent corrosion, and that it cannot be harmful to the boiler or tank. 
Some experiences go to disprove this belief, and in numerous cases zinc 
has not only been of no use, but has even been harmful. In one case a 
tubular boiler had been troubled with a deposit of scale consisting chiefly 
of organic matter and lime, and zinc was tried as a preventive. The bene- 
ficial action of the zinc was. so obvious that its continued use was advised, 
with frequent opening of the boiler and cleaning out of detached scale 
until all the old scale should be removed and the boiler become clean. 
Eight or ten months later the water-supply was changed, it being now 
obtained from another stream supposed to be free from lime and to con- 
tain only organic matter. Two or three months- after its introduction 
the tubes and shell were found to be coated with an obstinate adhesive 
scale, composed of zinc oxide and the organic matter or sediment of the 
water used. The deposit had become so heavy in places as to cause 
overheating and bulging of the plates over the fire. {The Locomotive.) 

Effect of Deposit on the Fire-surface of Flues. (Rankine.) — An 
external crust of a carbonaceous kind is often deposited from the flame 
and smoke of the furnaces in the flues and tubes, and if allowed to accu- 
mulate seriously impairs the economy of fuel. It is removed from time to 
time by means of scrapers and wire brushes. The accumulation of this 
'crust is the probable cause of the fact that in some steamships the con- 
sumption of coal per I.H.P. per hour goes on gradually increasing until it 
reaches one and a half times its original amount, and sometimes more. 

Dangerous Steam-boilers discovered by Inspection. — The Hart- 
ford Steam-boiler Inspection and Insurance Co. reports that its inspec- . 
tors during 1908 examined 317,537 boilers, inspected 124,990 boilers, both 
internally and externally, subjected 10,449 to hydrostatic pressure, and 
found 572 unsafe for further use. The whole number of defects reported 
was 151,359, of which 15,578 were considered dangerous. A summary 
is given below. {The Locomotive, Jan., 1909.) 



902 



THE STEAM-BOILER. 



Summary, by Defects, for the Year 1893. 



Whole Dan- 
No. gerous. 
' 2,136 



Nature of Defects. 

Defective tubes 8,026 

Tubes too light 1,636 '432 

Leakage at joints 4,845 392 

Water-gauges defective. 2,411 585 

Blow-offs defective 3,818 1,125 

Deficiency of water 391 147 

Safety-valves overloaded 1,216 379 

Safety-valves defective. 1,068 359 

Pressure-gauges def'tive 7,120 531 

Without pressure-gauges. . 322 322 

Unclassified defects 7 3 



Total 151,359 15,878 



Whole Dan- 
Nature of Defects. No. gerous. 

Deposit of sediment 18,879 1 ,242 

Incrustation and scale.. .37,924 1,193 

Internal grooving 2,649 249 

Internal corrosion 13,053 555 

External corrosion 9,400 698 

Def'tive braces and stays 1,993 503 

Settings defective 5,341 642 

Furnaces out of shape. . . 6,981 380 

Fractured plates 3,119 482 

Burned plates 4,605 440 

Laminated plates 666 44 

Defective riveting 3,395 713 

Defective heads 1,565 223 

Leakage around tubes. .. 10,929 2, 103 

The above-named company publishes annually a summary like the 
above, and also a classified list of boiler-explosions, compiled chiefly from 
newspaper reports, showing that from 200 to 300 explosions take place in 
the United States every year, killing from 200 to 300 persons, and injuring 
from 300 to 450. The lists are not pretended to be complete, and may 
include only a fraction of the actual number of explosions. 

Steam-boilers as Magazines of Explosive Energy. — Prof. P. H. 
Thurston (Trans. A. S. M. E., vol. vi), in a paper with the above title, 
presents calculations showing the stored energy in the hot water and 
steam of various boilers. Concerning the plain tubular boiler of the 
form and dimensions adopted as a standard by the Hartford Steam-boiler 
Insurance Co., he says: It is 60 ins. in diameter, containing 66 3-in. 
tubes, and is 15 ft. long. It has 850 sq. ft. of heating and 30 sq. ft. of 
grate surface is rated at 60 H.P., but is oftener driven up to 75; weighs 
9500 lbs., and contains nearly its own weight of water, but only 21 lbs. 
of steam when under a pressure of 75 lbs. per sq. in., which is below its 
safe allowance. It stores 52,000,000 foot-pounds of energy, of which 
but 4% is in the steam, and this is enough to drive the boiler just about 
one mile into the air, with an initial velocity of nearly 600 ft. per second. 



SAFETY-VALVES. 

Calculation of Weight, etc., for Lever Safety-valves. 

Let W = weight of ball at end of lever; w = weight of lever itself; V = 
weight of valve and spindle, all in pounds; L = distance between fulcrum 
and center of ball; I = distance between fulcrum and center of valve; 
g = distance between fulcrum and center of gravity of lever all in inches; 
A = area of valve, in sq. ins.; P = pressure of steam, in lbs. per sq. in., 
at which valve will open. 

Then PAXl = WXL+wXg + VXl; 
whence P = (WL + wg + VI) ■*- Al; W = (PAl - wg - VI) + L; L = 
(PAl - wg - VI) -^ W. 

Example. — Diameter of valve, 4 ins.; distance from fulcrum to center 
of ball, 36 ins.; to center of valve, 4 ins.; to center of gravity of lever, 
151/2 ins.; weight of valve and spindle, 3 lbs.; weight of lever, 7 lbs.; re- 
quired the weight of ball to make the blowing-off pressure 80 lbs. per sq. 
in.; area of 4-in. valve = 12.566 sq. ins. Then 



W- 



PAl - wg-Vl _ 80 X 12.566 X 4-7 X 15l/ 2 - 3X4 
L 36 



= 108.41 



By the rules of the U. S. Supervising Inspectors of Steam Vessels the 
use of lever safety-valves is prohibited on all boilers built for steam vessels 
after June 30, 1906. 



SAFETY-VALVES. 903 

Rules for Area of Safety-valves. 

(Rule of U. S. Supervising Inspectors of Steam-vessels (as amended 1909).) 

The areas of all safety-valves on boilers contracted for or the con- 
struction of which commenced on or after June 1, 1904, shall be deter- 
mined in accordance with the following formula: a = 0.2074 X W/P, 
where a = area of safety-valve, in sq. in., per sq. ft. of grate surface; W = 
pounds of water evaporated per sq. ft. of grate surface per hour; P — abso- 
lute pressure per sq. in. = working gauge pressure + 15. 

The value of a multiplied by the square feet of grate surface gives the 
area of safety valve or valves required. When this calculation results 
in an odd size of safety-valve use the next larger standard size. 

Example. — Boiler-pressure = 215 lbs. gauge, = 230 absolute, = P. 
Grate surface = 110 sq. ft. Water evaporated per pound coal = 10 lbs. 
Coal burned per sq. ft. grate per hour = 30 lbs. Evaporation per sq. ft. 
grate per hour = 300 lbs. = W. a = 0.2074 X 300 -s- 230 = 0.270. 
Therefore area of safety-valve = 110 X 0.270 = 29.7 sq. ins., which is 
too large for one valve. Use two, 14.85 sq. ins. each. Diameter = 43/ 8 
ins. Each spring-loaded valve shall be supplied with a lever that Will 
raise the valve from its seat a distance of not less than that equal to 
one-eighth of the diameter of the valve opening. 

The valves shall be so arranged that each boiler shall have at least one 
separate safety-valve, unless the arrangement is such as to preclude the 
possibility of shutting off the communication of any boiler with the 
safety valve or valves employed. 

Two safety-valves may be allowed on any boiler, provided their com- 
bined area is equal to that required by rule for one valve. Whenever 
the area of a safety-valve, as found by the rule, will be greater than that 
corresponding to 6 inches in diameter, two or more safety-valves, whose 
combined area shall be equal at least to the area required, must be used. 

The seats of all safety-valves shall have an angle of inclination of 45 
degrees to the center lines of their axes. 

Comparison of Various Rules for Area of Lever Safety-valves. 
(Condensed from an article by the author in American Machinist, May 24, 
1894, with some alterations.)' — Assume the case of a boiler rated at 100 
horse-power; 40 sq. ft. grate; 1200 sq. ft. heating-surface; using 400 lbs. 
of coal per hour, or 10 lbs. per sq. ft. of grate per hour, and evaporating 
3600 lbs. of water, or 3 lbs. per sq. ft. of heating-surface per hour; steam- 
pressure by gauge, 100 lbs. What size of safety-valve, of the lever type, 
should be required? 

A compilation of various rules for finding the area of the safety-valve 
disk, from The Locomotive of July, 1892, is given in abridged form below, 
together with the area calculated by each rule for the above example. 

Disk Area 
in sq. in. 

U. S. Supervisors, heating-surface in sq. ft. -s- 25 (old rule) 48 

English Board of Trade, grate-surface in sq. ft. -s- 2 20 

Molesworth, four-fifths of grate-surface in sq. ft 32 

Thurston, 4 times coal burned per hour X (gauge pressure + 10) ... 14.5 

Thurston, 2.5 X heating-surface h- gauge pressure + 10 27.3 

Rankine, 0.006 X water evaporated per hour 21 . 6 

Committee of U. S. Supervisors, 0.005 X water evaporated per hr.. 18 

Suppose that, other data remaining the same, the draught were in- 
creased so as to burn 13 1/3 lbs. coal per sq. ft. of grate per hour, and the 
grate-surface cut down to 30 sq. ft. to correspond, making the coal burned 
per hour 400 lbs., and the water evaporated 3600 lbs., the same as before; 
then the English Board of Trade rule and Molesworth's rule would give 
an area of disk of only 15 and 24 sq.in., respectively, showing the absurdity 
of making the area of grate the basis of the calculation of disk area. 

Other rules give for the area of safety-valve of the same 100-horse- 
power boiler results ranging all the way from 5.25 to 57.6 sq. ins. 

All of the rules quoted give the area of the disk of the valve as the 
thing to be ascertained, and it is this area which is supposed to bear 
6ome direct ratio to the grate-surface, to the heating-surface, to the 



904 THE STEAM-BOILER. 

water evaporated, etc. It is difficult to see why this area has been con- 
sidered even approximately proportional to these quantities, for with 
small lifts the area of actual opening bears a direct ratio, not to the area 
of disk, but to the circumference. 
Thus for various diameters of valve: 

Diameter, ins. 1 2 3 4 5 6 7 

Area, sq. ins 0.785 3.14 7.07 12.57 19.64 28.27 38.48 

Circumference 3.14 6.28 9.42 12.57 15.71 18.85 21.99 

Circum.Xliftof O.lin. 0.31 0.63 0.94 1.26 1.57 1.89 2.20 

Ratio to area 0.4 0.2 0.13 0.1 0.08 0.067 0.057 

A correct rule for size of safety-valves should make the product of the 
diameter and the lift proportional to the weight of steam to be discharged. 

A method for calculating the size of safety-valve is given in The Loco- 
motive, July, 1892, based on the assumption that the actual opening 
should be sufficient to discharge all the steam generated by the boiler. 
Napier's rule for flow of steam is taken, viz., flow through aperture of one 
sq. in. in lbs. per second = absolute pressure -s- 70, or in lbs. per hour = 
51.43 X absolute pressure. 

If the angle of the seat is 45°, the area of opening in sq. in. = circum- 
ference of the disk X the lift X 0.71, 0.71 being the cosine of 45°; or 
diameter of disk X lift X 2.23. 



Spring-loaded Safety Valves. 

Spring-loaded safety valves to be used on U. S. merchant vessels must 
conform to the rules prescribed by the Board of Supervising Inspectors, 
and on vessels for the U. S. Navy to specifications made by the Bureau 
of Steam Engineering, U. S. N. Valves to be used- on stationary boilers 
must conform in many cases to the special laws made by various states. 
Few of these rules are on a logical basis, in that they take no account of 
the lift of the valve, and it is quite clear that the rate of steam discharge 
through a safety-valve depends upon the area of opening, which varies 
with the circumference of the valve and the lift. Experiments made by 
the Consolidated Safety Valve Co. showed that valves made by the differ- 
ent manufacturers and employing various combinations of springs with 
different designs of valve lips and huddling chambers give widely different 
lifts. Lifts at popping point of different makes of safety-valves, at 200 
lbs. pressure, are as follows: 

4-in. stationary valves, in., 0.031, 0.056, 0.064, 0.082, 0.094, 0.094, 0.137. 

Av. 0.079 in. 
31/2-in. locomotive valves, in., 0.040, 0.051, 0.065, 0.072. 0.076, 0.140 ins. 

Av. 0.074 in. 

United States Supervising Inspectors' Rule (adopted in 1904). A = 
0.2074 W/P. A = area of safety valve in sq. in. per sq. ft. of grate 
surface; W = lbs. of water evaporated per sq. ft. of grate surface per 
hour; P = boiler pressure, absolute, lbs. per sq. in. This rule assumes 
a lift of 1/32 of the nominal diameter, and 75% of the flow calculated by 
Napier's rule. This 75% corresponds nearly to the cosine of 45°, or 0.707. 

Massachusetts Rule of 1909. A = 770 W/P, in which W = lbs. evapo- 
rated per sq. ft. of grate per second; A and P as above. This is the 
same as the U. S. rule with a 3.2% larger constant. 

Philadelphia Ride. — A = 22.5 G + (P + 8.62). A = total area of 
valve or valves, sq. in.; G = grate area, sq. ft.; P = boiler pressure 
(gauge). This rule came from France in 1868. It was recommended 
to the city of Philadelphia by a committee of the Franklin Institute, 
although the committee "had not found the reasoning upon winch the 
rule had been based." 

Philip G. Darling (Trans. A. S. M. E., 1909) commenting on the above 
rules says: The principal defect of these rules is that they assume that 
valves of the same nominal size have the same capacity, and they rate 
them the same without distinction, in spite of the fact that in actual prac- 
tice some have but one-third of the capacity of others. There are other 
defects, such as varying the assumed lift as the valve diameter, while in 



SAFETY-VALVES. 



905 



reality with a given design the lifts are more nearly the same in the differ- 
ent sizes, not varying nearly as rapidly as the diameters. And further 
than this, the actual lifts assumed for the larger valves are nearly double 
the actual average obtained in practice. The direct conclusion is that 
existing rules and statutes are not safe to follow. Some of these rules in 
use were formulated before, and have not been modified since, spring 
safety-valves were invented, and at a time when 120 lbs. was considered 
high pressure. None of these rules take account of the different lifts 
which exist in the different makes of valves of the same nominal size, and 
they thus rate exactly alike valves which actually vary in lift and relieving 
capacity over 300%. It would therefore seem the duty of all who are 
responsible for steam installation and operation to no longer leave the 
determination of safety-valve size and selection to such statutes as may 
happen to exist in their territory, but to investigate for themselves. 

Formulae for Spring-loaded Safety- Valves. — Let L = lift of valve 
in.; D = diam. in.; E = discharge, lbs. per hour; P = abs. pressure; 
A = area of opening; 6 = angle of seat with horizontal. By Napier's 
formula E = AP X 3600 -5- 70 = 51.43 AP. A = nDL cos (approx- 
imately). If = 45°, cos 6 = 0.707, whence E = 114.2 LDP. Experi- 
ments with six different valves, 3, 31/2 and 4 in. stationary, and 11/2. 3 
and 31/2 in. locomotive, gave an average flow equal to 92.5% of that 
calculated by the above formula, which is therefore modified by Mr. 
Darling to the forms E = 105 LDP, and D = 0.0095 E + LP. ... (1) 

To obtain formulae for safety valves in terms of the heating-surface 
of the boiler Mr. Darling takes for stationary boilers an average evapora- 
tion of 31/2 lbs. per sq. ft. of heating-surface per hour, with an overload 
capacity of 100%; for marine boilers, water-tube or Scotch, an overload 
or maximum evaporation of 10 lbs. per sq. ft. of heating-surface per hour. 
If H = total boiler heating-surface in sq. ft., these assumptions give for 
stationary boilers D = 0.068 H ■*- LP, ... (2) and for marine boilers 
D = 0.095 H -3- LP . . . (3). For locomotive boilers the proper con- 
stant in the formula was deduced from numerous experiments to be 
0.055 . . . (4). 

For flat valves the constants in the last four formulae are: (1) 0.0067; 
(2) 0.065; (3) 0.090; (4) 0.052. 

The following table is calculated from Napier's formula, on the assump- 
tion of a lift of 0.1 in. and a 45° valve-seat. For any other lift than 0.1 
in., the discharge is proportional to the lift. The figures should be multi- 
plied by a coefficient expressing the relation of the discharge of actual 
valves to the discharge through a plain round orifice (Napier's). In 
the Consolidated SafetyValve Co.'s experiments the average value of this 
coefficient was found to be 0.925. 



Steam Discharged in Lbs. per Hour by a Valve Lifting 0.10 in. 



£o5 


Valve diameters, inches. 


03 


1 


H/2 


2 


21/2 


3 


31/2 


4 


41/2 


5 


51/2 


6 


25 


460 


690 


920 


1150 


1380 


1610 


1840 


2080 


2300 


2540 


2770 


50 


750 


1130 


1500 


1880 


2250 


2630 


3000 


3380 


3760 


4130 


4500 


75 


1040 


1560 


2080 


2600 


3120 


3640 


4160 


4680 


5200 


5720 


6240 


100 


1330 


2000 


2660 


3330 


4000 


4660 


5320 


6000 


6650 


7320 


8000 


125 


1620 


2440 


3250 


4060 


4860 


5670 


6480 


7300 


8100 


8920 


9730 


150 


1910 


2870 


3830 


4790 


5740 


6700 


7650 


8610 


9560 


10520 


11470 


175 


2200 


3300 


4400 


5500 


6600 


7700 


8800 


9900 


11000 


12100 


13200 


200 


2500 


3740 


5000 


6240 


7480 


8730 


9970 


11200 


12460 


13700 


14950 


225 


2780 


4180 


5570 


6960 


8340 


9730 


11120 


12500 


13900 


15300 


16700 


250 


3070 


4610 


6140 


7680 


9200 


10740 


12300 


13800 


15360 


16900 


18450 


275 


3360 


5050 


6720 


8400 


10100 


11760 


13450 


15150 


16800 


18500 


20200 


300 


3650 


5480 


7310 


9150 


10960 


12800 


14600 


16470 


18300 


20100 


22000 



906 



THE STEAM-BOILER. 



Unequal expansion of safety-valve parts under steam temperatures 
tends to cause leakage, and as this temperature effect becomes more 
serious in the large sizes the manufacturers do not recommend the use 
of valves larger than 41/2 ins. If greater relieving capacity be required 
it is the best practice to use duplex valves or additional single valves. 



Relieving Capacities, Consolidated Pop Safety Valves, Stationary 
Type. (Pounds of Steam per hour.) 



> 

Is 


Gauge Pressures, (lbs. per sq. in.) 


60 


80 


100 


120 


140 


160 


180 


200 


220 


240 


260 


280 


300 


2 


1890 


2400 


2900 


3400 


3900 


4410 


4910 


5420 


5920 


6430 


6930 


7430 


7940 


21/9 


2360 


3000 


3620. 


4250 


4880 


5500 


6140 


6760 


7400 


8030 


8650 


9300 


9900 


3 


3070 


3890 


4700 


5530 


6350 


7170 


8000 


8800 


9620 


10400 


11200 


12100 


12900 


31/o 


3860 


4880 


5910 


6950 


7960 


9020 


10000 


11100 


12100 


13100 


14200 


15200 


16300 


4 


4410 


5580 


6770 


7950 


9120 


10300 


11500 


12600 


13800 


15000 


16200 


17300 


18500 


41/o 


5310 


6730 


8150 


9570 


11000 


12400 


13800 


15200 


16700 


18100 


19500 


20900 


22400 


5 


6300 


7970 


9650 


11330 


13000 


14700 


16400 


18100 


19700 


21400 


23100 


24800 


26500 



For an extended discussion on safety-valves, see Trans. A. S. M. E., 
1909. 

THE INJECTOR. 

Equation of the Injector. 

Let S be the number of pounds of steam used; 

W the number of pounds of water lifted and forced into the boiler; 
h the height in feet of a column of water, equivalent to the absolute 

pressure in the boiler; 
h n the height in feet the water is lifted to the injector; 
fi the temperature of the water before it enters the injector; 
ti the temperature of the water after leaving the injector; 
H the total heat above 32° F. in one pound of steam in the boiler, 

in heat-units; 
L the work in friction and the equivalent lost work due to radiation 

and lost heat; 
778 the mechanical equivalent of heat. 
Then 

S[ H-(U-S2^W(t 2 -t 1 ) + ^ W + S)h+Who + L 



An equivalent formula, neglecting Wh 
W[(jti-ti) d + 0.1851 p] 



778 

L as small, is 
1 



44.-] 1 

78j H-(h-32°)' 



orS = 



[J/-(t2- 32°)] d -0.1851 p' 



in which d = weight of 1 cu. ft. of water at temperature h; p — absolute 
pressure of steam, lbs. per sq. in. 

The rule for finding the proper sectional area for the narrowest part of 
the nozzles is given as follows by Rankine, S. E., p. 477: 



Area in square inches ■ 



cubic feet per hour gross feed-water 
800 ^pressure in atmospheres 



An important condition which must be fulfilled in order that the injec- 
tor will work is that the supply of water must be sufficient to condense 



THE INJECTOR. 



907 



the steam. As the temperature of the supply or feed-water is higher, the 
amount of water required for condensing purposes will be greater. 

The table below gives the calculated value of the maximum ratio of 
water to the steam, and the values obtained on actual trial, also the 
highest admissible temperature of the feed-water as shown by theory 
and the highest actually found by trial with several injectors. 



Gauge- 
pres- 
sure, 
pounds 

per 
sq. in. 


Maximum Ratio Water 
to Steam. 


Gauge- 
pres- 
sure, 

pounds 
per 

sq. in. 


Maximum Temperature 
of Feed-Water. 


Calculated 

from 

Theory. 


Actual Ex- 
periment. 


Theoreti- 
cal. 


Experimental 
Results. 


. Si 

ill 

H.g 


Kg 

73 


H. 


P. 


M. 




H. 


P. 


M. 


S. 


10 


36.5 

25.6 

20.9 

17.87 

16.2 

14.7 

13.7 

12.9 

12.1 

11.5 


30.9 
22.5 
19.0 
15.8 
13.3 
11.2 
12.3 
11.4 






10 
20 
30 
40 
50 
60 
70 
80 
90 
100 
120 
150 


J42°' 

132 

126 

120 

114 

.109 

105 

99 

95 

87 

77 










H?° 


20 
30 


19.9 
17.2 
15.0 
14.0 
11.2 
11.7 
11.2 


21.5 
19.0 
15.86 
13.3 
12.6 
12.9 


173° 
162 
156 
150 
143 
139 
134 
129 
125 
117 
107 


135° 


120° 


130° 


134 
134 


40 
50 
60 
70 
80 
90 


140 

141* 
141* 


113 
f 15 

118' 


125 

123' 
123 
122 


132 
131 
130 
130 
131 
137* 


100 














13?* 
















134* 










PI* 

















* Temperature of delivery above 212°. Waste-valve closed. 
H, Hancock inspirator; P, Park injector; M, Metropolitan injector; 
S, Sellers 1876 injector. 

Efficiency of the Injector. — Experiments at Cornell University, 
described by Prof. R. C. Carpenter, in Cassier's Magazine, Feb., 1892, 
show that the injector, when considered merely as a pump, has an exceed- 
ingly low efficiency, the duty ranging from 161,000 to 2,752,000 under 
different circumstances of steam and delivery pressure. Small direct- 
acting pumps, such as are used for feeding boilers, show a duty of from 
4 to 8 million ft.-lbs., and the best pumping-engines from 100 to 140 mil- 
lion. When used for feeding water into a boiler, however, the injector 
has a thermal efficiency of 100%, less the trifling loss due to radiation, 
since all the heat rejected passes into the water which is carried into the 
boiler. 

The loss of work in the injector due to friction reappears as heat which 
is carried into the boiler, and the heat which is converted into useful 
work in the injector appears in the boiler as stored-up energy. 

Although the injector thus has a perfect efficiency as a boiler-feeder, it 
is not the most economical means for feeding a boiler, since it can draw 
only cold or moderately warm water, while a pump can feed water which 
has been heated by exhaust steam which would otherwise be wasted. 

Performance of Injectors. — In Am. Mach., April 13, 1893, are a 
number of letters from different manufacturers of injectors in reply to the 
question: "What is the best performance of the injector in raising or 
lifting water to any height?" Some of the replies are tabulated below. 

W. Sellers & Co. — 25.51 lbs. water delivered to boiler per lb. of steam; 
temperature of water, 64°; steam pressure, 65 lbs. 

Schaeffer & Budenberg — 1 gal. water delivered to boiler for 0.4 to 
0.8 lb. steam. 

Injector will lift by suction water of 

140° F. 136° to 133° 122° to 118° 113° to 107° 

If boiler pres. is 30 to 60 lbs. 60 to 90 lbs. 90 to 120 lbs. 120 to 150 lbs. 



22 


22 


11 


54.1 


95.5 


75.4 


35.4° 


47.3° 


53.2 


117.4° 


173.7° 


131. r 


13.67 


8.18 


13.3 



908 THE STEAM-BOILER. 

If the water is not over 80° F., the injector will force against a pressure 
75 lbs. higher than that of the steam. 

Hancock Inspirator Co.: 

Lift in .feet 22 

Boiler pressure, absolute, lbs 75 . 8 

Temperature of suction 34.9° 

Temperature of delivery 134° 

Water fed per lb. of steam, lbs 11.02 

The theory of the injector is discussed in Wood's, Peabody's, and 
Rontgen's treatises on Thermodynamics. See also "Theory and Practice 
of the Injector," by Strickland L. Kneass, New York, 1910. 

Boiler-feeding Pumps. — Since the direct-acting pump, commonly 
used for feeding boilers, has a very low efficiency, or less than one-tenth 
that of a good engine, it is generally better to use a pump driven by belt 
from the main engine or driving shaft. The mechanical work needed to 
feed a boiler may be estimated as follows: If the combination of boiler 
and engine is such that half a cubic foot, say 32 lbs. of water, is needed 
per horse-power, and the boiler-pressure is 100 lbs. per sq. in., then the 
work of feeding the quantitv of water is 100 lbs. X 144 sq. in. X Vi ft— 
lb. per hour = 120 ft.-lbs. per min. = 120/33,000 = .0036 H.P., or less 
than 4/ 10 of 1 % of the power exerted by the engine. If a direct-acting 
pump, which discharges its exhaust steam into the atmosphere, is used 
for feeding, and it has only i/io the efficiency of the main engine, then the 
steam used by the pump will be equal to nearly 4% of that generated by 
the boiler. 

The low efficiency of boiler-feeding pumps, and of other small auxiliary 
steam-driven machinery, is, however, of no importance if all .the exhaust 
steam from these pumps is utilized in heating the feed-water. 

The following table by Prof. D. S. Jacobus gives the relative efficiency 
of steam and power pumps and injector, with and without heater, as used 
upon a boiler with 80 lbs. gauge-pressure, the pump having a duty of 
10,000,000 ft.-lbs. per 100 lbs. of coal when no heater is used; the injector 
heating the water from 60° to 150° F. 

Direct-acting pump feeding water at 60°, without a heater 1.000 

Injector feeding water at 150°, without a heater 0-985 

Injector feeding water through a heater in which it is heated from 

150° to 200° . 938 

Direct-acting pump feeding water through a heater, in which it is 

heated from 60° to 200° . 879 

Geared pump, run from the engine, feeding water through a heater, 

in which it is heated from 60° to 200° . 868 

Gravity Boiler-feeders. — If a closed tank be placed above the level 
of the water in a boiler and the tank be filled or partly filled with water, 
then on shutting off the supply to the tank, admitting steam from the 
boiler to the upper part of the tank, so as to equalize the steam-pressure 
in the boiler and in the tank, and opening a valve in a pipe leading from 
the tank to the boiler, the water will run into the boiler. An apparatus 
of this kind may be made to work with practically perfect efficiency as a 
boiler-feeder, as an injector does, when the feed-supply is at ordinary 
atmospheric temperature, since after the tank is emptied of water and the 
valves in the pipes connecting it with the boiler are closed the conden- 
sation of the steam remaining in the tank will create a vacuum which will 
lift a fresh supply of water into the tank. The only loss of energy in the 
cycle of operations is the radiation from the tank and pipes, which may 
be made very small by proper covering. 

When the feed-water supply is hot, such as the return water from a 
heating system, the gravity apparatus may be made to work by having 
two receivers, one at a low level, which receives the returns or other 
feed-supply, and the other at a point above the boilers. A partial vacuum 
being created in the upper tank, steam-pressure is applied above the 
water in the lower tank by which it is elevated into the upper. The 
operation of such a machine may be made automatic by suitable arrange- 
ment of valves. 



FEED-WATER HEATERS. 



909 



FEED-WATER HEATERS. 

Percentage of Saving for Each Degree of Increase in Temperature 
of Feed-water Heated by Waste Steam. 



Initial 


Steam Pressure in Boiler, lbs. per sq.in.above^Atmosphere. 




Temp. 

of 
Feed. 




Initial 
Temp. 





20 


40 


60 


80 


100 


120 


140 


160 


180 


200 


32° 


.0872 


.0861 


.0855 


.0851 


.0847 


.0844 


.0841 


.0839 


.0837 


.0835 


.0833 


32° 


40 


.0878 


.0867 


.0861 


.0856 


.0853 


.0850 


.0847 


.0845 


.0843 


.0841 


.0839 


40 


50 


.0886 


.0875 


.0868 


.0864 


.0860 


.0857 


.0854 


.0852 


.0850 


.0848 


.0846 


50 


60 


.0894 


.0883 


.0876 


.0872 


.0867 


.0864 


.0862 


.0859 


.0856 


.0855 


.0853 


60 


70 


.0902 


.0890 


.0884 


.0879 


.0875 


.0872 


.0869 


.0867 


.0864 


.0862 


.0860 


70 


80 


.0910 


.0898 


.0891 


.0887 


.0883 


.0879 


.0877 


.0874 


.0872 


.0870 


.0868 


80 


90 


.0919 


.0907 


.0900 


.0895 


.0888 


.0887 


.0884 


.0883 


.0879 


.0877 


.0875 


90 


100 


.0927 


.0915 


.0908 


.0903 


.0899 


.0895 


.0892 


.0890 


.0887 


.0885 


.0883 


100 


110 


.0936 


.0923 


.0916 


.0911 


.0907 


.0903 


.0900 


.0898 


.0895 


.0893 


.0891 


110 


120 


.0945 


.0932 


.0925 


.0919 


.0915 


.0911 


.0908 


.0906 


.0903 


.0901 


.0899 


120 


130 


.0954 


.0941 


.0934 


.0928 


.0924 


0920 


.0917 


.0914 


.0912 


.0909 


.0907 


130 


140 


.0963 


.0950 


.0943 


.0937 


.0932 


.0929 


.0925 


.0923 


.0920 


.0918 


.0916 


140 


150 


.0973 


.0959 


.0951 


.0946 


.0941 


.0937 


.0934 


.0931 


.0929 


.0926 


.0924 


150 


160 


.0982 


.0968 


.0961 


.0955 


.0950 


.0946 


.0943 


.0940 


.0937 


.0935 


.0933 


160 


170 


.0992 


.0978 


















.0941 


170 


180 


.1002 


.0988 


.0981 


.0973 


.0969 


.0965 


.0961 


.0958 


.0955 


.0953 


.0951 


180 


190 


.1012 


.0998 


.0989 


0983 


.0978 


.0974 


.0971 


.0968 


.0964 


.0962 


.0960 


190 


200 


.1022 


.1008 


.0999 


0993 


.0988 


.0984 


.0980 


.0977 


.0974 


.0972 


.0969 


200 


210 


.1033 


.1018 


.1009 


.1003 


0998 


.0994 


.0990 


.0987 


.0984 


.0981 


.0979 


210 


220 




.1029 


.1019 


.1013 


.1008 


.1004 


.1000 


.0997 


.0994 


.0991 


.0989 


220 


230 




.1039 


.1031 


.1024 


.1018 


.1012 


.1010 


.1007 


.1003 


.1001 


.0999 


230 


240 




.1050 


.1041 


.1034 


.1029 


.1024 


.1020 


.1017 


.1014 


.1011 


.1009 


240 


250 




.1062 


.1052 


.1045 


.1040 .1035 


.1031 


.1027 


.1025 


.1022 


.1019 


250 



An approximate rule for the conditions of ordinary practice is that a 
saving of 1% is made by each increase of 11° in the temperature of the 
feed-water. This corresponds to 0.0909% per degree. 

The calculation of saving is made as follows: Boiler-pressure, 100 lbs. 
gauge; total heat in steam above 32° = 1185B.T.U. Feed-water, original 
temperature 60°, final temperature 209° F. Increase in heat-units, 150. 
Heat-units above 32° in feed-water of original temperature = 28. Heat- 
units in steam above that in cold feed-water, 1185 — 28 = 1157. Saving 
by the feed-water heater = 150/1157 = 12.96%. The same result is 
obtained by the use of the table. Increase in temperature 150° X 
tabular figure 0.0864 = 12.96%. Let total heat of 1 lb. of steam at the 
boiler-pressure = H; total heat of 1 lb. of feed-water before entering the 
heater = hi, and after passing through the heater = hr, then the saving 

made by the heater is " _ , • 

Strains Caused by Cold Feed-water. — A calculation is made in 
The Locomotive of March, 1893, of the possible strains caused in the sec- 
tion of the shell of a boiler by cooling it by the injection of cold feed- 
water. Assuming the plate to be cooled 200° F., and the coefficient of 
expansion of steel to be 0.0000067 per degree, a strip 10 in. long would 
contract 0.013 in., if it were free to contract. To resist this contraction, 
assuming that the strip is firmlv held at the ends and that the modulus 
of elasticitv is 29,000,000, would require a force of 37,700 lbs. per sq. in. 
Of course this amount of strain cannot actually take place, since the strip 
is not firmlv held at the ends, but is allowed to contract to some extent 
by the elasticitv of the surrounding metal. But, says The Locomotive, 
we may feel prettv confident that in the case considered a longitudinal 
strain of somewhere in the neighborhood of 8000 or 10,000 lbs. per sq. in. 
may be produced by the feed-water striking directlv upon the plates; 
and this, in addition to the normal strain produced by the steam-pressure, 
is quite enough to tax the girth-seams beyond their elastic limit, if the 



910 



THE STEAM-BOILER. 



feed-pipe discharges anywhere near them. . Hence it is not surprising that 
the girth-seams develop leaks and cracks in 99 cases out of every 100 in 
which the feed discharges directly upon the fire-sheets. 

Capacity of Feed-water Heaters. (W. R. Billings, Eng. Rec, 
Feb., 1898.) — Closed feed-water heaters are seldom provided with 
sufficient surface to raise the feed temperature to more than 200°. The 
rate of heat transmission may be measured by the number of British 
thermal units which pass through a square foot of tubular surface in one 
hour for each degree of difference in temperature between the water and 
the steam. One set of experiments gave results as below: 

15° F 67 B.T.U. ) Transmitted in one 

6° " 79 " hour by each sq. ft. 

8° " 89 " I of surface for each 

11°" 114 " [ degree of average 

15°" 129 " difference in temper- 

18° " 139 " J atures. 

Even with the rate of transmission as low as 67 B.T.U. the water was 
still 5° from the temperature of the steam. At what rate would the heat 
have been transmitted if the water could have been brought to within 
2° of the temperature of the steam, or to 210° when the steam is at 212°? 

For commercial purposes feed-water heaters are given a H.P. rating 
which allows about one-third of a square foot of surface per H.P. — a 
boiler H.P. being 30 lbs. of water per hour. If the figures given in the 
table above are accepted as substantially correct, a heater which is to 
raise 3000 lbs. of water per hour from 60° to 207°, using exhaust steam 
at 212° as a heating medium, should have nearly 84 sq. ft. of heating 
surface or nearly a square foot of surface per H.P. That feed-water 
heaters do not carry this amount of heating surface is well known. 

Calculation of Surface of Heaters and Condensers. — (H. L. Hep- 
burn, Power, April, 1902.) Let W = lbs. of water per hour; A = area of 
surface in sq. ft.; T s = temperature of the steam; / = initial tempera- 
ture of the water; F = final temperature of the water; S = lbs. of steam 
per hour; H = B.T.U. above 32° F. in 1 lb. of steam; N = B.T.U. in 
1 lb. of condensed steam; U = B.T.U. transmitted per sq. ft. per hour 
per degree of mean difference of temperature between the steam and the 
water. 

Then AU = W log e ' ~ , for heaters. 
Is — * 

A U ~ S F - T * l0ge T - F ' f ° r condensers - 

The value of U varies widely according to the condition of the surface, 
whether clean or coated with grease or scale, and also with the velocity 
of the water over the surfaces. Values of 300 to 350 have been obtained 
in experiments with corrugated copper tubes, but ordinary heaters give 
much lower values. From the experiments of Loring and Emery on the 
U. S. S. Dallas, Mr. Hepburn finds U = 192. Using this value he finds 
the number of square feet of heating surface required per 1000 lbs. of 
feed-water per hour to be as follows, the temperature of the entering 
water being 60° F. 



Steam Temperature, 


212°. 




Steam 25 


in. Vacuum. 


F 


S 


F 


S 


F 


$ 


F 


S 


194 


11.11 


204 


15.34 


90 


2.38 


115 


6.78 


196 


11.73 


206 


. 16.85 


95 


3.03 


120 


8.60 


198 


12.44 


208 


18.93 


100 


3.76 


125 


11.15 


200 


13.20 


210 


22.52 


105 


4.62 


130 


16.25 


202 


14.17 


212 


Infinite 


110 


5.65 


133 


Infinite 



F = final temperature of feed -water- S = sq. ft. of surface. From this 
table it is seen that if 30 lbs. of water per hour is taken to equal 1 H.P. 



STEAM SEPARATORS. 911 



and a feed-water heater is made with 1/3 sq. ft. per H.P., it may be ex- 
pected to heat the feed-water from 60° to something less than 194°, or if 
made with 1/2 sq. ft. per H.P. it may heat the water to 204° F. 

For a further discussion of this subject, see Heat, pages 561 to 565. 

Proportions of Open Type Feed-water Heaters. — C. L. Hubbard 
(Practical Engineer, Jan. 1, 1909) gives the following: 

Exhaust heaters should be proportioned according to the quality of 
the water to be used, the size being increased with the amount of mud 
or scale-producing properties which the water contains regardless of the 
quantity of water to be heated. The general proportions of an open 
heater will depend somewhat upon the arrangement of the trays or pans, 
but an approximation of the size of shell for a cylindrical heater is as 
follows : A = H -*- aL; L = H ■*■ a A ; in which A = sectional area of shell 
in sq. ft.; L = length of shell in linear ft.; H = total weight of water to 
be heated per hour divided by the weight of steam used per horse-power 
per hour by the engine; a = 2.15 for very muddy water, 6.0 for slightly 
muddy water, and 8.0 for clear water. 

The pan or tray surface varies according to the quality of the water, 
both as regards the amount of mud and the scale-making ingredients. 
The surface in square feet for each 1000 lbs. of water heated per hour 
may be taken as follows, for the vertical and horizontal types respectively: 

Very bad water 8.5 and 9 . 1 

Medium muddy water 6 and 6 . 5 

Clear and little scale 2 and 2 . 2 

The space between the pans is made not less than 0.1 the width for 
rectangular and 0.25 the diameter for round pans. Under ordinary 
circumstances it is not customary to use more than six pans in a tier, 
in order to obtain a low velocity over each pan. The size of the storage 
or settling chamber in the horizontal type varies from 0.25 to 0.4 of the 
volume of the shell, depending on the quality of the water; 0.33 is about 
the average. In the case of vertical heaters, this varies from 0.4 to 0.6 
of the volume of the shell. Filters occupy from 10 to 15% of the volume 
of the shell in the horizontal type and from 15 to 20% in the vertical. 

Open versus Closed Feed-water Heaters. (W. E. Harrington, St. 
Rwy. Jour., July 22, 1905.) — There still exists some difference of opinion 
as to the relative desirability of open or closed type of feed-water heater, 
but the degree of perfection which the open heater has attained has elimi- 
nated formerly objectionable features. The chief objection which attended 
the early use of the open heater, namely, that the oil from the exhaust 
steam was carried into the boiler, did much to discourage its more general 
adoption. This objection does not hold good against the better designs 
of open heaters now on the market. There are thousands of installations 
in which the open heater is now being used where no difficulty is experi- 
enced from the contamination of the feed-water by oil. The perfection of 
oil separators for use in the exhaust steam connection to the heater has 
rendered this possible. 

STEAM SEPARATORS. 

If moist steam flowing: at a high velocity in a pipe has its direction sud- 
denly changed, the particles of water are by their momentum projected in 
their original direction against the bend in the pipe or wall of the chamber 
in which the chansre of direction takes place. By making proper provi- 
sion for drawing off the water thus separated the steam may be dried to a 
greater or less extent. 

For long steam-pipes a Targe drum should be provided near the engine 
for trapping the water condensed in the pipe. A drum 3 feet diameter, 
15 feet hierh, has srivpn good results in separating the water of condensa- 
tion of a steam-oine 10 inches diameter and 800 feet long. 

Efficiency of Steam Separators. — Prof. R. C. Carpenter, in 1891, 
made a series of tests of six steam separators, furnishing them with steam 
containine different Dercentages of moisture, and testing the quality of 
steam before entering and after passing the separator. A condensed 
table of the principal results is given below. 



912 



THE STEAM-BOILER. 



o 


Test with Steam of about 10% 
of Moisture. 


Tests with Varying Moisture. 


o £ 

1^ 


Quality 
of Steam 
before. 


Quality 

of Steam 

after. 


Efficiency, 
per cent. 


Quality of 
Steam be- 
fore. 


Quality of 
Steam after. 


Av'ge 
Effi- 
ciency. 


B 
A 
D 
C 
E 
F 


87.0% 

90.1 

89.6 

90.6 

88.4 

88.9 


98.8% 

98.0 

95.8 

93.7 

90.2 

92.1 


90.8 
80.0 
59.6 
33.0 
15.5 
28.8 


66.1 to 97.5% 
51.9 " 98 

72.2 " 96.1 
67.1 " 96.8 
68.6 " 98.1 
70.4 " 97.7 


97.8 to 99% 

97.9 " 99.1 
95.5 " 98.2 
93.7 " 98.4 
79.3 " 98.5 
84.1 " 97.9 


87.6 
76.4 
71.7 
63.4 
36.9 
28.4 



Conclusions from the tests were: 1. That no relation existed between 
the volume of the several separators and their efficiency. 2. No marked 
decrease in pressure was shown by any of the separators, the most being 
1.7 lbs. in E. 3. Although changed direction, reduced velocity, and per- 
haps centrifugal force are necessary for good separation, still some means 
must be provided to lead the water out of the current of the steam. The 
high efficiency obtained from B and A was largely due to this feature. In 
B the interior surfaces are corrugated and thus catch the water thrown 
out of the steam and readily lead it to the bottom. In A, as so on as the 
water falls or is precipitated from the steam, it comes in contact with the 
perforated diaphragm through which it runs into the space below, where 
it is not subjected to the action of the steam. Experiments made by 
Prof. Carpenter on a "Stratton" separator in 1894 showed that the 
moisture in the steam leaving the separator was less than 1 % when that 
in the steam supplied ranged from 6% to 21%. 

Experiments by Prof. G. F. Gebhardt (Power, May 11, 1909) on six 
separators of different makes led to the following conclusions: (1) The 
efficiency of separation decreases as the velocity of the steam increases. 
(2) The efficiency increases as the percentage of moisture in the enter- 
ing steam increases. (3) The drop in pressure increases rapidly with the 
increase in velocity. The six separators are described as follows: 

U: 2-in. vertical; no baffles; current reversed once. 

V: 4-in. horizontal with single baffle plate of the fluted type; current 
reversed once. 

W: 4-in. vertical with two baffle plates of the smooth type; current 
reversed once. 

X: 3-in. horizontal; several fluted baffle plates; no reversal of current. 

Y: 6-in. vertical; centrifugal type; current reversed once. 

Z: 3-in. horizontal; current reversed twice; steam impinges on hori- 
zontal fluted baffle during reversal. 

The efficiency is defined as the ratio of the water .removed from the 
steam by the separator to the water injected into the dry steam for the 
purpose of the test. With steam at 100 lbs. pressure containing 10% 
water, the efficiencies, taken approximately from plotted curves, were as 
follows: 

U V W X Y Z 

At 2000 ft. per min 64 69 86 88 79 66 

At 3000 ft. per min : 37 45 80 60 61 48 



IN STEAM — STEAM 



DETERMINATION OF THE MOISTURE 
CALORIMETERS. 

In all boiler-tests it is important to ascertain the quality of the steam, 
i.e., 1st, whether the steam is "saturated" or contains the quantity of 
heat due to the pressure according to standard experiments; 2d, whether 
the quantity of heat is deficient, so that the steam is wet; and 3d, whether 
the heat is in excess and the steam superheated. The best method of 
ascertaining the quality of the steam is undoubtedly that employed by a 
committee which tested the boilers at the American Institute Exhibition 
of 1871-2, of which Prof. Thurston was chairman, i.e., condensing all the 
water evaporated by the boiler by means of a surface condenser, weighing 



DETERMINATION OP THE MOISTURE IN STEAM. 913 

the condensing water, and taking its temperature as it enters and as it 
leaves the condenser; but this plan cannot always be adopted. 

A substitute for this method is the barrel calorimeter, which with careful 
operation and fairly accurate instruments may generally be relied on to 
give results within two per cent of accuracy (that is, a sample of steam 
which gives the apparent result of 2% of moisture may contain anywhere 
between and 4%). This calorimeter is described as follows: A sample 
of the steam is taken by inserting a perforated 1/2-inch pipe into and 
through the main pipe near the boiler, and led by a hose, thoroughly 
felted, to a barrel, holding preferably 400 lbs. of water, which is set upon 
a platform scale and provided with a cock or valve for allowing the water 
to flow to waste, and with a small propeller for stirring the water. 

To operate the calorimeter the barrel is filled with water, the weight 
and temperature ascertained, steam blown through the hose outside the 
barrel until the pipe is thoroughly warmed, when the hose is suddenly 
thrust into the water, and the propeller operated until the temperature 
of the water is increased to the desired point, say about 110° usually. 
The hose is then withdrawn quickly, the temperature noted, and the 
weight again taken. 

An error of 1/10 of a pound in weighing the condensed steam, or an 
error of 1/2 degree in the temperature, will cause an error of over 1% in 
the calculated percentage of moisture. See Trans. A. S. M. E., vi, 293. 

The calculation of the percentage of moisture is made as below: 



.. 1 ri- 
ff - Tlw 



E {hl _ h) _ iT _ hl q 



Q = quality of the steam, dry saturated steam being unity. 
H = total heat of 1 lb. of steam at the observed pressure. 
T = total heat of 1 lb. of water at the temperature of steam of the 

observed pressure. 
h = total heat of 1 lb. of condensing water, original. 
hi = total heat of 1 lb. of condensing water, final. 
W = weight of condensing water, corrected for water-equivalent of 

the apparatus. 
w = weight of the steam condensed. 

Percentage of moisture = 1 — Q. 

If Q is greater than unity, the steam is superheated, and the degrees of 
superheating = 2.0833 (H - T) (Q - 1). 

Difficulty of Obtaining a Correct Sample. — Experiments by Prof. 
D. S. Jacobua {Tranc<. A. S. M. E., xvi, 1017), show that it is practically 
impossible to obtain a true average sample of the steam flowing in a pipe. 
For accurate determinations all the steam made by the boiler should be 
passed through a separator, the water separated should be weighed and 
a calorimeter test made of the steam just after it has passed the separator. 

Coil Calorimeters. — Instead of the open barrel in which the steam 
is condensed, a coil acting as a surface-condenser may be used, which is 
placed in the barrel, the water in coil and barrel being weighed separately. 
For a description of an apparatus of this kind designed by the author, 
which he has found to give results with a probable error not exceeding 
1/2 per cent of moisture, see Trans. A. S. M. E., vi, 294. This calorimeter 
may be used continuously, if desired, instead of intermittently. In this 
case a continuous flow of condensing water into and out of the barrel 
must be established, and the temperature of inflow and outflow and of the 
condensed steam read at short intervals of time. 

Throttling Calorimeter. — For percentages of moisture not exceed- 
ing 3 per cent the throttling calorimeter is most useful and convenient 
and remarkably accurate. In this instrument the steam which reaches 
it in a 1/2-inch pipe is throttled by an orifice Vi6 inch diameter, opening 
into a chamber which has an outlet to the atmosphere. The steam in 
this chamber has its pressure reduced nearly or quite to the pressure of the 
atmosphere, but the total heat in the steam before throttling causes the 
steam in the chamber to be superheated more or less according to. whether 
the steam before throttling was dry or contained moisture. The only 
observations required are those of the temperature and pressure of the 
steam on each side of the orifice. 



914 



THE STEAM-BOILER. 



The author's formula for reducing the observations of the throttling 
calorimeter is as follows (Experiments on Throttling Calorimeters, Am. 

Mach., Aug. 4, 1892): w = 100 X J ^- = — ^^ — — , in which w = 

percentage of moisture in the steam; H = total heat, and L = latent heat 
of steam in the main pipe; h = total heat due the pressure in the discharge 
side of the calorimeter, = 1146.6 at atmospheric pressure; K= specific 
heat of superheated steam; T = temperature of the throttled and super- 
heated steam in the calorimeter; t = temperature due to the pressure in 
the calorimeter, = 212° at atmospheric pressure. 

Taking K at 0.4S and the pressure in the discharge side of the calo- 
rimeter as atmospheric pressure, the formula becomes 



100 X 



H 



1146.6 - 0.48 (T - 212°) 



From this formula the following table is calculated: 
Moisture in Steam — Determinations by Throttling Calorimeter 





Gauge-pressu 


res. 


Degree of 


























Super- 


5 


10 


20 


30 


40 


50 


60 


JO 


yi> 


80 


85 


90 


heating 




























Per Cent of Moisture 


in Steam. 


0° 


0.51 


0.90 


1.54 


2.06 


2 50 


2 90 


3 24 


3.56 


3.71 


3.86 


3 99 


4.13 


10° 


0.01 


0.39 


1.02 


1.54 


1 97 


2 36 


2.71 


3.02 


3.17 


3.32 


3 45 


3 58 


20° 






0.51 
0.00 


1.02 
0.50 


1.45 
0.92 
0.39 


1.83 
1.30 
0.77 
0.24 


2.17 
1.64 
1.10 
0.57 
0.03 


2.48 
1.94 
1.40 
0.87 
0.33 


2.63 
2.09 
1.55 
1.01 
0.47 


2.77 
2.23 
1.69 
1.15 
0.60 
0.06 


2.90 
2.35 
1.80 
1.26 
0.72 
0.17 


3.03 


30° 






2.49 


40° 






1.94 


50° 










1 40 


60° 












0.85 


70° 














31 
























Dif.p.deg. 


.0503 


.0507 


.0515 


.0521 


.0526 


.0531 


.0535 


.0539 


.0541 


.0542 


.0544 


.0546 




Gauge-pressu 


res. 


Degree of 


























Super- 


100 


1 10 


17,0 


130 


140 


150 


160 


170 


180 


190 


ZOO 


250 


heating 
T -212°. 
































Per Cent of Moistur 


e in Steam. 


0° 


4 39 


4.63 


4.85 


5.08 


5.29 


5.49 


5.68 


5.87 


6.05 


6.22 


6 39 


7.16 


10° 


3.84 


4 08 


4 29 


4 52 


4 73 


4 93 


5 12 


5 30 


5 48 


5 65 


5 82 


6.58 


20° 


3 29 


3 52 


3,74 


3.96 


4 17 


4 37 


4 56 


4.74 


4 91 


5 08 


5 25 


6.00 


30° 


7 74 


2 97 


3 18 


3.41 


3.61 


3 80 


3 99 


4,17 


4 34 


4 51 


4 67 


5.41 


40° 


2 19 


2 42 


2.6.3 


2.85 


3.05 


3 24 


3 43 


3 61 


3 78 


3.94 


4 10 


4.83 


50° 


1.64 


1.87 


2.08 


2.29 


2.49 


?, 68 


?. 87 


3.04 


3 21 


3 37 


3.53 


4.25 


60° 


1.09 


1.32 


1.52 


1 74 


1 93 


?, U 


2 30 


2 48 


?, 64 


?, 80 


2.96 


3.67 


70° 


0.55 


o.yy 


97 


1 18 


1 38 


1 56 


1 74 


1 91 


7 07 


? ?,3 


7. 38 


3.09 


80° 


0.00 


0.22 


0.42 


0.63 


82 


1 00 


1 IS 


1.34 


1 50 


1.66 


1 81 


2.51 


90° 








0.07 


0.26 


0.44 


0.61 
0.05 


78 
0.21 


0.94 
0.37 


1.09 
0.52 


1.24 
0.67 
0.10 


1.93 


100° 








1.34 


110° 














0.76 


























Dif.p.deg. 


.0549 


.0551 


.0554 


.0556 


.0559 


.0561 


.0564 


.0566 


.0568 


.0570 


.0572 


.0581 



Separating Calorimeters. — For percentages of moisture beyond the 
range of the throttling calorimeter the separating calorimeter is used,. 



CHIMNEYS. 915 

which is simply a steam separator on a small scale. An improved form 
of this calorimeter is described by Prof. Carpenter in Poiver, Feb., 1893. 

For fuller information on various kinds of calorimeters, see papers by 
Prof. Peabody, Prof. Carpenter, and Mr. Barrus in Trans. A. S. M. E., 
vols, x, xi, xif, 18S9 to 1891 ; Appendix to Report of Com. on Boiler Tests' 
A. S. M. E., vol. vi, 1884; Circular of Schaeffer & Budenberg, N. Y.', 
"Calorimeters, Throttling and Separating." 

Identification of Dry Steam by Appearance of a Jet. — Prof. 
Denton {Trans. A. S. M. E., vol. x) found that jets of steam show un- 
mistakable change of appearance to the eye when steam varies less than 
1% from the condition of saturation in the direction of either wetness 
or of superheating. 

If a jet of steam flow from a boiler into the atmosphere under circum- 
stances such that very little loss of heat occurs through radiation, etc., 
and the jet be transparent close to the orifice, or be even a grayish-white 
color, the steam may be assumed to be so nearly dry that no portable 
condensing calorimeter will be capable of measuring the amount of water 
in the steam. If the jet be strongly white, the amount of water may be 
roughly judged up to about 2%, but beyond this only a calorimeter^can 
determine the exact amount of moisture. 

A common brass pet-cock may be used as an orifice, but it should, if 
possible, be set into the steam-drum of the boiler and never be plated 
further away from the latter than 4 feet, and then only when the inter- 
mediate reservoir or pipe is well covered. 

Usual Amount of 3Ioisture in Steam Escaping from a Boiler. — 
In the common forms of horizontal tubular land boilers and water-tube 
boilers with ample horizontal drums, and supplied with water free from 
substances likely to cause foaming, the moisture in the steam does not 
generally exceed 2% unless the boiler is overdriven or the water-level is 
carried too high. 

CHIMNEYS. 

Chimney Draught Theory. — The commonly accepted theory of 
chimney draught, based on Peclet's and Rankine's hypotheses (Rankine, 
S. E.), is discussed by Prof. De Volson Wood, Trans. A. S. M. E., vol. xi. 

Peclet represented the law of draught by the formula 



2g\ 



2gV 



in which h is the " head, " defined as such a height of hot gases as, if added 
to the column of gases in the chimney, would produce the 
same pressure at the furnace as a column of outside air, of 
the same area of base, and a height equal to that of the 
chimney; 
u is the required velocity of gases in the chimney; 
G a constant to represent the resistance to the passage of air 

through the coal; 
I the length of the flues and chimney; 
m the mean hydraulic depth or the area of a cross-section divided 

by the perimeter; 
/ a constant depending upon the nature of the surfaces over 
which the gases pass, whether smooth, or sooty and rough. 
Rankine's formula (Steam Engine, p. 288), derived by giving certain 
values to the constants (so-called) in Peclet's formula, is 



-°f 0.0807^ , . 

^ { H-H= (0.96 T -i-lW; 

^(u.084 ) V r 2 / 



in which H = the height of the chimney in feet ; 

t = 493° F., absolute (temperature of melting ice); 
T!= absolute temperature of the gases in the chimney; 
t 2 = absolute temperature of the external air. 



916 



CHIMNEYS. 



Prof. Wood derives from this a still more complex formula which gives 
the height of chimney required for burning a given quantity of coal per 
second, and from it he calculates the following table, showing the height 
of chimney required to burn respectively 24, 20, and 16 lbs. of coal per 
square foot of grate per hour, for the several temperatures of the chimney 
gases given. 





Chimney Gas. 


Coal per sq. ft. of grate per hour, lbs. 


Outside Air. 






24 


20 


16 


T2- 


Absolute. 


Temp. 
Fahr. 










Height H, feet. 


520° 


700 


239 


250.9 


157.6 


67.8 


absolute or 


800 


339 


172.4 


115.8 


55.7 


59° F. 


1000 


539 


149.1 


100.0 


48.7 




1100 


639 


148.8 


98.9 


48.2 




1200 


739 


152.0 


100.9 


49.1 




1400 


939 


159.9 


105.7 


51.2 




1600 


1139 


168.8 


111.0 


53.5 




2000 


1539 


206.5 


132.2 


63.0 



Rankine's formula gives a maximum draught when t = 21/12 t 2 , or 
622° F., when the outside temperature is 60°. Prof. Wood says: "This 
result is not a fixed value, but departures from theory in practice do not 
affect the result largely. There is, then, in a properly constructed chimney 
properly working, a temperature giving a maximum draught,* and that 
temperature is not far from the value given by Rankine, although in 
special cases it may be 50° or 75° more or less." 

All attempts to base a practical formula for chimneys upon the theoret- 
ical formula of Peclet and Rankine have failed on account of the impos- 
sibility of assigning correct values to the so-called "constants" G and /. 
(See Trans. A. S. M. E., xi, 984.) 

Force or Intensity of Draught. — The force of the draught is equal 
to the difference between the weight of the column of hot gases inside of 
the chimney and the weight of a column of the external air of the same 
height. It is measured by a draught-gauge, usually a U-tube partly 
filled with water, one leg connected by a pipe to the interior of the flue, 
and the other open to the external air. 

If D is the density of the air outside, d the density of the hot gas inside, 

in lbs. per cubic foot, h the height of the chimney in feet, and 0.192 the 

factor for converting pressure in lbs. per sq. ft. into inches of water column, 

then the formula for the force of draught expressed in inches of water is, 

F = 0.192 h (D - d). 

The density varies with the absolute temperature (see Rankine). 



-0.084; D =0.0807 



to 



where t is the absolute temperature at 32° F., = 493, t x the absolute 
temperature of the chimney gases and t 2 that of the external air. Sub- 
stituting these values the formula for force of draught becomes 

F _0.192 k (™™ - iliiW* P-™ - ™ 5 ). 



* Much confusion to students of the theory of chimneys has resulted 
from their understanding the words maximum draught to mean maxi- 
mum intensity or pressure of draught, as measured by a draught-gauge. 
It here means maximum quantity or weight of gases passed up the 
chimney. The maximum intensity is found only with maximum tem- 
perature, but after the temperature reaches about 622° F. the density of 
the gas decreases more rapidly than its velocity increases, so that the 
weight is a maximum about 622° F., as shown by Rankine, — W. K, 



CHIMNEYS. 



917 



To find the maximum intensity of draught for any given chimney, the 
heated column being 600° F., and the external air 60°, multiply the height 
above grate in feet by 0.0073, and the product is the draught in inches 
of water. 

Height of Water Column Due to Unbalanced Pressure in Chimney 
100 Feet High. (The Locomotive, 1884.) 



.s >> 

age 
H 6 


Temperature of the External Air — Barometer, 14.7 lbs 


per sq. in. 


0° 
0.453 


10° 
0.419 


20° 


30° 


40° 


50° 


60° 
0.263 


70° 


80° 


90° 


100° 


200 


0.384 


0.353 


0.321 


0.292 


0.234 


0.209 


0.182 


0.157 


220 


.488 


.453 


.419 


.388 


.355 


.326 


.298 


.269 


.244 


.217 


.192 


240 


.520 


.488 


.451 


.421 


.388 


.359 


.330 


.301 


.276 


.250 


.225 


260 


.555. 


.528 


.484 


.453 


.420 


.392 


.363 


.334 


.309 


.282 


.257 


280 


.584 


.549 


.515 


.482 


.451 


.422 


.394 


.365 


.340 


.313 


.288 


300 


.611 


.576 


.541 


.511 


.478 


.449 


.420 


.392 


.367 


.340 


.315 


320 


.637 


.603 


.568 


.538 


.505 


.476 


.447 


.419 


;394 


.367 


.342 


340 


.662 


.638 


.593 


.563 


.530 


.501 


.472 


.443 


.419 


.392 


.367 


360 


.687 


.653 


.618 


.588 


.555 


.526 


.497 


.468 


.444 


.417 


.392 


380 


.710 


.676 


.641 


.611 


.578 


.549 


.520 


.492 


.467 


.440 


.415 


400 


.732 


.697 


.662 


.632 


.598 


.570 


.541 


.513 


.488 


.461 


.436 


420 


.753 


.718 


.684 


.653 


.620 


.591 


.563 


.534 


.509 


.482 


.457 


440 


.774 


.739 


.705 


.674 


.641 


.612 


.584 


.555 


.530 


.503 


.478 


460 


.793 


.758 


.724 


.694 


.660 


.632 


.603 


.574 


.549 


.522 


.497 


480 


.810 


.776 


.741 


.710 


.678 


.649 


.620 


.591 


.566 


.540 


.515 


500 


.829 


.791 


.760 


.730 


.697 


.669 


.639 


.610 


.586 


.559 


.534 



For any other height of chimney than 100 ft. the height of water column 
is found by simple proportion, the height of water column being directly 
proportioned to the height of chimney. 

The calculations have been made for a chimney 100 ft. high, with 
various temperatures outside and inside of the flue, and on the supposition 
that the temperature of the chimney is uniform from top to bottom. 
This is the basis on which all calculations respecting the draught-power 
of chimneys have been made by Rankine and other writers, but it is very 
far from the truth in most cases. The difference will be shown by com- 
paring the reading of the draught-gauge with the table given. In one 
case a chimney 122 ft. high showed a temperature at the base of 320°, 
and at the top of 230°. 

Box, in his "Treatise on Heat," gives the following table: 

Draught Powers of Chimneys, etc., with the Internal Air at 552° 
and the External Air at 62°, and with the Damper nearly 
Closed. 



«4-, G 


m 


Theoretical Velocity 


_ a 


<o 


Theoretical Velocity 


Z* • 


M.S ■£ 

PI'S 

P4 


in feet per second. 


|1| 


PI'S 


in feet per 


second. 




Cold Air 


Hot Air 


Cold Air 


Hot Air 


trj.3 


Entering. 


at Exit. 




Entering. 


at Exit. 


10 


0.073 


17.8 


35.6 


80 


0.585 


50.6 


101.2 


20 


0.146 


25.3 


50.6 


90 


0.657 


53.7 


107.4 


30 


0.219 


31.0 


62.0 


100 


0.730 


56.5 


113.0 


40 


0.292 


35.7 


71.4 


120 


0.876 


62.0 


124.0 


50 


0.365 


40.0 


80.0 


150 


1.095 


69.3 


138.6 


60 


0.438 


43.8 


87.6 


175 


1.277 


74.3 


149.6 


70 


0.511 


47.3 


94.6 


200 


1.460 


80.0 


160.0 



918 



CHIMNEYS. 



Rate of Combustion Due to Height of Chimney. — Trowbridge's 
"Heat and Heat Engines" gives the following figures for the heights of 
chimney for producing certain rates of combustion per sq. ft. of grate. 
They may be approximately true for anthracite in moderate and large 
sizes, but greater heights than are given in the table are needed to secure 
the given rates of combustion with small sizes of anthracite, and for 
bituminous coal smaller heights will suffice if the coal is reasonably free 
from ash — 5% or less. 





Lbs. of 




Lbs. of 




Lbs. of 




Lbs. of 


Height, 


Coal per 


Height, 


Coal per 


Height, 


Coal per 


Height, 


Coal per 


feet. 


Sq. Ft. of 


feet. 


Sq. Ft. of 
Grate. 


feet. 


Sq. Ft. of 


feet. 


Sq. Ft. of 




Grate. 






Grate. 




Grate. 


20 


7.5 


45 


12.4 


70 


15.8 


95 


18.5 


25 


8.5 


50 


13.1 


75 


16.4 


100 


19.0 


30 


9.5 


55 


13.8 


80 


16.9 


105 


19.5 


35 


10.5 


60 


14.5 


85 


17.4 


110 


20.0 


40 


11.6 


65 


15.1 


90 


18.0 













W. D. Ennis (Eng. Mag., Nov., 1907), gives the following as the force 
of draught required for burning No. 1 buckwheat coal: 



Draught, in. of water 0.3 . 45 

Lbs. coal per sq. ft. grate per hour 10 15 



0.7 
20 



1.0 
25 



Thurston's rule for rate of combustion effected by a given height of 
chimney (Trans. A. S. M. E., xi, 991) is: Subtract 1 from twice the square 
root of the height, and the result is the rate of combustion in pounds per 
square foot of grate per hour, for anthracite. Or rate = 2 V7i — 1, in 
which h is the height in feet. This rule gives the following: 

h = 50 60 70 80 90 100 110 125 150 175 200 
2^-1 = 13.14 14.49 15.73 16.89 17.97 19 19.97 21.36 23.49 25.45 27.28 

The results agree closely with Trowbridge's table given above. In 
practice the high rates of combustion for high chimneys given by the 
formula are not generally obtained, for the reason that with high chimneys 
there are usually long horizontal flues, serving many boilers, and the 
friction and the interference of currents from the several boilers are apt to 
cause the intensity of draught in the branch flues leading to each boiler 
to be much less than that at the base of the chimney. The draught of 
each boiler is also usually restricted by a damper and by bends in the gas- 
passages. In a battery of several boilers connected to a chimney 150 ft. 
high, the author found a draught of 3/ 4 -ineh water-column at the boiler 
nearest the chimney, and only 1/4-inch at the boiler farthest away. The 
first boiler was wasting fuel from too high temperature of the chimney- 
gases, 900°, having too large a grate-surface for the draught, and the last 
boiler was working below its rated capacity and with poor economy, on 
account of insufficient draught. 

The effect of changing the length of the flue leading into a chimney 
60 ft. high and 2 ft. 9 in. square is given in the following table, from Box 
on "Heat": 



Length of Flue in 
feet. 


Horse-power. 


Length of Flue in 
feet. 


Horse-power. 


50 
100 
200 
400 
600 


107.6 
100.0 
85.3 
70.8 
62.5 


800 
1,000 
1,500 
2,000 
3,000 


56.1 
51.4 
43.3 
38.2 
31.7 



The temperature of the gases in this chimney was assumed to be 552° F., 
and that of the atmosphere 62°. 



SIZE OP CHIMNEYS. 919 

High Chimneys not Necessary. — Chimneys above 150 ft. in height 
are very costly, and their increased cost is rarely justified by increased effi- 
ciency. In recent practice it has become somewhat common to build two 
or more smaller chimneys instead of one large one. A notable example 
is the Spreckels Sugar Refinery in Philadelphia, where three separate 
chimneys are used for one boiler-plant of 7500 H.P. The three chimneys 
are said to have cost several thousand dollars less than a single chimney 
of their combined capacity would have cost. Very tall chimneys have 
been characterized by one writer as "monuments to the folly of their 
builders." 

Heights of Chimney required for Different Fuels. — The minimum 
height necessary varies with the fuel, wood requiring the least, then good 
bituminous coal, and fine sizes of anthracite the greatest. It also varies 
with the character of the boiler — the smaller and more circuitous the 
gas-passages the higher the stack required ; also with the number of boilers, 
a single boiler requiring less height than several that discharge into a 
horizontal flue. No general rule can be given. 

C. L. Hubbard (Am. Electrician, Mar., 1904) says: The following heights 
have been found to give good results in plants of moderate size, and to 
produce sufficient draught to force the boilers from 20 to 30 per cent 
above their rating: 

With free-burning bituminous coal, 75 feet; with anthracite of medium 
and large size, 100 feet: with slow-burning bituminous coal, 120 feet; with 
anthracite pea coal, 130 feet; with anthracite buckwheat coal, 150 feet. 
For plants of 700 or 800 horse-power and over, the chimney should not 
be less than 150 feet high regardless of the kind of coal to be used. 

SIZE OF CHIMNEYS. 

The formula given below, and the table calculated therefrom for chim- 
neys up to 96 in. diameter and 200 ft. high, were first published by the 
author in 1884 (Trans. A. S. M. E., vi, 81). They have met with much 
approval since that date by engineers who have used them, and have been 
frequently published in boiler-makers' catalogues and elsewhere. The 
table is now extended to cover chimneys up to 12 ft. diameter and 300 ft. 
high. The sizes corresponding to the given commercial horse-powers 
are believed to be ample for all cases in which the draught areas through 
the boiler-flues and connections are sufficient, say not less than 20% 
greater than the area of the chimney, and in which the draught between 
the boilers and chimney is not checked by long horizontal passages and 
right-angled bends. 

Note that the figures in the tahle correspond to a coal consumption of 5 lbs. 
of coal per horse-power per hour. This liberal allowance is made to cover 
the contingencies of poor coal being used, and of the boilers being driven 
bevond their rated capacity. In large plants, with economical boilers 
and engines, good fuel and other favorable conditions, which will reduce 
the maximum rate of coal consumption at any one time to less than 5 lbs. 
per H.P. per hour, the figures in the table may be multiplied by the ratio 
of 5 to the maximum expected coal consumption per H.P. per hour. 
Thus, with conditions which make the maximum coal consumption only 
2.5 lbs. per hour, the chimnev 300 ft. high X 12 ft. diameter should be 
sufficient for 6155 X 2 = 12,310 horse-power. The formula is based on 
the following data: 

1. The draught power of the chimney varies as the square root of the 
height. 

2. The retarding of the ascending gases by friction may be considered 
as equivalent to a diminution of the area of the chimney, or to a lining of 
the chimney by a layer of gas which has no velocity. The thickness of 
this lining is assumed to be 2 inches for all chimneys, or the diminution 
of area equal to the perimeter X 2 inches (neglecting the overlapping of 
the corners of the lining). Let D = diameter in feet, A = area, and E = 
effective area in square feet: 

8 D 2 /—* 

For square chimneys, E = D* - -^- = A - ■= v A. 

For round chimneys, E = ^ (d* - ^\ = A - 0.591 ^A. 



920 CHIMNEYS. 

For simplifying calculations, the coefficient of ^ A may be taken as 0.6 
for both square and round chimneys, and the formula becomes 

E = A - 0.6 VI. 

3. The power varies directly as this effective area E. 

4. A chimney should be proportioned so as to be capable of giving 
sufficient draught to cause the boiler to develop much more than its rated 
power, in case of emergencies, or to cause the combustion of 5 lbs. of fuel 
per rated horse-power of boiler per hour. 

5. The power of the chimney varying directly as the effective area, E, 
and as the square root of the height, H, the formula for horse-power of 
boiler for a given size of chimney will take the form H.P. = CE Viy, in 
which C is a constant, the average value of which, obtained by plotting 
the results obtained from numerous examples in practice, the author 
finds to be 3.33. 

The formula for horse-power then is 

H.P. = 3.33 E V#, or H.P. = 3.33 (A - 0.6 ^A) Vjf. 

If the horse-power of boiler is given, to find the size of chimney, the 
height being assumed, 

E = 0.3 H.P. -*- Vtf; = A - 0.6 VI. 

For round chimneys, diameter of chimney = diam. of E + 4". 

For square chimneys, side of chimney = V ' e + 4". 

If effective area E is taken in square feet, the diameter in inches is d = 
13.54_V.Z2 + 4", and the side of a square chimney in inches is s = 
1 2 V_? + 4". 

/0 3 H P \ 2 

If horse-power is given and area assumed, the height H = I — — tt^^ ) ■ 

An approximate formula for chimneys above 1000 H.P. is H.P. = 
2.5 D 2 Vi_\ This gives the H.P. somewhat greater than the figures in 
the table. 

In proportioning chimneys the height should first be assumed, with due 
consideration of the heights of surrounding buildings or hills near to the 
proposed chimney, the length of horizontal flues, the character of coal to 
be used, etc. ; then the diameter required for the assumed height and horse- 
power is calculated by the formula or taken from the table. 

For Height of Chimneys see pages 918 and 919. No formula for 
height can be given which will be satisfactory for different classes of coal, 
kinds and amounts o" ash, styles of grate-bars, etc. A formula in " Ingeni- 
eurs Taschenbuch," translated into English measures, is/i = 0.216.R 2 + 6d. 
h= height in ft; R = lbs. coal burned per sq. ft. of grate per hour; d = 
diam. in ft. This formula gives an insufficient height for small sizes of 
anthracite, and a height greater than is necessary for free-burning bitu- 
minous coal low in ash. 

The Protection of Tall Chimney-shafts from Lightning. — C. 
Molyneux and J. M. Wood (Industries, March 28, 1890) recommend for 
tall chimneys the use of a coronal or heavy band at the top of the chimney, 
with copper points 1 ft. in height at intervals of 2 ft. throughout the cir- 
cumference. The points should be gilded to prevent oxidation. The 
most approved form of conductor is a copper tape about 3/ 4 in. by Vs in. 
thick, weighing 6 ozs. per ft. If iron is used it should weigh not less than 
2V4 lbs. per ft. There must be no insulation, and the copper tape should 
be fastened to the chimney with holdfasts of the same material, to pre- 
vent voltaic action. An allowance for expansion and contraction should 
be made, say 1 in. in 40 ft. Slight bends in the tape, not too abrupt, 
answer the purpose. For an earth terminal a plate of metal at least 3 ft. 
sq. and Vi6 in. thick should be buried as deep as possible in a damp spot. 
The plate should be of the same metal as the conductor, to which it 
should be soldered. The best earth terminal is water, and when a deep 
well or other large body of water is at hand, the conductor should be 
carried down into it. Right-angled bends in the conductor should be 
avoided. No bend in it should be over 30°. 



SIZE OP CHIMNEYS. 



921 





.p 






















































S 0> ^^w » 5 
















-2 53 2 ° !2 ^ 
















g-co^coGCiEsq 
w ° > 


vOC^Nt r^orsjir 


>> OOmoOT »tOin OvO — \0 — r^.r^tri 




--NN <S cc» t<"> «"> ifiT^tf 


1 u-i\Or»rN 000000 OO-N 




















8 


























^tS^lO 00^-<Nm tsmfift 
o 3" — © — in — o- os <v) tj- in 
<NTr-»© n>oo^ t~s eg — — 


(4 

3 




























— — — <M NNKMA rnTmsO 




































o 

<D 

ft 
TJ 
CD 




o 
























• T NOiftO \OfiOffl O in v© 00 

■ oo oc-imoo — ^;i^o -Sroovovo 
— — — — <n cs cs t<^ rcitntin 


*; 




















inoo © m in sO oDeoaoN OOtsi^ — 






























^ o o o ro oominm 


























\© oo O (N "3" r- or-i 




£i 


























- NNNf 


4 t^c^^-ir! 


3 
































£5 




£ 




















^2a 


00 OO O m OvOinf- 


-1-NO 


Hi 

o 






























s 






















- 


— CSCSCs 
























































Nomoo oomo- 


or^oe* 


OvOOs — 


o 






























ITS 


















m^rmN c --- ■ 


^ IsOfMA O^NO^In 




























-NNN NlAmt 


£5 
































43 
















v©nO — <\ 


O m Csl OO OsvOOO in \0 !*>. C^l 






"3 














s£ 






mrsmoN oo oo m m 






o 














<N 


<^ -"T rnsC 


COONt \© 00 — «"* -O O- vO m 




>> 






















— — «S«N 








— 


£ 






















4 Ph - 


43 












Tin 


CAO>t^N 


vCTt^^T ^ N ^ C 














o 

a 
i 












o^- 


00 00 O cr- 


Nc^OO 


O — T& 










d M 
« so 


IS 

o 


P4 












<NCN 


N«MTk>C 


PnO — <N tlNO\C 










"S 


43 












vO — & 




00 \D OO ^t" 
















w .2 




© 




W 

.5 










£2H 


t->. v© r>. o> 


IN00ON 
















h a 


1 
5 


































O 3 


p 


































K 




































&'5 


o 










— •<»• ao — 


in t T vO 
vN«*>-<rin 


OMn 






















© 










cs 


O 00 




















Ol 




o 


i 






























d 




vOCO 


S5SS 


mor-,v© 


























o ^ 




































sh 




«s 




^1'N^ 


sE?^ 


__ 




























s> 




0O 


; 


S-^-OOO 


Js^ 




























N o 


















































































02 O 








-, — OOOO 


©<QSoo 


vO 


































R 




































1 








— 


^ 






























^ 


_^ 














































-NOO-rtM 




































CO 










OS--TJ- 


































CO 




*© 








































CO* 












































II 








^ IPl O^ in 


"f 
















































00 






































Ah" 




m 




























































W 


















e8 

3 


> • 'h 


















M i 


?T©t^ 


oooor^r^ 


vo-r — oo 


SoRtS 


— O(N0C 


SH2S 


S 


d 1 c 


3 — c>i cn 


<*i-<rm\o 


is.'o?22 


(N(N(nS 


?*HS 


lAt^O^vO 


o 


H ^° 














~~ 


fa 


























s-tOO 


— gr i^o 


SkSS 


nO t>»00 00 


^oor^tnrvi 


qo^O 


o 




















" M ^^ 


■<r m r>! oo 


o> n its 2; 


f^vNr^cr 


JTS«S 


sss; 


2 




ll 




— Tt-s 


om>oo> 


ssss 


■orgoo'T 

VO 0tl~>00 


oooo 


=sa 


? 






















p. a 



















































922 



CHIMNEYS. 



Some Tall Brick Chimneys (1895). 



Outside 
Diameter. 



Capacity by the 
Author's 
Formula. 



Pounds 
Coal 



1. Hallsbriickner Hiitte, 

Saxony 

2. Townsend's, Glasgow ... 

3. Tennant's, Glasgow 

4. Dobson & Barlow, Bol- 

ton, Eng 

5. Fall River Iron Co., Bos- 

ton 

6. Clark Thread Co., New- 

ark, N.J 

7. Merrimac Mills, Lowell, 

Mass 

8. Washington Mills, Law- 

rence, Mass 

9. Amoskeag Mills, Man- 

chester, N. H 

10. Narragansett E. L. Co., 

Providence, R.I 

1 1 . Lower Pacific Mills, Law- 

rence, Mass 

12. Passaic Print Works, 

Passaic, N. J 

13. Edison Station Brooklyn, 

Two each 



460 

454 
435 

3671/2 

350 

335 

282' 9" 

250 

250 

238 

214 

200 

150 



15.7' 

'ii'6''" 

13' 2" 

11 

11 

12 

10 

10 

14 

8 

9 

50" x 120" 



32 
40 

33' 10" 

30 
28' 6 



13,221 



9,795 
8,245 
5,558 
5,435 
5,980 
3,839 
3,839 
7,515 
2,248 
2,771 
1,541 



66,105 
"48,975" 
41,225 
27,790 
27,175 
29,900 
19,195 
19,195 
37,575 
11,240 
13,855 
7,705 



Notes on the Above Chimneys. — 1. This chimney is situated near 
Freiberg, at an elevation of 219 ft. above that of the foundry works, so 
that its total height above the sea will be 7113/4 ft. The furnace-gases 
are conveyed across river to the chimney on a bridge, through a pipe 
3227 ft. long. It is built of brick, and cost about $40,000. — Mfr. & Bldr. 

2. Owing to the fact that it was struck by lightning, and somewhat 
damaged, as a precautionary measure a copper extension subsequently 
was added to it, making its entire height 488 feet. 

1, 2, 3, and 4 were built of these great heights to remove deleterious 
gases from the neighborhood, as well as for draught for boilers. 

5. The structure rests on a solid granite foundation, 55 X 30 feet, and 
16 feet deep. In its construction there were used 1,700,000 bricks, 
2000 tons of stone, 2000 barrels of mortar, 1000 loads of sand, 1000 barrels 
of Portland cement, and the estimated cost is $40,000. It is arranged for 
two flues, 9 feet 6 inches by 6 feet, connecting with 40 boilers, which are 
to be run in connection with four triple-expansion engines of 1350 horse- 
power each. 

6. It has a uniform batter of 2.85 ins. to every 10 ft. Designed for 
21 boilers of 200 H.P. each. It is surmounted by a cast-iron coping 
which weighs six tons, and is composed of 32 sections bolted together 
by inside flanges so as to present a smooth exterior. The foundation 
is 40 ft. square and 5 ft. deep. Two qualities of brick were used: the 
outer portions were of the first quality North River, and the backing up 
was of good quality New Jersey brick. Every twenty feet in vertical 
measurement an iron ring, 4 ins. wide and 3/ 4 to 1/2 in. thick, placed edge- 
wise, was built into the walls about 8 ins. from the outer circle. As the 
chimney starts from the base it is double. The outer wall is 5 ft. 2 ins. 
in thickness, and inside of this is a second wall 20 ins. thick and spaced 



SIZE OF CHIMNEYS. 923 

off about 20 ins. from main wall. From the interior surface of the main 
wall eight buttresses are carried, nearly touching this inner or main flue 
wall in order to keep it in line should it tend to sag. The interior wall, 
starting with the thickness described, is gradually reduced until a height 
of about 90 ft. is reached, when it is diminished to 8 inches. At 165 ft. 
it ceases, and the rest of the chimney is without lining. The total weight 
of the chimney and foundation is 5000 tons. It was completed in Sep- 
tember, 1888. 

7. Connected to 12 boilers, with 1200 sq. ft. of grate. Draught 19/ieins. 

8. Connected to 8 boilers, 6 ft. 8 in. diam. X 18 ft. Grate 448 sq. ft. 

9. Connected to 64 Manning vertical boilers, total grate surface 1810 
sq. ft. Designed to burn 18,000 lbs. anthracite per hour. 

10. Designed for 12,000 H.P. of engines; (compound condensing). 

11. Grate-surface 434 square feet; H.P. of boilers about 2500. 

13. Eight boilers (water-tube) each 450 H.P.; 12 engines, each 300 
H.P. For the first 60 feet the exterior wall is 28 ins. thick, then 24 ins. for 
20 ft., 20 ins. for 30 ft., 16 ins. for 20 ft., and 12 ins. for 20 ft. The inte- 
rior wall is 9 ins. thick of fire-brick for 50 ft., and then 8 ins. thick of red 
brick for the next 30 ft. Illustrated in Iron. Age, Jan. 2, 1890. 

A number of the above chimneys are illustrated in Power, Dec, 1890. 

More Recent Brick Chimneys (1909). — Heller & Merz Co., Newark, 
N. J. 350 ft. high, inside diam., 8 ft. Outside diam., top 9 ft. 101/4 in., 
bottom 27 ft. 6 1/2 in. Outside taper 5.2 in 100. Outer shell 7 1/8 in. at 
the top, 38 in. at the bottom. Custodis radial brick laid in mortar of 
1 cement, 2 lime, 5 sand. The changes in thickness are made by 2-in. 
offsets on the inside every 20 ft. Iron band 31/2 X 5/i6 in., three courses 
below the top. Lined with 4 in. of special brick to resist acids. The 
lining is sectional, being carried on corbels projecting from the shell every 
20 ft. An air space of 2 ins. is left between the lining and the shell. 
The lining bricks are laid in a mortar made of silicate of soda and white 
asbestos wool, tempered to the consistency of fire-clay mortar. This 
mortar is acid-proof, and its binding power, which is considerable in 
comparison to that of fire-clay mortar, is unaffected by temperatures up 
to 2000° F. (Eng. News, Feb. 15, 1906.) Supported on 324 piles driven 
69 ft. to solid rock, and covering an area 45 ft. square. Total cost $32,000. 
The standard Custodis radial brick is 41/2 in. thick and 6V2 in. wide; 
radial lengths are 4, 51/2. 7V8, 85/8 and lOVsins. The smallest size has 
six vertical perforations, 1 in. square, and the largest fifteen. 

Eastman Kodak Co., Pa>chester, N. Y. Height 366 ft.; internal diam. 
at top 9 ft. 10 ins., at bottom 20 ft. 10 ins.; outside diam., top 11 ft., bottom 
27 ft. 10 ins. Radial brick, with 4-in. acid-resisting brick lining. 

Some notable tall chimneys built by the Alphonse Custodis Chimney 
Construction Co. are: Dolgeville, N. Y., 6 X 175 ft. ; Camden, N. J., 7 X 210 
ft.; Newark, N. J., 8X 350 ft.; Rochester, N. Y., 9X 366 ft.; Constable 
Hook, N. J., 10 X 365 ft.; Providence, R. I., 16 X 308 ft.; Garfield, Utah, 
30 X 300 ft.; Great Falls, Mont., 50 X 506 ft. 

The Largest Chimney in the World, in 1908, is that of the Montana 
smelter, at Great Falls, Mont. Height 506 ft. Internal diam. at top 
50 ft. Built of Custodis radial brick. Designed to remove 4,000,000 cu. 
ft. of gases per minute at an average temperature of 600° F. Erected on 
top of a hill 500 ft. above the city, and 246 ft. above the floor of the fur- 
naces, which are about 2000 ft. distant. Designed for a wind pressure of 
331/3 lbs. per sq. ft. of projected area; bearing pressure limited to 21 lbs. 
per sq. ft. at any section. Foundation: 111 ft. max. diam., 221/2 ft. deep; 
bearing pressure on bottom (shale rock) 4.83 tons per sq. ft.; octagonal 
outside, 103 ft. across at bottom, 81 ft. at top. with inner circular open- 
ing 47 ft. diam. at bottom, 64 ft. at top; made of 1 cement, 3 sand, 5 
crushed slag. Four flue openings in the base, each 15 ft. wide, 36 ft. 
high. The stack proper consists of an octagonal base, 46 ft. in height, 
which has a taper of 8%, and above this a circular barrel, the first 180 ft. 
above the base having a taper of 7%, the next 100 ft. of 4%, and the 
remaining 180 ft. to the cap 2%. 

The chimney wall varies from 66 in. at the base to 18 1/8 in. at the top 
by uniform decrements of 2 in. per section, excepting at the section imme- 
diately above the top of the base, where the thickness decreases from 60 in. 
to 54 in. The outside diameters of the stack are 78 1/2 ft. at the base, 
53 ft. 9 in. at the base of the cap; the inside diameters range from 66 1/2 ft. 



924 CHIMNEYS. 

at the foundation line to 50 ft. at the top. The chimney is lined with 4-in. 
acid-proof brick, laid in sections carried on corbels from the main shell. 

A description of the methods of design and of erection of the Great 
Falls chimney is given in Eng. Rec, Nov. 28, 1908. 

Stability of Chimneys. — Chimneys must be designed to resist the 
maximum force of the wind in the locality in which they are built. A 
general rule for diameter of base of brick chimneys, approved by many 
years of practice in England and the United States, is to make the diam- 
eter of the base one-tenth of the height. If the chimney is square or 
rectangular, make the diameter of the inscribed circle of the base one- 
tenth of the height. The "batter" or taper of a chimney should be 
from Vie to 1/4 inch to the foot on each side. The brickwork should be 
one brick (8 or 9 inches) thick for the first 25 feet from the top, increasing 
1/2 brick (4 or 41/2 inches) for each 25 feet from the top downwards. If 
the inside diameter exceeds 5 feet, the top length should be 11/2 bricks; 
and if under 3 feet, it may be 1/2 brick for ten feet. 

(From The Locomotive, 1884 and 1886.) For chimneys of four feet in 
diameter and one hundred feet high, and upwards, the best form is cir- 
cular with a straight batter on the outside. 

Chimneys of any considerable height are not built up of uniform 
thickness from top to bottom, nor with a uniformly varying thickness of 
wall, but the wall, heaviest of course at the base, is reduced by a series 
of steps. 

Where practicable the load on a chimney foundation should not exceed 
two tons per square foot in compact sand, gravel, or loam. Where a 
solid rock-bottom is available for foundation, the load may be greatly 
increased. If the rock is sloping, all unsound portions should be removed, 
and the face dressed to a series of horizontal steps, so that there shall be 
no tendency to slide after the structure is finished. 

All boiler-chimneys of any considerable size should consist of an outer 
stack of sufficient strength to give stability to the structure, and an inner 
stack or core independent of the outer one. This core is by many engineers 
extended up to a height of but 50 or 60 feet from the base of the chimney, 
but the better practice is to run it up the whole height of the chimney: it 
may be stopped off, say, a couple of feet below the top, and the outer shell 
contracted to the area of the core, but the better way is to run it up to 
about 8 or 12 inches of the top and not contract the outer shell. But 
under no circumstances should the core at its upper end be built into or 
connected with the outer stack. This has been done in several instances 
by bricklayers, and the result has been the expansion of the inner core 
which lifted the top of the outer stack squarely up and cracked the brick- 
work. 

For a height of 100 feet we would make the outer shell in three steps, the 
first 20 feet high, 16 inches thick, the second 30 feet high, 12 inches thick, 
the third- 50 feet high and 8 inches thick. These are the minimum 
thicknesses admissible for chimneys of this height, and the batter should 
be not less than 1 in 36 to give stability. The core should also be built 
in three steps, each of which may be about one-third the height of the 
chimney, the lowest 12 inches, the middle 8 inches, and the upper step 
4 inches thick. . This will insure a good sound core. The top of a chimney 
may be protected by a cast-iron cap; or perhaps a cheaper and equally 
good plan is to lay the ornamental part in some good cement, and plaster 
the top with the same material. 

C. L. Hubbard (Am. Electrician, Mar., 1904) says: The following 
approximate method may be used for determining the thickness of walls. 
If the inside diameter at the top is less than 3 ft. the walls may be 4 ins. 
thick for the first 10 ft., and increased 4 ins. for each 25 ft. downward. 
If the inside diameter is more than 3 ft. and less than 5 ft., begin with a 
wall 8 ins. thick, increasing 4 ins. for each 25 ft. downward. If the diam- 
eter is over 5 ft., begin with a 12-in. wall, increasing below the first 10 ft. 
as before. The lining or core may be 4 ins. thick for the first 20 ft. from 
the top, 8 ins. for the next 30 ft., 12 ins. for the next 40 ft., 16 ins. for 
the next 50 ft., and 20 ins. for the next 50 ft. Using this method for an 
oftter wall 200 ft. high and assuming a cubic foot of brickwork to weigh 
130 lbs;, it gives a maximum pressure of 8.2 tons per sq. ft. of section at 
the base: while a lining 190 ft. high would have a maximum pressure of 
8.6 tons per sq. ft. The safe load for brickwork may be taken at from 



SIZE OF CHIMNEYS. 925 

8 to 10 tons per sq. ft., although the strength of best pressed brick will run 
much higher. 

James B. Francis, in a report to the Lawrence Mfg. Co. in 1873 {Eng. 
News, Aug. 28, 1880), concerning the probable effects of wind on that 
company's chimney as then constructed, says: 

The stability of the chimney to resist the force of the wind depends 
mainly on the weight of its outer shell, and the width of its base. The 
cohesion of the mortar may add considerably to its strength; but it is too 
uncertain to be relied upon. The inner shell will add a little to the 
stability, but it may be cracked by the heat, and its beneficial effect, if 
any, is too uncertain to be taken into account. 

The effect of the joint action of the vertical pressure due to the weight 
of the chimney, and the horizontal pressure due to the force of the wind is 
to shift the center of pressure at the base of the chimney, from the axis 
toward one side, the extent of the shifting depending on the relative 
magnitude of the two forces. If the center of pressure is brought too near 
the side of the chimney, it will crush the brickwork on that side, and the 
chimney will fall. A line drawn through the center of pressure, perpen- 
dicular to the direction of the wind, must leave an area of brickwork 
between it and the side of the chimney, sufficient to support half the weight 
of the chimney; the other half of the weight being supported by the brick- 
work on the windward side of the line. 

Different experimenters on the strength of brickwork give very different 
results. Kirkaldy found the weights which caused several kinds of 
bricks, laid in hydraulic lime mortar and in Roman and Portland cements, 
to fail slightly, to vary from 19 to 60 tons (of 2000 lbs.) per sq. ft. If 
we take in this case 25 tons per sq. ft. as the weight that would cause it 
to begin to fail, we shall not err greatly. 

Rankine, in a paper printed in the transactions of the Institution of 
Engineers, in Scotland, for 1867-68, says: "It had previously been ascer- 
tained by observation of the success and failure of actual chimneys, and 
especially of those which respectively stood and fell during the violent 
storms of 1856, that, in order that a round chimney may be sufficiently 
stable, its weight should be such that a pressure of wind, of about 55 lbs. per 
sq. ft. of a plane surface, directly facing the wind, or 27 1/2 lbs. per sq. ft. 
of the plane projection of a cylindrical surface, . . . shall not cause the 
resultant pressure at any bed-joint to deviate from the axis of the 
chimney by more than one-quarter of the outside diameter at that 
joint." 

Steel Chimneys are largely used, especially for tall chimneys of iron- 
works, from 150 to 300 feet in height. The advantages claimed are: 
greater strength and safety; smaller space required; smaller cost, by 
30 to 50 per cent, as compared with brick chimneys; avoidance of infiltra- 
tion of air and consequent checking of the draught, common in brick 
chimneys. They are usually made cylindrical in shape, with a wide curved . 
flare for 10 to 25 feet at the bottom. A heavy cast-iron base-plate is 
provided, to which the chimney is riveted, and the plate is secured to a 
massive foundation by holding-down bolts. No guys are used. 

Design of Self-supporting Steel Chimneys. — John D. Adams 
{Eng. News, July 20, 1905) gives a very full discussion of the design of steel 
chimneys, from which the following is adapted. The bell-shaped bottom 
of the chimney is assumed to occupy one-seventh of the total height, and 
the point of maximum strain is taken to be at the top of this bell portion. 
Let D = diam. in inches, H = height in feet, T = thickness in inches, 
S = safe tensile stress, lbs. per sq. in. The general formula for moment 
of resistance of a hollow cylinder is M = 1/32 w (D i — Z>i 4 ) S/D. When 
the thickness is a small fraction of the diameter this becomes approxi- 
mately M = 0.7854 D 2 TS. 

With steel plate of 60.000 lbs. tensile strength, riveting of 0.6 efficiency, ' 
and a factor of safety of 4, we have S = 9000 pounds per sq. in., and the 
safe moment of resistance = 7070 D 2 T. 

The effect of the wind upon a cylinder is equal to the wind pressure 
multiplied by one-half the diametral plane, and taking the maximum 
wind pressure at 50 lbs. per sq. ft., we get 

Total wind pressure = 50 X V12 D X 1/2 X 6/7 H = 25 DH /IA. 



926 



CHIMNEYS. 



The distance of the center of pressure above the top of the bell portion, 
•= 3/ 7 H, multiplied by the total wind pressure, gives us the bending mo- 
ment due to the wind, 

inch pounds, 25 DH/\ 4 X 8/7 H X 12 = 9.184 DH 2 . 

Equating the bending and the resisting moment we have T = 0.0013 
H 2 /D. 

With this formula the maximum thickness of plates was calculated for 
different sizes of chimneys, as given in the table below. 

In the above formula, no attention has been paid to the weight of the 
steel in the stack above the bell portion, which weight has a tendency 
to decrease the tension on the windward side and increase the compression 
on the leeward side of the stack. A column of steel 150 ft. high would 
exert a pressure of approximately 500 lbs. per sq. in., which, with steel 
of 60,000 lbs. tensile strength, is less than 1% of the ultimate strength, 
and may safely be neglected. 

From the table it appears that a chimney 12 X 120 ft. requires, as far 
as fracture by bending of a tubular section is concerned, a thickness of 
but little over Vs in. In designing a stack of such extreme proportions 
as 12 X 120 ft., there are other factors besides bending to take into con- 
sideration that ordinarily could be neglected. For instance, such a stack 
should be provided with stiffening angles, or else made heavier, to guard 
against lateral flattening. Ordinarily, however, the strength of the 
chimney determined as a tubular section will be the prime factor in deter- 
mining the maximum thickness of plates. 

Thickness of Base-ring Plates of Self-supporting Steel Stacks. 

For normal wind pressure of 50 lbs. per sq. ft. on half the diametral plane. 

Diameter of Stack in feet. 





3.5 


4 

.133 

.182 
.219 
.271 
328 
.390 
.458 
.531 
.609 
.693 


5 

.106 
.139 
.175 
.217 
.262 
.312 
.366 
.425 
.437 
.555 
676 


6 


7 


8 


8.5 


9 


9.5 


10 


11 


12 


70 


0.152 
0.198 
0.224 
0.310 
0.375 
0.446 
0.523 
0.607 
0.696 




















80 


.116 
.146 
.181 
.218 
.260 
.305 
.354 
.406 
.462 
.522 
.585 
.652 


.099 
.125 
.155 
.187 
.223 
.262 
.303 
.348 
.396 
.447 
.501 
.559 
.620 
.682 
















90 


.111 
.135 
.164 
.195 
.228 
.265 
.305 
.346 
.391 
.439 
.489 
.542 
.596 
.655 
.717 














100 


.127 
.154 
.183 
.215 
.250 
.286 
.326 
.368 
.413 
.460 
.510 
.562 
.617 
.674 
.734 


.120 
.146 
.173 
.203 
.236 
.271 
.308 
.348 
.390 
.434 
.481 
.531 
.582 
.637 
.693 
.752 










110 
120 
130 
140 
150 
160 
170 


.138 
.164 
.193 
.223 
.257 
.292 
.330 
.370 
.411 
.456 
.503 
.552 
.603 
.657 
.713 


.131 
.156 
.183 
.212 
.244 
.277 
.313 
.351 
.391 
.433 
.478 
.524 
.573 
.624 
.677 


.iJ9 
.142 
.166 
.193 
.222 
.252 
.285 
.319 
.356 
.394 
.434 
.476 
521 
.567 
.615 


",'\30 
.153 
.180 
.203 
.231 
.261 


180 






.702 


.293 


1Q0 






.326 


?00 








.361 


7.10 










.398 


7?0 










437 


?10 












477 


740 












.520 


7.50 














.564 





















Foundation. — Neglecting the increase of wind area due to the flare 
at the base of the chimney, which has but a very small turning effect, 
if all dimensions be taken in feet, we have 

Total wind pressure = 1/2 D X H X 50 = 25 DH; lever-arm =V 2 H; 
hence, turning moment = 12.5 DH 2 . 

Let d = diameter and h = height of foundation. For average con- 
ditions h = 0.4 d, then volume of foundation = 0.7854 d 2 h,' and for 
concrete at 150 lbs. per cu. ft., weight of foundation = W = 0.7854 d 2 h 
X 150 = 47.124 <P. 

The stability of the foundation or the tendency to resist overturning 
is equal to the weight of the foundation multiplied by its radius or 1/2 Wd 
= 23.562 d*. Applying a factor of safety of 2 1/2, which is indicated by 



SIZE OF CHIMNEYS. 927 



current practice, gives safe stability = 9.4 25 d 4 . Equating this to the 
overturning moment we obtain d = 1.07 \JDH 2 , in which all dimensions 
are in feet. 

Anchor-bolts. — The holding power of the bolts depends on three 
factors: the number of bolts, the diameter of the bolt circle, and the 
diameter of the bolts. The number of bolts is largely conventional and 
may be selected so as not to necessitate bolts of too large a diameter. The 
diameter of the bolt circle is also more or less arbitrary. The bolts will 
be stretched and therefore strained, in proportion to their distance from 
the axis of turning, assuming, as we must, that the cast-iron ring at the 
base of the chimney is rigid. The leverage at which any bolt acts is also 
directly proportional to its distance from the axis of turning. Therefore, 
since the effectiveness of any one bolt, as regards overturning, depends 
upon the strain in that bolt, multiplied by its leverage, it is evident that 
the effectiveness of any bolt varies as the square of its distance from the 
axis of turning. If we lay out, say, 12 or 24 bolts equidistant on a circle 
and add all the squares of these distances, we will find that we may con- 
sider the total as though the bolts were all placed at a distance of >7 8 
the diameter of the bolt circle from the axis of turning, which is the tan- 
gent to the bolt circle. 

Let b = diameter of bolt in inches, n = number of bolts, diameter 
of bolt circle = 2/ 3 d. Take safe working stress at 8000 pounds per sq. 
inch. Then resistance to overturning = 0.7854 b 2 X 8000 X 2 fad X 3/gX 
N = 6283 b 2 Nd/4. Equa ting this to the turning mom ent, 12.5 DH 2 , 
gives b = 0.0257H.V D/d for 12 bolts, 0.0222 H ^D/d for 18 bolts, 
and 0.0182 H VD/d for 24 bolts. 

The Babcock & Wilcox Co.'s book "Steam" illustrates a steel chimney 
at the works of the Maryland Steel Co., Sparrow's Point, Md. It is 
225 ft. in height above the base, with internal brick lining 13' 9" uniform 
inside diameter. The shell is 25 ft. diam. at the base, tapering in a curve 
to 17 ft. 25 ft. above the base, thence tapering almost imperceptibly to 
14' 8" at the top. The upper 40 feet is of 1/4-inch plates, the next four 
sections of 40 ft. each are respectively 8/32, 5 /i6, xl /32, and 3/ 8 inch. 

Reinforced Concrete Chimneys began extensively to come into use 
in the United States in 1901. Some hundreds of them are now (1909) 
in use. The following description of the method of construction of these 
chimneys is condensed from a circular of the Weber Chimney Co., Chicago. 

The foundation is comparatively light and made of concrete, consisting 
of 1 cement, 3 sand, and 5 gravel or macadam. The steel reinforcement 
consists of two networks usually made of T steel of small size. The bars 
for the lower network are placed diagonally and the bars for the second 
network (about 4 to 6 ins. above. the first one) run parallel to the sides. 
The vertical bars, forming the re'enforcement of the chimney itself, also 
go down into the foundation and a number of these bars are bent in order 
to secure an anchorage for the chimney. 

The chimney shaft consists of two parts, the lower double shell and the 
single shell above, which are united at the offset. The inside shell is 
usually 4 in#. thick, while the thickness of the outer shell depends on the 
height and varies from 6 to 12 ins. The single shell is from 4 to 10 ins. 
thick. The height of the double shell depends upon the purpose of the 
chimney, nature and heat of the gases, etc. 

Between the two shells in the lower part there is a circular air space 4 
ins. in width. An expansion joint is provided where the two shells unite. 

The concrete above the ground level consists of one part Portland 
cement and three parts of sand. No gravel or macadam is used. 

The bending forces caused by wind pressure are taken up by the vertical 
steel reenforcement. The resistance of the concrete itself against tension 
is not considered in calculation. 

The vertical T bars are from 1 X 1 X Vs to 1 1/2 XI 1/2 X 1/2 in., the weight 
and number depending upon the dimensions of the chimney. The bars 
are from 16 to 30 ft. long and overlap not less than 24 ins. They are 
placed at regular intervals of 18 ins. and encircled by steel ringrs bent to 
the desired circle. The work of erection is done from the inside of the 
chimney: no outside scaffolding is needed. 

The following is a list of some of the tallest concrete chimneys that have 
been built of their respective diameters: Butte, Mont., 350 X 18 ft.; Seattle, 



928 



CHIMNEYS. 



Wash., 278 X 17 ft.; Portland, Ore., 230 X 12 ft.; Lawrence, Mass., 250 X 
11 ft.; Cincinnati, Ohio, 200 X 10 ft.; Worcester, Mass., 220X9 ft.; 
Atlanta, Ga., 225 X 8 ft.; Chicago, 175 X 7 ft.; Rockville, Conn., 175 X 
6 ft.; Seymour, Ind., 150 X 5 ft.; Iola, Kans., 143 X 4 ft.; St. Louis, Mo., 
130 X 3 ft. 4 in. ; Dayton, Ohio, 94 X 3 ft. 

Sizes of Foundations for Steel Chimneys. 

(Selected from circular of Phila. Engineering Works.) 
Half-Lined Chimneys. 

Diameter, clear, feet 3 4 5 6 7 9 11 

Height, feet 100 100 150 150 150 150 150 

Least diam. foundation.. 15'9" 16' 4" 20'4" 21'10" 22'7" 23'8" 24'8" 

Least depth foundation.. 6' 6' 9' 8' 9' 10' 10' 

Height, feet 125 200 200 250 275 300 

Least diam. foundation 18'5" 23'8" 25' 29'8" 33'6" 26' 

Least depth foundation 7' 10' 10' 12' 12' 14' 

Weight of Sheet-iron Smoke-stacks per Foot. 

(Porter Mfg. Co.) 



Diam. 


Thick- 


Weight 


Diam. 


Thick- 


Weight 


Diam. 


Thick- 


Weight 


inches. 


W. G. 


per ft. 


inches. 


W. G. 


per ft. 


inches. 


W. G. 


per ft. 


10 


No. 16 


7.20 


26 


No. 16 


17.50 


20 


No. 14 


18.33 


12 




8.66 


28 




18.75 


22 




20.00 


14 




9.58 


30 




20.00 


24 




21.66 


16 




11.68 


10 


No. 14 


9.40 


26 




23.33 


20 




13.75 


12 




11.11 


28 




25.00 


22 


" 


15.00 


14 




13.69 


30 


" 


26.66 


24 


" 


16.25 


16 




15.00 



















Sheet-iron Chimneys. 


(Columbus Machine Co.) 




Diameter 

Chimney, 

inches. 


Length 

Chimney, 

feet. 


Thick- 
ness 
Iron, 
B. W. G. 


Weight 
lbs. 


Diameter 

Chimney, 

inches. 


Length 

Chimney, 

feet. 


Thick- 
ness 
Iron, 
B.W.G. 


Weight 
lbs. 


10 


20 


No. 16 


160 


30 


40 


No. 15 


960 


15 


20 


" 16 


240 


32 


40 


" 15 


1020 


20 


20 


" 16 


320 


34 


40 


" 14 


1170 


22 


20 


" 16 


350 


36 


40 


" 14 


1240 


24 


40 


" 16 


760 


38 


40 


" 12 


1800 


26 


40 


" 16 


826 


40 


40 


" 12 


1890 


28 


40 


" 15 


900 











THE STEAM-ENGINE. 



929 



THE STEAM-ENGINE. 

Expansion of Steam. Isothermal and Adiabatic. — According to 
. Mariotte's law, the volume of a perfect gas, the temperature being kept 
constant, varies inversely as its pressure, or p & l/v; pv = a constant. The 
curve constructed from this formula is called the isothermal curve, or 
curve of equal temperatures, and is a common or rectangular hyperbola. 
The expansion of steam in an engine is not isothermal, since the temper- 
ature decreases with increase of volume, but its expansion curve approxi- 
mates the curve of pv = a constant. The relation of the pressure and 
volume of saturated steam, as deduced from Regnault's experiments, and 
as given in steam tables, is approximately, according to Rankine (S. E., 
p. 403), for pressures not exceeding 120 lbs., p <* 1/vB, or p cc-jris or pvi* = 
p V i-0625 = a constant. Zeuner has found that the exponent 1.0646 gives a 
closer approximation. 

When steam expands in a closed cylinder, as in an engine, according to 
Rankine (S. E., p. 385), the approximate law of the expansion is p <* l/v V, 
or p ocy _1 s ' or pv 1 ' m = a constant. The curve constructed from this 
formula is called the adiabatic curve, or curve of no transmission of heat. 

Peabody (Therm., p. 112) says: "It is probable that this equation was 
obtained by comparing the expansion lines on a large number of indicator- 
diagrams. . . . There does not appear to be any good reason for using an 
exponential equation in this connection, . . . and the action of a lagged 
steam-engine cylinder is far from being adiabatic. . . . For general pur- 
poses the hyperbola is the best curve for comparison with the expansion 
curve of an indicator-card. ..." Wolff and Denton, Trans. A. S. M.E., 
ii, 175, say: " From a number of cards examined from a variety of steam- 
engines in current use, we find that the actual expansion line varies between 
the 10/9 adiabatic curve and the Mariotte curve." 

Prof. Thurston (Trans. A.£.ilf.£ , .,h\ 203) says he doubts if the exponent 
ever becomes the same in any two engines, or even in the same engine 
at different times of the day and under varying conditions of the day. 

Expansion of Steam according to Mariotte's Law and to the 
Adiabatic Law. (Trans. A. S. M. E., ii, 156.) — Mariotte's law pv = 

Pivv, values calculated from formula ■ — = -^ (1 + hyp log R), in which 
R = V2 -5- vi, pi = absolute initial pressure, P m = absolute mean pressure, 
vi = initial volume of steam in cylinder at pressure pi, vt = final volume 

of steam at final pressure. Adiabatic law: pv$ = pivys ; values calcu- 

p 
lated from formula — = 10 R^-QR' 1 ^- 



Ratio 
of Ex- 
pansion 


Ratio of Mean 
to Initial 
Pressure. 


Ratio 
of Ex- 
pansion 


Ratio of Mean 
to Initial 
Pressure. 


Ratio 
of Ex- 
pansion 


Ratio of Mean 
to Initial 
Pressure. 












R. 


Mar. 


Adiab. 


R. 


Mar. 


Adiab. 


R. 


Mar. 


Adiab. 


1.00 


1.000 


1.000 


3.7 


0.624 


0.600 


6. 


0.465 


0.438 


1.25 


.978 


.976 


3.8 


.614 


.590 


6.25 


.453 


.425 


1.50 


.937 


.931 


3.9 


.605 


.580 


6.5 


.442 


.413 


1.75 


.891 


.881 


4. 


.597 


.571 • 


6.75 


.431 


.403 


2. 


.847 


.834 


4.1 


.588 


.562 


7. 


.421 


.393 


2.2 


.813 


.798 


4.2 


.580 


.554 


7.25 


.411 


.383 


2.4 


.781 


.765 


4.3 


.572 


.546 


7.5 


.402 


.374 


2.5 


.766 


.748 


4.4 


.564 


.538 


7.75 


.393 


.365 


2.6 


.752 


.733 


4.5 


.556 


.530 


8. 


.385 


.357 


2.8 


.725 


.704 


4.6 


.549 


.523 


8.25 


.377 


.349 


3. 


.700 


.678 


4.7 


.542 


.516 


8.5 


.369 


.342 


3.1 


.688 


.666 


4.8 


.535 


.509 


8.75 


.362 


.335 


3.2 


.676 


.654 


4.9 


.528 


.502 


9. 


.355 


.328 


3.3 


.665 


.642 


5.0 


.522 


.495 


9.25 


.349 


.321 


3.4 


.654 


.630 


5.25 


.506 


.479 


9.5 


.342 


.315 


3.5 


.644 


.620 


5.5 


.492 


.464 


9.75 


.336 


.309 


. 3.6 


.634 


.610 


5.75 


.478 


450 


10. 


.330 


.303 



930 



THE STEAM-ENGINE. 



Mean Pressure of Expanded Steam. — For calculations of engines 
it is generally assumed that steam expands according to Mariotte's law, 
the curve of the expansion line being a hyperbola. The mean pressure, 
measured above vacuum, is then obtained Irom the formula 



=Pi- 



1 4- hyp log R 
R 



or P m =P;(l + hyplog#), 



in which P m is the absolute mean pressure, pi the absolute initial pressure 
taken as uniform up to the point of cut-off, P t the terminal pressure, and 
R the ratio of expansion. If I = length of stroke to the cut-off, L = total 
stroke. £ 

Pi!+p , lhyplog _ ____£. p ^ 1+hyplogB 



-P™= - 



-; and if R = 



L ' """ " " I \~ m "* R 

Mean and Terminal Absolute Pressures. — Mariotte's Law. — The 

values in the following table are based on Mariotte's law, except those 
in the last column, which give the mean pressure of superheated steam, 
which, according to Rankine, expands in a cylinder according to the 
law ptxv~i%. These latter values are calculated from the formula 



17-16 R-tb 



Pi 



R ib may be found by extracting the square root 



back pressure (absolute) to obtain the 


mean effective pressure. 


Rate 
of 
Expan- 
sion. 


Cut- 
off. 


Ratio of 

Mean to 

Initial 

Pressure. 


Ratio of « 
Mean to 
Terminal 
Pressure. 


Ratio of 
Terminal 
to Mean 
Pressure. 


Ratio of 
Initial 
to Mean 
Pressure. 


Ratio of 

Mean to 

Initial 

Dry Steam. 


30 

28 


0.033 
0.036 
0.038 
0.042 
0.045 
0.050 
0.055 
0.062 
0.066 
0.071 
0.075 
0.077 
0.083 
0.091 
0.100 
0.111 
0.125 
0.143 
0.150 
0.166 
0.175 
0.200 
0.225 
0.250 
0.275 
0.300 
0.333 
0.350 
0.375 
0.400 
0.450 
0.500 
0.550 
0.600 
0.625 
0.650 
0.675 


0.1467 
0.1547 
0.1638 
0.1741 
0.1860 
0.1998 
0.2161 
0.2358 
0.2472 
0.2599 
0.2690 
0.2742 
0.2904 
0.3089 
0.3303 
0.3552 
0.3849 
0.4210 
0.4347 
0.4653 
4807 
0.5218 
0.5608 
0.5965 
0.6308 
0.6615 
0.6995 
0.7171 
0.7440 
0.7664 
0.8095 
0.8465 
0,8786 
0.9066 
0.9187 
0.9292 
0.9405 


4.40 

4.33 

4.26 

4.18 

4.09 

4.00 

3.89 

3.77 

3.71 

3.64 

3.59 

3.56 

3.48 . 

3.40 

3.30 

3.20 

3.08 

2.95 

2.90 

2.79 

2.74 

2.61 

2.50 

2.39 

2.29 

2.20 

2.10 

2.05 

1.98 

1.91 

1.80 

1.69 

1.60 

1.5.1 

1.47 

1.43 

1.39 


0.227 
0.231 
0.235 
0.239 
0.244 
0.250 
0.256 
0.265 
0.269 
0.275 
0.279 
0.280 
0.287 
0.294 
0.303 
0.312 
0.321 
0.339 
0.345 
0.360 
0.364 
0.383 
0.400 
0.419 
0.437 
0.454 
0.476 
0.488 
0.505 
0.523 
0.556 
0.591 
0.626 
0.662 
0.680 
0.699 
0.718 


6.82 
6.46 
6.11 
5.75 
5.38 
5.00 
4.63 
4.24 
4.05 
3.85 
3.72 
3.65 
3.44 
3.24 
3.03 
2.81 
2.60 ' 
2.37 
2.30 
2.15 
2.08 
1.92 
1.78 
1.68 
• 1.58 
1.51 
1.43 
1.39 
1.34 
1.31 
1.24 
1.18 
1.14 
1.10 
1.09 
1.07 
1.06 


0.136 


26 




24 




22 




20 
18 


0.186 


16 




15 




14 




13.33 
13 


0.254 


12 




11 




10 
9 


0.314 


8 
7 


0.370 


6.66 
6.00 


0.417 


5.71 




5.00 
4.44 


0.506 


4.00 
3.63 


0.582 


3.33 

3.00 


0.6'8 


2.86 
2.66 


0.707 


2.50 
2.22 
2.00 
1.82 
1.66 
1.60 


0.756 
0.800 
0.840 
0.874 
0.900 


1.54 
1.48 


0.926 



THE STEAM-ENGINE. 



931 




Calculation of Mean Effective Pressure, Clearance and Com- 
pression Considered. — In the above tables no account is taken of 

clearance, which in actual 
\ ei L — £, — $ steam-engines modifies the 

ratio of expansion and the 
mean pressure ; nor of com- 
pression and back-pressure, 
which diminish the mean 
effective pressure. In the 
following calculation these 
elements are considered. 

L = length of stroke, I = 
length before cut-off, x = 
length of compression part of 
stroke, c = clearance, pi = 
initial pressure, pb = back 
pressure, p c = pressure of 
clearance steam at end of 
compression. All pressures 
are absolute, that is, measured 
from a perfect vacuum. 

Area of ABCD ^ fa (1+ c) (l + hyp log l A ; 
B = pb(L-x); 

C = p c c (l + hyp log ^-jp) =Pb (x+c) (l + hyp log ^r~/ : 
D = (pi-p c ) c = pic-pb (x + c). 
Area of A = ABCD - (8 + C + D) 

= Pi(Z+c)(l + hyplogy^) 

- \pb (L-x) + Pb (x + c) (l + hyp log ^~j^)+ Pic-Ph (x 4-c)J 

= Pi(Z+c)(l+hyplog|^) 

I X + c~\ 

- pb I (L - x) + (x + c) hyp log — — I -pic. 

_ „ area of A 
Mean effective pressure = y 



Example. — Let L = l, 1 = 0.25, z = 0.25, c = 0.1, pi=6Q lbs., Pb = 2 lbs. 

1.1 > 



Area A = 60 (0.25 + 0.1) (l + hyp log ^) 



■■[ 



(1-0.25) +0.35 hyp log - 



-60X0.1. 

= 21 (1 + 1.145) - 2 [0.75 + 35 X 1.253] - 6 

= 45.045 -2.377- 6 = 36. 668 = mean effective pressure. 

The actual indicator-diagram generally shows a mean pressure con- 
siderablv less than that due to the initial pressure and the rate of expan- 
sion. The causes of loss of pressure are: 1. Friction in the stop-valves 
and steam-pipes. 2. Friction or wire-drawing of the steam during 
admission and cut-off, due chieflv to defective valve-gear and contracted 
steam-passages. 3. Liquefaction during expansion. 4. Exhausting 
before the engine has completed its stroke. 5. Compression due to early 
closure of exhaust. 6. Friction in the exhaust-ports, passages, and 
pipes. 



932 THE STEAM-ENGINE. 

Re-evaporation during expansion of the steam condensed during admis- 
sion, and valve-leakage after cut-off, tend to elevate the expansion line 
of the diagram and increase the mean pressure. 

If the theoretical mean pressure be calculated from the initial pressure 
and the rate of expansion on the supposition that the expansion curve 
follows Mariotte's law, pv = a constant, and the necessary corrections 
are made for clearance and compression, the expected mean pressure in 
practice may be found by multiplying the calculated results by the factor 
(commonly called the "diagram factor") in the following table, according 
to Scaton. 

Particulars of Engine. Factor. 

Expansive engine, special valve-gear, or with a sepa- 
rate cut-off valve, cylinder jacketed . 94 

Expansive engine having large ports, etc., and good 

ordinary valves, cylinders jacketed . 9 to . 92 

Expansive engines with the ordinary valves and gear 

as in general practice, and unjacketed . 8 to . 85 

Compound engines, with expansion valve to h.p. 
cylinder; cylinders jacketed, and with large ports, 
etc . 9 to . 92 

Compound engines, with ordinary slide-valves, cylin- 
ders jacketed, and good ports, etc . 8 to . 85 

Compound engines as in general practice in the 
merchant service, with early cut-off in both cylin- 
ders, without jackets and expansion- valves 0.7 to 0.8 

Fast-running engines of the type and design usually 

fitted in war-ships . 6 to . 8 

If no correction be made for clearance and compression, and the engine 
is in accordance with general modern practice, the theoretical mean 
pressure may be multiplied by 0.96, and the product by the proper factor 
in the table, to obtain the expected mean pressure. 

Given the Initial Pressure and the Average Pressure, to Find the 
Ratio of Expansion and the Period of Admission. 

P = initial absolute pressure in lbs. per sq. in.; 

p = average total pressure during stroke in lbs. per sq. in.; 

L =■ length of stroke in inches; 

I = period of admission measured from beginning of stroke; 

c = clearance in inches ; 

R = actual ratio of expansion = ; ■ ■ (1) 

= P(l + hyploga) 
p R 

To find average pressure p, taking account of clearance, 
= P(l + c) + P(l + c) hyp log R-Pc 

whence pL + Pc = P(l + c) (1 + hyp log R) ; 

. . _ pL + Pc , P +C „ ,„. 

hyplogi^L-^-^-^-l. ... (3) 

Given p and P, to find R and I (by trial and error). — There being two 
unknown quantities R and I, assume one of them, viz., the period of 
admission I, substitute it in equation (3) and solve for R. Substitute this 

value of R in the formula (1), or I = — =-^ — c, obtained from formula 

(1), and find I. If the result is greater than the assumed value of I, 
then the assumed value of the period of admission is too long; if less, the 
assumed value is too short. Assume a new value of I, substitute it in 
formula (3) as before, and continue by this method of trial and error till 
the required values of R and Z are obtained. 



(2) 



THE STEAM-ENGINE. 



933 



Example. — P = 70, p = 42.78, L= 60 in., c = 3 in., to find I. Assume 
I - 21 in. 

P L + C ^- 8 X60 + 3 

hyplogfl^ t+e -1= 21 + 3 1 = 1.653-1 = 0.653; 

hyp log R = 0.653, whence R = 1.92. 

<-*£-'—:&-»-»* 

which is greater than the assumed value, 21 inches. 
Now assume i = 15 inches: 

42 78 
^X60+3 

hyp log R = 15 + 3 1 = 1.204, whence R= 3.5; 

I = — 5 c= o-g— 3 = 18-3 = 15 inches, the value assumed. 

Therefore # = 3.5, and 1 = 15 inches. 

Period of Admission Required for a Given Actual Ratio of Expansion: 
1= — = c, in inches (4) 

T . . . , T 100 + p. ct. clearance . , 

In percentage of stroke, I =■ — „ p. ct. clearance . (5) 

P (1 + c) P 
Terminal pressure = — ■ = — (6) 

Pressure at any other Point of the Expansion. — Let Li = length of 
stroke up to the given point. 

Pressure at the given point = — — (7) 

Mechanical Energy of Steam Expanded Adiabatically to Various 
Pressures. — The figures in the following table are taken from a chart 
constructed by R. M. Neilson in Power, Mar. 16, 1909. The pressures 
are absolute, lbs per sq. in. 



[3 g 


15 


20 


25 


40 


60 


80 


100 


120 


140 


170 


200 


250 


"3 s 
a ® 


Mechanical Energy, Thousands of Foot-Pounds per Lb. of Steam. 


faC4 




1^ 





17 


29.5 


55.5 


77.5 


94.5 


107 


116.5 121 


136.5 


146 


160 


]?. 


12 


29 


41 


66.5 


88 


104 


116 


126 


135 


145 


154.5 


168.5 


in 


22 


39 


50.5 


75.5 


97 


113 


125 


135.5 


144 


154 


163.5 


176 


8 


34 


50 


62 


86.5 


109 


124 


136 


147 


155 


165.5 


174.5 


186 


6 


49 


64 


76 


101 


123 


138 


150 


160 


168.5 


179.5 


188 


199 


4 


68 


85 


95.5 


120 


142 


157 


168 


177.5 


186 


196 


204.5 


216 


2 


100 


116 


128 


151 


171 


186.5 


197.5 


207 


215 


224 


232.5 


244 


1 


131 


147 


157.5 


181.5 


200.5 


215 


225 


234.5 


243 


250.5 


260.5 


270.5 



Measures for Comparing the Duty of Engines. — Capacity is meas- 
ured in horse-powers, expressed by the initials, H.P.: 1 H.P. = 33,000 
ft.-lbs. per minute, =550 ft.-lbs. per second, = 1,980,000 ft.-lbs. per hour. 
1 ft .-lb. = a pressure of 1 lb. exerted through a space of 1 ft. 

Economy is measured, 1, in pounds of coal per horse-power per hour; 
2, in pounds of steam per horse-power per hour. The second of these 
measures is the more accurate and scientific, since the engine uses steam 
and not coal, and it Is independent of the economy of the boiler. 



934 THE STEAM-ENGINE. 



In gas-engine tests the common measure is the number of cubic feet 
of gas (measured at atmospheric pressure) per horse-power, but as all gas 
is not of the same quality, it is necessary for comparison of tests to give 
the analysis of the gas. When the gas for one engine is made in one 
gas-producer, then the number of pounds of coal used in the producer per 
hour per horse-power of the engine is a measure of economy. Since 
different coals vary in heating value, a more accurate measure is the 
number of heat units required per horse-power per hour. 

Economy, or duty of an engine, is also measured in the number of foot- 
pounds of work done per pound of fuel. As 1 horse-power is equal to 
1,980,000 ft.-lbs. of work in an hour, a duty of 1 lb. of coal per H.P. per 
hour would be equal to 1,980,000 ft.-lbs. per lb. of fuel; 2 lbs. per H.P. 
per hour equals 990,000 ft.-lbs. per lb. of fuel, etc. 

The duty of pumping-engines is expressed by the number of foot- 
pounds of work done per 100 lbs. of coal, per 1000 lbs. of steam, or per 
million heat units. 

When the duty of a pumping-engine is given, in ft.-lbs. per 100 lbs. of 
coal, the equivalent number of pounds of fuel consumed per horse-power 
per hour is found by dividing 198 by the number of millions of foot-pounds 
of duty. Thus a. pumping-engine giving a duty of 99 millions is equiva- 
lent to 198/99 = 2 lbs. of fuel per horse-power per hour. 

Efficiency Measured in Thermal Units per Minute. — The efficiency 
of an engine is sometimes expressed in terms of the number of thermal 
units used by the engine per minute for each indicated horse-power, instead 
of by the number of pounds of steam used per hour. 

The heat chargeable to an engine per pound of steam is the difference 
between the total heat in a pound of steam at the boiler-pressure and that 
in a pound of the feed-water entering the boiler. In the case of con- 
densing engines, suppose we have a temperature in the hot-well of 100° F., 
corresponding to a vacuum of 28 in. of mercury; we may feed the water 
into the boiler at that temperature. In the case of a non-condensing 
engine, by using a portion of the exhaust steam in a good feed-water 
heater, at a pressure a trifle above the atmosphere (due to the resistance 
of the exhaust passages through the heater), we may obtain feed-water 
at 212°. One pound of steam used by the engine then would be equivalent 
to thermal units as follows: 

Gauge pressure 50 75 100 125 150 175 200 

Absolute pressure. ...65 90 115 140 165 190 215 

Total heat in steam above 32°: 

1178.5 1184.4 1188.8 1192.2 1195.0 1197.3 1199.2 

Subtracting 68 and 180 heat-units, respectively, the heat above 32° in 
feed-water of 100° and 212° F., we have — 

Heat given by boiler per pound of steam: 

Feed at 100° 1110.5 1116.4 1120.8 1124.2 1127.0 1129.3 1131.2 

Feed at 212° 998.5 1004.4 1008.8 1012.2 1015.0 1017.3 1019.2 

Thermal units per minute used by an engine for each pound of steam 
used per indicated horse-power per hour: 

Feed at 100° 18.51 18.61 18.68 18.74 18.78 18.82 18.85 

Feed at 212° 16.64 16.76 16.78 16.87 16.92 16.96 16.99 

Examples. — A triple-expansion engine, condensing, with steam at 
175 lbs. gauge, and vacuum 28 in., uses 13 lbs. of water per I. H.P. per hour, 
and a high-speed non-condensing engine, with steam at 100 lbs. gauge, 
uses 30 lbs. How many thermal units per minute does each consume? 

Ans. — 13 X 18.82 = 244.7, and 30 X 16.78 = 503.4 thermal units 
per minute. 

A perfect engine converting all the heat-energy of the steam into work 
would require 33,000 ft.-lbs. <*- 778 = 42.4164 thermal units per minute 
per indicated horse-power. This figure, 42.4164, therefore, divided by 
the number of thermal units per minute per I. H.P. consumed by an 
engine, gives its efficiency as compared with an ideally perfect engine. 
In the examples above, 42.4164 divided by 244.3 and by 503.4 gives 
17.33% and 8.42% efficiency, respectively. 



ACTUAL EXPANSIONS. 



935 



ACTUAL EXPANSIONS 

With Different Clearances and Cut-offs. 

Computed by A. F. Nagle. 









Per Cent of Clearance. 


Cut- 
off. 













1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


.01 


100.00 


50.5 


34.0 


25.75 


20.8 


17.5 


15.14 


13.38 


12.00 


10.9 


10 


.02 


50.00 


33.67 


25.50 


20.60 


17.33 


15.00 


13.25 


11.89 


10.80 


9.91 


9.17 


.03 


33.33 


25.25 


20.40 


17.16 


14.86 


13.12 


11.78 


10.70 


9.82 


9.08 


8.46 


.04 


25.00 


20.20 


17.00 


14.71 


13.00 


11.66 


10.60 


9.73 


9.00 


8.39 


7.86 


.05 


20.00 


16.83 


14.57 


12.87 


11.55 


10.50 


9.64 


8.92 


8.31 


7.79 


7.33 


.06 


16.67 


14.43 


12.75 


11.44 


10.40 


9.55 


8.83 


8.23 


7.71 


7.27 


6.88 


.07 


14.28 


12.62 


11.33 


10.30 


9.46 


8.75 


8.15 


7.64 


7.20 


6.81 


6.47 


.08 


12.50 


11.22 


10.2 


9.36 


8.67 


8.08 


7.57 


7.13 


6.75 


6.41 


6.11 


.09 


11.11 


10.10 


9.27 


8.58 


8.00 


7.50 


7.07 


6.69 


6.35 


6.06 


5.79 


.10 


10.00 


9.18 


8.50 


7.92 


7.43 


7.00 


6.62 


6.30 


6.00 


5.74 


5.50 


.11 


9.09 


8.42 


7.84 


7.36 


6.93 


6.56 


6.24 


5.94 


5.68 


5.45 


5.24 


.12 


8.33 


7.78 


7.29 


6.86 


6.50 


6.18 


5.89 


5.63 


5.40 


5.19 


5.00 


.14 


7.14 


6.73 


6.37 


6.06 


5.78 


5.53 


5.30 


5.10 


4.91 


4.74 


4.58 


.16 


6.25 


5.94 


5.67 


5.42 


5.20 


5.00 


4.82 


4.65 


4.50 


4.36 


4.23 


.20 


5.00 


4.81 


4.64 


4.48 


4.33 


4.20 


4.08 


3.96 


3.86 


3.76 


3.67 


.25 


4.00 


3.88 


3.77 


3.68 


3.58 


3.50 


3.42 


3.34 


3.27 


3.21 


3.14 


.30 


3.33 


3.26 


3.19 


3.12 


3.06 


3.00 


2.94 


2.90 


2.84 


2.80 


2.75 


.40 


2.50 


2.46 


2.43 


2.40 


2.36 


2.33 


2.30 


2.28 


2.25 


2.22 


2.20 


.50 


2.00 


1.98 


1.96 


1.94 


1.92 


1.90 


1.89 


1.88 


1.86 


1.85 


1.83 


.60 


1.67 


1.66 


1.65 


1.64 


1.63 


1.615 


1.606 


1.597 


1.588 


1.580 


1.571 


.70 


1.43 


1.42 


1.42 


1.41 


1.41 


1.400 


1.395 


1.390 


1.385 


1.380 


1.375 


.80 


1.25 


1.25 


1.244 


1.241 


1.238 


1.235 


1.233 


1.230 


1.227 


1.224 


1.222 


.90 


1.111 


1.11 


1.109 


1.108 


1.106 


1.105 


1.104 


1.103 


1.102 


1.101 


1.100 


1.00 


1.00 


1.00 


1.000 


1.000 


1.000 


1.000 


1.000 


1.000 


1.000 


1.000 


1.000 



Relative Efficiency of 1 lb. of Steam with and without Clearance; 

back pressure and compression not considered. 

= p d + c ) + P d + c) hyp log R - Pc 

L 
25; c = 7. 



Mean total pressure — 
Let P = 1 ; L = 100 ; I 



32 + 32 hyp log ^ - 7 



32+ 32 X 1.209 



- = 0.637. 



v 100 100 

If the clearance be added to the stroke, so that clearance becomes zero, 
the same quantity of steam being used, admission I being then = I + c = 
32, and stroke L + c = 107, 

32 + 32 hyp log ^ - 



32 



32 + 32 X 1.209 



= 0.707. 



^ 107 107 

That is, if the clearance be reduced to 0, the amount of the clearance 7 
being added to both the admission and the stroke, the same quantity 
of steam will do more work than when the clearance is 7 in the ratio 
707:637, or 11% more. 

BackPressure Considered. — If back pressure = 0.10 of P, this amount 
has to be subtracted from p and pi giving p = 0.537, pi = 0.607, the 
work of a given quantity of steam used without clearance being greater 
than when clearance is 7 per cent in the ratio of 607: 537, or 13% more. 

Effect of Compression. — By early closure of the exhaust, so that a 
portion of the exhaust-steam is compressed into the clearance-space, 
much of the loss due to clearance may be avoided. If expansion is con- 
tinued down to the back pressure, if the back pressure is uniform through- 
out the exhaust-stroke, and if compression begins at such point that the 



936 



THE STEAM-ENGINE. 



exhaust-steam remaining in the cylinder is compressed to the initial 
pressure at the end of the back stroke, then the work of compression of the 
exhaust-steam equals the work done during expansion by the clearance- 
steam. The clearance-space being filled by the exhaust-steam thus com- 
pressed, no new steam is required to fill the clearance-space for the next 
forward stroke, and the work and efficiency of the steam used in the 
cylinder are just the same as if there were no clearance and no compression. 
When, however, there is a drop in pressure from the final pressure of the 
expansion, or the terminal pressure, to the exhaust or back pressure (the 
usual case), the work of compression to the initial pressure is greater than 
the work done by the expansion of the clearance-steam, so that a loss of 
efficiency results. In this case a greater efficiency can be attained by 
inclosing for compression a less quantity of steam than that needed to fill 
the clearance-space with steam of the initial pressure. (See Clark, 
S. E., p. 399, et seq. ; also F. H. Ball, Trans. A. S. M. E., xiv, 1067.) It is 
shown by Clark that a somewhat greater efficiency is thus attained 
whether or not the pressure of the steam be carried down by expansion 
to the back exhaust-pressure. 

Cylinder-condensation may have considerable effect upon the best 
point of compression, but it has not yet (1893) been determined by 
experiment. (Trans. A. S. M. E., xiv, 1078.) 

Clearance in Low- and High-speed Engines. (Harris Tabor, Am. 
Mach., Sept. 17, 1891.) — The construction of the high-speed engine is 
such, with its relatively short stroke, that the clearance must be much 
larger than in the releasing-valve type. The short-stroke engine is, 
of necessity, an engine with large clearance, which is aggravated when 
variable compression is a feature. Conversely, the engine with releasing- 
valve gear is, from necessity, an engine of slow rotative speed, where 
great power is obtainable from long stroke, and small clearance is a 
feature in its construction. In one case the clearance will vary from 
8% to 12% of the piston-displacement, and in the other from 2% to 3%. 
In the case of an engine with a clearance equaling 10% of the piston- 
displacement the waste room becomes enormous when considered in con- 
nection with an early cut-off. The system of compounding reduces the 
waste due to clearance in proportion as the steam is expanded to a lower 
pressure. The farther expansion is carried through a train of cylinders 
the greater will be the reduction of waste due to clearance. This is shown 
from the fact that the high-speed engine, expanding steam much less than 
the Corliss, will show a greater gain when changed from simple to com- 
pound than its rival under similar conditions. 

Cylinder-condensation. — Rankine, S. E., p. 421, says: Conduction 
of heat to and from the metal of the cylinder, or to and from liquid water 
contained in the cylinder, has the effect of lowering the pressure at the 
beginning and raising it at the end of the stroke, the lowering effect being 
on the whole greater than the raising effect. In some experiments the 
quantity of steam wasted through alternate liquefaction and evaporation 
in the cylinder has been found to be greater than the quantity which 
performed the work. 

Percentage of Loss by Cylinder-condensation, taken at Cut-off. 

(From circular of the Ashcroft Mfg. Co. on the Tabor Indicator, 1889.) 



IK 

85 ° ""S 


Per cent of Feed-water ac- 
counted for by the Indicator. 


Per cent of Feed-water due 
to Cylinder-condensation. 


g8|o 


Simple 
Engines. 


Compound 
Engines, 
h.p. cyl. 


Triple-ex- 
pansion 

Engines, 
h.p. cyl. 


Simple 
Engines. 


Compound 
Engines, 
h.p. cyl. 


Triple-ex- 
pansion 
Engines, 
h.p. cyl. 


5 


58 
66 
71 
74 

78 
82 
86 






42 
34 
29 
26 
22 
18 
14 






10 


74 
76 

78 
82 
85 
88 




26 
24 
22 
18 
15 
12 




15 
20 
30 

40 
50 


78 
80 
84 
87 
90 


22 
20 
16 
13 
10 



CYLINDER CONDENSATION. 



937 



Theoretical Compared with Actual Water-consumption, Single- 
cylinder Automatic Cut-off Engines. (From the catalogue of the 
Buckeye Engine Co.) — The following table has been prepared on the 
basis of the pressures that result in practice with a constant boiler-pressure 
of 80 lbs. and different points of cut-off, with Buckeye engines and others 
with similar clearance. Fractions are omitted, except in the percentage 
column, as the degree of accuracy their use would seem to imply is not 
attained or aimed at. 





Mean 


Total 


Indicated 


Assurr" 1 *^ 




Cut-off 


Effective 


Terminal 


Rate, lbs. 






Product 


Part of 
Stroke. 


Pressure, 
lbs. pet 
sq. in. 


Pressure, 
lbs. per 
sq. in. 


Water per 

I.H.P. per 

hour. 






of Cols. 
1 and 6. 


Act'lRate. 


% Loss. 


0.10 


18 


11 


20 


32 


58 


5.8 


0.15 


27 


15 


19 


27 


41 


6.15 


0.20 


35 


20 


19 


25 


31.5 


6.3 


0.25 


42 


25 


20 


25 


25 


6.25 


0.30 


48 


30 


20 


24 


21.8 


6.54 


0.35 


53 


35 


21 


25 


19 


6.65 


0.40 


57 


38 


22 


26 


16.7 


6.68 


0.45 


61 


43 


23 


27 


15 


6.75 


0.50 


64 


48 


24 


27 


13.6 


6.8 



It will be seen that while the best indicated economy is when the cut-off 
is about at 0.15 or 0.20 of the stroke, giving about 30 lbs. M.E.P., and a 
terminal 3 or 4 lbs. above atmosphere, when we come to add the per- 
centages due to a constant amount of unindicated loss, as per sixth 
column, the most economical point of cut-off is found to be about 0.30 of 
the stroke, giving 48 lbs. M.E.P. and 30 lbs. terminal pressure. This 
showing agrees substantially with modern experience under automatic 
cut-off regulation. 

The last column shows that the actual amount of cylinder condensation 
is nearly a constant quantity, increasing only from 5.8% of the cylinder 
volume at 0.10 cut-off to 6.8% at 0.50 cut-off. 

Experiments on Cylinder-condensation. — Experiments by Major 
Thos. English (Eng'g, Oct. 7, 1887, p. 386) with an engine 10 X 14 in., 
jacketed in the sides but not on the ends, indicate that the net initial 
condensation (or excess of condensation over re-evaporation) by the 
clearance surface varies directly as the initial density of the steam, and 
inversely as the square root of the number of revolutions per unit of time. 
The mean results gave for the net initial condensation by clearance-space 
per sq. ft. of surface at one rev. per second 6.06 thermal units in the engine 
when run non-condensing and 5.75 units when condensing. 

G. R. Bodmer (Eng'g, March 4, 1892, p. 299) says: Within the ordinary 
limits of expansion desirable in one cylinder the expansion ratio has 
practically no influence on the amount of condensation per stroke, which 
for simple engines can be expressed by the following formula for the 
weight of water condensed [per minute, probably; the original does not 

state]: W = C-^ — . where T denotes the mean admission temper- 

L ^J N 2 

ature, t the mean exhaust temperature, S clearance-surface (square feet)> 
N the number of revolutions per second, L latent heat of steam at the 
mean admission temperature, and C a constant for any given type of 
engine. 

Mr. Bodmer found from experimental data that for high-pressure non- 
jacketed engines C = about 0.11, for condensing non-jacketed engines 
0.085 to 0.11, for condensing jacketed engines 0.085 to 0.053. The 
figures for jacketed engines apply to those jacketed in the usual way, 
and not at the ends. 

C varies for different engines of the same class, but is practically con- 
stant for any given engine. For simple high-pressure non-jacketed 
engines it was found to range from 0.1 to 0.112. 

Applying Mr, Bodmer's formula to the case of a Corliss non-jacketed 



938 



THE STEAM-ENGINE. 




non-condensing engine, 4-ft. stroke, 24 in. diam., 60 revs, per min., initial 
pressure 90 lbs. gauge, exhaust pressure 2 lbs., we have T — t = 112°, 
N = 1, L = 880, S = 7 sq. ft.; and, taking C = 0.112 and TP= lbs. 

112V 112 Y7 

water condensed per minute, W = 1X880 = ° -09 lb- per 

minute, or 5.4 lbs. per hour. If the steam used per I.H.P. per hour 
according to the diagram is 20 lbs., the actual water consumption is 
25.4 lbs., corresponding to a cylinder condensation of 27%. 

INDICATOR-DIAGRAM OF A SINGLE-CYLINDER ENGINE. 

Definitions. — The Atmospheric Line, AB, is a line drawn by the pencil 
of the indicator when the connections with the engine are closed and both 

sides of the piston 
are open to the 
atmosphere. 

The Vacuum Line, 
OX, is a reference 
line usually drawn 
about 14.7 pounds 
by scale below the 
atmospheric line. 

The Clearance 
Line, OF, is a refer- 
ence line drawn at a 
distance from the 
end of the diagram 
equal to the same 
per cent of its length 
as the clearance and 
B waste room is of the 
piston-displacement . 
-X p, The Line of Boiler- 
„ . „„ 'pressure, JK, is 

Fig. 154. drawn parallel to the 

atmospheric line, and at a distance from it by scale equal to the boiler- 
pressure shown by the gauge. 

The Admission Line, CD, shows the rise of pressure due to the admission 
of steam to the cylinder by opening the steam-valve. 

The Steam Line, DE, is drawn when the steam-valve is open and steam 
is being admitted to the cylinder. 

The Point of Cut-off, E, is the point where the admission of steam is 
stopped by the closing of the valve. It is often difficult to determine 
the exact point at which the cut-off takes place. It is usually located 
where the outline of the diagram changes its curvature from convex to 
concave. 

The Expansion Curve, EF, shows the fall in pressure as the steam in the 
cylinder expands doing work. 

The Point of Release, F, shows when the exhaust- valve opens. 
The Exhaust Line, FG, represents the change in pressure that takes 
place when the exhaust-valve opens. 

The Back-pressure Line, GH, shows the pressure against which the 
piston acts during its return stroke. 

The Point of Exhaust Closure, H, is the point where the exhaust-valve 
closes. It cannot be located definitely, as the change in pressure is at first 
due to the gradual closing of the valve. 

The Compression Curve, HC, shows the rise in pressure due to the com- 
pression of the steam remaining in the cylinder after the exhaust-valve 
has closed. 

The Mean Height of the Diagram equals its area divided by its length. 
The Mean Effective Pressure is the mean net pressure urging the piston 
forward = the mean height X the scale of the indicator-spring. 

To find the Mean Effective Pressure from the Diagram. — Divide the 
length, LB, into a number, say 10, equal parts, setting off half a part at 
L, half a part at B, and nine other parts between; erect ordinates perpen- 
dicular to the atmospheric line at the points of division of LB, cutting 
the diagram; add together the lengths of these ordinates intercepted 



INDICATOR-DIAGRAMS. 



939 



between the upper and lower lines of the diagram and divide by their 
number. This gives the mean height, which multiplied by the scale of 
the indicator-spring gives the M.E.P. Or hnd the area by a planimeter, 
or other means (see Mensuration, p. 57), and divide by the length LB 
to obtain the mean height. 

The Initial Pressure is the pressure acting on the piston at the beginning 
of the stroke. 

The Terminal Pressure is the pressure above the line of perfect vacuum 
that would exist at the end of the stroke if the steam had not been released 
earlier. It is found by continuing the expansion-curve to the end of the 
diagram. 

A single indicator card shows the pressure exerted by the steam at 
each instant on one side of the piston; a card taken simultaneously from 
the opposite end of the engine shows the pressure exerted on the other 
side. By superposing these cards the pressure or tension on the piston 
rod may be determined. The pressure or pull on the crank pin at any 
instant is the pressure or tension in the rod modified by the angle of the 
connecting rod and by the effect of the inertia of the reciprocating parts. 
For discussion of this subject see Klein's "High-speed Steam Engine," 
also papers by S. A. Moss, Trans. A. S. M. E., 1904, and by F. W. Holl- 
mann, in Power, April 6, 1909. 

Errors of Indicators. ■ — The most common error is that of the spring, 
which may vary from its normal rating; the error may be determined by 
proper testing apparatus and allowed for. But after making this correc- 
tion, even with the best work, the results are liable to variable errors 
which may amount to 2 or 3 per cent. See Barrus, Trans. A. S. M. E., 
v, 310; Denton, Trans. A. S. M. E., xi, 329; David Smith, U. S. N., Proc. 
Eng'g Congress, 1893, Marine Division. 

Other errors of indicator diagrams are those due to inaccuracy of the 
straight-line motion of the indicator, to the incorrect design or position 
of the "rig" or reducing motion, to long pipes between the indicator and 
the engine, to throttling of these pipes, to friction or lost motion in the 
indicator mechanism, and to drum-motion distortion. For discussion of 
the last named see Power, April, 1909. For methods of testing indicators, 
see paper by D. S. Jacobus, Trans. A. S. M. E., 1898. 

Indicator "Rigs," or Reducing-motions; Interpretation of Diagrams 
for Errors of Steam-distribution, etc. For these see circulars of manu- 
facturers of Indicators; also works on the Indicator. 

Pendulum Indicator Rig. — Power (Feb., 1893) gives a graphical 
representation of the errors in indicator-diagrams, caused by the use of 
incorrect forms of the pendulum rigging. It 
is shown that the "brumbo" pulley on the C E 

pendulum, to which the cord is attached, 
does not generally give as good a reduction 
as a simple pin attachment. When the end 
of the pendulum is slotted, working in a pin 
on the crosshead, the error is apt to be con- 
siderable at both ends of the card. With a 
vertical slot in a plate fixed to the cross- 
head, and a pin on the pendulum working in 
this slot, the reduction is perfect, when the 
cord is attached to a pin on the pendulum, 
a slight error being introduced if the brumbo 
pulley is used. With the connection be- 
tween the pendulum and the crosshead made 
by means of a horizontal link, the reduction 
is nearly perfect, if the construction is such that the connecting link 
vibrates equally above and below the horizontal, and the cord is attached 
by a pin. If the link is horizontal at mid-stroke a serious error is intro- 
duced, which is magnified if a brumbo pulley also is used. The adjoin- 
ing figures show the two forms recommended. 

The Manograph, for indicating engines of very high speed, invented 
by Prof. Hospitalier, is described by Howard Greene in Power, June, 1907. 
It is made by Carpentier, of Paris. A small mirror is tilted upward and 
downward by a diaphragm which responds to the pressure variations in 
the cylinder, and the same mirror is rocked from side to side by a reducing 
mechanism which is geared to the engine and reproduces the reciprocations 



Fig. 155. 



940 THE STEAM-ENGINE. 

of the engine piston on a smaller scale. A beam of light is reflected by 
the mirror to the ground-glass screen, and this beam, by the oscillations 
of the mirror, is made to traverse a path corresponding to that of the 
pencil point of an ordinary indicator. The diagram, therefore, is made 
continuously but varies with varying conditions in the cylinder. 

A plate-holder carrying a photographic dry plate can be substituted for 
the ground-glass screen, and the diagram photographed, the exposure 
required varying from half a second to three seconds. By the use of 
special diaphragms and springs the effects of low pressures and vacuums 
can be magnified, and thus the instrument can be made to show with 
remarkable clearness the action of the valves of a gas engine on the suction 
and exhaust strokes. 

The Lea Continuous Recorder, for recording the steam consumption 
of an engine, is described by W. H. Booth in Power, Aug. 31, 1909. It 
comprises a tank into which flows the condensed steam from a condenser, 
a triangular notch through which the water flows from the tank, and a 
mechanical device through which the variations in the level of the water 
in the tank are translated into the motion of a pencil, which motion is 
made proportionate to the quantity flowing, and is recorded on paper 
moved by clockwork. 

INDICATED HORSE-POWER OF ENGINES, SINGLE-CYLINDER. 

Indicated Horse-power, I.H.P. = i^-^rx » 

in which P = mean effective pressure in lbs. per sq. in.; L — length of 
stroke in feet; a = area of piston in square inches. For accuracy, one 
half of the sectional area of the piston-rod must be subtracted from the 
area of the piston if the rod passes through one head, or the whole area of 
the rod if it passes through both heads; n = No. of single strokes per min. 
= 2 X No. of revolutions of a double-acting engine. 

I.H.P. = ■ -„ n - . in which S = piston speed in feet per minute. 

PLd 2 n Pd?S 
I.H.P.^ fg"" = 42Qi 7 = 0.0000238 PLd 2 n = 0.0000238 Pd 2 S, 

in which d = diam. of cyl. in inches. (The figures 238 are exact, since 
7854 -4- 33 = 23.8 exactly.) If product of piston-speed X mean effec- 
tive pressure = 42,017, then the horse-power would equal the square of 
the diameter in inches. 

Handy Rule for Estimating the Horse-power of a Single-cylinder 
Engine. — Square the diameter and divide by 2. This is correct whenever 
the product of the mean effective pressure and the piston-speed = 1/2 
of 42,017, or, say, 21,000, viz., when M.E.P. = 30 and S = 700; when 
M.E.P. = 35 and S = 600; when M.E.P. = 38.2 and S = 550; and when 
M.E.P. = 42 and S = 500. These conditions correspond to those of 
ordinary practice with both Corliss engines and shaft-governor high-speed 
engines. 

Given Horse-power, Mean Effective Pressure, and Piston-speed, 
to find Size of Cylinder. — 



Diameter = 205 \ - HJ 



PLn ^la-iuoMsi ~vu y ps 

Brake Horse-power is the actual horse-power of the engine as measured 
at the fly-wheel by a friction-brake or dynamometer. It is the indicated 
horse-power minus the friction of the engine. 

Electrical Horse-power is the power in an electric current, usually 
measured in kilowatts, translated into horse-power. 1 H.P. = 33,000 
ft. lbs. per min.; 1 K.W.= 1.3405 H.P.; 1 H.P. = 0.746 kilowatts, or 
746 watts. 

Example. — A 100-H.P. engine, with a friction loss of 10% at rated 
load, drives a generator whose efficiency is 90%, furnishing current to a 
motor of 90% effy., through a line whose loss is 5%. I.H.P. = 100; 
B.H.P. = 90; E.H.P. at generator 81, at end of line 76.95. H.P. delivered 
by motor 69.26. 



INDICATED HOKSE-POWER OF ENGINES. 



941 



Table for Roughly Approximating the Horse-power of a Com- 
pound Engine from the Diameter of its Low-pressure Cylinder. — 

The indicated horse-power of an engine being in which P = 

mean effective pressure per sq. in., s = piston-speed in ft. per min., and 
d = diam. of cylinder in inches; if s = 600 ft. per min., which is approxi- 
mately the speed of modern stationary engines, and P = 35 lbs., which is 
an approximately average figure for the M.E.P. of single-cylinder engines, 
and of compound engines referred to the low-pressure cylinder, then 
I.H.P. = V2d 2 ; hence the rough-and-ready rule for horse-power given 
above: Square the diameter in inches and divide by 2. This applies to 
triple and quadruple expansion engines as well as to single cylinder and 
compound. For most economical loading, the M.E.P. referred to the 
low-pressure cylinder of compound engines is usually not greater than 
that of simple engines; for the greater economy is obtained by a greater 
number of expansions of steam of higher pressures, and the greater the 
number of expansions for a given initial pressure the lower the mean 
effective pressure. The following table gives approximately the figures 
of mean total and effective pressures for the different types of engines, 
together with the factor by which the square of the diameter is to be 
multiplied to obtain the horse-power at most economical loading, for a 
piston-speed of 600 ft. per minute. 



Type of Engine. _ 



"3 » oi 


"3 i 


"rid r 
.S"o g 


1 Ratio Mean 
Total to 
Initial 
Pressure. 


II 

d w ™; 


W gj d 
Eh 


a> © 2 

0>-*> CO 


IS 

i. o> 

d q. 
o . 



A.<5 



Non-condensing. 



Single Cylinder . 

Compound 

Triple 

Quadruple 



100 


5. 


20 


0.522 


52.2 


15.5 


120 


7.5 


16 


.402 


48.2 


15.5 


160 


10. 


16 


.330 


52.8 


15.5 


200 


12.5 


16 


.282 


56.4 


15.5 



36.7 i 
32.7 
37.3 
40.9 I 



0.524 
467 
533 
584 







Condensing Engines. 










Single Cylinder . . 

Compound 

Triple 

Quadruple 


100 
120 
160 
200 


10. 
15. 

20. 
25. 


10 
8 
8 
8 


0.330 
.247 
.200 
.169 


33.0 
29.6 
32.0 
33.8 


2 
2 
2 
2 


31.0 
27.6 
30.0 
31.8 


600 


0.443 
.390 
.429 
.454 



For any other piston-speed than 600 ft. per min., multiply the figures 
In the last column by the ratio of the piston-speed to 600 ft. 

Horse-power Constant of a given Engine for a Fixed Speed = 

product of its area of piston in square inches, length of stroke in feet 

and number of single strokes per minute divided by 33,000, or ' 

oo, UUU 

= C. The product of the mean effective pressure as found by the dia- 
gram and this constant is the indicated horse-power. 

Horse-power Constant of any Engine of a given Diameter of 
Cylinder, whatever the length of stroke, = area of piston -*- 33,000 = square 
of the diameter of piston in inches X 0.0000238. A table of constants 
derived from this formula is given on page 943. 

The constant multiplied by the piston-speed in feet per minute and 
by the M.E.P. gives the I.H.P. 

Table of Engine Constants for Use in Figuring Horse-power. — 
"Horse-power constant" for cylinders from 1 inch to 60 inches in diam- 
eter, advancing by 8ths. for one foot of piston-speed per minute and one 
pound of M.E.P. Find the diameter of the cylinder in the column at the 
side. If the diameter contains no fraction the constant will be found in, 
the column headed Even Inches. If the diameter is not in even inches, 
follow the line horizontally to the column corresponding to the required 
fraction. The constants multiplied by the piston-speed and by the 
M.E.P. give the horse-power. 



THE STEAM-ENGINE. 



Engine Constants, 


Constant X Piston Speed X M.E.P. = H.P. 


Diam. of 
Cylinder. 


Even 
Inches. 


+ 1/8 


+ V4 


+ 3/8 


+ 1/2 


+ 5/ 8 


+ 3/4 


+ 7/8 


1 


.0000238 


.0000301 


.0000372 


.0000450 


.0000535 


.0000628 


. 0000729 


.0000837 


2 


.0000952 


.0001074 


.0001205 


.0001342 


.0u01487 


.0001640 


.0001800 


.0001967 


3 


.0002142 


.0002324 


.0002514 


.000/711 


.0u02915 


.0003127 


. 0003347 


.0003574 


4 


.0003808 


.0004050 


.0004299 


.0004554 


.0004819 


.0005091 


. 000537C 


.0005656 


5 


.0005950 


.0006251 


.0006560 


.0006876 


.0007199 


. 0007530 


.0007869 


.0008215 


6 


.0008568 


.0008929 


.0009297 


. 0009672 


.0010055 


. 0010445 


.0010844 


.0011249 


7 


.0011662 


.0012082 


.0012510 


.0012944 


.0013387 


.0013837 


.0014295 


.0014759 


8 


.0015232 


.0015711 


.0016198 


.0016693 


.0017195 


.0017705 


.0018222 


.0018746 


9 


.0019278 


.0019817 


.0020363 


.0020916 


.0021479 


. 0022048 


.002262! 


.0023209 


10 


.0023800 


.0024398 


.0025004 


.0025618 


. 0026239 


. 0026867 


.0027502 


.0028147 


11 


.0028798 


.0029456 


.0030121 


. 0030794 


.0031475 


.0032163 


.003285? 


.0033561 


12 


.0034272 


.0034990 


.0035714 


. 0036447 


. 0037187 


.0037934 


.003869C 


.0039452 


13 


.0040222 


.0040999 


.0041783 


. 0042576 


. 0043375 


.0044182 


.004499; 


.0045819 


14 


.0046648 


.0047484 


.0048328 


. 0049181 


. 005003? 


.0050906 


C05178C 


.0052661 


15 


.0053550 


.0054446 


.0055349 


. 0056261 


.005717? 


.0058105 


.005903? 


.0059979 


16 


.0060928 


.0061884 


.0062847 


.0063817 


. 0064795 


.0065780 


.0066774 


.0067774 


17 


.0068782 


.0069797 


.0070819 


. 0071850 


. 007288} 


.0073932 


.0074985 


.0076044 


18 


.0077112 


.0078187 


.0079268 


. 0080360 


.0081452 


.0082560 


.0083672 


.0084791 


19 


.0085918 


.0087052 


.0088193 


. 0089343 


. C09049C 


.0091663 


.0092835 


.0094013 


20 


.0095200 


.0096393 


.0097594 


. 0098803 


.010001* 


.0101243 


.0102474 


.0103712 


21 


.0104958 


.0106211 


.0107472 


. 0108739 


.011001! 


.0111299 


.0112589 


.0113886 


22 


.0115192 


.0116505 


.0117825 


.0119152 


.012048} 


.0121830 


.0123179 


.0124537 


23 


.0125902 


.0127274 


.0128654 


.0130040 


.013143! 


.0132837 


.0134247 


.0135664 


24 


.0137088 


.0138519 


.0139959 


.0141405 


.014285 C 


.0144321 


.0145789 


.0147266 


25 


.0148750 


.0150241 


.0151739 


.0153246 


.015475 c 


.0156280 


.0157809 


.0159345 


26 


.0160888 


.0162439 


.0163997 


.0165563 


.016713! 


.0168716 


.0170304 


.0171899 


27 


.0173502 


.0175112 


.0176729 


.0178355 


.017998* 


.0181627 


.0183275 


.0184929 


28 


.0186592 


.0188262 


.0189939 


.0191624 


.01933ie 


.0195015 


.0196722 


.0198436 


29 


.0200158 


.0201887 


.0203634 


. 0205368 


.020711? 


.0208879 


.0210645 


.0212418 


30 


.0214200 


.0215988 


.0217785 


.0219588 


.022139? 


.0223218 


.0225044 


.0226877 


31 


.0228718 


.0230566 


.0232422 


. 0234285 


.023615! 


.0238033 


.0239919 


.0241812 


32 


.0243712 


.0245619 


.0247535 


. 0249457 


.025138/ 


.0253325 


.0255269 


.0257222 


33 


.0259182 


.0261149 


.0263124 


.0265106 


.026709! 


.0269092 


.0271097 


.0273109 


34 


.0275128 


.0277155 


.0279189 


.0281231 


.028327? 


.0285336 


.0287399 


.0289471 


35 


.0291550 


.0293636 


.0295729 


.0297831 


.029993? 


.0302056 


.0304179 


.0306309 


36 


.0308448 


.0310594 


.0312747 


.0314908 


.0317075 


.0319251 


.0321434 


.0323624 


37 


.0325822 


.0328027 


.0330239 


. 0332460 


.0334687 


.0336922 


.0339165 


.0341415 


38 


.0343672 


.0345937 


.0348209 


. 0350489 


.0352775 


.0355070 


.0357372 


.0359681 


39 


.0361998 


.0364322 


.0366654 


. 0368993 


.037133? 


.0373694 


.0376055 


.0378424 


40 


.0380800 


.0383184 


.0385575 


. 0387973 


.0390379 


.0392793 


.0395214 


.0397642 


41 


.0400078 


.0402521 


.0404972 


. 0407430 


. 0409895 


.0412368 


.0414849 


.0417337 


42 


.0419832 


.0422335 


.0424845 


. 0427362 


. 0429887 


.0432420 


.0434959 


.0437507 


43 


.0440062 


.0442624 


.0445194 


.0447771 


. 0450355 


.0452947 


.0455547 


.0458154 


44 


.0460768 


.0463389 


.0466019 


. 0468655 


.0471299 


.0473951 


.0476609 


.0479276 


45 


.0481950 


.0484631 


. 0487320 


.0490016 


.0492719 


.0495430 


.0498149 


.0500875 


46 


.0503608 


.0506349 


. 0509097 


.0511853 


.0514615 


.0517386 


.0520164 


.0522949 


47 


.0525742 


.0528542 


.0531349 


.0534165 


. 0536988 


.0539818 


.(542655 


.0545499 


48 


.0548352 


.0551212 


. 0554079 


. 0556953 


. 0559835 


.0562725 


.0565622 


.0568526 


49 


.0571438 


.0574357 


. 0577284 


.0580218 


.0583159 


.0586109 


.0589065 


.0592029 


50 


.0595000 


.0597979 


. 0600965 


. 0603959 


. 0606959 


.0609969 


.0612984 


.0616007 


51 


.0619038 


.0622076 


.0625122 


.0628175 


. 0632235 


.0634304 


.0637379 


.0640462 


52 


.0643552 


.0646649 


.0649753 


. 0652867 


.0655987 


.0659115 


.0662250 


.0665392 


53 


.0668542 


.0671699 


. 0674864 


. 0678036 


.0681215 


.0684402 


.0687597 


.0690799 


54 


.0694008 


.0697225 


. 0700449 


. 0703681 


.0705293 


.0710166 


.0713419 


.0716681 


55 


.0719950 


.0724226 


.0726510 


. 0729801 


. 0733099 


.0736406 


.0739719 


.0743039 


56 


.0746368 


.0749704 


.0753047 


. 0756398 


. 0759755 


.0763120 


. 0766494 


.0769874 


57 


.0773262 


.0776657 


.0780060 


.0783476 


. 0786887 


.0790312 


.0793745 


.0797185 


58 


.0800632 


.0804087 


.0807549 


.0811019 


.0814495 


.0817980 


.0821472 


.0824971 


59 


.0828478 


.0831992 


.0835514 


.0839043 


.0842579 


.0846123 


0849675 


.0853234 


60 


.0856800 


.0860374 


.0863955 


.0867543 


.0871139 


.0874743 


0878354 


.0881973 



INDICATED HORSE-POWER OF ENGINES. 



943 



Horse-power per Pound Mean Effective Pressure. 

Formula, Area in sq. in. X piston-speed -*- 33,000. 



Diam of 
Cylinder, 
inches. 


Speed of Piston in feet per minute. 


100 


200 


300 


400 


500 


600 


700 


800 


900 


4 


.0381 


.0762 


.1142 


.1523 


.1904 


.2285 


.2666 


.3046 


.3427 


41/2 


.0482 


.0964 


.1446 


.1928 


.2410 


.2892 


.3374 


.3856 


.4338 


5 


.0595 


.1190 


.1785 


.2380 


.2975 


.3570 


.4165 


.4760 


.5355 


51/2 


.0720 


.1440 


.2160 


.2880 


.3600 


.4320 


.5040 


.5760 


.6480 


6 


.0857 


.1714 


.2570 


.3427 


.4284 


.5141 


.5998 


.6854 


.7711 


61/2 


.1006 


.2011 


.3017 


.4022 


.5028 


.6033 


.7039 


.8044 


.9050 


7 


.1166 


.2332 


.3499 


.4665 


.5831 


.6997 


.8163 


.9330 


1.0496 


71/2 


.1339 


.2678 


.4016 


.5355 


.6694 


.8033 


.9371 


1.0710 


1.2049 


8 


.1523 


.3046 


.4570 


.6093 


.7616 


.9139 


1 .0662 


1.2186 


1 .3709 


81/2 


.1720 


.3439 


.5159 


.6878 


.8598 


1.0317 


1.2037 


1 .3756 


1.5476 


9 


.1928 


.3856 


.5783 


.7711 


.9639 


1.1567 


1.3495 


1.5422 


1.7350 


91/2 


.2148 


.4296 


.6444 


.8592 


1.0740 


1.2888 


1.5036 


1.7184 


1.9532 


10 


.2380 


.4760 


.7140 


.9520 


1.1900 


1.4280 


1.6660 


1 .9040 


2.1420 


11 


.2880 


.5760 


.8639 


1.1519 


1.4399 


1.7279 


2.0159 


2.3038 


2.5818 


12 


.3427 


.6854 


1.0282 


1.3709 


1.7136 


2.0563 


2.3990 


2.7418 


3.0845 


13 


.4022 


.8044 


1.2067 


1.6089 


2.0111 


2.4133 


2.8155 


3.2178 


3.6200 


14 


.4665 


.9330 


1 .3994 


1.8659 


2.3324 


2.7989 


3.2654 


3.7318 


4.1983 


15 


.5355 


1.0710 


1.6065 


2.1420 


2.6775 


3.2130 


3.7485 


4.2840 


4.8195 


16 


.6093 


1.2186 


1.8278 


2.4371 


3.0464 


3.6557 


4.2650 


4.8742 


5.4835 


17 


.6878 


1.3756 


2.0635 


2.7513 


3.4391 


4.1269 


4.8147 


5.5026 


6.1904 


18 


.7711 


1.5422 


2.3134 


3.0845 


3.8556 


4.6267 


5.3978 


6.1690 


6.9401 


19 


.8592 


1.7184 


2.5775 


3.4367 


4.2959 


5.1551 


6.0143 


6.8734 


7.7326 


20 


.9520 


1.9040 


2.8560 


3.8080 


4.7600 


5.7120 


6.6640 


7.6160 


8.5680 


21 


1 .0496 


2.0992 


3.1488 


4.1983 


5.2479 


6.2975 


7.3471 


8.3966 


9.4462 


22 


1.1519 


2.3038 


3.4558 


4.6077 


5.7596 


6.9115 


8.0634 


9.2154 


10.367 


23 


1.2590 


2.5180 


3.7771 


5.0361 


6.2951 


7.5541 


8.8131 


10.072 


11.331 


24 


1 .3709 


2.7418 


4.1126 


5.4835 


6.8544 


8.2253 


9.5962 


10.967 


12.338 


25 


1.4875 


2.9750 


4.4625 


5.9500 


7.4375 


8.9250 


10.413 


11.900 


13.388 


26 


1 .6089 


3.2178 


4.8266 


6.4355 


8.0444 


9.6534 


11.262 


12.871 


14.480 


27 


1.7350 


3.4700 


5.2051 


6.9401 


8.6751 


10.410 


12.145 


13.880 


15.615 


28 


1.8659 


3.7318 


5.5978 


7.4637 


9.3296 


11.196 


13.061 


14.927 


16.793 


29 


2.0016 


4.0032 


6.0047 


8.0063 


10.008 


12.009 


14.011 


16.013 


18.014 


30 


2.1420 


4.2840 


6.4260 


8.5680 


10.710 


12.852 


14.994 


17.136 


19.278 


31 


2.2872 


4.5744 


6.8615 


9.1487 


11.436 


13.723 


16.010 


18.297 


20.585 


32 


2.4371 


4.8742 


7.3114 


9.7485 


12.186 


14.623 


17.060 


14.497 


21 .934 


33 


2.5918 


5.1836 


7.7755 


10.367 


12.959 


15.551 


18.143 


20.735 


23.326 


34 


2.7513 


5.5026 


8.2538 


11.005 


13.756 


16.508 


19.259 


22.010 


24.762 


35 


2.9155 


5.8310 


8.7465 


11.662 


14.578 


17.493 


20.409 


23.324 


26.240 


36 


3.0845 


6.1690 


9.2534 


12.338 


15.422 


18.507 


21.591 


24.676 


27.760 


37 


3.2582 


6.5164 


9.7747 


13.033 


16.291 


19.549 


22.808 


26.066 


29.324 


38 


3.4367 


6.8734 


10.310 


13.747 


17.184 


20.620 


24.057 


27.494 


30.930 


39 


3.6200 


7.2400 


10.860 


14.480 


18.100 


21.720 


25.340 


28.960 


32.580 


40 


3.8080 


7.6160 


11:424 


15.232 


19.040 


22.848 


26.656 


30.464 


34.272 


41 


4.0008 


8.0016 


12.002 


16.003 


20.004 


24.005 


28.005 


32.006 


36.007 


42 


4.1983 


8.3866 


12.585 


16.783 


20.982 


25.180 


29.378 


33.577 


37.775 


43 


4.4006 


8.8012 


13.202 


17.602 


22.003 


26.404 


30.804 


35.205 


39.606 


44 


4.6077 


9.2154 


13.823 


18.431 


23.038 


27.646 


32.254 


36.861 


41.469 


45 


4.8195 


9.6390 


14.459 


19.278 


24.098 


28.917 


33.737 


38.556 


43.376 


46 


5.0361 


10.072 


15.108 


20.144 


25.180 


30.216 


35.253 


40.289 


45.325 


47 


5.2574 


10.515 


15.772 


21 .030 


26.287 


31.545 


36.802 


42.059 


47.317 


48 


5.4835 


10.967 


16.451 


21.934 


27.418 


32.901 


38.385 


43.868 


49.352 


49 


5.7144 


11.429 


17.143 


22.858 


28.572 


34.286 


40.001 


45.715 


51.429 


50 


5.9500 


11.900 


17.850 


23.800 


29.750 


35.700 


41.650 


47.600 


53.550 


51 


6.1904 


12.381 


18.571 


24.762 


30.952 


37.142 


43.333 


49.523 


55.713 


52 


6.4355 


12.871 


19.307 


25.742 


32.178 


38.613 


45.049 


51.484 


57.920 


53 


6.6854 


13.371 


20.056 


26.742 


33.427 


40.113 


46.798 


53.483 


60.169 


54 


6.9401 


13.880 


20.820 


27.760 


34.700 


41.640 


48.581 


55.521 


62.461 


55 


7.1995 


14.399 


21.599 


28.798 


35.998 


43.197 


50.397 


57.596 


64.796 


56 


7.4637 


14.927 


22.391 


29.855 


37.318 


44.782 


52.246 


59.709 


67.173 


57 


7.7326 


15.465 


23.198 


30.930 


38.663 


46.396 


54.128 


61.861 


69.597 


58 


8.0063 


16.013 


24.019 


32.025 


40.032 


48.038 


56.044 


64.051 


72.054 


59 


8.2848 


16.570 


24.854 


33.139 


41.424 


49.709 


57.993 


66.278 


74.563 


60 


8.5680 


17.136 


25.704 


34.272 


42.840 


51.408 159.976 


68.544 


77.112 



944 



THE STEAM-ENGINE. 



Nominal Horse-power. — The term " nominal horse-power ' 'originated 
in the time of Watt, and was used to express approximately the power 
of an engine as calculated from its diameter, estimating the mean pressure 
in the cylinder at 7 lbs. above the atmosphere. It has long been obsolete. 

Horse-power Constant of a given Engine for Varying Speeds = 
product of its area of piston and length of stroke divided by 33,000. 
This multiplied by the mean effective pressure and by the number of 
single strokes per minute is the indicated horse-power. 

To draw the Clearance-line on the Indicator-diagram, the ac- 
tual clearance not being known. — The clearance-line may be obtained 
approximately by drawing a straight line, chad, across the compression 




Fig. 156. 
curve first having drawn OX parallel to the atmospheric line and 14.7 
lbs. below. Measure from a the distance ad, equal to cb, and draw YO 
perpendicular to OX through d; then will TB divided by AT be the per- 
centage of clearance. The clearance may also be found from the expan- 
sion-line by constructing a rectangle efhg, and drawing a diagonal gf 
to intersect the line XO. This will give the point O, and by erecting a 
perpendicular to XO we obtain a clearance-line OY. 

Both these methods for finding the clearance require that the expan- 
sion and compression curves be hyperbolas. Prof. Carpenter (Power, 
Sept., 1893) says that with good diagrams the methods are usually very 
accurate, and give results which check substantially. 

The Buckeye Engine Co., however, says that, as the results obtained are 
seldom correct, being sometimes too little, but more frequently too much, 
and as the indications from the two curves seldom agree, the operation 
has little practical value, though when a clearly defined and apparently 
undistorted compression curve exists of sufficient extent to admit of the 
application of the process, it may be "relied on to give much more correct 
results than the expansion curve. 

To draw the Hyperbolic Curve on the Indicator-diagram. — Select 
any point I in the actual curve, and 
from this point draw a line perpen- 
dicular to the line JB, meeting the 
latter in the point J. The line JB 
may be the line of boiler-pressure, 
but this is not material; it may be 
drawn at any convenient height near 
the top of the diagram and parallel 
to the atmospheric line. From / 
draw a diagonal to K, the latter 
point being the intersection of the 
vacuum and clearance lines; from Z 
draw IL parallel with the atmos- 
pheric line. From L, the point of 



J 3 2 1 M 


E 


l^MT" 


r. 


C_ Lj^oo/ 




^^i. 



Fig. 157. 



intersection of the diagonal JK and the horizontal line IL, draw the verti- 



WATER CONSUMPTION OF ENGINES. 945 

c&l line LM . The point M is the theoretical point of cut-off, and LM the 
cut-off line. Fix upon any number of points 1, 2, 3, etc., on the line JB, 
and from these points draw diagonals to K. From the intersection of these 
diagonals with LM draw horizontal lines, and from 1,2, 3, etc., vertical 
lines. Where these lines meet will be points in the hyperbolic curve. 

Theoretical Water-consumption calculated from the Indicator- 
card. — The following method is given by Prof. Carpenter (Power, 
Sept., 1893): p = mean effective pressure, I = length of stroke in feet! 
a = area of piston in square inches, a -s- 144 = area in square feet, c = 
percentage of clearance to the stroke, b = percentage of stroke at point 
where water rate is to be computed, n = number of strokes per minute, 
60 n = number per hour, w = weight of a cubic foot of steam having a 
pressure as shown by the diagram corresponding to that at the point where 
water rate is required, w' = that corresponding to pressure at end of 
compression. 

Number of cubic feet per stroke = 1 (v^tt! ttt* 
\ 100 / 144 

Corresponding weight of steam per stroke in lbs. =1 ( .. . J - 



Volume of clearance — . 

14,400 



Weight of steam in clearance = 



144 
lea 



14,400 

Total weight of I , ( b + c \ wa _ leaw' la Uh ,. 9n M „« 

steam per stroke / \ 100 / 144 14,400 14,400 u T ; w ~ cw J ' 



Total weight of steam ) = 60 nla 
from diagram per hour) 14,400 L 



- c) w — cw']. 



The indicated horse-power is plan + 33,000. Hence the steam-con- 
sumption per hour per indicated horse-power is 

60 nla _., , . ., 

14400 [(& + C)W - CW] 137.50 r ^ , 

JU^ — 7T-[(6 + »-«•]. 

33,000 

Changing the formula to a rule, we have: To find the water rate from 
the indicator diagram at any point in the stroke. 

Rule. — To the percentage of the entire stroke which has been com- 
pleted by the piston at the point under consideration add the percentage 
of clearance. Multiply this result by the weight of a cubic foot of steam, 
having a pressure of that at the required point. Subtract from this the 
product of percentage of clearance multiplied by weight of a cubic foot 
of steam having a pressure equal to that at the end of the compression. 
Multiply this result by 137.50 divided by the mean effective pressure.* 

Note. — This method applies only to points in the expansion curve 
or between cut-off and release. 

The beneficial effect of compression in reducing the water-consumption 
of an engine is clearly shown by the formula. If the compression is 
carried to such a point that it produces a pressure equal to that at the 
point under consideration, the weight of steam per cubic foot is equal, 
and w = w'. In this case the effect of clearance entirely disappears, and 
137 5 

the formula becomes — (bw). 

V 

In case of no compression, w' becomes zero, and the water-rate = 

137.5 .„ , . , 
— — [(b + c) w]. 

* For compound or triple-expansion engines read: divided by the equiv- 
alent mean effective pressure, on the supposition that all work is done 
in one cylinder. 



946 



THE STEAM-ENGINE. 



Prof. Denton {Trans. A. S. M. E., xiv, 1363) gives the following table 
of theoretical water-consumption for a perfect Mariotte expansion with 
steam at 150 lbs. above atmosphere, and 2 lbs. absolute back pressure; 




The difference between the theoretical water-consumption found by the 
formula and the actual consumption as found by test represents " water 
not accounted for by the indicator," due to cylinder condensation, leak- 
age through ports, radiation, etc. 

Leakage of Steam. — Leakage of steam, except in rare instances, has 
so little effect upon the lines of the diagram that it can scarcely be 
detected. The only satisfactory way to determine the tightness of an 
engine is to take it when not in motion, apply a full boiler-pressure to 
the valve, placed in a closed position, and to the piston as well, which 
is blocked for the purpose at some point away from the end of the stroke, 
and see by the eye whether leakage occurs. The indicator-cocks provide 
means for bringing into view steam which leaks through the steam- 
valves, and in most cases that which leaks by the piston, and an opening 
made in the exhaust-pipe or observations at the atmospheric escape- 
pipe, are generally sufficient to determine the fact with regard to the 
exhaust-valves. 

The steam accounted for by the indicator should be computed for both 
the cut-off and the release points of the diagram. If the expansion-line 
departs much from the hyperbolic curve a very different result is shown 
at one point from that shown at the other. In such cases the extent of 
the loss occasioned by cylinder condensation and leakage is indicated in a 
much more truthful manner at the cut-off than at the release. (Tabor 
Indicator Circular.) 

COMPOUND ENGINES. 

Compound, Triple- and Quadruple-expansion Engines. — A com- 
pound engine is one having two or more cylinders, and in which the steam 
after doing work in the first or high-pressure cylinder completes its 
expansion in the other cylinder or cylinders. 

The term "compound" is Commonly restricted, however, to engines in 
which the expansion takes place in two stages only — high and low 
pressure, the terms triple-expansion and quadruple-expansion engines 
being used when the expansion takes place respectively in trree and 
four stages. The number of cylinders may be greater than the number 
of stages of expansion, for constructive reasons; thus in the compound or 
two-stage expansion engine the low-pressure stage may be effected in two 
cylinders so as to obtain the advantages of nearly equal sizes of cylinders 
and of three cranks at angles of 120°. In triple-expansion engines there 
are frequently two low-pressure cylinders, one of them being placed 
tandem with the high-pressure, and the other with the intermediate 
cylinder, as in mill engines with two cranks at 90°. In the triple-expan- 
sion engines of the steamers Campania and Lucania, with three cranks at 
120°, there are five cylinders, two high, one intermediate, and two low, 
the high-pressure cylinders being tandem with the low. 

Advantages of Compounding. — The advantages secured by divid- 
ing the expansion into two or more stages are twofold: 1. Reduction 
of wastes of steam by cylinder-condensation, clearance, and leakage; 
2. Dividing the pressures on the cranks, shafts, etc., in large engines so 
as to avoid excessive pressures and consequent friction. The diminished 



COMPOUND ENGINES. 



947 



loss by cylinder-condensation is effected by decreasing the range of tem- 
perature of the metal surfaces of the cylinders, or the difference of tempera- 
ture of the steam at admission and exhaust. When high-pressure steam 
is admitted into a single-cylinder engine a large portion is condensed by 
the comparatively cold metal surfaces; at the end of the stroke and during 
the exhaust the water is re-evaporated, but the steam so formed escapes 
into the atmosphere or into the condenser, doing no work; while if it is 
taken into a second cylinder, as in a compound engine, it does work. 
The steam lost in the first cylinder by leakage and clearance also does 
work in the second cylinder. Also, if there is a second cylinder, the 
temperature of the steam exhausted from the first cylinder is higher than 
if there is only one cylinder, and the metal surfaces therefore are not 
cooled to the same degree. The difference in temperatures and in pres- 
sures corresponding to the work of steam of 150 lbs. gauge-pressure ex- 
panded 20 times, in one, two, and three cylinders, is shown in the 
following table, by W. H. Weightman, Am. Mach., July 28, 1892: 



Diameter of cylinders, in. . 

Area ratios 

Expansions 

Initial steam-pressures — 

absolute — pounds 

Mean pressures, pounds. . . 
Mean effective pressures, 

pounds 

Steam temperatures into 

cylinders , 

Steam temperatures out 

of the cylinders 

Difference in temperatures 



Single 
Cyl- 
inder. 



165 
32.96 



28.96 
366° 



184.2° 
181.8 



Compound 
Cylinders. 



33 
1 
5 

165 
86.11 

53.11 

366° 

259.9° 
106.1 



61 
3.416 



33 
19.68 



15.68 
259.9° 



184.2° 
75.7 



Triple-expansion 
Cylinders. 



165 

121.44 



60.64 
366° 



293.5° 
72.5 



46 
2.70 
2.714 

60.8 
44.75 

22.35 

293.5° 

234.1° 
59.4 



61 

4.740 
2.714 

22.4 
16.49 

12.49 

234.1° 

184.2° 
49.9 



"Woolf " and Receiver Types of Compound Engines. — The 

compound steam-engine, consisting of two cylinders, is reducible to two 
forms, 1, in which the steam from the h.p. cylinder is exhausted direct 
into the l.p. cylinder, as in the Woolf engine; and 2, in which the steam 
from the h.p. cylinder is exhausted into an intermediate reservoir, whence 
the steam is supplied to, and expanded in, the l.p. cylinder, as in the 
" receiver-engine. " 

If the steam be cut off in the first cylinder before the end of the stroke, 
the total ratio of expansion is the product of the two ratios of expansion; 
that is, the product of the ratio of expansion in the first cylinder, into the 
ratio of the volume of the second to that of the first cylinder. 

Thus, let the areas of the first and second cylinders be as 1 to 31/2, the 
strokes being equal, and let the steam be cut off in the first at 1/2 stroke; 
then 

Expansion in the 1st cylinder 1 to 2 

Expansion in the 2d cylinder , 1 to 31/2 



Total or combined expansion, the product of the two ratios 1 to 7 

Woolf Engine, without Clearance — Ideal Diagrams. — The 

diagrams of pressure of an ideal Woolf engine are shown in Fig. 158, as 
they would be described by the indicator, according to the arrows. In 
these diagrams pq is the atmospheric line, mn the vacuum line, cd the 
admission line, dg the hyperbolic curve of expansion in the first cylinder, 
and gh the consecutive expansion-line of back pressure for the return- 
stroke of the first piston, and of positive pressure for the steam-stroke 
of the second piston. At the point h, at the end of the stroke of the 
second piston, the steam is exhausted into the condenser, and the pressure 
falls to the level of perfect vacuum, mn. 



948 



THE STEAM-ENGINE. 



The diagram of the second cylinder, below gh, is characterized by the 
absence of any specific period of admission; the whole of the steam-line 
gh being expansional, generated by the 
expansion of the initial body of steam 
r n . contained in the first cylinder into the 
Mbs - second. When the return-stroke is 
completed, the whole of the steam 
transferred from the first is shut into 
the second cylinder. The final pres- 
sure and volume of the steam in the 
second cylinder are the same as if the 
whole of the initial steam had been 
admitted at once into the second cylin- 
der, and then expanded to the end of 
the stroke in the manner of a single- 
cylinder engine. The net work of the 
steam is also the same, according to 
both distributions. 

Receiver-engine, without Clear- 
ance — Ideal Diagrams. — In the 
Fig. 158. - Woolf Engine, Ideal j deal receiver-engine the pistons of the 
Indicator-diagrams. two cylinders are connected to cranks 

at right angles to each other on the 
same shaft. The receiver takes the steam exhausted from the first cylin- 
der and supplies it to the second, in which the steam is cut off and then 
expanded to the end of the stroke. On the assumption that the initial 
pressure in the second cylinder is equal to the final pressure in the first, 
and of course eaual to the pressure in the receiver, the volume cut off in 
the second cylinder must be equal to the volume of the first cylinder, for 
the second cylinder must admit as much steam at each stroke as is dis- 
charged from the first cylinder. 

In Fig. 159, cd is the line of admission and hg the exhaust-line for the 
first cylinder; and dg is the expansion-curve and pq the atmospheric line. 

& G ^ do 




fj 




y 


I 






^y 




p 






2 

1 

3 



^60 lbs 








r 












rd* 




-40 


i — 


—%- 




-W--» 




-20 






i 
/ 


/ 


h 




- P 

k 
-o 7 


— ^ 




1 



Fig. 159. — Receiver-engine, 
Ideal Indicator-diagram. 



Fig. 160. —Receiver Engine, Ideal 
Diagrams Reduced and Combined. 
In the region below the exhaust-line of the first cylinder, between it and 
the line of perfect vacuum, ol, the diagram of the second cylinder is 
formed; hi, the second line of admission, coincides with the exhaust-line 
hg of the first cylinder, showing in the ideal diagram no intermediate 
fall of pressure, and ik is the expansion-curve. The arrows indicate 
the order in which the diagrams are formed. 

In the action of the receiver-engine, the expansive working of the 
steam, though clearly divided into two consecutive stages, is, as in the 
Woolf engine, essentially continuous from the point of cut-off in the first 
cylinder to the end of the stroke of the second cylinder, where it is 
delivered to the condenser; and the first and second diagrams may be 
placed together and combined to form a continuous diagram. For this 
purpose take the second diagram as the basis of the combined diagram, 
namely, hiklo, Fig. 160. The period of admission, hi, is one-third of the 
Stroke, and as the ratios of the cylinders areas 1 to 3, hi is also the propor^ 



COMPOUND ENGINES. 



949 



tional length of the first diagram as applied to the second. Produce oh up- 
wards, and set off oc equal to the total height of the first diagram above the 
vacuum-line; and, upon the shortened base/a, and the height he, complete 
the first diagram with the steam-line cd and the expansion line di. 

It is shown by Clark (S. E., p. 432 et seq.) in a series of arithmetical calcu- 
lations, that the receiver-engine is an elastic system of compound engine, in 
which considerable latitude is afforded for adapting the pressure in the re- 
ceiver to the demands of the second cylinder, without considerably dimin- 
ishing the effective work of the engine. In the Woolf engine, on the 
contrary, it is of much importance that the intermediate volume of space 
between the first and second cylinders, which is the cause of an interme- 
diate fall of pressure, should be reduced to the lowest practicable amount. 

Supposing that there is no loss of steam in passing through the engine, 
by cooling and condensation, it is obvious that whatever steam passes 
through the first cylinder must also find its way through the second 
cylinder. By varying, therefore, in the receiver-engine, the period of 
admission in the second cylinder, and thus also the volume of steam ad- 
mitted for each stroke, the steam will be measured into it at a higher 
pressure and of a less bulk, or at a lower pressure and of a greater bulk; 
the pressure and density naturally adjusting themselves to the volume 
that the steam from the receiver is permitted to occupy in the second 
cylinder. With a sufficiently restricted admission, the pressure in the 
receiver may be maintained at the pressure of the steam as exhausted 
from the first cylinder. On the contrary, with a wider admission, the 
pressure in the receiver may fall or "drop" to three-fourths or even one- 
half of the pressure of the exhaust steam from the first cylinder. 

(For a more complete discussion of the action of steam in the Woolf 
and receiver engines, see Clark on the Steam-engine.) 

Combined Diagrams of Compound Engines. — The only way of 
making a correct combined diagram from the indicator-diagrams of 
the several cylindersj 
in a compound engine' 
is to set off all the 
diagrams on the same 
horizontal scale of vol- 
umes, adding the 
clearances to the cyl- 
inder capacities prop- 
er. When this is 
attended to, the suc- 
cessive diagrams fall 
exactly into their right 
places relatively to one 
another, and would 
compare properly with 
any theroretical ex- 
pansion-curve, (Prof. 
A. B. W. Kennedy, 
Proc. Inst. M. E., Oct., 
1886.) 

This method of com- 
bining diagrams is 
commonly adopted, 
but there are objec- 
tions to its accuracy, 
since the whole quan- 
tity of steam con- Fig. 161. 
sumed in the first cylinder at the end of the stroke is not carried forward 
to the second, but a part of it is retained in the first cylinder for com- 
pression. For a method of combining diagrams in which compression 
is taken account of, see discussions by Thomas Mudd and others, in Proc. 
Inst M. E., Feb., 1887, p. 48. The usual method of combining diagrams 
is also criticised by Frank H. Ball as inaccurate and misleading {Am. 
Mach., April 12, 1894; Trans. A. S. M. E., xiv, 1405, and xv, 403). 

Figure 161 shows a combined diagram of a quadruple-expansion engine, 
drawn according to the usual method, that is, the diagrams are first 
reduced in length to relative scales that correspond with the relative 




950 THE STEAM-ENGINE. 

piston-displacement of the three cylinders. Then the diagrams are 
placed at such distances from the clearance-line of the proposed combined 
diagram as to represent correctly the clearance in each cylinder. 

Proportions of Cylinders in Compound Engines. — Authorities 
differ as to the proportions by volume of the high and low pressure 
cylinders v and V. _ Thus Grashof gives V -f- v = 0.85 Vr; Hrabak, 
0.90 Vr; Werner, Vr; and Rankine, \/r 2 , r being the ratio of expansion. 
Busley makes the ratio dependent on the boiler-pressure thus: 

Lbs. per sq. in 60 90 105 120 

V + v =3 4 4.5 5 

(See Seaton's Manual, p. 95, etc., for analytical method; Sennett, p. 496, 
etc.; Clark's Steam-engine, p. 445, etc.; Clark's Rules, Tables, Data, p. 849, 
etc.) 

Mr. J. McFarlane Gray states that he finds the mean effective pressure 
in the compound engine reduced to the low-pressure cylinder to be approx- 
imately the square root of 6 times the boiler-pressure. 

Ratio of Cylinder Capacity in Compound Marine Engines. (Sea- 
ton.) — The low-pressure cylinder is the measure of the power of a com- 
pound engine, for so long as the initial steam-pressure and rate of expansion 
are the same, it signifies very little, so far as total power only is concerned, 
whether the ratio between the low and high pressure cylinders is 3 or 
4; but as the power developed should be nearly equally divided between 
the two cylinders, in order to get a good and steady working engine, 
there is a necessity for exercising a considerable amount of discretion 
in fixing on the ratio. 

In choosing a particular ratio the objects are to divide the power evenly 
and to avoid as much as possible "drop" and high initial strain. [Some 
writers advocate drop in the high-pressure cylinder making it smaller 
than is the usual practice and making the cylinder ratio as high as 6 or 7.] 

If increased economy is to be obtained by increased boiler-pressures 
the rate of expansion should vary with the initial pressure, so that the 
pressure at which the steam enters the condenser should remain constant. 
In this case, with the ratio of cylinders constant, the cut-off in the high- 
pressure cylinder will vary inversely as the initial pressure. 

Let R be the ratio of the cylinders; r the rate of expansion; p t the 
initial pressure: then cut-off. in high-pressure cylinder = R •*- r; r varies 
with pi, so that the terminal pressure p n is constant, and consequently 
r = Pi-i- p n \ therefore, cut-off in high-pressure cylinder — R X p n -5- p\. 

Ratios of Cylinders as Found in Marine Practice. — The rate of 
expansion may be taken at one-tenth of the boiler-pressure (or about one- 
twelfth the absolute pressure), to work economically at full speed. There- 
fore, when the diameter of the low-pressure cylinder does not exceed 
100 inches, and the boiler-pressure 70 lbs., the ratio of the low-pressure 
to the high-pressure cylinder should be 3.5; for a boiler-pressure of 80 lbs., 
3.75; for 90 lbs., 4.0; for 100 lbs., 4.5. If these proportions are adhered 
to, there will be no need of an expansion-valve to either cylinder. If, 
however, to avoid "drop," the ratio be reduced, an expansion-valve 
should be fitted to the high-pressure cylinder. 

Where economy of steam is not of first importance, but rather a large 
power, the ratio of cylinder capacities may with advantage be decreased, 
so that with a boiler-pressure of 100 lbs. it may be 3.75 to 4. 

In tandem engines there is no necessity to divide the work equally. 
The ratio is generally 4, but when the steam-pressure exceeds 90 lbs. 
absolute 4.5 is better, and for 100 lbs. 5.0. 

When the power requires that the l.p. cylinder shall be more than 100 in. 
diameter, it should be divided in two cylinders. In this case the ratio of the 
combined capacity of the two l.p. cylinders to that of the h.p. may be 
3.0 for 85 lbs. absolute, 3.4 for 95 lbs., 3.7 for 105 lbs., and 4.0 for 115 lbs. 

Receiver Space in Compound Engines should be from 1 to 1.5 times 
the capacity of the high-pressure cylinder, when the cranks are at an 
angle of from 90° to 120°. When the cranks are at 180° or nearly this, 
the space may be very much reduced. In the case of triple-compound 
engines, with cranks at 120°, and the intermediate cylinder leading the 
high-pressure, a very small receiver will do. The pressure in the receiver 
should never exceed half the boiler-pressure. (Seaton.) 



COMPOUND ENGINES. 951 



Formula for Calculating the Expansion and the Work of Steam 
in Compound Engines. 

(Condensed from Clark on the "Steam-engine.") 

a = area of the first cylinder in square inches; 
a' = area of the second cylinder in square inches; 
r = ratio of the capacity of the second Cylinder to that of the first; 
L = length of stroke in feet, supposed to be the same for both cylinders 
I = period of admission to the first cylinder in feet, excluding clearance 
c = clearance at each end of the cylinders, in parts of the stroke, in ft. 
U = length of the stroke plus the clearance, in feet; 
V = period of admission plus the clearance, in feet; 
5 = length of a given part of the stroke of the second cylinder, in feet; 
P = total initial pressure in the first cylinder, in lbs. per square inch, 

supposed to be uniform during admission; 
P' = total pressure at the end of the given part of the stroke s; 
p .= average total pressure for the whole stroke; 
R «s= nominal ratio of expansion in the first cylinder, or L -*- I; 
W — actual ratio of expansion in the first cylinder, of L' -i- V ; 
R" — actual combined ratio of expansion, in the first and second cylin- 
ders together; 
n = ratio of the final pressure in the first cylinder to any intermediate 

fall of pressure between the first and second cylinders; 
N — ratio of the volume of the intermediate space in the Woolf engine, 
reckoned up to, and including the clearance of, the second pis- 
ton, to the capacity of the first cylinder plus its clearance. The 
value of N is correctly expressed by the actual ratio of the 
volumes as stated, on the assumption that the intermediate space 
is a vacuum when it receives the exhaust-steam from the first 
cylinder. In point of fact, there is a residuum of unexhausted 
steam in the intermediate space, at low pressure, and the value 
of ./Vis thereby practically reduced below the ratio here stated. 



w = whole net work in one stroke, in foot-pounds. 
Ratio of expansion in the second cylinder: 

Hit* 



Iti the Woolf engine, 
In the receiver-engine 



1+ N 
(n-l)r 



Total actual ratio of expansion = product of the ratios Of the three 
consecutive expansions, in the first cylinder, in the intermediate space, 
and in the second cylinder, 

In the Woolf engine.; R' (r p 4- N\; 
In the receiver-engine, r -p-t of rR f . 



Wofk done in the two cylinders for one stroke, with a givert cut-off 
and a given combined actual ratio of expansion : 

Woolf engine, w = aP [V(l 4- hyp log R") — c\; 
Receiver engine, w^aP ft' (1 + hyp log R") -c ( i + ^p- ) 1 1 
when there is no intermediate fall of pressure. 



952 THE STEAM-ENGINE. 

"When there is an intermediate fall, when the pressure falls to S/ 4 2/3 
1/2 of the final pressure in the 1st cylinder, the reduction of work is 2% 
1.0%, 4.6% of that when there is no fall. ■ ■ ' 

Total work in the two cylinders of a receiver-engine, for one stroke 
for any intermediate fall of pressure, 

Example. — Let a = 1 sq. in., P = 63 lbs., U = 2.42 ft., n = 4, R" =a 
5.969, c = 0.42 ft., r = 3, B' = 2.653; 

w = l X 63 [2.42 (5/ 4 hyp log 5.969) -.42 (l + ^ ^ * ^ 1 =421.55 ft .-lbs. 

Calculation of Diameters of Cylinders of a compound condensing 
engine of 2000 H.P. at a speed of 700 feet per minute, with 100 lbs. boiler- 
pressure. 

100 lbs. gauge-pressure = 115 absolute, less drop of 5 lbs. between 
boiler and cylinder = 110 lbs. initial absolute pressure. Assuming 
terminal pressure in l.p. cylinder = 6 lbs., the total expansion of steam 
in both cylinders == 110 -f- 6 = 18.33. Hyp log 18.33 = 2.909. Back 
pressure in l.p. cylinder, 3 lbs. absolute. 

The following formulae are used in the calculation of each cylinder: 

*. ". - .. . H.P. X 33,000 

(1) Area of cylinder = „ „, ^, - — r— -r- 

' J M.E.P. X piston-speed 

(2) Mean effective pressure = mean total pressure — back pressure. 

(3) Mean total pressure = terminal pressure X (1 + hyp log R). 

(4) Absolute initial pressure = absolute terminal pressure X ratio of 
expansion. 

First calculate the area of the low-pressure cylinder as if all the work 
were done in that cylinder. 

From (3), mean total pressure = 6 X (1 + hyp log 18.33) = 23.454 
lbs. 

From (2), mean effective pressure = 23.454 - 3 = 20.454 lbs. 
2000 X 33 000 

From (1), area of cylinder = ' = 4610 sq. ins. = 76.6ins.diam. 

If half the work, or 1000 H.P.', is done in the l.p. cylinder the M.E.P. 
will be half that found above, or 10.227 lbs., and the mean total pressure 
10.227 + 3 = 13.227 lbs. 

From (3), 1 4- hyp log R = 13.227 -h 6 = 2.2045. 

Hyp log R = 1.2045, whence R in l.p. cyl. = 3.335. 

From (4), 3.335 X 6 = 20.01 lbs. initial pressure in l.p. cyl. and ter- 
minal pressure in h.p. cyl., assuming no drop between cvlinders. 

110 -h 20.01 = 18.33 -h 3.335 = 5.497, R in h.p. cyl. 

From (3), mean total pres. in h.p. cyl. = 20.01 X (1 + hyp log 5.497) 
= 54.11. 

From (2), 54.11 - 20.01 = 34.10, M.E.P. in h.p. cyl. 

/-.x t u i 1000X33,000 100rt . ._. ,. 

From (1), area of h.p. cyl. = ■ — =1382 sq. ins. = 42 ins. diam. 

Cylinder ratio = 4610 h- 1382 = 3.336. 

The area of the h.p. cylinder may be found more directly by dividing 
the area of the l.p. cyl. by the ratio of expansion in that cylinder. 4610 
-4- 3.335 = 1382 sq. ins. 

In the above calculation no account is taken of clearance, of com- 
pression, of drop between cylinders, nor of area of piston-rods. It also 
assumes that the diagram in each cylinder is the full theoretical diagram, 
with a horizontal steam-line and a hyperbolic expansion line, with no 
allowance for rounding of the corners. To make allowance for these, 
the mean effective pressure in each cylinder must be multiplied by a 
diagram factor, or the ratio of the area of an actual diagram of the class 
of engine considered, with the given initial and terminal pressures, to the 
area of the theoretical diagram. Such diagram factors will range from 
0.6 to 0.94, as in the table on p. 932. 

Best Ratios of Cylinders. — The question what is the best ratio of 
areas of the two cylinders of a compound engine is still (1901) a disputed 



TRIPLE-EXPANSION ENGINES. 953 



one, but there appears to be an increasing tendency in favor of large 
ratios, even as great as 7 or 8 to 1, with considerable terminal drop in the 
high-pressure cylinder. A discussion of the subject, together with a 
description of a new method of drawing theoretical diagrams of multiple- 
expansion engines, taking into consideration drop, clearance, and com, 
pression will be found in a paper by Bert C. Ball, in Trans. A. S. M. E.- 
xxi, 1002. 

TRIPLE-EXPANSION ENGINES. 

Proportions of Cylinders. — H. H. Suplee, Mechanics, Nov., 1887, 
gives the following method of proportioning cylinders of triple-expansion 
engines: 

As in the case of compound engines the diameter of the low-pressure 
cylinder is first determined, being made large enough to furnish the entire 
power required at the mean pressure due to the initial pressure and 
expansion ratio given; and then this cylinder is given only pressure enough 
to perform one-third of the work, and the other cylinders are proportioned 
so as to divide the other two-thirds between them. 

Let us suppose that an initial pressure of 150 lbs. is used and that 
900 H.P. is to be developed at a piston-speed of 800 ft. per min., and that 
an expansion ratio of 16 is to be reached with an absolute back-pressure 
of 2 lbs. 

The theoretical M.E.P. with an absolute initial pressure of 150 + 14.7 = 
164.7 lbs. initial at 16 expansions is 

P(! 4- hyp log 16) _ 164 7 x 3^6 _ ^ 

less 2 lbs. back pressure, = 38.83 - 2 = 36.83. 

In practice only about 0.7 of this pressure is actually attained, so that 
36.83 X 0.7 = 25.781 lbs. is the M.E.P. upon which the engine is to be 
proportioned. 

To obtain 900 H.P. we must have 33,000 X 900 = 29,700,000 foot- 
pounds, and this divided by the mean pressure (25.78) and by the speed 
in feet (800) will give 1440 sq. in. as the area of the l.p. cylinder, about 
equivalent to 43 in. diam. 

Now as one-third of the work is to be done in the l.p. cylinder, the 
M.E.P. in it will be 25.78 -h 3 = 8.59 lbs. 

The cut-off in the high-pressure cylinder is generally arranged to cut off 
at 0.6 of the stroke, and so the ratio of the h.p. to the l.p. cylinder is equal 
to 16 X 0.6 = 9.6, and the h.p. cylinder will be 1440 ■*- 9.6 = 150 sq. 
in. area, or about 14 in. diameter, and the M.E.P. in the h.p. cylinder is 
equal to 9.6 X 8.59 = 82.46 lbs. 

If the intermediate cylinder is made a mean size between the other two, 
its size would be determined by dividing the area of the l.p. cylinder by 
the square root of the ratio between the low and the high; but in practice 
this is found to give a result too large to equalize the stresses, so that 
instead the area of the int. cylinder is found by dividing the area of the 
l.p. piston by 1.1 times the square ro ot of the ratio of l.p. to h.p. cylinder, 
which in this case is 1440 -*- (1.1 V9.6) = 422.5 sq. in., or a little more 
than 23 in. diam. 

The choice of expansion ratio is governed by the initial pressure, and is 
generally chosen so that the terminal pressure in the l.p. cylinder shall be 
about 10 lbs. absolute. 

Formulae for Proportioning Cylinder Areas of Triple-Expansion 
Engines. — The following formulae are based on the method of first 
finding the cylinder areas that would be required if an ideal hyperbolic dia- 
gram were obtainable from each cylinder, with no clearance, compression, 
wire-drawing, drop by free expansion in receivers, or loss by cylinder 
condensation, assuming equal work to be done in each cylinder, and 
then dividing the areas thus found by a suitable diagram factor, such as 
those given on page 932, expressing the ratio which the area of an actual 
diagram, obtained in practice from an engine of the type under consider- 
ation, bears to the ideal or theoretical diagram. It will vary in different 
classes of engine and in different cylinders of the same engine, usual 



954 



THE STEAM-ENGINE. 



values ranging from 0.6 to 0.9. When any one of the three stages of 
expansion takes place in two cylinders, the combined area of these cylin- 
ders equals the area found by the formulae. 

Notation. 

pi = Initial pressure in the high-pressure cylinder. 

p t = terminal pressure in the low-pressure cylinder. 
Pb = back pressure in the low-pressure cylinder. 

pt = term press, in h.p. cyl. and initial press, in intermediate cyl. 

P2 = term, press, in int. cyl. and initial press, in l.p. cyl. 

Pi, Ri, Ra. ratio of exp in h.p. int. and l.p. cyls. 

R = total ratio of exp. = Ri X Ri X Rz. 

P = mean effec. press, of the combined ideal diagram, referred to the 
l.p. cyl. 

Pi, P2, P% = M.E.P. in the h.p., int., and l.p. cyls. 
HP = horse-power of the engine = PLA3N ■+ 33,000. 

L = length of stroke in feet: N = number of single strokes per min. 

Ai, At, A3, areas (sq. ins.) of h.p. int. and l.p. cyls. (ideal). 

W = work done in one cylinder per foot of stroke. 

ri = ratio of Ai to A\\ rz = ratio of A3 to Ai. 

F\, Fi, F3, diagram factors of h.p. int. and 1 p. cyl. 

ai, ai, a,3, areas (actual) of h.p. int. and l.p. cyl. 



Formula. 

(1) R = Pi -*■ p t . 

(2) P = p t (1 + hyp log R) - p h . 

(3) Ps = 1/3 P. 

(4) Hyp log R 3 = (P3 - Vt + Vb> + Pt- 
R1R2 = R -*- R3; Ri = Ri = ^RiRi. 



(5) 

(6) p 3 - V t X R3. 

(7) Pi = P3 X Ri. 

(8) m = Pi X Ru 

(9) P 2 = Ps (hyp log 7Z 2 ) = P3R3. 

(10) Pi = Pi (hyp log fli) = P2R2. 

(11) T7 = 11,000 HP -h LiV. 

(12) Ai = W -h Pi; ^2 = W + Pi; A 3 = W -4- P 3 . 

(13) n = A2 -f- Ai = Pi -h P 2 = Ri or P 2 ; r 3 = A3 ■*■ Ai = Pi +■ P 3 . 

(14) ai = Ai *- Pi; a 2 = Ai -4- F 2 ; as = A3 -*■ F z . 

From these formulae the figures in the following tables have been 
calculated: 



Theoretical Mean Effective Pressures, Cylinder Ratios, Etc., 
of Triple Expansion Engines. 

Back pressure 3 lbs. Terminal pressure, 8 lbs. (absolute). 



Pi- 


,R. 


P. 


Pi, 


P 3 - 


orr2- 


P3- 


P2- 


Pi- 


Pi. 


ri- 


120 


15 


26.66 


8.89 


1.626 


3.037 


13.01 


39.51 


14.45 


43.89 


4.939 


140 


17.5 


27.90 


9.30 


1.712 


3.197 


13.70 


43.79 


15.92 


50.89 


5.472 


160 


20 


28.97 


9.66 


1.790 


3.343 


14.32 


47.86 


17.29 


57.76 


5.980 


180 


22.5 


29.91 


9.97 


1.861 


3.477 


14.89 


51.77 


18.55 


64.52 


6.471 


200 


25 


30.75 


10.25 


1.928 


3.601 


15.42 


55.54 


19.76 


71.16 


6.942 


220 


27.5 


31.51 


10.50 


1.990 


3.718 


15.91 


59.16 


20.90 


77.69 


7.397 


240 


30 


32.21 


10.74 


2.049 


3.826 


16.39 


62.72 


22.00 


84.16 


7.839 



TRIPLE-EXPANSION ENGINES. 



955 



Theoretical Mean Effective Pressures, Cylinder Ratios, Etc., 
of Triple Expansion Engines. 





Back pressure, 3 lbs. Terminal pressure, 


10 lbs. (absolute). 




pi- 


R. 


P. 


P 3 - 


R 3 . 


ffi, R2, 

or ro- 


P3- 


V-z- 


Pa. 


Pi. 


r%. 


rn 


12 


31.85 


10.62 


1.436 


2.890 


14.36 


41.50 


15.24 


44.04 


4.148 


140 


14 


33.39 


11.13 


1.511 


3.044 


15.11 


45.99 


16.82 


51.20 


4.600 


160 


16 


34.73 


11.58 


1.580 


3.182 


15.80 


50.28 


18.29 


58.20 


5.027 


180 


18 


35.90 


11.97 


1.643 


3.310 


16.43 


54.38 


19.66 


65.09 


5.439 


200 


20 


36.96 


12.32 


1.702 


3.428 


17.02 


58.34 


20.97 


71.88 


5.834 


220 


22 


37.91 


12.64 


1.757 


3.538 


17.57 


62.15 


22.20 


78.54 


6.215 


240 


24 


38.78 


12.93 


1.809 


3.642 


18.09 


65.88 


23.38 


85.15 


6.587 



Given the required H.P. of an engine, its speed and length of stroke, 
and the assumed diagram factors Fi, Fz, Fs for the three cylinders, the 
areas of the cylinders may be found by using formulae (11), (12), and 
(14), and the values of Pi, P2, and Pz in the above table. 

A Common Rule for Proportioning the Cylinders of multiple- 
expansion engines is: for two-cylinder compound engines, the cylinder 
ratio is the square root of the number of expansions, and for triple- 
expansion engines the ratios of the high to the intermediate and of the 
intermediate to the low are each equal to the cube root of the number of 
expansions, the ratio of the high to the low being the product of the two 
ratios, that is, the square of the cube root of the number of expansions. 
Applying this rule to the pressures above given, assuming a terminal 
pressure (absolute) of 10 lbs. and 8 lbs. respectively, we have, for triple- 
expansion engines: 





Terminal Pressure, 10 lbs. 


Terminal Pressure, 8 lbs. 


pressure 
(Absolute) . 


No. of Ex- 
pansions. 


Cylinder Ratios, 
areas. 


No. of Ex- 
pansions. 


Cylinder Ratios, 
areas. 


130 
140 
150 
160 


13 
14 
15 
16 


1 to 2.35 to 5.53 
1 to 2.41 to 5.81 
1 to 2.47 to 6.08 
1 to 2.52 to 6.35 


I6I/4 
171/2 
183/4 
20 


1 to 2.53 to 6.42 
1 to 2.60 to 6.74 
1 to 2.66 to 7.06 
1 to 2.71 to 7.37 



The ratio of the diameters is the square root of the ratios of the areas, 
and the ratio of the diameters of the first and third cylinders is the same 
as the ratio of the areas of first and second. 

Seaton, in his Marine Engineering, says: When the pressure of steam 
employed exceeds 115 lbs. absolute, it is advisable to employ three 
cylinders, through each of which the steam expands in turn. The ratio 
of the low-pressure to high-pressure cylinder in this system should be 5, 
when the steam-pressure is 125 lbs. absolute; when 135 lbs., 5.4; when 
145 lbs., 5.8; when 155 lbs., 6.2; when 165 lbs., 6.6. The ratio of low- 
pressure to intermediate cylinder should be about one-half that between 
low-pressure and high-pressure, as given above. That is, if the ratio 
of l.p. to h.p. is 6, that of l.p. to int. should be about 3, and consequently 
that of int. to h.p. about 2. In practice the ratio of int. to h.p. is nearly 
2.25, so that the diameter of the int. cylinder is 1.5 that of the h.p. The 
introduction of the triple-compound engine has admitted of ships being 
propelled at higher rates of speed than formerly obtained without exceed- 
ing the consumption of fuel of similar ships fitted with ordinary com- 
pound engines; in such cases the higher power to obtain the speed has been 
developed by decreasing the rate of expansion, the low-pressure cylin- 
der being only 6 times the capacity of the high-pressure, with a working 
pressure of 170 lbs. absolute. It is now a very general practice to make 
the diameter of the low-pressure cylinder equal to the sum of the diameters 
of the h.p. and int. cylinders; hence 

Diameter of int. cylinder =1.5 diameter of h.p. cylinder; 

Diameter of l.p. cylinder = 2.5 diameter of h.p. cylinder. 



956 THE STEAM-ENGINE. 

In this case the ratio of l.p. to h.p. is 6.25; the ratio of int. to h.p. is 2.26; 
and ratio of l.p. to int. is 2.78. 

Ratios of Cylinders for Different Classes of Engines. (Proc. Inst. 
M. E., Feb., 1887, p. 36.) — As to the best ratios for the cylinders in a 
triple engine there seems to be great difference of opinion. Considerable 
latitude, however, is due to the requirements of the case, inasmuch as 
it would not be expected that the same ratio would be suitable for an 
economical land engine, where the space occupied and the weight were of 
minor importance, as in a war-ship, where the conditions were reversed. 
In the land engine, for example, a theoretical terminal pressure of about 
7 lbs. above absolute vacuum would probably be aimed at, which would 
give a ratio of capacity of high pressure to low pressure of 1 to 8 1/2 or 1 to 
9; whilst in a war-ship a terminal pressure would be required of 12 to 13 
lbs. which would need a ratio of capacity of 1 to 5; yet in both these 
instances the cylinders were correctly proportioned and suitable to the 
requirements of the case. It is obviously unwise, therefore, to introduce 
any hard-and-fast rule. 

Types of Three-stage Expansion Engines. — 1. Three cranks at 
120 deg. 2. Two cranks with 1st and 2d cylinders tandem. 3. Two 
cranks with 1st and 3d cylinders tandem. The most common type is the 
first, with cylinders arranged in the sequence high, intermediate, low. 

Sequence of Cranks. — Mr. Wyllie {Proc. Inst. M. E., 1887) favors 
the sequence high, low, intermediate, while Mr. Mudd favors high, inter- 
mediate, low. The former sequence, high, low, intermediate, gave an 
approximately horizontal exhaust-line, and thus minimizes the range of 
temperature and the initial load; the latter sequence high, intermediate, 
low, increased the range and also the load. 

Mr. Morrison, in discussing the question of sequence of cranks, pre- 
sented a diagram showing that with the cranks arranged in the sequence 
high, low, intermediate, the mean compression into the receiver was 
191/2 per cent of the stroke; with the sequence high, intermediate, low, 
it was 57 per cent. 

In the former case the compression was just what was required to keep 
the receiver-pressure practically uniform ; in the latter case the compression 
caused a variation in the receiver-pressure to the extent sometimes of 
221/2 lbs. 

Velocity of Steam through Passages in Compound Engines. 
{Proc. Inst. M. E., Feb., 1887.) — In the SS. Para, taking the area of the 
cylinder multiplied by the piston-speed in feet per second and dividing 
by the area of the port the velocity of the initial steam through the high- 
pressure cylinder port would be about 100 feet per second; the exhaust 
would be about 90. In the intermediate cylinder the initial steam had 
a velocity of about 180, and the exhaust of 120. In the low-pressure 
cylinder, the initial steam entered through the port with a velocity of 250, 
and in the exhaust-port the velocity was about 140 feet per second. 

A Double-tandem Triple-expansion Engine, built by Watts, 
Campbell & Co., Newark, N. J., is described in Am . Mach., April 26, 1894. 
It is two three-cylinder tandem engines coupled to one shaft, cranks at 
90°, cylinders 21, 32 and 48 by 60 in. stroke, 65 revolutions per minute, 
rated H.P. 2000; fly-wheel 28 ft. diameter, 12 ft. face, weight 174,000 
lbs.; main shaft 22 in. diameter at the swell; main journals 19 X 38 in.; 
crank-pins 91/2 X 10 in.; distance between center lines of two engines 
24 ft. 71/2 in.; Corliss valves, with separate eccentrics for the exhaust- 
valves of the l.p. cylinder. 

QUADRUPLE-EXPANSION ENGINES. 

H. H. Suplee (Trans. A. S. M. E., x, 583) states that a study of 14 
different quadruple-expansion engines, nearly all intended to be operated 
at a pressure of 180 lbs. per sq. in., gave average cylinder ratios of 1 to 2, 
to 3.78, to 7.70, or nearly in the proportions 1, 2, 4, 8. 

If we take the ratio of areas of any two adjoining cylinders as the fourth 
root of the number of expansions, the ratio of the 1st to the 4th will be 
the cube of the fourth root. On this basis the ratios of areas for different 
pressures and rates of expansion will be as follows: 



ECONOMIC PERFORMANCE OF STEAM-ENGINES. 957 



Gauge- 


Absolute 


Terminal 


Ratio of 


Ratios of Areas 


pressures. 


Pressures. 


Pressures. 


Expansion. 


of Cylinders. 






(12 


14.6 


1 : 1.95 : 3.81 


7.43 


160 


175 


10 


17.5 


1 : 2.05 : 4.18 


8.55 






( 8 


21.9 


1 : 2.16: 4.68 


10.12 






(12 


16.2 


1 : 2.01 : 4.02 


8.07 


180 


195 


10 


19.5 


1 : 2.10: 4.42 


9.28 






I 8 


24.4 


1 : 2.22: 4.94 


10.98 






(12 


17.9 


1 : 2.06: 4.23 


8.70 


200 


215 


10 


21.5 


1 : 2.15 : 4.64 


9.98 






( 8 


26.9 


1 : 2.28: 5.19 


11.81 






(12 


19.6 


1 : 2.10: 4.43 


9.31 


220 


235 


10 


23.5 


1 : 2.20: 4.85 


10.67 






8 


29.4 


1 : 2.33 : 5.42 


12.62 



Seaton says: When the pressure of steam employed exceeds 190 lbs. 
absolute, four cylinders should be employed, with the steam expanding 
through each successively; and the ratio of l.p. to h.p. should be at least 
7.5, and if economy of fuel is of prime consideration it should be 8; then 
the ratio of first intermediate to h.p. should be 1.8, that of second inter- 
mediate to first int. 2, and that of l.p. to second int. 2.2. 

In a paper read before the North East Coast Institution of Engineers 
and Shipbuilders, 1890, William Russell Cummins advocates the use of a 
four-cylinder engine with four cranks as being more suitable for high 
speeds than the three-cylinder three-crank engine. The cylinder ratios, 
he claims, should be designed so as to obtain equal initial loads in each 
cylinder. The ratios determined for the triple engine are 1, 2.04, 6.54, 
and for the quadruple, 1, 2.08, 4.46, 10.47. He advocates long stroke, 
high piston-speed, 100 revolutions per minute, and 250 lbs. boiler-pressure, 
unjacketed cylinders, and separate steam and exhaust valves. 



ECONOMIC PERFOR3IANCE OF STEAM-ENGINES. 

Economy of Expansive Working under Various Conditions, Single 
Cylinder. 

(Abridged from Clark on the Steam Engine.) 

1. Single Cylinders with Superheated Steam, Non-condensing. — 
Inside cylinder locomotive, cylinders and steam-pipes enveloped by the 
hot gases in the smoke-box. Net boiler pressure 100 lbs.; net maximum 
pressure in cylinders 80 lbs. per sq. in. 

Cut-off , per cent 20 25 30 35 40 50 60 70 80 

Actual ratio of expan- 
sion 3.91 3.31 2.87 2.53 2.26 1.86 1.59 1.39 1.23 

Water per I. H.P. per 

hour, lbs 18.5 19.4 20 21.2 22.2 24.5 27 30 33 

2. Single Cylinders with Superheated Steam, Condensing. — 
The best results obtained by Hirn, with a cylinder 233/ 4 x 67 in. and steam 
superheated 150° F., expansion ratio 33/4 to 41/2, total maximum pressure 
in cylinder 63 to 69 lbs., were 15.63 and 15.69 lbs. of water per I. H.P. per 
hour. 

3. Single Cylinders of Small Size, 8 or 9 in. Diam., Jacketed, 
Non-condensing. — The best results are obtained at a cut-off of 20 
per cent, with 75 lbs. maximum pressure in the cylinder; about 25 lbs. 
of water per I. H.P. per hour. 

4. Single Cylinders, not Steam-jacketed, Condensing. — The best 
result is from a Corliss- Wheelock engine 18 X 48 in.; cut-off, 12.5%; 
actual expansion ratio, 6.95; maximum absolute pressure in cylinder, 
104 lbs.: steam per I. H.P. hour, 19.58 lbs. Other engines, with lower 
steam pressures, gave a steam consumption as high as 26.7 lbs. 

Feed-water Consumption of Different Types of Engines. — The 
following tables are taken from the circular of the Tabor Indicator (Ash- 
croft Mfg. Co., 1889). In the first of the two columns under Feed-water 
required, in the tables for simple engines, the figures are obtained by 



958 



THE STEAM-ENGINE. 



computation from nearly perfect indicator diagrams, with allowance 
for cylinder condensation according to the table on page 936, but without 
allowance for leakage, with back-pressure in the non-condensing table 
taken at 16 lbs. above zero, and in the condensing table at 3 lbs. above zero. 
The compression curve is supposed to be hyperbolic, and commences at 
0.91 of the return-stroke, with a clearance of 3% of the piston-displace- 
ment. 

Table No. 2 gives the feed-water consumption for jacketed compound- 
condensing engines of the best class. The water condensed in the jackets 
is included in the quantities given. The ratio of areas of the two cylinders 
is as 1 to 4 for 120 lbs. pressure: the clearance of each cylinder is 3% 
and the cut-off in the two cylinders occurs at the same point of stroke. 
The initial pressure in the l.p. cylinder is 1 lb. per sq. in. below the back- 
pressure of the h.p. cylinder. The average back-pressure of the whole 
stroke in the l.p. cylinder is 4.5 lbs. for 10% cut-off; 4.75 lbs. for 20% 
cut-off; and 5 lbs. for 30% cut-off. The steam accounted for by the 
indicator at cut-off in the h.p. cylinder (allowing a small amount for leak- 
age) is 0.74 at 10% cut-off, 0.78 at 20%, and 0.82 at 30% cut-off. The 
loss by condensation between the cylinders is such that the steam ac- 
counted for at cut-off in the l.p. cylinder, expressed in proportion of that 
shown at release in the h.p. cylinder, is 0.85 at 10% cut-off, 0.87 at 20% 
cut-off, and 0.89 at 30% cut-off. 



TABLE No. 1. 

Feed-water Consumption, Simple Engines. 

r-condensing engines. condensing engines. 





i 




Feed-water Re- 




h 




Feed-water Re- 




O 
| 


£ 


quired per I.H.P. 




o 


m 


quired per I.H.P. 






per Hour. 




2 


J2 


per Hour. 




<i 










<j 










> 
o 


3 


e3J*f 
58 


Z-, v 3 • 




> 
O 


3 






to 


S3 


PM 






to 


03 


£ 


s^ 




o 




> 


WK! * 


o 


3 

"3 ® 


a> 


M§ 


w<! o> 


3 

c 

4> 


13 ® 


o 

to 

a 




espondin 
[Results 
Practice, 
Slight Li 


3 

u 

3 

0J 


> 

to 
a 
d 


C 

o & »; 
|S~1 


espondin 
1 Results 
Practice, 
Slight I 


£ 


"3 ft 




H a v 

gas? 


o 


£ 


Oft 


a; 


3 t. hfi 


t 2 M 


( 


80 


16.07 


27.61 


29.88 


( 


80 


29.72 


17.30 


18.89 


10 


90 


19.76 


25.43 


27.43 


10 


90 


33.41 


17.15 


18.70 


( 


100 


23.45 


23.90 


25.73 


i 


100 


37.10 


17.02 


18.56 


( 


80 


32.02 


21.04 


25.68 


( 


80 


38.28 


17.60 


19.09 


20 | 


90 


37.47 


23.00 


24.57 


15 


90 


42.92 


17.45 


18.91 


( 


100 


42.92 


22.25 


23.77 


I 


100 


47.56 


17.32 


18.74 


( 


80 


43.97 


24.71 


26.29 


{ 


80 


45.63 


18.27 


19.69 


30 


90 


50.73 


23.91 


25.38 


20 \ 


90 


51.08 


18.14 


19.51 


( 


100 


57.49 


23.27 


24.68 


I 


100 


56.53 


18.02 


19.36 


( 


80 


53.25 


25.76 


27.17 


( 


80 


57.57 


19.91 


21.25 


40{ 


90 


61.01 


25.03 


26.35 


30 


90 


64.32 


19.78 


21.06 


( 


too 


68.76 


24.47 


25.73 


( 


100 


71.08 


19.67 


20.93 


( 


80 


60.44 


26.99 


28.38 


( 


80 


66.85 


21.36 


22.56 


50 


90 


68.96 


26.32 


27.62 


40 


90 


74.60 


21.24 


22.41 


( 


100 


77.48 


25.78 


26.99 




100 


82.36 


21.13 


22.24 



ECONOMIC PERFORMANCE OF STEAM-ENGINES. 959 

The data upon which table No. 3 is calculated are not given, but the 
feed-water consumption is somewhat lower than has yet been reached 
(1894), the lowest steam consumption of a triple-expansion engine yet 
recorded being 11.7 lbs. 

TABLE No. 2. 
Feed-water Consumption for Compound Condensing Engines. 



Cut-off 


Initial Pressure above 
Atmosphere. 


Mean Effective Press. 


Feed-water 
Required 




H.P. Cyl., 
lbs. 


L.P.Cyl., 

lbs. 


H.P. Cyl., 
lbs. 


L.P.Cyl., 

lbs. 


Hour, lbs. 


■ 1 


80 
100 
120 


4.0 
7.3 
11.0 


11.67 
15.33 
18.54 


2.65 
3.87 
5.23 


16.92 
15.00 
13.86 


20 j 


80 
100 
120 


4.3 
8.1 
12.1 


26.73 
33.13 
39.29 


5.48 
7.56 
9.74 


14.60 
13.67 
13.09 


30 j 


80 
100 
120 


4.6 
8.5 
11.7 


37.61 
46.41 
56.00 


7.48 
10.10 
12.26 


14.99 
14.21 
13.87 



TABLE No. 3. 
Feed-Water Consumption for Triple-expansion Condensing Engines. 



Cut-off, 


Initial Pressure above 
Atmosphere. 


Mean Effective Pressure. 


Feed-water 
Required 
per I.H.P. 


cent. 


H.P. 
Cyl., lb. 


I. Cyl., 
lbs. 


L.P.Cyl., 
lbs. 


H.P. Cyl., 
lbs. 


I. Cyl., 

lbs. 


L.P.Cyl., 
lbs. 


per Hour, 
lbs. 


-:■! 

40 j 


120 
140 
160 

120 
140 
160 

120 
140 
160 


37.8 
43.8 
49.3 

38.8 
45.8 
51.3 

39.8 
46.8 
52.8 


1.3 
2.8 
3.8 

2.8 
3.9 
5.3 

3.7 
4.8 
6.3 


38.5 
46.5 
55.0 

51.5 
59.5 
70.0 

60.5 
70.5 
82.5 


17.1 
18.6 
20.0 

22.8 
23.7 
25.5 

26.7 
28.0 
30.0 


6.5 
7.1 
8.0 

8.6 
9.1 
10.0 

10.1 
10.8 
11.8 


12.05 
11.4 
10.75 

11.65 
11.4 
10.85 

12.2 
11.6 
11.15 



Sizes and Calculated Performances of Vertical High-speed 
Engines^ — The following tables are taken from an old circular, describ- 
ing the engines made by the Lake Erie Engineering Works, Buffalo. N. Y. 
The engines are fair representatives of the type largely used for driving 
dynamos directly without belts. The tables were calculated by E. F. 
Williams, designer of the engines. They are here somewhat abridged to 
save space. 



960 



THE STEAM-ENGINE. 









Simple Engines — 


- Non-condensing. 










05 




H.P. when 


H.P. when 


H.P. when 


Dimen- 
sions of 

Wheels. 

dia. face 






uli 


a 


u 


cutting off 


cutting off 


cutting off 


a, 




*°'Z' 


O 




at 1/5 stroke. 


at 1/4 stroke. 


at 1/3 stroke 


a 
S 

«3 02 


3 . 


tj. 


70 


80 


90 


70 


80 


90 


70 


80 


90 


Ft. 




"* * 


Q' J 


W 


"370 


lbs. 

"~20 


lbs. 
"~25 


lbs. 

~lso 


lbs. 
~~ 26 


lbs. 


lbs. 
~~36 


lbs. 

~32 


lbs. 
~~37 


lbs. 

~~ 43 


In. 


~2V^ 


pqa 


71/9 


10 


4 


3 


»V? 


12 


318 


27 


32 


39 


34 


41 


47 


41 


48 


56 


41/o 


5 


23/ \ 


31/2 


10 V?, 


14 


277 


41 


49 


60 


52 


62 


71 


63 


74 


85 


5'9" 


6 l/o 


31/o 


4 


12 


16 


245 


53 


64 


11 


67 


81 


93 


82 


96 


111 


6' 8" 


9 


4 


41/9 


131/, 


18 


222 


66 


80 


96 


84 


100 


116 


102 


120 


138 


71/9 


!1 


4 


5'" 


16 


20 


181 


95 


115 


138 


120 


144 


166 


146 


177 


198 


8'4" 


15 


41/9 


6 


18 


24 


b8 


119 


144 


173 


151 


181 


208 


183 


215 


748 


10 


19 


5 " 


7 


22 


28 


138 


179 


216 


261 


227 


272 


313 


276 


324 


373 


1 1'8" 


28 


6 


8 


24l/ ? , 


32 


120 


221 


267 


322 


281 


336 


386 


340 


400 


460 


13' 4" 


34 


7 


9 


27 


34 


112 


269 


^25 


392 


342 


409 


470 


414 


487 


560 


14' 2" 


41 


8 


10 


M.E.P., lbs 




24 


29 


35 


30.5 


36.5 


42 


37 


43.5 


50 


Note. — Th ? 










nominal-power 




ess. 








rating of the en- 


Term'l pr 




















gines is at 80 lbs. 


(about), It 


s. . 


17.9 


20 


22.3 


22.4 


25 


27.6 


29.8 


ii.i 


36.8 


gauge Dressure, 


Cyl. cond'n 


% 


26 


26 


26 


24 


24 


24 


21 


21 


21 


steam cut-off at 


Steam perl, 
hour, lbs. . 


H.P. 




















1/4 stroke. 




32.9 


30 


27.4 


31.2 


29.0 27.9 


32 


31.4 


30 





Compound Engines 


— Non-condensing - 


-High- 


pressure Cylinder 


and Receiver Jacketed. 








H.P., cutting off 


H.P., cutting off 


H.P., cutting off 


Diam. 
Cylinder, 




5 


at 1/4 Stroke 


at 1/3 Stroke 


at 1/2 Stroke 




a 

a 



in h.p. Cylinder. 


in h.p. Cylinder. 


in h.p. Cylinder. 


inches. 


Cyls. 


Cyls. 


Cyls. 


Cyls. 


Cyls. 


Cyls. 









31/3: 1. 


41/2: 1. 


31/3: 1- 


41/2: 1. 


31/3: 1. 


41/2: 1. 


h 


P4 


P4 


80 


90 


130 


150 


80 


90 


130 


150 


80 


90 


130 


150 


H 


W 


A 


J2 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


53/4 


61/9 


U 


10 


370 


7 


15 


19 


32 


23 


31 


35 


46 


44 


55 


64 


79 


63/ 8 


71/9 


131/9 


17. 


318 


9 


19 


24 


40 


29 


39 


45 


59 


% 


70 


81 


101 


;a/ 4 


9 


16 1/9 


14 


7,77 


14 


28 


36 


60 


43 


58 


67 


87 


83 


104 


121 


159 


9 


IOI/9 


19 


16 


7,46 


18 


37 


47 


78 


57 


76 


87 


114 


109 


136 


158 


196 


101/9, 


12 


221/9 


18 


777 


26 


53 


68 


112 


81 


109 


175 


164 


156 


195 


226 


281 


12 


131/, 


7.5 


70 


185 


32 


65 


84 


139 


100 


135 


154 


202 


192 


241 


279 


34« 


131/9, 


151/9 


281/9 


24 


158 


43 


88 


112 


186 


135 


181 


706 


271 


258 


323 


374 


464 


16 


181/9 


331/9 


28 


138 


57 


118 


151 


7.49 


180 


242 


277 


363 


346 


433 


502 


623 


18 


201/9 


38 


32 


170 


74 


152 


194 


321 


7.32 


312 


357 


468 


446 


558 


647 


803. 


20 


221/9 


43 


34 


117 


94 


194 


249 


417. 


297 


400 


457 


601 


572 


715 


829 


103C 


241/9, 


281/9 


52 


42 


93 


138 


285 


365 


603 


436 


587 


670 


880 


838 


1048 


1215 


150« 


281/ 2 


33 


60 


48 


80 


180 


374 


477 


789 


570 


767 


877 


1151 


1096 


1370 


1589 


1973 


Mean eff. pressure, lbs.. 


3.3 


6.8 


8.7 


14.4 


10.4 


14.0 


16 


21 


20 


25 


29 


36 


Ratio of expansion 


131/2 


181/4 


IOI/4 


133/ 4 


63/ 4 


91/4 


Cyl. condensation, %.. 


14 


14 


16 


16 


12 


12 


13 


13 


10 


10 


11 


11 


Ter. pres. (abt.), lbs. . . 


7.3 


7.7 


7.9 


9 


9,2 


10,4 


10 5 


12 


14 


15 5 


14 6 


17, fi 


Loss from expanding 


























below atmosphere, % 


34 


15 


17 


3 


5 























St.perl.H.P.hour.lbs. 55 


42 


47 


29 


33.3 


77.7 


28.7 


25.4 


30 


26.2 


21 


20 



ECONOMIC PERFORMANCE OF STEAM-ENGINES. 961 





Compound Engines - 


- Condensing — 


Steam-jacketed 










H.P. when 


H.P. when 


H.P. when 








cutting off at 


cutting off at 


cutting off at 


Diam 




u 


1/4 Stroke 


1/3 Stroke 


1/2 Stroke 


Cylinder, 
inches. 


s 


a 


in h. p. Cylinder. 


in h.p. Cylinder. 


in h.p. Cylinder. 














c 




Ratio, 


Ratio, 


Ratio, 


Ratio, 


Ratio, 


Ratio, 




J* 

s 


33 

US 


31/3: 1. 


4: 1. 


31/3: 1. 


4: 1. 


31/3: 1. 


4: I. 


pi 


Pi 


Pi 


80 


110 


115 


125 


80 


110 


115 


125 


80 


110 


115 


125 


W 


W 


J 


m 


rt 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


6 


61/9 


12 


10 


370 


44 


59 


53 


62 


55 


70 


68 


75 


70 


97 


95 


106 


ftV? 


71/o 


131/9 


12 


318 


56 


76 


67 


78 


70 


90 


87 


95 


90 


123 


120 


134 


8Vl 


9 


161/o 


14 


27^ 


83 


112 


100 


116 


104 


133 


129 


141 


133 


183 


179 


200 


9V"> 


101/9 


19 


16 


246 


109 


147 


131 


152 


136 


174 


169 


185 


174 


239 


234 


261 


II 


12 


221/9 


18 


222 


156 


210 


187 


218 


195 


250 


242 


265 


250 


343 


335 


374 


l?V? 


131/-> 


25 


20 


18!) 


192 


260 


231 


26^ 


241 


308 


298 


Ml 


308 


423 


414 


462 


14 


151/-, 


281/o 


24 


158 


7.58 


348 


310 


361 


.323 


413 


400 


439 


413 


568 


555 


619 


17 


18l/o 


331/o 


28 


138 


346 


467 


415 


484 


433 


554 


536 


588 


554 


761 


744 


830 


19 


201/o 


38 


32 


120 


446 


602 


535 


624 


558 


714 


691 


758 


714 


981 


959 


1070 


21 


22l/o 


43 


34 


112 


572 


772 


686 


801 


715 


915 


887 


972 


915 


1258 


1230 


1373 


26 


281/o 


52 


42 


93 


838 


1131 


1006 


1174 


1048 


1341 


1299 


1425 


1341 


1844 


1801 


2012 


30 


33 


60 


48 


80 


1096 


1480 


1316 


1534 


1370 


1757 


1699 


1863 


1757 


2411 


2356 


2632 


Mean eff. press., lbs 


%... 


20 


27 


24 


28 


25 


32 


31 


34 


32 


44 


43 


48 


Ratio of expansion 


131/2 


I6I/4 


10 


121/4 


63/4 


81/ 4 




18 | 18 


20 1 20 


15 1 15 


18 1 18 


12 1 12 


14 1 14 


St. per I.H.P. hour 


lbs. 17. 3| 16.6 


16.6|15.2 


17.0|16.4 


16.3|15.8 


17.5|17.0 


16.8|16.0 



Triple-expansion Engines, 


Non-condensing — Receiver 


only 




Jacketed 












u 


Horse-power 


Horse-power 


Horse 


-power 


Diameter 


if) 


a 


when cutting 


when cutting 


when 


jutting 


Cylinders, 


A 


a 


off at 42% of 


off at 50% of 


off at 67% of 


inches. 




Stroke in First 


Stroke in First 


Stroke 


in First 




p 
10 


■43 © 

n 


Cylinder. 


Cylinder. 


Cylinder. 


H.P. 


LP. 


L.P. 


180 lbs. 


200 lbs. 


180 lbs. 


200 lbs. 


180 lbs. 


200 lbs. 


43/4 


71/9 


12 


370 


55 


64 


70 


84 


95 


108 


51/2 


81/9 


131/9 


12 


318 


70 


81 


90 


106 


120 


137 


6 1/2 


IOI/9 


16 1/9 


14 


277 


104 


121 


133 


158 


179 


204 


71/2 


12 


19 


16 


246 


136 


158 


174 


207 


234 


267 


9 


141/9 


221/9 


18 


222 


195 


226 


250 


296 


335 


382 


10 


16 


25 


70 


185 


241 


279 


308 


366 


414 


471 


1U/? 


18 


281/ ?1 


24 


158 


323 


374 


413 


490 


555 


632 


13 


22 


331/9 


28 


138 


433 


502 


554 


657 


744 


848 


15 


241/9 


38 


32 


120 


558 


647 


714 


847 


959 


1093 


17 


27 


43 


34 


112 


715 


829 


915 


1089 


1230 


1401 


20 


33 


52 


42 


93 


1048 


1215 


1341 


1592 


1801 


2053 


231/2 


38 


60 


48 


80 


1370 


1589 


1754 


2082 


2356 


2685 


Mean eff. press., lbs 


25 


29 


32 


38 


43 


49 


No. of expansions. 
Cyl. condensation, 




16 

14 


13 
12 


1 
1 





%.... 





Steam p. I.H.P.p.hr., lbs. 


20.76 1 19.36 


19.25 1 17.00 


17.89 


17.20 


Lbs. coal at 81b. evap., lbs. 


2.59 1 2.39 


2.40 | 2.12 


2.23 


2.15 



962 



THE STEAM-ENGINE. 





Triple-expansion Engines — 


Condensing - 


— Steam-ja 


cket 


ed. 








u 


Horse- 


Horse- 


Horse- 


Horse- 


Diameter 


a> 


a 


power when 


power when 


power when 


power when 


Cylinders, 


.d 


a 


cutting off 


cutting off 


cutting off 


cutting off 


inches. 


G 


c rp 


at 1/4 Stroke 


at 1/3 Stroke 


at 1/2 Stroke 


at 3/4 Stroke 




2 


3 3 

"o.S 


in First Cyl. 


in First Cyl. 


in First Cyl. 


in First Cyl. 


pi 


Ph 


P* 


120 


140 


160 


120 


140 


160 


120 


140 


160 


120 


140 


160 


w 




Hi 


03 


« 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


Lbs. 


lbs. 


lbs. 


43/4 


71/9 


12 


10 


370 


35 


42 


48 


44 


53 


59 


57 


72 


84 


81 


97 


110 


51/9 


81/9 


131/9 


12 


318 


45 


53 


62 


56 


67 


76 


73 


92 


107 


104 


123 


140 


6 V? 


J 01/9 


161/9 


14 


277 


67 


79 


92 


83 


100 


112 


108 


137 


159 


154 


183 


208 


71/9 


12 


19 


16 


246 


87 


103 


120 


109 


131 


147 


141 


ItO 


208 


201 


239 


272 


9 


141/9 


221/9 


18 


222 


125 


148 


172 


156 


187 


211 


203 


257 


299 


289 


343 


390 


10 


16 


25 


20 


185 


154 


183 


212 


192 


231 


260 


250 


317 


368 


356 


423 


481 


mi-* 


18 


281/9 


24 


158 


206 


245 


284 


258 


310 


348 


335 


426 


494 


477 


D68 


645 


13 


22 


331/9 


28 


138 


277 


329 


381 


346 


415 


467 


450 


571 


663 


640 


761 


865 


15 


241/9 


38 


32 


120 


357 


424 


491 


446 


535 


602 


580 


736 


854 


825 


981 


1115 


17 


27 


43 


34 


112 


458 


543 


629 


572 


686 


772 


744 


944 


1095 


1058 


1258 


1430 


20 


33 


52 


42 


93 


670 


796 


922 


838 


1006 


1131 


1089 


1383 


1605 


1551 


1844 


2096 


23l/ 2 


38 


60 


48 


80 


877 


1041 


1206 


1096 


1316 


1480 


1424 


1808 


2099 


2028 


2411 


2740 


Mean eff. press., lbs 


16 


19 


22 


20 


24 


27 


26 


33 


38.3 


37 


44 


50 


















Cyl. condensation, % . . • 


19 


19 


19 


16 


16 


16 


12 


12 


12 


8 


8 1 8 


St. p. I.H.P.p. hr., lbs- 
Coal at 8 lbs. evap., lbs- 


14 1 


13 9 


15 i 


14 3 


1* 9 


13 2 


14 3 


13.6 


13 


15.7 14.9114.7 


1.8 


1.73 


1.66 


1.78 


1.7 


41.65 


1.78 


1.70 


1.62 


1.96 1.86 1.72 



The Willans Law. Total Steam Consumption at Different Loads. 

— Mr. Willans found with his engine that when the total steam consump- 
tion at different loads was plotted as ordinates, the loads being abscissas, 
the result would be a straight inclined line cutting the axis of ordinates at 
some distance above the origin of coordinates, this distance representing 
the steam consumption due to cylinder condensation at zero load. This 
statement applies generally to throttling engines, and is known as the 
Willans law. It applies also approximately to automatic cut-off engines 
of the Corliss, and probably of other types, up to the most economical 
load. In Mr. Barrus's book there is a record of six tests of a 16 X 42-in. 
Corliss twin-cylinder non-condensing engine, which gave results as follows : 

I.H.P 37 100 146 222 250* 287 342 

Feed-water per I.H. P. hour. 73.63 38.28 31.47 25.83 25.0* 25.39 25.91 

Total feed-water per hour.. . 2724 3825 4595 5734 6250 7287 8861 

* Interpolated from the plotted curve. 

The first five figures in the last line plot in a straight line whose equa- 
tion is y = 2122 + 16.55 H.P., and a straight line through the plotted 
position of the last two figures has the equation y = 28.62 H.P. — 927. 
These two lines cross at 253 H.P., which is the most economical load, the 
water rate being 24.96 lbs. and the total feed 6314 lbs. The figure 2122 
represents the constant loss due to cylinder condensation, which is just 
over one-third of the total feed-water at the most economical load. 

In Geo. H. Barrus's book on "Engine Tests " there is a diagram of 
condensation and leakage in tight or fairly tight simple engines using sat- 
urated steam. The average curve drawn through the several observations 
shows the condensation and leakage to be about as follows for different 
percentages of cut-off: 



Cut-off, % of stroke = I 

Condens. and leakage, % = p. . 
c = IX P -*■ (100 - p) = 



5 
60 

7.5 



10 
43 
7.5 



15 20 25 30 35 42 
35 29 24 20 17 15 

.8 8.2 7.9 7.5 7.2 7.4 



The figures in the last line represent the condensation and leakage as 
a percentage of the volume of the stroke of the piston, that is, in the same 



ECONOMIC PERFORMANCE OF STEAM-ENGINES. 963 

terms as the first line, instead of as a percentage of the total steam sup- 
plied, in which terms the figures of the second line are expressed. They 
indicate that the amount of cylinder condensation is nearly a constant 
quantity for a given engine with a given steam pressure and speed, what- 
ever may be the point of cut-off. 

Economy of Engines under Varying Loads. (From Prof. W. C. 
Unwin's lecture before the Society of Arts, London, 1S92.) — The general 
result of numerous trials with large engines was that with a constant load an 
indicated horse-power should be obtained with a consumption of 1 1/2 lbs. 
of coal per I.H.P. for a condensing engine, and 13/4 lbs. for a non-conden- 
sing engine, corresponding to about 13/4 lbs. to 2Vs lbs. per effective H. P. 

In electric-lighting stations the engines work under a very fluctuating 
load, and the results are far more unfavorable. An excellent Willans 
non-condensing engine, which on full-load trials worked with under 
2 lbs. per effective H.P. hour, in the ordinary daily working of the station 
used 7 1/2 lbs. in 1886, which was reduced to 4.3 lbs. in 1890 and 3.8 lbs. in 
1891 . . Probably in very few cases were the engines at electric-light stations 
working under a consumption of 41/2 lbs. per effective H.P. hour. In the 
case of small isolated motors working with a fluctuating load, still more 
extravagant results were obtained. 

At electric-lighting stations the load factor, viz., the ratio of the average 
load to the maximum, is extremly small, and the engines worked under 
very unfavorable conditions, which largely accounted for the excessive 
fuel consumption at these stations. 

In steam-engines the fuel consumption has generally been reckoned on 
the indicated horse-power. At full-power trials this was satisfactory 
enough, as the internal friction is then usually a small fraction of the total. 

Experiment has, however, shown that the internal friction is nearly 
constant, and hence, when the engine is lightly loaded, its mechanical 
efficiency is greatly reduced. At full load small engines have a mechan- 
ical efficiency of 0.8 to 0.85, and large engines might reach at least 0.9, 
but if the internal friction remained constant this efficiency would be 
much reduced at low powers. Thus, if an engine working at 100 I.H.P. 
had an efficiency of 0.85, then when the I.H.P. fell to 50 the effective H.P. 
would be 35 H.P. and the efficiency only 0.7. Similarly, at 25 H.P. the 
effective H.P. would be 10 and the efficiency 0.4. 

Experiments on a Corliss engine at Creusot gave the following results: 

Effective power at full load 1.0 0.75 0.50 0.25 0.125 

Condensing, mechanical efficiency . 82 . 79 . 74 . 63 . 48 

Non-condensing, mechanical efficiency. . 86 0.83 0.78 0.67 0.52 

Steam Consumption of Engines of Various Sizes. — W. C. Unwin 
(Cassier's Magazine, 1894) gives a table showing results of 49 tests of 
engines of different types. In non-condensing simple engines, the steam 
consumption ranged from 65 lbs. per hour in a 5-horse-power engine to 22 
lbs. in a 134-H.P. Harris-Corliss engine. In non-condensing compound 
engines, the only type tested was the Willans, which ranged from 27 lbs. 
in a 10-H.P. slow-speed engine, 122 ft. per minute, with steam-pressure 
of 84 lbs., to 19.2 lbs. in a 40-H.P. engine, 401 ft. per minute, with steam- 
pressure 165 lbs. A Willans triple-expansion non-condensing engine, 
39 H.F., 172 lbs. pressure, and 400 ft. piston speed per minute, gave a 
consumption of 18.5 lbs. In condensing engines, nine tests of simple 
engines gave results ranging only from 18.4 to 22 lbs. In compound- 
condensing engines over 100 H.P., in 13 tests the range is from 13.9 to 
20 lbs. In three triple-expansion engines the figures are 11.7, 12.2, and 
12.45 lbs., the lowest being a Sulzer engine of 360 H.P. In marine com- 
pound engines, the Fusiyama and Colchester, tested by Prof. Kennedy, 
gave steam consumption of 21.2 and 21.7 lbs.; and the Meteor and Tartar 
triple-expansion engines gave 15.0 and 19.8 lbs. 

Taking the most favorable results which can be regarded as not excep- 
tional it appears that in test trials, with constant and full load, the ex- 
penditure of steam and coal is about as follows: 

l bs. Per I.H.P. hour . Per Effective H.P. h r. 
Kind of Engine. ^ ^®w," C^I, Steam,' 

Non-condensing 1.80 16.5 2.00 18.0 

Condensing 1.50 13.5 1.75 15.8 



964 



THE STEAM-ENGINE. 



These may be regarded as minimum values, rarely surpassed by the 
most efficient machinery, and only reached with very good machinery in 
the favorable conditions of a test trial. 

Small Engines and Engines with Fluctuating Loads are usually 
very wasteful of fuel. The following figures, illustrating their low econ- 



omy, are given by Prof. Unwin, _ 
in workshops in Birmingham, Eng. 

Probable I.H.P. at full 

load 

Average I.H.P. during 

observation 

Coal per I.H.P. per hour 

during observation, lbs. 



i Magazine, 1894. Small engines 



2.96 7.37 8.2 



23.64 19.08 20.08 



36.0 21.25 22.61 18.13 11.68 9.53 8.50 

It is largely to replace such engines as the above that power will be 
distributed from central stations. 



Tests at Royal Agricultural Society's show at Plymouth, Eng. 
neering, June 27, 1890. 



Engi- 



Rated 
H.P. 


Com- 
pound or 
Simple. 


Diam. of 
Cylinders. 


Stroke, 
ins. 


Max. 
Steam- 
pressure. 


Per Brake H.P. 

per hour. 


u ~ • 


h.p. 


l.p. 


Coal. 


Water. 




5 

3 
2 


simple 

compound 

simple 


7 
3 

41/2 


"6" 


10 
6 

71/2 


75 
110 
75 


12.12 
4.8-> 
11.77 


78.1 lbs. 
42.03 " 
89.9 " 


6.11b. 
8.72" 
7.64" 



24 


32 


40 


48 


56 


72 


88 


9.3 


29 


28.7 


28.5 


28.3 


28 


27.7 


29 


28.4 


28 


27.5 


27.1 


26.3 


25.6 


32 


30.8 


29.8 


29.2 


28.8 


28.7 





Steam-consumption of Engines at Various Speeds. (Profs. Den- 
ton and Jacobus, Trans. A. S. M. E., x, 722.) — 17 X 30 in. engine, 
non-condensing, fixed cut-off, Meyer valve. (From plotted diagrams.) 

Revs, per min.. 8 12 16 20 

1/8 cut-off, lbs. . . 39 35 32 30 

l/ 4 cut-off, lbs... 39 34 31 29.5 

1/2 cut-off, lbs. . . 39 36 34 33 

Steam-consumption of same engine ; fixed speed, 60 revs, per minute. 
Varying cut-off compared with throttling-engine for same horse-power 
and boiler-pressures: 
Cut-off, fraction 

of stroke 0.1 

Steam, 90 lbs... 29 
Steam, 60 lbs.. . 39 



0.15 0.2 0.25 0.3 0.4 
27.5 27 27 27.2 27.8 
34.2 32.2 31.5 31.4 31.6 



0.5 0.6 0.7 0.8 

28.5 . 

32.2 34.1 36.5 39 



Throttling-engine, 7/ 8 cut-off, for corresponding horse-powers. 

Steam, 90 lbs. . . 42 37 33.8 31.5 29.8 

Steam, 60 lbs 50.1 49 46.8 44.6 41 ... 

Some of the principal conclusions from this series of tests are as follows: 

1. There is a distinct gain in economy of steam as the speed increases 
for 1/2, Vs. and 1/4 cut-off at 90 lbs. pressure. The loss in economy for 
about 1/4 cut-off is at the rate of 1/12 lb. of water per I.H.P. per hour for each 
decrease of a revolution per minute from 86 to 26 revolutions, and at the 
rate of 5/g lb. of water below 26 revolutions. Also, at all speeds the 1/4 
cut-off is more economical than either the 1/2 or Vs cut-off. 

2. At 90 lbs. boiler-pressure and above 1/3 cut-off, to produce a given 
H.P. requires about 20% less steam than to cut off at 7/ 8 stroke and regu- 
late by the throttle. 

3. For the same conditions with 60 lbs. boiler-pressure, to obtain, by 
throttling, the same mean effective pressure at 7/ 8 cut-off that is obtained 
by cutting off about 1/3, requires about 30% more steam than for the 
latter condition. 

Capacity and Economy of Steam Fire Engines. (Eng. News, 
Mar. 28, 1895.) — The tests were made by Dexter Brackett for the Board 
of Fire Commissioners. Boston. Mass. 



ECONOMIC PERFORMANCE OF STEAM-ENGINES. 965 



No. of 
engine. 


60 
« . 

PQ 


8°* 


Water evap. 
per lb. coal, 
from and at 
212°. 


II 






v 


1 


101.0 


lbs. 
191.0 
184.0 
191.0 
141.6 
138.4 
163.7 
103.3 
181.6 
117.3 
MIA 
142.5 
91.1 
151.4 
148.4 


lbs. 
2.26 


lbs. 
90.2 
92.3 
78.4 
75.7 
71.5 

102.7 
72.1 
92.7 
68.8 

101.3 
76.5 
59.0 
87.8 
74.7 


lbs. 

143.2 

124.0 

123.3 

113.8 

136.4 

121.2 

119.6 

143.0 

119.2 

112.8 

111.5 

102.1 

126.8 

128.1 


7,619,800 
9,632,700 
5,900,000 
5,882,000 
8,112,900 
8,736,300 

14,026,000 
9,678,400 

10,201,600 
7,758,300 
7,187,400 
6,482,100 
7,993,400 
7,265,000 


galls. 
549 


1 


499 


2 

3 

4 


85.0 
74.0 
86.5 
86.0 


2.66 
3.57 

2.88 


535 

482 
459 


5 


449 


5 


5.87 
3.45 
4.94 
3.51 
4.49 
4.22 
4.10 
3.76 


545 


6 

7 


86.0 
112.0 
140.5 
174.0 
225.0 


536 
596 


8 


910 


9 


482 


10 


419 


10 


564 


11 


229.0 


572 



Nos. 1, 2, 3 and 4, Amoskeag engines; Nos. 5, 6, 7 and 8, Clapp & 
Jones; Nos. 9, 10, 11, Silsby. The engines all show an exceedingly high 
rate of combustion, and correspondingly low boiler efficiency and pump 
duty. 

Economy Tests of High-speed Engines. (F. W. Dean and A. C. 
Wood, Jour. A. S. M. E., June, 1908.) — Some of these engines had been in 
service for a long time, and therefore their valves may not have been in 
the best condition. The results may be taken as fairly representing the 
economy of average engines of the type, under usual working conditions. 
The engines were all non-condensing. The 16 X 15-in. engine was 
vertical, the others horizontal. They were all direct-connected to gen- 
erators. 



No. of Test. 
Size of engine, ins.. . . 

Hours in service 

Revs, permin 


1 

15 X H 

15,216 

240 

lflat 

100 

37.2,t 36.2* 

60.2, 58.4 


2 
16X15 
20,000 

240 

1 flat 

2-50 

36.7.f 35.8 

61.0 59.7 


3 
14X12 
28,644 

300 

1 flat 

2-40 

31. 7, t 32.0 

57.1, 57.4 


4 

16X 14 

719 

270 

4 flat 


Generator, K.W 

Steam per I .H .P .-hr. 
Steam per K.W.-hr . . 


125 
37.5,* 36.7 
54.9, 54.7 



No. of Test. 

Size of engine, ins 

Hours in service 


5 

18 X 18 

32,000 

220 

1 piston 

150 

39.8,f34.7,* 29.5J 

61.8, 51.8, 43.4 


6 

15 X 16 
5,600 
250 

1 piston 

100 

36.3,* 33.6 

55.2, 49.4 


7 

12X 18 

10,800 

190 




f 2 flat inlet 
) 2 Corliss exh. 

75 
44.0, f 36.7, 34.1 § 
79.3, 60.5, 53.7 


Generator, K.W 

Steam per I .H . P.-hr . . . 
Steam per K.W.-hr 



* 3/ 4 load ; f 1/2 load ; t 1 1/4 load ; §1 1/ 2 load ; the others full load. 

Some of the conclusions of the authors from the results of these tests 
are as follows: 

The performances of the perfectly balanced flat valve engines are so 
relatively poor as to disqualify them, unless this type of valve can be made 
with some mechanism by which wear will not increase leakage. The four 
valve engines, which were built to be more economical than single-valve 



966 THE STEAM-ENGINE. 



engines, have utterly failed in their object. The duplication of valves 
used in both four-valve engines simply increased the opportunity for leak- 
age. The most economical result was obtained from a piston valve engine, 
No. 5, heavily loaded. With the lighter loads that are comparable the 
flat valve engine, No. 3, surpassed No. 5 in economy. The flat valve 
engines give a flatter load cu.ve than the piston valve engines. Compar- 
ing the lesults of the flat valve engines, the most economical results v. ere 
obtained from engine No. 3, which had a valve which automatically takes 
up wear, and if it does not cut, must maintain itself tigiit for long periods. 

From the results we are justified in thinking that most high-speed en- 
gines rapidly deteriorate in economy. On the contrary, slower running 
Corliss or gridiron valve engines improve in economy for some time and 
then maintain the economy for many years. It is difficult to see that 
the speed is the cause of this, and it must depend on the nature of the 
valve. 

The steam consumption of small single-valve high-speed engines non- 
condensing, is not often less than 30 lbs. per I.H.P. per hour. 1 o "Water- 
town engines, 10 X 12 tested by J. W. Hill for the Philadelphia Dept. of 
Public Works in 1904, gave respectively 30.67 and 29.70 lbs. at full load, 
61.8 and 63.9 I.H.P., and 28.87 and 29.54 lbs. at approximately half-load, 
37.63 and 36.36 I.H.P. 

High Piston-speed in Engines. (Proc. Inst. M. E., July, 1883, p. 
321.) — The torpedo boat is an excellent example of the advance towards 
high speeds, and shows' what can be accomplished by studying lightness 
and strength in combination. In running at 221/2 knots an hour, an engine 
with cylinders of 16 in. stroke will make 480 revolutions per- minute, which 
gives 1280 ft. per minute for piston-speed; and it is remarked that engines 
running at that high rate work much more smoothly than at lower speeds, 
and that the difficulty of lubrication diminishes as the speed increases. 

A High-speed Corliss Engine. — A Corliss engine, 20 X 42 in., ha.s 
been running a wire-rod mill at the Trenton Iron Co.'s works since 1877, at 
160 revolutions or 1120 ft. piston-speed per minute {Trans. A. S. M. E., ii, 
72). A piston-speed of 1200 ft. per min. has been realized in locomotive 
practice. 

The Limitation of Engine-speed. (Chas. T. Porter, in a paper on the 
Limitation of Engine-speed, Trans. A. S. M. E., xiv, 806.) — The practical 
limitation to high rotative speed in stationary reciprocating steam-engines 
is not found in the danger of heating or 01 excessive wear, nor, as is gen- 
erally believed, in the centrifugal force of the fly-wheel, nor in the tendency 
to knock in the centers, nor in vibration. He gives two objections to very 
high speeds: First, that "engines ought not to be run as fast as they can 
be; " second, the large amount of waste room in the port, which is required 
for proper steam distribution. In the important respect of economy of 
steam, the high-speed engine has thus far proved a failure. Large gain 
was' looked for from high speed, because the loss by condensation on a, 
given surface would be divided into a greater weight of steam, but this 
expectation has not been realized. For this unsatisfactory result we have 
to lay the blame chiefly on the excessive amount of waste room. The 
ordinary method of expressing the amount of waste r-oom in the percentage 
added by it to the total piston displacement, is a misleading one. It 
should be expressed as the percentage which it adds to the length of 
steam admission. For example, if the steam is cut off at 1/5 of the stroke, 
8% added by the waste room to the total piston displacement means 
40% added to the volume of steam admitted. Engines of four, five and 
six feet stroke may properly be run at from 700 to 800 ft. of piston travel 
per minute, but for ordinary sizes, says Mr. Porter, 600 ft. per minute 
should be the limit. 

British High-speed Engines. (John Davidson, Power. Feb. 9, 1909.) 
— The following figures show the general practice of leading builders: 

I.H.P. 50 100 200 500 

Revs, per min . 

600-700 550-600 500 350-375. 
Piston speed, ft. per min. 

600 650 675 750 

Rapid strides have been made during the last few years, despite the 



750 1000 


1500 


2000 


325 250 


200 


160-18(1 


775 800 


900 


1000 



ECONOMIC PERFORMANCE OF STEAM-ENGINES. 967 



competition of the steam turbine. The single-acting type (Brotherhood, 
Willans and others) has been superseded by double-acting engines with 
forced lubrication. There is less wear in a high-speed than in a low-speed 
engine. A 500-H.P. 3-crank engine after running 7 years, 12 hours per 
day and 300 days per year, showed the greatest wear to be as follows: 
crank pins, 0.003 in.; main bearings, 0.003 in.; eccentric sheaves, 0.015 in.; 
crosshead pins, 0.005 in. All pins, where possible, are of steel, case- 
hardened. High-speed engines have at least' as high economy and effi- 
ciency as any other type of engine manufactured. A triple-expansion 
mill engine, with steam at 175 lbs., vacuum 26 ins., superheat 100° F., 
gave results as shown below, [figures taken from curves in the original]. 

Fraction of full 

load 

Lbs. steam per 

I.H.P. hour.. 12.7 11.85 11.4 11.1 
Lbs. steam per 

B.H.P. hour.. 16.0 14.8 13.7 12.9 



0.2 0.3 0.4 0.5 0.6 0.7 



10.9 10.8 10.75 10.75 10.8 11.0 
12.4 12.05 11.85 11.8 11.8 11.8 



Owing to the forced lubrication and throttle-governing, the economical 
performance at light loads is relatively much better than in slow-speed 
engines. The piston valves render the use of superheat practicable. 
At 200° superheat the saving in steam consumption of a triple-expansion 
engine is 26%. [A curve of the relation of superheat to saving shows 
that the percentage of saving is almost uniformly 1.4% for each additional 
10° from 0° to 160° of superheat.] 

The method of governing small high-speed engines is by means of a 
plain centrifugal governor fixed to the crank shaft and acting directly 
on a throttle. Several makers use a governor which at light loads acts 
by throttling, and at heavy loads by altering the expansion in the high- 
pressure cylinder. The crank-shaft governor used in America has been 
found impracticable for high speeds, except perhaps for small engines. 

Advantage of High Initial and Low Back Pressure. — The theo- 
retical advantage due to the use of low back pressures or high vacua is 
shown by the following table, in which the efficiencies are those of the 
Carnot cycle, E = (Ti - T 2 ) + Ti. With 100 lbs. absolute initial 
pressure the efficiency is increased from 0.270 to 0.353, or 30.7%, by rais- 
ing the vacuum from 27.02 to 29.56 ins. of mercury, and with 200 lbs. it 
is increased from 0.317 to 0.394, or 24.3%, with the same change in 
the vacuum. 



Abs. Initial Pressure. 


100 


125 


150 


175 


200 


225 


250 


275 


300 


Temp. 

d F- 


Vacuum, 

In. of 
Mercury. 


Lbs. per 
Sq. In. 


Carnot Efficiencies. 


115 


27.02 


1.47 


7.70 


285 


298 


308 


317 


325 


332 


339 


345 


108 


27.48 


1.20 


279 


293 


306 


316 


325 


333 


341 


.347 


353 


100 


28.00 


0.95 


289 


.303 


.316 


325 


335 


.343 


350 


.356 


.362 


90 


28.50 


0.70 


302 


.316 


328 


.338 


.347 


.355 


.361 


.368 


.373 


70 


29.18 


0.74 


37.7 


341 


353 


362 


371 


378 


38'? 


391 


.396 


50 


29.56 


0.36 


0.353 


.366 


.377 


.386 


.394 


.402 


.408 


.414 


.419 



The same table shows the advantage of high initial pressure. Thus 
with a vacuum 27.02 ins. the efficiency is increased from 0.270 to 0.317, 
or 17.4%, by raising the initial absolute-pressure from 100 to 200 lbs., and 
with a vacuum of 28.5 ins. the efficiency is increased from 0.302 to 0.347, 
or 14.9%, by the same rise of pressure. In practice the efficiencies given 
in the table for the given pressures and temperatures cannot be reached 
on account of imperfections of the steam-engine, and the fact that the 
engine does not work on the ideal Carnot cycle. The relative advantages, 
however, are probably proportional to those indicated by the table, pro- 
vided the expansion is divided into two or more stages at pressures above 



968 THE STEAM-ENGINE. 

100 lbs. The possibility of obtaining very high vacua is limited by he 
temperature of the condensing water available and by the imperfections 
of the air pump. The use of high initial pressures is limited by the safe 
working pressure of the boiler and engine. 

Comparison of the Economy of Compound and Single-cylinder 
Corliss Condensing Engines, each expanding about Sixteen 
Times. (D. S. Jacobus, Trans., A. S. M. E., xii, 943.) 

The engines used in obtaining comparative results are located ta 
Stations I and II of the Pawtucket Water Co. 

The tests show that the compound engine is about 30% more economical 
than the single-cylinder engine. The dimensions of the two engines are 
as follows: Single 20 X 48 ins.; compound 15 and 30V8 X 30 ins. The 
steam used per I.H.P. hour was: single 20.35 lbs., compound 13.73 lbs. 

Both of the engines are steam-jacketed, practically on the barrels only, 
with steam at full boiler-pressure, viz., single 106.3 lbs., compound 127.5 lbs. 

The steam-pressure in the case of the compound engine is 127 lbs., or 
21 lbs. higher than for the single engine. If the steam-pressure be raised 
this amount in the case of the single engine, and the indicator-cards be 
increased accordingly, the consumption for the single-cylinder engine 
would be 19.97 lbs. per hour per horse-power. 

Two-cylinder vs. Three-cylinder Compound Engine. — A Wheelock 
triple-expansion engine, built for the Merrick Thread Co., Holyoke, Mass., 
is constructed so that the intermediate cylinder may be cut out of the 
circuit and the high-pressure and low-pressure cylinders run as a two- 
cylinder compound, using the same conditions of initial steam-pressure 
and load. The diameters of the cylinders are 12, 16, and 24 13/32 ins., the 
stroke of the first two being 36 ins. and that of the low-pressure cylinder 
48 ins. The results of a test reported by S. M. Green and G. I. Rockwood, 
Trans. A. S. M. E., vol. xiii, 647, are as follows: In lbs. of dry steam used 
per I.H.P. per hour, 12 and 2413/32 in. cylinders only used, two tests 13.06 
and 12,76 lbs., average 12.91. All three cylinders used, two tests 12.67 
and 12.90 lbs., average 12.79. The difference is only 1%, and would 
indicate that more than two cylinders are unnecessary in a compound 
engine, but it is pointed out by Prof. Jacobus, that the conditions of the 
test were especially favorable for the two-cylinder engine, and not rela- 
tively so favorable for the three cylinders. The steam-pressure was 142 
lbs. and the number of expansions about 25. (See also discussion on 
the Rockwood type of engine, Trans. A. S. M. E., vol. xvi.) 

Economy of a Compound Engine. (D. S. Jacobus, Trans. A. S. M. E., 
1903.) — A Rice & Sargent engine, 20 and 40 X 42 ins., was tested with 
steam about 149 lbs., vacuum 27.3 to 28.8 ins. or 0.82 to 1.16 lbs. abso- 
lute, r.p.m. 120 to 122, with results as follows: 

I.H.P 1004 853 820 627 491 340 

Water per I.H.P. per hr 12.75 12.33 12.55 12.10 13.92 14.58 

B.T.U. per I.H.P. per min. . 231.8 226.3 229.9 222.7 256.8 267.7 

The Lentz Compound Engine is described in The Engineer (London), 
July 10, 1908. It is the latest development of the reciprocating engine 
with four double-seated poppet valves to each cylinder, each valve op- 
erated by a separate eccentric mounted on a lay-shaft driven by bevel- 
gearing from the main shaft. The throw of the high-pressure steam 
eccentrics is varied by slide-blocks which are caused to slide along the lay- 
shaft by the action of a centrifugal inertia governor, which is also mounted 
on the lay-shaft. No elastic packing is used in the engine, the piston-rod 
stuffing box being fitted with ground cast-iron rings, and the valve stems 
being provided with grooves and ground to fit long bushings to 0.001 in. 
Two tests of a Lentz engine built in England, 14 1/2 and 243/ 4 by 271/2 in., 
gave results as follows: 

Saturated steam, 170 lbs., vacuum 26 in., I.H.P. 366, steam per I.H.P. 
per hour 12.3 lbs. Steam 170 lbs. superheated 150° F., vac. 26 in., I.H.P. 
366, steam per I.H.P. per hour, 10.4 lbs. Revs, per min. in both cases, 
167. Piston speed 767 ft. per min. Engines are built for speeds up to 
900 ft. per min., and up to 350 r.p.m. 

The Lentz engine is built in the United States by the Erie City Iron 
Works. 



ECONOMIC PERFORMANCE OF STEAM-ENGINES. 969 



Steam Consumption of Sulzer Compound and Triple-expansion 
Engines with Superheated Steam. 

The figures in the table below were furnished to the author (Aug., 1902) 
by Sulzer Bros., Winterthur, Switzerland. They are the results of official 
tests by Prof. Schroter of Munich, Prof. Weber of Zurich, and other 
eminent engineers. 

COMPOUND ENGINES- 



fs 

o 

PL, 






3 


a 






&u 


Dimensions of 


G-2 


I 


W 






w 3 




Cylinders, 


"43 a 




ft • 

a M 


a\S 

3 M 






Inches. 


n 




i" 




&* 


flPn 


gR 


> 


sr* 


1500 


30.5 and 


85 


130 


356 


2d. A 


850 


13.30 


to 


49.2 x 59.1 




132 


428 


26.4 


842 


12.05 


1800 






122 


482 


26.6 


1719 


12.42 


800 


24 and 


83 


136 


357 


28 


481 


13.00 


to 


40.4 X 51.2 




134 


356 


28 


750 


13.10 


1000 






135 


356 


27.6 


1078 


14.10 








135 


547 


28 


515 


11.32 








132 


533 


27.8 


788 


11.52 








134 


545 


27.2 


1100 


11.88 


950 


26 and 


86 


130 


358 


28.2 


1076 


14.10 


to 


42.3 X51.2 




129 


358 


28 


1316 


14.50 


1150 






. 132 


496 


28.3 


1071 


11.73 




do., non-cond'g 




136 


527 




1021 


15.37 


400 


17.7 and 


110 


135 


577 


26.4 


519 


10.80* 


to 


30.5 X35.4 




135 


554 


26.4 


347 


10.35* 


500 
















1000 


26.9 and 


65 


127 


655 


27.2 


788 


9.91* 


to 


47.2 X 66.9 




127 


664 


27.2 


797 


9.68* 


1200 






128 


572 


27.1 


788 


10.70* 



TRIPLE-EXPANSION ENGINES. 



3000 


321/4,471/4,58x59 


85 


188 
190 


606 
397 


28 
271/4 


2860 
2880 


8.97 
11.28 


3000 


34, 49, 61 X 51 


83.5 


189 
196 


613 

381 


27 

261/4 


2908 
3040 


9.41 
11.57 



* With intermediate superheating. 
to l.p. cylinder, 307 to 349° F. 



Temperature of steam at entrance 



Steam Consumption of Different Types of Engines. 

Tests of a Ridgway 4-valve non-condensing engine, 19 X 18 in., at 
200 r.p.m. and 100 lbs. pressure, are reported in Power, June, 1909, as 
follows: 

Load 

Steam per I.H.P. hour 



1/4 


1/2 


3/4 


Full 


H/4 


50.7 


24.4 


23.2 


23.8 


25.4 



The best result obtained at 130 lbs. pressure was 21.6 lbs., at 115 lbs. 
pressure 22.6 lbs., and at 85 lbs. pressure 24.3 lbs. Maintained economy 



970 THE STEAM-ENGINE. 

in this type of engine is dependent upon reduction of unnecessary over- 
travel, properly fitted valves, valves which do not span a wide arc, close 
approach of the movement of the valves to that of a Corliss engine, and 
good materials. 

The probable steam consumption of condensing engines of different 
types with different pressures of steam is given in a set of curves by 
R. H. Thurston and L. L. Brinsmade, Trans. A. S. M. E., 1897, from 
which curves the following approximate figures are derived. 

Steam pressure, absolute, lbs. per sq. in. 

400 300 250 200 150 100 75 50 
Ideal Engine 

(Rankine cycle) 6.95 7.5 7.9 8.45 9.20 10.50 11.40 12.9 
Quadruple Exp. 

Wastes 20% 8.75 9.15 9.75 10.50 11.60 13.0 14.0 15.6 

Triple Exp. 

Wastes 25% 9.25 9.95 10.50 11.15 12.30 14.0 15.1 16.7 

Compound. 

Wastes 33% 10.50 11.25 11.80 12.70 13.90 15.6 16.9 18.9 

Simple Engine. 

Wastes 50% 14.00 15.00 15.80 16.80 18.40 20.4 22.7 25.2 

The same authors give the records of tests of a three-cylinder engine 
at Cornell University, cylinders 9, 16 and 24 ins., 36-in. stroke, first as a 
triple-expansion engine; second, with the intermediate cylinder omitted, 
making a compound engine with a cylinder ratio of 7 to 1 and third, 
omitting the third cylinder, making a compound engine with a ratio of 
a little over 3 to 1. The boiler pressure in the first case was 119 lbs., 
in the second 115, and in the third 117 lbs. Charts are given showing 
the steam consumption per I.H.P. and per B.H.P. at different loads, 
from which the following figures are taken. 

Indicated Horse-Power 40 60 80 100 110 120 130 

Steam consumption per I.H.P. per hour. 

Triple Exp 19.1 16.7 15.3 14.2 13.7 13.8 14.4 

Comp. 7 to 1 19.6 18.2 17.0 16.3 16. 15.8 15.8 

Comp. 3 to 1 19.7 18.4 18.1 18.5 

Steam consumption per B.H.P. hour. 

Triple Exp 30.5 23.0 19.6 17.1 16.2 16.2 16.7 

Comp. 7 to 1 26.2 21.7 19.3 18.7 18.5 18.4 18.5 

Comp. 3 to 1 23.4 20.6 20. 20 

The most economical performance was as follows: 

Triple Comp. 7 to 1 Comp. 3 to 1 

Indicated Horse-Power 112.7 130.0 67.7 

Steam per I.H.P. hour 13.68 15.8 18.03 

A test of a 7500-H.P. engine, at the 59th St. Station of the Interborough 
Rapid Transit Co., New York, is reported in Pmtrer, Feb., 1906. It is a 
double cross compound enerine. with horizontal h.p. and vertical l.p. 
cylinders. With steam at 175 lbs. eauere and vacuum 25.02 ins., 75 r.p.m. 
it developed 7365 I.H.P., 5079 K.W. at switchboard. Friction and elec- 
trical losses 417.3 K.W. Dry steam per K.W. hour 17.34 lbs.; per I.H.P. 
hour, 11.96 lbs. 

A test of a Fleminer 4-valve eneine. 15 and 40.5 in. diam., 27-in. stroke, 
positive-driven Corliss valves, flv-wbeel governor, is reported bv B. T. 
Allen in Trans. A. S. M. E., 1903. The following results were obtained. 
The speed was above 150 r.p.m. and the vacuum 26 in. 

Fraction of full load about 1/6 V8 7 Ao Full load 1 .1 

Horse-power 87.1 321.5 348.3 501.6 553.5 

Steam per I.H.P hour 14.42 13.59 12.33 12.66 12.7 



170 


140 


115 


100 


80 


50 


21.9 


22.2 


22.2 


22.4 


24.6 


28.8 


18.1 


18.2 


18.2 


18.3 


18.3 


20.4 



ECONOMIC PERFORMANCE OF STEAM-ENGINES. 971 



Relative Economy of Compound Non-condensing Engines 
under Variable Loads. — F. M. Rites, in a paper on the Steam Dis- 
tribution in a Form of Single-acting Engine (Trans. A. S. M. E., xiii, 537), 
discusses an engine designed to meet the following problem: Given an 
extreme range of conditions as to load or steam-pressure, either or both, 
to fluctuate together or apart, violently or with easy gradations, to 
construct an engine whose economical performance should be as good as 
though the engine were specially designed for a momentary condition — 
the adjustment to be complete and automatic. In the ordinary non-con- 
densing compound engine with light loads the high-pressure cylinder is 
frequently forced to supply all the power and in addition drag along with 
it the low-pressure piston, whose cylinder indicates negative work. Mr. 
Rites shows the peculiar value of a receiver of predetermined volume 
which acts as a clearance chamber for compression in the high-pressure 
cylinder. The Westinghouse compound single-acting engine is designed 
upon this principle. The following results of tests of one of these engines 
rated at 175 H.P. for most economical load are given: 

Water Rates under Varying Loads, lbs. per H.P. per Hour. 

Horse-power 210 

Non-condensing 22 . 6 

Condensing 18.4 

Efficiency of Non-eOndensing Compound Engines. (W. Lee 

Church, Am. Mach., Nov. 19, 1891.) — The compound engine, non-con- 
densing, at its best performance will exhaust from the low-pressure cylin- 
der at a pressure 2 to 6 pounds above atmosphere. Such an engine will 
be limited in its economy to a very short range of power, for the reason 
that its valve-motion will not permit of any great increase beyond its 
rated power, and any material decrease below its rated power at once 
brings the expansion curve in the low-pressure cylinder below atmos- 
phere. In other words, decrease of load tells upon the compound engine 
romewhat sooner, and much more severely, than upon the non-compound 
engine. The loss commences the moment the expansion line crosses a 
line parallel to the atmospheric line, and at a distance above it repre- 
senting the mean effective pressure necessary to carry the frictional load 
of the engine. When expansion falls to this point the low-pressure 
cylinder becomes an air-pump over more or less of its stroke, the power 
to drive which must come from the high-pressure cylinder alone. Under 
the light loads common in many industries the low-pressure cylinder is 
thus a positive resistance for the greater portion of its stroke. A careful 
study of this problem revealed the functions of a fixed intermediate 
clearance, always in communication with the high-pressure cylinder, 
and having a volume bearing the same ratio to that of the high-pressure 
cvlinder that the high-pressure cylinder bears to the low-pressure. Engines 
laid down on these lines have fully confirmed the judgment of the de- 
signers. The effect of this constant clearance is to supply sufficient steam 
to the low-pressure cylinder under light loads to hold its expansion curve 
up to atmosphere, and at the same time leave a sufficient clearance volume 
in the high-pressure cylinder to permit of governing the engine on its 
compression under light loads. 

Tests of two non-condensing Corliss engines by G. H. Barrus are re- 
ported in Power, April 27, 1909. The engines were built by Rice & 
Sargent. One is a simple engine 22 X 30, and the other a tandem 
compound 22. and 36 X 36 ins. Both engines are jacketed in both 
heads, and the compound engine has a. reheating receiver with 0.6 sq. ft. 
of brass pipes per rated H.P. (600). The guarantees were: compound 
engine, not to exceed 19 lbs. of steam per I. H.P. per hour, with 130 lbs. 
steam pressure and 1 lb. back pressure in the exhaust pipe, and the 
simple engine not to exceed 23 lbs. The friction load, engine run with 
the brushes off the generator and the field not excited, was not to exceed 
4V2 H.P. in either engine. The results were: compound engine, 99.2 
r.p.m.; 608.3 H.P.; 18.33 lbs. steam per I. H.P. per hour; friction load 
3.8% of 600 H.P.; simple engine, 98.5 r.p.m.; 306.2 LH.P.; 20.98 lbs. per 
I.H.P, per hour; friction 3.6% of 300 H.P. 



972 



THE STEAM-ENGINE. 



A single-cylinder engine 12 X 12 ins., made by the Buffalo Forge Co., 
was tested by Profs. Reeve and Allen. El. World, May 23, 1903. Some 
of the results were: 

I.H.P 16.39 37.20 56.00 69.00 74.10 81.4 89.3 125.9* 86.42f 

Water-rate 52.3 35.3 33.3 31.9 30.6 34.6 33.1 27.6 27.5 

* Steam pressure 125 lbs. gauge, all the other tests 80 lbs. t Con- 
densing, other tests all non-condensing. 

Effect of Water contained in Steam on the Efficiency of the 
Steam-engine. (From a lecture by Walter C. Kerr, before the Franklin 
Institute, 1891.) — Standard writers make little mention of the effect 
of entrained moisture on the expansive properties of steam, but by 
common consent rather than any demonstration they seem to agree that , 
moisture produces an ill effect simply proportional to the percentage 
amount of its presence. That is, 5% moisture will increase the water rate 
of an engine 5%. 

Experiments reported in 1893 by R. C. Carpenter and L. S. Marks, 
Trans. A. S. M. E., xv, in which water in varying quantity was intro- 
duced into the steam-pipe, causing the quality of the steam to range from 
99% to 58% dry, showed that throughout the range of qualities used the 
consumption of dry steam per indicated horse-power per hour remains 
practically constant, and indicated that the water was an inert quantity, 
doing neither good nor harm. 

Influence of Vacuum and Superheat on Steam Consumption. (Eng. 
Digest, Mar., 1909.)— Herr Roginsky ('"Die Turbine") discusses the 
economies effected by the use of superheat and high vacuums. 

In a certain triple-expansion engine, working under good average 
conditions, there was found a saving of approximately 6% for each 10% 
increase in vacuum beyond 50%. 

The Batulli-Tumlirz formula for superheated steam is: p (v + a) = RT. 
in which p = steam pressure in kgs. per sq. meter, v = cubic meters in 
1 kg. of superheated steam at pressure p, a = 0.0084, R = 46.7, and 
T = absolute temperature in deg. C. 

Using this expression, it is found that, neglecting the fuel used for 
superheating, for each 10° C. of superheat at pressures ranging from 
100 to 185 lbs., per sq. in. there is an average increase of volume of 2.8%. 
The work done by the expansion of superheated steam, as shown by 
diagrams, is about 1.6% less for 10° of superheating, so that the net 
saving for each 10° of superheat is 2.8 — 1.6 = 1.2%, approx. (0.66% 
for each 10° F.). 

Rateau's formula for the steam consumption (K) per H.P.-hr. of an 
ideal steam turbine, in which the steam expands from pressure pi to p s , is 

K = 0.85 (6.95 - 0.92 log p 2 ) /(log Pi - logp 2 ), 

K being in kilograms and pi and P2 in kgs. per sq. meter. From this 
formula the following table is calculated, the values being transformed 
into British units. 



Lbs. per 


Lbs. Steam 

at 50% 
Vacuum . 


Reduction of Steam Consumption (%) by 
using a Vacuum of 


sq. m. 


60% 


70% 


80% 


90% 


95% 


184.9 
156.5 
128 
99.6 


11.11 
11.75 
12.57 
13.84 


5. 

5.8 
6.6 
7.6 


11.1 
11.8 
12.9 
14.4 


18.1 
19.3 
20.5 
22. 


27.8 
28.8 
30.8 
33.3 


34.6 
36.4 
38.5 
40.6 



From the entropy diagram it is seen that in expanding from pressures 
in excess of 100 lbs. per sq. in. down to 1.42 lbs. absolute, approximately 
1% more work is performed for every 10° F. of superheat. The effect of 
increasing the degree of vacuum is summed up in the following table; 



ECONOMIC PERFORMANCE OF STEAM-ENGINES. 973 



Increasing 

the 

Vacuum from 


Decreases Steitn Consumption 


in Reciprocating 
Engines. 


in Steam 
Turbines. 


50% to 60% 
50% to 70% 
50% to 80% 
50% to 90% 
50% to 95% 


5.8% 
11.6% 

17.3% 
23.1% ' 
26.0% 


6.2% 
12.6% 
20.0% 
30.1% 

37.4% 



In the last case (from 50% to 95%) the decrease in steam consumption 
is 44% greater for a steam turbine than for a reciprocating engine. 

The following results of tests of a compound engine using superheated 
steam are reported in Power, Aug., 1905. The cylinders were 21 and 
36 X 36 ins. The steam pressure was about 117 lbs. gauge. R.p.m. 100, 
vacuum 26.5 ins. 

Test No 1 2 3 4 5 6 

Indicated H.P 481 461 347 145 333 258 

Superheat of steam 

entering h.p.cyl... 253° F. 242° 221° 202° 232° 210° 
B.T.U. supplied per 

I.H.P. per min. ... 198.2 201.7 197.6 192.1 194.0 194.0 
B.T.U. theoretically 

required. Rankine 

cycle.... 142.4 142.5 130.2 128.0 126.0 128.5 

Efficiency ratio 0.72 0.71 0.66 0.67 0.65 0.66 

Thermal efficiency % 21.39 21.02 21.46 22.07 21.86 21.86 
Lbs. steam per I.H.P. 

hour 9.098 9.267 8.886 8.585 8.682 8.742 

The Practical Application of Superheated Steam is discussed in a 
paper by G. A. Hutchinson in Trans. A. S. M. E., 1901. Many different 
forms of superheater are illustrated. 

Some results of tests on a 3000-H.P., four-cylinder, vertical, triple-ex- 
pansion Sulzer engine, using steam from Schmidt independently fired 
superheaters, are as follows. (Eng. Rec, Oct. 13, 1900.) 



Tests Using Steam. 



Highly Superheated. 





Mod- 




erately 




Super- 




heated 


188.4 


190.3 


614 


531 


868 


2,850 


9.56 


10.29 


479 


447 



Initial pressure in h.p. cyl. 

(absolute), lbs 

Temp, of steam in valve 

chest, deg. F 

Total I.H.P 

Lbs. Steam per I.H.P. hour 
Watt hours per lb. of coal. 



187.3 


195.5 


582 
2,900 
9.64 
477 


585 
2,779 
9.67 
482 



194.6 

381 
2,951 
11.77 
438 



195.9 

381 
2,999 
11.75 
435 



The saving due to the use of highly superheated steam is (482-438) + 
482 = 9.1%. 

Tests of a 4000-H.P. double-compound engine (Van den Kerchove, of 
Brussels) with superheated steam are reported in Power, Dec. 29, 1908. 
The cylinders are 341/4 and 60 ins., stroke 5 ft. Ratio of areas 2.97. The 
following are the principal results, the first figures given being for the full- 
load test, and the second (in parentheses) for the half-load test. Steam 



974 THE STEAM-ENGINE. 

pressure at drier, 136.5 lbs. (137.9). R.p.m. 84.3 (84.06). Temp, of 
steam entering engine 519° F. (498), leaving l.p. cyl. 121.5° (121.5). 
Vacuum in condenser, ins., 27.5 (27). I.H.P. 3776 (2019). Steam per 
I.H.P. hour, lbs., 9.62 (9.60). 

The saving due to the use of superheated steam is reported in numerous 
tests as being all the way from less than 10% to more than 40%. The 
greater saving is usually found with engines that are the most inefficient 
with saturated steam, such as single-cylinder engines with light loads, in 
which the cylinder condensation is excessive. 

R. P. Bolton (Eng. Mag., May, 1907) states that tests of superheated 
steam in locomotives, by. the Prussian Railway authorities in 1904, with 
50°, 104° and 158° F. superheat, showed a saving of water respectively 
of 2.5, 10 and 16%, and a saving of coal of 2, 7 and 12%. Mr. Bolton's 
paper concludes with a long list of references on the subject of super- 
heated steam. A paper by J. R. Bibbins in Elec. Jour., March, 1906, gives 
a series of charts showing the saving made by different degrees of super- 
heating in different types of engines, including steam turbines. 

For description of the Foster superheater, see catalogue of the Power 
Specialty Co., New York. 

The Wolf (French) semi-portable compound engine of 40 H.P. with 
superheater and reheater, the engine being mounted on the boiler, is 
reported by R. E. Mathot, Power, July, 1906, to have given a steam 
consumption as low as 9.9 lbs. per I.H.P. hour, and 10.98 lbs. per B.H.P. 
hour. The steam pressure in the boiler was 172.6 lbs., and was super- 
heated initially to 657° F., and reheated to 361° before entering the l.p. 
cylinder. . This is a remarkable record for a small engine. 

A test of a Rice & Sargent cross-compound horizontal engine 16 and 
28 X 42 ins., with superheated steam, is reported by D. S. Jacobus in 
Trans. A. S. M. E., 1904. The steam pressure at the throttle was 140 lbs. 
gauge, the superheating was 350 to 400°, and the vacuum 25 to 26 ins., 
r.p.m. 102. In three tests with superheated and one with saturated, 
steam the results were: 

I.H.P. developed 474.5 420.4 276.8 406.7 

Water consumption per I.H.P. hour 9.76 9.56 9.70 13.84 

Coal consumption per I.H.P. hour 1.265 1.257 1.288 1.497 

B.T.U. per min. per I.H.P 205.0 203.7 208.8 248.2 

Temp, of steam entering h.p. cyl 634 659 672 

Temp, of steam leaving h.p. cyl 346 331 288 262 

Temp, of steam entering l.p. cyl 408 396 354 269 

Temp, of steam leaving l.p. cyl 135 141 117 , 

Performance of a Quadruple Engine. — O. P. Hood (Trans. A. S. 
M. E., 1906) describes a test of a high-duty air compressor, with four 
steam cylinders, 14.5, 22, 38 and 54 in. diam., 48-in. stroke. The clear- 
ances were respectively 6, 5.7, 4.4 and 3.5%. R.p.m. 57. Steam pressure, 
gauge, near throttle, 242.8 lbs., in 1st. receiver 120.7 lbs., in 2d, 30. S lbs., 
in 3d, vac, — 1.24 ins. Moisture in steam near throttle, 5.74%. Steam 
in No. 1 receiver, dry; in No. 2, 17° superheat: in No. 3, 9° superheat. 
The engine has poppet valves on the h.p. cylinder and Corliss valves on 
the other cylinders. The feed-water heaters are four in number, in series, 
on the Nordberg system; No. 1 receives its steam from the exhaust of 
No. 4 cylinder; No. 2 from the jacket of No. 4 cyl.: No. 3 from the jackets 
of No. 3 cylinder and No. 3 reheater; No. 4 from the jacket of No. 2 
cylinder. The reheaters are supplied with steam from the boilers. The 
temperatures of steam and water were as follows: Temperatures of steam: 
Fed to No. 1 engine, 403°; leaving receivers, No. 1, 351°; No. 2, 291°; 
No. 3, 216°. Exhaust entering preheater. 114°. Temperature corre- 
sponding to condenser pressure, 109.6°. Temperatures of water: Fed to 
preheater, 93° : fed to heaters, No. 1, 114°; No. 2, 173°; No. 3, 202°; No. 4, 
269°; leaving heater No. 4 as boiler feed, 334°. Mr. Hood gives a dia- 
gram showing graphically the transfer of heat through the several parts 
of the apparatus, from which the following is taken. The figures are in 
B.T.U. transferred per minute. 



ECONOMIC PERFORMANCE OF STEAM-ENGINES. 975 





Received 

from 
Boiler or 
Receiv'rs. 


Received 

from 
Jackets. 


Convert- 
ed into 
Work. 


Delivered 

to 

Heater. 


Delivered 

to 
Jackets. 




194,183 
187,348 
174,872 
165,973 
160,083 
149,538 
148,683 
128,835 
125,885 
120,285 


862 
6,624 
2,000 
8,060 
1,150 
5,185 

940 


7,697 








17,100 


2,000 


No. 2 Cylinder 


10,899 






12,800 


1,150 




11,695 






5,100 
9,100 
2,350 
5,690 


940 




ii,688 



































The principal results of the test are as follows: 

Cylinder 1 2 3 4 

I.H.P. developed in steam cylinders 181.47 256.96 275.71 275.56 

I.H.P. used in the cylinders 220.04 222.12 226.20 214.84 

Total indicated horse-power, steam cylinders 989.7 

Total horse-power used in air cylinders 883.2 

Total indicated horse-power of auxiliaries 11.0 

Horse-power representing friction of the 

machine 95.5 

Per cent of friction . . 9.65% 

Mechanical efficiency engine and compressor 90.35% 

Heat consumed by engine per hour per I.H.P., 10,157 B.T.U.; per 
B.H.P., 11,382 B.T.U. Equivalent standard coal consumption per 
hour assuming 10,000 B.T.U. imparted to the boiler per pound coal, per 
I.H.P., 1.016 lbs. ; per B.H.P., 1.138 lbs. Dry steam per hour per I.H.P., 
11.23 lbs.; per B.H.P., 12.58 lbs. Heat units consumed per minute, per 
I.H.P., 169.29 B.T.U.; per B.H.P., 189.70 B.T.U. 

Efficiency of Carnot cycle between the temperature of incoming 

steam and that corresponding to pressure in the condenser. . .34.0 % 

Actual heat efficiency attained by this engine 25.05% 

Relative efficiency compared with Carnot cycle 73.69% 

Relative efficiency compared with Rankine cycle 88.2 % 

Duty, ft.-lbs. per million B.T.U. supplied : . 194,930,000 

This engine establishes a new low record for the heat consumed per hour 
per I.H.P., being 9% lower than that used by the Wild wood pumping 
engine reported in 1900. (See Pumping Engines.) 

The Use of Reheaters in the receivers of multiple-expansion engines is 
discussed by R. H . Thurston in Trans. A.S.M.E., xxi, 893 . He shows that 
such receivers improve the economy of an engine very little unless they 
are also superheaters; in which case marked economy may be effected 
by the reduction of cylinder condensation. The larger the amount of 
cylinder condensation and the greater the losses, exterior and interior, 
the greater the effect of any given amount of superheating. The same 
statement will hold of the use of reheaters: the more wasteful the engine 
without them and the more effectively they superheat, the larger the 
gain by their use. A reheater should be given such area of heating surface 
as will insure at least moderate superheating. 

Influence of the Steam-jacket. — Tests of numerous engines with 
and without steam-jackets show an exceeding diversity of results, ranging 
all the way from 30% saving down to zero, or even in some cases showing 
an actualloss. The opinions of engineers at this date (1894) is also as 
diverse as the results, but there is a tendency towards a general belief 
that the jacket is not as valuable an appendage to an engine as was for- 
merly supposed. An extensive resume of facts and opinions on the steam- 
jacket is given by Prof. Thurston in Trans. A. S. M. E., xiv, 462. See 



976 



THE STEAM-ENGINE. 



also Trans. A. S. M. E., xiv, 873 and 1340; xiii, 176; xii, 426 and 1340; 
and Jour. F. I., April, 1891, p. 276. The following are a few statements 
selected from these papers. 

The results of tests reported by the research committee on steam-jackets 
appointed by the British Institution of Mechanical Engineers in 1886, 
indicate an increased efficiency due to the use of the steam-jacket of from 
1% to over 30%, according to varying circumstances. 

Sennett asserts that "it has been abundantly proved that steam-jackets 
are not only advisable but absolutely necessary, in order that high rates of 
expansion may be efficiently carried out and the greatest possible economy 
of heat attaned." 

Isherwood finds the gain by its use, under the conditions of ordinary 
practice, as a general average, to be about 20% on small and 8% or 9% on 
large engines, varying through intermediate values with intermediate 
sizes, it being understood that the jacket has an effective circulation, and 
that both heads and sides are jacketed. 

Professor Unwin considers that "in all cases and on all cylinders the 
jacket is useful; provided, of course, ordinary, not superheated, steam is 
used; but the advantages may diminish to an amount not worth the in- 
terest on extra cost." 

Professor Cotterill says: Experience shows that a steam-jacket is advan- 
tageous, but the amount to be gained will vary according to circumstances. 
In many cases it may be that the advantage is small. Great caution is 
necessary in drawing conclusions from any special set of experiments on 
the influence of jacketing. 

Mr. E. D. Leavitt has expressed the opinion that, in his practice, steam- 
jackets produce an increase of efficiency of from 15% to 20%. 

In the Pawtucket pumping-engine, 15 and 30VsX 30 in., 50 revs, per 
min., steam-pressure 125 lbs. gauge, cut-off 1/4 in h.p. and 1/3 in l.p. cylinder, 
the barrels only jacketed, the saving by the jackets was from 1% to 4%. 

The superintendent of the Holly Mfg. Co. (compound pumping-engines) 
says: " In regard to the benefits derived from steam-jackets on our steam- 
cylinders, I am somewhat of a skeptic. From data taken on our own 
engines and tests made I am yet to be convinced that there is any practical 
value in the steam-jacket." 

Professor Schrboter from his work on the triple-expansion engines at 
Augsburg, and Mm the results of his tests of the jacket efficiency on a 
small engine of the Sulzer type in his own laboratory, concludes: (1) The 
value of the jacket may vary within very wide limits, or even become 
negative. (2) The shorter the cut-off the greater the gain by the use of a 
jacket. (3) The use of higher pressure in the jacket than in the cylinder 
produces an advantage. The greater this difference the better. (4) The 
high-pressure cylinder may be left unjacketed without great loss, but the 
other should always be jacketed. 

The test of the Laketon triple-expansion pumping-engine showed a gain 
of 8.3% by the use of the jackets, but Prof. Denton points out (Trans. 
A.S. M. E., xiv, 1412) that all but 1.9% of the gain was ascribable to the 
greater range of expansion used with the jackets. 

Test of a Compound Condensing Engine with and without Jackets 
at different Loads. (R. C. Carpenter, Trans. A. S. M. E., xiv, 428.) -7- 
Cylinders 9 and 16 in. X 14 in. stroke; 112 lbs. boiler- pressure; rated 
capacity 100 H.P. ; 265 revs, per min. Vacuum, 23 in. From the results 
of several tests curves are plotted, from which the following principal 
figures are taken. 



Indicated H.P 


30 
22.6 


40 

21.4 


50 
20.3 


60 

19.6 
22 
10.9 


70 

19 

20.5 
7.3 


80. 

18.7 
19.6 
4.6 


90 

18.6 
19 2 
3.1 


100 

18.9 
19.1 
1.0 


110 

19.5 

19.3 

-1.0 


120 

20.4 
20.1 
-1.5 


]?•> 


Steam per I. H.P. per hr. 
With jackets, lbs 


21.0 





















This table gives a clue to the great variation in the apparent saving due 
to the steam-jacket as reported by different experimenters. With this 



ECONOMIC PERFORMANCE OF STEAM-ENGINES. 977 

particular engine it appears that when running at its most economical 
rate of 100 H.P., without jackets, very little saving is made by use of the 
jackets. When running light the jacket makes a considerable saving, but 
when overloaded it is a detriment. 

At the load which corresponds to the most economical rate, with no 
steam in jackets, or 100 H.P., the use of the jacket makes a saving of only 
1%; but at a load of 60 H.P. the saving by use of the jacket is about 
11%, and the shape of the curve indicates that the relative advantage of 
the jacket would be still greater at lighter loads than 60 H.P. 

The Best Economy of the Piston Steam Engine at the Advent of the 
Steam Turbine is the subject of a paper by J. E. Denton at the Inter- 
national Congress of Arts and Sciences, St. Louis, 1904. {Power, Oct. 
26, 1905.) Prof. Denton says: 

During the last two years the following records have been established: 

(1) With an 850-H.P. Rice & Sargent compound Corliss engine, running 
at 120 r.p.m., having a 4 to 1 cylinder ratio, clearances of 4% and 7%, 
live jackets on cylinder heads and live steam in reheater, Prof. Jacobus 
found for 600 H.P. of load, with 150 lbs. saturated steam, 28.6 ins. vacuum, 
and 33 expansions, 12.1 lbs. of water per I.H.P., with a cylinder-conden- 
sation loss of 22%, and a jacket consumption of 10.7% of the total steam 
consumption. 

(2) With a 250-H.P. Belgian poppet-valve compound engine, 126 r.p.m.. 
with 2.97 to 1 cylinder ratio, clearances of 4%, steam-chest jackets on 
barrels and head, and no reheater, Prof. Schroter, of Munich, found with 
117 H.P. of load, 130 lbs. saturated steam, 27.6 ins. of vacuum, and 32 ex- 
pansions, 11.98 lbs. of water per H.P. per hour, with a cylinder-condensa- 
tion loss of 23.5%, and a jacket consumption of 7% of the total steam 
consumption in the high cylinder jacket and 7% in the low jacket. 

(3) With the Westinghouse. twin compound combined poppet-valve 
and Corliss- valve engine, at the New York Edison plant, running 76 r.p.m., 
with 5.8 to 1 cylinder ratio, clearances of 10.5% and 4%, without jackets 
or reheater, Messrs. Andrew, Whitham and Wells found for the full load 
of 5400 H.P., 185 lbs. steam pressure, 27.3 ins. vacuum, and 29 expan- 
sions, 11.93 lbs. of water per I. H.P. per hour, with an initial condensation 
of about 32%. 

These facts show that the minimum water consumption of the compound 
engine of the present date, using saturated steam, is not dependent upon 
any particular cylinder ratio and clearance nor upon any system of jacket- 
ing, but that the essential condition is the use of a ratio of expansion 
of about 30, above which the cylinder-condensation loss is liabie to prevail 
over the influence of the law of expansion. The conclusion appears 
warranted, therefore, that if this ratio of expansion is secured with any 
of the current cylinder and clearance ratios, and with any existing system 
of jackets and reheaters, or without them, a water consumption of 12.4 lbs. 
per horse-power is possible, and that a variation of 0.4 lb. below or above 
this figure may occur by the accidental favorable, or unfavorable, jacket 
and cylinder-wall expenses which are beyond the exact control of the 
designer. 

Compound Piston Engine Economy vs. that of Steam Turbine. — In order 
to compare the economy of the piston engine with that of the steam tur- 
bine, we must use the water consumption per brake horse-power, since no 
indicator card is possible from the turbine; and furthermore, we must use 
the average water consumption for the range of loads to which engines are 
subject in practice. 

In all of the public turbine tests to date, with one exception the output 
was measured through the electric power of a dynamo whose efficiency is 
not given for the range of loading employed, so that the average brake 
horse-power is not known. This exception is the Dean and Main test of 
a 600-H.P. Westinghouse-Parsons turbine using saturated steam at 150 lbs. 
pressure, and a 28-in. vacuum. We may compare the results of this test 
with that of the 850-H.P. Rice & Sargent and of the 250-H.P. Belgian 
engine, by assuming that the power absorbed by friction in these engines 
is 3% of the indicated load plus the power shown by friction cards taken 
with the engine unloaded. The latter showed 5% of the rated power in 
the R. & S. engine and 8% in the Belgian engine. The results are: 



978 THE STEAM-ENGINE. 

Per cent of full load 41 75 100 125 Avg. 85% 

Lbs. Water per Brake H.P. Hour. 

600-H. P. Turbine 13.62 13.91 14.48 16.05 14.51 

800-H. P. Comp. Engine 13.78 13.44 13.66 17.36 14.56 

250 H.P. Belgian Engine 15.10 14.15 13.99 15.31 14.64 

These figures show practical equality in economy of the types of engines. 
The full report of the Van den Kerchove Belgian engine is given in Power, 
June, 1903. 

For large-sized units Prof. Denton compares the Elberfeld test of a 
Parsons turbine at the full load of 1500 electric H.P., allowing 5% for 
attached air pump, 95% for generator efficiency, with the 5400-H.P. 
Westinghouse compound engine at the New York Edison station, whose 
friction at full load was found to be 4%. The turbine with 150 lbs. steam 
and 28 ins. vacuum required 13.08 lbs. of saturated steam per B.H.P. 
hour, a gain of 4% over the 600-H. P. turbine. The engine with 18.5 lbs. 
boiler pressure gave 12.5 lbs. per B.H.P. hour. Crediting the turbine 
with the possible influence of the difference in size and steam pressure, 
there is again practical equality in economy between it and the piston 
engine. 

Triple-expansion Pumping Engines. — The triple-expansion engine has 
failed to supplant the compound for electric light and mill service, be- 
cause the gain in fuel economy due to its use was not sufficient to over- 
come its higher first cost, depreciation, etc. It is, however, almost uni- 
versally used in marine practice, and also in large-sized pumping engines. 
Prof. Denton says: Pumping engines in the United States have been de- 
veloped in the triple-expansion fly-wheel type to a degree of economy 
superior to that afforded by any compound mill or electric engine, and, 
for saturated steam, superior to that of the pumping engines of any other 
country. This is because their slow speed permits of greater benefit 
from jackets and reheaters and of less losses from wire-drawing and back 
pressure. These causes, together with the greater subdivision of the range 
of expansion, have resulted in records made between 1894 and 1900 of 
11.22, 11.26 and 11.05 lbs. of saturated steam per I.H.P., with 175 lbs. 
steam pressure and from 25 to 33 expansions, in the cases of the Leavitt, 
Snow and Allis pumping engines, respectively, the corresponding heat 
consumption being by different dispositions of the jacket drainage, 204, 
208 and 212 thermal units per I.H.P. minute; while laterthe Allis pump, 
with 85 lbs. steam pressure, has lowered the record to 10.33 lbs. of satu- 
rated steam per I.H.P., with 196 B.T.U. per H.P. rrinute. 

Gain from Superheating. — In the Belgian compound engine above de- 
scribed, with steam at 130 lbs., vacuum 27.6 ins., the average consumption 
of saturated steam, between 45 and 125% of load, was 12.45 lbs. per 
I.H.P. hour, or 225 B.T.U. per I.H.P. minute. With steam superheated 
224° F. the average consumption for the same loads was 10.09 lbs. per 
I.H.F. hour, computed to be equivalent to 209 B.T.U. per H.P. rrinute, 
a gain due to superheating of 7%. With steam superheated 307° and 
the load about 80% of rating the water consun ption was 8.99 lbs. per 
I.H.P. hour, equivalent to 192 B.T.U. per H.P. ninute. The same load 
with saturated steam requires 221 B.T.U., showing a gain due to super- 
heating of 13%. 

The best performance reported for superheated steam used in the tur- 
bine is that of Brown & Boveri Parsons Frankfort 4000-H.P. nachine, 
which, with 183 lbs. gauge pressure and 190° F. superheat, afforded 10.28 
lbs. per B.H.P. hour, assuming a generator efficiency of 0.95. Beckoning 
from the feed temperature of its vacuum of 27.5 ins., the heat consumption 
is 214 B.T.U. per H.P. minute. 

The heat consumption of the 250-H.P. Belgian compound engine per 
B.H.P. hour at the highest superheating of 307° F. is 220 B.T.U. The 
turbine, therefore, probably holds the record for brake horse-power econ- 
omy over the piston engine for superheated steam by a margin of about 
3%, although had the compound engine been of the same horse-power as 
the turbine, so that its friction load would be onlv 8% of its power instead 
of the 13% here allowed, it would have excelled the turbine in brake 
horse-power economy by a margin of about 2.5%. 

The Sulphur-dioxide Addendum. — If the expansion in piston engines 



ECONOMIC PERFORMANCE OF STEAM-ENGINES. 979 



could continue until the pressure of 1 pound was attained before exhaust 
occurred, considerable more work could be obtained from the steam. 
This cannot be done, for two reasons: first, because the low cylinder would 
have to be about five times greater in volume, which is commercially 
impracticable; and, second, because the velocity of exit through the 
largest exhaust ports possible is so great that the frictional resistance of 
the steam makes the back pressure from 1 to 3 pounds higher than the 
condenser pressure in the best engines of ordinary piston speed. 

All the work due to this extra expansion can be obtained by exhausting 
the steam at 6 lbs. pressure against a nest of tubes containing sulphur 
dioxide which is thereby boiled to a vapor at about 170 lbs. pressure. 

Professor Josse, of Berlin, has perfected this sulphur-dioxide system 
of improvement, and reliable tests have shown that if cooling water of 
65° is available, and to the extent of about twice the quantity usually em- 
ployed for condensing steam under 28 ins. of vacuum, a sulphur-dioxide 
cylinder of about half the size of the high-pressure cylinder of a com- 
pound engine will do sufficient work to improve the best economy of 
such engines at least 15%. The steam turbine expands its steam to the 
pressure of its exhaust chamber, and as unlimited escape ports can be 
provided from this chamber to a condenser, it follows that the turbine 
can practically expand its steam to the pressure of the condenser. There- 
fore a steam turbine attached to a piston engine to operate with the latter's 
exhaust should effect the same saving as the sulphur-dioxide cylinder. 

Standard Dimensions of Direct-connected Generator Sets. From 
a report by a committee of the A. S. M. E., 1901. 

Capacity of unit, K.W 25 35 50 75 100 150 200 

Revolutions per minute 310 300 290 275 260 225 200 

Armature bore, center crank engines . 4 4 41/2 51/2 6 7 8 

Armature bore, side-crank engines .. . 41/2 51/2 6V2 71/2 8 1/2 10 11 

The diameter of the engine shaft at the armature fit is 0.001 in. greater 
than the bore, for bores up to and including 6 ins., and 0.002 in. greater 
for bores 6 1/2 ins. and larger. 

Dimensions of Some Parts of Large Engines in Electric Plants. — 

The Electrical World, Sept. 27, 1902, gives a table of dimensions of the 
engines in the five large power stations in New York City at that date. 
The following figures are selected from the table. 



Name of station 


Metro- 
politan. 


Manhat- 
tan. 


Kings- 
bridge. 


Rapid 

Transit. 


Edison. 


Type of engine 


Vert. 
Cross- 
Comp. 


Double, 
2hor. 

2 vert. 
Cyis. 


Vert. 
Cross- 
Comp. 


Double, 
2 hor. 
2 vert. 
Cyls. 


3 Cyl. Vert. 


Rated H.P 

Cylinders, all 60-in. 


4500 

46,86 
9, 10 
14 X 14 
14 X 14 
27 ft. 4 in. 
37 in. 
34X60 


8000 

44,88 

8 
18 x 18 
12X 12 
25 ft. 3 in. 
37 in. 
34X60 


4500 

46, 86 
9, 10 

14 X 14 

14 X 14 
27 ft. 
39 in. 

34X60 


8900 

42, 86 

8, 10 

20 X 18 

12X 12 

25 ft. 3 in. 

37 in. 
34X60 


5200 

431/2,2-751/2 

9 
22 & 16 X 14 


Piston rods, diam. in., 




14 X 14 


Shaft length 


35 ft 


max. diam 

bearings 


293/ 8 in. 
26X60 



The shafts are hollow, with a 16-in. hole, except the Edison which has 
10 in. The speed of all the engines is 75 r.p.m., or 750 ft. per min. The 
crank pins of the Manhattan and Rapid Transit engines each are attached 
to two connecting rods, side by side, hor. and vert., each rod having a 
bearing 9 in. long on the pin. The crank pins of the Edison engine are 
16 in. diam. for the side-cranks, and 22 in. for the center-crank. 



980 



THE STEAM-ENGINE. 



Some Large Rolling-Mill Engines. 







P, 




J 


Fly-wheel. 








Cylinders. 


Ph 


Type. 


g^ 




Location. 


Builders. 








o 




rt 




Ph~ 


Diam. 


Wt. 
















ft. 


lbs. 






1 


44 & 82x60 


65 


Cross-C. 


140 


24 


150,000 


Republic I. &S 
Co., Youngs- 
town, Ohio. 


Filer & 
Stowell. 


2 


46 & 80x60 


80 


Tandem. 


150 


24 


110,000 


Carnegie S. Co., 
Donora, Pa. 


Wiscon- 
sin Eng. 

Co. 
Wm. Tod 


3 


52 & 90x60 








25 


250,000 


















Youngstown, 


Co. 














Ohio. 




4 


2 each 




Double 


150 


none 


Carnegie S. Co., 


Allis 




42& 70x54 




Tandem. 






S. Sharon, Pa. 

Carnegie S. 
Co.,Du- 
quesne, Pa. 


Chal- 
mers Co. 

Mackin- 
tosh, 


b 


2 each 


60 


Double 


150 


none 


Jones & 


Hemp- 




44 & 70X60 




Tandem 






Laughlin 
Steel Co., 


hill & 














Co. 














Alequippa, 
















I Pa. J 





Some details: Main bearings, No. 1, 25 X 431/2 in.; No. 2, 30 X 52 in.; 
No. 3, 30 X 60 in. Shaft diam. at wheel pit, No. 1, 26 in.; No. 3, 36 in. 
Crank pins, No. 1, h.p. 14 X 14; l.p., 14 X 23 in.; No. 2, 18 X 18 in. 
Crosshead pins, No. 1, 12 X 14; No. 2, 16 X 20 in. No. 4 is a reversing 
engine, with the Marshall gear. No. 5 is a reversing engine with piston 
valves below the cylinders. 

Counterbalancing Engines. — Prof. Unwin gives the formula for 

counterbalancing vertical engines: Wi = W2r/p (1) 

in which Wi denotes the weight of the balance weight and p the radius to 
its center of gravity, Wi the weight of the crank-pin and half the weight of 
the connecting-rod, and r the length of the crank. For horizontal engines: 



Wi = 2/ 3 (W 2 + Wz) r/p to 3/ 4 (Wo + Wz) r/p, 



. • (2) 

in which W3 denotes the weight of the piston, piston-rod, cross-head, and 
the other half of the weight of the connecting-rod. 

The American Machinist, commenting on these formulae, says: For 
horizontal engines formula (2) is often used; formula (1) will give a coun- 
terbalance too light for vertical engines. We should use formula (2) for 
computing the counterbalance for both horizontal and vertical engines, 
excepting locomotives, in which the counterbalance should be heavier. 

For an account of experiments on counterbalancing large engines, with 
a method of recording vibrations, see paper by D. S. Jacobus, Trans. 
A. S. M. E., 1905. 

Preventing Vibrations of Engines. — Many suggestions have been 
made for remedying the vibration and noise attendant on the working 
of the big engines which are employed to run dynamos. A plan which has 
given great satisfaction is to build hair-felt into the foundations of the 
engine. An electric company has had a 90-horse-power engine removed 
from its foundations, which were then taken up to the depth of 4 feet. A 
layer of felt 5 inches thick was then placed on the foundations and run 
up 2 feet on all sides, and on the top of this the brickwork was built up. — 
Safety Valve. 

Steam-engine Foundations Embedded in Air. — In the sugar- 
refinery of Claus Spreckels, at Philadelphia, Pa., the engines are distrib- 
uted practically all over the buildings, a large proportion of them being 
on upper floors. Some are bolted to iron beams or girders, and are con- 



COMMERCIAL ECONOMY — COSTS OF POWER. 981 

sequently innocent of all foundation. Some of these engines ran noise- 
lessly and satisfactorily, while others produced more or less vibration and 
rattle. To correct the latter the engineers suspended foundations from 
the bottoms of the engines, so that, in looking at them from the lower 
floors, they were literally hanging in the air. — Iron Age, Mar. 13, 1890. 

COMMERCIAL ECONOMY. — COSTS OF POWER. 

The Cost of Steam Power is an exceedingly variable quantity. The 
principal items to be considered in estimating total annual cost are: load 
factor ; hours run per year ; percentage of full load at different hours of 
the day ; cost and quality of fuel ; boiler efficiency and steam consumption 
of engines at different loads ; cost of water and other supplies ; cost of 
labor, first cost of plant, depreciation, repairs, interest, insurance and taxes. 

In figuring depreciation not only should the probable life of the several 
parts of the plant, such as buildings, boilers, engines, condensers, etc., be 
considered, but also the possibility of part of the plant, or the whole of it, 
depreciating rapidly in value on account of obsolescence of the machinery 
or of changes in the conditions of the business. 

When all of the heat in the exhaust steam from engines and pumps, in- 
cluding water of condensation, is used for heating purposes the fuel cost of 
steam-engine power may be practically nothing, since the exhaust contains 
all of the heat in the steam delivered to the engine except from 5 to 10 
per cent which is converted into work, and a trifling amount lost by 
radiation. 

Most Economical Point of Cut-off in Steam-engines. (See paper 
by Wolff and Denton, Trans. A. S. M. E., vol. ii, p. 147-281; also, Ratio 
of Expansion at Maximum Efficiency, R. H. Thurston, vol. ii, p. 128.) 
— The problem of the best ratio of expansion is not one of economy of con- 
sumption of fuel and economy of cost of boiler alone. The question of in- 
terest on cost of engine, depreciation of value of engine, repairs of engine, 
etc., enters as well; for as we increase the rate of expansion, and thus, 
within certain limits fixed by the back-pressure and condensation of 
steam, decrease the amount of fuel required and cost of boiler per unit of 
work, we have to increase the dimensions of the cylinder and the size 
of the engine, to attain the required power. We thus increase the cost 
of the engine, etc., as we increase the ^ate of expansion, while at the same 
time we decrease the fuel consumption, the cost of boiler, etc. So that 
there is in every engine some point of cut-off, determinable by calculation 
and graphical construction, which will secure the greatest efficiency for 
a given expenditure of money, taking into consideration the cost of fuel, 
wages of engineer and firemen, interest on cost, depreciation of value, 
repairs to and insurance of boiler and engine, and oil, waste, etc., used 
for engine. In case of freight-carrying vessels, the value of the room 
occupied by fuel should be considered in estimating the cost of fuel. 

Type of Engine to be used where Exhaust-steam is needed for 
Heating. — In many factories more or less of the steam exhausted from 
the engines is utilized for boiling, drying, heating, etc. Where all the 
exhaust-steam is so used the question of economical use of steam in the 
engine itself is eliminated, and the high-pressure simple engine is entirely 
suitable. Where only part of the exhaust-steam is used, and the quantity 
so used varies at different times, the question of adopting a simple, a 
condensing, or a compound engine becomes more complex. This problem 
is treated by C. T. Main in Trans. A. S. M. E., vol. x, p. 48. He shows 
that the ratios of the volumes of the cylinders in compound engines should 
vary according to the amount of exhaust-steam that can be used for 
heating. A case is given in which three different pressures of steam are 
required or could be used, as in a worsted dye-house: the high or boiler 
pressure for the engine, an intermediate pressure for crabbing, and low- 
pressure for boiling, drying, etc. If it did not make too much compli- 
cation of parts in the engine, the boiler-pressure might be used in the high- 
pressure cylinder, exhausting into a receiver from which steam could be 
taken for running small engines and crabbing, the steam remaining in the 
receiver passing into the intermediate cylinder and expanded there to 
from 5 to 10 lbs. above the atmosphere and exhausted into a second 
receiver. From this receiver is drawn the low-pressure steam needed for 
drying, boiling, warming mills, etc., the steam remaining in the receiver 
passing into the condensing cylinder. 



982 THE STEAM-ENGINE* 



Cost of Steam-power. (Chas. T. Main, Trans. A. S. M. E„ X.* 48;)— 
Estimated costs in New England in 1888, per horse-power* based on engines 
of 1000 H.P. 

Compound Condens* Non^con- 

Engine. ing Engine, densing 

Engine. 

1. Cost engine and piping, complete. .. .$25.00 $20.00 $17.50 

2. Engine-house 8.00 7.50 7.50 

3. Engine foundations 7.00 5.50 4.50 

4. Total engine plant 40.00 33.00 29.50 

5. Depreciation, 4% on total cost. ..... 1.60 1-32 1.18 

6. Repairs, 2% on total cost 0.80 0.66 0.59 

7. Interest, 5% on total cost 2.00 1.65 1.475 

8. Taxation, 1.5% on 3/ 4 cost 0.45 0.371 0.332 

9. Insurance on engine and house. .... . 0.165 0.138 0.125 

10. Total of lines 5, 6, 7, 8, 9 5.015 4.139 3.702 

11. Cost boilers, feed-pumps, etc 9.33 13.33 16.00 

12. Boiler-house 2.92 4.17 5.00 

13. Chimney and flues 6.11 7.30 8.00 

14. Total boiler-plant 18.36 24.80 29.00 

15. Depreciation, 5% on total cost 0.918 1.240 1.450 

16. Repairs, 2% on total cost 0.367 0.496 0.580 

17. Interest, 5% on total cost 0.918 1.240 1.450 

18. Taxation, 1.5% on 3/ 4 cost 0.207 0.279 0.326 

19. Insurance, 0.5% on total cost. 0.092 0.124 0.145 



20. Total of lines 15 to 19 ...... . 2.502 3.379 3.951 

21. Coal used per I.H.P. per hour, lbs. . . 1.75 2.50 3.00 

22. Cost of coal per I.H.P. per day of 10 1/4 cts. cts. cts. 

hours at $5.00 per ton of 2240 lbs 4.00 5.72 6.86 

23. Attendance of engine per day 0.60 0.40 0.35 

24. Attendance of boilers per day. ..... . 0.53 0.75 0.90 

25. Oil, waste, and supplies, per day .... 0.25 0.22 0.20 

26. Total daily expense 5.38 7.09 8.31 

27. Yearly running expense, 308 days, per 

I.H.P $16,570 $21,837 $25,595 

28. Total yearly expense, lines 10, 20, 

and 27 24.087 29,355 33.248 

29. Total yearly expense per I.H.P. for 

power if 50% of exhaust-steam is 

used for heating 12.597 14.90? 16,663 

30. Total if all exhaust-steam is used for 

heating 8.624 7.916 7.700 

When exhaust-steam or a part of the receiver-steam is used for heating, 
or if part of the steam in a condensing engine is diverted from the con- 
denser, and used for other purposes than power, the value of such steam 
should be deducted from the cost of the total amount of steam generated 
in order to arrive at the cost properly chargeable to power. The figures 
in lines 29 and 30 are based on an assumption made by Mr. Main of losses 
Of heat amounting to 25% between the boiler and the exhaust-pipe, an 
allowance which is probably too large. 

See also two papers by Chas. E. Emery on "Cost of Steam Power," 
Trans. A. S. M. E., vol. xii, Nov., 1883, and Trans. A. I. E. E., vol. x, 
Mar., 1893. 

Decourcey May (Trans. A. S. M.E., 1894) gives the following estimates 



COMMERCIAL ECONOMY — COSTS OF POWER. 983 



of the annual cost of power with different types of engine. He figures 
interest and depreciation each at 5%, insurance at 1%, and taxes at 11/2% 
of the cost of the plant. No cost of water is charged. 



Cost of coal per 2240 lbs . 



Cost of 1 I.H.P. per year. 



365 days of 24 hours. 



308 days of 10 1/4 hours. 



Triple-expansion pumping, 
20 revs 

Triple-expansion without 
pumps, 50 revs 

Compound mill, best engine 

Compound mill, average.. . 

Compound elec. light, av. . 

Compound trolley 

Triple-expansion trolley. . . 

Condensing mill 

Non-cond., 50 to 200 H.P.. . 



55 


61 


33 


39 


36 


44 


46 


52 


139 


157 


58 


68 


54 


64 


52 


61 


76 


81 



33 


35 


18 


20 


19 


21 


25 


28 


84 


90 


32 


36 


29 


33 


29 


33 


53 


57 



Cost of Coal for Steam-power. — The following table shows the 
amount and the cost of coal per day and per year for various horse-powers, 
from 1 to 1000, based on the assumption of 4 lbs. of coal being used per 
hour per horse-power. It is useful, among other tilings , in estimating the 
saving that may be made in fuel by substituting more economical boilers 
and engines for those already in use. Thus with coal at $3.00 per ton of 
2000 lbs., a saving of $9000 per year in fuel may be made by replacing a 
steam plant of 1000 H.P., requiring 4 lbs. of coal per hour per horse-power, 
with one requiring only 2 lbs. 





Coal Consumption, at 4 lbs. 
















per H.P. hour; 10 hours a 
















day; 300 days per Year. 


$2 per 
Short 
Ton. 


$3 per 
Short 
Ton. 


$ 
S 


4 per 
hort 


% 



1 


Lbs. 


Long Tons. 


Short 
Tons. 


ron. 












Cost in 


Cost in 


Cost in 





Per 
Day. 


Per 
Day. 


Per 

Year. 


Per 
Dav. 


Per 
Yr. 


Dollars. 


Dollars. 


Dollars. 




























Day. 


Yr. 


Day. 


Yr. 


Day. 


Yr. 


1 


40 


0.0179 


53.57 


0.02 


6 


0.04 


12 


0.06 


18 


08 


24 


10 


400 


0.1786 


53.57 


0.20 


60 


0.40 


120 


0.60 


180 


80 


240 


25 


1,000 


0.4464 


133.92 


0.50 


150 


1.00 


300 


1.50 


450 


2 00 


600 


50 


2,000 


0.8928 


267.85 


1.00 


300 


2.00 


600 


3.00 


900 


4 00 


1,200 


75 


3,000 


1.3393 


401.78 


1.50 


450 


3 00 


900 


4 50 


1,350 


6 00 


1,800 


100 


4,000 


1.7857 


535.71 


2.00 


600 


4 00 


1,200 


6 00 


1.800 


8 00 


2,400 


150 


6,000 


2.6785 


803.56 


3.00 


900 


6 00 


1,800 


9 00 


2,700 


12 00 


3,600 


200 


8,000 


3.5714 


1,071.42 


4 00 


1,200 


8 00 


2,400 


17 00 


3,600 


16 00 


4,800 


250 


10,000 


4.4642 


1,339.27 


5 00 


1 500 


10 CO 


3,000 


15 00 


4.500 


20 00 


6,000 


300 


12,000 


5.3571 


1,607.13 


6 00 


1 800 


12 00 


3,600 


18 00 


5,400 


24.00 


7,200 


350 


14,000 


6.2500 


1,874.98 


7.00 


2 100 


14 00 


4,200 


7.1 00 


6,200 


28.00 


8,400 


400 


16,000 


7.1428 


2,142.84 


8.00 


2 400 


16 00 


4,800 


24 00 


7,200 


32.00 


9.600 


450 


18,000 


8.0356 


2,410.69 


9.00 


2 700 


18,00 


5,400 


27 00 


8,100 


36.00 


10,800 


500 


20.000 


8.9285 


2,678.55 


10 00 


3,000 


20 00 


6,000 


30 00 


9,000 


40.00 


12,000 


600 


24,000 


10.7142 


3,214.26 


12 00 


3 600 


7.4 00 


7,200 


36 00 


10,800 


48.00 


14,400 


700 


28,000 


12.4999 


3,749.97 


14.00 


4 200 


28 00 


8,400 


42 00 


11,600 


56.00 


16,800 


800 


32,000 


14.2856 


4,285. 68 


16.00 


4,800 


32 00 


9,600 


48 00 


12,400 


64.00 


19,200 


900 


36,000 


16.0713 


4,821.39 


18 00 


5,400 


36 00 


10,800 


54 00 


14.200 


72 (Ml 


21,600 


1000 


40,000 


17.8570 


5,357. 10 


20.00 


6,000 


40.00 


12,000 


60.00 


18,000 


80.00 


24,000 



984 



THE STEAM-ENGINE. 



It is usual to consider that a factory working 10 hours a day requires 
10 1/2 hours coal consumption on account of the coal used in banking or 
in starting the fires, and that there are 306 working days in the year. For 
these conditions multiply the costs given in the table by 1.071. For 
24 hours a day 365 days in the year, multiply them by 2.68. For other 
rates of coal consumption than 4 lbs. per H.P. hour, the figures are to be 
modified proportionately. 

Relative Cost of Different Sizes of Steam-engines. 

(From catalogue of the Buckeye Engine Co., Part III.) 



Horse-power. 
Cost per H.P., $ 



50 75 
20 171/2 



150 
141/2 



200 
131/2 



300 
123/ 4 



500 600 700 800 
12.8 131/4 14 15 



Relative Commercial Economy of Best Modern Types of Com- 
pound and Triple-expansion Engines. (J. E. Denton, American 
Machinist, Dec. 17, 1891.) — The following table and deductions show 
the relative commercial economy of the compound and triple types for 
the best stationary practice in steam plants of 500 indicated horse-power. 
The table is based on the tests of Prof. Schroter, of Munich, of engines 
built at Augsburg, and those of Geo. H. Barrus on the best plants of 
America, and of detailed estimates of cost obtained from several first- 
class builders. 

Trip motion, or Corliss engines 
of the twin-compound-re- 
ceiver condensing type, ex- 
panding 16 times. Boiler 
pressure 120 lbs. 

Trip motion, or Corliss engines 
of the triple-expansion four- 
cylinder-receiver condensing 
type, expanding 22 times. 
Boiler pressure 150 lbs. 

The figures in the first column represent the best recorded performance 
(1891), and those in the second column the probable reliable performance. 

The following table shows the total annual cost of operation, with coal 
at $4.00 per ton, the plant running 300 days in the year, for 10 hours and 
for 24 hours per day. 



f Lbs. water per hour per ) , Q A 1 a n 

H.P., by measurement, j ld, ° 14,u 
Lbs. coal per hour per j 

H.P., assuming 8.5 lbs. J 1 . 60 1 . 65 

actual evaporation. ) 
Lbs. water per hour per I 1Q , R ,„ on 

H.P., by measurement. J lzOD l^.ou 
Lbs. coal per hour per ) 

H. P., assuming 8.5 lbs. J 1.48 1.50 

actual evaporation. ) 





10 


24 








PerH.P. 
$9.90 
9.00 
0.90 


Per H.P. 

$28.50 




25.92 




2.60 








$0.23 
0.23 

0.15 

0.06 


$0.23 




0.23 


Annual extra cost of oil, 1 gallon per 24-hour day, 
at $0.50, or 15% of extra fuel cost 


0.36 


Annual extra cost of repairs at 3% on $4.50 per 24 


0.14 








$0.67 


$0.96 




$0.23 


$1.64 







Increased cost of triple-expansion plant per horse-power, including 
boilers, chimney, heaters, foundations, piping and erection $4.50 

Taking the total cost of plants at $36.50 and $41 per horse- power re- 
spectively, the figures in the table imply that for coal at $4 per ton a 



COMMERCIAL ECONOMY — COSTS OF POWER. 985 

triple expansion 500 H.P. plant costs $20,500, and saves about $114 per 
year in 10-hour service, or $826 in 24-hour service, over a compound 
plant, thereby saving its extra cost in 10-hour service in about 193/4 years, 
or in 24-hour service in about 23/4 years. 

Power Plant Economics. (H. G. Stott, Trans. A. I. E. E., 1906.) — 
The following table gives an analysis of the heat losses found in a year's 
operation of one of the most efficient plants in existence. 

AVERAGE LOSSES IN THE CONVERSION OF 1 LB. OF COAL INTO ELECTRICITY. 

B.T.U. % B.T.U. % 

1. B.T.U. per lb. of coal supplied 14,150 100.0 

2. Loss in ashes 340 2.4 

3. Loss to stack 3,212 22.7 

4. Loss in boiler radiation and air leakage 1,131 8.0 

5. Returned by feed-water heater 441 3.1 

6. Returned by economizer 960 6.8 

7. Loss in pipe radiation 28 0.2 

8. Delivered to circulator 223 1.6 

9. Delivered to feed pump 203 1.4 

10. Loss in leakage and high-pressure drips 152 1.1 

11. Delivered to small auxiliaries 51 0.4 

12. Heating 31 0.2 

13. Loss in engine friction Ill 0.8 

14. Electrical losses 36 0.3 

15. Engine radiation losses 28 0.2 

16. Rejected to condenser 8,524 60.1 

17. To house auxiliaries 29 0.2 



14,099 99.6 

Delivered to bus bar 1,452 10.3 

The following notes concerning power-plant economy are condensed 
from Mr. Stott's paper. 

Item 1. B.T.U. per lb. of coal. The coal is bought and paid for on the 
basis of the B.T.U. found by a bomb calorimeter. 

Item 3. The chimney loss is very large, due to admitting too much air 
to the combustion chamber. This loss can be reduced about half by the 
use of a CO2 recorder and proper management of the fire. 

Item 4. This loss is largely due to infiltration of air into the brick 
setting. It can be saved by having an air-tight sheet-iron casing enclosing 
a magnesia lining outside of the brickwork. 

Item 5. All auxiliaries should be driven by steam, so that their exhaust 
may be utilized in the feed-water heater. 

Item 6. In all cases where the load factor exceeds 25% the investment 
in economizers will be justified. 

Item 7. The pipes are covered with two layers of covering, each about 
1.5 in. thick. 

Item 10. The high-pressure drips can be returned to ttie boiler, so 
practically all the loss under this heading is recoverable. 

Item 13. Recent tests of a 7500-H.P. reciprocating engine show a 
mechanical efficiency of 93.65%, or an engine friction of 6.35%. The 
engine is lubricated by the flushing system. 

Item 16. The maximum theoretical efficiency of an engine working 
between 175 lbs. gauge and 28 ins. vacuum is 

(Ti - r 2 ) h- Ti = (837 - 560) -h 837 = 33%. 

The actual best efficiency of this engine is 17 lbs. per K.W.-hour = 16.7% 
thermal efficiency: dividing by 0.98, the generator efficiency, gives the net 
thermodynamic efficiency of the engine, = 17%. The difference between 
the theoretical and the actual efficiency is 33 - 17 = 16%, of which 6.35% 
is due to engine friction, and the balance, 9.65%, is due to cylinder con- 



986 THE STEAM-ENGINE. 

densation, incomplete expansion, and radiation. [Some of this difference 
is due to the fact that the engine does not work on the Carnot cycle, in 
which the heat is all received at the highest temperature, and part of this 
loss might be saved by the Nordberg feed-water heating system. There 
may also be a slight loss from leakage. W.K.J Superheated steam, to 
such an extent as to insure dry steam at the point of cut-off in the low- 
pressure cylinder, might save 5 or 6%. 

The present type of power plant using reciprocating engines can be im- 
proved in efficiency as follows: Reduction of stack losses, 12%; boiler 
radiation and leakage, 5%; by superheating, 6%; resulting in a net in- 
crease of thermal efficiency of the entire plant of 4.14% and bringing the 
total from 10.3 to 14.44%. 

The Steam Turbine. — The best results from the steam turbine up to 
date show that its economy on dry saturated steam is practically equal 
to that of the reciprocating engine, and that 200° superheat reduces its 
steam consumption 13.5%. The shape of the economy curve is much 
flatter [from 3300 to 8000 K. W. the range of steam consumption is between 
14.6 and 15.0 lbs. per K.W.-hour], so that the all-day efficiency would be 
considerably better than that of the reciprocating engine, and the cost 
would be about 33% less for the combined steam motor and electric 
generator. 

High-pressure Reciprocating Engine with Low-pressure Turbine. — The 
reciprocating engine is more efficient than the turbine in the higher pres- 
sures, while the turbine can expand to lower pressures and utilize the gain 
of full expansion. The combination of the two would therefore be more 
efficient than a turbine alone. 

The Gas Engine. — The best result up to date obtained from gas pro- 
ducers and gas engines is about as follows: Loss in producer and auxiliaries, 
20%; in jacket water, 19%; in exhaust gases, 30%; in engine friction, 
6.5%; in electric generator, 0.5%. Total losses, 76%. Converted into 
electric energy, 24%. Only one important objection can be raised to this 
motor, that its range of economical load is practically limited to between 
50% and full load. This lack of overload capacity is probably a fatal 
defect for the ordinary railway power plant acting under a violently 
fluctuating load, unless protected by a large storage-battery. 

At light loads the economy of gas and liquid fuel engines fell off even 
more rapidly than in steam-engines. The engine friction was large and 
nearly constant, and in some cases the combustion was also less perfect 
at light loads. At the Dresden Central Station the gas-engines were kept 
working at nearly their full power by the use of storage-batteries. The 
results of some experiments are given below: 

Brake-load, per Gas-engine, cu. ft. Petroleum Eng., Petroleum Eng., 
cent of full of Gas per Brake Lbs. of Oil per Lbs. of Oil per 

Power. H.P. per hour. B.H.P. per hr. B.H.P. per hr. 

100 22.2 0.96 0.88 

75 23.8 1.11 0.99 

59 28.0 1.44 1.20 

20 40.8 2.38 1.82 

121/2 66.3 4.25 3.07 

Combination of Gas Engines and Turbines. — A steam turbine unit can 
be designed to take care of 100% overload for a few seconds. If a plant 
were designed with 50% of its normal capacity in gas engines and 50% 
in steam turbines, any fluctuations in load likely to arise in practice could 
be taken care of. By utilizing the waste heat' of the gas engine in econ- 
omizers and superheaters there can be saved approximately 37% of this 
waste heat, to make steam for the turbines. The average total thermal 
efficiency of such a combination plant would be 24.5%. This combina- 
tion offers the possibility of producing the kilowatt-hour for less than one- 
half its present cost. 

The following table shows the distribution of estimated relative main- 
tenance and operation costs of five different types of plant, the total cost 
of current with the reciprocating engine plant being taken at 100. 



COMMERCIAL ECONOMY — COSTS OF POWER. 987 



Recip- 
rocating 
Engines. 



Steam 
Turbines 



Recip- 
rocating 
Engines 

and 

Steam 

Turbines. 



Gas- 
Engine 
Plant. 



Gas 

Engines 

and 

Steam 

Turbines. 



Maintenance. 

1. Engine room mechan- 

ical . 

2. Boiler room or pro- 

ducer room 

3. Coal- and ash-han- 

dling apparatus . . . 

4. Electrical apparatus 

Operation. 

5. Coal- and ash-han- 

dling labor 

6. Removal of ashes .... 

7. Dock rental 

8. Boiler-room labor. . . . 

9. Boiler-room oil, waste, 

etc 

10. Coal 

11. Water 

12. Engine-room me- 

chanical labor 

13. Lubrication 

14. Waste, etc 

15. Electrical labor 

Relative cost of mainte- 
nance and operation . . 

Relative investment in 
per cent 



2.57 
4.61 



0.58 
1.12 



2.26 
1.06 
0.74 
7.15 

0.17 
61.30 

7.14 

6.71 
1.77 
0.30 
2.52 



0.51 
4.30 



0.54 
1.12 



2.11 
0.94 
0.74 

6.68 

0.17 
57.30 
0.71 

1.35 
0.35 
0.30 
2.52 



1.54 
3.52 



0.44 
1.12 



1.74 
0.80 
0.74 
5.46 

0.17 
46.87 
5.46 

4.03 
1.01 
0.30 

2.52 



2.57 
1.15 



0.29 
1.12 



1.13 
0.53 
0.74 
1.79 

0.17 
26.31 
3.57 

6.71 
1.77 
0.30 

2.52 



1.54 
1.95 



0.29 
1.12 



1.13 
0.53 
0.74 
3.03 

0.17 
25.77 
2.14 

4.03 
1.06 
0.30 
2.52 



Storing Heat in Hot Water. — (See also p. 897.) There is no satisfac- 
tory method for equalizing the load on the engines and boilers in electric- 
light stations. Storage-batteries have been used, but they are expensive 
in first cost, repairs, and attention. Mr. Halpin, of London, proposes to 
store heat during the day in specially constructed reservoirs. As the 
water in the boilers is raised to 250 lbs. pressure, it is conducted to cylin- 
drical reservoirs resembling English horizontal boilers, and stored there 
for use when wanted. In this way a comparatively small boiler-plant 
can be used for heating the water to 250 lbs. pressure all through the 
twenty-four hours of the day, and the stored water may be drawn on at 
any time, according to the magnitude of the demand. The steam-engines 
are to be worked by the steam generated by the release of pressure from 
this water, and the valves are to be arranged in such a way that the steam 
shall work at 130 lbs. pressure. A reservoir 8 ft. in diameter and 30 ft. 
long, containing 84,000 lbs. of heated water at 250 lbs. pressure, would 
supply 5250 lbs. of steam at 130 lbs. pressure. As the steam consump- 
tion of a condensing electric-light engine is about 18 lbs. per horse-power 
hour, such a reservoir would supply 286 effective horse-power hours. In 
1878, in France, this method of storing steam was used on a tramway. 
M. Francq, the engineer, designed a smokeless locomotive to work by 
steam-power supplied by a reservoir containing 400 gallons of water at 
220 lbs. pressure. The reservoir was charged with steam from a stationary 
boiler at one end of the tramway. 

An installation of the Rateau low-pressure turbine and regenerator 
system at the rolling mill of the International Harvester Co., in Chicago, 
is described in Power, June, 1907. The regenerator is a cylindrical shell 
11 1/2 ft. diam., 30 ft. long, containing six large elliptical tubes perforated 
with many 3/4-in. holes through which exhaust steam from a reversing 



THE STEAM-ENGINE. 



blooming-mill engine enters the water contained in the shell. A large 
steam pipe leads from the shell to the turbine. A series of tests of the 
combination was made, giving results as follows: The 42 X 60 in. blooming 
mill engine developed 820 I.H.P. on the average, with a water rate of 64 
lbs. per I.H.P. hour. It delivered its exhaust, averaging a little above at- 
mospheric pressure, to the regenerator, at an irregular rate corresponding 
to the varying work of the rolling-mill engine. The regenerator furnished 
steam to the turbine, which in four different tests developed 444, 544, 
727 and 869 brake H.P. at the turbine shaft, with a steam consumption 
of 47.7, 37.1, 30.7 and 33.7 lbs. of steam per B.H.P. hour at the turbine. 
Had the turbine been of sufficient capacity to use all the exhaust of the 
mill engine, 1510 H.P. might have been delivered at the switchboard, 
which added to the 820 of the mill engine would make 2330 H.P. for 
52,400 lbs. of steam, or a steam rate of 22.5 lbs. per H.P. hour for the 
combination. 

UTILIZING THE SUN'S HEAT AS A SOURCE OF POWER. 

John Ericsson, 1868-1875, experimented on "solar engines," in which 
reflecting surfaces concentrated the sun's rays at a central point causing 
them to boil water. A large motor of this type was built at Pasadena, 
Cal., in 1898. The rays were concentrated upon a water heater through 
which ether or sulphur dioxide was pumped in pipes, and utilized in a 
vapor engine. The apparatus was commercially unsuccessful oh account 
of variable weather conditions. Eng. News, May 13, 1909, describes the 
solar heat systems of F. Shuman and of H. E. Willsie and John Boyle, Jr. 

In the Shuman invention a tract of land is rolled level, forming a shallow 
trough. This is lined with asphaltum pitch and covered with about 
3 ins. of water. Over the water about Vi6 in. of paraffine is flowed, leaving 
between this and a glass cover about 6 ins. of dead air space. It is esti- 
mated that a power plant of this type to cover a heat-absorption area of 
160,000 sq. ft., or nearly four acres, would develop about 1000 H.P. 
Provision is made for storing hot water in excess of the requirements of 
a low-pressure turbine during the day, to be utilized for running the 
turbine during the period when there is no absorption of heat. The 
heated water is run from the heat absorber to the storage tank, thence 
to the turbine, through a condenser and back to the heat absorber. The 
water enters the thermally insulated storage tank, or the turbine, at about 
202° F. With a vacuum of 28 ins. in the condenser, the boiling-point of 
the water is reduced to 102°, and as it enters the turbine nearly 10% 
explodes into steam. Mr. Shuman estimates that a 1000-H.P. plant built 
upon his plan would cost about $40,000. 

The Willsie and Boyle plant also utilizes the indirect system of absorb- 
ing solar heat and storing the hot water in tanks. This hot water cir- 
culates in a boiler containing some volatile liquid, and the vapor generated 
is used to operate the engine, is condensed, and returned to the boiler 
to be used again. Mr. Willsie compares the cost per H.P.-hour in a 
400-H.P. steam-electric and solar-electric power plant, and finds that the 
steam plant would have to obtain its coal for $0.66 a ton to compete with 
the sun power plant in districts favorable to the latter. 

RULES FOR CONDUCTING STEAM-ENGINE TESTS. 

A committee of the Am. Soc. M. E. in 1902 made a report on Engine 
Tests, which is printed in the Transactions for that year, and also in a 
pamphlet of 78 pages. A greatly condensed abstract only can be given 
here. Engineers making tests of engines should have the complete report. 
In the introduction to the report the Committee says: 
The heat consumption of a steam-engine plant is ascertained by meas- 
uring the quantity of steam consumed by the plant, calculating the total 
heat of the entire quantity, and crediting this total with that portion of 
the heat rejected by the plant which is utilized and returned to the boiler. 
The term "engine plant" as here used should include the entire equip- 
ment of the steam plant which is concerned in the production of the power, 
embracing the main cylinder or cylinders: the jackets and reheaters: the 
air, circulating, and boiler-feed pumps, if steam driven; and any other 



RULES FOR CONDUCTING STEAM-ENGINE TESTS. 989 

steam-driven mechanism or auxiliaries necessary to the working of the 
engine. It is obligatory to thus charge the engine with the steam used 
by necessary auxiliaries in determining the plant economy, for the reason 
that it is itself finally benefited, or should be so benefited, by the heat 
which they return; it being generally agreed that exhaust steam from 
such auxiliaries should be passed through a feed-water heater, and the 
heat thereby carried back to the boiler and saved. 

In that large class of steam engines which are required to run at a cer- 
tain limited and constant speed, there should be a considerable reserve of 
capacity beyond the rated power. It is our recommendation that when a 
steam engine is operating at its rated power at a given pressure there 
should be a sufficient reserve to allow a drop of at least 15 per cent in the 
gauge pressure without sensible reduction in the working speed of the 
engine, and to allow an overload at the stated pressure amounting to at 
least 25 per cent. 

Rules for Conducting Steam-engine Tests. Code of 1902. 

I. Object of Test. — Ascertain at the outset the specific object of the test, 
whether it be to determine the fulfillment of a contract guarantee, to 
ascertain the highest economy obtainable, to find the working economy 
and defects under conditions as they exist, to ascertain the performance 
under special conditions, to determine the effect of changes in the condi- 
tions, or to find the performance of the entire boiler and engine plant, 
and prepare for the test accordingly. 

II. General Condition of the Plant. — Examine the engine and the 
entire plant concerned in the test ; note its general condition. and any points 
of design, construction, or operation which bear on the objects in view. 
Make a special examination of the valves and pistons for leakage by apply- 
ing the working pressures with the engine at rest, and observe the quantity 
of steam, if any, blowing through per hour. 

III. Dimensions, etc. — Measure or check the dimensions of the cylin- 
ders when they are hot. If they are much worn, the average diameter 
should be determined. Measure also the clearance. If the clearance 
cannot be measured directly, it can be determined approximately from 
the working drawings of the cylinder. 

IV. Coal. — When the trial involves the complete plant, embracing 
boilers as well as engine, determine the character of coal to be used. The 
class, name of the mine, size, moisture, and quality of the coal should be 
stated in the report. It is desirable, for purposes of comparison, that the 
coal should be of some recognized standard quality for the locality where 
the plant is situated. 

V. Calibration of Instruments. — All instruments and apparatus should 
be calibrated and their reliability and accuracy verified by comparison 
with recognized standards. 

VI. Leakages of Steam, Water, etc. — In all tests except those of a com- 
plete plant made under conditions as they exist/the boiler and its con- 
nections, both steam and feed, as also the steam piping leading to the 
engine and its connections, should, so far as possible, be made tight. 
All connections should, so far as possible, be visible and be blanked off, 
and where this cannot be done, satisfactory assurance should be obtained 
that there is no leakage either in or out. 

VII. Duration of Test. — The duration of a test should depend largely 
upon its character and the objects in view. The standard heat test of 
an engine, and, likewise, a test for the simple determination of the feed- 
water consumption, should be continued for at least five hours, unless the 
class of service precludes a continuous run of so long duration. It is 
desirable to prolong the test the number of hours stated to obtain a num- 
ber of consecutive hourly records as a guide in analyzing the reliability 
of the whole. 

The commercial test of a complete plant, embracing boilers as well as 
engine, should continue at least one full dav of twenty-four hours, whether 
the engine is in motion during the entire time or not. A continuous coal 
test of a boiler and engine should be of at least ten hours' duration, or the 
nearest multiple of the interval between times of cleaning fires. 

VIII. Starting and Stopping a Test. — (a) Standard Heat Test and 
Feed- Water Test of Engine: The engine having been brought to the normal 



990 THE STEAM-ENGINE. 

condition of running, and operated a sufficient length of time to be thor- 
oughly heated in all its parts, and the measuring apparatus having been 
adjusted and set to work, the height of water in the gauge glasses of the 
boilers is observed, the depth of water in the reservoir from which the 
feed water is supplied is noted, the exact time of day is observed, and 
the test held to commence. Thereafter the measurements determined upon 
for the test are begun and carried forward until its close. When the time 
for the close of the test arrives, the water should, if possible, be brought 
to the same height in the glasses and to the same depth in the feed-water 
reservoir as at the beginning, delaying the conclusion of the test if neces- 
sary to bring about this similarity of conditions. If differences occur, 
the proper corrections must be made. 

(&) Complete Engine and Boiler Test: For a continuous running test 
of combined engine or engines, and boiler or boilers, the same directions 
> apply for beginning and ending the feed-water measurements as those just 
referred to. The time of beginning and ending such a test should be the 
regular time of cleaning the fires, and the exact time of beginning and 
ending should be the time when the fires are fully cleaned, just preparatory 
to putting on fresh coal. 

For a commercial test of a combined engine and boiler, whether the 
engine runs continuously for the full twenty-four hours of the day, or only 
a portion of the time, the fires in the boilers being banked during the time 
when the engine is not in motion, the beginning and ending of the test 
should occur at the regular time of cleaning the fires, the method followed 
being that already given. In cases where the engine is not in continuous 
motion, as, for example, in textile mills, where the working time is ten or 
eleven hours out of the twenty-four, and the fires are cleaned and banked 
at the close of the day's work, the best time for starting and stopping a 
test is the time just before banking, when the fires are well burned down 
and the thickness and condition can be most satisfactorily judged. 

IX. Measurement of Heat Units Consumed by the Engine. — The meas- 
urement of the heat consumption requires the measurement of each 
supply of feed water to the boiler — that is, the water supplied by the 
main feed pump, that supplied by auxiliary pumps, such as jacket water, 
water from separators, drips, etc., and water supplied by gravity or other 
means; also the determination of the temperature of the water supplied 
from each source, together with the pressure and quality of the steam. 
The temperatures at the various points should be those applying to the 
working conditions. 

The heat to be determined is that used by the entire engine equipment, 
embracing the main cylinders and all auxiliary cylinders and mechanism 
concerned in the operation of the engine, including the air pump, circu- 
lating pump, and feed pumps, also the jacket and reheater when these 
are used. 

The steam pressure and the quality of the steam are to be taken at 
some point conveniently near the throttle valve. The quantity of steam 
used by the calorimeter must be determined and properly allowed for. 

X. Measurement of Feed Water or Steam Consumption of Engine, etc. — 
The method of determining the steam consumption applicable to all plants 
is to measure all the feed water supplied to the boilers, and deduct there- 
from the water discharged by separators and drips, as also tne water and 
steam which escapes on account of leakage of the boiler and its pipe con- 
nections and leakage of the steam main and branches connecting the boiler 
and the engine. In plants where the engine exhausts into a surface con- 

. denser the steam consumption can be measured by determining the quan- 
tity of water discharged by the air pump, corrected for any leakage of the 
condenser, and adding thereto the steam used by jackets, reheaters, and 
auxiliaries as determined independently. 

The corrections or deductions to be made for leakage above referred to 
should be applied only to the standard heat-unit test and tests for deter- 
mining simply the steam or feed-water consumption, and not to coal tests 
of combined engine and boiler equipment. In the latter, no corrections 
should be made except for leakage of valves connecting to other engines 
and boilers, or for steam used for purposes other than the operation of the 
plant under test. Losses of heat due to imperfections of the plant should 
be charged to the plant, and only such losses as are concerned in the work- 
ing of the engine alone should be charged to the engine. 



KULES FOR CONDUCTING STEAM-ENGINE TESTS. 991 

XI. Measurement of Steam used by Auxiliaries. — It is highly desirable 
that the quantity of steam used by the auxiliaries, and in many cases that 
used by each auxiliary, should be determined exactly, so that the net con- 
sumption of the main engine cylinders may be ascertained and a complete 
analysis made of the entire work of the engine plant. 

XII. Coal Measurement. — The coal consumption should be deter- 
mined for the entire time of the test. If the engine runs but a part of the 
time, and during the remaining portion the fires are banked, the measure- 
ment of coal should include that used for banking. 

XIII. Indicated Horse-power. — The indicated horse-power should be 
determined from the average mean effective pressure of diagrams taken 
at intervals of twenty minutes, and at more frequent intervals if the 
nature of the test makes this necessary, for each end of each cylinder. 
With variable loads, such as those of engines driving generators for elec- 
tric railroad work, and of rubber-grinding and rolling-mill engines, the 
diagrams cannot be taken too often. 

The most satisfactory driving rig for indicating seems to be some form 
of well-made pantograph, with driving cord of fine annealed wire leading 
to the indicator. The reducing motion, whatever it may be, and the 
connections to the indicator, should be so perfect as to produce diagrams 
of equal lengths when the same indicator is attached to either end of the 
cylinder, and produce a proportionate reduction of the motion of the 
piston at every point of the stroke, as proved by test. 

The use of a three-way cock and a single indicator connected to the 
two ends of the cylinder is not advised, except in cases where it is imprac- 
ticable to use an indicator close to each end. If a three-way cock is used, 
the error produced should be determined and allowed for. 

XIV. Testing Indicator Springs. — To make a perfectly satisfactory 
comparison of indicator springs with standards, the calibration should be 
made, if this were practical, under the same conditions as those pertaining 
to their ordinary use. 

XV. Brake Horse-power. — This term applies to the power delivered 
from the flywheel shaft of the engine. It is the power absorbed by a fric- 
tion brake applied to the rim of the wheel, or to the shaft. A form of 
brake is preferred that is self-adjusting to a certain extent, so that it will, 
of itself, tend to maintain a constant resistance at the rim of the wheel. 
One of the simplest brakes for comparatively small engines, which may be 
made to embody this principle, consists of a cotton or hemp rope, or a 
number of ropes, encircling the wheel, arranged with weighing scales. 
or other means for showing the strain. An ordinary band brake may also 
be constructed so as to embody the principle. The wheel should be pro- 
vided with interior flanges for holding water used for keeping the rim cool. 

XVI. Quality of Steam. — When ordinary saturated steam is used, its 
quality should be obtained by the use of a throttling calorimeter attached 
to the main steam pipe near the throttle valve. When the steam is super- 
heated, the amount of superheating should be found by the use of a ther- 
mometer placed in a thermometer-well filled with mercury, inserted in 
the pipe. The sampling pipe for the calorimeter should, if possible, be 
attached to a section of the main pipe having a vertical direction, with 
the steam preferably passing upward, and the sampling nozzle should be 
made of a half-inch pipe, having at least 20 Vs-in. holes in its perforated 
surface. 

XVII. Speed. — There are several reliable methods of ascertaining 
the speed, or the number of revolutions of the engine crank-shaft per 
minute. The most reliable method is the use of a continuous recording 
engine register or counter, taking the total reading each time that the 
general test data are recorded, and computing the revolutions per minute 
corresponding to the difference in the readings of the instrument. When 
the speed is above 250 revolutions per minute, it is almost impossible to 
make a satisfactory counting of the revolutions without the use of some 
form of mechanical counter. 

XVIII. Recording the Data. — Take note of every event connected with 
the progress of the trial whether it seems at the time to be important or 
unimportant. Record the time of every event, and time of taking every 
weight, and every observation. Observe the pressures, temperatures, 
water heights, speeds, etc., every twenty or thirty minutes when the con- 



992 THE STEAM-ENGINE. 



ditions are practically uniform, and at much more frequent intervals ir 
the conditions vary. 

XIX. Uniformity of Conditions. — In a test having for an object the 
determination of the maximum economy obtainable from an engine, or 
where it is desired to ascertain with special accuracy the effect of pre- 
determined conditions of operation, it is important that all the condi- 
tions under which the engine is operated should be maintained uniformly 
constant. 

XX. Analysis of Indicator Diagrams. — (a) Steam Accounted for by 
the Indicator: The simplest method of computing the steam accounted 
for by the indicator is the use of the formula, 



M.E.P. ' 

which gives the weight in pounds per indicated horse-power per hour. 
In this formula the symbol " M.E.P. " refers to the mean effective pressure. 
In multiple-expansion engines, this is the combined mean effective pres- 
sure referred to the cylinder in question. C is the proportion of the stroke 
completed at points on the expansion line of the diagram near the actual 
cut-off or release; H the proportion of compression; and E the proportion 
of clearance; all of which are determined from the indicator diagram. 
Wc is the weight of one cubic foot of steam at the cut-off or release pressure; 
and Wh the weight of one cubic foot of steam, at the compression pressure; 
these weights being taken from steam tables. 

Should the point in the compression curve be at the same height as the 
point in the expansion curve, then Wc = Wh, and the formula becomes 

(13,750 + M.E.P.) X (C - H) X Wc, 

in which (C — H) represents the distance between the two points divided 
by the length of the diagram. 

When the load and all other conditions are substantially uniform, it is 
unnecessary to work -up the steam accounted for by the indicator from all 
the diagrams taken. Five or more sample diagrams may be selected and 
the computations based on the samples instead of on the whole. 

(6) Sample Indicator Diagrams: In order that the report of a test may 
afford complete information regarding the conditions of the test, sample 
indicator diagrams should be selected from those taken and copies ap- 
pended to the tables of results. In cases where the engine is of the 
multiple-expansion type these sample diagrams may also be arranged in 
the form of a "combined" diagram. 

(c) The Point of Cut-off: The term " cut-off" as applied to steam engines, 
although somewhat indefinite, is usually considered to be at an earlier 
point in the stroke than the beginning of the real expansion line. That 
the cut-off point may be defined in exact terms for commercial purposes 
as used in steam-engine specifications and contracts, the Committee 
recommends that, unless otherwise specified, the commercial cut-off, which 
seems to be an appropriate expression for this term, be ascertained as 
follows: Through a point showing the maximum pressure during admis- 
sion, draw a line parallel to the atmospheric line. Through the point on 
the expansion line near the actual cut-off, referred to in Section XX (a), 
draw a hyperbolic curve. The point where these two lines intersect is 
to be considered the commercial cut-off point. The percentage is then 
found by dividing the length of the diagram measured to this point, by 
the total length of the diagram, and multiplying the result by 100. 

The commercial cut-off, as thus determined, is situated at an earlier 
point of the stroke than the actual cut-off used in computing the "steam 
accounted for" bv the indicator and referred to in Section XX (a). 

(d) Ratio of Expansion: The "commercial" ratio of expansion is the 
auotient obtained bv dividing the volume corresponding to the piston 
displacement, including clearance, by the volume of the steam at the 
commercial cut-off, including clearance. In a multiple-expansion engine 
the volumes are those pertaining to the low-pressure cylinder and high- 
pressure cvlinder, respectively. 

The "ideal" ratio of expansion is the quotient obtained by dividing 
the volume of the piston displacement by the volume of the steam at the 



RULES FOR CONDUCTING STEAM-ENGINE TESTS. 993 



cut-off (the latter being referred to the throttle-valve pressure), less the 
volume equivalent to that retained at compression. In a multiple-ex- 
pansion engine, the volumes to be used are those pertaining to the low- 
pressure cylinder and high-pressure cylinder, respectively. 
| (e) Diagram Factor: The diagram factor is the proportion borne by 
the actual mean effective pressure measured from the indicator diagram 
[ to that of a diagram in which the various operations of admission, expan- 
sion, release and compression are carried on under assumed conditions. 
The factor recommended refers to an ideal diagram which represents the 
maximum power obtainable from the steam accounted for by the indicator 
t diagrams at the point of cut-off, assuming first that the engine has no 
I clearance; second, that there are no losses through wire-drawing the 
steam during either the admission or the release; third, that the expansion 
line is a hyperbolic curve; and fourth, that the initial pressure is that of 
the boiler and the back pressure that of the atmosphere for a non-con- 
i densing engine, and of the condenser for a condensing engine. 

In cases where there is a considerable loss of pressure between the boiler 
1 and the engine, as where steam is transmitted from a central plant to a 
i number of consumers, the pressure of the steam in the supply main should 
j be used in place of the boiler pressure in constructing the diagrams. 

XXI. Standards of Economy and Efficiency. — The hourly consumption 
of heat, determined by employing the actual temperature of the feed 
water to the boiler, as pointed out in Article IX of the Code, divided by 
the indicated and brake horse-power, that is, the number of heat units 
consumed per indicated and per brake horse-power per hour, are the stand- 
ards of engine efficiency recommended by the Committee. The consump- 
tion per hour is chosen rather than the consumption per minute, so as to 
conform with the designation of time applied to the more familiar units 
of coal and water measurement, which have heretofore been used. The 
British standard, where the temperature of the feed water is taken as 
that corresponding to the temperature of the back-pressure steam, allow- 
ance being made for any drips from jackets or reheaters, is also included 
in the tables. 

It is useful in this connection to express the efficiency in its more scien- 
tific form, or what is called the "thermal efficiency ratio." The thermal 
efficiency ratio is the proportion which the heat equivalent of the power 
developed bears to the total amount of heat actually consumed, as deter- 
mined by test. The heat converted into work represented by one horse- 
power is 1,980,000 foot-pounds per hour, and this divided by 778 equals 
2545 British thermal units. Consequently, the thermal efficiency ratio 
is expressed by the fraction 

2545 -h B.T.U. per H.P. per hour. 

XXII. Heat Analysis. — For certain scientific investigations, it is 
useful to make a heat analysis of the diagram, to show the interchange of 
heat from steam to cylinder walls, etc., which is going on within the cylin- 
der. This is unnecessary for commercial tests. 

XXIII. . Temperature- Entropy Diagram. — The study of the heat anal- 
ysis is facilitated by the use of the temperature-entropy diagram in which 
areas represent quantities of heat, the coordinates being the absolute 
temperature and entropy. 

XXIV. Ratio of Economy of an Engine to that of an Ideal Engine. — 
The ideal engine recommended for obtaining this ratio is that which was 
adopted by the Committee appointed by the Civil Engineers, of London, 
to consider and report a standard thermal efficiency for steam engines. 
This engine is one which follows the Rankine cycle, where steam at a con- 
stant pressure is admitted into the cvlinder with no clearance, and after 
the point of cut-off, is expanded adiabatically to the back pressure. In 
obtaining the economy of this engine the feed water is assumed to be 
returned to the boiler at the exhaust temperature. 

The ratio of the economy of an engine to that of the ideal engine is 
obtained by dividing the heat consumption per indicated horse-power per 
minute for the ideal engine bv that of the actual engine. 

XXV. Miscellaneous. — In the case of tests of combined engines and 
boiler plants, where the full data of the boiler performance are to be deter- 
mined, reference should be made to the directions given by the Boiler 
Test Committee of the Society, Code of 1899. (See Vol. XXI, p. 34.) 



994 THE STEAM-ENGINE. 

In testing steam pumping engines and locomotives in accordance with 
the standard methods of conducting such tests, recommended by the 
committees of the Society, reference should be made to the reports of those 
committees in the Transactions, Volume XII, p. 530, and in Volume XIV, 
p. 1312. 

XXVI. Report of Test. — The data and results of the test should be 
reported in tne manner and in the order outlined in one of the following 
tables, the first of which gives a summary of all the data and results as 
applied not only to the standard heat-unit test, but also to tests of com- 
bined engine and boiler for determining all questions of performance, 
whatever the class of service; the second refers to a short form of report 
giving the necessary data and results for the standard heat test; and the 
third to a short form of report for a feed-water test. 

It is recommended that any report be supplemented by a chart in which 
the data of the test are graphically presented. [Of the three forms of 
report mentioned above, the second is given below.] 

Data and Results of Standard Heat Test of Steam Engine. 

Arranged according to the Short Form advised by the Engine Test Com- 
mittee of the American Society of Mechanical Engineers. Code of 1902. 

1. Made by of 

on engine located at 

to determine 






2. Date of trial 

3. Type and class of engine; also of condenser. . 



Dimensions of main engine 

(a) Diameter of cylinder in. 

(b) Stroke of piston it. 

(c) Diameter of piston rod in. 

(d) Average clearance p.c. 

(e) Ratio of volume of cylinder to 

high-pressure cylinder 

(/) Horse-power constant for one 
pound mean effective pressure 
and one revolution per minute 
Dimensions and type of auxiliaries. . . . 



1st Cyl. 2d Cyl. 3d Cyl. 



Total Quantities, Time, etc. 

6. Duration of test . hours 

7. Total water fed to boilers from main source of supply lbs. 

8. Total water fed from auxiliary supplies: 

(a) 

(6) 

(c) 

9. Total water fed to boilers from all sources. . 

10. Moisture in steam or superheating near throttle p. c. or deg. 

11. Factor of correction for quality of steam 

T2. Total dry steam consumed for all purposes lbs. 

Hourly Quantities. 

13. Water fed from main source of supply lbs. 

14. Water fed from auxiliary supplies: 

(a) 

(6) ■ 

(c) 

15. Total water fed to boilers per hour 

1 6. Total dry steam consumed per hour 

17. Loss of steam and water per hour due to drips from 

main steam pipes and to leakage of plant 

18. Net dry steam consumed per hour by engine and aux- 

iliaries 



RULES FOR CONDUCTING STEAM-ENGINE TESTS. 995 



Pressures and Temperatures (Corrected). 

19. Pressure in steam pipe near throttle by gauge lbs. per sq. in. 

20. Barometric pressure of atmosphere in ins. of mercury ins. 

21. Pressure in receivers by gauge lbs. per sq. in. 

22. Vacuum in condenser in inches of mercury ins. 

23. Pressure in jackets and reheaters by gauge lbs. per sq. in. 

24. Temperature of main supply of feed water deg. Fahr. 

25. Temperature of auxiliary supplies of feed water: 

(a) 

(6) 

(c) 

26. Ideal feed-water temperature corresponding to pres- 

sure of steam in the exhaust pipe, allowance being 

made for heat derived from jacket or reheater drips . " 

Data Relating to Heat Measurement. 

27. Heat units per pound of feed water, main supply B.T.U. 

28. Heat units per pound of feed water, auxiliary supplies: 

(a) 

(b) 

(c) 

29. Heat units consumed per hour, main supply 

30. Heat units consumed per hour, auxiliary supplies: 

(a) 

(6) 

(c) • . 

31. Total heat units consumed per hour for all purposes. 

32. Loss of heat per hour due to leakage of plant, drips, 

etc " 

33. Net heat units consumed per hour: 

(a) By engine alone " 

(6) By auxiliaries 

34. Heat units consumed per hour by engine alone, reck- 

oned from temperature given in line 26 

Indicator Diagrams. 

35. Commercial cut-off in per cent of stroke [Separate 

36. Initial pressure, lbs. persq. in. above atmosphere . .. Columns 

37. Back pressure at mid-stroke, above or below atmos- for each 

phere, in lbs. per sq. in Cylinder.] 

38. Mean effective pressure in lbs. per sq. in 

39. Equivalent M.E.P. in lbs. per sq. in.: 

(a) Referred to first cylinder 

(6) Referred to second cylinder 

(c) Referred to third cylinder • 

40. Pressure above zero in lbs. per sq. in.: 

(a) Near cut-off 

(b) Near release 

(c) Near beginning of compression 

Percentage of stroke at points where pressures are 

measured: 

(a) Near cut-off 

(&) Near release 

(c) Near beginning of compression 

41. Steam accounted for by indicator in (pounds per 

I.H.P. per hour: (a) Near cut-off; (b) Near release. 

42. Ratio of expansion: (a) Commercial; (6) Ideal 

Speed. 

43. Revolutions per minute rev. 

Power. 

44. Indicated horse-power developed by main-engine cylinders: 

First cylinder H.P. 

Second cylinder 

Third cylinder 

Total 

45. Brake horse-power developed by engine 



996 THE STEAM-ENGINE. 

Standard Efficiency and other Results * 

46. Heat units consumed by engine and auxiliaries per hour: 

(a) per indicated horse-power B.T.U. 

(b) per brake horse-power 

47. Equivalent standard coal in lbs. per hour: 

(a) per indicated horse-power. .• lbs. 

(b) per brake horse-power 

48. Heat units consumed by main engine per hour corre- 

sponding to ideal maximum temperature of feed 

water given in line 26: 

(a) per indicated horse-power B.T.U. 

(6) per brake horse-power 

40. Dry steam consumed per indicated horse-power per hour: 

(a) Main cylinders including jackets lbs. 

(b) Auxiliary cylinders • 

(c) Engine and auxiliaries 

50. Dry steam consumed per brake horse-power per hour: 

(a) Main cylinders including jackets 

(b) Auxiliary cylinders 

(c) Engine and auxiliaries 

51. Percentage of steam used by main-engine cylinders 

accounted for by indicator diagrams, near cut-off 

of high-pressure cylinder per cent. 

Additional Data. 

Add any additional data bearing on the particular objects of the test 
or relating to the special class of service for which the engine is used. 
Also give copies of indicator diagrams nearest the mean, and the corre- 
sponding scales. 

DIMENSIONS OF PARTS OF ENGINES. 

The treatment of this subject by the leading authorities on the steam- 
engine is very unsatisfactory, being a confused mass of rules and formulae 
based partly upon theory and partly upon practice. The practice of 
builders shows an exceeding diversity of opinion as to correct dimensions. 
The treatment given below is chiefly the result of a study of the works 
of Rankine, Seaton, Unwin, Thurston, Marks, and Whitham, and is 
largely a condensation of a series of articles by the author published in 
the American Machinist, in 1894, with many alterations and much addi- 
tional matter. In order to make a comparison of many of the formulae 
they have been applied to the assumed cases of six engines of different 
sizes, and in some cases this comparison has led to the construction of new 
formulae. 

[Note, 1909. Since the first edition of this book was published, in 
1895, no satisfactory treatise on this entire subject has appeared, and 
therefore the matter on pages 997 to 1020 has been left, in the revision 
for the 8th edition, in practically its original shape. Two notable papers 
on the subject, however, have appeared: 1, Current Practice in Engine 
Proportions, by Prof. John H. Barr, 1897, and 2, Current Practice in 
Steam-engine Design, by Ole N. Trooien, 1909. Both of these are ab- 
stracted on pages 1021 and 1022.] 

Cylinder. (Whitham.) — Length of bore = stroke + breadth of piston- 
ring — 1/8 to 1/2 in.; length between heads = stroke + thickness of piston 
+ sum of clearances at both ends; thickness of piston = breadth of ring + 
thickness of flange on one side to carry the ring 4- thickness of follower- 
plate. 

Thickness of flange or follower 3/ 8 to 1/2 in. 3/ 4 in. 1 in. 

For cylinder of diameter 8 to 10 in. 36 in. 60 to 100 in. 

Clearance of Piston. (Seaton.) — The clearance allowed varies with 
the size of the engine from Vs to 3/ 8 in. for roughness of castings and 1/1 6 to 
1/8 in. for each working joint. Naval and other very fast-running engines 



* The horse-power referred to above items 46-50 is that of the main 
engine, exclusive of auxiliaries. 



DIMENSIONS OF PARTS OF ENGINES. 997 

have a larger allowance. In a vertical direct-acting engine the parts 
which wear so as to bring the piston nearer the bottom are three, viz., 
the shaft journals, the crank-pin brasses, and piston-rod gudgeon-brasses. 
Thickness of Cylinder. (Thurston.) — For engines of the older 
types and under moderate steam-pressures, some builders have for many 
years restricted the stress to about 2550 lbs. per sq. in. 

t = apiD+ b (1) 

is a common proportion; t, D, and b being thickness, diam., and a con- 
stant added quantity varying from to 1/2, all in inches; pi is the initial un- 
balanced steam-pressure, lbs. per sq. in. In this expression b is made 
larger for horizontal than for vertical cylinders, as, for example, in large 
engines 0.5 in the one case and 0.2 in the other, the one requiring reboring 
more than the other. The constant a is from 0.0004 to 0.0005; the first 
value for vertical cylinders, or short strokes; the second for horizontal 
engines, or for long strokes. 

Thickness of Cylinder and its Connections for Marine Engines. 
(Seaton.) — D = the diam. of the cylinder in inches; p = load on the 
safety-valves in lbs. per sq. in.; /, a constant multiplier, = thickness of 
barrel + 0.25 in. 

Thickness of metal of cylinder barrel or liner, not to be less than p X D 

-*- 3000 when of cast iron * (2) 

Thickness of cylinder-barrel = p X D -4- 5000 + 0.6 in (3) 

Thickness of liner = 1.1 X/ (4) 

Thickness of liner when of steel = p X D -*• 6000 + 0.5 in. 
Thickness of metal of steam-ports =0.6 X /. 
Thickness of metal valve-box sides = 0.65 X /. 
Thickness of metal of valve-box covers =0.7 X /. 

cylinder bottom =1.1 X /, if single thickness. 
= 0.65 X /, if double 
" " " covers =1.0 Xf, if single 

= 0.6 X/, if double 
cylinder flange =1.4 X /. 

" -cover-flange =1.3 X /. 

" " valve-box flange = 1 . X /. 

door-flange =0.9 X /. 

" " face over ports =1.2 Xf. 

" " " =1.0 X /, when there is a false- 

face. 
" false-face =0.8 Xf, when cast iron. 

" " " =0.6 Xf, when steel or bronze. 

Whitham gives the following from different authorities: 

VanBuien:i t - - 0001 / ^2 +0 - 15v ^; • ■ ■ < 5 > 
1 t= 0.03 VDp . . (6) 

Tredgold: t = (D + 2.5) p-4-1900 (7) 

Weisbach: t= 0.8 + 0.00033 pD (8) 

Seaton: t= 0.5 + 0.0004 pD (9) 

TTa «wp11 • ft=0. 0004 pD + i/ 8 (vertical) ; . . .(10) 

nasweu. }£= 0.0005 pZ>+ i/ 8 (horizontal) . .(11) 

Whitham recommends (6) where provision is made for the reboring, 
and where ample strength and rigidity are secured, for horizontal or 
vertical cylinders of large or small diameter; (9) for large cylinders using 
steam under 100 lbs. gauge-pressure, and 

t = 0.003 D Vp for small cylinders (12) 

The following table gives the calculated thickness of cylinders of 
engines of 10, 30, and 50 in. diam., assuming p the maximum unbalanced 
pressure on the piston = 100 lbs. per sq. in. As the same engines will 
be used for calculations of other dimensions, other particulars concerning 
them are here given for reference. . 

* When made of exceedingly good material, at least twice melted, 
the thickness may be 0.8 of that given by the above rules. 



THE STEAM-ENGINE, 



Dimensions, etc., of Engines. 



Engine, No 1 and 2. 



5 and 6. 



Indicated horse-power I.H.P, 

Diam. of cyl., in D 

Stroke, feet L 

Revs, per min r 

Piston speed, ft. per min 5 

Area of piston, sq. in a 

Mean effective pressure M.E.P 

Max. total unbalanced pressure P 

Max. total pressure per sq. in p 



50 

10 

1 ... 

250 ... 

500 

78.54 

42 

7854 

100 



450 
30 
21/2 ... 
130 
650 
706.86 
32.3 
70,686 
100 



1250 

50 

4 ... 8 

90 ... 45 

700 

1963.5 

30 . 

196,350 

100 



The thickness of the cylinders of these engines, according to the first 
eleven formuhe above quoted, ranges for engines 1 and 2 from 0.33 to 
1.13 ins., for 3 and 4 from 0.99 to 2.00 ins., and for 5 and 6 from 1.56 to 
3.00 ins. The averages of the 11 are, for 1 and 2, 0.76 in.; for 3 and 4, 
1.48 ins.; for 5 and 6, 2.26 ins. 

The average corresponds nearly to the formula t = 0.00037 Dp + 0.4 in. 
A convenient approximation is t = 0.0004 Dp + 0.3 in., which gives for 

Diameters 10 20 30 40 50 60 in. 

Thicknesses 0.70 1.10 1.50 1.90 2.30 2.70in. 

The last formula corresponds to a tensile strength of cast iron of 12,500 
lbs., with a factor of safety of 10 and an allowance of 0.3 in. for reboring. 

Cylinder-heads. — Thurston says: Cylinder-heads may be given a 
thickness, at the edges and in the flanges, exceeding somewhat that of 
the cylinder. An excess of not less than 25% is usual. It may be 
thinner in the middle. Where made, as is usual in large, engines, of two 
disks with intermediate radiating, connecting ribs or webs, that section 
which is safe against shearing is probably ample. An examination of the 
designs of experienced builders, by Professor Thurston, gave 

t = Dp h- 3000 +1/4 inch, (1) 

D being the diameter of that circle in which the thickness is taken. 

Thurston also gives t = 0.005 D_Vp + 0.25 (2) 

Marks gives t = 0.003 Vp (3) 

He also says a good practical rule for pressures under 100 lbs. per sq. 
in. is to make the thickness of the cylinder-heads 1 1/4 times that of the 
walls; and applying- this factor to his formula for thickness of walls, or 
0.00028 pD, we have 

£ = 0. 00035 pD (4) 

Whitham quotes from Seaton, 
t = (pD + 500) -*• 2000, which is equal to 0.0005 pD + 0.25 inch . . (5) 

Beaton's formula for cylinder bottoms, quoted above, is 
t = 0.1/, in which /= 0.0002 pD + 0.85 in., or £ = 0.00022 pD +0.93 . (6) 

Applying the above formulae to the engines of 10, 30, and 50 inches 
diameter, with maximum unbalanced steam-pressure of 100 lbs. per sq. 
in., we have 

For cylinder 10-in. diam., 0.35 to 1.15 in.; for 30-in. diam., 0.90 to 
1.75 in.; for 50-in. diam., 1.50 to 2.75 in. The averages are respectively 
0.65, 1.38 and 2.10 in. 

The average is expressed by the formula t = 0.00036 Dp + 0.31 inch. 

Web-stiffened Cylinder-covers. — Seaton objects to webs for 
stiffening cast-iron cylinder-covers as a source of danger. The strain on 
the web is one of tension, and if there should be a nick or defect in the 
outer edge of the web the sudden application of strain is apt to start 
a crack. He recommends that high-pressure cylinders over 24 in. and 



DIMENSIONS OF PARTS OF ENGINES. 999 

low-pressure cylinders over 40 in. diam. should have their covers cast 
hollow, with two thicknesses of metal. The depth of the cover at the 
middle should be about 1/4 the diam. of the piston for pressures of 80 lbs. 
and upwards, and that of the low-pressure cylinder-cover of a com- 
pound engine equal to that of the high-pressure cylinder. Another 
rule is to make the depth at the middle not less than 1.3 times the diameter 
of the piston-rod. In the British Navy the cylinder-covers are made of 
steel castings, 3/ 4 to 1 1/4 in. thick, generally cast without webs, stiffness 
being obtained by their form, which is often a series of corrugations. 

Cylinder-head Bolts. — Diameter of bolt-circle for cylinder-head = 
diameter of cylinder + 2 X thickness of cylinder + 2 X diameter of bolts. 
The bolts should not be more than 6 inches apart (Whitham). 

Marks gives for number of bolts 6 = 0. 7854 D 2 p ■*- 5000 c, in which 
c = area of a single bolt, p = boiler-pressure in lbs. per sq. in.; 5000 lbs. 
is taken as the safe strain per sq. in. on the nominal area of the bolt. 

Seaton says: Cylinder-cover studs and bolts, when made of steel, should 
be of such a size that the strain in them does not exceed 5000 lbs. per 
sq. in. When of less than 7/ 8 inch diameter it should not exceed 4500 lbs. 
per sq. in. When of iron the strain should be 20% less. 

Thurston says: Cylinder flanges are made a little thicker than the 
cylinder, and usually of equal thickness with the flanges of the heads. 
Cylinder-bolts should be so closely spaced as not to allow springing of the 
flanges and leakage, say, 4 to 5 times the thickness of the flanges. Their 
diameter should be proportioned for a maximum stress of not over 4000 
to 5000 lbs. per square inch. 

If D = diameter of cylinder, p = maximum steam-pressure, b = 
number of bolts, s = size or diameter of each bolt, and 5000 lbs. be 
allowed per sq. in. of actual area at the root of the thread, 0.7854 D 2 p = 
3927 6^; whence &s 2 = 0.0002 D 2 p; 

b =0.0002 -~; s = 0.01414 D y £• For the three engines we have: 

Diameter of cylinder, inches 10 30 50 

Diameter of bolt-circle, approx 13 35 57 . 5 

Circumference of circle, approx 40 . 8 110 180 

Minimum no. of bolts, circ. -5- 6_j 7 18 30 

Diam. of bolts, s = 0.01414Dy/| 3/ 4 in. 1.00 1.29 

The diameter of bolt for the 10-inch cylinder is 0.54 in. by the formula, 
but 3/4 inch is as small as should be taken, on account of possible over- 
strain by the wrench in screwing up the nut. 

The Piston. Details of Construction of Ordinary Pistons. (Seaton.) 
— Let D be the diameter of the piston in inches, p the effective pressure per 
square inch on it, x a constant multiplier, found as follows: 

x = (Dh-50)X^P + 1. 

The thickness of front of piston near the boss =0.2 X x. 

" rim = 0.17 X x. 

back " = 0.18 X x. 

boss around the rod =0.3 Xi. 

flange inside packing-ring = . 23 X x. 

'-' at edge =0.25 X x. 

packing-ring =0.15 X x. 

junk-ring at edge = . 23 Xx. 

inside packing-ring =0.21 Xx. 

at bolt-holes = . 35 Xx. 

„, " metal around piston edge = . 25 Xx. 

The breadth of packing-ring = . 63 X x. 

depth of piston at center =1.4 Xx. 

' lap of junk-ring on the piston =0.45 Xx. 

SDace between piston bodv and packing-ring =0.3 X x. 

" diameter of junk-ring bolts =0.1 X x + 0.25 In. 

" pitch of junk-ring bolts = 10 diameters. 

" number of webs in the piston = (D 4- 20) -*■ 12. 

" thickness of webs in the piston =0.18 X x. 



1000 



THE STEAM-ENGINE. 



Marks gives the approximate rule: Thickness of piston-head = \JlD, 
in which I = length of stroke, and D= diameter of cylinder in inches. 
Whitham says: in a horizontal engine the rings support the piston, or at 
least a part of it, under ordinary conditions. The pressure due to the 
weight of the piston upon an area eaual to 0.7 the diameter of the cylinder 
X breadth of ring-face, should never exceed 200 lbs. per sq. in. He also 
gives a formula much used in this country: Breadth of ring-face = 
0.15 X diameter of cylinder. 

For our engines we have diameter = 10 30 50 

Thickness of piston-head. 

Marks, \JlD; long stroke 3.31 5.48 7.00 

Marks, -\/lb; short stroke 3.94 6.51 8.32 

Seaton, depth at center = 1.4a; 4.20 9.80 15.40 

Seaton, breadth of ring = 0.63 x 1.89 4.41 6.93 

Whitham, breadth of ring = 0.15 D 1.50 4.50 7.50 

Diameter of Piston Packing-rings. — These are generally turned, 
before they are cut, about 1/4 inch diameter larger than the cylinder, 
for cylinders up to 20 inches diameter, and then enough is cut out of the 
rings to spring them to the diameter of the cylinder. For larger cylinders 
the rings are turned proportionately larger. Seaton recommends an 
excess of 1% of the diameter of the cylinder. 

A theoretical paper on Piston Packing Rings of Modern Steam Engines 
by O. C. Reymann will be found in Jour. Frank. Inst., Aug., 1897. 

Cross-section of the Rings. ■ — The thickness is commonly made 
1/30 of the diam. of cyl. + Vs inch, and the width = thickness + l/g inch. 
For an eccentric ring the mean thickness may be the same as for a ring 
of uniform thickness, and the minimum thickness = 2/3 the maximum. 

A circular issued by J. H. Dunbar, manufacturer of packing-rings, 
Youngstown, Ohio, says: Unless otherwise ordered, the thickness of 
rings will be made equal to 0.03 X their diameter. This thickness has 
been found to be satisfactory in practice. It admits of the ring being 
made about 3/igin. to the foot larger than the cylinder, and has, when new, 
a tension of about two pounds per inch of circumference, which is ample 
to prevent leakage if the surface of the ring and cylinder are smooth. 

As regards the width of rings, authorities "scatter" from very narrow 
to very wide, the latter being fully ten times the former. For instance, 
Unwin gives W = 0.014 d + 0.08. Whitham's formula is W= 0.15 d. 
In both formulae W is the width of the ring in inches, and d the diameter 
of the cylinder in inches. Unwin's formula makes the width of a 20 in. 
ring W = 20 X 0.014+0.08 =0.36 in., while Whitham's is 20 X 0.15 = 
3 in. for the same diameter of ring. There is much less difference in the 
practice of engine-builders in this respect, but there is still room for a 
standard width of ring. It is believed that for cylinders over 16 in. diam- 
eter 3/ 4 in. is a popular and practical width, and 1/2 in. for cylinders of 
that size and under. 

E. R. McGahey, Machy., Feb., 1906, gives the following tables for sizes 
of piston rings for cylinders 6 to 20 in., diameter. A = (outside diam. of 
ring — bore of cylinder); B= thickness (radial) of equal section ring, or 
least, thickness of eccentric ring; C = width of ring (axial); D = amount 
cut out or lap; E = greatest thickness of eccentric ring. 

Equal Section Rings. 



5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


15 


16 


17 


18 


19 


20 


A 


5 /32 


•V32 


3/16 


3/16 


7/32 


1/4 


V4 


9/32 


9/3 > 


5/16 


H/32 


H/32 


3/8 


13/32 


13/32 


B 


1/4 


9/3? 


5/16 


3/8 


13/32 


7/16 


15/32 


1/2 


9 /l6 


19/ 3 , 


5/8 


11/16 


•74 


3/4 


1?/16 


C 


5/16 


3/8 


3/8 


7/16 


7/16 


1/2 


1/2 


9 /l6 


9/16 


H/16 


11/16 


3/4 


3/4 


13/16 


13/16 


D 


3V64 


39/64 


21/32 


23/32 


25/3, 


27/32 


7/8 


15/16 


1 


H/16 


11/8 


13/16 


11/4 


'9/32 


1 11/32 



DIMENSIONS OF PARTS OF ENGINES. 



1001 















Eccentric Rings. 












1 

.2 
Q 


6 


7 


8 


9 


10 


11 


12 


13 


14 


15 


16 


17 


18 


19 


20 


A 


5/32 


5 /32 


3/16 


3/16 


7/32 


1/4 


1/4 


9/32 


9/32 


5/16 


H/32 


U/32 


3/8 


13/32 


13/32 


B 


3/16 


7/32 


V4 


9/32 


9 /32 


5/16 


H/32 


3/8 


13/32 


7/16 


15/32 


15/32 


1/2 


17/32 


9/16 


C 


5/16 


3/8 


3/8 


Vl6 


7/16 


V2 


1/2 


9/16 


9/16 


H/16 


11/16 


3/4 


3/4 


13/16 


13/16 


D 


35/64 


39/64 


21/32 


23/32 


25/32 


27/32 


7/8 


15/16 


I 


U/16 


U/8 


13/16 


H/4 


19/32 


1 H/32 


E 


9/32 


5/16 


H/32 


3/8 


13/32 


7/16 


15/32 


1/2 


9/16 


5/8 


H/16 


H/16 


3/4 


13/16 


7/8 



Fit of Piston-rod into Piston. (Seaton.) — The most convenient 
and reliable practice is to turn the piston-rod end with a shoulder of Vie 
inch for small engines, and Vs inch for large ones, make the taper 3 in. to 
the foot until the section of the rod is three-fourths of that of the body, 
then turn the remaining part parallel; the rod should then fit into the 
piston so as to leave i/s in. between it and the shqulder for large pistons 
and Vie in. for small. The shoulder prevents the -rod from splitting the 
piston, and allows of the rod being turned true after long wear without 
encroaching on the taper. 

The piston is secured to the rod by a nut, and the size of the rod should 
be such that the strain on the section at the bottom of the thread does 
not exceed 5500 lbs. per sq. in. for iron, 7000 lbs., for steel. The depth 
of this nut need not exceed the diameter which would be found by allow- 
ing these strains. The nut should be locked to prevent its working loose. 

Diameter of Piston-rods. — Unwin gives 

d"=bD Vp, ......... (1) 

in which D is the cylinder diameter in inches, p is the maximum unbal- 
anced pressure in lbs. per sq. in., and the constant b = 0.0167 for iron, 
and b = 0.0144 for steel. Thurston, from an examination of a con- 
siderable number of rods in use, gives 

-•-V^S-r* ' • •:• • • • < 2 > 

(L in feet, D and d in inches), in which a = 10,000 and upward in the 
various types of engines, the marine screw engines or ordinary fast engines 
on shore are given the lowest values, while "low-speed engines" being 
less liable to accident from shock are given a = 15,000, often. 

Connections of the piston-rod to the piston and to the cross-head should 
have a factor of safety of at least 8 or 10. Marks gives 

d" = 0.0179 D y/ Pt for iron; for steel d" =0 r 0105 D^p; . . (3) 
and d" = . 03901 $ ' DWp, for iron; for steel d"=0 , 03525 ^D 2 l 2 p, . (4) 
in which I is the length of stroke, all dimensions in inches. Deduce the 
diameter of piston-rod by (3), and if this diameter is less than 1/12 1, then 
use (4). 

_ . . t-.. „ . . , Diameter of cvlinder ._ 
Seaton gives: Diameter of piston-rod = =, — -v/p 

The following are the values of F: 

Naval engines, direct-acting F = 60 

return connecting-rod, 2 rods -.-... F — 80 

Mercantile ordinary stroke, direct-acting ...... F = 50 

long " " F = 48 

very long " •" F = 45 

'* medium stroke, oscillating F = 45 

Note. — Long and very long, as compared with the stroke usual for 
the power of engine or size of cylinder. 



1002 



THE STEAM-ENGINE. 



In considering an expansive engine, p, the effective pressure, should be 
taken as the absolute working pressure, or 15 lbs. above that to which 
the boiler safety-valve is loaded; for a compound engine the value of p 
for the high-pressure piston should be taken as the absolute pressure, 
less 15 lbs., or the same as the load on the safety-valve; for the medium- 
pressure the load may be taken as that due to half the absolute boiler- 
pressure; and for the low-pressure cylinder the pressure to which the 
escape-valve is loaded ,+ 15 lbs., or the maximum absolute pressure 
which can be got in the receiver, or about 25 lbs. It is an advantage to 
make all the rods of a compound engine alike, and this is now the rule. 

Applying the above formulae to the engines of 10, 30, and 50 in. diam- 
eter, both short and long stroke, we have: 



Diameter of Piston-rods. 










10 


30 


50 








12 

1.67 
1.44 

1.13 


24 
1.67 
1.44 

1.40 
1.91 
1.73 

2.22 


30 
5.01 
4.32 

3.12 

5.37 
3.70 
(3.15) 
3.34 
5.01 


60 
5.01 
4.32 

3.88 
5.37 
5.13 

4.72 
6.67 


48 
8.35 
7.20 

5.10 

8.95 
6.04 

(5.25) 
5.46 
8.35 


96 


Unwin, iron, .0167 D Vp 


8.35 


Unwin, steel, 0.0144 D "^p 


7 20 


Thurston y'^g + l (Lin feet).... 


6 35 


Marks iron 0179 D ^p 


1.79 
1.35 
(1.05) 
1.22 
1.67 


8.95 


Marks, iron 03901 -\j D-Pp 


8.54 


Marks, steel, 0.0105 D ^p 




Marks, steel, 0.03525 ^J D 2 l 2 p 


7 72 






60 


11.11 










1.49 


1.82 


4.30 


5.26 


7.11 


8 74 







The figures in parentheses opposite Marks's third formula would be re- 
jected since they are-less than i/s of the stroke, and the figures derived 
by his fourth formula would be taken instead. The figure 1.79 opposite 
his first formula would be rejected for the engine of 24-inch stroke. 

An empirical formula which gives results approximatin g th e above 
averages is d" = 0.0145 "^ Dip for short stroke and 0.013 *^Dlp for long 
stroke engines. 

The calculated results for this formula, for the six engines, are, re- 
spectively, 1.58, 2.02,4.35, 5.52, 7.10, 9.01. 

Piston-rod Guides. — The thrust on the guide, when the connecting- 
rod is at its maximum angle with the line of the piston-rod, is found from 
the formula: Thrust = total load on piston X tangent of maximum angle 
of connecting rod = p tan 0. This angle, 0, is the angle whose sine = 
half stroke of piston -*- length of connecting-rod. 

Ratio of length of connecting-rod to stroke 2 21/2 3 

Maximum angle of connecting-rod with line of 

piston-rod 14° 29' 11° 33' 9° 36' 

Tangent of the angle . 258 . 204 . 169 

Secant of the angle 1 . 0327 1 . 0206 1 . 014 

Seaton says: The area of the guide-block or slipper surface on which the 
thrust is taken should in no case be less than will admit of a pressure of 
400 lbs., on the square inch; and for good working those surfaces which 
take the thrust when going ahead should be sufficiently large to prevent 



DIMENSIONS OF PARTS OF ENGINES 1003 

the maximum pressure exceeding 100 lbs. per sq. in. When the surfaces 
are kept well lubricated this allowance may be exceeded. 

Thurston says: The rubbing surfaces of guides are so proportioned that 
if V be their relative velocity in feet per minute, and p be the intensity 
of pressure on the guide in lbs. per sq. in., p V < 60,000 and pV > 40,000. 

The lower is the safer limit; but for marine and stationary engines it 
is allowable to take p = 60,000 -*- V. According to Rankine, for loco- 

44 goo 
motives, p = ' , where p is the pressure in lbs. per sq. in. and V the 

velocity of rubbing in feet per minute. This includes the sum of all 
pressures forcing the two rubbing surfaces together. 

Some British builders of portable engines restrict the pressure between 
the guides and cross-heads to less than 40, sometimes 35 lbs. per square 
inch. 

For a mean velocity of 600 feet per minute, Prof. Thurston's formulas 
give, p < 100, p > 66.7; Rankine's gives p = 72.2 lbs. per sq. in. 
Whitham gives, 

--,.-. • , P 0.7854 d 2 p\ 

A = area of slides in square inches = - — == . 

Po^n 2 - 1 po^n 2 - 1 

in which P = total unbalanced pressure, p\ = pressure per square inch 
on piston, d = diameter of cylinder, p = pressure allowable per square 
inch on slides, and n = length of connecting-rod -s- length of crank. 
This is equivalent to the formula, A = P tan -r- p . For n = 5, pi = 
100 and p = 80, A = . 2004 d 2 . For the three engines 10, 30 and 50 in. 
diam., this would give for area of slides, A = 20, 180 and 500 sq. in., 
respectively. Whitham says: The normal pressure on the slide may be 
as high as 500 lbs. per sq. in., but this is when there is good lubrication 
and freedom from dust. Stationary and marine engines are usually 
designed to carry 100 lbs. per sq. in., and the area in this case is reduced 
from 50% to 60% by grooves. In locomotive engines the pressure 
ranges from 40 to 50 lbs. per sq. in. of slide, on account of the inaccessi- 
bility of the slide, dirt, cinder, etc. 

There is perfect agreement among the authorities as to the formula for 
area of the slides, A = P tan 9 -f- p p ; but the value given to p , the allow- 
able pressure per square inch, ranges all the way from 35 lbs. to 500 lbs. 

The Connecting-rod. Ratio of length of connecting -rod to length of 
stroke. — Experience has led generally to the ratio of 2 or 21/2 to 1, the 
latter giving a long and easy-workinsr rod, the former a rather short, but 
yet a manageable one (Thurston). Whitham gives the ratio of from 2 to 
41/2, and Marks from 2 to 4. 

Dimensions of the Connecting-rod. — The calculation of the diameter 
of a connecting-rod on a theoretical basis, considering it as a strut subject 
to both compressive and bending stresses, and also to stress due to<?its 
inertia, in high-speed engines, is quite complicated. See Whitham, 
Steam-engine Design, p. 217; Thurston, Manual of S. E., p. 100. Empiri- 
cal formulas are as follows: For circular rods, largest at the middle, Z> = 
diam. of cylinder, I = length of connecting-rod in inches, p = maximum 
steam-pressure, lbs. per sq. in. 

(1) Whitham, diam. at middle, d" = 0.0272 ^ Dl ^p. 

(2) Whitham, diam. at necks, d" =1.0 to_l.l X diam. of piston-rod. 

(3) Sennett, diam. at middle, d" = D Vp-J-55. 

(4) Sennett, diam. at necks, d" == D Vp-r-60. 

(5) Marks, diam., d"=0.0179 D "S p, if dia m. is greater than 1/24 length. 

(6) Marks, diam., d" = 0.02758 ^ Dl ^p, if diam. found by (5) is less 
than 1/24 length. 

(7) Thurston, diam., at middle, d" = a A vDL A ^ / p+ C, D in inches, 
L in feet, a = 0.15 and C = 1/2 inch for fast engines, a = 0.08 and C = 3/ 4 
inch for moderate speed. 

(8) Seaton says: The rod may be considered as a strut free at both 
ends, and, calculating its diameter accordingly, 

diameter at middle = V/2 (1 + 4 ar 2 ) -=- 48.5, 



1004 



THE STEAM-ENGINE. 



where R = the total load on piston P multiplied by the secant of the 
maximum angle of obliquity of the connecting-rod. 

For wrought iron and mild steel a is taken at 1/3000. The following are 
the values of r in practice: 

Naval engines — Direct-acting r = 9 to 11; 

Return connecting-rod r = 10 to 13, old; 
Return connecting-rod r = 8 to 9, modern; 
Trunk r = 11.5 to 13. 

Mercantile " Direct-acting, ordinary r = 12. 

Mercantile " Direct-acting, long stroke r = 13 to 16. 

(9) The following empirical formula is given by Seaton as agreeing 
closely with good modern practice: 

Diameter of connecting- rod at middle = ^IK h- 4, I = le ngth of rod 
in inches, and K = 0.03 v effective load on piston in pounds. 
The diam. at the ends may be 0.875 of the diam. at the middle. 
Seaton's empirical formula when translated into terms of D and p 

is the same as the second one by Marks, viz., d" = 0.02758 vDJ Vp. 
Whitham's (1) is also practically the same. 

(10) Taking Seaton's more complex formula, with length of connecting- 
rod = 2.5 X length of stroke, and r_= 12 and 16, respectively, it reduces 
to: Diam. at middle = 0.02294 Vp and 0.0241iv / p for short and long 
stroke engines, respectively. 

Applying the above formulas to the engines of our list, we have 



Diameter of Connecting-rods. 










10 


30 


50 








12 
30 

1.82 

1.79 


24 
60 

1.82 

2.14 

2.54 
2.67 
2.14 


30 
75 

5.46 

5.37 

7.00 

7.97 
6.09 


60 
150 

5.46 

5.85 

5.65 
7.97 
6.41 


48 
120 

9.09 

8.95 

11.11 

13.29 
10.16 


96 




240 


(3) d"=^v / p = 0.0182 D^p 


9.09 


(5) d"-0 0179£) Vp~ 




(6) d"~ 02758 \/ Dl ^p 


9.51 


(7) d"- 0.15 ^DL ~fp+ 1/2 


2.87 




(7) d"-0.08'V / DL'V / p+3/4........... 


8.75 


(9) d"~ 0.03 Vp 


2.67 
2.03 


13 29 


(10) d" = 0.02294 Vp ; 0.02411 Vp 


10.68 




2.24 


2.26 


6.38 


6.27 


10.52 


10.26 







Formulae 5 and 6 (Marks), and also formula 10 (Seaton), give the 
larger diameters for the long-stroke engine; formulae 7 give the larger 
diameters for the short-stroke engines. The average figures show but 
little difference in diameter between long- and short-stroke engines; this 
is what might be expected, for while the connecting-rod, considered simply 
as a column, would require an increase of diameter for an increase of 
length, the load remaining the same, yet in an engine generally the shorter 
the connecting-rod the greater the number of revolutions, and conse- 
quently the greater the strains due to inertia. The influences tending 
to increase the diameter therefore tend to balance each other, and to 
render the diameter to some extent independent of the length. The 
average figures correspond nearly to the simple formula d" = 0.021 D "^v. 
The diameters of rod for the three diameters of engine by this formula 
are, respectively, 2.10, 6.30, and 10.50 in. Since the total pressure on the 

piston P = . 7854 D 2 p, the formula is equivalent to d" = . 0237 \ZP. 



DIMENSIONS OF PARTS OF ENGINES. 1005 



Connecting-rod Ends. — For a connecting-rod end of the marine 
type, where the end is secured with two bolts, each bolt should be pro- 
portioned for a safe tensile strength equal to two-thirds the maximum 
pull or thrust in the connecting-rod. 

The cap is to be proportioned as a beam loaded with the maximum pull 
of the connecting-rod, and supported at both ends. The calculation 
should be made for rigidity as well as strength, allowing a maximum 
deflection of Vioo inch. For a strap-and-key connecting-rod end the strap 
is designed for tensile strength, considering that two-thirds of the pull on 
the connecting-rod may come on one arm. At the point where the 
metal is slotted for the key and gib, the straps must be thickened to make 
the cross-section equal to that of the remainder of the strap. Between 
the end of the strap and the slot the strap is liable to fail in double shear, 
and sufficient metal must be provided at the end to prevent such failure. 

The breadth of the key is generally one-fourth of the width of the strap, 
and the length, parallel to the strap, should be such that the cross-section 
will have a shearing strength equal to the tensile strength of the section 
of the strap. The taper of the key is generally about 5/ 8 inch to the foot. 

Tapered Connecting-rods. — In modern high-speed engines it is cus- 
tomary to make the connecting-rods of rectangular instead of circular 
section, the sides being parallel, and the depth increasing regularly from 
the crosshead end to the crank-pin end. According to Grashof, the 
bending action on the rod due to its inertia is greatest at 6/ 10 the length 
from the crosshead end, and, according to this theory, that is the point 
at which the section should be greatest, although in practice the section 
is made greatest at the crank-pin end. 

Professor Thurston furnishes the author with the following rule for 
tapered connecting-rod of rectangular section: Take the section as com- 
puted by the formula d" = 0.1 V DL V/? + 3/ 4 for a circular section, 
and for a rod 4/ 3 the actual length, placing the computed section at 
2/3 the length from the small end, and carrying the taper straight through 
this fixed section to the large end. This brings the computed section at 
the surge point and makes it heavier than the rod for which a tapered 
form is not required. 

Taking the above formula, mu ltiplyin g L by 4/ 3 , and changing it to I 

in inches, it becomes d = 1/30 '^Dl ^p 4- 3/ 4 in. Taking a rectangular 
section of the same area as the round section whose diameter is d, 
and making the depth of the section h = twice the thickness t, we have 

0.7854 d* = ht = 2 P, whence t = 0.627, d = 0.0209 ^ Dl Vp + 0.47 in., 
which is the formula for the thickness or distance between the parallel 
sides of the rod. Making the depth at the crosshead end = 1.5 t, and 
at 2/3 the length = 2 t, the equivalent depth at the crank end is 2.25 t. 
Applying the formula to the short-stroke engines of our examples, we 
have 



Diameter of cylinder, inches 


10 
12 
30 

1.61 
2.42 
3.62 


30 
30 
75 

3.60 
5.41 
8.11 


50 

48 




120 


Thickness,* - 0209 V Dl V^ + 0.47= 


5.59 




8.39 




12.58 







The thicknesses t, found by the formula t = 0.0209 V Dl Vp + 0.47, 

aerree closely with the more simple formula t = 0.01 D *^p+ 0.60 in., the 
thicknesses calculated by this formula being respectively 1.6, 3.6, and 5.6 
inches. 

The Crank-pin. — A crank-pin should be designed (1) to avoid heat- 
ing, (2) for strength, (3) for rigidity. The heating of a crank-pin 
depends on the pressure on its rubbing surface, and on the coefficient 
of friction, which latter varies greatly according to the effectiveness of 



1006 THE STEAM-ENGINE. 

the lubrication. It also depends upon the facility with which the heat 
produced may be carried away: thus it appears that locomotive crank- 
pins may be prevented to some degree from overheating by the cooling 
action of the air through which they pass at a high speed. 

Marks gives I = . 0000247 fpND* = 1.038/ (I.H.P.) + L . (1) 
Whitham gives I = 0.9075/. (I.H.P.) -=- L (2) 

in which I = length of crank-pin journal in inches,/ == coefficient of fric- 
tion, which may be taken at 0.03 to 0.05 for perfect lubrication, and 
0.08 to 0.10 for imperfect; p = mean pressure in the cylinder in pounds 
per square inch; D = diameter of cylinder in inches; N = number of single 
strokes per minute; I.H.P. = indicated horse-power; L = length of stroke 
in feet. These formulae are independent of the diameter of the pin, and 
Marks states as a general law, within reasonable limits as to pressure 
and speed of rubbing, the longer a bearing is made, for a given pressure 
and number of revolutions, the cooler it will work; and its diameter has 
no effect upon its heating. Both of the above formulae are deduced 
empirically from dimensions of crank-pins of existing marine engines. 
Marks says that about one-fourth the length required for crank-pins of 
propeller engines will serve for the pins of side-wheel engines, and one- 
tenth for locomotive engines, making the formula for locomotive crank- 
pins I = 0.00000247 fpND*, or if p = 150, / = 0.06, and N == 600, I = 
O.013D 2 . 

Whitham recommends for pressure per square inch of projected area, 
for naval engines 500 pounds, for merchant engines 400 pounds, for 
paddle-wheel engines 800 to 900 pounds. 

Thurston says the pressure should, in the steam-engine, never exceed 
500 or 600 pounds per square inch for wrought-iron pins, or about twice 
that figure for steel. He gives the formula for length of a steel pin, in 
inches, 

I = PR -s- 600,000, (3) 

in which P and R are the mean total load on the pin in pounds, and the 
number of revolutions per minute. For locomotives, the divisor may be 
taken as 500,000. Where iron is used this figure should be reduced to 
300,000 and 250,000 for the two cases taken. Pins so proportioned, if 
well made and well lubricated, may always be depended upon to run cool; 
if not well formed, perfectly cylindrical, well finished, and kept well oiled, 
no crank-pin can be relied upon. It is assumed above that good bronze 
or white-metal bearings are used. 

Thurston also says: The size of crank-pins required to prevent heating 
of the journals may be determined with a fair degree of precision by 
either of the formulae given below: 

I = P(V + 20) -*- 44,800 d (Rankine, 1865); ... (4) 

I = PV -5- 60,000 d (Thurston, 1862); (5) 

I = PN - 350,000 (Van Buren, 1866) (6) 

The first two formulae give what are considered by their authors fair 
working proportions, and the last gives minimum length for iron pins. 
(V = velocity of rubbing surface in feet per minute.) 

Formula (1) was obtained by observing locomotive practice in which 
great liability exists of annoyance by dust, and great risk occurs from 
inaccessibility while running, and (2) by observation of crank-pins of 
naval screw-engines. The first formula is therefore not well suited for 
marine practice. 

Steel can usually be worked at nearly double the pressure admissible 
with iron running at similar speed. 

Since the length of the crank-pin will be directly as the power expended 
upon it and inversely as the pressure, we may take it as 

I = a (I.H.P.) -r L (7) 

in which a is a constant, and L the stroke of piston, in feet. The values 
of the constant, as obtained by Mr. Skeel, are about as follows: a = 0.04 
where water can be constantly used; a = 0.045 where water is not gen- 
erally used; a = 0.05 where water is seldom used; a = 0.06 where water 
is never needed, Unwin gives 

I = a (I.H.P.) -*- r (8) 



DIMENSIONS OF PARTS OF ENGINES. 



1007 



in which r = crank radius in inches, a = 0.3 to a == 0.4 for iron and for 
marine engines, and a = . 066 to a = . 1 for the case of the best steel 
and for locomotive work, where it is often necessary to shorten up out- 
side pins as much as possible. 

J. B. Stanwood {Eng'g, June 12, 1891), in a table of dimensions of 
parts of American Corliss engines from 10 to 30 inches diameter of cylin- 
der, gives sizes of crank-pins which approximate closely to the formula 

I = 0.275 D"+ 0.5 in.; d = 0.25D" (9) 

By calculating lengths of iron crank-pins for the engines 10, 30, and 
50 inches diameter, long and short stroke, by the several formulae above 
given, it is found that there is a great difference in the results, so that 
one formula in certain cases gives a length three times as great as another. 
Nos. (4), (5), and (6) give lengths much greater than the others. Marks 
(1), Whitham (2), Thurston (7), I = 0.06 I.H.P. -^ L, and Unwin (8), 
I = 0.4 I.H.P.-*- r, give results which agree more closely. 

The calculated lengths of iron crank-pins for the several cases by 
formulae (1), (2), (7), and (8) are as follows: 

Length of Crank-pins. 



Diameter of cylinder D 

Stroke L (ft.) 

Revolutions per minute R 

Horse-power I.H.P. 

Maximum pressure lbs. 

Mean pressure per cent of max 

Mean pressure P. 

Length, of crank-pin: 

(1) Whitham, 1 = 0.9075 x. 05 I.H.P. -5- L 

(2) Marks, i= 1 .038 x .05 I.H.P. h-L 

(7) Thurston, 1=0. 06 I.H.P. + L.. 

(8) Unwin, 1 = 0.4 I.H.P. s-r. . . 
(8) Unwin, 1=0.3 I.H.P. -*-r.,. 



Average 2 . 72 



10 


10 


30 


30 


50 


1 


2 


21/-, 


5 


4 


250 


\ti 


130 


65 


90 


50 


50 


450 


450 


1,250 


7,854 


7,854 


70,686 


70,686 


196,350 


42 


42 


32.3 


32.3 


30 


3,299 


3,299 


22,832 


22,832 


58,905 


2 18 


1.09 


8.17 


4.08 


14.18 


2 59 


1.30 


9.34 


4.67 


16.22 


3.00 


1.50 


10.80 


5.40 


18.75 


3.33 


1.67 


12.0 


6.0 


20.83 


2.50 


1.25 


9.0 


4.5 


15.62 


2.72 


1.36 


9.86 


4.93 


17.12 



50 
8 

45 

1,250 
196,350 

30 
58,905 

7.09 
8.11 
9.38 
10.42 
7.81 



(8) Unwin, best steel, 1=0.] I.H.P. + 
(3) Thurston, steel, 1= PR -h 600,000 . 



83 0.42 3.0 1.5 5.21 
• 1.37 0.69 4.95 2.47 8.84 



2.61 

4.42 



The calculated lengths for the long-stroke engines are too low to pre- 
vent excessive pressures. See "Pressures on the Crank-pins," below. 

The Strength of the Crank-pin is determined substantially as is that 
of the crank. In overhung cranks the load is usually assumed as carried 
at its extremity, and, equating its moment with that of the resistance 
of the pin, 

V2Pl=V32tnd\ and d = V/^y^> 

in which d = diameter of pin in inches, P = maximum load on the 
piston, t = the maximum allowable stress on a square inch of the metal. 
For iron it may be taken at 9000 lbs. For steel the diameters found by 
this formula may be reduced 10%. (Thurston.) 
Unwin gives the same formula in another form, viz.: 



r^Sf^K-VrV' 



the last form to be used when the ratio of length to diameter is assumed. 
For wrought iron, t = 6000 to 9000 lbs. per sq. in., 

yb.l/t= 0.0947 to 0.0827; ^5.1/t = 0.0291 to 0.0238. 
For steel, t = 9000 to 13,000 lbs. per sq. in., 

^5jjt = 0.0827 to 0.0723; ^5.1/t = 0.0238 to 0.0194. 



1008 



THE STEAM-ENGINE. 



Whitham gives d = 0.0327 f/Pl = 2.1058 fy X I.H.P. + LR for 
strength, and d = 0.0405 *\JPl 3 for rigidity, and recommends that the 
diameter be calculated by both formulae, and the largest result taken. 
The first is the same as Unwin's formula, with t taken at 9000 lbs. per sq. 
in. The second is based upon an arbitrary assumption of a deflection of 
V300 in. at the center of pressure (one-third of the length from the free 
end). 

Marks, calculating the diameter for rigidity, gives 

d = 0.066 \ft 



2 = 0.945 <^(H.P.)Z» + LN; 

p = maximum steam-pressure in pounds per square inch, D = diameter 
of cylinder in inches, L = length of stroke in feet, N = number of single 
strokes per minute. He says there is no need of an investigation of the 
strength of a crank-pin, as the condition of rigidity gives a great excess 
of strength. 

Marks's formula is based upon the assumption that the whole load 
may be concentrated at the outer end, and cause a deflection of 0.01 in. 
at that point. It is serviceable, he says, for steel and for wrought iron 
alike. 

Using the average lengths of the crank-pins already found, we have 
the following for our six engines: 



Diameter of Crank-pins. 



Diameter of cylinder. . . 

Stroke, ft 

Length of crank-pin. . . . 

Unwin, d = u — '— — . . . 
Marks, d= 0.066 $pl a D< 



10 

1 

2.72 


10 

2 
1.36 


30 

21/2 
9.86 


30 
5 

4.93 


50 

4 

17.12 


2.29 


1.82 


7.34 


5.82 


12.40 


1.39 


0.85 


6.44 


3.78 


12.41 



50 

8 

8.56 

9.84 
7.39 



Pressures on the Crank-pins. — If we take the mean pressure upon 
the crank-pin = mean pressure on piston, neglecting the effect of the 
varying angle of the connecting-rod, we have the following, using the 
average lengths already found, and the diameters according to Unwin 
and Marks: 





1 


2 


3 


4 


5 


6 








10 
1 

3,299 
6.23 
3.78 
530 

873 


10 

2 
3,299 
2.36 
1.16 

1,398 

2,845 


30 

21/2 
22,832 
72.4 
63.5 
315 
360 


30 
5 
22,832 
28.7 
18.6 
796 
1,228 


50 
4 
58,905 
212.3 
212.5 
277 
277 


50 




8 




58,905 




84.2 




63.3 


Pressure per square inch, Unwin 

Pressure per square inch, Marks 


700 
930 



The results show that the application of the formulae for length and 
diameter of crank-pins give quite low pressures per square inch of pro- 
jected area for the short-stroke high-speed engines of the larger sizes, but 
too high pressures for all the other engines. It is therefore evident that 
after calculating the dimensions of a crank-pin according to the formulae 
given the results should be modified, if necessary, to bring the pressure 
per square inch down to a reasonable figure. 

In order to bring the pressures down to 500 pounds per square inch, 
we divide the mean pressures by 500 to obtain the projected area, or 
product of length by diameter. Making I = 1.5 d for engines Nos. 1, 
2, 4, and 6, the revised table for the six engines is as follows: 



DIMENSIONS OF PARTS OF ENGINES. 1009 

Engine No 12 3 4 5 6 

Length of crank-pin, inches.. 3.15 3.15 9.86 8.37 17.12 13.30 

Diameter of crank-pin 2.10 2.10 7.34 5.58 12.40 8.87 

Crosshead-pin or Wrist-pin. — Whitham says the bearing surface 
for the wrist-pin is found by the formula for crank-pin design. Seaton 
says the diameter at the middle must, of course, be sufficient to withstand 
the bending action, and generally from this cause ample surface is provided 
for good working; but in any case the area, calculated by multiplying the 
diameter of the journal by its length, should be such that the pressure 
does not exceed 1200 lbs. per sq. in., taking the maximum load on the 
piston as the total pressure on it. 

For small engines with the gudgeon shrunk into the jaws of the con- 
necting-rod, and working in brasses fitted into a recess in the piston-rod 
end and secured by a wrought-iron cap and two bolts, Seaton gives: 

Diameter of gudgeon = 1 . 25 X diam. cf piston-rod, 

Length of gudgeon = 1 . 4 X diam. of piston-rod. 

If the pressure on the section, as calculated by multiplying length by 
diameter, exceeds 1200 lbs. per sq. in., this length should be increased. 

J. B. Stanwood, in his "Ready Reference" book, gives for length of 
crosshead-pin 0.25 to 0.3 diam. of piston, and diam. = 0.18 to 0.2 
diam. of piston. Since he gives for diam. of piston-rod 0.14 to 0.17 
diam. of piston, his dimensions for diameter and length of crosshead-pin 
are about 1.25 and 1.8 diam. of piston-rod respectively. Taking the 
maximum allowable pressure at 1200 lbs. per sq. in. and making the 
length of the crosshead-pin = 4/3 of its diameter, we have d= Vp-f- 40, Z = 
Vp-8- 30, in which P = maximum total load on piston in lbs., d = diam. 
and 1= length of pin in inches. For the engines of our example we have: 

Diameter of piston, inches 10 30 50 

Maximum load on piston, lbs 7854 70,686 196,350 

Diameter of crosshead-pin, inches 2 . 22 6 . 65 1 1 . 08 

Length of crosshead-pin, inches 2.96 8.86 14.77 

Stanwood's rule gives diameter, ins 1 . 8 to 2 5 . 4 to 6 9 . to 10 

Stanwood's rule gives length, inches. . . 2.5 to 3 7.5 to 9 12.5 to 15 
Stanwood's largest dimensions give 

pressure per sq. in., lbs 1309 1329 1309 

Which pressures are greater than the maximum allowed by Seaton. 

The Crank-arm. — The crank-arm is to be treated as a lever, so that 
if ais the thickness in adirection parallel to the shaft-axis and b its breadth 
at a section x inches from the crank-pin center, then, bending moment 
M at that section = Px, P being the thrust of the connecting-rod, and 

/ the safe strain per square inch, 

D fab* , aX& 2 T 67 , 4 /6T 

If a crank-arm were constructed so that b varied as Vx (as given by 
the above rule) it would be of such a curved form as to be inconvenient 
to manufacture, and consequently it is customary in practice to find the 
maximum value of b and draw tangent lines to the curve at the points; 
these lines are generally, for the same reason, tangential to the boss of 
the crank-arm at the shaft. 

The shearing strain is the same throughout the crank-arm; and, con- 
sequently, is large compared with the bending strain close to the crank- 
in; and so it is not sufficient to provide there only for bending strains, 
'he section at this point should be such that, in addition to what is given 
by the calculation from the bending moment, there is an extra square 
inch for every 8000 lbs. of thrust on the connecting-rod (Seaton). 

The length of the boss h into which the shaft is fitted is from 0.75 to 
1.0 of the diameter of the shaft D, and its thickness e must be calculated 
from the twisting strain PL. (L = length of crank.) 

For different values of length of boss h, the following values of thick- 
ness of boss e are given by Seaton: 

When h = D, then e = . 35 D ; if steel, . 3. 
h = 0.9 D, thene = 0.38 D; if steel, 0.32. 
h = 0.8 D, then e = 0.40 D; if steel, 0.33. 
h = 0.7 D, then e = 0.41 D; if steel, 0.34. 



Pi 
T 



1010 



THE STEAM-ENGINE. 



The crank-eye or boss into which the pin is fitted should bear the same 
relation to the pin that the boss does to the shaft. 

The diameter of the shaft-end onto which the crank is fitted should be 
1.1 X diameter of shaft. 

Thurston says: The empirical proportions adopted by builders will 
commonly be found to fall well within the calculated safe margin. These 
proportions are, from the practice of successful designers, about as follows: 

For the wrought-iron crank, the hub is 1.75 to l.S times the least 
diameter of that part of the shaft carrying full load; the eye is 2.0 to 2.25 
the diameter of the inserted portion of the pin, and their depths are, 
for the hub, 1.0 to 1.2 the diameter of shaft, and for the eye, 1.25 to 1.5 
the diameter of pin. The web is made 0.7 to 0.75 the width of adjacent 
hub or eye, and is given a depth of 0.5 to 0.6 that of adjacent hub or 
eye. 

For the cast-iron crank the hub and eye are a little larger, ranging in 
diameter respectively from 1.8 to 2 and from 2 to 2.2 times the diameters 
of shaft and pin. The flanges are made at either end of nearly the full 
depth of hub or eye. Cast iron has, however, fallen very generally into 
disuse. 

The crank-shaft is usually enlarged at the seat of the crank to about 
1.1 its diameter at the journal. The size should be nicely adjusted to 
allow for the shrinkage or forcing on of the crank. A difference of diam- 
eter of 0.2% will usually suffice; and a common rule of practice gives an 
allowance of but one-half of this, or 0.1%. 

The formulae given by different writers for crank-arms practically agree, 
since they all consider the crank as a beam loaded at one end and fixed 
at the other. The relation of breadth to thickness may vary according 
to the taste of the designer. Calculated dimensions for our six engines 
are as follows: 

Dimensions of Crank-arms. 



Diam. of cylinder, ins 

Stroke S, ins 

Max. pressure on pin P 

(approx.) , lbs 

Diam. crank-pin d 

Dia. shaft, a y -^ — '-, D 
(a = 4.69, 5.09 and 5.22)... 

Length of boss, 0.8 D 

Thickness of boss, 0.4 D. . . 

Diam. of boss, I.8D 

Length crank-pin eye, 0.8 d 
Thickness of crank-pin eye, 

0.4d 

Max. mom. T at distance 

V2S— 1/2 D from center of 

pin, inch-lbs 

Thickness of crank-arm a = 

0.75 D 

Greatest b readth, 

b= \/6 T + 9000 a 
Min. mom. T at distance 

dfrom center of pin= Pd 
Least breadth, 

&! = V6 T - 9000 a 



10 

12 


10 

24 


30 
30 


30 
60 


50 

48 


7854 
2.10 


7854 
2.10 


70,686 
7.34 


70,686 
5.58 


196,350 
12.40 


k.74 


3.46 


7.70 


9.70 


12.55 


J 
2.19 
1.10 
4.93 
1.76 


2.77 
1.39 
6.23 
1.76 


6.16 
3.08 
13.86 
5.87 


7.76 
3.88 
17.46 
4.46 


10.04 
5.02 

22.59 
9.92 


0.88 


0.88 


2.94 


2.23 


4.46 


37,149 


80,661 


788,149 


1,848,439 


3,479,322 


2.05 


2.60 


5.78 


7.28 


9.41 


3.48 


4.55 


9.54 


13.0 


15.7 


16,493 


16,493 


528,835 


394,428 


2,434,740 


2.32 


2.06 


7.81 


6.01 


13.13 



50 
96 



196,350 
8.87 



12.65 
6.32 

28.47 
7.10 

3.55 



7,871,671 
11.87 
21.0 

1,741,625 
9.89 



The Shaft. — Twisting Resistance. — From the general formula 
for torsion, we have: T = ^d s S = 0.19635 d s S, whence d = t/^4p' 



16 



in which T = torsional moment in inch-pounds, d = diameter in inches, 
and S = the shearing resistance of the material in pounds per square 
inch, 



DIMENSIONS OF PARTS OF ENGINES. 



1011 



If a constant force P were applied to the crank-pin tangentially to its 
path, the work done per minute would be 

PXLX2tz + 12XR = 33,000 X I.H.P., 
in which L = length of crank in inches, and R = revs, per min., and the 
mean twisting moment T = I.H.P. ■*■ R X 63,025. Therefore 

d = yj 5 . 1 T -*- S = ^321,427 I.H.P. -5- US. 

This may take the form 

d = ^I.H.P. X FIR, or d = a \/l.H.P. -s- R, 
in which F and a are factors that depend on the strength of the material 
and on the factor of safety. Taking S at 45,000 pounds per square inch 
for wrought iron, and at 60,000 for steel, we have, for simple twisting by 
a uniform tangential force, 
Factor of safety =568 10 5 6 810 

Iron F = 35.7 42.8 57.1 71.4 a =3.3 3.5 3.85 4.15 

Steel F = 26.8 32.1 42.8 53.5 a = 3.0 3.18 3.5 3.77 

Unwin, taking for safe working strength of wrought iron 9000 lbs., 
steel 13,500 lbs., and cast iron 4500 lbs., gives a = 3.294 for wrought 
iron, 2.877 for steel, and 4.15 for cast iron. Thurston, for crank-axles 
of wrought iron, gives a = 4.15 or more. 

Seaton says: For wrought iron, /, the safe strain per square inch, should 
not exceed 9000 lbs., and when the shafts are more than 10 inches diameter, 
8000 lbs. Steel, when made from the ingot and of good materials, will 
admit of a stress of 12,000 lbs. for small shafts, and 10,000 lbs. for those 
above 10 inches diameter. 

The difference in the allowance between large and small shafts is to com- 
pensate for the defective material observable in the heart of large shaft- 
ing, owing to the hamm ering failing to affect it. 

The formula d = a -\/l.H.P. -f- R assumes the tangential force to be 
uniform and that it is the only acting force. For engines, in which the 
tangential force varies with the angle between the crank and the connect- 
ing-rod, and with the variation in steam-pressure in the cylinder, and also 
is influenced by the inertia of the reciprocating parts, and in which also 
the shaft may be subjected to bending as well as torsion, the factor 
a must be increased, to provide for the maximum tangential force and 
for bending. 

Seaton gives the following table showing the relation between the 
maximum and mean twisting moments of engines working under various 
conditions, the momentum of the moving parts being neglected, which is 
allowable: 



Description of Engine. 


Steam Cut-off 
at 


Max. 

Twist 

Divided 

by 

Mean 

Twist. 
Moment. 


Cube 
Root 
of the 
Ratio. 




0.2 
0.4 
0.6 
0.8 
0.2 
0.3 
0.4 
0.5 
0.6 
0.7 
0.8 
h.p. 0.5, l.p.0.66 


2.625 
2.125 
1.835 
1.698 
1.616 
1.415 
1.298 
1.256 
1.270 
1.329 
1.357 
1.40 

1.26 


1.38 




1.29 


«i (i 


1.22 


« a 


1.20 


Two-cylinder expansive, cranks at 90° 

Three-cylinder compound, cranks 120° 

Three-cylinder compound, l.p. cranks op- ) 
posite one another, and h.p. midway j 


1.17 
1.12 
1.09 
1.08 
1.08 
1.10 
1.11 
1.12 

1.08 



1012 THE STEAM-ENGINE. 

Seaton also gives the following rules for ordinary practice for ordinary 

two-cylinder marine engines: 

Diameter of the tunnel-shafts = -^I.H.P. X F/2?,ora ^I.H.P. + R. 
Compound engines, cranks at right angles: 

Boiler pressure 70 lbs., rate of expansion 6 to 7, F = 70, a = 4.12. 

Boiler pressure 80 lbs., rate of expansion 7 to 8, F = 72, a = 4.16. 

Boiler pressure 90 lbs., rate of expansion 8 to 9, F = 75, a = 4.22. 

Triple compound, three cranks at 120 degrees: 

Boiler pressure 150 lbs., rate of expansion 10 to 12, F = 62, a = 3.96, 
Boiler pressure 160 lbs., rate of expansion 11 to 13, F = 64, a = 4. 
Boiler pressure 170 lbs., rate of expansion 12 to 15, F = 67, a = 4.06. 

Expansive engines, cranks at right angles, and the rate of expansion 5, 
boiler-pressure 60 lbs., F = 90, a = 4.48. 

Single-crank compound engines, pressure 80 lbs., F = 96, a = 4.587 

For the engines we are considering it will be a very liberal allowance for 

ratio of maximum to mean twisting moment if we take it as equal to the 

ratio of the maximum to the mean pressure on the piston. The factor a, 

then, in the formula for diameter of the shaft will be multiplied by the cube 

root of this ratio, or t/^ = 1.34, CI ^p%= 1 • 45, and C/^ = 1.49 

for the 10, 30, and 50-in. engines, respectively. Taking a = 3.5, which 
corresponds to a shearing strength of 60,000 and a factor of safety of 8 for 
steel, or to 45,000 and a factor of 6 for iron, we have for the new coeffi- 
cient a t in the formula d t = a t ^/i.H.P. •*- R, the values 4.69, 5.08, and 
5.22 from which we obtain the diameters of shafts of the six engines as 
follows : 

Engine No 1 2 3 4 5 6 

Diam. of cyl 10 10 30 30 50 50 

Horse-power, I.H.P 50 50 450 450 1250 1250 

Revs, per min., R 250 125 130 65 90 45 

Diam. of shaft d = 2.74 3.46 7.67 9.70 12.55 15.82 

These diameters are calculated for twisting only. When the shaft is 
also subjected to bending strain the calculation must be modified as 
below: 

Resistance to Bending. — The strength of a circular-section shaft 
to resist bending is one-half of that to resist twisting. If B is the bending 
moment in inch-lbs., and d the diameter of the shaft in inches, 



B = ~ X /; and d = <Uj X 10. 2; 



32 ' 



/ is the safe strain per square inch of the material of which the shaft is 
composed, and its value may be taken as given above for twisting (Seaton). 

Equivalent Twisting Moment. — When a shaft is subject to both 
twisting and bending simultaneously, the combined strain on any section 
of it may be measured by calculating what is called the equivalent twisting 
moment; that is, the two strains are so combined as to be treated as a 
twisting strain only of the same magnitude and the size of shaft calculated 
accordingly. Rankine gave the following solution of the combined action 
of the two strains. 

If T = the twisting moment, and B = the bending moment o n a sect ion 
of a shaft, then the equivalent twisting moment T\ = B + ^B 2 + T 2 . 

Seaton says: Crank-shafts are subject always to twisting, bending, and 
shearing strains; the latter are so small compared with the former that 
they are usually neglected directly, but allowed for indirectly by means 
of the factor f. 

The two principal strains vary throughout the revolution, and the 
maximum equivalent twisting moment can only be obtained accurately 
by a series of calculations of bending and twisting moments taken at fixed 
intervals, and from them constructing a curve of strains. 

Considering the engines of our examples to have overhung cranks, the 
maximum bending moment resulting from the thrust of the connecting- 



DIMENSIONS OF PARTS OF ENGINES. 



1013 



rod on the crank-pin will take place when the engine is passing its centers 
(neglecting the effect of the inertia of the reciprocating parts), and it will 
be the product of the total pressure on the piston by the distance between 
two parallel lines passing through the centers of the crank-pin and of the 
shaft bearing, at right angles to their axes; which distance is equal to 
1/2 length of crank-pin bearing + length of hub + 1/2 length of shaft- 
bearing 4- any clearance that may be allowed between the crank and the 
two bearings. For our six engines we may take this distance as equal 
to 1/2 length of crank-pin + thickness of crank-arm + 1.5 X the diam- 
eter of the shaft as already found by the calculation for twisting. The 
calculation of diameter is then as below: 



Engine No. 


1 


2 


3 


4 


5 


6 


Diam. of cyl., in.... 

Horse-power 

Revs, per min 

Max. press, on pis.P 
Leverage,* Lin... . 
Bd.mo.PL= J Bin.-lb 
Twist, mom. T .... 
Equiv. twist mom. 


10 
50 
250 
7,854 
6.32 
49,637 
47,124 

118,000 


10 
50 
125 

7,854 
7.94 
62,361 
94,248 

175,000 


30 
450 
130 

70,686 

22.20 

1,569,222 

1,060,290 

3,463,000 


30 

450 

65 

70,686 

26.00 

1,837,836 

2,120,580 

4,647,000 


50 

1250 

90 

196,350 

36.80 

7,225,680 

4,712,400 

15,840,000 


50 

1250 

45 

196,350 

42.25 

8,295,788 

9,424,800 


(approx.) 


20,850,000 



* Leverage = distance between centers of crank-pin and shaft bearing 
= l/ 2 2 + 2.25 d. 

Having already found the diameters, on the assumption that the shafts 
were subjected to a twisting moment T only, we may find the diameter 
for resisting combined bending and twisting by multiplying the diameters 
already found by the cube roots of the ratio T\ -5- T, or 

1.40 1.27 1.46 1.34 1.64 1.36 
Giving corrected diameters di = 3.84 4.39 11.35 12.99 20.58 21.52 

By plotting these results, using the diameters of the cylinders for abscis- 
sas and diameters of the shafts for ordinates, we find that for the long- 
stroke engines the results lie almost in a straight line expressed by the 
formula, diameter of shaft = 0.43 X diameter of cylinder; for the short- 
stroke engines the line is slightly curved, but does not diverge far from a 
straight line whose equation is, diameter of shaft = 0.4 diameter of 
cylinder. Using these two formulas, the diameters of the shafts will be 
4.0, 4.3, 12.0, 12.9, 20.0, 21.5. 

J. B. Stanwood, in Engineering, June 12, 1891, gives dimensions of 
shafts of Corliss engines in American practice for cylinders 10 to 30 in. 
diameter. The diameters range from 4i5/i6to 14i5/i6, following precisely 
the equation, diameter of shaft = 1/2 diameter of cylinder — Vie inch. 

Fly-wheel Shafts. — Thus far we have considered the shaft as resist- 
ing the force of torsion and the bending moment produced by the pressure 
on the crank-pin. In the case of fly-wheel engines the shaft on the 
opposite side of the bearing from the crank-pin has to be designed with 
reference to the bending moment caused by the weight of the fly-wheel, 
the weight of the shaft itself, and the strain of the belt. For engines 
in which there is an outboard bearing, the weight of fly-wheel and shaft 
being supported by two bearings, the point of the shaft at which the 
bending moment is a maximum may be taken as the point midway 
between the two bearings or at the middle of the fly-wheel hub, and the 
amount of the moment is the product of the weight supported by one of 
the bearings into the distance from the center of that bearing to the 
middle point of the shaft. The shaft is thus to be treated as a beam 
supported at the ends and loaded in the middle. In the case of an over- 
hung fly-wheel, the shaft having only one bearing, the point of maximum 
moment should be taken as the middle of the bearing, and its amount is 
very nearly the product of half the weight of the fly-wheel and the shaft 



1014 



THE ^STEAM-ENGINE. 



into the distance of the middle of its hub from the middle of the bear- 
ing. The bending moment should be calculated and combined with the 
twisting moment as above shown, to obtain the equivalent twisting 
moment, and the diameter necessary at the point of maximum moment 
calculated therefrom. 

In the case of our six engines we assume that the weights of the fly- 
wheels, together with the shaft, are double the weight of fly-wheel rim 

i d 2 s 
obtained from the formula W= 785,400 j^™ (given under Fly-wheels); 

that the shaft is supported by an outboard bearing, the distance between 
the two bearings being 2 1/2, 5, and 10 feet for the 10-in., 30-in., and 50-in. 
engines, respectively. The diameters of the fly-wheels are taken such 
that their rim velocity will be a little less than 6000 feet per minute. 

Engine No 1 2 3 4 5 6 

Diam. of cyl., inches 10 10 30 30 50 50 

Diam. of fly-wheel, ft 7.5 15 14.5 29 21 42 

Revs, per min 250 125 130 65 90 45 

Half wt. fly-wheel and 

shaft, lbs 268 536 5,968 11,936 26,384 52,769 

Lever arm for maximum 

moment, in 15 15 30 30 60 60 

Maximum bending mo- 
ment, in.-lbs 4020 8040 179,040 358,080 1,583,070 3,166,140 

As these are very much less than the bending moments calculated from 
the pressures on the crank-pin, the diameters already found are sufficient 
for the diameter of the shaft at the fly-wheel hub. 

In the case of engines with heavy band fly-wheels and with long fly- 
wheel shafts it is of the utmost importance to calculate the diameter of 
the shaft with reference to the bending moment due to the weight of the 
fly-wheel and the shaft. 

B. H. Coffey (Power, October, 1892) gives the formula for combined 
be nding a nd twisting resistance, T\ = 0.196 d 3 S, in which Ti = B + 
v / B 2 + T 2 ; T being the maximum, not the mean twisting moment; and 
finds empirical working values for 0.196 S as below. He says: Four 
points should be considered in determining this value: First, the nature 
of the material; second, the manner of applying the loads, with shock 
or otherwise; third, the ratio of the bending moment to the torsional 
moment — the bending moment in a revolving shaft produces reversed 
strains in the material, which tend to rupture it; fourth, the size of the 
section. Inch for inch, large sections are weaker than small ones. He 
puts the dividing line between large and small sections at 10 in. diameter, 
and gives the following safe values of S X 0.196 for steel, wrought iron, 
and cast iron, for these conditions. 

Value of S X 0.196. 



Ratio. 


Heavy Shafts 
with Shock. 


Light Shafts 

with Shock. 

Heavy Shafts 

No Shock. 


Light Shafts 
No Shock. 


B to T. 


Steel. 


Wro't 
Iron. 


Cast 
Iron. 


Steel. 


Wro't 
Iron. 


Cast 
Iron. 


Steel. 


Wro't 
Iron. 


Cast 
Iron. 


3 to 10 or less 

3 to 5 or less 

I to 1 or less 

B greater than T . . 


1045 
941 
855 
784 


880 
785 
715 
655 


440 
393 
358 
328 


1566 
1410 
1281 
1176 


1320 
1179 
1074 
984 


660 
589 
537 
492 


2090 
1882 
1710 
1568 


1760 
1570 
1430 
1310 


880 
785 
715 
655 



Mr. Coffey gives as an example of improper dimensions the fly-wheel 
shaft of a 1500 H.P. engine at Willimantic, Conn., which broke while the 
engine was running at 425 H.P. The shaft was 17 ft. 5 in. long between 



DIMENSIONS OF PARTS OF ENGINES. 1015 



centers of bearings, 18 in. diam. for 8 ft. in the middle, and 15 in. diam. 
for the remainder, including the bearings. It broke at the base of the 
fillet connecting the two large diameters, or 56 1/2 in. from the center of 
the bearing. He calculates the mean torsional moment to be 446,654 
inch-pounds, and the maximum at twice the mean; and the total weight 
on one bearing at 87,530 lbs., which, multiplied by 56 1/2 in., gives 
4,945,445 i n.-lbs. b ending moment at the fillet. Applying the formula 
T\ = £+ v'.B 2 + T 2 , gives for equivalent twisting moment 9,971,045 in.- 
lbs. Substituting this value in the formula T\ = 0.196 Sa 3 gives for S 
the shearing strain 15,070 lbs. per sq. in., or if the metal had a shearing 
strength of 45,000 lbs., a factor of safety of only 3. Mr. Coffey considers 
that 6000 lbs. is all that should be allowed for S under these circum- 
stances. This would give d = 20.35 in. If we take from Mr. Coffey's 
table a value of 0.196 S = 1100, we obtain d s = 9000 nearly, or d = 20.8 
in. instead of 15 in., the actual diameter. 

Length of Shaft-bearings. — There is as great a difference of opinion 
among writers, and as great a variation in practice concerning length of 
journal-bearings, as there is concerning crank-pins. The length of a 
journal being determined from considerations of its heating, the observa- 
tions concerning heating of crank-pins apply also to shaft-bearings, and 
the formulae for length of crank-pins to avoid heating may also be used, 
using for the total load upon the bearing the resultant of all the pressures 
brought upon it, by the pressure on the crank, by the weight of the fly- 
wheel, and by the pull of the belt. After determining this pressure, how- 
ever, we must resort to empirical values for the so-called constants of the 
formulae, really variables, which depend on the power of the bearing 
to carry away heat, and upon the quantity of heat generated, which 
latter depends on the pressure, on the number of square feet of rubbing 
surface passed over in a minute, and upon the coefficient of friction. This 
coefficient is an exceedingly variable quantity, ranging from 0.01 or less 
with perfectly polished journals, having end-play, and lubricated by a 
pad or oil-bath, to 0. 10 or more with ordinary oil-cup lubrication. 

For shafts resisting torsion only, Marks gives for length of bearing I = 
0. 0000247 fpND 2 , in which /is the coefficient of friction, p the mean 
pressure in pounds per square inch on the piston, N the number of 
single strokes per minute, and D the diameter of the piston. For shafts 
under the combined stress due to pressure on the crank-pin, weight of 
fly-wheel, etc., he gives the following: Let Q = reaction at bearing due 
to weight, S = stress due steam pressure on p iston, a nd Ri = the 
resultant force; for horizontal engines, Ri = *v / Q 2 +S 2 , for vertical 
engines Ri = Q + S, when the pressure on the crank is in the same 
direction as the pressure of the shaft on its bearings, and Ri = Q — S 
when the steam pressure tends to lift the shaft from its bearings. Using 
empirical values for the work of friction per square inch of projected area, 
taken from dimensions of crank-pins in marine vessels, he finds the 
formula for length of shaft-journals I = 0.0000325/^1 N, and recom- 
mends that to cover the defects of workmanship, neglect of oiling, and the 
introduction of dust, / be taken at 0. 16 or even greater. He says that 
500 lbs. per sq. in. of projected area may be allowed for steel or wrought- 
iron shafts in brass bearings with good results if a less pressure is not 
attainable without inconvenience. Marks says that the use of empirical 
rules that do not take account of the number of turns per minute has 
resulted in bearings much too long for slow-speed engines and too short 
for high-speed engines. 

Whitham gives the same formula, with the coefficient 0.00002575. 

Thurston says that the maximum allowable mean intensity of pressure 
may be, for all cases, computed bv his formula for journals, I = PV ■*■ 
60,000 d, or by Rankine's, I = P (V + 20) -*- 44,800 d, in which P is the 
mean total pressure in pounds, V the velocity of rubbing surface in feet 
per minute, and d the diameter of the shaft in inches. It must be borne 
in mind, he says, that the friction work on the main bearing next the crank 
is the sum of that due the action of the piston on the pin and that due 
that portion of the weight of wheel and shaft and of pull of the belt which 
is carried there. The outboard bearing carries practically only the 
latter two parts of the total. The crank-shaft journals will be made 
longer on one side, and perhaps shorter on the other, than that of the 
crank-pin, in proportion to the work falling upon each, i.e., to their 



1016 



THE STEAM-ENGINE. 



respective products of mean total pressure, speed of rubbing surfaces, and 
coefficients of friction. 

Unwin says: Journals running at 150 revolutions per minute are often 
only one diameter long. Fan shafts running 150 revolutions per minute 
have journals six or eight diameters long. The ordinary empirical mode 
of proportioning the length of journals is to make the length proportional 
to the diameter, and to make the ratio of length to diameter increase 
with the speed. For wrought-iron journals: 

Revs, per mi n. = 50 100 150 200 250 500 1000 l/d = 0.004 R+l. 
Length -h diam. = 1.2 1.4 1.6 1.8 2.0 3.0 5.0. 

Cast-iron journals may have Z-e-d = 9/i , and steel journals l-^-d = l^Ii, 
of the above values. 

Unwin gives the following, calculated from the formula !=0.4H.P.+ r, 
in which r is the crank radius in inches, and H.P. the horse-power trans- 
mitted to the crank-pin. 

Theoretical Journal, Length in Inches. 



Load on 

Journal in 

pounds. 



Revolutions of Journal per Minute. 



1,000 
2,000 
4,000 
5,000 
10,000 
15,000 
20,000 
30,000 
40,000 
50,000 



0.2 

0.4 

0.8 

1.0 

2. 

3. 

4. 

6, 



0.4 
0.8 
1.6 
2. 



12. 

16. 
20. 



0.8 

1.6 

3.2 

4. 

8. 

12. 

16. 

24. 

32. 



1.2 
2.4 
4.8 
6. 

12. 

18. 

24. 

36. 



2. 

4. 

8. 
10. 
20. 
30. 
40. 



16. 

20. 
40. 



Applying these different formulae to our six engines, we have: 



Engine No 

Diam. cyl 

Horse-power 

Revs, per min 

Mean pressure on crank-pin = S 

Half wt. of fly-wheel and shaft = Q. . . . 
Resultant pressure on bearing 

Diam. of shaft journal 

Length of shaft journal: 
Marks, 1 = 0. 0000325 /P,7V(/=0. 10) 
Whitham, Z = 0.00005 15 fRiRif =0.10) 

Thurston, Z = PF-^ (60,000 d) 

Rankine, l = P (V+20) -~ (44,800d).. . 

Unwin, 1= (0.004 R+ 1) d 

Unwin, Z=<MH.P.-^r 

Average 



10 

50 
250 
3,299 
268 

3,310 

3.84 

5.38 

4.27 
3.61 
5.22 
7.68 
3.33 



4.92 



30 
450 
130 

23,185 
5,968 



23,924 
11.35 

20.87 
16.53 
14.00 
21.70 
17.25 
12.00 



17.05 



30 
450 

65 
23,185 
11,936 

26,194 
12.99 

11.07 

8.77 
7.43 
10.85 
16.36 
6.00 



10.00 



50 

1,250 

90 

58,905 
26,470 

64,580 
20.58 

37.78 
29.95 
25.36 
35.16 
27.99 
20.83 



29.54 



50 

1,250 

45 
58,905 
52,940 

79,200 
21.52 

23. .17 
18.35 
15.55 
22.47 
25.39 
10.42 

19.22 



If we divide the mean resultant pressure on the bearing by the pro- 
jected area, that is, by the product of the diameter and length of the 
journal, using the greatest and smallest lengths out of the seven lengths 



DIMENSIONS OF PARTS OF ENGINES. 



1017 



j for each journal given above, we obtain the pressure per square inch upon 
(the bearing, as follows: 





1 


2 


3 


4 


5 


6 






Press, per sq. in., shortest journal 

Longest journal 


259 
112 
175 


455 
115 
254 
173 


176 
97 
124 


336 
123 
202 
155 


151 
83 
106 


353 
145 
191 




175 









I Many of the formulae give for the long-stroke engines a length of journal 
j less than the diameter, but such short journals are rarely used in practice. 
! The last line in the above table has been calculated on the supposition 

that the journals of the long-stroke engines are made of a length equal 
i to the diameter. 

In the dimensions of Corliss engines given by J. B. Stanwood (Eng., 
; June 12, 1891), the lengths of the journals for engines of diam. of cyl. 
: 10 to 20 in. are the same as the diam. of the cylinder, and a little more 

than twice the diam. of the journal. For engines above 20 in. diam. of 

cyl. the ratio of length to diam. is decreased so that an engine of 30 in. 
\ diam. has a journal 26 in. long, its diameter being 14ij/i6 in. These 

lengths of journal are greater than those given by any of the formulae 

above quoted. 

There thus appears to be a hopeless confusion in the various formulae 
, for length of shaft journals, but this is no more than is to be expected 

from the variation in the coefficient of friction, and in the heat-conducting 
i power of journals in actual use, the coefficient varying from 0.10 (or 
1 even 0.16 as given by Marks) down to 0.01, according to the condition 
: of the bearing surfaces and the efficiency of lubrication. Thurston's 

PV 
j formula, I = gTTT^Tr^' reduces to the form I = 0.000004363 PR, in which 

P = mean total load on journal, and R = revolutions per minute. This • 
lis of the same form as Marks's and Whitham's formulae, in which, if/, the 
j coefficient of friction, be taken at 0.10, the coefficients of PR are, respec- 
tively, 0.0000065 and 0.00000515. Taking the mean of these three 
; formulae, we have I = 0.0000053 PR, if / = 0.10 or I = 0.000053 fPR 
for any other value of /. The author believes this to be as safe a formula 
as any for length of journals, with the limitation that if it brings a result 
of length of journal less than the diameter, then the length should be 
made equal to the diameter. Whenever, with/ = 0.10 it gives a length 
: which is inconvenient or impossible of construction on account of limited 
space, then provision should be made to reduce the value of the coefficient 
of friction below 0.10 by means of forced lubrication, end play, etc., and 
to carry away the heat, as by water-cooled journal-boxes. The value of 
P should be taken as the resultant of the mean pressure on the crank, 
and the load brought on the bearing by the weight of the shaf t, fly-wh eel, 

etc., as calculated by the formula already given, viz., Ri = ^Q 2 + S 2 for 
horizontal engines, and Ri = Q + S for vertical engines. 

For our six engines the formula I = 0.0000053 PR gives, with the 
limitation for the long-stroke engines that the length shall not be less 
than the diameter, the following: 

Engine No . . 1 2 3 4 5 6 

Length of journal 4.39 4.39 16.48 12.99 30.80 21.52 

Pressure per square inch 

on journal 196 173 128 155 102 171 

Crank-shafts with Center-crank and Double-crank Arms. — In 

center-crank engines, one of the crank-arms, and its adjoining journal, 
called the after journal, usually transmit the power of the engine to the 
work to be done, and the journal resists both twisting and bending mo- 
ments, while the other journal is subjected to bending moment only. 
For the after crank-journal the diameter should be calculated the same 
as for an overhung crank, using the formula for combined bending and 



1018 



THE STEAM-ENGINE. 



twisting moment, T\ = B + ^B 2 + T 2 , in which Ti is the equivalent 
twisting moment, B the bending moment, and T the twis ting mo ment. 

This value of T\ is to be used in the formula diameter = "^5.1 T/S. The 
bending moment is taken as the maximum load on piston multiplied by I 
one-fourth of the length of the crank-shaft between middle points of the 
two journal bearings, if the center is midway between the bearings, or I 
by one-half the distance measured parallel to the shaft from the middle J 
of the crank-pin to the middle of the after bearing. This supposes the J 
crank-shaft to be a beam loaded at its middle and supported at the ends, i 
but Whitham would make the bending moment only one-half of this, 
considering the shaft to be a beam secured or fixed at the ends, with a 
point of contraflexure one-fourth of the length from the end. The first 
supposition is the safer, but since the bending moment will in any case 
be much less than the twisting moment, the resulting diameter will be \ 
but little greater than if Whitham's supposition is used. For the for- i 
ward journ al, which is subjected to bending moment only, diameter of ' 

shaft = *\/l0.2 BIS, in which B is the maximum bending moment and 
S the safe shearing strength of the metal per square inch. 

For our six engines, assuming them to be center-crank engines, and 
considering the crank-shaft to be a beam supported at the ends and 
loaded in the middle, and assuming lengths between centers of shaft 
bearings as given below, we have: 





1 


2 


3 


4 


5 


6 






Length of shaft, 














assumed, in., L. . 


20 


24 


48 


60 


76 


96 


Max. press, on 














crank-pin, P 


7,854 


7,854 


70,686 


70,686 


196,350 


196,350 


Max. bending mo- 














ment, 5 = V4PL, 


39,270 


49,637 


848,232 


1,060,290 


3,729,750 


4,712,400 


Twisting mom., T 


47,124 


94,248 


1,060,290 


2,120,580 


4,712,400 


9,424,800 


Equiv. twist, mom. 














B + V52 + T 2 ... 


101,000 


156,000 


2,208,000 


3,430,000 


9,740,000 


15,240,000 


Diam. of after jour. 














A iV 5 - 1 Tl 

V 800 ° "" 


3.98 


4.60 


11.15 


13.00 


18.25 


21.20 


Diam. of forw. jour. , 














t 7l0.2 B 

dl ~ V"8000~--" 


3.68 


3.99 


10.28 


11.16 


16.82 


18.18 



The lengths of the journals would be calculated in the same manner as 
in the case of overhung cranks, by the formula I = 0.000053 fPR, in 
which P is the resultant of the mean pressure due to pressure of steam on 
the piston, and the load of the fly-wheel, shaft, etc., on each of the two 
bearings. Unless the pressures are equally divided between the two 
bearings, the calculated lengths of the two will be different; but it is 
usually customary to make them both of the same length, and in no case 
to make the length less than the diameter. The diameters also are usually 
made alike for the two journals, using the largest diameter found by 
calculation. 

The crank-pin for a center crank should be of the same length as for 
an overhung crank, since the length is determined from considerations 
of heating, and not of strength. The diameter also will usually be the 
same, since it is made great enough to make the pressure per square inch 
on the projected area (product of length by diameter) small enough to 
allow of free lubrication, and the diameter so calculated will be greater 
than is required for strength. 

Crank-shaft with Two Cranks coupled at 90°. — If the whole 
power of the engine is transmitted through the after journal of the after 



DIMENSIONS OF PARTS OF ENGINES. 1019 



crank-shaft, the greatest twisting moment is equal to 1.414 times the 
maximum twisting moment due to the pressure on one of the crank-pins. 
If T = the maximum twisting moment produced by the steam-pressure 
on one of the pistons, then T\, the maximum twisting moment on the 
after part of the crank-shaft, and on the line-shaft produced, when each 
crank makes an angle of 45° with the center line of the engine, is 1.414 T. 
Substituting this va lue in the formula for diam eter to resist sim ple 

torsion, viz., d = -^5.1 T + S, we have d = ^5.1 X 1.414 T +■ S, or 
d = 1.932 \j T jS, in which T is the maximum twisting moment pro- 
duced by one of the pistons, d = diameter in inches, and S = safe 
working shearing strength of the material. For the forward journal of 
the after crank, and the after journal of the forward crank, the torsional 
moment is that due to the pressure of steam on the forward piston only, 
and for the forward journal of the forward crank, if none of the power 
of the engine is transmitted through it, the torsional moment is zero, and 
its diameter is to be calculated for bending moment only. 

For Combined Torsion and Flexure. — Let B t = bending moment 
on either journal of the forward crank due to maximum pressure on 
forward piston, B 2 = bending moment on either journal of the after crank 
due to maximum pressure on after piston, T\ = maximum twisting 
moment on after journal of forward crank, and Ti = maximum twisting 
moment on after journal of after crank, due to pressure on the after 
piston. 

Then equivale nt twisting moment on after journal of forward crank =?= 
B\ + ^Bi 2 + TV. 

On forward journal of after crank = B<i 4- v / .g 2 2 + TV. 

On after journal of after crank = Bi + V# 2 2 + (Ti + T 2 ) 2 . 

These values of equivalent twisting moment are to be used in the 

formula for diameter of journals d = \/5.1 T IS. For the forward 

journal of the forward crank-shaft d = -^10.2 Bi IS. 

It is customary to make the two journals of the forward crank of one 
diameter, viz., that calculated for the after journal. 

For a Three-cylinder Engine with cranks at 120°, the greatest 
twisting moment on the after part of the shaft, if the maximum pressures 
on the three pistons are equal, is equal to twice the maximum pressure on 
any one piston, and it takes place when two of the cranks make angles 
Of 30° with the center line, the third crank being: at right angles to it. 
t(For demonstration, see Whitham's "Steam-engine Design," p. 252.) 
?For combined torsion and flexure the same method as above given for 
[two crank engines is adooted for the first two cranks; and for the 
third, or after crank, if all the power of the three cylinders is transmitted 
through it, we have the equivalent twisting moment [on the forward 

jo urnal = Bz 4- Vff 3 2 T (Ti + T^, and on the after journal = B s + 

VBz\+ (7 7 i+ T 2 + T 3 ) 2 , B 3 and T s being respectively the bending and 
twisting moments due to the pressure on the third piston. 

Crank-shafts for Triple-expansion Marine Engines, according to 
an article in The Engineer, April 25, 1890, should be made larger than the 
formulae would call for, in order to provide for the stresses due to the 
racing of the propeller in a sea-way, which can scarcely be calculated, 
A kind of unwritten law has sprung up for fixing the size of a crank- 
shaft, according to which the diameter of the shaft is made about 0.45 D, 
where D is the diameter of the high-pressure cvlinder. This is for solid 
shafts. When the speeds are high, as in war-ships, and the stroke short, 
the formula becomes 0.4 D, even for hollow shafts. 

The Valve-stem or Valve-rod. — The valve-rod should be designed 
to move the valve under the most unfavorable conditions, which are when 
the stem acts bv thrusting, as a long column, when the valve is unbalanced 
(a balanced valve mav become unbalanced bv thp joint lpaking) and when 
it is imperfectiv lubricated. The load on the valve is the product of the 
area into the greatest unbalanced pressure upon it per square inch, and 
the coefficient of friction may be as high as 20%. The product of this 
coefficient and the load is the force necessary to move the valve, which 



1020 THE STEAM-ENGINE. 

equals the maximum thrust on the valve-rod. From this force the diam- 
eter of the valve-rod may be calculated by the usual formula for 
co lumns . An empirical formula given by Seaton is: Diam. of rod= d = 
"vWp/F, in which I = length, and b = breadth of valve, in inches; 
p = maximum absolute pressure on the valve in lbs. per sq. in., and 
F a coefficient whose values are, for iron: long rod 10,000, short 12 000- 
for steel: long rod 12,000, short 14,500. 

Whitham gives the short empirical rule: Diam. of valve-rod = 3/3fl| 
diam. of cyl. = 1/3 diam. of piston-rod. 

Size of Slot-link. (Seaton.) — Let D be the diam. of the valve-rod 

D^^lbp h- 12,000; 

then Diameter of block-pin when overhung = D. 

secured at both ends = 0.75 X Z>. 

eccentric-rod pins =0.7 X D. 

suspension-rod pins = 0.55X D. 

" pin when overhung =0.75XD. 

Breadth of link = . 8 to . 9 X D. 

Length of block = 1 . 8 to 1 . 6 X D. 

Thickness of bars of link at middle = . 7 X D. 

If a single suspension rod of round section, its diameter =0.7 X D. 
If two suspension rods of round section, their diameter = 0.55 X D. 

Size of Double-bar Links. — When the distance between centers of 
eccentric pins = 6 to 8 times throw of eccentrics (throw = eccentricity = 
half-travel of valve at full gear) D as before: 

Depth of bars = 1 . 25 X D + 3/ 4 in. 

Thickness of bars = . 5 X D + 1/4 in. 

Length of sliding-block = 2.5 to 3 X D. 

Diameter of eccentric-rod pins = . 8 X D + 1/4 in. 
center of sliding-block = 1.3 X D. 

When the distance between eccentric-rod pins= 5 to 51/2 times throw 
of eccentrics: 

Depth of bars = 1 . 25 XD + 1/2 in. 

Thickness of bars = . 5 X D + 1/4 in. 

Length of sliding-block = 2.5 to 3 X D. 

Diameter of eccentric-rod pins = 0.75 X D. 

Diameter of eccentric bolts (top end) at bottom of thread = . 42 X D 
when of iron, and 0.38 X D when of steel. 

The Eccentric. — Diam. of eccentric-sheave = 2.4 X throw of eccen- 
tric + 1 . 2 X diam. of shaft. D as before 

Breadth of the sheave at the shaft ...... = 1 . 15 X D + . 65 in. 

Breadth of the sheave at the strap = D + . 6 in. 

Thickness of metal around the shaft .... =0.7 X D + . 5 in. 

Thickness of metal at circumference .... ^=0.6 X D + . 4 in. 

Breadth of key. =0.7 XD+0.5in. 

Thickness of key = . 25 X D + . 5 in. 

Diameter of bolts connecting parts of strap =0.6 XD+0.1in. 

Thickness of Eccentric-strap. 

When of bronze or malleable cast iron: 

Thickness of eccentric-strap at the middle =0.4XZ>+0.6in. 

Thickness of eccentric-strap at the sides =0.3XD+0.5in. 

When of wrought iron or cast steel: 
Thickness of eccentric-strap at the middle. ... = . 4 X D + . 5 in. 
Thickness of eccentric-strap at the sides = . 27 X D + . 4 in. 

The Eccentric-rod. — The diameter of the eccentric-rod in the body 
and at the eccentric end may be calculated in the same way as that of the 
connecting-rod, the length being taken from center of strap to center of 
pin. Diameter at the link end = 0.8 D + 0.2 in. 

This is for wrought iron; no reduction in size should be made for steel. 

Eccentric-rods are often made of rectangular section. 

Reversing-gear should be so designed as to have more than sufficient 
strength to withstand the strain of both the valves and their gear at the 



DIMENSIONS OF PARTS OF ENGINES. 1021 

same time under the most unfavorable circumstances; it will then have 
|the stiffness requisite for good working. 

Assuming the work done in reversing the link-motion, W, to be only 
that due to overcoming the friction of the valves themselves through their 
Whole travel, then, if T be the travel of valves in inches, for a compound 
engine 

61, and p t being length, breadth, and maximum steam-pressure on 
valve of the second cylinder; and for an expansive engine 



W = 2X 



&(**"*)■■«§> «*>**>■ 



To provide for the friction of link-motion, eccentrics, and other gear, 
and for abnormal conditions of the same, take the work at one and a half 
times the above amount. 

To find the strain at any part of the gear having motion when reversing, 
divide the work so found by the space moved through by that part in 
feet; the quotient is the strain in pounds; and the size may be found from 
:the ordinary rules of construction for any of the parts of the gear. (Sea- 
ton.) 

Current Practice in Engine Proportions, 1897. (Compare pages 996 
to 1020.) — A paper with this title by Prof. John H. Barr, in Trans. 
A. S. M. E., xviii, 737, gives the results of an examination of the propor- 
tions of parts of a great number of single-cylinder engines made by 
different builders. The engines classed as low speed (L. S.) are Corliss 
or other long-stroke engines usually making not more than 100 or 125 revs. 
per min. Those classed as high speed (H. S.) have a stroke generally of 
1 to H/2 diameters and a speed of 200 to 300 revs, per min. The results 
are expressed in formulas of rational form with empirical coefficients, 
and are here abridged as follows (dimensions in inches): 

Thickness of Shell, L. S. only. —t = CD + B; D = diam. of piston in 

. ; B = . 3 in. ; C varies from . 04 to . 06, mean = . 05. 

Flanges and Cylinder-heads.^ 1 to 1.5 X thickness of shell, mean 1.2. 

Cylinder-head Studs. — No studs less than 3/ 4 in. nor greater than 13/gin. 
diam. Least number, 8, for 10 in. diam. Average number = 0.7 D. 
Average diam. = D/40 + 1/2 in. 

Ports and Pipes. — a = area of port (or pipe) in sq. in.: A = area of 
piston, sq. in.; V = mean piston-speed, ft. per min.; a = AV /C, in which 
C = mean velocity of steam through the port or pipe in ft. per min. 

Ports, H. S. (same ports for steam as for exhaust). — C = 4500 to 
6500, mean 5500. For ordinary piston-speed of 600 ft. per min. a = 
KA; K = 0.09 to 0.13, mean 0.11. 

Steam-ports, L. S. — C = 5000 to 9000, mean 6800; K = 0.08 to 0.10, 
mean 0.09. 

Exhaust-ports, L. S. — C = 4000 to 7000, mean 5500; K = 0.10 to 0.125, 
mean 0.11. 

Steam-pipes, H. S. — C = 5800 to 7000, mean 6500. If d = diam. of 
pipe and D = diam. of piston, d = . 29 D to . 32 D, mean . 30 D. 

Steam-vipes, L. S. — C = 5000 to 8000, mean 6000; d = . 27 to . 35 Z>; 
mean 0.32 D. 

Exhaust-pipes, H. S. — C = 2500 to 5500, mean 4400; d = 0.33 to 
0.50 D, mean 0.37 D. 

Exhaust-vipes, L. S. — C = 2800 to 4700, mean 3800; d = 0.35 to 
. 45 D, mean . 40 D 

Face of Pistons. — F = face; D = diameter. F = CD. H. S.: C = 
0.30 to 0.60, mean 0.46. L. S.: C = 0.25 to 0.45, mean 0.32. 

Piston-rods. — - d = diam. of rod: D = diam. of piston; L = stroke, in.; 
d= C V DL . H s . c= 12 t0 175 mean 145 L g . c= 10 to 
0.13, mean 0.11. 

Connecting-rods. — H. S. (generallv 6 cranks loner, rectangular section): 
= breadth; h = height of section; Li = length of connecting-rod; 
D = diam. of piston; b = C ^DLi; C = 0.045 to 0.07. mean 0.057; 
h = Kb: K = 2.2 to 4, mean 2.7. L. S. (generallv 5 cranks long, cir- 
cular sections only): C = 0.082 to 0.105, mean 0.092. 



1022 THE STEAM-ENGINE. 



Cross-head Slides. — Maximum pressure in lbs. per sq. in. of shoe, due 
to the vertical component of the force on the connecting-rod. H. S.: 
10.5 to 38, mean 27. L. S.: 29 to 58, mean 40. 

Cross-head Pins. — I = length; d = diam.; projected area = a = dl = 
CA; A = area of piston; I = Kd. H. S.: C = 0.06 to 0.11, mean 0.08; 
K = 1 to 2, mean 1.25. L. S.: C = 0.054to0.10, mean0.07; K = 1 to 
1.5, mean 1.3. 

Crank-pin. — H.P. = horse-power of engine; L= length of stroke; 

1 = length of pin; I = C X H.P. /L+ B; d = diam. of pin; A = area of 
piston; dl = KA. H. S.: C = 0.13 to 0.46, mean 0.30; B = 2.5 in.; 
K = 0.17 to 0.44, mean 0.24. L. S.: C = 0.4 to 0.8, mean 0.6; B = 

2 in.; K = 0.065 to 0.115, mean 0.09. 

Crank-shaft Main Journal. — d= C a^H.P.-j- TV; d= diam.; Z = length; 
N = revs, per min.; projected area = MA; A = area of piston. H. S.: 
C — 6.5 to 8.5, mean 7.3; l = Kd; i£ = 2 to 3, mean 2.2; M = 0.37 to 
0.70, mean 0.46. L. S.: C = 6 to 8, mean 6.8; K= 1.7 to 2.1, mean 
1.9; M = 0.46 to 0.64, mean 0.56. 

Piston-speed. — H. S.: 530 to 660, mean 600; L. S.: 500 to 850, mean 
600. 

Weight of Reciprocating Parts (piston, piston-rod, cross-head, and one- 
half of connecting-rod). — W = CD 2 h- LN 2 ; D = diam. of piston; 
L = length of stroke, in.; N = revs, per min. H. S. only: C = 1,200,000 
to 2,300,000, mean 1,860,000. 

Belt-surface per I.H.P. — S = C X H.P. + B; *S = product of width of 
belt in feet by velocity of belt in ft. per min. H. S.: C = 21 to 40, mean 
28; 5 = 1800. L. S.; S = C X H.P., C = 30 to 42, mean = 35. 

Fly-wheel (H. S. only). — Weight of rim in lbs.: W = C x XH.P.r 
Z>i 2 A 3 ; Di = diam. of wheel in in.; C = 65 X 10 10 to 2 X 10 12 mean = 
12 X 10", or 1,200,000,000,000. 

Weight of Engine per I.H.P. in lbs., including fly-wheel. — W = 
C X H.P. H. S.: C= 100 to 135, mean 115. L. S.: C = 135 to 240, 
mean 175. 

Current Practice in Steam-engine Design, 1909. (Ole N. Trooien, 
Bull. Univ'y of Wis., No. 252; Am. Mach., April 22, 1909.) — Practice in 
proportioning standard steam-engine parts has settled down to certain 
definite values, which have by long usage been found to give satisfactory 
results. These values can readily be expressed in formulas showing the 
relation between the more important factors entering the problem of 
design. 

These formulas may be considered as partly rational and partly em- 
pirical; rational in the sense that the variables enter in the same manner 
as in a strict analysis, and empirical in the sense that the constants, 
instead of being obtained from assumed working strength, bearing 
pressures, etc., are derived from actual practice and include elements 
whose values are not accurately known but which have been found safe 
and economical. 

The following symbols of notation are used in the formulas given: 

D = diameter of piston. A = area of piston. L = length of stroke. 
p = unit steam pressure, taken as 125 lbs. per sq. in. above exhaUst as 
a standard pressure. H.P. = rated horse-power. N = revs, per min. 
C and K, constants, and d = diam. and Z=length of unit under consider- 
ation. All dimensions in inches. 

_ The commercial point of cut-off is taken at 1/4 of the stroke. H. S., 
high-speed engines. L. S., low-speed, or long-stroke engines. 

Piston Eod.—d = C^ r DL. H. S.: C = 0.15 (min., 0.125; max., 
0.187); L. S.: C - 0.114 (min., 0.1; max., 0.156). 

Cylinder. — Thickness of wall in ins. = CD 4- 0.28. C =0.054 
(min., 0.035; max., 0.072). Clearance volume 5 to 11% for H. S. engines, 
and from 2 to 5% for Corliss en sines. 

Stud Bolts. — Number = . 72 D for H. S. (0 . 65 D for Corliss.) Diam. 
in ins. = 0.04 D + 0.375. 

Ratio (C) of Stroke to Cylinder Diameter (L ID). — For TV > 900, 
C = 1.07 (min., 0.82: max., 1.55): for N = 110 to 200, C = 136 (min.. 
1.03; max., 1.88): for AT < 110 (Corliss engines), C = (L - 8) ID = 1.63 
(min., 1.15; max.. 2.4). 

Piston. — Width of face in ins. = CD + 1. Mean value of C = 0.32 



DIMENSIONS OF PARTS OF ENGINES. 1023 

! or H. S. (0.26 for Corliss). Thickness of shell = thickness of cylinder 
vail X 0.6 (0.7 for Corliss). 

Piston Speeds. — H. S., 605 ft. per min. (min. 320; max., 920); Corliss, 
>92 ft. per min. (min., 400; max., 800). 

Cross-head. — Area of shoes in sq. ins. =0.53 A (min., 0.37; max., 
).72). 

Cross-head Pin. — Diameter = 0.25 D (min., 0.17; max., 0.28). 
Length for H. S. = diam. X 1.25 (min., 1; max., 1.5); for Corliss == 
liam. X 1.43 (min., 1; max., 1.9). 

Connecting-rods. — Breadth for H. S. =0.073 ^L C D (min., 0.55; max., 
).094). Height = breadth X 2. 28 (min., 1.85; max., 3). For L. S., diam. 
)f circular rod = . 092 ^L C D (min., 0.081; max., 0.104). L c = length 
center to center of bearings. 

Crank-pin. — Diam. for H. S. center-crank engines = 0. 4 D (min., 

28; max., 0.526). Diam. for side-crank Corliss = 0.27 D (min., 
).21; max., 0.32). Length for H. S. = diam. X 0.87 (min., 0.66; 
max., 1.25). Length for Corliss = diam. X 1.14 (min., 1; max., 1.3). 

Main Journals of Crank-shaft. — For H. S. center-crank engines, diam. 
= 6.6 yTLP ./A (min., 5.4; max., 8.2). For Corliss, diameter = 7.2 
[^/(H. P./ A) -0.3] (min., 6.4; max., 8). 

Fly-xoheels. — Total weight in pounds for H. S. up to 175 H.P. 
= 1,300,000,000,000 H.P. /Di 2 A 3 , where Di = diam. of wheel in ins. 
(min., 660,000,000,000; max., 2,800,000,000,000). For larger H. S. 
engines, weight = (C X H.P. /Z>i 2 A 3 ) + 1000, where C = 720,000,000,000 
(min., 330,000,000,000; max., 1,140,000,000,000). For Corliss engines, 
'weight = (C X H.P. /DJN^-K, where C = 890,000,000,000 (min., 625,- 
000,000,000; max., 1,330,000,000,000), and #=4000 (min., 2,800; max., 
16000). Diam. in ins.= 4.4X length of stroke. 

Belt Surface per I.H.P. ■ — Square feet of belt surface per minute (S) 
ifor H. S. = H.P. x 26.5 (min., 10; max., 55). For Corliss engines, 
\S = 1000 4- (21 X H.P.) (min., 18.2; max., 35). 

; Velocity of Wheel Rim. — For H. S. 70 ft. per sec. (min., 48; max., 
70) ; for Corliss, 68 ft. per sec. (min., 40; max., 68). 

Weight of Reciprocating Parts (Piston + piston rod + crosshead + 1/2 
!connecting-rod). — Weight in lbs. W = (D 2 1 LA 2 ) X 2,000,000 (min., 
1,370,000; max., 3,400,000). Balance weight opposite crank-pin = 
0.75 W. 

Weight of engine per I.H.P. — Lbs. per I.H.P. for belt-connected H. S. 
engines = H.P. X 82 (min., 52; max., 120). Do., for Corliss = H.P. 
X 132 (min., 102; max., 164). 

Shafts and Bearings of Engines. (James Christie, Proc. 
Engrs. Club of Phila., 1898.) — The dimensions are determined by two 
independent considerations: 1. Sufficient size to prevent excessive 
deflection or torsional yield. 2. To provide sufficient wearing surface; 
to prevent excessive wear of journals. Usually, when the first condi- 
tion is preserved, the other is provided for. When the bearings are 
flexible, — and excessive deflection within the limit of ordinary safety 
affects nothins? external to the bearings, — considerable deflection can be 
tolerated. When bearings are rigid, or defection may derange external 
mechanism, — for example, an overhung crank, — then the deflection 
must be more restricted. The effect of deflection is to concentrate 
pressure on the ends of journals, rendering the apparent bearing surface 
inefficient. 

In direct-driven electric generators a deflection of 0.01 in. per foot of 
lensrth has caused much trouble from hot bearings. I have proportioned 
such shafts so that the deflection will not exceed one-half this extent. 

Tn some shafts, especially those having an oscillating movement, 
torsional elasticity is a prime' consideration, and the limits can be known 
onlv by experience. Reuleauv says: "Limit the torsional yield to 0.1 
degree per foot of length." This in some cases can be readily tolerated; 
in others, it has proved excessive. Thave adopted the following as a gen- 
eral sruide: Permissible twist per foot of length =0.10 degree for easy 
service, without severe fluctuation of load: 0.075 degree for fluctuating 
loads suddenly applied: 0.050 degree for loads suddenly reversed. 

Sufficiency of wearing surface and the limitation of pressure per unit 



1024 THE STEAM-ENGINE. 

of surface are determined by several conditions: 1. Speed of movement, 
2. Character of material. 3. Permissible wear of journals or bearings. 
4. Constancy of pressure in one direction. 5. Alternation of the direction 
of pressure. 

Taking the product of pressure per sq. in. of surface in lbs., and speed 
of movement in ft. per min., we obtain a quantity, which we can term 
the permissible foot-pounds per minute for each sq. in. of wearing sunaee. 
Tnis product varies in good practice under various conditions lrom: 
50,000 to 500,000 ft.-lbs. per mm. For instance, good practice, in later 
years, has largely increased the. area of crosshead slide surfaces, For 
crossneads having maximum speed of 1000 feet per minute, the pressure 
per inch of wearing surface should not exceed 50 pounds, giving 50,000 
ft.-lbs. per min.; whereas crank-pins of the requisite grade of steel, with 
gOod lining metal in the boxes and efficient lubrication, will endure 
200,000 ft.-lbs. per min. satisfactorily, and more than double this when 
speeds are very high and the pressure intermittent. On main shaits, 
with pressures constant in one direction, it is advisable not to exceed 
50,000 ft.-lbs. per min. for heavily loaded shafts at low velocity. This 
may be increased to 100,000 for lighter loads and higher velocities. It 
can be inferred, therefore, that the product of speed and pressure cannot 
be used, in any comprehensive way, as a rational basis for proportioning 
wearing surfaces. The pressure per unit of surface must be reduced as the 
speed is increased, but not in a constant ratio. A good example of 
journals severely tested are the recent 110,000-pound freight cars, which 
bear a pressure of 400 lbs. per sq. in. of journal bearing, and at a speed 
of ten miles per hour make about 60,000 foot-pounds per minute. 

Calculating the Dimensions of Bearings. (F. E. Cardullo, Mach'y, 
Feb., 1907.) — The durability of the lubricating film is affected in great 
measure by the character of the load that the bearing carries. When the 
load is unvarying in amount and direction, as in the case of a shaft carry- 
ing a heavy bandwheel, the film is easily ruptured. In those cases where 
the pressure is variable in amount and direction, as in railway journals 
and crank-pins, the film is much more durable. When the journal only 
rotates through a small arc, as with the wrist-pin of a steam-engine, the 
circumstances are most favorable. It has been found that when all other 
circumstances are exactly similar, a car journal will stand about twice 
the unit pressure that a fly-wheel journal will. A crank-pin, since the 
load completely reverses every revolution, will stand three times, and a 
wrist-pin will stand four times the unit pressure that the fly-wheel journal 
will. 

The amount of pressure that commercial oils will endure at low speeds 
without breaking down varies from 500 to 1000 lbs. per sq. in., where the 
load is steady. It is not safe, however, to load a bearing to this extent, 
since it is only under favorable circumstances that the film will stand this 
pressure without rupturing. On this account, journal bearings should 
not be required to stand more than two-thirds of this pressure at slow 
speeds, and the pressure should be reduced when the speed increases. 
The approximate unit pressure which a bearing will endure without 
seizing is p = PK ■*• (DN + K) (1). p = allowable pressure in lbs. per 
sq. in. of projected area, D = diam. of the bearing in ins., N = revs. 
per min., and P and K depend upon the kind of oil, manner of lubrica- 
tion, etc. 

P is the maximum safe unit pressure for the given circumstances, at a 
very slow speed. In ordinary cases, its value is 200 for collar thrust 
bearings, 400 for shaft bearings, 800 for car journals, 1200 for crank-pins, 
and 1600 for wrist-pins. In exceptional circumstances, these values 
may be increased by as much as 50%, but only when the workmanship 
is of the best, the care the most skillful, the bearing readily accessible, 
and the oil of the best quality, and unusually viscous. In the great units 
of the Subway power plant in New York, the value of P for the crank- 
pins is 2000. 

The factor K depends upon the method of oiling, the rapidity of cool- 
ing, and the care which the journal is likely to get. It will have about 
the following values: Ordinary work, drop-feed lubrication, 700; first- 
class care, drop-feed lubrication, 1000; force-feed lubrication or ring- 
oiling, 1200 to 1500; extreme limit for perfect lubrication and air-cooled 
bearings, 2000. The value 2000 is seldom used, except in locomotive 



DIMENSIONS OF PARTS OF ENGINES. 1025 

Lork where the rapid circulation of the air cools the journals. Higher 
Ulues than this may only be used in the case of water-cooled bearings. 
( In case the bearing is some form of a sliding shoe, the quantity 240 V 
should be substituted for the quantity DN, V being the velocity of rubbing 
n feet per second. There are a few cases where a unit pressure sufficient 
;o break down the oil film is allowable, such as the pins of punching and 
shearing machines, pivots of swing bridges, etc. 

In general, the diameter of a shaft or pin is fixed from considerations of 
-strength or stiffness. Having obtained the proper diameter, we must 
next make the bearing long enough so that the unit pressure shall not 
exceed the required value. This length may be found by means of the 

nation: i - lW + PKi X& + *0> (2) 

where L is the length of the bearing in ins., W the load upon it in lbs., 
and P, K, N, and D are as before. . . , „ 

A bearing may give poor satisfaction because it is too long, as well as 
because it is too short. Almost every bearing is in the condition of a 
loaded beam, and therefore it has some deflection. 

Shafts and crank-pins must not be made so long that they will allow 
the load to concentrate at any point. A good rule for the length is to 
make the ratio of length to diameter about equal to lfgyN. This 
quantity may be diminished by from 10 to 20% in the case of crank-pins 
and increased in the same proportion in the case of shaft bearings, but 
it is not wise to depart too far from it. In the case of an engine making 
100 r p.m., the bearings would be by this rule from 11/4 to IV2 diams. in 
length. In the case of a motor running at 1000 r.p.m., the bearings 
would be about 4 diams. long. 

The diameter of a shaft or pin must be such that it will be strong and 
stiff enough to do its work properly. In order to design it for strength 
and stiffness, it is first necessary to know its length. This may be assumed 
tentatively from the equation _ 

L = 20 W ^SN + PK (3) 

The diameter may then be found by any of the standard equations for 
the strength of shafts or pins given in the different works on machine 
design. [See The Strength of the Crank-pin, page 1007.] The length is 
then recomputed from formula No. 2, taking this new value if it does 
not differ materially from the one first assumed. If it does, and espe- 
cially if it is greater than the assumed length, take the mean value of the 
assumed and computed lengths, and try again. _ .... 

Example. — We will take the case of the crank-pin of an engine with a 
20-in cylinder, running at 80 r.p.m., and having a maximum unbalanced 
steam pressure of 100 lbs. per sq. in. The total steam load on the piston 
is 31,400 pounds. P is taken at 1200, and K as 1000. We will therefore 
obtain for our trial length: 

L = (20X 31,400 X v'io)-*- (1200X1000) =4. 7, or say 43/ 4 ins. 
In order that the deflection of the pin shall not be sufficient to destroy 

the lubricating film we have 

Z) = 0.09 \JWL Z , 

which limits the deflection to . 003 in. This gives D = 3 . 85 or say 37/ 8 
ins. With this diameter, formula No. 2 gives L = 8.9, say 9 ins. _ 

The mean of this value and the one obtained before is about 7 ins. 
Substituting this in the equation for the diameter, we get 51/4 ins. Sub- 
stituting this new diameter in equation No. 2 we have L = 7.05, say 

Probably most good designers would prefer to take about half an inch 
off the length of this pin, and add it to the diameter, making it 53/ 4 X6 1/2 
inches, and this will bring the ratio of the length to the diameter nearer 

to 1/8 "^N 

Engine-frames or Bed-plates.— No definite rules for the design 
of engine-frames have been given by authors of works on the steam- 
engine The proportions are left to the designer who uses ' rule of 
thumb " or copies from existing engines. F. A. Halsey (Am. Mach., 



1026 THE STEAM-ENGINE. 

Feb. 14, 1895) has made a comparison of proportions of the frames of 
horizontal Corliss engines of several builders. The method of comparison 
is to compute from the measurements the number of square inches in the 
smallest cross-section of the frame, that is, immediately behind the 
pillow block, also to compute the total maximum pressure upon the piston, 
and to divide the latter quantity by the former. The result gives the 
number of pounds pressure upon the piston allowed for each square inch 
of metal in the frame. He finds that the number of lbs. per sq. in. of 
smallest section of frame ranges from 217 for a 10 X 30 in. engine up to 
575 for a 28 X 48 in. A 30 X 60 in. engine shows 350 lbs., and a 32-in. 
engine which has been running for many years shows 667 lbs. Generally 
the strains increase with the size of the engine, and more cross-section of 
metal is allowed with relatively long strokes than with short ones. 

From the above Mr. Halsey formulates the general rule that in engines 
of moderate speed, and having strokes up to 1 1/2 times the diameter of the 
cylinder, the load per square inch of smallest section should be for a 10-in. 
engine 300 lbs., which-figure should be increased for larger bores up to 500 
lbs. for a 30-in. cylinder of the same relative stroke. For high speeds or 
for longer strokes the load per square inch should be reduced. 

FLY-WHEELS. 

The function of a fly-wheel is to store up and to restore the periodical 
fluctuations of energy given to or taken from an engine or machine, and 
thus to keep approximately constant the velocity of rotation. Rankine 
AE 
2E Q 

steadiness, in which E is the mean actual energy, and AE the excess 
of energy received or of work performed, above the mean, during a 
given interval. The ratio of the periodical excess or deficiency of energy 
AE to the whole energy exerted in one period or revolution General 
Morin found to be from 1/6 to 1/4 for single-cylinder engines using expan- 
sion; the shorter the cut-off the higher the value. For a pair of engines 
with cranks coupled at 90° the value of the ratio is about 1/4, and for 
three engines with cranks at 120°, 1/12 of its value for single-cylinder 
engines. For tools working at intervals, such as punching, slotting and 
plate-cutting machines, coining-presses, etc., AE is nearly equal to the 
whole work performed at each operation. 

AE 

A fly-wheel reduces the coefficient — ^- to a certain fixed amount, being 

about 1/32 for ordinary machinery, and 1/50 or 1/6O for machinery for fine 
purposes. 

If m be the reciprocal of the intended value of the coefficient of fluc- 
tuation of speed, AE the fluctuation of energy, / the moment of inertia 

of the fly-wheel alone, and a its mean angular velocity, / = — ^ — As 

the rim of a fly-wheel is usually heavy in comparison with the arms, 
/ may be taken to equal Wr 2 , in which W = weight of rim in pounds, and 

tyiqAE tnoAE 
r the radius of the wheel; then W = . _ = -~ — , if v be the velocity 

of the rim in feet per second. The usual mean radius of the fly-wheel 
in steam-engines is from three to five times the length of the crank. The 
ordinary values of the product mg, the unit of time being the second, lie 
between 1000 and 2000 feet. (Abridged from Rankine, S. E., p. 62.) 
Thurston gives for engines with automatic valve-gear W = 250,000 

- m Jy 2 , in which A = area of piston in square inches, S = stroke in feet, 

j) = mean steam-pressure in lbs. per sq. in., R = revolutions' per minute, 
D = outside diameter of wheel in feet. Thurston also gives for ordinary 
forms of non-condensing engine with a ratio of expansion between 3 and 

5 ' W = 1227)2' in wnicn a ran £ es from 10,000,000 to 15,000,000, averaging 
12,000,000. For gas-engines, in which the charge is fired with everv 
revolution, the American Machinist gives this latter formula, with a 



FLY-WHEELS. 1027 

doubled, or 24,000,000. Presumably, if the charge is fired every other 
revolution, a should be again doubled. 

Ranirine ("Useful Rules and Tables," p. 247) gives W = 475,000 

• i , in which V is the variation of speed per cent of the mean speed. 

Thurston's first rule above given corresponds with this if we take V = 1.9. 

Hartnell (Proc. Inst. M. E., 1882, 427) says: The value of V, or the 
variation permissible in portable engines, should not exceed 3% with an 
ordinary load, and 4% when heavily loaded. In fixed engines, for ordi- 
nary purposes, V = 2V2 to 3%. For good governing or special purposes, 
such as cotton-spinning, the variation should not exceed 11/2 to 2%. 

F. M. Rites (Trans. A. S. M. E., xiv, 100) develops a new formula for 
C X I H P 
weight of rim, viz., W = ■ — R ' ' ' , and weight of rim per horse-power 

■= -557^, in which C varies from 10,000,000,000 to 20,000,000,000; also 

using the latter value of C, he obtains for the energy of the fly-wheel 
Mv 2 = _W_ (3.14) 2 D 2 fl 2 = CX H.P. (3.14) 2 D 2 R 2 = 850,000 H.P . F1 

2 "64.4 3600 ^£,2 x 64-4 x 360 R 

wheel energy per H.P. = 850,000 -4- R. 

The limit of variation of speed with such a weight of wheel from excess 
of power per fraction of revolution is less than 0.0023. 

The value of the constant C given by Mr. Rites was derived from 
practice of the Westinghouse single-acting engines used for electric- 
lighting. For double-acting engines in ordinary service a value of C — 
5,000,000,000 would probably be ample. 

From these formulae it appears that the weight of the fly-wheel for a 
given horse-power should vary inversely with the cube of the revolutions 
and the square of the diameter. 

J. B. Stanwood (Eng'g, June 12, 1891) says: Whenever 480 feet is the 
lowest piston-speed probable for an engine of a certain size, the fly-wheel 
weight for that speed approximates ciosely to the formula 

W = 700,000 d 2 s -h D 2 R 2 . 
W = weight in pounds, d = diameter of cylinder in inches, s = stroke 
in inches, D = diameter of wheel in feet, R = revolutions per minute, 
corresponding to 480 feet piston-speed. 

In a Ready Reference Book published by Mr. Stanwood, Cincinnati, 
1892, he gives the same formula, with coefficients as follows: For slide- 
valve engines, ordinary dutv, 350,000; same, electric lighting, 700.000; 
for automatic high-speed engines, 1.000,000; for Corliss engines, ordinary 
dutv 700,000, electric lighting 1,000.000. 

Thurston's formula above given, W = aAS ■*- R*D 2 with a = 12,000,000, 
when reduced to terms of d and s in inches, becomes W = 785,400 d 2 s -«- 

If we reduce it to terms of horse-power, we have I. H.P. = 2 ASPR ■*■ 
33,000, in which P = mean effective pressure. Taking this at 40 lbs., 
we obtain W = 5.000.000.000 I.H.P. h- RW 2 . If mean effective pressure 
- 30 lbs., then W = 6,666,000.000 I.H.P. -^ R S D 2 . 

Emil Theiss (Am. Moch., Sept. 7 and 14, 1893) gives the following 
values of d, the coefficient of steadiness, which is the reciprocal of what 
Rankine calls the coefficient of fluctuation: 
For engines operating — 

Hammering and crushing machinery d = 5 

Pumoing and shearing machinery d = 20 to 30 

Weaving and paper-making machinery d = 40 

Milling machinery ^=50 

Spinning machinery a = 50 to 100 

Ordinarv driving-engines (mounted on bed-plate), 

belt transmission d = 35 

Gear-wheel transmission d — 50 

Mr. Theiss's formula for weight of fly-wheel in pounds is W =t'X y 2 y^ n ' 

where d is the coefficient of steadiness, V the mean velocity of the fly- 
wheel rim in feet per second, n the number of revolutions per minute, 



1028 



THE STEAM-ENGINE. 



i = a coefficient obtained by graphical solution, the values of which for 
different conditions are given in the following table. In the lines under 
"cut-off," p means "compression to initial pressure," and O "no com- 
pression." 

Values of i. Single-cylinder Non-condensing Engines. 



Piston- 
speed, ft. 
per min. 


Cut-off, 1/6- 


Cut-off, 1/4. 


Cut-off, 1/3. 


Cut-off, l/ 2 . 


Comp. 
V 





Comp. 
V 


O 


Comp. 
V 


O 


Comp. 
V 





200 
400 
600 


272,690 
240,810 
194,670 
158,200 


218,580 
187,430 
145,400 
108,690 


242,010 
208,200 
168,590 
162,070 


209,170 
179,460 
136,460 
135,260 


220,760 
188,510 
165,210 


201,920 
170,040 
146,610 


193,340 
174,630 


182,840 
167,860 


800 





















Single-cylinder 


Condensing 


Engines. 






$-6 & 


Cut-off, i/ 8 . 


Cut-off, 1/6- 


Cut-off, 1/4. 


Cut-off, 1/3. 


Cut-off, 1/2. 


*u 


Comp. 
V 


O 


Comp. 
V 


O 


Comp. 
V 


O 


Comp. 
V 


O 


Comp. 
V 





200 

400 


265,560 
194,550 
148,780 


176,560 
117,870 
140,090 


234,160 
174,380 


173,660 
118,350 


204,210 
164,720 


167,140 
133,080 


189,600 
174,630 


161,830 
151,680 


172,690 


156,990 


600 

























Two-cylinder Engines, Cranks at 90°. 



Piston- 
speed, ft. 
per min . 


Cut-off, 1/6- 


Cut-off, 1/4. 


Cut-off, 1/3. 


Cut-off, 1/2. 


Comp. 
V 





Comp. 
V 





Comp. 
V 





Comp. 
V 





200 
400 
600 
800 


71,980 
70,160 
70,040 
70,040 


1 Mean 
f 60,140 


59,A2Q 
57,000 
57,480 
60,140 


1 Mean 
[ 54,340 


49,272 
49,150 
49,220 


1 Mean 
[ 50,000 


37,920 
35,000 


\ Mean 
f 36,950 



Three-cylinder Engines, Cranks at 120°. 



Piston- 


Cut-off, 1/6- 


Cut-off, 1/4. 


Cut-off, 1/3. 


Cut-off, l/ 2 . 


speed, ft. 
per min. 


Comp. 
V 





Comp. 
V 





Comp. 
V 





Comp. 

v - 





200 
800 


33,810 
30,190 


32,240 
31,570 


33,810 
35,140 


35,500 
33,810 


34,540 
36,470 


33,450 
32,850 


35,260 
33,810 


32,370 
32,370 



As a mean value of i for these engines we may use 33,810. 

Weight of Fly-wheels for Alternating-current Units. (J. Begtrup. 
Am. Mach., July 10, 1902.) — 

WD* + WJ>t - 14 -~ W . 



FLY-WHEELS. 1029 

in which W= weight of rim of fly-wheel in pounds, D = mean diameter 
of rim in feet, Wi = weight of armature in pounds, Di= mean diameter 
of armature in feet, H = rated horse-power of engine, U = a factor of 
steadiness, N = number of revolutions per minute, V = maximum 
instantaneous displacement in degrees, not to exceed 5 degrees divided 
by the number of poles on the generator, according to the rule of the 
General Electric Company. 

For simple horizontal engines, length of connecting-rod = 5 cranks, 
U = 90; (ditto, no account being taken of angularity of connecting-red, 
U = 64); cross-compound horizontal engines, connecting-rod = 5 cranks. 
U = 51; ditto, vertical engines, heavy reciprocating parts, unbalanced, 
U = 78; vertical compound engines, cranks 180 degrees apart, recipro- 
cating parts balanced, U = 60. 

The small periodical variation in velocity (not angular displacement) 
can be determined from the following formula: 

p = 387,700,000 HZ 



N*(WD*+ WiDi 2 )' 
in winch H = rated horse-power, Z = a factor of steadiness, N = revs, 
per min., D = mean diameter of fly-wheel rim in feet, W = weight of fly- 
wheel rim in pounds, Di = mean diameter of armature or field in feet, 
Wi = weight of armature, F = variation in per cent of mean speed. 

For simple engines and tandem compounds, Z = 16; for horizontal 
cross-compounds, Z = 8.5; for vertical cross-compounds, heavy recip- 
rocating parts, Z = 12.5; for vertical compounds, cranks opposite, 
weights balanced, Z = 14. F represents here the entire variation, 
between extremes — not variation from mean speed. It generally varies 
from 0.25% of mean speed to 0.75% — evidently a negligible quantity. 

A mathematical treatment of this subject will be found in a paper 
by J. L. Astrom, in Trans. A. S. M. E., 1901. 

Centrifugal Force in Fly-wheels. — Let W = weight of rim in 
pounds; R = mean radius of rim in feet; r = revolutions per minute, 
g —= 32.16; v = velocity of rim in feet per second = 2nRr -4- 60. 

W,i2 a Wn 2 Rr 2 

Centrifugal force of whole rim = F = ^- = '" =0. 000341 WRr 2 . 

gR 3600 g 
The resultant, acting at right angles to a diameter, of half of this force, 
tends to disrupt one half of the wheel from the other half, and is resisted 
by the section of the rim at each end of the diameter. The resultant of 

2 
half the radial forces taken at right angles to the diameter is 1 -s- 1/21- — - 

of the sum of these forces; hence the total force F is to be divided by 
2 X 2 X 1 .5708 = 6.2832 to obtain the tensile strain on the cross-section 
of the rim, or, total strain on the cross-section = 5 = 0.00005427 WRr 2 . 
The weight W\ of a rim of cast iron 1 inch square in section is 2 nR x 
3.125 = 19.635 72 pounds, whence strain per square inch of sectional 
area of rim = Si = 0.0010656 # 2 r 2 = 0.0002664 D 2 r 2 = 0.0000270 V 2 , 
in which D = diameter of wheel in feet, and V is velocitv of rim in feet 
per minute. 5i = . 0972 v 2 , if v is taken in feet per second. 
For wrought iron: 

Si = 0.0011366 R 2 r* = 0.0002842 D 2 r 2 = 0.0000288 V 2 . 
For steel: 

Si = 0.0011593 R 2 r 2 = 0.0002901 D 2 r 2 = 0.0000294 V 2 . 
For wood: 

Si = 0.0000888 R 2 r 2 = 0.0000222 D 2 r 2 = 0.00000225 V 2 . 

The specific gravity of the wood being taken at . 6 = 37 . 5 lbs. per cu. ft., 
or 1/12 the weight of cast iron. 

Example. — Required the strain per square inch in the rim of a cast- 
iron wheel 30 ft. diameter, 60 revolutions per minute. 

Answer. — 15 2 . X 60 2 X 0.0010656 = 863. 1 lbs. 

Required the strain per square inch in a cast-iron wheel-rim running a 
mile a minute. Answer. — 0.000027 X 5280 2 = 752.7 lbs. 

In cast-iron fly-wheel rims, on account of their thickness, there is . 
difficulty in securing soundness, and a tensile strength of 10.000 lbs. 
per sq. in, is as much as can be assumed with safety. Using a factor of 



1030 THE STEAM-ENGINE. 

safety of 10 gives a maximum allowable strain in the rim of 1000 lbs. 
per sq. in., which corresponds to a rim velocity of 6085 ft. per minute. 

For any given material, as cast iron, the strength to resist centrifugal 
force depends only on the velocity of the rim, and not upon its bulk or 
weight. 

Chas. E. Emery (Cass. May., 1892) says: It does not appear that fly- 
wheels of customary construction should be unsafe at the comparatively 
low speeds now in common use if proper materials are used in con- 
struction. The cause of rupture of fly-wheels that have failed is usually 
either the "running away" of the engine, such as may be caused by 
the breaking or slackness of a governor-belt, or incorrect design or de- 
fective materials of the fly-wheel. 

Chas. T. Porter (Trans. A. S. M. E., xiv, 808) states that no case of the 
bursting of a fly-wheel with a solid rim in a high-speed engine is known. 
He attributes the bursting of wheels built in segments to insufficient 
strength of the flanges and bolts by which the segments are held together. 
[The author, however, since the above was written, saw a solid rim fly- 
wheel of a high-speed engine which had burst, the cause being a large 
shrinkage hole at the junction between one of the arms and the rim. The 
wheel was about 6 ft. diam. Fortunately no one was injured by the 
accident.] (See also Thurston, "Manual of the Steam-engine," Part II, 
page 413.) 

Diameters of Fly-wheels for Various Speeds. — If 6000 feet per 
minute be the maximum velocity of rim allowable, then 6000 = nRD, 
in which R = revolutions per minute, and D= diameter of wheel in feet, 
whence D = 6000 + -*R = 1910 -h R. 

W. H. Boehm, Supt. of the Fly-wheel Dept. of the Fidelity and Casu- 
alty Co. (Eng. News, Oct. 2, 1902), sa.s: For a given material there is a 
definite speed at which disruption will occur, regardless of the amount 
of material used. This mathematical truth is expressed by the formula: 

7 = 1.6 VsJW, 

in which V is the velocity of the rim of the wheel in feet per second at 
which disruption will occur, W the weight of a cubic inch of the material 
used, and S the tensile strength of 1 square inch of the material. 

For cast-iron wheels made in one piece, assuming 20,000 lbs. per sq. 
in. as the strength of small test bars, and 10,000 lbs. per s q. in. in lar ge 
castings, and applying a factor of safety of 10, V = 1.6 Viooo/0.26 <= 
100 ft. per second for the safe speed. For cast steel of 60,000 lbs. per 
sq. in., V = 1.6 ^6000 + 0.28 = 233 ft. per second. This is for wheels 
made in one piece. If the wheel is made in halves, or sections, the 
efficiency of the rim joint must be taken into consideration. For belt 
wheels with flanged and bolted rim joints located between the arms, the 
joints average only one-fifth the strength of the rim, and no such joint 
can be designed having a strength greater than one-fourth the strength 
of the rim. If the rim is thick enough to allow the joint to be reinforced 
by steel links shrunk on, as in heavy balance wheels, one-third the 
strength of the rim may be secured in the joint; but this construction can 
not be applied to belt wheels having thin rims. 

For hard maple, having a tensile strength of 10,500 lbs. per sq. in., 
and weighing 0.0283 lb. per cu. in., we have, using a factor of safety of 
20, and remembering that the strength is reduced one-ha lf because the 
wheel is built up of segments, F = 1.6 V262.5 -*- 0.0283 = 154 ft. per 
second. The stress in a wheel varies as the square of the speed, and the 
factor of safety on speed is the square root of the factor of safety on 
strength. 

Mr. Boehm gives the following table of safe revolutions per minute 
of cast-iron wheels of different diameters. The flange joint is taken at 
. 25 of the strength of a wheel with no joint, the pad joint, that is a wheel 
made in six segments, with bolted flanges or pads on the arms, = 0.50, 
and the link joint = 0.60 of the strength of a solid rim. 



FLY-WHEELS. 



1031 



Safe Revolutions per Minute of Cast-Iron Fly-wheels. 





No 


Flange 


Pad 


Link 




No 


Flange 


Pad 


Link 




joint. 


joint. 


joint. 


joint. 




joint. 


joint. 


joint. 


joint. 


Diam. 










Diam. 










in 


R.P.M. 


R.P.M. 


R.P.M. 


R.P.M. 


in 


R.P.M. 


R.P.M. 


R.P.M. 


R.P.M. 


Ft. 










Ft. 










1 


1910 


955 


1350 


1480 


16 


120 


60 


84 


92 


2 


955 


478 


675 


740 


17 


112 


56 


79 


87 


3 


637 


318 


450 


493 


18 


106 


53 


75 


82 


A 


478 


239 


338 


370 


19 


100 


50 


71 


78 


5 


382 


191 


270 


296 


20 


95 


48 


68 


74 


6 


318 


159 


225 


247 


21 


91 


46 


65 


70 


7 


273 


136 


193 


212 


22 


87 


44 


62 


67 


8 


239 


119 


169 


185 


23 


84 


42 


59 


64 


9 


212 


106 


150 


164 


24 


80 


40 


56 


62 


10 


191 


96 


135 


148 


25 


76 


38 


54 


59 


11 


174 


87 


123 


135 


26 


74 


37 


52 


57 


12 


159 


80 


113 


124 


27 


71 


35 


50 


55 


13 


147 


73 


104 


114 


28 


68 


34 


48 


53 


14 


136 


68 


96 


106 


29 


66 


33 


47 


51 


15 


128 


64 


90 


99 


30 


64 


32 


45 


49 



The table is figured for a margin of safety on speed of approximately 
3, which is equivalent to a margin on stress developed, or factor of safety 
in the usual sense, of 9. (Am. Mach., Nov. 17, 1904.) 

Strains in the Rims of Fly-band Wheels Produced by Centrif- 
ugal Force. (James B. Stanwood, Trans. A. S. M. E., xiv, 251.) — 
Mr. Stanwood mentions one case of a fly-band wheel where the periphery 
velocity on a 17 ft. 9 in. wheel is over 7500 ft. per minute. 

In band-saw mills the blade of the saw is operated successfully over 
wheels 8 and 9 ft. in diameter, at a periphery velocity of 9000 to 10,000 ft. 
per minute. These wheels are of cast iron throughout, of heavy thick- 
ness, with a large number of arms. 

In shingle-machines and chipping-machines where cast-iron disk# 
from 2 to 5 ft. in diameter are employed, with knives inserted radially, 
the speed is frequently 10,000 to 11,000 ft. per minute at the periphery. 

If the rim of a fly-wheel alone be considered, the tensile strain in pounds 
per square inch of the rim section is T = F 2 /10 nearly, in which V = 
velocity in feet per second; but this strain is modified by the resistance 
of the arms, which prevent the uniform circumferential expansion of the 
rim, and induce a bending as well as a tensile strain. Mr. Stanwood 
discusses the strains in band-wheels due to transverse bending of a section 
of the rim between a pair of arms. 

When the arms are few in number, and of large cross-section, the rim 
will be strained transversely to a greater degree than with a greater num- 
ber of lighter arms. To illustrate the necessary rim thicknesses for vari- 
ous rim velocities, pulley diameters, number of arms, etc., the following 
table is given, based upon the formula 



t = 0.475 d -*- A 72 



Vf 2 10/ 



in which .£= thickness of rim in inches, d= diameter of pulley in inches, 
N = number of arms. V — velocity of rim in feet per second, and F= the 
greatest strain in pounds per square inch to which any fiber is subjected. 
The value of F is taken at 6000 lbs. per sq. in. 



1032 THE STEAM-ENGINE. 

Thickness of Rims in Solid Wheels. 



Diameter of 
Pulley in 
inches. 


Velocity of 

Rim in feet per 

second. 


Velocity of 

Rim in feet per 

minute. 


No. of Arms. 


Thickness in 
inches. 


24 
24 
48 
108 
108 


50 
88 
88 

184. 

184 


3,000 
5,280 
5,280 
11,040 
11,040 


6 
6 
6 
16 
36 


2/10 
15/32 
15/16 
21/2 
1/2 



If the limit of rim velocity for all wheels be assumed to be 88 ft. per 
second, equal to 1 mile per minute, F = 6000 lbs., the formula becomes 

t = . 475 d ■*■ . 67 iV 2 = . 7 d + A 2 . 

When wheels are made in halves or in sections, the bending strain may 
be such as to make t greater than that given above. Thus, when the 
joint comes half way between the arms, the bending action is similar to 
a beam supported simply at the ends, uniformly loaded, and t is 50% 

(F 1 \ 
greater. Then the formula becomes t = 0.712 dn- A 2 !-™ — —J, or for a 

fixed maximum rim velocity of 88 ft. per second and F = 6000 lbs., t = 
1.05 d -s- A 2 . In segmental wheels it is preferable to have the joints 
opposite the arms. Wheels in halves, if very thin rims are to be em- 
ployed, should have double arms along the line of separation. 

Attention should be given to the proportions of large receiving and 
tightening pulleys. The thickness of rim for a 48-in. wheel (shown in 
table) with a rim velocity of 88 ft. per second, is 17:6 in. Many wrecks 
have been caused by the failure of receiving or tightening pulleys whose 
rims have been too thin. Fly-wheels calculated for a given coefficient 
of steadiness are frequently lighter than the minimum safe weight. This 
is true especially of large wheels. A rough guide to the minimum weight 
of wheels can be deduced from our formula?. The arms, hub, lugs, etc., 
usually form from one-quarter to one-third the entire weight of the wheel. 
If b represents the face of a wheel in inches, the weight of the rim (con- 
sidered as a simple annular ring) will bew = . 82 dtb lbs. If the limit 
of speed is 88 ft. per second, then for solid wheels t = 0.7 d ■*- A 2 . For 
sectional wheels (joint between arms) t = 1 . 05 d -*- A 2 . Weight of rim 
for solid wheels, w = 0.57 d 2 b ■*- A 2 , in pounds. Weight of rim in sec- 
tional wheels with joints between arms, w = . 86 d 2 b ■*- A 2 , in pounds. 
Total weight of wheel: for solid wheel, W = 0.76 d 2 b h- A 72 to 0.86 d 2 b h- 
A 2 , in pounds. For segmental wheels with joint between arms, W = 
1 . 05 d 2 b -^ A 2 to 1 . 3 d 2 & -r- A 2 , in pounds. 

(This subject is further discussed by Mr. Stanwood, in vol. xv, and by 
Prof. Gaetano Lanza, in vol. xvi, Trans. A. S. M. E.) 

Arms of Fly-wheels and Pulleys. — Professor Torrey (Am. Mach., 
July 30, 1891) gives the following formula for arms of elliptical cross- 
section of cast-iron wheels: 

W = load in pounds acting on one arm: S = strain on belt in pounds 
per inch of width, taken at 56 for single and 112 for double belts; v = 
width of belt in inches; n = number of arms; L = length of arm in feet; 
b = breadth of arm at hub; d = depth of arm at hub, both in inches; 
W = Sv -^ n; b - WL -^ 30 cP. The breadth of the arm is its least 
dimension = minor axis of the ellipse, and the depth the major axis. 
This formula is based on a factor of safety of 10. 

In using the formula, first assume some depth for the arm, and calcu- 
late the required breadth to go with it. If it gives too round an arm, 
assume the depth a little greater, and repeat the calculation. A second 
trial will almost always give a good section. 

The size of the arms at the hub having been calculated, they may be 
somewhat reduced at the rim end. The actual amount cannot be cal- 
culated, as there are too many unknown quantities. However, the depth 



FLY-WHEELS. 1033 

and breadth can be reduced about one-third at the rim without danger, 
and this will give a well-shaped arm. 

Pulleys are often cast in halves, and bolted together. When this is 
done the greatest care should be taken to provide sufficient metal in the 
bolts. This is apt to be the very weakest point in such pulleys. The 
combined area of the bolts at each joint should be about 28/100 the 
cross-section of the pulley at that point. (Torrey.) 

Unwin gives d = 0.6337 ^/ BD/n for single belts; 

d = . 798 ^JBDIn for double belts ; 

D being the diameter of the pulley, and B the breadth of the rim, both in 
inches. These formulae are based on an elliptical section of arm in which 
b = 0.4 d or d = 2.5b on a width of belt = 4/ 5 the width of the pulley 
rim, a maximum driving force transmitted by the belt of 56 lbs. per inch 
of width for a single belt and 112 lbs. for a double belt, and a safe working 
stress of cast iron of 2250 lbs. per square inch. 

If in Torrey's formula we make & = . 4 d, it reduces to 

WL 



7 WL , 3 /WL 

6= Vi87T5 ;(Z= v/i2 



Example. — Given a pulley 10 feet diameter; 8 arms, each 4 feet long; 
face, 36 inches wide; belt, 30 inches: required the breadth and depth of the 
arm at the hub. According to Unwin, 

ci = 0.6337 ^JBD/n = 0.633^/36X120/8 = 5.16 for single belt, 6 = 2.06; 

d = 0.798 $BD/n = 0.798 ^36 X 120/8 = 6.50 for double belt, & = 2.60. 

According to Torrey, if we take the formula b = WL -■ 30 d 2 and 
assume d = 5 and 6.5 inches, respectively, for single and double belts, 
we obtain 6 = 1.08 and 1.33, respectively, or practically only one-half 
of the breadth according to Unwin, and, since transverse strength is pro- 
portional to breadth, an arm only one-half as strong. 

Torrey's formula is said to be based on a factor of safety of 10, but this 
factor can be only apparent and not real, since the assumption that the 
strain on each arm is equal to the strain on the belt divided by the num- 
ber of arms, is, to say the least, inaccurate. It would be more nearly 
correct to say that the strain of the belt is divided among half the number 
of arms. Unwin makes the same assumption in developing his formula, 
but says it is only in a rough sense true, and that a large factor of safety 
must be allowed. He therefore takes the low figure of 2250 lbs. per square 
inch for the safe working strength of cast iron. Unwin says that his 
equations agree well with practice. 

A Wooden-rim Fly-wheel, built in 1891 for a pair of Corliss engines 
at the Amoskeag Mfg. Co.'s mill, Manchester, N.H., is described by 
C. H. Manning in Trans. A. S. M. E., xiii, 618. It is 30 ft. diam. and 
108 in. face. The rim is 12 inches thick, and is 'built up of 44 courses of 
ash plank, 2, 3, and 4 inches thick, reduced about 1/2 inch in dressing, 
set edgewise, so as to break joints, and glued and bolted together. There 
are two hubs and two sets of arms, 12 in each, all of cast iron. The weights 
are as follows: 

Weight (calculated) of ash rim 31,855 lbs. 

Weight of 24 arms (foundry 45,020) 40,349 

Weight of 2 hubs (foundry 35,030) 31,394± " 

Counter-weights in 6 arms 664 " 

Total, excluding bolts and screws 104,262± " 

The wheel was tested at 76 revs, per min., being a surface speed of 
nearly 7200 feet per minute. 

Wooden Fly-wheel of the Willimantic Linen Co. (Illustrated in 
Power, March, 1893.) — Rim 28 ft. diam., 110 in. face. The rim is 
carried upon three sets of arms, one under the center of each belt, with 
12 arms in each set. 

The material of the rim is ordinary whitewood, 7/ 8 in. in thickness, cut 
into segments not exceeding 4 feet in length, and either 5 or 8 inches in 



1034 THE STEAM-ENGINE. 



width. These were assembled by building a complete circle 13 inches in 
width, first with the 8-inch inside and the 5-inch outside, and then beside 
it another circle with the widths reversed, so as to break joints. Each 
piece as it was added was brushed over with glue and nailed with three- 
inch wire nails to the pieces already in position. The nails pass through 
three and into the fourth thickness. At the end of each arm four 14- 
inch bolts secure the rim, the ends being covered by wooden plugs glued 
and driven into the face of the wheel. 

Wire-wound Fly-wheels for Extreme Speeds. (Eng'g A T ews, 
August 2, 1890.) — The power required to produce the Mannesmann 
tubes is very large, varying from 2000 to 10,000 H.P., according to the 
dimensions of the tube. Since this power is needed for only a short time 
(it takes only 30 to 45 seconds to convert a bar 10 to 12 ft. long and 4 in. 
in diameter into a tube), and then some time elapses before the next bar 
is ready, an engine of 1200 H.P. provided with a large fly-wheel for stor- 
ing the energy will supply power enough for one set of rolls. These 
fly-wheels are so large and run at such great speeds that the ordinary 
method of constructing them cannot be followed. A wheel at the Mannes- 
mann Works, made in Komotau, Hungary, in the usual manner, broke at 
a tangential velocity of 125 ft. per second. The fly-wheels designed to 
hold at more than double this speed consist of a cast-iron hub to which 
two steel disks, 20 ft. in diameter, are bolted; around the circumference 
of the wheel thus formed 70 tons of No. 5 wire are wound under a tension 
of 50 lbs. In the Mannesmann Works at Landore, Wales, such a wheel 
makes 240 revolutions a minute, corresponding to a tangential velocity 
of 15,080 ft. or 2.85 miles per minute. 

THE SLIDE-VALVE. 

Definitions. — Travel = total distance moved by the valve. 

Throw of the Eccentric = eccentricity of the eccentric = distance from 
the center of the shaft to the center of the eccentric disk = 1/2 the travel 
of the valve. 

Lap of the valve, also called outside lap or steam-lap = distance the 
outer or steam edge of the valve extends beyond or laps over the steam 
edge of the port when the valve is in its central position. 

Inside lap, or exhaust-lap = distance the inner or exhaust edge of the 
valve extends beyond or laps over the exhaust edge of the port when the 
valve is in its central position. The inside lap is sometimes made zero, 
or even negative, in which latter case the distance between the edge of 
the valve and the edge of the port is sometimes called exhaust clearance, 
or inside clearance. 

Lead of the valve = the distance the steam-port is opened when the 
engine is on its center and the piston is at the beginning of the stroke. 

Lead-angle = the angle between the position of the crank when the 
valve begins to be opened and its position when the piston is at the 
beginning of the stroke. 

The valve is said to have lead when the steam-port opens before the 
piston begins its stroke. If the piston begins its stroke before the admis- 
sion of steam begins, the valve is said to have negative lead, and its amount 
is the lap of the edge of the valve over the edge of the port at the instant 
when the piston stroke begins. 

Lap-angle = the angle through which the eccentric must be rotated to 
cause the steam edge to travel from its central position the distance of 
the lap. 

Angular advance of the eccentric == lap-angle 4- lead-angle. 

Linear advance = lap + lead. 

Effect of Lap, Lead, etc., upon the Steam Distribution. — Given 
valve-travel 2 3/ 4 in., lap 3/ 4 in., lead 1/16 in., exhaust-lap 1/8 in., required 
crank position for admission, cut-off, release and compression, and 
greatest port-opening. (Halsey on Slide-valve Gears.) Draw a circle 
of diameter fh = travel of valve. From O the center set off Oa = lap 
and ab = lead, erect perpendiculars Oe, ac, bd; then ec is the lap-angle 
and cd the lead-angle, measured as arcs. Set off fg = cd, the lead- 
angle; then Og is the position of the crank for steam admission. Set off 
2 ec + cd from h to i; then Oi is the crank-angle for cut-off, and fk 4- fh 
is the fraction of stroke completed at cut-off. Set off Ol = exhaust- 



THE SLIDE-VALVE. 



1035 



lap and draw lm; em is the exhaust-lap angle. Set off hn — ec + cd — em, 
and On is the position of crank at release. Set off fp = ec + cd + em, 
and Op is the position of crank for compression, fo -h fh is the fraction 
of stroke completed at release, and hq -5- hf is the fraction of the return 
stroke completed when compression begins; Oh, the throw of the eccentric, 
minus Oa the lap, equals ah the maximum port-opening. 



^Cut-off 




Fig. 162. 

If a valve has neither lap nor lead, the line joining the center of the 
eccentric disk and the center of the snaft being at right angles to the line 
of the crank, the engine would follow full stroke, admission of steam 
beginning at the beginning of the stroke and ending at the end of the 

Adding lap to the valve enables us to cut off steam before the end of 
the stroke. The eccentric being advanced on the shaft an amount equal 
to the lap-angle enables steam to be admitted at the beginning of the 
stroke, as before lap was added, and advancing it a further amount equal 
to the lead-angle causes steam to be admitted before the beginning of the 
stroke. 

Having given lap to the valve, and having advanced the eccentric 
on the shaft from its central position at right angles to the crank, 
through the angular advance = lap-angle + lead-angle, the four events, 
admission, cut-off, release or exhaust-opening, and compression or exhaust- 
closure, take place as follows: Admission, when the crank lacks the lead- 
angle of having reached the center; cut-off, when the crank lacks two 
lap-angles and one lead-angle of having reached the center. During 
the admission of steam the crank turns through a semicircle less twice 
the lap-angle. The greatest port-opening is equal to half the travel of the 
valve less the lap. Therefore for a given port-opening the travel of the 
valve must be increased if the lap is increased. When exhaust-lap is 
added to the valve it delays the opening of the exhaust and hastens its 
closing by an angle of rotation equal to the exhaust-lap amde, which is 
the angle through which the eccentric rotates from its middle position 



1036 



THE STEAM-ENGINE. 



while the exhaust edge of the valve uncovers its lap. R.elease then 
takes place when the crank lacks one lap-angle and one lead-angle minus 
one exhaust-lap angle of having reached the center, and compression when 
the crank lacks lap-angle + lead-angle + exhaust-lap angle of having 
reached the center. 

The above discussion of the relative position of the crank, piston, and 
valve for the different points of the stroke is accurate only with a con- 
necting-rod of infinite length. 

For actual connecting-rods the angular position of the rod causes a 
distortion of the position of the valve, causing the events to take place too 
late in the forward stroke and too early in the return. The correction of 
this distortion may be accomplished to some extent by setting the valve 
so as to give equal lead on both forward and return stroke, and by alter- 
ing the exhaust-lap on one end so as to equalize the release and com- 
pression. F. A. Halsey, in his Slide-valve Gears, describes a method of 
equalizing the cut-off without at the same time affecting the equality of 
the lead. In 'designing slide-valves the effect of angularity of the con- 
necting-rod should be studied on the drawing-board, and preferably by 
the use of a model. 

Sweet's Valve-diagram. — To find outside and inside lap of valve 
for different cut-offs and compressions (see iFig. 163): Draw a circle 
whose diameter equals travel of valve. Draw diameter BA and con' 
tinue to A 1 , so that the length AA X bears the same ratio to XA as the 













^ M 1 


B f 


aNt/ 


\ x y 




B l 


"""—-^ 




ILMm 


)cy c n / 



Fig. 163. — Sweet's Valve Diagram, 
length of connecting-rod does to length of engine-crank. Draw small 
circle K with a radius equal to lead. Lay off AC so that ratio of AC to 
AB = cut-off in parts of the stroke. Erect perpendicular CD. Draw 
DL tangent to K; draw XS perpendicular to DL; XS is then outside lap 
of valve. 

To find release and compression: If there is no inside lap, draw FE 
through X parallel to DL. F and E will be position of crank for release 
and compression. If there is an inside lap, draw a circle about X, in 
which radius XY equals inside lap. Draw HG tangent to this circle and 
parallel to DL; then H and G are crank positions for release and for com- 
pression. Draw HN and MG, then AN is piston position at release and 
A'M piston position at compression, AB being considered stroke of 
engine. 

To make compression alike on each stroke it is necessary to increase 
the inside lap on crank end of valve, and to decrease by the same amount 
the inside lap on back end of valve. To determine this amount, through 
M with a radius MM 1 = A A 1 , draw arc MP, from P draw PT perpen- 
dicular to AB, then TM is the amount to be added to inside lap on crank 
end, and to be deducted from inside lap on back end of valve, inside lap 
being XY. 

For the Bilgram Valve-Diagram, see Halsey on Slide-valve Gears. 

The Zeuner Valve-diagram is given in most of the works on the 
steam-engine, and in treatises on valve-gears, as Zeuner's, Peabody's,,and 
Spangler's. The following paragraphs show how the Zeuner valve-diagram 
may be employed as a convenient means (1) for finding the lap, lead, 
etc., of a slide-valve when the points of admission, cut-off, and release 



THE SLIDE-VALVE. 



1037 



are given; and (2) for obtaining the points of admission, cut-off, release, 
and compression, etc., when the travel, the laps, and the lead of the valve 
are given. In working out these two problems, the connecting-rod is 
supposed to be of infinite length. 

Determination of the Lap, Lead, etc., of a Slide-valve for Given Steam 
Distribution. — Given the points of admission, cut-off, and release, to find 
the point of compression, the lap, the lead, the exhaust lap, the angular 
advance, and the port-openings at different fractions of the stroke. 

Draw a straight line A A', Fig. 164, to represent on any scale the travel 
of the valve, and on it draw a circle, with the center O, to represent the 
path of the center of the eccentric. The line and the circle will also repre- 
sent on a different scale the length of stroke of the piston and the path 
of the crank-pin. On the circle, which is called the crank circle, mark B, 

K 



/I ' ^^ 


X ^<^o/ 

\ 


/ i Center of^ 
\ / | Eccentric \ 


i 


// 1 ^ 

/ \ I ^ 

M \|E F 


?/ \ \ 

7 \ N 

P' N*, 


1 iH i KeleaseV- 

/■/ L-J^^ ' \ 

U^^H] \R' X 1 


A 


B 


VAdmissiXDa 


\ L^ — "^L^/7 ^\ -W \ 

j / ^^i^__ClrcVe^< 



-Saofr 



Circle 



Fig. 164. — Zeuner's Valve Diagram. 

the position of the crank-pin when admission of steam begins, the direc- 
tion of motion of the crank being shown by the arrow; C, the position of 
the crank-pin at cut-off; and L, its position at release. From these points 
draw perpendiculars BM, CN, and LV, to the line A A'; M, N, and V 
will then represent the positions of the piston at admission, cut-off, and 
release respectively, the admission taking place, as shown, before the 
piston reaches the end of the stroke in the direction OA, and release 
taking place before the end of the stroke in the direction OA'. 

Bisect the arc BC at D, and draw the diameter DOD' . On DO draw 
the circle DHOGE, called the valve circle. Draw OB, cutting the valve 
circle at G; and OC, cutting it at H. Then OG = OH is the lap of the 
valve, measured on the scale in which OA is the half-travel of the valve. 
With OG as radius draw the arc GFH, called the steam-lap circle, or, for 
short, the lap circle. 



1038 THE STEAM-ENGINE. 



Mark the point E, at which the valve circle cuts the line OA. The 
distance FE represents the lead of the valve, and BG = AF is the max- 
imum port-opening. A perpendicular drawn from OA at E will cut the 
valve circle and the crank circle at D, since the triangle DEO is a right- 
angled triangle drawn in the semicircle DEGO. 

Erect the perpendicular FJ, then angle DOJ = AOB is the lead-angle 
and JOK is the lap-angle, OK being a perpendicular to AA' drawn from 
O. DOK is the sum of the lap and lead angles, that is, the angular 
advance, by which the eccentric must be set beyond 90° ahead of the 
crank. Set off KY = KD ; then Y is the position of the center of the 
eccentric when the crank is in the position OA. 

To find the point of compression, set off D'P = D'L; then P is the 
point of compression. 

Draw OP and Oh. On OD r draw the valve circle ORD'S, cutting 
OL at R and OP at S. With OR as a radius draw the arc of the exhaust- 
lap circle, RTS; OR = OS is the exhaust lap. 

The port-opening at any 'part of the stroke, or corresponding position 
of the crank, is represented by the radial distances, as EF, DW, and JX, 
intercepted between the lap and the valve circles on radii drawn from O. 
Thus, on the radius OB, the port-opening is zero when steam admission is 
about to begin; on the radius OA, when the crank is on the dead center 
the opening is EF, or equal to the lead of the valve; on the radius DO, 
midway between the point of admission and the point of cut-off, the 
opening is a maximum DW = AF = BG; on the radius OC it is zero 
again when steam has just been cut off. 

In like manner the exhaust opening is represented by the radial dis- 
tances intercepted between the exhaust-lap circle, RR'TS, and the valve 
circle, ORD'S. On the radius OL it is zero when release begins; on OD' 
it is TD', a maximum; and on OP it is zero again when compression begins. 

Determination of the Steam Distribution, etc., for a Given Valve. — Given 
the valve travel, the lap, the lead, and the exhaust. lap, to find the maxi- 
mum port-opening, the angular advance, and the points of admission, 
cut-off, release, and compression. 

This problem is the reverse of the preceding. Draw AOA' to represent 
the valve travel on a certain scale, O being the middle point, and on this 
line on the same scale set off OF = the lap, FE = the lead, and OR' = 
the exhaust lap. A F then will be the maximum port-opening. Draw the 
perpendiculars OK and ED. DOK is the angular advance. 

Draw the diameter DOD', and on DO and D'O draw the two valve 
circles. From 0, the center, with a radius OF, the lap, draw the arc of 
the steam-lap circle cutting the valve circle in G and H. Through G 
draw OB, and through H draw OC; B then is the point of admission, 
and C the point of cut-off. With OR, the exhaust lap, as a radius, draw 
the arc of the exhaust-lap circle, RTS, cutting the valve circle in R and 
S. Through R draw OL, and through S draw OP. Then L is the point 
of release and P the point of compression. Draw the perpendiculars 
BM, CN, LV, and PP' , to find M, N, V, and P' , the respective positions 
on the stroke of the piston when admission, cut-off, release, and com- 
pression take place. 

Practical Application of Zeunefs Diagram. — In problems solved by 
means of the Zeuner diagram, the results obtained on the drawings are 
relative dimensions or the ratios of the several dimensions to a given 
dimension the scale of which is known, such as the valve travel, the 
maximum port-opening, or the length of stroke. In problems similar to 
the first problem given above, the known dimensions are usually the 
length of stroke, the maximum port-opening, AF, which is calculated 
from data of the dimensions of cylinder, the piston speed, and the allow- 
able velocity of steam through the port. The length of the stroke being 
represented on a certain scale by AA', the points of admission, cut-off, 
release, and compression, in fractions of the stroke, are measured respec-. 
tively by A'M, AN, AV, and A'P on the same scale. The actual dimen- 
sion of the maximum port-opening is represented on a different scale by 
AF, therefore the actual dimensions of the lap, lead, and exhaust lap are 
measured respectively by OF, FE, and OR' on the same scale as AF; 
or, in other words, the lap, lead, and exhaust lap are respectively the 

OF FW OR' 

ratios -j-=> -r-^< and -j-^- > each multiplied by the maximum port-opening. 



THE SLIDE-VALVE. 



1039 



0.017 .033 .05 .067 .083 .1 .107 .133 .15 .167 .2 



In problems similar to the second problem, the actual dimensions of 
the lap, the lead, the exhaust lap, and the valve travel are all known, 
and are laid down on the same scale on the line AA', representing the 
valve travel; and the maximum port-opening is found by the solution of 
the problem to be AF, measured on tne same scale; or the maximum 
port-opening = 1/2 valve travel minus trie lap. Also in this problem 
AA' represents tne known length of stroke on a certain scale, and the 
points of admission, cut-off, release, and compression, in fractions of the 
stroke, are represented by the ratios which A'M, AN, AV, and A'P, 
respectively, bear to AA'. 

Port-opening. — The area of port-opening is usually made such that 
the velocity of the steam in passing through it should not exceed 6000 ft. 
per min. The ratio of port area to piston area will vary with the piston- 
speed as follows: 
Forspeed^of^piston, J 10Q 200 3QQ AQQ 5QQ 60Q 7QQ SQQ 9QQ 10QQ 12Q0 

Port area = piston ) 
area X 

For a velocity of 6000 ft. per min., 

Port area = sq. of diam. of cyl.X piston speed -h 7639. 

The length of the port-opening may be equal to or something less than 
the diameter of the cylinder, and the width = area of port-opening -s- 
its length. 

The bridge between steam and exhaust ports should be wide enough 
to prevent a leak of steam into the exhaust due to overtravel of the 
valve. 

The width of exhaust port = width of steam port + 1/2 travel of valve 
+ inside lap - width of bridge. 

Lead. (From Peabody's Valve-gears.) — The lead, or the amount 
that the valve is open when the engine is on a dead point, varies, with the 
type and size of the engine, from a very small amount, or even nothing, 
up to 3/ 8 of an inch or more. Stationary -engines running at slow speed 
may have from 1/64 to 1/16 inch lead. The effect of compression is to fill 
the waste space at the end of the cylinder with steam; consequently, 
engines having much compression need less lead. Locomotive-engines 
having the valves controlled by the ordinary form of Stephenson link- 
motion may have a small lead when running slowly and with a long 
cut-off, but when at speed with a short cut-off the lead is at least 1/4 inch ; 
and locomotives that have valve-gear which gives constant lead com- 
monly have 1/4 inch lead. The lead-angle is the angle the crank makes 
with the line of dead points at admission. It may vary from 0° to 8°. 

Inside Lead. — Welsbach (vol. ii, p. 296) says: Experiment shows 
that the earlier opening of the exhaust ports is especially of advantage, 
and in the best engines the lead of the valve upon the side of the exhaust, 
or the inside lead, is 1/25 to 1/15; i.e., the slide-valve at the lowest or highest 
position of the piston has made an opening whose height is 1/25 to 1/15 of 
the whole throw of the slide-valve. The outside lead of the slide-valve 
or the lead on the steam side, on the other hand, is much smaller, and is 
often only 1/100 of the whole throw of the valve. 

Effect of Changing Outside Lap, Inside Lap, Travel and 
Angular Advance. (Thurston.) 





Admission. 


Expansion. 


Exhaust. 


Compression. 


Incr. 
O.L. 


is later, 
ceases sooner 


occurs earlier, 
continues longer 


is unchanged 


begins at 
same point 


Incr. 
I.L. 


unchanged 


begins as before, 
continues longer 


occurs later, 
ceases earlier 


begins sooner, 
continues longer 


Incr. 
T. 


begins sooner, 
continues longer 


begins later, 
ceases sooner 


begins later, 
ceases later 


begins later, 
ends sooner 


Incr. 
AA. 


begins earlier, 
period unaltered 


begins sooner, 
per. the same 


begins earlier, 
per. unchanged 


begins earlier, 
per. the same 



1040 



THE STEAM-ENGINE. 



Zeuner gives the following relations (Weisbach-Dubois, vol.ii, p. 307): 
US — travel of valve, p = maximum port opening; 

L = steam-lap, I = exhaust-lap; 

R = ratio of steam-lap to half travel = n K g , L = — X S; 



r = ratio of exhaust-lap to half travel = 



0.5 S' 
I 



l = 2p+2L=2p+RXS;S = 



1-R 



If a = angle BOC between positions of crank at admission and at 
cut-off, and = angle LOP between positions of crank at release and at 

.. „ 1; sin (180° -a) sin (180° -j8) 
compression, then R = 1/2 = — 77 ; r = 1/2 



sin 1/2 



sin 1/2 /3 



Crank-angles for Connecting-rods of Different Lengths. 

Forward and Return Strokes. 



"•5 <D fl 

O,^ CD 




Ratio of Length of Connecting-rod to Length of Stroke. 




2 


21/2 


3 


31/2 


4 


5 


Infi- 
nite 










































For. 


CO 


For. 


Ret. 


For. 


Ret. 


For. 


Ret. 


For. 


Ret. 


For. 


Ret. 


For. 


Ret. 


or 





























Ret. 


.01 


10.3 


13.2 


10.5 


12.8 


10.6 


12.6 


10.7 


12.4 


10.8 


12.3 


10.9 


12.1 


11.5 


.02 


14.6 


18.7 


14.9 


18.1 


15.1 


17.8 


15.2 


17.5 


15.3 


17.4 


15.5 


17.1 


16.3 


.03 


17.9 


22.9 


18.2 


22.2 


18.5 


21.8 


18.7 


21.5 


18.8 


21.3 


19.0 


21.0 


19.9 


.04 


20.7 


26.5 


21.1 


25.7 


21.4 


25.2 


21.6 


24.9 


21.8 


24.6 


22.0 


24.3 


23.1 


.05 


23.2 


29.6 


23.6 


28.7 


24.0 


28.2 


24.2 


27.8 


24.4 


27.5 


24.7 


27.2 


25.8 


.10 


33.1 


41.9 


33.8 


40.8 


34.3 


40.1 


34.6 


39.6 


34.9 


39.2 


35.2 


38.7 


36.9 


.15 


41 


51.5 


41.9 


50.2 


42.4 


49.3 


42.9 


48.7 


43.2 


48.3 


43.6 


47.7 


45.6 


.20 


48 


59.6 


48.9 


58.2 


49.6 


57.3 


50.1 


56.6 


50.4 


56.2 


50.9 


55.5 


53.1 


.25 


54.3 


66.9 


55.4 


65.4 


56.1 


64.4 


56.6 


63.7 


57.0 


63.3 


57.6 


62.6 


60.0 


.30 


60.3 


73.5 


61.5 


72.0 


62.2 


71.0 


62.8 


70.3 


63.3 


69.8 


63.9 


69.1 


66.4 


.35 


66.1 


79.8 


67.3 


78.3 


68.1 


77.3 


68.8 


76.6 


69.2 


76.1 


69.9 


75.3 


72.5 


.40 


71.7 


85.8 


73.0 


84.3 


73.9 


83.3 


74.5 


82.6 


75.0 


82.0 


75.7 


81.3 


78.5 


.45 


77.2 


91.5 


78.6 


90.1 


79.6 


89.1 


80.2 


88.4 


80.7 


87.9 


81.4 


87.1 


84.3 


.50 


82.8 


97.2 


84.3 


95.7 


85.2 


94.8 


85.9 


94.1 


86.4 


93.6 


87.1 


92. ¥ 


90.0 


.55 


88.5 


102.8 


89.9 


101.4 


90.9 


100.4 


91.6 


99.8 


92.1 


99.3 


92.9 


98.6 


95.7 


.60 


94.2 


108.3 


95.7 


107.0 


96.7 


106.1 


97 4 


105.5 


98.0 


105.0 


98.7 


104.3 


101:5 


.65 


100.2 


113.9 


101.7 


112.7 


102.7 


111.9 


103.4 


111.2 


103.9 


110.8 


104.7 


110.1 


107.5 


.70 


106.5 


119.7 


108.0 


118.5 


109.0 


117.8 


109.7 


117.2 


110.2 


116.7 


110.9 


116.1 


113.6 


.75 


113.1 


125.7 


114.6 


124.6 


115.6 


123.9 


116.3 


123.4 


116.7 


123.0 


117.4 


122.4 


120.0 


.80 


120.4 


132 


121.8 


131.1 


122.7 


130.4 


123.4 


129.9 


123.8 


129.6 


124.5 


129.1 


126.9 


.85 


128.5 


139 


129.8 


138.1 


130.7 


137.6 


131,3 


137.1 


131.7 


136.8 


132.3 


136.4 


134.4 


.90 


138.1 


146.9 


139.2 


146.2 


139.9 


145.7 


140.4 


145.4 


140.8 


145.1 


141.3 


144.8 


143.1 


.95 


150.4 


156.8 


151.3 


156.4 


151.8 


156.0 


152.2 


155.8 


152.5 


155.6 


152.8 


155.3 


154.2 


.96 


153.5 


159.3 


154.3 


158.9 


154.8 


158.6 


155.1 


158.4 


155.4 


158.2 


155.7 


158.0 


156.9 


.97 


157.1 


162.1 


157.8 


161.8 


158.2 


161.5 


158.5 


161.3 


158.7 


161.2 


159.0 


161.0 


160.1 


.98 


161.3 


165.4 


161.9 


165.1 


162.2 


164.9 


162.5 


164.8 


162.6 


164.7 


162.9 


164.5 


163.7 


.99 


166.8 


169.7 


167.2 


169.5 


167.4 


169.4 


167.6 


169.3 


167.7 


169.2 


167.9 


169.1 


168.5 


1.00 


180 


180 


180 


180 


180 


180 


180 


180 


180 


180 


180 


180 


180 



Ratio of Lap and of Port-opening to Valve-travel. — The table 
on page 1041, giving the ratio of lap to travel of valve and ratio of travel 
to port-opening, is abridged from one given by Buel in Weisbach-Dubois, 



THE SLIDE-VALVE. 



1041 



vol. ii. It is calculated from the above formulae,. Intermediate values 
may be found by the formulae, or with sufficient accuracy by interpolation 
from the figures in the table. By the table on page 1040 the crank-angle 
may be found, that is, the angle between its position when the engine is 
on the center and its position at cut-off, release, or compression, when 
these are known in fractions of the stroke. To illustrate the use of the 
tables the following example is given by Buel: width of port = 2 .2 in.; 
width of port-opening = width of port + 0.3 in.; overtravel = 2.5 in.; 
length of connecting-rod = 21/2 times stroke; cut-off = 0.75 of stroke; 
release = 0.95 of stroke; lead-angle, 10°. From the first table we find 
crank-angle = 114.6; add lead-angle, making 124.6°. From the second 
table, for angle between admission and cut-off, 125°, we have ratio of 
travel to port-opening = 3.72, or for 124.6° = 3.74, which, multiplied 
by port-opening 2.5, gives 9.45 in. travel. The ratio of lap to travel, 
by the table, is 0.2324, or 9.45 X 0.2324 = 2.2 in. lap. For exhaust- 
lap, we have for release at 0.95, crank-angle = 151.3; add lead-angle 
10° = 161 .3°. From the second table, by interpolation, ratio of lap to 
travel = 0.0811, and 0.0811 X 9.45 = 0.77 in., the exhaust-lap. 

Lap-angle = 1/2(180° — lead -angle — crank-angle at cut-off); 

= 1/2(180° - 10 - 114.6) = 27.7°. 
Angular advance =lap-angle + lead-angle = 27.7 + 10 = 37.7°. 
Exhaust lap-angle = crank-angle at release + lap-angle + lead -angle — 180° 

= 151. 3+27. 7+10-180° = 9°. 
Crank-angle at com- ) 

pression measured > =180°— lap-angle — lead-angle — exhaust lap-angle 
on return stroke ) 

= 180-27.7-10-9=133.3°; corresponding, by 
table, to a piston position of .81 of the return stroke; or 
Crank-angle at compression = 180°- (angle at release— angle at cut-off) 

+ lead-angle 
= 180 - (151 .3-114.6) +10= 133.3°. 

The positions determined above for cut-off and release are for the 
forward stroke of the piston. On the return stroke the cut-off will take 
place at the same angle, 114.6°, corresponding by table to 66.6% of the 
return stroke, instead of 75%. By a slight adjustment of the angular 
advance and the length of the eccentric-rod the cut-off can be equalized. 
The width of the bridge should be at least 2.5 + .25 - 2.2 = .55 in. 







Lap and Travel of 


Valve 








§"3*6 h 


"3 


33 A 


» ? O 


*o 


> g 


3*8 ia £i 


*o 


j> g 


•— 


"c3 a 


% 


"d ft 


m ? § 


*a3 


"a a 


•Sfl=° 


> 


>o 


: 1«3° 


> 


>o 


•s-S=° 


> 


> ? 


o-SOts 


2? 

13 Ph 


o'SO-d 






O'SOtj 






een P 
at P< 
ti and 
se an 


H 


een P 
at P 
n and 
se an 





*P Ph 


een P 
at P« 
nand 
se an 








ft 


03 O 


ft 


£ ° 


ft 


>«*- 


^•2 gd 


03 
l_3 


eh£ 


B^-2 % a 


oj 
h3 


H£ 


£^•2 S3 d 


3 


H-5 


ngle be 
of Crai 
Admiss 
or Rel 
pressio 




.2^bi 
■g-S.9 


ngle be 
of Crai 
Admiss 
or Rel 
pressio 


II 

~*3> 


■gg 


ngle be 
of Cra: 
Admisi 
or Rel 
pressio 


11 

03 !> 


25 i 


< 


tf 


« 


< 


S 


p? 


< 


tf 


& 


30° 


0.4830 


58.70 


85° 


0.3686 


7.61 


135° 


0.1913 


3.24 


35 


.4769 


43.22 


90 


.3536 


6.83 


140 


.1710 


3.04 


40 


.4699 


33.17 


95 


.3378 


6.17 


145 


.1504 


2.86 


45 


.4619 


26.27 


100 


.3214 


5.60 


150 


.1294 


2.70 


50 


.4532 


21.34 


105 


.3044 


5.11 


155 


.1082 


2.55 


55 


.4435 


17.70 


110 


.2868 


4.69 


160 


.0868 


2.42 


60 


.4330 


14.93 


115 


.2687 


4.32 


165 


.0653 


2.30 


65 


.4217 


12.77 


120 


.2500 


4.00 


170 


.0436 


2.19 


70 


.4096 


11.06 


125 


.2309 


3.72 


175 


.0218 


2.09 


75 


.3967 


9.68 


130 


.2113 


3.46 


180 


.0000 


2.00 


80 


.3830 


8.55 






























1042 



THE STEAM-ENGINE. 



Relative Motions of Crosshead and Crank. — L = length of con- 
necting-rod, R = length of crank, 9 = angle of crank with center line of 
engine, D = displacement of crosshead from the beginning of its stroke, 
V = velocity of crank- pin, V x = velocity of piston. 

For R = l, D = ver sin 9± (L- ^ L 2 - sin 2 9) , 
V 1 ~Vsin9/l±- COS& 



^L 2 -sin 2 9) 

From these formulae Mr. A. F. Nagle computes the following: 
Piston Displacement and Piston Velocity for eace 10° op Motion 

of Crank. Length of crank = 1. Length of connecting-rod = 5. 

Piston velocity V\ for vel. of crank-pin = 1. 



Angle 


Displacement. 


Veloc 


ty. 


Angle 

of 
Cr'nk 


Displacement. 


Velocity. 


of 
Cr'nk 


For- 
ward. 


Back. 


For- 
ward. 


Back. 


For- 
ward. 


Back. 


For- 
ward. 


Back. 


10° 
20° 
30° 
40° 
50° 


0.018 
0.072 
0.159 
0.276 
0.416 


0.012 
0.048 
0.109 
0.192 
0.298 


0.207 

0.406 
0.587 
0.742 
0.865 




60° 
70° 
80° 
84° 
90° 


0.576 
0.747 
0.924 
1.000 
1. 101 


0.424 
0.569 
0.728 

"6.899 


0.954 
1.005 
1.019 
1.011 
1.000 


0.778 
0.875 
0.950 

"\.obb 



PERIODS OF ADMISSION, OR CUT-OFF, FOR VARIOUS LAPS 
AND TRAVELS OF SLIDE- VALVES. 

The two following tables are from Clark on the Steam-engine. In the 
first table are given the periods of admission corresponding to travels of 
valve of from 12 in. to 2 in., and laps of from 2 in. to 3/ 8 in., with 1/4 in. 
and 1/8 in. of lead. With greater leads than those tabulated, the steam 
would be cut off earlier than as shown in the table. 

The influence of a lead of $/iq in. for travels of from 15/ 8 in. to 6 in., 
and laps of from 1/2 in. to 1 1/2 in., as calculated for in the second table, 
is exhibited by comparison of the periods of admission in the table, for 
the same lap and travel. The greater lead shortens the period of admis- 
sion, and increases the range for expansive working. 

Periods of Admission, or Points of Cut-oflf, for Given Travels and 
Laps of Slide-valves. 









Periods of Admission, or 


Points of Cut-off, fc 


r the 




"3 6 


T3 






following L 


aps of Valves in inches. 






H > 


2 


13/ 4 


H/2 


11/4 

% 


1 


7/8 


3/ 4 


5/8 


1/2 


3/8 


in. 


in 


% 


% 


% 


% 


% 


% 


% 


% 


% 


12 


1/4 


88 


90 


93 


95 


96 


97 


98 


98 


99 


99 


10 


1/4 


82 


87 


89 


92 


95 


96 


97 


98 


98 


99 


8 


1/4 


72 


78 


84 


88 


92 


94 


95 


96 


98 


98 


6 


1/4 


50 


62 


71 


79 


86 


89 


91 


94 


96 


97 


51/2 


1/8 


43 


56 


68 


77 


85 


88 


91 


94 


96 


97 


5 


1/8 


32 


47 


61 


72 


82 


86 


89 


92 


95 


97 


41/2 


1/8 


14 


35 


51 


66 


78 


83 


87 


90 


94 


96 


4 


1/8 




17 


39 


57 


72 


78 


83 


88 


92 


95 


31/2 


1/8 






20 


44 


63 


71 


79 


84 


90 


94 


3 


1/8 
1/8 








23 


50 
27 


61 

43 


71 

57 


79 
70 


86 
80 


91 


21/2 








88 


2 


1/8 














33 


52 


70 


81 



















THE SLIDE-VALVE. 



1043 



Periods of Admission, or Points of Cut-off, for given Travels and 
Laps of Slide-valves. 

Constant lead, 5/ 16 . 



Travel. 








Lap. 










Inches. 


1/2 


5/8 


3/4 


7/8 


1 


H/8 


11/4 


13/8 


U-2 


1 ; V8 


19 


















13/4 


39 


















17/8 


47 


17 
















2 


55 
61 


34 
42 
















21/8 


14 














21/4 


65 


50 


30 














23/8 


68 
71 
74 
76 
78 
80 
8! 
83 
84 


55 
59 
63 
67 
70 
73 
74 
76 
78 


38 
45 
49 
56 
59 
62 
65 
68 
71 


13 
27 
36 
43 
47 
50 
55 
59 
62 












21/2 












25/ 8 


12 
26 
32 
38 
44 
48 
51 










23/ 4 










27/8 


11 
23 
30 
34 
40 








3 








31/8 


10 
22 
29 






31/4 






33/ 8 


9 




31/2 


85 


80 


73 


64 


53 


45 


34 


20 




35/g 


86 


81 


75 


66 


57 


49 


38 


26 


9 


33/4 


87 


82 


76 


68 


60 


52 


42 


32 


19 


37/s 


87 


83 


78 


70 


63 


55 


46 


36 


25 


4 


88 


84 


79 


72 


66 


58 


49 


40 


29 


41/4 


89 


86 


81 


76 


70 


63 


56 


47 


37 


41/2 


90 


87 


83 


79 


73 


67 


61 


54 


45 


43/ 4 


92 


89 


85 


81 


76 


70 


65 


58 


51 


5 


93 


90 


87 


83 


78 


73 


67 


62 


56 


51/2 


94 


92 


89 


86 


82 


78 


73 


68 


63 


6 


95 


93 


91 


88 


85 


82 


78 


74 


69 



Piston- valve. — The piston-valve is a modified form of the slide- 
valve. The lap, lead, etc., are calculated in the same manner as for the 
common slide-valve. The diameter of valve and amount of port-opening 
are calculated on the basis that the most contracted portion of the steam- 
passage between the valve and the cylinder should have an area such that 
the velocity of steam through it will not exceed 6000 ft. per minute. The 
area of the opening around the circumference of the valve should be about 
double the area of the steam-passage, since that portion of the opening 
that is opposite from the steam-passage is of little effect. 

Setting the Valves of an Engine. — The principles discussed above 
are applicable not only to the designing of valves, but also to adjustment 
of valves that have been improperly set; but the final adjustment of the 
eccentric and of the length of the rod depends upon the amount of lost 
motion, temperature, etc.; and can be effected only after trial. After 
the valve has been set as accurately as possible when cold, the lead and 
lap for the forward and return strokes being equalized, indicator diagrams 
should be taken and the length of the eccentric-rod adjusted, if necessary, 
to correct slight irregularities. 

To Put an Engine on its Center. — Place the engine in a position 
where the piston will have nearly completed its outward stroke, and 
opposite some point on the crosshead, such as a corner, make a mark 
upon the guide. Against the rim of the pullev or crank-disk place a 
pointer and mark a line with it on the pulley. Then turn the engine over 
the center until the crosshead is again in the same position on its inward 
stroke. This will bring the crank as much below the center as it was 
above it before. With the pointer in the same position as before make 
a second mark on the pulley rim. Divide the distance between the marks 
in two and mark the middle point. Turn the engine until the pointer 
is opposite this middle point, and it will then be on its center. To avoid 



1044 THE STEAM-ENGINE. 

the error that may arise from the looseness of crank-pin and wrist-Din 
bearings the engine should be turned a little above the center and then 
be brought up to it, so that the crank-pin will press against the same 
brass that it does when the first two marks are made 

Link-motion. — Link-motions, of which the Stephenson link is the 
most commonly used, are designed for two purposes: first, for reversing the 
motion of the engine, and second, for varying the point of cut-off bv 
varying the travel of the valve. The Stephenson link-motion is a com- 
bination of two eccentrics, called forward and back eccentrics with a link 
connecting the extremities of the eccentric-rods ; so that bv 'varying the 
position of the link the valve-rod may be put in direct connection with 
either eccentric, or may be given a movement controlled in part bv one 
and in part by the other eccentric. When the link is moved by the revers- 
ing lever into a position such that the block to which the valve-rod is 
attached is at either end of the link, the valve receives its maximum 
travel, and when the link is in mid-gear the travel is the least and cut-off 
takes place early in the stroke. 

, j 11 VVL ordi , nal 7 shifting-link with open rods, that is, not crossed, the 
lead ot the valve increases as the link is moved from full to mid-gear, that 
is, as the period of steam admission is shortened. The variation of lead 
is equalized for the front and back strokes by curving the link to the radius 
ot the eccentric-rods concavely to the axles. With crossed eccentric-rods 
the lead decreases as the link is moved from full to mid-gear. In a 
valve-motion with stationary link the lead is constant. (For illustration 
see Clark's Steam-engine, vol. ii, p. 22.) 

The linear advance of each eccentric is equal to that of the valve in full 
gear, that is, to lap + lead of the valve, when the eccentric-rods are 
attached to the link in such position as to cause the half-travel of the 
valve to equal the eccentricity of the eccentric. 

The angle between the two eccentric radii, that is, between lines drawn 
from the center of the eccentric disks to the center of the shaft, equals 
180 less twice the angular advance. 

Buel, in Appleton's Cyclopedia of Mechanics, vol. ii, p. 316, discusses 
the Stephenson link as follows: "The Stephenson link does not give a 
perfectly correct distribution of steam; the lead varies for different points 
of cut-off . The period of admission and the beginning of exhaust are not 
alike for both ends of the cylinder, and the forward motion varies from 
the^ backward. 

"The correctness of the distribution of steam by Stephenson's link- 
motion depends upon conditions which, as much as the circumstances 
will permit, ought to be fulfilled, namely: 1. The link should be curved 
in the arc of a circle whose radius is equal to the length of the eccentric- 
rod. 2. The eccentric-rods ought to be long: the longer they are in pro- 
portion to the eccentricity the more symmetrical will the travel of the 
valve be on both sides of the center of motion. 3. The link ought to be 
short. Each of its points describes a curve in a vertical plane, whose 
ordinates grow larger the farther the considered point is from the center 
of the link: and as the horizontal motion only is transmitted to the valve, 
vertical oscillation will cause irregularities. 4. The link-hanger ought 
to be: long. The longer it is the nearer will be the arc in which the link 
swings to a straight line, and thus the less its vertical oscillation. If the 
link is suspended in its center, the curves that are described by points 
equidistant on both sides from the center are not alike, and hence results 
the variation between the forward and backward gears. If the link is 
suspended at its lower end, its lower half will have less vertical oscillation 
and the upper half more. 5. The center from which the link-hanger 
swings changes its position as the link is lowered or raised, and also 
causes irregularities. To reduce them to the smallest amount the arm 
of the lifting-shaft should be made as long as the eccentric-rod, and 
the center of the lifting-shaft should be placed at the height corre- 
sponding to the central position of the center on which the link-hanger 
swings." 

All these conditions can never be fulfilled in practice, and the variations 
in the lead and the period of admission can be somewhat regulated in an 
artificial way, but for one gear only. This is accomplished by giving 
different lead to the two eccentrics, which difference will be smaller the 
longer the eccentric-rods are and the shorter the link, and by suspending 



THE STEPHENSON LINK-MOTION. 



1045 



the link not exactly on its center line but at a certain distance from it, 
giving what is called "the offset." 

For application of the Zeuner diagram to link-motion, see Holmes on 
the Steam-engine, p. 290. See also Clark's Railway Machinery (1855), 
Clark's Steam-engine, Zeuner's and Auchincloss's Treatises on Slide- 
valve Gears, and Halsey's Locomotive Link Motion. (See page 1095.) 

The following rules are given by the American Machinist for laying out 
a link for an upright slide-valve engine. By the term radius of link is 
meant the radius of the link-arc, ab, Fig. 165, drawn through the center 
of the slot; this radius is generally made equal to the distance from the 

\ 




center of shaft to center of the link-block pin P when the latter stands 
midway of its travel. The distance between the centers of the eccentric- 
rod pins ei 62 should not be less than 21/2 times, and, when space will 
permit, three times the throw of the eccentric. By the throw we mean 
twice the eccentricity of the eccentric. The slot link is generally sus- 
pended from the end next to the forward eccentric at a point in the link- 
arc prolonged. This will give comparatively a small amount of slip to the 
link-block when the link is in forward gear; but this slip will be increased 
when the link is in backward gear. This increase of slip is, however, 
considered of little importance, because marine engines, as a rule,' work 
but very little in the backward gear. When it is necessary that the 
motion shall be as efficient in backward gear as in forward gear, then the 
link should be suspended from a point midway between the two eccentric- 
rod pins; in marine engine practice this point is generally located on the 
link-arc; for equal cut-offs it is better to move the point of suspension 
a small amount towards the eccentrics. 

For obtaining the dimensions of the link in inches: Let L denote the 
length of the valve, B the breadth, p the absolute steam-pressure per sq. in ., 
and R a factor of computation used as below; then R = 0.01 *^L XB X p 

Breadth of the link = 72X16 . 

Thickness T of the bar = RX 0.8 

Length of sliding-block = RX 2.5 

Diameter of eccentric-rod pins = (R X . 7) + 1/4 in. 

Diameter of suspension-rod pin = (R X . 6) + 1/4 in. 

Diameter of suspension-rod pin when overhung. . . = (R X . 8) + 1/4 in. 

Diameter of block-pin when overhung = RXVa 

Diameter of block-pin when secured at both ends . = (R X . 8) + 1/4 in. 



1046 THE STEAM-ENGINE. 



The length of the link, that is, the distance from a to 6, measured on a 
straight line joining the ends of the link-arc in the slot, should be such 
as to allow tne center of the link-block pin P to be placed in a line with 
the eccentric-rod pins, leaving sufficient room for the slip of the block. 
Another type of link frequently used in marine engines is the double-bar 
link, and this type is again divided into two classes: one class embraces 
those links which have the eccentric-rod ends as well as the valve-spindle 
end between the bars, as shown at B (with these links the travel of the 
valve is less than the throw of the eccentric); the other class embraces 
those links, shown at C, for which the eccentric-rods are made with fork- 
ends, so as to connect to studs on the outside of the bars, allowing the 
block to slide to the end of the link, so that the centers of the eccentric- 
rod ends and the block-pin are in line when in full gear, making the travel 
of the valve equal to the throw of the eccentric. The dimensions of these 
links when the distance between the eccentric-rod pins is 21/2 to 23/4 times 
the throw of eccentrics can be found as follows: 

Depth of bars = (R X 1 . 25) + l/2in. 

Thickness of bars = (R X . 5 ) + 1/4 in. 

Diameter of center of sliding-block — R X 1.3 

When the distance between the eccentric-rod pins is equal to 3 or 4 
times the throw of the eccentrics, then 

Depth of bars = (R X 1 . 25) + 3/ 4 in. 

Thickness of bars = (R X 0.5 ) + 1/4 in. 

All the other dimensions may be found by the first table. These are 
empirical rules, and the results may have to be slightly changed to suit 
given conditions. In marine engines the eccentric-rod ends for all 
classes of links have adjustable brasses. In locomotives the slot-link is 
usually employed, and in these the pin-holes have case-hardened bushes 
driven into the pin-holes, and have no adjustable brasses in the ends of 
the eccentric-rods. The link in B is generally suspended by one of the 
eccentric-rod pins; and the link in C is suspended by one of the pins in 
the end of the link, or by one of the eccentric-rod pins. (See note on 
Locomotive Link Motion, p. 1095.) 

The Walschaert Valve-gear. Fig. 166. — This gear, which was 
invented in Belgium, has for many years been used on locomotives in 
Europe, and it has now (1909) come largely into use in the United States. 
The return crank Q, which takes the place of an eccentric, through the 
rod B oscillates the link on the fixed pin F. The block D is raised and 




Fig. 166. — The Walschaert Valve-gear. 

lowered in the link by the reversing rod I, operating through the bell- 
crank levers H, H and the supporting rod G. When the block is in its 
lowest position the radius rod U has a motion corresponding in direction 
to that of the rod B; when the block is at its upper position U moves in 
an opposite direction to B. The valve-rod E is moved by the combined 
action of U and a lever T whose lower end is connected through the rod S 
to the crosshead R. Constant lead is secured by this gear. 



GOVERNORS. . 1047 

Other Forms of Valve-gear, as the Joy, Marshall, Hackworth, 
Bremrae, Walschaert, Corliss, etc., are described in Clark's Steam-engine 
vol. ii. Power, May 11, 1909, illustrates the Stephenson, Gooch, Allen' 
Polenceau, Marshall, Joy, Waldegg, Walschaert, fink, and Baker-Pilliod 
gears. The design of the Reynolds-Corliss valve-gear is discussed by 
A. H. Eldridge in Power, Sept., 1893. See also Henthorn on the Corliss 
Engine. Rules for laying down the center lines of the Joy valve-gear 
are given in American Machinist, Nov. 13, 1890. For Joy's "Fluid- 
pressure Re versing- valve," see Eng'g, May 25, 1894. 

GOVERNORS. 

Pendulum or Fly-ball Governor. — The inclination of the arms of a 
revolving pendulum to a vertical axis is such that the height of the point 
of suspension h above the horizontal plane in which the center of gravity 
of the balls revolves (assuming the weight of the rods to be small compared 
with the weight of the balls) bears to the radius r of the circle described 
by the centers of the balls the ratio 

h _ weight _ w _ gr 

r centrifugal force wtf v 2 
gr 

which ratio is independent of the weight of the balls, v being the velocity 
of the centers of the balls in feet per second. 

If T = number of revolutions of the balls in 1 second, v = 2irrT = or, 
in which a = the angular velocity, or 2 nT, and 

. gr 2 g . 0.8146. . 9.775. , 

h = tfT = 4^2- 0r h = ~W~ feet = ~W mcheS ' 
g — 32.16. If N = revs, per minute, h = 35,190 -h iV 2 . 

For revolutions per minute. .. . 40 45 50 60 75 

The height in inches will be .. . 21.99 17.38 14.08 9.775 6.256 

Number of turns per minute required to cause the arms to take a given 
angle with the vertical axis: Let I = length of the arm in inches from 
the center of suspension to the center of gyration, and a. the required 
angle; then _ 

N ,Jp*L , 18 7.6./-L_ = 187.6 JL 

V I COS a T I COS a T h 

The simple governor is not isochronous; that is, it does not revolve 
at a uniform speed in all positions, the speed changing as the angle of the 
arms changes. To remedy this defect loaded governors, such as Porter's, 
are used. From the balls of a common governor whose collective weight 
is A let there be hung by a pair of links of lengths equal to the pendulum 
arms a load B capable of sliding on the spindle, having its center of gravity 
in the axis of rotation. Then the centrifugal force is that due to A alone, 
and the effect of gravity is that due to A + 2 B; consequently the alti- 
tude for a given speed is increased in the ratio (A + 2 B) : A, as com- 
pared with that of a simple revolving pendulum, and a given absolute 
variation in altitude produces a smaller proportionate variation in speed 
than in the common governor. (Rankine, S. E., p. 551.) 

For the weighted governor let Z = the length of the arm from the point 
of suspension to the center of gravitv of the ball, and let the length of the 
suspending-link h = the length of the portion of the arm from the point 
of suspension of the arm to the point of attachment of the link; G = the 
weight of one ball, Q = half the weight of the sliding weight, h = the 
height of the governor from the point of suspension to the plane of revolu- 
tion of the balls, a = the angular velocity = 2 ttT, T being the number of 

^ .u . /32-.16A , 2hQ\ . 32.16 /, , 2l t Q\ 

revolutions per second ; then a = 4/ — j- — ^1 + —r- ^ J ; n = — -^— \± + -j- g 1 

in feet, or h = 3 ^° /l + — |) in inches, N being the number of revo- 
lutions per minute. 



1048 THE STEAM-ENGINE. 

(1 S7 7\2 7? 4- 1 TV 
' \ - , in which B is the combined 

weight of the two balls and W the central weight. 

For various forms of governor see App. Cyl. Mech., vol. ii, 61, and 
Clark's Steam-engine, vol. ii, p. 65. 

To Change the Speed of an Engine Having a Fly-baii Governor. — 

A slight difference in the speed of a governor changes the position of its 
weights from that required for full load to that required for' no load. 
It is evident therefore that, whatever the speed of the engine, the normal 
speed of the governor must be that for which the governor was designed; 
i.e., the speed of the governor must be kept the same. To change the 
speed of the engine the problem is to so adjust the pulleys which drive 
the governor that the engine at its new speed shall drive it just as fast as 
it was driven at its original speed. In order to increase the engine-speed 
we must decrease the pulley upon the shaft of the engine, i.e., the driver, 
or increase that on the governor, i.e., the driven, in the proportion that 
the speed of the engine is to be increased. 

Fly-wheel or Shaft-governors. — At the Centennial Exhibition in 
1876 there were shown a few steam-engines in which the governors were 
contained in the fly-wheel or band-wheel, the fly-balls or weights revolving 
around the shaft in a vertical plane with the wheel and shifting the eccen- 
tric so as automatically to vary the travel of the valve and the point of 
cut-off. This form of governor has since come into extensive use, espe- 
cially for high-speed engines. In its usual form two weights are carried on 
arms the ends of which are pivoted to two points on the pulley near its 
circumference, 180° apart. Links connect these arms to the eccentric. 
The eccentric is not rigidly keyed to the shaft but is free to move trans- 
versely across it for a certain distance, having an oblong hole which allows 
of this movement. Centrifugal force causes the weights to fly towards 
the circumference of the wheel and to pull the eccentric into a position of 
minimum eccentricity. This force is resisted by a spring attached to 
each arm which tends to pull the weights towards the shaft and shift the 
eccentric to the position of maximum eccentricity. The travel of the valve 
is thus varied, so that it tends to cut off earlier in the stroke as the engine 
increases its speed. Many modifications of this general form are in use. 
In the Buckeye and the Mcintosh & Seymour engines the governor shifts 
the eccentric around on the shaft so as to vary the angular advance 
In the Sweet "Straight-line" engine and in some others a single weight 
and a single spring are used. For discussions of this form of governor 
see Hartnell, Proc. Inst. M. E., 1882, p. 408: Trans. A. S. M. E., ix, 300- 
xi, 1081; xiv, 92; xv, 929; Modern Mechanism, p. 399: Whitham's Con- 
structive Steam Engineering; J. Begtrup, Am. Mach., Oct. 19 and Dec. 14, 
1893, Jan. 18 and March 1, 1894. 

More recent references are: J. Richardson, Proc. Inst. M. E., 1895 
(includes electrical regulation of steam-engines); A. K. 'Mansfield, Trans. 
A. S. M. E., 1894; F. H. Ball, Trans. A. S. M. E., 1896; R. C. Carpenter, 
Power, May and June, 1898; Thos. Hall, El. World, June 4, 1898; F. M. 
Rites, Power, July, 1902; E. R. Briggs, Am. Mach., Dec. 17, 1903. 

The Rites Inertia Governor, which is the most common form of the 
shaft governor at this date (1909). has a long bar, usually made heavy at 
the ends, like a dumb-bell, instead of the usual weights. This is carried 
on an arm of the fly-wheel by a pin located at some distance from the 
center line of the bar, and also at some distance from its middle point. 
To pins located at two other points are attached the valve-rod and the 
spring. The bar acts both by inertia and by centrifugal force. When 
the wheel increases its speed the inertia of the bar tends to make it fall 
behind, and thus to change the relative position of the fly-wheel arm and 
the bar, and to change the travel of the valve. A small book on " Shaft 
Governors " (Hill Pub. Co., 1908) describes and illustrates this and many 
other forms of shaft governors, and gives practical directions for adjusting 
them. 

Calculation of Springs for Shaft-governors. (Wilson Hartnell, 
Proc. Inst. M. E., Aug., 1882.) — The springs for shaft-governors may be 
conveniently calculated as follows, dimensions being in inches: 

Let W = weight of the balls or weights, in pounds: 

n and r% = the maximum and minimum radial distances of the 
center of the balls or of the centers of gravity of the weights; 



GOVERNORS. 1049 

li and h = the leverages, i.e., the perpendicular distances from the 
center of the weight-pin to a line in the direction of the centrif- 
ugal force drawn through the center of gravity of the weights 
or balls at radii n and n ; 

mi and m 2 = the corresponding leverages of the springs; 

Ci and C'i = the centrifugal forces, for 100 revolutions per minute, 
at radii n and r 2 ; 

Pi and Pi = the corresponding pressures on the spring; 

(It is convenient to calculate these and note them down for refer- 
ence.) 

Cz and C 4 = maximum and minimum centrifugal forces; 

S = mean speed (revolutions per minute); 

Si and Si = the maximum and minimum number of revolutions 
per minute; 

Pz and P4, = the pressures on the spring at the limiting number 
of revolutions (Si and £2); 

P 4 — P3 = D = the difference of the maximum and minimum 
pressures on the springs; 

V = the percentage of variation from the mean speed, or the 
sensitiveness ; 

t = the travel of the spring; 

u = the initial extension of the spring; 

v = the stiffness in pounds per inch; 

w = the maximum extension = u + t. 

The mean speed and sensitiveness desired are supposed to be given. 
Then 



„ sv. 




s '= s + Wo ; 


Ci = 0.28XnX W; 




C 2 =0.28Xr 2 XTF; 


**>&&• 




p 2 =c 2 x— ; 

mi 


*=M#o) !; 




*<-™<m-' 


D 

v= 1 ,u- 


= Pz 

V 


p t 

» w = — 

V 



It is usual to give the spring-maker the values of P 4 and of v or w. 
To ensure proper space being provided, the dimensions of the spring should 
be calculated by the formulae for strength and extension of springs, and 
the least length of the spring as compressed be determined. 

The governor-power = 5 — X j- 9 - 

With a straight centripetal line, the governor-power 
_ C3+C4 v [ ri-n \ 
~ 2 X \ 12 )' 

For a preliminary determination of the governor-power it may be taken 
as equal to this in all cases, although it is evident that with a curved cen- 
tripetal line it will be slightly less. The difference D must be constant for 
the same spring, however great or little its initial compression. Let the 
spring be screwed up until its minimum pressure is P 5 . Then to find the 
speed P G = P 5 + D, _ _ 

s 5 =iooy/|2. s fl -iooy|*. 

The speed at which the governor would be isochronous would be 



Vf 



Suppose the pressure on the spring with a speed of 100 revolutions, at 
the maximum and minimum radii, was 200 lbs, and 100 lbs,, respectively, 



1050 



THE STEAM-ENGINE. 



then the pressure of the spring to suit a variation from 95 to 105 revolu- 
tions will be 100 X (^)'= 90 .2 and 200x(j^) 2 = 220.5 That is, the 

increase of resistance from the minimum to the maximum radius must be 
220-90 = 130 lbs. 

The extreme speeds due to such a spring, screwed up to different 
pressures, are shown in the following table: 



Revolutions per minute, balls shut 

Pressure on springs, balls shut 

Increase of pressure when balls open fully 

Pressure on springs, balls open fully 

Revolutions per minute, balls open fully . . 
Variation, per cent of mean speed 



80 


90 


95 


100 


110 


64 


81 


90 


100 


121 


130 


130 


130 


130 


130 


194 


211 


220 


230 


251 


98 


102 


105 


107 


112 


10 


6 


5 


3 


1 



130 
274 
117 
-1 



The speed at which the governor would become isochronous is 114. 

Any spring will give the right variation at some speed; hence in experi- 
menting with a governor the correct spring may be found from any wrong 
one by a very simple calculation. Thus, if a governor with a spring 
whose stiffness is 50 lbs. per inch acts best when the engine runs at 95, 90 

/90\ 2 
being its proper speed, then 50 X \qz) =45 lbs. is the stiffness of spring 

required. 

To determine the speed at which the governor acts best, the spring 
may be screwed up until the governor begins to " hunt " and then be 
slackened until it is as sensitive as is compatible with steadiness. 



Another formula is: Q 



WH 



CONDENSERS, AIR-PUMPS, CIRCULATING-PUMPS, ETC. 

The Jet Condenser. — In practice the temperature in the hot-well 
varies from 110° to 120°, and occasionally as much as 130° is maintained. 
To find the quantity of injection-water per pound of steam to be condensed : 
Let T\ = temperature of steam at the exhaust pressure; T = temper- 
ature of the cooling-water; Ti = temperature of the water after condensa- 
tion, or of the hot-well; Q = pounds of the cooling-water per lb. of steam 
condensed; then 

1114° + 0.3 T1-T2 
Q T2-T0 

in which W is the weight of steam con- 
densed, H the units of heat given up by 1 lb. of steam in condensing, and 
R the rise in temperature of the cooling-water. This is applicable both 
to jet and to surface condensers. 

Quantity of Cooling-water. — The quantity depends chiefly upon 
its initial temperature, which in Atlantic practice may vary from 40° in 
the winter of temperate zone to 80° in subtropical seas. To raise the 
temperature to 100° in the condenser will require three times as many 
thermal units in the former case as in the latter, and therefore only one- 
third as much cooling-water will be required in the former case as in the 
latter. It is usual to provide pumping power sufficient to supply 40 times 
the weight of steam for general traders, and as much as 50 times for ships 
stationed in subtropical seas, when the engines are compound. If the 
circulating pump is double-acting, its capacity may be 1/53 in the former 
and 1/42 in the latter case of the capacity of the low-pressure cylinder. 
(Seaton.) 

The following table, condensed from one given by W. V. Terry in Power, 
Nov. 30, 1909, shows the amount of circulating water required under 
different conditions of vacuum, temperature of water entering the con- 
denser, and drop. The "drop" is the difference between the temperature 
of steam due to a given vacuum and the temperature of the water leaving 
the condenser. 



CONDENSERS, AIR-PUMPS, ETC. 



1051 



Pounds of Circulating Water per Pound 


of Steam Condensed. 


Vac- 


Drop. 

Deg. 

F. 






Inject 


on Water Temperature, Deg. F. 


Ins. 


45 


50 


55 


60 


65 


70 


75 


80 


85 


90 


29.0 


6 

12 
18 


37.5 

47.8 
65.7 


45.7 
61.8 
95.5 


58.3 
87.5 


80.8 














28.5 


6 
12 
18 


25.6 
30.0 
36.2 


29.2 
35.0 

43.8 


33.9 
42.0 
55.3 


40.3 
52.5 
75.0 


50.0 
70.0 


65.7 


95.5 








28.0 


6 
12 

18 


21.5 

24.4 
28.4 


23.9 
27.7 
32.8 


26.9 
31.8 
38.9 


30.9 
37.5 
47.8 


36.3 
45.7 
61.8 


43.8 
58.3 
87.5 


55.3 
80.8 


75.0 






27.0 


6 

12 
18 


16.4 
18.1 
20.2 


17.8 
19.8 
22.4 


19.5 
21.9 
25.0 


21.5 
24.4 
28.4 


23.9 
27.7 
32.8 


27.0 
31.8 
38.9 


30.9 
37.5 
47.8 


36.2 

45.7 
61.8 


43.8 
58.3 
87.5 


55.3 
80.8 


26.0 


6 
12 
18 


14.0 
15.2 
16.8 


15.0 
16.4 
18.1 


16.2 
17.8 
19.8 


17.5 
19.5 
21.9 


19.1 
21.5 
24.4 


21.0 
23.9 
27.7 


23.4 
26.9 
31.8 


26.3 
30.9 
37.5 


30.0 
36.3 
45.7 


35.0 
43.8 
58.3 



Ejector Condensers. — For ejector or injector condensers (Bulkley's, 
Schutte's, etc.) the calculations for quantity of condensing-water is the 
same as for jet condensers. 

The Barometric Condenser consists of a vertical cylindrical chamber 
mounted on top of a discharge pipe whose length is 34 ft. above the level 
of the hot well. The exhaust steam and the condensing water meet in the 
upper chamber, the water being delivered in such a manner as to expose 
a large surface to the steam. The external atmosphere maintains a col- 
umn of water in the tube, as a column of mercury is maintained in a 
barometer, and no air pump is needed. The Bulkley condenser is the 
original form of the type. In some modern forms a small air pump draws 
from the chamber the residue of air which is not drawn out by the de- 
scending column of water, discharging it into the column below the 
chamber. 

The Surface Condenser — Cooling Surface. — In practice, with the 
compound engine, brass condenser-tubes, 18 B.W.G. thick, 13 lbs. of 
steam per sq. ft. per hour, with the cooling-water at an initial temperature 
of 60°, is considered very fair work when the temperature of the feed^ 
water is to be maintained at 120°. It has been found that the surface in 
the condenser may be half the heating surface of the boiler, and under 
some circumstances considerably less than this. In general practice the 
following holds good when the temperature of sea-water is about 60°: 
Terminal pres., lbs., abs. . 30 20 15 12l/ 2 10 8 6 

Sq. ft. per I.H.P 3 2.50 2.25 2.00 1.80 1.60 1.50 

For ships whose station is in the tropics the allowance should be in- 
creased by 20%, and for ships which occasionally visit the tropics 10% 
increase will give satisfactory results. If a ship is constantly employed 
in cold climates 10% less suffices. (Seaton, Marine Engineering.) 

Whitham (Steam-engine Design, p. 283, also Trans. A.S.M. E., ix, 431 ) 

gives the following: S= , ,„ ,. , in which S = condensing-surface in 

sq. ft.; T\ = temperature Fahr. of steam of the pressure indicated by the 
vacuum-gauge; t = mean temperature of the circulating water, or the 
arithmetical mean of the initial and final temperatures; L = latent heat 
of saturated steam at temperature Tv, k = perfect conductivity of 1 sq. 
ft. of the metal used for the condensing-surface for a range of 1° F. (or 
550 B.T.U. per hour for brass, according to Isherwood's experiments); 
c = fraction denoting the efficiency of the condensing-surface; W = 



1052^ THE STEAM-ENGINE. 

pounds of steam condensed per hour. From experiments by Loring and 
Emery, on U.S.S. Dallas, c is found to be 0.323, and ck = 180; making 

WL 
the equation S = 18Q (7W) - 

Whitham recommends this formula for designing engines having inde- 
pendent circulating-pumps. When the pump is worked by the main 
engine the value of S should be increased about 10%. 

Taking T\ at 135° F., and L = 1020, corresponding to 25 in. vacuum, 

a ** . * + ^ C o 1020 TF 17 W 

and t for summer temperatures at 75°, we have: £= ■)= „„ ■• 

Much higher results than those quoted by Whitham are obtained from 
modern forms of condensers. The literature on the subject of condensers 
from 1900 to 1909 has been quite voluminous, and much difference of 
opinion as to rules of proportioning condensers is shown. 

Coefficient of Heat Tranference in Condensers. (Prof. E. Josse 
of Berlin. Condensed from an abstract in Power, Feb. 2, 1909. See also 
Transmission of Heat from Steam to Water, pages 561 to 563.) 

The coefficient U, the number of heat units transferred per hour through 
1 sq. ft. of metallic condenser wall when the temperature of the steam is 
1° F. higher than that of the water, can be deduced from the formula 

1/U = 1/Ai+ d/L + I/A2, 
in which 1/Ai is the resistance to transmission from steam to metal, I/A2 
the resistance to transmission from metal to water, and d/L the resistance 
to transmission of heat through the metal, d being the usual thickness of 
condenser tubes (1 m.m. or .0393 in.). For this thickness the value of 
L is fairly well known and may be given as 18,430 for brass, 6,500 for 
copper, 11,270 for iron, 5740 for zinc, 11,050 for tin and 2660 for alumi- 
num. The middle term d/L would have the value of 1/18,430 and be of 
comparatively little importance. 

The term I/A2 is the most important and has been investigated with 
the aid of two concentric tubes, water being sent both through the inner 
tube and the annular jacket. The values of various experimenters differ 
greatly. Ser gives the approximate formula 

A - 2 = 510 V?, 
where V is the velocity of water through the tubes in ft. per sec. This 
velocity is far more important than the material of the condenser tubes 
and their thickness, and also of greater consequence than the velocity 
of the steam, about which, or, rather, the term 1/Ai, there is even less 
agreement. Prof. Josse adopts the figure 3900. The velocity of the 
steam has its influence, but the whole term does not count for much. 
For water flowing at the rate of 1 .64 ft. per sec. Josse's formula would be: 
1/U = 1/3900 + 1/18,430 + 1/653 = 1/445, 

and U = 445. 

If A 1 be increased to twice its value IT would rise only to 475, and if the 
tube thickness be doubled U would hardly be affected. An increase, 
however, in the rate of flow of water from 1.64 to 5 feet per second would 
raise U to 625. As an increase of the steam flow is undesirable the best 
plan is to accelerate the flow of the circulating water, and by introducing 
the baffle strips or retarders into his condenser tubes, in order to break the 
water currents up into vortices, Josse raised the value of U at a velocity of 
3.28 feet per second from 614 to 922. 

Opinions differ concerning the increase of U with greater differences of 
temperature. According to some the heat transferred should increase 
proportionately to the difference; according to Weiss and others, pro- 
portionally to the square of the temperature differences. Josse's investi- 
gations were conducted by placing thermo couples in different portions 
of the condenser tubes. If the heat transferred increases as a linear 
function of the difference, then the rise of the temperature in the cool- 
ing, water should follow an exponential law, and it was found to be so. 

Curves showing the relation of the extent of surface to the temperatures 
of steam and water show an agreement with the formula 

tg — to 

Surface = S - g log e j^f* 



CONDENSERS, AIR-PUMPS, ETC. 1053 

where t s is the saturation temperature and i e the temperature of the cooling- 
water at entrance, t being the discharge temperature. 

Air Leakage. — Air passes into the condenser with the exhaust steam, 
the temperature of the air being that of the steam; the pressure of the 
mixture will be the sum of the partial steam pressure and of the partial 
air pressure. The air must be withdrawn by the air-pump. If the with- 
drawal takes place at the temperature corresponding to the condenser 
pressure the partial steam pressure would be equal to the condenser 
pressure, and the pump would have to deal with an enormous air volume. 
The air temperature should, therefore, be lowered, at the spot where the 
air is withdrawn, below the saturation temperature of the condenser 
pressure. 

In steam turbines it is more easy to keep air out than in reciprocating 
engines. Experiments with a 300-kw. Parsons turbine show that not more 
than 1/2 lb. of air was delivered per hour when 6600 lbs. of steam was used 
per hour. 

Condenser Pumps. — The air and condensed water may either be 
removed separately, by a so-called dry-air pump, or both together, by 
a wet-air pump. As dry-air pumps have to deal with high compression 
ratios, with high vacua and single-stage pumps, the clearances must be 
small. When the clearance amounts to 5% the vacuum cannot be main- 
tained at more than 95%, and the clearance must be reduced, or other 
expedients adopted. Three are mentioned: (1) the air-pump may be 
built in two stages; (2) the pump may be fitted with an equalizing pipe 
so that the two sides of the piston are connected near the end of each 
stroke; the volumetric efficiency is raised by this expedient, but consider- 
ably more power is absorbed to accomplish the result ; (3) with the wet- 
air pump the clearance space is made to receive the condensed water, 
which will fill at least part of it. 

Contraflow and Ordinary Flow. — Prof. Josse questions the distinction 
between contraflow and ordinary flow. For the greater portion of the 
condenser there is a rise of temperature only on the water side; the tem- 
perature of the steam side remains that of the saturated steam, and the 
term "contraflow" should, strictly speaking, only be applied if there is a 
temperature fall in the one direction and a corresponding temperature rise 
in the opposite direction. As far as the condensation is concerned, it is 
immaterial in which direction the water flows. The contraflow principle 
is, however, correct and necessary for the smaller portion of the condenser 
in which the condensed liquid is cooled together with the air; for the 
air must be withdrawn from the coldest spot. It seems inadvisable to 
attempt to direct the flow of the steam on the contraflow principle, as that 
would obstruct the steam flow and create a pressure difference between 
different portions of the condenser which would be injurious to the main- 
tenance of high vacua. 

The Power Used for Condensing Apparatus varies from about 
11/2 to 5% of the indicated power of the main engine, depending on the 
efficiency of the apparatus, on the degree of vacuum obtained, the tem- 
perature of the cooling-water, the load on the engine, etc. J. R. Bibbins 
(Power, Feb., 1905) gives the records of test of a 300-kw. plant from which 
the following figures are taken. Cooling-water per lb. of steam 32 to 37 
lbs. Vacuum 27.3 to 27.8 ins. Temp, cooling-water 73. Hot-well 102 
to 105. 



Indicated H.P 151 220 238 260 291 294 457 589 

% of total power used. . . 4.69 3.51 3.22 3.22 3.08 2.97 2.80 2.47 

% for air cylinder 1.63 1.36 1.27 1.21 1.19 1.09 0.95 0.85 

% for water pump 3.07 2.14 1.95 2.00 1.90 1.89 1.85 1.52 



Vacuum, ins. of Mercury, and Absolute Pressures. — The vacuum 
as shown by a mercury column is not a direct measure of pressure, but 
only of the difference between the atmospheric pressure and the absolute 
pressure in the vacuum chamber. Since the atmospheric pressure varies 
with the altitude and also with atmospheric conditions, it is necessary 
when accuracy is desired to give the reading of the barometer as well as 



1054 



THE STEAM-ENGINE. 



that of the vacuum gauge, or preferably to give the absolute pressure in 
lbs. per sq. in. above a perfect vacuum. 

Temperatures, Pressures and Volumes of Saturated Air. (D. B. 

Morison, on The Influence of Air on Vacuum in Surface Condensers, Eng'g, 
April 17, 1908.) 

Volume of 1 Lb. of Air with Accompanying Vapor. 





Is 


Vacuum, ins. of Mercury, and lbs. absolute. 


24 in., 
2.947. 


26 in., 
1.962. 


27 in., 
1.474. 


28 in., 
0.9823. 


28.5 in., 
0.7368. 


28.8 in., 
0.5894. 


29 in., 
0.4912. 


50° 
60° 
70° 
80° 


0.17 
0.23 
0.36 
0.50 
0.69 
0.94 
1.26 
1.68 


P 

2.78 
2.70 
2.59 
2.45 
2.26 
2.01 
1.69 
1.27 


V 

68 
71 
75 
81 
90 
103 
125 
170 


P 

1.79 
1.71 
1.60 
1.46 
1.27 
1.02 
0.70 
0.28 


V 

!05 
113 
124 
137 
163 
203 
304 
770 


P 
1.30 

1.22 
1.11 
0.97 
0.78 
0.53 
0.21 


V 

147 
158 
178 
204 
260 
390 
(a) 


P 

0.81 
0.73 
0.62 
0.48 
0.29 
0.042 


V 
233 
263 
315 
420 
700 
(6) 


P 

0.57 
0.49 
0.38 
0.24 
0.05 


V 

336 
393 
520 
832 
(c) 


P 

0.42 
0.34 
0.2.3 
0.09 


V 
450 
566 
852 
id) 


P 

0.32 
0.24 
0.13 


V 
592 
800 
1536 


90° 






100° 










110° 














120° 









































P = partial pressure of air, lbs. per sq. in. V = volume of 1 lb. of 
air with accompanying vapor, cu. ft. (a) over 1000; (6) nearly 5000; 
(c) about 4000; (d) over 2000. 

Temperatures and Pressures of Saturated Air. 



Vacuum, Ins. 


Proportions of Air and Steam by Weight. 


with Barom. 
at 30 in. 


Saturated 


Air, 0.25. 


Air, 0.5. 


Air, 0.75. 


Air, 1. 


Steam. 


Steam, 1 . 


Steam, 1 . 


Steam, 1 . 


Steam, I. 


29 


79.5°F. 


75 


71 


67.5 


64.5 


28 


101.5 


96.5 


92.4 


88.8 


85.3 


27 


115 


110 


105.6 


101.7 


98.6 


26 


126 


120.2 


115.5 


111.5 


108.3 


25 


134 


128.4 


123.5 


119.2 


116.2 


24 


141 


135.2 


130.3 


125.8 


122.3 



From this table it is seen that a temperature of 126° F. corresponds to 
a 24-in. vacuum if the steam in the condenser has 75% of its weight of 
air mingled with it, and to a 26-in. vacuum if it is free from air. 

One cubic foot of air measured at 60° F. and atmospheric pressure 
becomes 10 cu. ft. at 27 in. and 30 cu. ft. at 29 in. vacuum at the same 
temperature; 10.9 cu. ft. at 105° and 27 in.; 30.5 cu. ft. at 70° F. and 
29 in. The same cu. ft. of air saturated with water vapor at 70° F. and 
29 in. becomes 124.3 cu. ft., or 44.9 cu. ft. at 105° and 27 in. vacuum. 
The temperatures 105° and 70° are about 10% below the temperatures 
of saturated steam at 27 in. and 29 in. respectively. 

Condenser Tubes are generally made of solid-drawn brass tubes, and 
tested both by hydraulic pressure and steam. They are usually made of 
a composition of 68% of best selected copper and 32% of best Silesian 
spelter. The Admiralty, however, always specify the tubes to be made 
of 70% of best selected copper and to have 1% of tin in the composition, 
and test the tubes to a pressure of 300 lbs. per sq. in. (Seaton.) 

The diameter of the condenser tubes varies from 1/2 in. in small con- 
densers, when they are very short, to 1 in. in very large condensers and 
long tubes. In the mercantile marine the tubes are, as a rule, 3/ 4 in. 
diam. externally, and 18 B.W.G. thick (0.049 inch); and 16 B.W.G. 
(0 .065), under some exceptional circumstances. In the British Navy the 
tubes are also, as a rule, 3/ 4 in. diam., and 18 to 19 B.W.G., tinned on 
both sides; when the condenser is brass the tubes are not required to be 
tinned. Some of the smaller engines have tubes s/ 8 in. diam., and 19 



CONDENSERS, AIR-PUMPS, ETC. 



1055 



B.W.G. The smaller the tubes, the larger is the surface which can be got 
in a certain space. (Seaton.) 

In the merchant service the almost universal practice is to circulate 
the water through the tubes. 

Whitham says the velocity of flow through the tubes should not be 
less than 400 nor more than 700 ft. per min. 

Bimetallic Condenser Tubes. (E. K. Davis, Eng. News, Sept. 2, 
1909.) —Condenser tubes are usually made of a brass containing about 
40% zinc. When this alloy is found to be short-lived, due to the presence 
of corrosive substances in the cooling-water, recourse is had to bronze 
tubing of "admiralty mixture " (87% copper, 8% tin, 5% zinc) or to pure 
copper. Sometimes also the tubes for further protection are tinned on the 
inside or on both sides. 

A condenser tube should not split, should be comparatively free from 
localized corrosion or pit holes, and should not become brittle under the 
combined action of steam and cooling-water. 

A bimetallic tube, composed of a copper envelope over an aluminum 
lining (or vice versa) is unlikely to split, owing to its being composed of 
two layers of metal. It is slow to corrode with the aluminum surface 
exposed to the cooling-water, and there is no tendency shown toward 
becoming brittle. Aluminum, being electro-positive to copper, protects 
it from corrosion in somewhat the same way that even porous galvanizing 
protects iron. No corrosion of the copper will take place until the alumi- 
num has been entirely eaten away for a considerable distance around the 
perforation, thus leaving a sound tube for a much longer time than is the 
case when brass or copper is used alone. The usual proportions of metal 
are, .022 in. thickness of copper and .043 in. of aluminum, making a 
total of .065 in., or No. 16 Stubs gauge. 

Tube-plates are usually made of brass. Rolled-brass tube-plates 
should be from 1.1 to 1.5 times the diameter of tubes in thickness, 
depending on the method of packing. When the packings go completely 
through the plates, the latter thickness, but when only partly through, 
the former, is sufficient. Hence, for 3/ 4 -in. tubes the. plates are usually 
7/s to 1 in. thick with glands and tape-packings, and 1 to 1 1/4 ins. thick 
with wooden ferrules. The tube-plates should be secured to their seat- 
ings by brass studs and nuts, or brass screw-bolts; in fact there must be 
no wrought iron of any kind inside a condenser. When the tube-plates 
are of large area it is advisable to stay them by brass rods, to prevent 
them from collapsing. 

Spacing of Tubes, etc. — The holes for ferrules, glands, or india- 
rubber are usually 1/4 inch larger in diameter than the tubes; but when 
absolutely necessary the wood ferrules may be only 3/ 32 inch thick. 

The pitch of tubes when packed with wood ferrules is usually 1/4 inch 
more than the diameter of the ferrule-hole. For example, the tubes are 
generally arranged zigzag, and the number which may be fitted into a 
square foot of plate is as follows: 



Pitch of 

Tubes. 

in. 


No. in a 
sq. ft. 


Pitch of 

Tubes. 

in. 


No. in a 
sq;ft. 


Pitch of 

Tubes. 

in. 


No. in a 
sq. ft. 


1 
H/16 

H/8 


172 
150 
137 


15/32 
13/ie 
17/32 


128 
121 
116 


11/4 
19/32 
15/16 


110 
106 
99 



Air-pump. — ■ The air-pump in all condensers abstracts the water 
condensed and the air originally contained in the water when it entered 
the boiler. In the case of jet-condensers it also pumps out the water of 
condensation and the air which it contained. The size of the pump is cal- 
culated from these conditions, making allowance for efficiency of the pump. 

In surface condensation allowance must be made for the water occasion- 
ally admitted to the boilers to make up for waste, and the air contained 
in it, also for slight leaks in the joints and glands, so that the air-pump 
is, made about half as large as for jet-condensation, 

Seaton says: The efficiency of a single-acting air-pump is generally 
taken at .5 and that of a double-acting pump at M. When the tem- 



1056 



THE STEAM-ENGINE. 



perature of the sea is 60°, and that of the (jet) condenser is 120°, Q being 
the volume of the cooiing-water and q the volume of the condensed water 
in cubic feet, and n the number of strokes per minute. 

The volume of the single-acting pump = 2.74 (Q + q) -s- n. 

The volume of the double-acting pump = 4 (Q + q) -h n. 

W. H. Booth, in his " Treatise on Condensing Plant," says the volume 
to be generated by an air-pump bucket should not be less than 0.75 
cu. ft. per pound of steam dealt with by the condensing plant. Mr. R W 
Allen has made tests with as little air-pump capacity as 0.5 cu. ft. and 
he gives .6 cu. ft. as a minimum. An Edwards pump with three 14-in 
barrels, 12 in. stroke, single-acting, 150 r.p.m., is rated at 45,000 lbs. of 
steam per hour from a surface condenser, which is equivalent to .66 cu. 
ft. per pound of feed-water. 

In the Edwards pump, the base of the pump and the bottom of the 
piston are conical in shape. The water from the condenser flows by 
gravity into the space below the piston, which descending projects it 
through ports into the space in the barrel above the piston, whence on 
the ascending stroke of the piston it is discharged through the outlet 
valves. There are no bucket or foot- valves, and the pump may be run 
at much higher speeds than older forms of pump. (See Catalogue of the 
Wheeler Condenser and Engineering Co.) 

The Area through Valve-seats and past the valves should not be 
less than will admit the full quantity of water for condensation at a veloc- 
ity not exceeding 400 ft. per minute. In practice the area is generally in 
excess of this. (Seaton.) 

Area through foot-valves = D 2 X S <- 1000 square inches. 
Area through head-valves = D 2 X S -*- 800 square inches. 
Diameter of discharge-pipe = Z> X v o ■*- 35 inches. 
D = diam. of air-pump in inches, S = its speed in ft. per min. 

James Tribe (Am. Mach., Oct. 8, 1891) gives the following rule for air- 
pumps used with jet-condensers: Volume of single-acting air-pump driven 
by main engine = volume of low-pressure cylinder in cubic feet, multiplied 
by 3 .5 and divided by the number of cubic feet contained in one pound 
of exhaust steam of the given density. For a double-acting air-pump the 
same rule will apply, but the volume of steam for each stroke of the 
pump will be but one-half. Should the pump be driven independently 
of the engine, then the relative speed must be considered. Volume of jet- 
condenser = volume of air-pump X 4. Area of injection valve = vol. of 
air-pump in cubic inches -J- 520. 

The Work done by an Air-pump, per stroke, is a maximum the- 
oretically, when the vacuum is between 21 and 22 ins. of mercury. As- 
suming adiabatic compression, the mean effective pressure per stroke 

r/p 2 \0-29 -i 

is P — 3 .46 V\ I ( ) - 1 • where p = absolute pressure of the vacuum 

and P2 the terminal, or atmospheric, pressure, = 14 .7 lbs. per sq. in. The 
horse-power required to compress and deliver 1 cu. ft. of air per minute, 
measured at the lower pressure, is, neglecting friction, P X 144 -4- 33,000. 

The following table is calculated from these formulae (R. R. Pratt, Power, 
Sept. 7, 1909). 



Vac. in 
Ins. of 
Mer- 


Abs. 
Press., 
Ins. of 


V2 


Theo- 
retic. 


Theo- 
retic. 


Vac. in 
Ins. of 
Mer- 


Abs. 
Press., 
Ins. of 


P2 


Theo- 
retic. 


Theo- 
retic. 


Mer- 


Pi 


M.E.P. 


H.P. 


Mer- 


Pi 


M.E.P. 


H.P. 


cury. 


cury. 








cury. 


cury. 








29 


1 


30.00 


2.86 


0.0124 


18 


12 


2.50 


6.21 


0.0271 


28 


2 


15.00 


4.05 


0.0177 


16 


14 


2.14 


5.89 


0.0256 


27 


3 


10.00 


4.83 


0.0211 


14 


16 


1.87 


5.42 


0.0236 


26 


4 


7.50 


5.40 


0.0235 


12 


18 


1.67 


4.88 


0.0212 


25 


5 


6.00 


5.78 


0.0252 


10 


20 


1.50 


4.23 


0.0184 


24 


6 


5.00 


6.05 


0.0264 


8 


22 


1.36 


3.52 


0.0153 


23 


7 


4.28 


6.23 


0.0271 


6 


24 


1.25 


2.73 


0.0119 


22 


8 


3.75 


6.33 


0.0276 


4 


26 


1.15 


1.88 


0.0082 


21 


9 


3.33 


6 37 


0.0278 


2 


28 


1.97 


0.96 


0.0042 


20 


10 


3.00 


6.36 


0.0277 


1 


29 


1.03 


0.49 


0021 



CONDENSERS, AIR-PUMPS, ETC. 1057 

Circulating-pump. — Let Q be the quantity of cooling-water in 
cubic feet, n the number of strokes per minute, and S the length of stroke 
in feet. 

Capacity of circulating-pump = Q -~ n c ubic fee t. 

Diameter of circulating-pump = 13.55 ^Q-i-nS inches. 

The clear area through the valve-seats and past the valves should be 
such that the mean velocity of flow does not exceed 450 feet per minute. 
The flow through the pipes should not exceed 500 ft. per min, in small 
pipes and 600 in large pipes. (Seaton.) 

For Centrifugal Circulating-pumps, the velocity of flow in the inlet and 
outlet pipes should not exceed 400 ft. per min. The diameter of the fan- 
wheel is from 21/2 to 3 times the diam. of the pipe, and the speed at its 
periphery 450 to 500 ft. per min. 

The Leblanc Condenser (made by the Westinghouse Machine Co.) 
accomplishes the separate removal of water and air by means of a pair of 
relatively small turbine-type rotors on a common shaft in a single casing, 
which is integral with or attached directly to the lower portion of the 
condensing chamber. The condensing chamber itself is but little more 
than an enlargement of the exhaust pipe. The injection water is pro- 
jected downwards through a spray nozzle, and the combined injection 
water and condensed steam flow downward to a centrifugal discharge 
pump under a head of 2 or 3 ft., which insures the filling of the pump. 
The space above the water level in the condensing chamber is occupied 
by water vapor plus the air which entered with the injection water and 
with the exhaust steam, and this space communicates with the air-pump 
through a relatively small pipe. 

The air-pump differs from pumps of the ejector type in that the vanes 
in traversing the discharge nozzle at high speed constitute a series of 
pistons, each one of which forces ahead of it a small pocket of air, the 
high velocity of which effectually prevents its return to the condenser. 
A small quantity of water is supplied to the suction side of the air-pump 
to assist in the performance of its functions. The power required for the 
pumps is said to approximate 2 to 3 per cent of the power generated by 
the main engine. 

Feed-pumps for Marine Engines. — "With surface-condensing 
engines the amount of water to be fed by the pump is the amount con- 
densed from the main engine plus what may be needed to supply auxiliary 
engines and to supply leakage and waste. Since an accident may happen 
to the surface-condenser, requiring the use of jet-condensation, the pumps 
of engines fitted with surface-condensers must be sufficiently large to do 
duty under such circumstances. With jet-condensers and boilers using 
salt water the dense salt water in the boiler must «be blown off at intervals 
to keep the density so low that deposits of salt will not be formed. Sea- 
water contains about 1/32 of its weight of solid matter in solution. The 
boiler of a surface-condensing engine may be worked with safety when 
the quantity of salt is four times that in sea-water. If Q = net quantity 
of feed-water required in a given time to make up for what is used as 
steam, n = number of times the saltness of the water in the boiler is to 
that of sea- water, then the gross feed-water =nQ-^ (n — 1). In order to be 
capable of filling the boiler rapidly each feed-pump is made of a capacity 
equal to twice the gross feed-water. Two feed-pumps should be supplied, 
so that one may be kept in reserve to be used while the other is out of 
repair. If Q be the quantity of net feed-water in cubic feet, I the length 
of stroke of feed-pump in feet, and n the number of strokes per minute, 

Diameter of each feed-pump plunger in inches = ^550 Q + nl. 
If W be the net feed-water in pounds, 

Diameter of each feed-pump plunger in inches = Vs. 9 W+nl. 

An Evaporative Surface Condenser built at the Virginia Agricul- 
tural College is described by James H. Fitts (Trans. A.S. M. E., xiv, 690). 
It consists of two rectangular end chambers connected by a, series of 
horizontal rows of tubes, each row of tubes immersed in a pan of water. 
Through the spaces between the surface of the water in each pan and the 
bottom of the pan above air is drawn by means of an exhaust-fan. At 
the top of one of the end chambers is an inlet for steam, and a horizontal 



1058 



THE STEAM-ENGINE. 



diaphragm about midway causes the steam to traverse the upper half 
of the tubes and back through the lower. An outlet at the bottom leads 
to the air-pump. The passage of air over the water surfaces removes 
the vapor as it rises and thus hastens evaporation. The heat necessary 
to produce evaporation is obtained from the steam in the tubes, causing 
the steam to condense. It was designed to condense 800 lbs. steam per 
hour and give a vacuum of 22 in., with a terminal pressure in the cylinder 
of 20 lbs. absolute. Results of tests show that the cooling-water required 
is practically equal in amount to the steam used by the engine. And 
since the consumption of steam is reduced by the application of a con- 
denser, its use will actually reduce the total quantity of water required. 

The Continuous Use of Condensing-water is described in a series 
of articles in Power, Aug.-Dec, 1892. It finds its application in situations 
where water for condensing purposes is expensive or difficult to obtain. 

The different methods described include cooling pans on the roof; 
fountains and other spray pipes in ponds, fine spray discharged at an 
elevation above a pond; trickling the water discharged from the hot-well 
over parallel narrow metal tanks contained in a large wooden structure, 
while a fan blower drives a current of air against the films of water falling 
from the tanks, etc. These methods are suitable for small powers, but 
for large powers they are cumbersome and require too much space, and 
are practically supplanted by cooling towers. 

The Increase of Power that may be obtained by adding a condenser 
giving a vacuum of 26 inches of mercury to a non-condensing engine may 




40 30 "24 20 17 

Per Cent ot Power Gained by Vacuum 



Fig. 166. 

be approximated by considering it to be equivalent to a net gain of 12 lbs. 
mean effective pressure per sq. in. of piston area. If A = area of piston 



CONDENSERS, AIR-PUMPS, ETC. 1059 

in sq. ins., S = piston speed in ft. per min., then 12 AS -s- 33,000 = 
AS -4- 2750 = H.P. made available by the vacuum. If the vacuum = 
13.2 lbs. per sq. in. = 27.9 in. of mercury, then H.P. = AS h- 2500. 

The saving of steam for a given horse-power will be represented approxi- 
mately by the shortening of the cut-off when the engine is run with the 
condenser. Clearance should be included in the calculation. To the 
mean effective pressure non-condensing, with a given actual cut-off, 
clearance considered, add 3 lbs. to obtain the approximate mean total 
pressure, condensing. From tables of expansion of steam find what 
actual cut-off will give this mean total pressure. The difference between 
this and the original actual cut-off, divided by the latter and by 100, will 
give the percentage of saving. 

The diagram on page 1058 (from catalogue of H. R. Worthington) shows 
the percentage of power that may be gained by attaching a condenser 
to a non-condensing engine, assuming that the vacuum is 12 lbs. per sq. 
in. The diagram also shows the mean pressure in the cylinder for a given 
initial pressure and cut-off, clearance and compression not considered. 

The pressures given in the diagram are absolute pressures above a 
vacuum. 

To find the mean effective pressure produced in an engine cylinder with 
90 lbs. gauge (= 105 lbs. absolute) pressure, cut-off at 1/4 stroke: find 
105 in the left-hand or initial-pressure column, follow the horizontal line 
to the right until it intersects the oblique line that corresponds to the V4 
cut-off, and read the mean total pressure from the row of figures directly 
above the point of intersection, which in this case is 63 lbs. From this 
subtract the mean absolute back pressure (say 3 lbs. for a condensing 
engine and 15 lbs. for a non-condensing engine exhausting into the 
atmosphere) to obtain the mean effective pressure, which in this case, for 
a non-condensing engine, gives 48 lbs. To find the gain of power by the 
use of a condenser with this engine, read on the lower scale the figures 
that correspond in position to 48 lbs. in the upper row, in this case 25%. 
As the diagram does not take into consideration clearance or compression, 
the results are only approximate. 

Advantage of High Vacuum in Reciprocating Engines. (R. D. 
Tomlinson, Power, Feb. 23, 1909.) — Among the transatlantic liners, 
the best ships with reciprocating engines are carrying from 26 to 28 and 
more inches of vacuum. Where the results are looked into, the engineers 
are required to keep the vacuum system tight and carry all the vacuum 
they can get, and while it is true that greater benefits can be derived 
from high vacua in a steam turbine than in a reciprocating engine, it is 
also true that, where primary heaters are not used, the higher the vacuum 
carried the greater is the justifiable economy which can be obtained from 
the plant. 

The Interborough Rapid Transit Company, New York City, changed 
the motor-driven air-pump and jet-condenser for a barometric type of 
condenser and increased the vacuum on each of the 8000-H.P. Allis- 
Chalmers horizontal vertical engines at the 74th Street station from 
26 to 28 ins., thereby increasing the power on each of the eight units 
approximately 275 H.P., and the economy of the station was increased 
nearly in the same ratio. This change was made about seven years ago 
and the plant is still operating with 28 ins. of vacuum, measured with 
mercury columns connected to the exhaust pipe at a point just below the 
exhaust nozzle of the low-pressure cylinders. 

A careful test made on the 59th Street station showed a decrease in 
steam consumption of 8% when the vacuum was raised from 25 to 28 ins. 
These engines drive 5000-kw. generators. 

The Choice of a Condenser. — Condensers may be divided into two 
general classes: 

First. — Jet condensers, including barometric condensers, siphon 
condensers, ejector condensers, etc., in which the cooling-water mingles 
with the steam to be condensed. 

Second. — Surface condensers, in which the cooling-water is separated 
from the steam, the cooling-water circulating on one side of this surface 
and the steam coming into contact with the other. 

In the jet-condenser the steam, as soon as condensed, becomes mixed 
with the cooling-water, and if the latter should be unsuitable for boiler- 
feed because of scale-forming impurities, acids, salt, etc., the pure distilled 



1060 THE STEAM-ENGINE. 

water represented by the condensed steam is wasted, and, if it were 
necessary to purchase other water for boiler-feeding, this might represent 
a considerable waste of money. On the other hand, if the cooling-water 
is suitable for boiler-feeding, or if a fresh supply of good water is easily 
obtainable, the jet-condenser, because of its simplicity and low cost, is 
unexcelled. 

Surface condensers are recommended where the cooling-water is un- 
fitted for boiler-feed and where no suitable and cheap supply of pure 
boiler-feed is available. 

Where a natural supply of cooling-water, as from a well, spring, lake or 
river, is not available, a water-cooling tower can be installed and the same 
cooling-water used over and over again. (Wheeler Condenser and Eng. 
Co.) 

Owing to their great cost as compared with jet-condensers, surface 
condensers should not be used except where absolutely necessary, i.e., 
where lack of feed-water for the boiler warrants the extra cost. Of course 
there are cases, such as at sea, where surface condensers are indispensable. 
On land, suitable feed-water can always be obtained at some expense, 
and that cost capitalized makes it a simple arithmetical problem to 
determine the extra investment permissible in order to be able to return 
condensed steam as feed-water to the boiler. Unfortunately there is 
another point which greatly complicates the matter, and one which makes 
it impossible to give exact figures, viz., the corrosion and deterioration of 
the condenser tubes themselves, the exact cause of which is not often 
understood. With clean, fresh water, free from acid, the tubes of a con- 
denser last indefinitely, but where the cooling-water contains sulphur, 
as in drainage from coal mines, or sea-water contaminated by sewage, 
such as harbor water, the deterioration is exceedingly rapid. 

A better vacuum may possibly be obtained from a surface condenser 
where there is plenty of cooling-water easily handled. The better vacuum 
is due to the fact that the air-pump will have much less air to handle inas- 
much as the air carried in suspension by the cooling-water does not have 
to be extracted as in the case of jet-condensers. Water in open rivers, 
the ocean, etc., is said to carry in suspension 5% by volume of air. It 
may be said that except for leakages, which should not exist, the air- 
pump will have no work to do at all inasmuch as the water will have no 
opportunity to become aerated. On the other hand, if the cooling-water 
is limited, these advantages are offset by the fact that a surface condenser 
cannot heat the cooling-water so near to the temperature of the exhaust 
steam as can a jet-condenser. (F. Hodgkinson, El. Jour., Aug., 1909.) 

A barometric condenser used in connection with a 15,000-k.w. steam- 
engine-turbine unit at the 59th St. station of the Rapid Transit Co., New 
York, contains approximately 25,000 so., ft. of cooling surface arranged in 
the double two-pass system of water circulation, with a 30-in. centrifugal 
circulating pump having a maximum capacity of 30,000 gal. per hour. 
The dry vacuum pump is of the single-stage type, 12- and 29-in. X 24-in., 
with Corliss valves on the air cylinder. The condensing plant is capable 
of maintaining a vacuum within 1.1 in. of the barometer when condensing 
150,000 lb. of steam per hour when supplied with circulating waler at 70° F. 
— (H. G. Stott, Jour. A.S.M.E., Mar., 1910.) 

Cooling Towers are usually made in the shape of large cylinders of 
sheet steel, filled with narrow boards or lath arranged in geometrical 
forms, or hollow tile, or wire network, so arranged that while the water, 
which is sprayed over them at the top, trickles down through the spaces it 
is met by an ascending air column. The air is furnished either by disk 
fans at the bottom or is drawn in by natural draught. In the latter case 
the tower is made very high, say 60 to 100 ft., so as to act like a chimney. 
When used in connection with steam condensers, the water produced by 
the condensation of the exhaust steam is sufficient to compensate for the 
evaporation in the tower, and none need be supplied to the system. There 
is, on the contrary, a slight overflow, which carries with it the oil from 
the engine cylinders, and tends to clean the system of oil that would 
otherwise accumulate in the hot-well. 

The cooling of water in a pond, spray, or tower goes on in three ways — 
first, by radiation, which is practically negligible; second, by conduction 
or absorption of heat by the air, which may vary from one-fifth to one- 
third of the entire effect; and, lastly, by evaporation. The latter is the 



CONDENSERS, AIR-PUMPS, ETC. 



1061 



chief effect. Under certain conditions the water in a cooling tower can 
actually be cooled below the temperature of the atmosphere, as water is 
cooled by exposing it in porous vessels to the winds of hot and dry climates. 

The evaporation of 1 lb. of water absorbs about 1000 heat units. The 
rapidity of evaporation is determined, first, by the temperature of the 
water, and, second, by the vapor tension in the air in immediate contact 
with the water. In ordinary air the vapor present is generally in a con- 
dition corresponding to superheated steam, that is, the air is not saturated. 
If saturated air be brought into contact with colder water, the cooling 
of the vapor will cause some of it to be precipitated out of the air; on the 
other hand, if saturated air be brought into contact with warmer water, 
some of the latter will pass into the form of vapor. This is what occurs in 
the cooling tower, so that the latter is in a large measure independent 
of climatic conditions; for even if the air be saturated, the rise in tem- 
perature of the atmospheric air from contact with the hot water in the 
cooling tower will greatly increase the water-carrying capacity of the air, 
enabling a large amount of heat to be absorbed through the evaporation 
of the water. The two things to be sought after in cooling-tower design 
are, therefore, first, to present a large surface of water to the air, and, 
second, to provide for bringing constantly into contact with this surface 
the largest possible volume of new air at the least possible expenditure of 
energy. (Wheeler Condenser and Engineering Co.) 

The great advantage of the cooling tower lies in the fact that large 
surfaces of water can be presented to the air while the latter is kept in 
rapid motion. 

Tests of a Cooling Tower and Condenser are reported by J. H. Vail 
in Trans. A.S. M . E ., 1898. The tower was of the Barnard type, with two 
chambers, each 12 ft. 3 in. X 18 ft. X 29 ft. 6 in. high, containing gal- . 
vanized-wire mats. Four fans supplied a strong draught to the two cham- 
bers. The rated capacity of each section was to cool the circulating 
water needed to condense 12,500 lbs. of steam, from 132° to 80° F., when 
the atmosphere does not exceed 75° F. nor the humidity 85%. The fol- 
lowing is a record of some observations. 



Date, 1898. 


Jan. 
31. 


Feb. 


June 
20. 


July 


Aug. 
26. 


Nov. 
4. 


Aug. 2. 


Temperature atmosphere 

Temp, condenser discharge 

Temp, water from tower 

Heat extracted by tower 

Speed of fans, r.p.m 


30° 
110° 
65° 

45° 
36 

251/2 


36° 
110° 
84° 
26° 

26 


78° 
120° 

84° 

36° 
145 

25 


96° 
130° 
93° 

37° 
162 

241/ 2 


85° 
118° 
88° 
30° 
150 
251/2 


59° 
129° 

92° 

37° 
148 

25 


Max. 
103 
128 
98 
32 
160 
26 


Min- 

83 
106 

91 

21 
140 

26 







The quantity of steam condensed or of water circulated is not stated, 
but in the two tests on Aug. 2 the H.P. developed was 900 I.H.P. in the 
first and 400 in the second, the engine being a tandem compound, Corliss 
type, 20 and 36 X 42 in., 120 r.p.m. 

J. R. Bibbins {Trans. A.S.M.E., 1909) gives a large amount of informa- 
tion on the construction and performance of different styles of cooling 
towers. He suggests a type of combined fan and natural draft tower 
suited to most efficient running on peak as well as light loads. 

Evaporators and Distillers are used with marine engines for the pur- 
pose of providing fresh water for the boilers or for drinking purposes. 

Weir's Evaporator consists of a small horizontal boiler, contrived so as 
to be easily taken to pieces and cleaned. The water in it is evaporated by 
the steam from the main boilers passing through a set of tubes placed in 
its bottom. The steam generated in this boiler is admitted to the low- 
pressure valve-chest, so that there is no loss of energy, and the water con- 
densed in it is returned to the main boilers. 

In Weir's Feed-heater the feed-water before entering the boiler is heated 
up very nearly to boiling-point by means of the waste water and steam 
from the low-pressure valve-chest of a compound engine. 



1062 THE STEAM-ENGINE. 

ROTARY STEAM-ENGINES — STEAM TURBINES. 

Rotary Stea n-engines, other than steam turbines, have been invented 
by the thousands, but not one has attained a commercial success, as regards 
economy of steam. For all ordinary uses the possible advantages, such 
as saving of space, to be gained by a rotary engine are overbalanced by 
its waste of steam. Rotary engines are in use, however, for special pur- 
poses, such as steam fire-engines and steam feeds for sawmills, in which 
steam economy is not a matter of importance. 

Impulse and Reaction Turbines. — A steam turbine of the simplest 
form is a wheel similar to a water wbeel, which is moved by a jet of steam 
impinging at high velocity on its blades. Such a wheel was designed 
by Branca, an Italian, in. 1629. The De Laval steam turbine, which is 
similar in many respects to a Pelton water wheel, is of this class. It. is 
known as an impulse turbine. In a book written by Hero, of Alexan- 
dria, about 150 b.c, there is shown a revolving hollow metal ball, into 
which steam enters through a trunnion from a boiler beneath, and 
escapes tangentially from the outer rim through two arms which are 
bent backwards, so that the steam by its reaction causes the ball to 
rotate in an opposite direction to that of the escaping jets. This wheel 
is the prototype of a reaction turbine. In most modern steam turbines 
both the impulse and reaction principles are used, jets of steam striking 
blades or buckets inserted in the rim of a wheel, so as to give it a forward 
impulse, and escaping from it in a reverse direction so as to react upon 
it. The name impulse wheel, however, is now generally given to wheels 
like the De Laval, in which the pressure on the two sides of a wheel con- 
taining the blades is the same, and the name reaction wheel to one in 
which the steam decreases in pressure in passing through the blades. 
The Parsons turbine is of this class. 

The De Laval Turbine. — The distinguishing features of this turbine 
are the diverging nozzles, in which the steam expands down to the at- 
mospheric pressure in non-condensing, and to the vacuum pressure in 
condensing wheels; a single forged steel disk carrying the blades on its 
periphery; a slender, flexible shaft on which the wheel is mounted and 
which rotates about its center of gravity; and a set of reducing gears, 
usually 10 to 1 reduction, to change the very high speed of the turbine 
to a moderate speed for driving machinery. Following are the sizes 
and speeds of some De Laval turbines: 

Horse-power 5 30 100 300 

Revolutions per minute.. ... 30,000 20,000 13,000 10,000 
Diam. to center of blades, ins. 3.94 8.86 19.68 29.92 

The number and size of nozzles vary with the size of the turbine. 
The nozzles are provided with valves, so that for light loads some of 
them may be closed, and a relatively high efficiency is obtained at light 
loads. The taper of the nozzles differs for condensing and non-condens- 
ing turbines. Some turbines are provided with two sets of nozzles, one 
for condensing and the other for non-condensing operation. 

The Zolley or Rateau Turbine. — The Zolley or Rateau turbines 
are developments of the De Laval and consist of a number of De Laval 
elements in series, each succeeding element utilizing the exhaust steam 
from the preceding. The steam is partly expanded in the first row of 
nozzles, strikes the first row of buckets and leaves them with practically 
zero velocity. It is then further expanded through the second row of 
nozzles, strikes a second row of moving buckets and again leaves them 
with zero velocity. This process is repeated until the steam is com- 
pletely expanded. 

The Parsons Turbine. — In the Parsons, or reaction type of turbine, 
there are a large number of rows of blades, mounted on a rotor or revolv- 
ing drum. Between each pair of rows there is a row of stationary blades 
attached to the casing, which take the place of nozzles. A set of sta- 
tionary blades and the following set of moving blades constitute what is 
known as a stage. The steam expands and loses pressure in both sets. 
The speed of rotation, the peripheral speed of the blades and the velocity 
of the steam through the blades are very much lower than in the De Laval 
turbine. The rotor, or drum, on which the moving blades are carried, 
is usually made in three sections of different diameters, the smallest at 
the high-pressure end, where steam is admitted, and the largest at the 



ROTARY STEAM-ENGINBS — STEAM TURBINES. 1063 

exhaust end. In each section the radial length of the blades and also 
their width increase from one end to the other, to correspond with the 
increased volume of steam. The Parsons turbine is built in the United 
States by the Westinghouse Machine Co. and by the Allis-Chalmers Co. 

The Westinghouse Double-flow Turbine. — For sizes above 5000 K.W. 
a turbine is built in which the impulse and reaction types are combined. 
It has a set of non-expanding nozzles, an impulse wheel with two velocity 
stages (that is two wheels with a set of stationary non-expanding blades 
between), one intermediate section and two low-pressure sections with 
Parsons blading. After steam has passed through the impulse wheel 
and the intermediate section it is divided into two parts, one going to 
the right and the other to the left hand low-pressure section. There is 
an exhaust pipe at each end. In this turbine, the end thrust, which has 
to be balanced in reaction turbines of the usual type, is almost entirely 
avoided. Other advantages are the reduction in size and weight, due to 
higher permissible speed; blades and casing are not exposed to high 
temperatures; reduction of size of exhaust pipes and of length of shaft; 
avoidance of large balance pistons. 

The Curtis Turbine, made by the General Electric Company, is an 
impulse wheel of several stages. Steam is expanded in nozzles and 
enters a set of three or more blades, at least one of which is stationary. 
The blades are all non-expanding, and the pressure is practically the same 
on both sides of any row of blades. In smaller sizes of turbines, only 
one set of stationary and movable blades is used, but in large sizes there 
are from two to five sets, each forming a pressure stage, separated by 
diaphragms containing additional sets of nozzles. The smaller sizes have 
horizontal shafts, but the larger ones have vertical shafts supported on a 
step bearing supplied with oil or water under a pressure sufficient to 
support the whole weight of the shaft and its attached rotating disks. 
Curtis turbines are made in sizes from 15 K.W. at 3600 to 4000 revs, per 
minute up to 9000 K.W. at 750 revs, per minute. 

Mechanical Theory of the Steam Turbine. — In the impulse turbine 
of the De Laval type, with a single disk containing blades at its rim, 
steam at high pressure enters the smaller end or throat .of a tapering 
nozzle, and, as it passes through the nozzle, is expanded adiabatically 
down to the pressure in the casing of the turbine, that is to the pressure 
of the atmosphere, in a non-condensing turbine, or to the pressure of 
the vacuum, if the turbine is connected to a condenser. The steam 
thus expanded has its volume and its velocity enormously increased, 
its pressure energy being converted into energy of velocity. It then 
strikes tangentially the concave surfaces of the curved blades, and thus 
drives the wheel forward. In passing through the blades it has its direc- 
tion reversed, and the reaction of the escaping jet also helps to drive the 
wheel forward. If it were possible for the direction of the jet to be com- 
pletely reversed, or through an arc of 180°, and the velocity of the blade 
in the direction of the entering jet was one-half the velocity of the jet, 
then all the kinetic energy due to the velocity of the jet would be con- 
verted into work on the blade, and the velocity of the jet with reference 
to the earth would be zero. This complete reversal, however, is impos- 
sible, since room has to be allowed between the blades for the passage of 
the steam, and the blades, therefore, are curved through an arc consid- 
erably less than 180°, and the jet on leaving the wheel still has some 
kinetic energy, which is lost. The velocity of the entering steam jet 
also is so great that it is not practicable to give the wheel rim a velocity 
equal to one-half that of the jet, since that would be beyond a safe speed. 
The speed of the wheel being less than half that of the entering jet, also 
causes the jet to leave the wheel with some of its energy unutilized. 
The mechanical efficiency of the wheel, neglecting radiation, friction, and 
other internal losses, is expressed by the fraction (E t — Ei) ■*- E x , in 
which E t is the kinetic energy of the steam jet impinging on the wheel 
and Ei that of the steam as it leaves the blades. 

In multiple-stage impulse turbines, the high velocity of the wheel is 
reduced by causing the steam to pass through two or more rows of 
blades, which rows are separated by a row of stationary curved blades 
which direct the steam from the outlet of one row to the inlet of the 
next. The passages through all the blades, both movable and secondary, 
are parallel, or non-expanding, so that the steam does not change its 



1064 



THE STEAM-ENGINE. 



f 



d D/ 



bA 



T2 /, 



pressure in passing through them. The wheel with two rows of movable 
blades running at half the velocity of a single-stage turbine, or one with 
three rows at one-third the velocity, causes the same total reduction in 
velocity as the single-stage wheel; and a greater reduction in the velocity 
of the wheel can be obtained by increasing the number of rows. It is, 
therefore, possible by having a sufficient number of rows of blades, or 
velocity stages, to run a wheel at comparatively slow speed and yet 
have the steam escape from the last set of blades at a lower absolute 
velocity than is possible with a single-stage turbine. In the reaction 
turbine the reduction of the pressure and its conversion into kinetic 
energy, or energy of velocity, takes place in the blades, which are made 
of such shape as to allow the steam to expand while passing through them. 
The stationary blades also allow of expansion 
in volume, thus taking the place of nozzles. 
In all turbines, whether of the impulse, 
reaction, or combination type, the object is 
to take in steam at high pressure and to dis- 
charge it into the atmosphere, or into the 
condenser, at the lowest pressure and largest 
volume possible, and with the lowest pos- 
sible absolute velocity, or velocity with ref- 
erence to the earth, consistent with getting 
the steam away from the wheel, and to do 
this with the least loss of energy in the wheel 
due to friction of the steam through the 
passages, to shock due to incorrect shape, or 
position of the blades, to windage or fric- 
tional resistance of the steam in contact 
with the rotating wheel, or other causes. 
The minimizing of these several losses is a 
problem of extreme difficulty which is being 
solved by costly experiments. 

Heat Theory of the Steam Turbine. — 
The steam turbine may also be considered 
as a heat engine, the object of which is to 
take a pound of steam containing a certain 
quantity of heat, H x , transform as great a 
part of this heat as possible into work, and 
discharge the remaining part, Hi, into the condenser. The thermal effi- 
ciency of the operation is (H t — Hi) -*■ Hi, and the theoretical limit of 
this efficiency is (7\ — Ti) -s- !T2,in which 7\is the initial and Ti the final 
absolute temperature. 

Referring to temperature entropy diagram, Fig. 167, the total heat 
above 32° F. of 1 lb. of steam at the temperature 7\ is represented by 
the area OACDG and its entropy is fa. Expanding adiabatically to Ti 
part of its heat energy is converted into work, represented by the area 
BCDF, while OABFG represents the heat discharged into the condenser. 
The total heat of 1 lb. of dry saturated steam at T 2 is greater than this by 
the area EFGH, the fraction FE -f- BE representing moisture in the 1 lb. 
of wet steam discharged. If H t = heat units in 1 lb. of dry steam at 
the state-point D, and Hi = heat units in 1 lb. of dry steam at the state- 
point E, at the temperature Ti, then the energy converted into work = 
BCDF = Hi - Hi + (fa - fa) Ti. This quantity is called the avail- 
able energy E a , of 1 lb. of steam between the temperatures T x and Ti. 

If the steam is initially wet, as represented by the state-point d and 
entropy <j> x , then the work done in adiabatic expansion is BCdfB, 
which is equal to E a = H x - Hi + (fa - fa) Ti -{fa - <j> x )(T x - Ti). 
The quantity fa — <j> x = {L/T\) (1 — x), in which L = latent heat of 
evaporation at the temperature T lt and x = the moisture in 1 lb. of 
steam. The values of H lt Hi, fa, fa, etc., for different temperatures, 
may be taken from steam tables or diagrams. 

If the steam is initially superheated to the temperature T s , as repre- 
sented by the state-point j, the entropy being fa, then the total heat at 
j is Hi + C (T s — Ti), in which C is the mean specific heat of super- 
heated steam between Ti and T s . The increase of entropy above fa 



H 



Fig. 167. 



KOTARY STEAM-ENGINES — STEAM TURBINES. 1065 

is & - $1 = Clog e (T s /Tt). The energy converted into work is # = 
H t - Hz + (& - ft) ^2 + [1/2 (T s + Ti) - T 2 ] (<f> 3 - 4>x). 

Velocity of Steam in Nozzles. — Having obtained the total available 
energy in steam expanding adiabatically between two temperatures, as 
shown above, the maximum possible flow into a vacuum is obtained 
from the common formula, Energy, in foot-pounds, = 1/2 W/g X V 2 , in 
which W is the weight (in this case 1 lb.). V is the velocity in feet per 
second, and g = 32.2. As the energy E a is in heat units, it is multi- 
plied by 778 to convert it into foot-pounds, and we have 

V =^778 X 2gE a = 223.8 ^E~ a . 
This is the theoretically maximum possible velocity. It cannot be 
obtained in a short nozzle or orifice, but is approximated in the long 
expanding nozzles used in turbines. In the throat or narrow section of 
an orifice, the velocity and the weight of steam flowing per second may 
be found by Napier's or Rateau's formula, see page 847, or from Gras- 
hof's formula as given by Moyer, F = A Pi ' 9 ' ■*■ 60, or A = 60 F ■*■ 
. P J - 97 , in which A is the area of the smallest section of the nozzle, 
sq. in., F is the flow of steam (initially dry saturated) in lbs. per sec, 
and P is the absolute pressure, lbs. per sq. in. This formula is applicable 
in all cases where the final pressure P2 does not exceed 58% of the initial 
pressure. For wet steam the formula becomes F = A Pi ' 97 h- 60 Va;, 
A = 60 F "^x •*- Pi 0-97 , in which x is the dryness quality of the inflow- 
ing steam, 1 — x being the moisture. 

For superheated steam F = A P 1 °' m (l+ 0.00065 D) -f- 60; A = 60P + 
PjO-9/ (i + 0.00065 D), D being the superheat in degrees F. 

When the final pressure Pi is greater than 0.58 Pi, a coefficient is to 
be applied to F in the above formulae, the value of which is most con- 
veniently taken from a curve given by Rateau. The values of this co- 
efficient, c, for different ratios of P1/P2, are approximately as follows: 
P 2 -hPi= 0.58 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 
c= 1. 0.995 0.985 0.975 0.965 0.955 0.945 0.93 0.910.88 0.85 
Pi + P t = 0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00 
c= 0.82 0.79 0.76 0.72 0.675 0.625 0.57 0.51 0.42 0.30 0.00 

The quality of steam after adiabatic expansion, X2, is found from the 
formula x 2 = {x x Lr/T x + X - 2 ) T2/L2, (8) 

in which 0i and 02 are the entropies of the liquid, Li and L2 the latent 
heats of evaporation, and x 1 and X2 the dryness quality, at the initial 
and final conditions respectively. Curves of steam quality are plotted in 
an entropy-total heat chart given in Moyer's "Steam Turbines" and 
also in Marks and Davis's "Steam Tables and Diagrams." 

The area of the smallest section or throat of the nozzle being found, 
the area of any section beyond the throat is inversely proportional to the 
velocity and directly proportional to the specific volume and to the 
dryness, or A 1 /A Q =V /V 1 X v^/Vq X Xt/x b , in which A is in the area in 
sq. ins., V the velocity in ft. per sec, v the volume of 1 lb. of steam in 
cu. ft., and x the dryness fraction, the subscript referring to the 
smallest section and the subscript 1 to any other section. The ratio 
Ai/A for the largest cross section of a properly designed nozzle is nearly 
proportional to the ratio of the initial to the final pressure. Moyer 
gives it as At/A = 0.172 P^/Pt + 0.70, and for Pi/P2 greater than 25, 
Ai/A Q = 0.175 (P 1 /P 2 )°- 94 + 0.70. 

In practice expanding nozzles are usually made so that an axial sec- 
tion shows the inner walls in straight lines. The transverse section is 
usually either a circle or a square with rounded corners. The diver- 
gence of the walls is about 6 degrees from the axis for the non-condens- 
ing and as much as 12 degrees for condensing turbines for low vacuums. 
Moyer gives an empirical formula for the length between the throat and 
the mouth, L = Vl5 Aq inches. The De Laval turbine uses a much 
longer nozzle for mechanical reasons. The entrance to the nozzle above 
the throat should be well rounded. The efficiency of a well-made nozzle 
with smooth surfaces as measured by the velocity is about 96 to 97%, 
corresponding to an energy efficiency of 92 to 94%. 



1066 



THE STEAM-ENGINE. 



Speed of the Blades. — If V b = peripheral velocity of the blade, 
V x = absolute velocity of the steam entering the blades and a the nozzle 
angle, or angle of the nozzle to the plane of the wheel, then (in impulse 
turbines with equal entrance and exit angles of the blade with the plane 
of the wheel) for maximum theoretical efficiency of the blade, V b = 1/2 V x 
cos a. The nozzle angle is usually about 20°, cos a = 0.940, and the 
efficiency of a single row of blades is (0.94 — V b /Vi) 4 V^/Vl 

For Vi = 3000 ft. per sec, the efficiency for different blade speeds is 
about as follows: 

V b = 200 400 600 800 1000 1200 1400 1600 1800 2000 

Efficiency % 23 44 60 72 81 87 89 87 80 71 

The highest efficiency is obtained when V b = about 1/2 V2. It is 
difficult, for mechanical reasons, to use speeds much greater than 500 ft. 
per sec, therefore the highest efficiencies are often sacrificed in commer- 
cial machines. The blade speeds used in practice vary from 500 to 1200 
ft. per sec. For an impulse wheel with more than one row of moving 

4JVF 6/ NV b . 
blades in a single pressure stage, efficiency = — ^ — (cos a — J • 

Referring to Fig. 168, if Vi is the absolute direction and velocity of the 
entering jet, V b the direction and velocity of the blade, the resultant, 
V r , is the velocity and direction of the jet rela- 
tively to the blade, and the edge of the blade 
is made tangent to this direction. Also V x , the 
resultant of V b and V r at the other edge of the 
blade, is the absolute velocity and direction of 
the steam escaping from the wheel. If /? is the 
angle between F r and V b , the maximum energy 
is abstracted from the steam when the angle 
between V z and V b = 90 - 1/2 /?, and the effi- 
ciency is cos /? -*- cos 2 1/2 0. 

For details of design of blades, and of turbines 
in general, see Moyer, Foster, Thomas, Stodola 
and other works on Steam Turbines, also Pea- 
body's "Thermodynamics." Calculations of 
stages, nozzles, etc., are much facilitated by the use of Peabody's "Steam 
Tables" and Marks and Davis's "Steam Tables and Diagrams." 
Comparison of Commercial Impulse and Reaction Turbines. (Moyer.) 




Impulse. 

1. Few stages. 

2. Expansion in nozzles. 

3. Large drop in pressure in a 

stage. 

4. Initial steam velocities 1000 to 

4000 ft. per sec. 

5. Blade velocities 400 to 1200 ft. 

per sec 

6. Best efficiency when the blade 

velocity is nearly half the ini- 
tial velocity of steam. 



Reaction. 

Many stages. 

No nozzles. 

Small drop in pressure in a 

stage. 
All steam velocities low, 300 to 

600 ft. per sec. 
Blade velocities 150 to 400 ft. 

per sec. 
Best efficiency when the blade 

velocity is nearly equal to 

the highest velocity of the 

steam. 



Loss due to Windage (or friction of a turbine wheel rotating in steam). 
— Moyer gives for the friction of a plain disk without blades, F w , and of 
one row of blades without the disk, F b , in horse-power: 

F w = 0.08 d 2 (m/100) 2 - s w + (1 + 0.00065 D) 2 , 
F b = 0.3 d 7.i- c (m/100)2- 8 w-h (1 + 0.00065 D) 2 , 
in which d ■= diam. of disk to inner edge of blade, in feet; u = peripheral 
velocity of disk, in ft. per sec: w = density of dry saturated steam at 
the pressure surrounding the disk, in lbs. per cu. ft., and D = super- 
heat in degrees F. The sum of F w and F b is the friction of the di^k and 
blades. For moist steam the term 1 + 0.00065 D is to be omitted, and 
the expression multiplied by a coefficient c, whose value is approxi- 
mately as follows: 



ROTARY STEAM-ENGINES STEAM TURBINES. 1067 



Per cent mois- 
ture in steam 2 4 6 8 10 12 16 20 24 
Coefficient c. . . 1.01 1.05 1.10 1.16 1.25 1.37 1.65 2.00 2.44 
At high rotative speeds the rotation loss of a non-condensing turbine 
with wheels revolving in steam at atmospheric pressure is quite large, 
and in small turbines it may be as much as 20% of the total output. 
The loss ^decreases rapidly with increasing vacuum. In a turbine with 
more than one stage part of the friction loss of rotation is converted into 
heat which in the next stage is converted into kinetic energy, thus partly 
compensating for the loss. 

Efficiency of the Machine. — The maximum possible thermodynamic 
efficiency of a steam turbine, as of any other steam engine, is expressed 
by the ratio which the available energy between two temperatures bears 
to the total heat, measured above absolute zero, of the steam at the 
higher temperature. In the temperature-entropy diagram Fig. 167 it is 
represented by the ratio of the area BCDF to OACDG. Of this avail- 
able energy, from 50 to 75 and possibly 80 per cent is obtainable at the 
shaft of turbines of different sizes and designs. As with steam engines, 
the highest mechanical and thermal efficiencies are reached only with 
large sizes and the most expensive designs. The several losses which 
tend to reduce the efficiency of turbines below the theoretical maximum 
are: 1, residual velocity, or the kinetic energy due to the velocity of the 
steam escaping from the turbine; 2, friction and imperfect expansion 
in the nozzles; 3, windage, or friction due to rotation of the wheel in 
steam; 4, friction of the steam traveling through the blades; 5, shocks, 
impacts, eddies, etc., due to imperfect shape or roughness of blades; 6, 
leakage around the ends of the blades or through clearance spaces; 7, shaft 
friction; 8, radiation. The sum of all these losses amounts to about 
25% of the available energy in the largest and best designs and to 50% 
or more in small sizes or poor designs. 

Steam Consumption of Turbines. — The steam consumption of any 
steam turbine is so greatly influenced by the conditions of pressure, 
moisture or superheat, and vacuum, that it is necessary to know the effect 
of these conditions on any turbines whose performances are to be com- 
pared with each other or with a given standard. Manufacturers usually 
furnish with their guarantees of performance under standard conditions 
of pressure, superheat and vacuum, a statement or set of curves showing 
the amount that the steam consumption per K.W.-hour will be increased 
or diminished by stated variations from these standard conditions. 
When a test of steam consumption is made under any conditions varying 
from the standard, the results should be corrected in order to compare 
them with other tests. Moyer gives the following example of applying 
corrections to a pair of tests made in 1907, to reduce them both to a steam 
pressure of 179 lbs. gauge, 28.5 ins. vacuum, and 100° F. superheat. 



7500-K.W. 

Westing- 

house- 
Parsons. 



Correc- 
tions, 
per cent. 



9000-K.W. 

Curtis, 



Correc- 
tions, 
per cent. 



Average steam pressure 

Average vacuum, ins., referred 

to 30-in. barometer 

Average superheat, deg. F 

Average load on generator,K.W. 
Steam cons., lbs.. per K.W.-hr. . 

Net correction, per cent 

Corr. st. cons., lbs. per K.W.-hr. 



177.5 

27.3 

95.7 

9830.5 

15.15 



-3.36 
-0.29 



179 

29.55 
116 
8070 
13.0 



h 12.39 
h 1.28 



14.57 



14.77 



For the 7500-K.W. turbine, the following corrections given by the manu- 
facturer were used: pressure, 0.1% for each pound; vacuum. 2.8% fo r 
each inch; superheat, 7% for each 100° F. For the 9000-K.W. turbine, 
the following corrections were used: superheat, 8% for 100° F.; vacuum, 
8% for each inch. 

The results as corrected show that the two turbines would give practi- 
cally the same economy if tested under uniform conditions. The results 



1068 



THE STEAM-ENGINE. 



are equivalent respectively to 9.58 and 9.72 lbs. per I.H.P.-hour, assum- 
ing 97% generator efficiency and 91% mechanical efficiency of a steam 
engine. 

The proper correction for moisture in a steam turbine test is stated to 
be a little more than twice the percentage of moisture. There is a large 
increase in the disk and blade rotation losses when wet steam is used. 

The gain in economy per inch of vacuum at different vacuums is given 
as follows in Mech. Engr., Feb. 24, 1906. 



Inches of Vacuum. 


28 


27 


26 


25 


Curtis, per cent gain per inch of vacuum. . 
Parsons, per cent gain per inch of vacuum 
Westinghouse-Parsons, per cent gain per 


5.1 
5.0 

3.14 
5.2 


4.8 
4.0 

3.05 
4.4 


4.6 
3.5 

2.95 
3.7 


4.2 
3.0 

2.87 


Theoretical per cent gain per inch of vac. 


3.0 



The following results of tests of turbines of different makes are selected 
from a series of tables in Moyer's "Steam Turbines". 



lis 


1^ 


MS 




a 


0) 1 


$£ 




£ 

MS 
3 £ 




i ■ 

ji 




s* 


8* 


o^ 


£*-* 


o3 "' 

!> 


&* 


XT 


<§« 


O^ 


£*-* 


g«* 


2000 ( 

c. | 


555 


155 


204 


28.5 


18.09 


300 ( 
W.-P.j 


233 


145 


4.1 


28.0 


15.99 


1067 


170 


120 


28.4 


16.31 


461 


145 


4.8 


28.0 


13.99 


2024 


166 


207 


28.5 


15.02 


688 


140 


7.0 


27.2 


15.73 


1 


5374 


182 


133 


29.4 


13.15 


( 


383 


153 


2 


28.2 


14.15 


9000 1 


8070 


179 


116 


29.4 


13.00 


1 


756 


149 


1 


27.8 


13.28 


C, ) 


10186 


176 


147 


29.5 


12.90 


500 J 


1122 


149 


5 


26.5 


14.32 


1 


13900 


198 


140 


29.3 


13.60 


w.-p.i 


386 


148 


3 


0.8 


24.94 


1500 ( 


530 
1071 


145 
131 


110 
124 


28.9 

28.3 


21.58 
18.24 


I 


767 
1144 


14; 

126 


3 
11 


0.8 
0.8 


22.10 
24.36 


1585 


128 


125 


27.5 


17.60 


1000 ( 
W.-P.J 


752 


151 





27.5 


14.77 


300/ 
P. i 


303 
297 


158 
161 






26.6 



23.15 
34.20 


1503 
2253 


147 
145 






27.0 
25.2 


13.61 
15.29 


f 


194 


171 


47 


27 7 


31 97 


3000 t 


2295 


152 


102 


26.2 


12.36 


1000 I 


425 


144 


21 


27.6 


24.91 


W.-P.I 


4410 


144 


87 


26.2 


11.85 


R. ) 


871 


166 


11 


23.6 


24.61 


300 ( 

D I 


196 


198 


16 


27.4 


15.62 




1024 


164 


10 


25.0 


21.98 


298 


197 


64 


27.4 


14.35 














352 


199 


84 


27.2 


13.94 



C, Curtis; P., Parsons; W.-P., Westinghouse-Parsons; R., Rateau; 
D., De Laval. Note that the figures of steam consumption in the first 
half of the table are in lbs. per K.W.-hour ; in second half, in lbs. per Brake 
H.P.-hour. 

A test of a Westinghouse double-flow turbine at the Williamsburg 
power station, Brooklyn N. Y., gave the following results (Eng. News, 
Dec. 30, 1909): Speed, 750 r.p.m.; Steam pressure at throttle, 203.4 lbs.; 
Superheat, 80.1° F.; Vacuum, 28.6 ins.; Load, 13,384 K.W.; Steam per 
K.W.-hour, 14.4 lbs.; Efficiency of generator, 98%; Windage, 2.0%; 
Equivalent B.H.P., 18,620; Steam per B. H.P.-hour, 10.3 lbs. 

The Largest Steam Turbine, 1909. (Eng. News, Dec. 30.) — A 
Westinghouse combination double-flow turbine is about to be tested 
which is capable of developing 22,000 H.P. with 1.75 lbs. steam pressure 
and 28 ins. vacuum, and it is estimated that the steam consumption will 
be about 10 lbs. per B. H.P.-hour. The principal dimensions are: length 
over all. 19 ft. 8 ins.; height, 9 ft.; width, 9 ft.; weight, 110,000 lbs.; weight 
per H.P. developed, 5 lbs.; speed, 1800 r.p.m. 



ROTARY STEAM-ENGINES — STEAM TURBINES. 1069 



Steam Consumption of Small Steam Turbines. — Small turbines, 
from 5 to 200 H.P., are extensively used for purposes where high speed of 
rotation is not an objection, such as for driving electric generators, cen- 
trifugal fans, etc., and where economy of fuel is not as important as 
saving of space, convenience of operation, etc. The steam consump- 
tion of these turbines varies as greatly as does that of small high-speed 
steam-engines, according to the design, speed, etc. A paper by Geo. A. 
Orrok in Trans. A. S. M. E., 1909, discusses the details of several makes 
of machines. From a curve presented by R. H. Rice in discussion of 
this paper the following figures are taken showing the steam consumption 
in lbs. per B.H.P.-hour of different makes of impulse turbines. 



Type. 



Rated H.P 
Water f1 '" 



lated H.F 

%1&SS:::: 

™ te i Full load.. 
at 11 1/4 load. . . 



Sturte- 
vant. 



20 
72 
65 
61 
58 



Terry. 



50 
59 



46 
44 



100 
58 
48 
43 
40 



200 
55 
47 
42 
39 



150 
52 
44 
41 
39 



50 
44 
36 
33 
31 



200 
32 
30 
29 
28 



Dry steam, 150 lbs. pressure; atmospheric exhaust. 

Mr. Orrok shows that the steam consumption of these turbines largely 
depends on their peripheral speed. From a set of curves plotted with 
speed as the base it appears that the steam consumption per B.H.P.-hour 
ranges about as follows: 
Peripheral speed, ft. 

permin 5,000 10,000 15,000 20,000 25,000 

Steam per B.H.P.-hour 45 to 70 38 to 60 31 to 52 29 to 45 29 to 40 

Low-Pressure Steam Turbines. — Turbines designed to utilize the ex- 
haust steam from reciprocating engines are used to some extent. For 
steam at or below atmospheric pressure the turbine has a great advan- 
tage over reciprocating engines in its ability to expand the steam down 
to the vacuum pressure, while a reciprocating condensing engine generally 
does not expand below 8 or 10 lbs. absolute pressure. In order to ex- 
pand to lower pressures the low-pressure cylinder would have to be 
inordinately large, and therefore costly, and the increased loss from 
cylinder condensation and radiation would more than counterbalance 
the gain due to greater expansion. 

Mr. Parsons (Proc. Inst. Nav. Arch., 1908) gives the following figures 
showing that the theoretical economy of the combination of a recipro- 
cating engine and an exhaust steam turbine is about the same whether 
the turbine receives its steam at atmospheric pressure or at 7 lbs. abso- 
lute, the initial steam pressure in the engine being 200 lbs. absolute and 
the vacuum 28 ins. 

Back pressure of engines, lbs. abs 

Initial pressure, turbine, lbs. abs 

Theoretical B.T.U. ( £ Jjgg? • — 

utilized per lb of steam \ ^1 

The following figures, by the General Electric Co., show the percentage 
over the output of a condensing reciprocating engine that may be made 
by installing a low-pressure turbine between the engine and the con- 
denser, the vacuum being 28 1/2 ins. 
Inches vacuum at admission 

valve 4 8 12 16 20 24 

Per cent of work gained .. . 26.1 26.5 26.8 26.3 25.3 23.6 20 

It appears that a well-designed reciprocating compound engine work- 
ing down to about atmospheric pressure is a more efficient machine than 
a turbine with the same terminal pressure, and that between the atmos- 
phere and the condenser pressure the turbine is far more economical; 
therefore a combination of an engine and a turbine can be designed 
which will give higher economy than either an engine or a turbine work- 
ing through the whole range of pressure, 



16 


13V2 8 


15 


121/2 7 


178 


189 218 


142 


131 100 


320 


320 318 



1070 THE STEAM-ENGINE. 

When engines are run intermittently, such as rolling-mill and hoisting 
engines, their exhaust steam may be made to run low-pressure turbines 
by passing it first into a heat accumulator, or thermal storage system, 
where it gives up its heat to water, the latter furnishing steam continu- 
ously to the turbines. (See Thermal Storage, pages 897 and 987.) 

The following results of tests of a Westinghouse low-pressure turbine 
are reported by Francis Hodgkinson. 

Steam press., 

lb. abs.. . . 17.4 12.4 11.8 7.7 5.2 11.6 8.7 6.1 4.5 
Vacuum,ins. 26.0 26.0 27.0 27.0 27.0 27.8 28.0 27.9 28.0 
Brake H.P. . 920 472 592 321 102 586 458 234 114 
Steam per 

B.H.P.-hr., 

lbs 27.9 37.1 29.9 37.3 64.4 28.0 30.4 38.6 54.8 

Tests of a 1000-K.W. low-pressure double-flow Westinghouse turbine 
are reported to have given results as follows. (Approximate figures, 
from a curve.) 

Load, Brake H.P 200 400 600 800 1000 1200 1500 2000 

Pressure at inlet, lbs. 

abs 4.1 5.1 6.1 7.2 8.3 9.4 11.0 13.5 

Steam per ) 2 7i/ 2 in vac. 75 47.5 38 33 30 28 26.5 24.5 

hour lbs ) 28 in - vac - 62 42 33 29 27 25.5 24.5 22.5 

The total steam consumption per hour followed the Willans law, 
being directly proportional to the power after adding a constant for 
load, viz.: for 271/2-in. vacuum the total steam consumption per hour 
was 12,000 lbs. + 18 X H.P., and for 28-in. vacuum, 9000 lbs. + 18 X 
H.P. (approx.). 

The guaranteed steam consumption of a 7000-K.W. Rateau-Smoot 
low-pressure turbine generator is given in a curve by R. C. Smoot {Power, 
June 22, 1909), from which the following figures are taken. The admis- 
sion pressure is taken at 16 lbs. absolute and the vacuum 281/2 ins. 

K.W. output 1500 2000 3000 4000 5000 6000 7000 

Steam per K.W.-hr., lb.. .. 40 37 32.5 29.5 27.6 26.2 25.7 
Over-all efficiency, % 43 47 54 60 65 68 70 

The performance of a combined plant of several reciprocating 2000- 
K.W. engines and a 7000-K.W. low-pressure turbine is estimated as fol- 
lows, the engines expanding the steam from 215 to 16 lbs. absolute, and 
the turbines from 16 lbs. to 0.75 lb., the vacuum being 28.5 ins. with 
the barometer at 30 ins. 

Engine. Turbine. 

Theoretical steam per K.W.-hour, lbs 18 17.8 

Steam per K.W.-hr. at switchboard, lbs 27 . 7 26 . 6 

Combined efficiency of engine and dynamo, per cent ... 65 67 

Steam per K.W.-hour for combined plant = 1 -^ (1/27.7 + 1/26.6) = 

13.6 lbs. 

The combined efficiency is 66%, representing the ratio of the energy 
at the switchboard to the available energy of the steam delivered to the 
engine and expanded down to the condenser pressure, after allowing for 
all losses in engine, turbine, and dynamo. 

Very little difference is made in the plant efficiency if the intermediate 
pressure is taken anywhere from 3 or 4 lbs. below atmosphere to 15 or 
20 lbs. above. 

M. B. Carroll {Gen. Elec. Rev., 1909) gives an estimate of the steam 
consumption of a combined unit of a 1000-K.W. engine and a low-pres- 
sure turbine. The engine, non-condensing, will develop 1000 H.P., 
with 32,000 lbs. of steam per hour. Allowing 8% for moisture in the 
exhaust, 29,440 lbs. of dry steam will be available for the turbine, which 
at 33 lbs. per K.W.-hour will develop 893 K.W., making a total output of 
1893 K.W. for 32,000 lbs. steam, or 16.9 lbs. per K.W.-hour. The engine 
alone as a condensing engine will develop 1320 K.W. at 24.2 lbs. per K.W.- 
hour. The combined unit therefore develops 573 K.W., or 43.5% more 
than the condensing , engine using the same amount of steam. The 
maximum capacity of the engine, non-condensing, is 1265 K.W., and 
condensing, 1470 K.W., and of the combined unit 2500 K.W. 



INTERNAL-COMBUSTION ENGINES. 1071 

Tests of a 15,000 K.W. Steam-Engine-Turbine Unit are reported 
by H. G. Stott and R. J. S. Pigott in Jour. A.S.M.E., Mar., 1910. The 
steam-engine is one of the 7500 K.W. Manhattan type engines at the 59th 
St. station of the Rapid Transit Co., New York, with two 42-in. horizontal 
h.p. and two 86-in. vertical l.p. cylinders, and the turbine, also 7500 K.W:, 
is of the vertical three-stage impulse type. The principal results are sum- 
marized as follows: An increase of 100% in the maximum capacity and 
146% in the economical capacity of the plant; a saving of about 85% of 
the condensed steam for return to the boilers [it was previously wasted]; 
an average improvement in economy of 13% over the best high-pressure 
turbine results, and of 2.5% (between 7500 and 15,000 K.W.) over the re- 
sults obtained by the engine alone ; an average thermal efficiency between 
6500 and 15,500 K.W. of 20.6%. [This efficiency is not quite equal to 
that reached by triple-expansion pumping engines. See page 774.] 

Reduction Gear for Steam Turbines. — Double spiral reduction gears, 
usually of a ratio of 1 to 10, are used with the DeLaval turbine to obtain 
a velocity of rotation suitable for dynamos, centrifugal pumps, etc. G. W. 
Melville and J. H. McAlpine have designed a similar gear, with the pinion 
carried in a floating frame supported at a single point between the bear- 
ings to equalize the strain on the gear teeth, for reducing the speed of 
large horizontal turbines to suitable speeds for marine propellers. A 
6000 H.P. gear with reduction from 1500 to 300 r.p.m. has been tested, 
giving an efficiency of 98.5% (Eng'g, Sept. 17; Eng. News, Oct. 21 and Dec. 
30, 1909). 

NAPHTHA ENGINES. —HOT-AIR ENGINES. 

Naphtha engines are in use to some extent in small yachts and 
launches. The naphtha is vaporized in a boiler, and the vapor is used ex- 
pansively in the engine cylinder, as steam is used ; it is then condensed and 
returned to the boiler. A portion of the naphtha vapor is used for fuel un- 
der the boiler. According to the circular of the builders, the Gas Engine 
and Power Co. of New York, a 2-H.P. engine requires from 3 to 4 quarts! of 
naphtha per hour, and a 4-H.P. engine from 4 to 6 quarts. The chief 
advantages of the naphtha-engine and boiler for launches are the saving 
of weight and the quickness of operation. A 2-H.P. engine weighs 200 lbs., 
a 4-H.P. 300 lbs. It takes only about two minutes to get under headway. 
(Modern Mechanism, p. 270.) 

Hot-air (or Caloric) Engines. — Hot-air engines are used to some 
extent, but their bulk is enormous compared with their effective power. 
For an account of the largest hot-air engine ever built (a total failure) see 
Church's Life of Ericsson. For theoretical investigation, see Rankin's 
Steam-engine and Roentgen's Thermodynamics. For description of con- 
structions, see Appleton's Cyc. of Mechanics and Modern Mechanism, and 
Babcock on Substitutes for Steam, Trans. A. S. M. E., vii, p. 693. 

Test of a Hot-air Engine (Robinson). — A vertical double-cylinder 
(Caloric Engine Co.'s) 12 nominal H.P. engine gave 20.19 I. H.P. in the 
working cylinder and 11.38 I. H.P. in the pump, leaving 8.81 net I.H.P.; 
while the effective brake H.P. was 5.9, giving a mechanical efficiency of 
67%. Consumption of coke, 3.7 lbs. per brake H.P. per hour. Mean 
pressure on pistons 15.37 lbs. per square inch, and in pumps 15.9 lbs., the 
area of working cylinders being twice that of the pumps. The hot air 
supplied was about 1160° F. and that rejected at end of stroke about 
890° F. 

INTERNAL-COMBUSTION ENGINES. 

References. — For theory of the internal-combustion engine, see paper 
by Dugald Clerk, Proc. Inst. C. E., 1882, vol. lxix; and Van Nostrand's 
Science Series, No. 62. See also Wood's Thermodynamics. Standard 
works on gas-engines are " A Text-book on Gas, Air, and Oil Engines," 
by Bryan Donkin; " The Gas and Oil Engine," by Dugald Clerk; " In- 
ternal Combustion Engines," by Carpenter and Diederichs; "Gas Engine 
Design," by C. E. Lucke: " Gas and Petroleum Engines," by W. Robin- 
son; "The Modern Gas Engine and the Gas Producer," by A. M. Levin. 
For practical operation of gas and oil engines, see "The Gas Engine," 
by F. R. Jones, and "The Gas Engine Handbook," by E. W. Roberts. 



1072 INTERNAL-COMBUSTION ENGINES. 

For descriptions of large gas-engines using blast furnace gas see papers 
in Proc. Iron and Steel Inst, 1906, and Trans. A. I. M. E., 1906. Many- 
papers on gas-engines are in Trans. A.S.M.E., 1905 to 1909. 

An Internal-combustion Engine is an engine in which combustible 
gas, vapor, or oil is burned in a cylinder, generating a high temperature 
and high pressure in the gases of combustion, which expand behind a 
piston, diiving it forward. ( Rotary gas-engines or gas turbines, are still, 
1910, in the experimental stage.) 

Four-cycle and Two-cycle Gas-Engines. — In the ordinary type of 
single-cylinder gas-engine (for example the Otto) known as a four-cycle 
engine, one ignition of gas takes place in one end of the cylinder every 
two revolutions of the fly-wheel, or every two double strokes. The fol- 
lowing sequence of operations takes place during four consecutive strokes: 
(a) inspiration of a mixture of gas and air during an entire stroke; (b) 
compression during the second (return) stroke; (c) ignition at or near the 
dead-point, and expansion during the third stroke; (d) expulsion of the 
burned gas during the fourth (return) stroke. Beau de Rochas in 1862 
laid down the law that there are four conditions necessary to realize the 
best results from the elastic force of gas: (1) The cylinders should have 
the greatest capacity with the smallest circumferential surface; (2) the 
speed should be as high as possible; (3) the cut-off should be as early as 
possible; (4) the initial pressure should be as high as possible. 

(Strictly speaking four-cycle should be called four-stroke-cycle, but the 
term four-cycle is generally used in the trade.) 

The two great sources of waste in gas-engines are: 1. The high tempera- 
ture of the rejected products of combustion; 2. Loss of heat through the 
cylinder walls to the water-jacket. As the temperature of the water- 
jacket is increased the efficiency of the engine becomes higher. 

Fig. 169 is an indicator diagram of a four-cycle gas-engine. AB, the 
lower line, shows the admission of the mixture, at a pressure slightly 
below the atmosphere on account of the re- 
sistance of the inlet valve, .BC is the com- 
pression into the clearance space, ignition 
taking place at C and combustion with 
increase of pressure continuing from C to D. 
The gradual termination of the combustion 
is shown by the rounded corner at D. DE 
is the expansion line, EF the line of pressure 
drop as the exhaust valve opens, and FA the 
line of expulsion of the burned gases, the 
= — ■ £ ' pressure being slightly above the atmos- 
A t?^„ i<;q B phere on account of the resistance of the 

* IG - lby - exhaust valve. 

In a two-cycle single-acting engine an explosion takes place with every 
revolution, or with each forward stroke of the piston. Referring to the 
diagram Fig. 169 and beginning at E, when the exhaust port begins to 
open to allow the burned gases to escape, the pressure drops rapidly to F. 
Before the end of the stroke is reached an inlet port opens, admitting 
a mixture of gas and air from a reservoir in which it has been compressed. 
This mixture being under pressure assists in driving the burned gases 
out through the exhaust port. The inlet port and the exhaust port close 
early in the return stroke, and during the remainder of the stroke BC 
the mixture, which may include some of the burned gas, is compressed and 
the ignition takes place at C, as in the four-cycle engine. 

In one form of the two-cycle engine only compressed air is admitted 
while the exhaust port is open, the fuel gas being admitted under pressure 
after the exhaust port is closed. By this means a greater proportion of 
the burned gases are swept out of the cylinder. This operation is known 
as " scavenging." '■ _ . 

Theoretical Pressures and Temperatures in Gas-Engines. — Referring 
to Fig. 169, let P s be the absolute pressure at B, the end of the suction 
stroke, P c the pressure at C, the end of the compression stroke; P^the 
maximum pressure at Z>, when the gases of combustion are at their 
highest temperature; P e the pressure at E, when the exhaust valve begins 
to open. For the hypothetical case of a cylinder with walls incapable of 
absorbing or conducting heat, and of perfect and instantaneous combustion 




INTERNAL COMBUSTION ENGINES. 1073 

or explosion of the fuel, an ideal diagram might be constructed which 
would have the following characteristics. In a four-cycle engine receiv- 
ing a charge of air and gas at atmospheric pressure and temperature, 
the pressure at B, or P s , would be 14.7 lbs. per sq. in. absolute, and the 
temperature say 62° F., or 522° absolute. The pressure at C, or P c , would 
depend on the ratio V x -h F 2 , V x being the original volume of the mixture 
in the cylinder before compression, or the piston displacement plus the 
volume of the clearance space, and 7 2 the volume after compression, or 
1 the clearance volume, and its value would be P c = P s ( VJ V2) . The 
1 absolute temperature at the end of compression would be T c = 522 X 
j ( Vi/Vt) 1 ]^, or it may be found from the formula P S V S + T s = P c V p + T c , 
I the subscripts 5 and c referring respectively to conditions at the beginning 
and end of compression. The compression would be adiabatic, and the 
' value of the exponent n would be about the value for air, or 1.406. ine 
j work done in compressing the mixture would be calculated by the formula 
! for compressed air (see page 607). The theoretical rise of tempera- 
j ture at the end of the explosion, T x , above the temperature at the end of 
I the compression T c may be found from the formula (T x - T c ) C v = H, 
\ in which U is the amount of heat in British thermal units generated by 
\ the combustion of the fuel in 1 lb. of the mixture, and C v the mean specific 
heat, at constant volume, of the gases of combustion between the tem- 
peratures T x and T c . Having obtained the temperature, the correspond- 
ing pressure P x may be found from the formula P x = P C X (T x /T£ n ~ I . 
In like manner the pressure and temperature at the end of expansion, 
P e and T e , and the work done during expansion, may be calculated by 
the formula for adiabatic expansion of air. 

-The ideal diagram of the adiabatic compression of air, instantaneous 
heating, and adiabatic expansion, differs greatly from the actual diagram 
of a gas-engine, and the pressures, temperatures, and amount of worn; 
done are different from those obtained by the method described above. 
In the first place the mixture at the beginning of the compression stroke 
is usually below atmospheric pressure, on account of the resistance 91 
the inlet" valve, in a four-cycle engine, but may be above atmospheric 
pressure in a two-cycle engine, in which the mixture is delivered from a 
receiver under pressure. Then the temperature is much higher than 
that of the atmosphere, since it is heated by the walls of the cylinder 
as it enters. The compression is not adiabatic, since heat is received 
from the walls during the first part of the stroke. If the clearance space 
is small and the pressure and temperature at the end of compression there- 
fore high, the gas may give up some heat to the walls during the latter 
part of the stroke. The explosion is not instantaneous, and during its 
continuance heat is absorbed by the cylinder walls, and therefore neither 
the temperature nor the pressure found by calculation will be actually 
reached. Poole states that the rise in temperature produced by com- 
bustion is from 0.4 to 0.7 of what it would be with instantaneous com- 
bustion and no heat loss to the cylinder walls. Finally the expansion 
is not adiabatic, as the gases of combustion, at least during the first part 
of the expanding stroke, are giving up heat to the cylinder. 

Calculation of the Power of Gas-Engines.— If the mean effective pres- 
sure in a gas-engine cylinder be obtained from an indicator diagra m - ^ 
power is found by the usual formula for steam-engines, H.P. = f^j.i; 
33,000, in which P is the mean effective pressure in lbs. per sq. in., L trie 
length of stroke in feet, A the area of the piston in square inches, and J\ 
the number of explosion strokes per minute. ... 

For purposes of design, however, the mean effective pressure_ either 
; has to-be assumed from a knowledge of that found in other engines or 
the same type and working under the same conditions as those of the 
design/or it may be calculated from the ideal air diagram and modified 
by the use of a coefficient or diagram factor depending on the kind of 
fuel used and the compression pressure. Lucke gives the following 



1074 



INTERNAL-COMBUSTION ENGINES. 



factors for four-cycle engines by which the mean effective pressure 
of a theoretical air diagram is to be multiplied to obtain the actual M.E.P. 
for the several conditions named. 



Kind of Fuel and Method of Use. 



Compres- 
sion. 
Gauge 
Pressure. 



Factor. 
Per Cent. 



Kerosene, when previously vaporized 

Kerosene, injected on a hot bulb, may be as low a, 
Casoline, used in carburetor requiring a vacuum. 

Gasoline, with but little initial vacuum 

Producer gas 

Coal gas 

Blast-furnace gas 

Natural gas 



Lb. 
45-75 



80-130 
100-160 
Av. 80 
130-180 

90-140 



30-40 
20 

25-40 
50-30 
56-40 
Av. 45 
48-30 
52-40 



Factors for two-cycle engines are about 0.8 those for four-cycle engines. 

Pressures and Temperatures at end of Compression and at Re- 
lease. — The following tables, greatly condensed from very full tables 
given by C. P. Poole, show approximately the pressures and tempera- 
tures that may be realized in practice under different conditions. Poole 
says that the value of n, the exponent in the formula for compression, 
ranges from 1.2 to 1.38, these being extreme cases; the values most 
commonly obtained are from 1.28 to 1.35. The tables for compression 
pressures and temperatures are based on n = 1.3 and 1.4, on compres- 
sion ratios or Vi/V 2 from 3 to 8, on absolute pressures in the cylinder 
before compression from 13 to 16 lbs., and on absolute temperatures 
before compression of 620° to 780° (160° to 320° F.). The release pres- 
sures and temperatures are based on values of n of 1.29 and 1.32, abso- 
lute pressures at the end of the explosion from 240 to 360 lbs. per sq. in., 
and absolute temperatures at the end of the explosion of 1800° to 3000° F. 
Compression Pressures. 



* ,£ 


n = 1.3. 


m *? 


n=1.34. 


* 5 o 
















S' B « 












B m 03 












6 * 


P s =13 


13.5 


14 


15 


16 


o p3 

o 


P s =13 


13.5 


14 


15 


16 


3.00 


54.2 


56.3 


58.4 


62.6 


66.7 


3.00 


56.7 


58.9 


61 


65.4 


69.7 


4.00 


78.8 


81.9 


84.9 


90.9 


97.0 


4.00 


83.3 


86.5 


89,7 


96.1 


102.5 


5.00 


105.4 


109.4 


113.5 


121.6 


129.7 


5.00 


112.3 


116.7 


121 


129.6 


138.3 


6.00 


133.5 


138.7 


143.8 


154.1 


164.3 


6.00 


143.4 


148.9 


154.5 


165.5 


176.5 


7.00 


163 2 


169.4 


175 7 


188.3 


200.8 


7.00 


176.3 


183.1 


189.9 


203.5 


217.0 


8.00 


194.0 


201.5 


209.0 


223.9 


238.7 


8.00 


210.9 


219.0 


227.1 243.4 


259.6 



Compression Temperatures. 



A w 






n=1.3 






s ,? 






n = 1.34. 




kg.S 

8 & 












a§.2 

1 a 










620° 


660° 


700° 


740° 


780° 


620° 


660° 


700° 


740° 


780° 


3.00 


862 


918 


973 


1029 


1084 


3.00 


901 


959 


1017 


1075 


1132 


4.00 


940 


1000 


1061 


1122 


1182 


4.00 


993 


1057 


1122 


1186 


1750 


5.00 


1C05 


1070 


1134 


1199 


1264 


5.00 


1072 


1141 


1210 


1279 


1348 


6.00 


1061 


1130 


1198 


1267 


1335 


6.00 


1140 


1214 


1287 


1361 


1434 


7.00 


1112 


1183 


1255 


1327 


1398 


7.00 


1201 


1279 


1357 


1434 


1512 


8.00 


1157 


1232 


1306 


1381 


1456 , 


8.00 


1257 


1338 


1420 


1501 


1582 



INTERNAL-COMBUSTION ENGINES. 



1075 



Absolute Pressures per Square Inch at Release. 
Corresponding to Explosion Pressures commonly obtained. 
Note: — The expansion ratios in the left-hand column are based on 
the volume behind the piston when the exhaust valve begins to open. 



« . 
O » 

"to *- 


n e =1.29. 


a 
o k 


n e =1.32. 










G O 








ft a 




Value of P x 




«3-£ 




Value of P x 




fl« 


240 


270 300 330 


360 




240 


270 300 330 


360 


3.00 


58.2 


65.4 


72.7 


80.0 


87.2 


3.00 


56.3 


63.3 


70.4 


77.4 


84.4 


4.00 


40.1 


45.2 


50.2 


55.2 


60.2 


4.00 


38.5 


43.3 


48.1 


52.9 


57.8 


5.00 


30.1 


33.9 


37.6 


41.4 


45.1 


5.00 


28.7 


32.3 


35.8 


39.4 


43.0 


6.00 


23.8 


26.8 


29.7 


32.7 


35.7 


6.00 


22.5 


25.4 


28.2 


31.0 


33.8 


7,00 


19.5 


21.9 


24.4 


26.8 


29.2 


7.00 


18.4 


20.7 


23.0 


25.3 


27.6 


8.00 


16.4 


18.5 


20.5 


22.6 


24.6 


8.00 


15.4 


17.3 


19.3 


21.2 


23.1 



Absolute Temperatures at Release. 
Corresponding to Explosion Temperatures commonly obtained. 



a 

.2 « 


n e =1.29. 


a 
S.2 


n e =1.32. 


is 




Value of T x 






Value of T x 




1800 


2100 2400 2700 


3000 


1800 


2100 2400 2700 


3000 


3.00 


1309 


1527 


1745 


1963 


2182 


3.00 


1266 


1478 


1689 


1900 


2111 


4.00 


1204 


1405 


1606 


1806 


2007 


4.00 


1155 


1348 


1540 


1733 


1925 


5.00 


1129 


1317 


1505 


1693 


1881 


5.00 


1075 


1255 


1434 


1613 


1792 


6.00 


1070 


1249 


1427 


1606 


1784 


6.00 


1015 


1184 


1353 


1522 


1691 


7.00 


1024 


1194 


1365 


1536 


1706 


7.00 


966 


1127 


1288 


1449 


1610 


8.00 


985 


1149 


1313 


1477 


1641 


8.00 


925 


1079 


1234 


1388 


1542 



Pressures and Temperatures after Combustion. — According to 
Poole, the maximum temperature after combustion may be as high as 
3000° absolute, F., and the maximum pressure as high as 400 lbs. per 
sq. in. absolute; these are high figures, however, the more usual figures 
being about 2300° and 250 lbs. Poole gives the following figures for 
the average rise in pressure, above the pressure at the end of compres- 
sion, produced by combustion of different fuels, with different ratios of 
compression. 

Average Pressure Rise in lbs. per sq. in. Produced by 
Combustion. 



.2 


* 






w 6 


* 

^5 


_d 


OP 


.2 


g P 


Oj 

ft 

B 


So 


6 
a 


o 

8 


d 

a 


OH 


03 

ft 
ft 


T30 


03 
ft 

s 


r 3 §H 

§ 2 


o 




03 






^2 








O 


K 


o 


M 


o 


£ 


o 


PM 


o 


3 


4.0 


146 


195 


168 


5.0 


192 


6.0 


225 


7.0 


211 


4.2 


156 


208 


179 


5.2 


202 


6.2 


234 


7.2 


218 


4.4 


166 


221 


190 


5.4 


211 


6.4 


243 


7.4 


225 


4.6 


175 


234 


202 


5.6 


221 


6.6 


252 


7.6 


232 


4.8 


185 


247 


213 


5.8 


230 


6.8 


261 


7.8 


239 


5.0 


195 


260 


224 


6.0 


240 


7.0 


270 


8.0 


246 



* Per cubic foot measured at 32° F. 
The following figures are given by Poole as a rough approximate 
guide to the mean effective pressures in lbs. per sq. in. obtained with 



1076 



INTERNAL-COMBUSTION ENGINES. 



different fuels and different compression pressures in a four-cycle engine. 
In a two-cycle engine the mean effective pressure of the pump diagram 
should be subtracted. The delivery pressure is usually from 4 to 8 lbs. 
per sq. in. above the atmosphere, and the corresponding mean effective 
pressure of the pump about 3.8 to 7. 

Probable Mean Effective Pressure. 



Suction Anthracite Producer Gas. 


Mond Producer Gas. 


Engine 
H.P. 


Compression Pressure, 
abs. lbs. per sq. in. 


Engine 
H.P. 


Compression Pressure. 




100 


115 


130 


145 


160 


100 


115 


130 


145 
65 


160 


10 


55 


60 


65 






10 




65 


65 




25 


60 


65 


70 


75 




25 


60 


65 


65 


70 


75 


50 


65 


70 


75 


80 


80 


50 


65 


70 


70 


75 


80 


100 


70 


75 


80 


85 


85 


100 


65 


70 


75 


80 


85 


250 


75 


80 


85 


90 


90 


250 


70 


75 


80 


85 


90 


500 


80 


85 


90 


90 


90 


500 


75 


80 


85 


90 


90 



Natural and Illuminating Gases. 



Engine 
H.P. 


Compression Pressure. 


Engine 
H.P. 


Compression Pressures. 


65 


75 


85 


100 


115 


75 


85 


100 


115 


130 


10 
25 
50 


60 
65 
70 


65 
70 
75 


70 
75 
80 


75 
80 
90 


85" 
90 


100 
250 
500 


80 

85 


85 
90 
95 


90 
95 
100 


95 
100 
105 


100 
105 
110 


Kerosene Spray. 


Gasoline Vapor. 


Engine 
H.P. 


Compression Pressures. 


Engine 
H.P. 


Compression Pressures. 


65 


75 


85 


100 


M5 


65 


75 


85 


100 




5 

10 
25 
50 


50 
55 
60 
65 


55 
60 
65 
70 


60 
65 
70 
75 


65 
70 
75 
80 


70 
75 

80 
85 


5 
10 
25 
50 


70 
75 
80 
85 


75 
80 
85 
90 


80 
85 
90 
95 


85 
90 
90 
95 





Sizes of Large Gas Engines. — From a table of sizes of the Nurnberg 

gas engine, as built by the Allis-Chalmers Co., the following figures are 
taken. These figures relate to two-cylinder tandem double-acting engines. 

Diam. cyl., ins 18 20 21 22 24 24 26 28 30 32 

Stroke cyl., ins 24 24 30 30 30 36 36 36 42 42 

Revs, per min 150 150 125 125 125 115 115 115 100 100 

Piston speed, ft. per 

min 600 600 625 625 625 690 690 690 700 700 

Rated B.H.P 260 320 370 405 490 545 630 740 855 985 

Factor of C 0.8 0.8 0.84 0.84 0.85 0.95 0.93 0.94 0.95 0.96 

Diam., ins 34 36 38 40 42 44 46 48 50 52 

Stroke, ins 42 48 48 48 54 54 54 60 60 62 

Revs, per min 100 92 92 92 86 86 86 78 78 78 

Piston speed 700 736 736 736 774 774 774 780 780 780. 

Rated B.H.P 1105 1300 1460 1630 1875 2080 2280 2475 2720 2950 

Factor of C 0.96 1 1.01 1.02 1.06 1.07 1.08 1.07 1.09 1.09 



INTERNAL-COMBUSTION ENGINES. 



1077 



The figures "factor C" are the values of C in the equation B.H.P = 
C X D 2 , in which D = diam. of cylinder in ins. For twin-cylinder double- 
acting engines, multiply the B.H.P. and the value of C by 0.95; for twin- 
tandem double-acting engines, multiply by 2; for two-cylinder single- 
acting, or for single-cylinder double-acting engines, divide by 2; for 
single-acting single-cylinders, divide by 4. The figures for B.H.P. corre- 
spond to mean effective pressures of about 66, 68, and 70 lbs. per sq. in. 
for 20, 40, and 50 in. cylinders respectively if we assume 0.85 as the me- 
chanical efficiency, or the ratio B.H.P. -*■ I.H.P. 

Engine Constants for Gas Engines. — The following constants for 
figuring the brake H.P. of gas engines are given in Power, Dec. 7, 1909. 
They refer to four-stroke cycle single-cylinder engines, sinele acting; for 
double-acting engines multiply by 2. Producer gas, 0.000056. Illumi- 
nating gas, 0.000065. Natural gas, 0.00007. Constant X diam. 2 X stroke 
in ins. X revs, per min. = probable B.H.P. A deduction should be made 
for the space occupied by the piston rods, about 5% for small engines up 
to 10% for very large engines. 

Rated Capacity of Automobile Engines. — The standard formula for 
the American Licensed Automobile Manufacturers Association (called 
the A. L. A. M. formula) for approximate rating of gasoline engines 
used in automobiles is Brake H.P. = Diam. 2 X No. of cylinders -*- 2.5. 
It is based on an assumed piston speed of 1000 ft. per min. The following 
ratings are derived from the formula: 

Bore, ins 2V2 

Bore, mm 64 

H. P., 1 cylinder... . 2 1/2 
H.P., 2 cylinders. . . 5 
H.P., 4 " ... 10 
H.P., 6 " ... 15 

Approximate Estimate of the Horse-power of a Gas Engine. — 
From the formula I.H.P. = PLAN -J- 33,000, in which P= mean effective 
pressure in lbs. per sq. in., L = length of stroke in ft., A = area of piston 
in sq. ins., iV = No. of explosion strokes per min., we have I.H.P. = Pd 2 S + 
42,017, in which d = diam. of piston, and <S = piston speed in ft. per min., 
for an engine in which there are two explosion strokes in each revolution, 
as in a 4-cycle double-acting, 2-cylinder engine, or a 2-cycle, 2-cylinder, 
single-acting engine. If the mechanical efficiency is taken at 0.84, then 
the brake horse power B.H.P. = Pd 2 S ■*- 50,000. Under average con- 
ditions the product of P and S is in the neighborhood of 50,000, and in 
that case B.H.P. — d 2 . 

Generally, B.H.P. = CX d 2 , in which C is a coefficient having values as 
below: 



3 


31/2 


4 


41/2 


5 


5V2 


6 


76 


89 


102 


114 


127 


140 


154 


3.6 


4.9 


6.4 


8.1 


10 


12.1 


14.4 


7.2 


9.8 


12.8 


16.2 


20 


24.2 


28.8 


14.4 


19.6 


25.6 


32.4 


40 


48.4 


57.6 


21.6 


29.4 


38.4 


48.6 


60 


72.6 


86.4 





Piston speed, ft. per minute. 


M.E.P. 






lbs. per 
sq. in. 


500 600 700 800 900 


1000 








Value of C for two explosions per revolution 




50 


0.50 


0.60 


0.70 


0.80 


0.90 


1.00 


60 


0.60 


0.72 


0.84 


0.96 


1.08 


1.20 


70 


0.70 


0.84 


0.98 


1.12 


1 .26 


1.40 


80 


0.80 


0.96 


1.12 


1.28 


1.44 


1.60 


90 


0.90 


1.08 


1.26 


1.44 


1.62 


1.80 


100 


1.00 


1.20 


1.40 


1.60 


1.80 


2.00 


110 


1.10 


1.32 


1.54 


1.76 


1.98 


2.20 



These values of C apply to 4-cylinders, 4-cycle, single-acting, to 2-cyl., 
2-cycle, single-acting, and to 1-cyl., 2-cycle double-acting. For single 
cylinders, 4-cycle, single-acting, divide by 4; for single cylinders, 4-cycle, 
double-acting, or 2-cycle, single acting, divide by 2. 

Oil and Gasoline Engines. — The lighter distillates of petroleum, such 
as gasoline, are easily vaporized at moderate temperatures, and a gaso- 
line engine differs from a gas-engine only in having an atomizer attached, 
for spraying a fine jet of the liquid into the air-admission pipe. With 
kerosene and other heavier distillates, or crude oils, it is necessary to 



1078 INTERNAL-COMBUSTION ENGINES. 



provide some method of atomizing and vaporizing the oil at a high tem- 
perature, such as injecting it into a hot vaporizing chamber at the end 
of the cylinder, or into a chamber heated by the exhaust gases. In the 
Diesel oil engine the oil is ignited by the heat of the highly compressed 
air in the cylinder. 

The Diesel Oil Engine. — The distinguishing features of the Diesel 
engine are: It compresses air only, to a predetermined temperature above 
the firing point of the fuel. This fuel is blown as a cloud of vapor (by 
air from a separate small compressor) into the cylinder when compres- 
sion has been completed, ignites spontaneously without explosion, 
solely by reason of the heat of the air generated by the compression, 
and burns steadily with no essential rise in pressure. The temperature 
of gases, developed and rejected, is much lower than with engines of the 
explosive type. The engine uses crude oil and residual petroleum prod- 
ucts. Guarantees of fuel consumption are made as low as 8 gallons of 
oil (not heavier than 19° Baume) for each 100 brake H.P. hour at any 
load between half and full rated load. 

American Diesel engines are built for stationary purposes, in sizes of 
120, 170, and 225 H.P. in three cylinders, and in "double units" (six 
cylinders) of 240, 340 and 450 H.P. See catalogue of the American 
Diesel Engine Co., St. Louis, 1909. 

Much larger sizes have been built in Europe, where they are also 
built for marine purposes, including submarines in the French and other 
navies. For the theory of the Diesel engine see a lecture by Rudolph 
Diesel, in Zeit. des Ver Deutscher Ing., 1897, trans, in Progressive Age, 
Dec. 1 and 15, 1897, and paper by E. D. Meier in Jour. Frank. Inst., 
Oct. 1898. 

The De La Vergne Oil Engine is described in Eng. News, Jan. 13, 1910. 
It is a four-cycle engine. After the charge of air is compressed to about 
200 lbs. per sq. in., the charge of oil is injected, by a jet of air-at about 
600 lbs. per sq. in., into a vaporizing bulb at the end of the cylinder. Ig- 
nition of the oil is caused by the high temperature in this bulb. Average 
results of tests of an engine developing 128 H.P. showed an oil consump- 
tion per B.H.P. hour of 0.408 lb. with Solar fuel oil, and 0.484 lb. with 
California crude oil. 

Alcohol Engines. — Bulletin No. 392 of the U.S. Geol. Survey (1909,) 
on Comparisons of Gasolene and Alcohol Tests in Internal Combustion 
Engines, by R. M. Strong, contains the following conclusions: 

The "low" heat value of completely denatured alcohol will average 
10,500 B.T.U. per lb., or 71,900 B.T.U. per gallon. The low heat value 
of 0.71 to 0.73 sp. gr. gasolene will average 19,200 B.T.U. per lb., or 
115,800 B.T.U. per gallon. 

A gasolene engine having a compression pressure of 70 lbs. but other- 
wise as well suited to the economical use of denatured alcohol as gasolene, 
will, when using alcohol, deliver about 10% greater maximum power 
than when using gasolene. 

When the fuels for which they are designed are used to an equal advan- 
tage, the maximum B.H.P. of an alcohol engine having a compression 
pressure of 180 lbs. is about 30% greater than that of a gasolene engine 
of the same size and speed having a compression pressure of 70 lbs. 

Alcohol diluted with water in any proportion, from denatured alcohol, 
which contains about 10 % water, to mixtures containing about as much 
water as denatured alcohol, can be used in gasolene and alcohol engines if 
the engines are properly equipped and adjusted. 

When used in an engine having constant compression, the amount of 
pure alcohol required for any given load increases and the maximum 
available horse-power of the engine decreases with diminution in the 
percentage of pure alcohol in the diluted alcohol supplied. The rate of 
increase and decrease, respectively, however, is such that the use of 
80% alcohol instead of 90% has but little effect upon the performance; ■ 
so that if 80% alcohol can be had for 15% less cost than 90% alcohol and 
could be sold without tax when denatured, it would be more economical 
to use the 80% alcohol. 

Ignition. — The "hot-tube" method of igniting the compressed mixture 
of gas and air in the cylinder is practically obsolete, and electric systems 
are used instead. Of these the " make-and-.break " and the " jump- 
spark " systems are in common use. In the former two insulated contact 



INTEKNAL-COMBUSTION ENGINES. 1079 

pieces are located in the end of the cylinder, and through them an electric 
current passes while they are in contact. A spark-coil is included in the 
circuit, and when the circuit is suddenly broken at the proper time for 
ignition, by mechanism operated from the valve-gear shaft, a spark is 
made at the contacts, which ignites the gas. In the "jump-spark" 
system two insulated terminals separated about 0.03 in. apart are located 
in the cylinder, and the secondary or high-tension current of an induction 
coil causes a spark to jump across the space between them when the 
circuit of the primary current is closed by mechanism operated by the 
engine. In some oil engines the mixture of air and oil vapor is ignited 
automatically by the temperature generated by compression of the vapor, 
in a chamber at the end of the cylinder, called the vaporizer, which is 
not water-jacketed and therefore is kept hot by the repeated ignitions. 
Before starting the engine the vaporizer is heated by a Bunsen burner 
or other means. 

Timing. — By adjusting the cam or other mechanism operated by the 
valve-gear shaft for causing ignition, the time at which the ignition takes 
place, with reference to the end of the compression stroke, can be regulated. 
The mixture is usually ignited before the end of the stroke, the advance 
depending upon the inflammability of the mixture and on the speed of 
the engine. A slow-burning mixture requires to be ignited earlier than 
a rapid-burning one and a high-speed earlier than a slow-speed engine. 

Governing. — Two methods of governing the speed of an engine are 
in common use, the " hit-and-miss " and the throttling methods. In the 
former the engine receives its usual charge of air and gas only when the 
engine is running at or below its normal speed ; at higher speeds the ad- 
mission of -the charge is suspended until the engine regains its normal 
speed. One method of accomplishing this is to interpose between the 
valve-rod and its cam or other operating mechanism, a push-rod, or 
other piece, the position of which with reference to the end of the valve- 
rod is controlled by a centrifugal governor so that it hits the valve-rod if 
the speed is at or below normal and misses it if the speed is above normal. 
The hit-and-miss method is economical of fuel, but it involves irregularity 
of speed, making a large and heavy fly-wheel necessary if reasonable 
uniformity of speed is desired. The throttling method of regulating is 
similar to that used in throttling steam engines; the quantity of mixture 
admitted at each charge being varied by varying the position of a butter- 
fly valve in the inlet pipe. Cut-off methods of governing are also used, 
such as varying the time of closing the admission valve during the suction 
stroke, or varying the time of admission of the gas alone, or " quality 
regulation." 

Gas and Oil Engine Troubles. — The gas engine is subject to a 
greater number of troubles than the steam engine on account of its greater 
mechanical complexity and of the variable quality of its operating fluid. 
Among the causes of troubles are: the variable composition of the fuel; 
too much or too little air supply; compression ratio not right for the 
kind of fuel; ignition timer set too late or too early; pre-ignition; back- 
firing; electrical and mechanical troubles with the igniting system; 
carbon deposits in the cylinder and on the igniting contacts. For a very 
full discussion of these and many other troubles and the remedies for 
them, see Jones on the Gas-Engine. 

Conditions of Maximum Efficiency. — The conditions which appear 
to give the highest thermal efficiency in gas and oil engines are: 1, high 
temperature of cooling water in the jackets; 2, high pressure at the end 
of compression; 3, lean mixture; 4, proper timing of the ignition; 5, 
maximum load. The higher economy of a lean mixture may be due to 
the fact that high compressions may be used with such a mixture, while 
with rich mixtures high compression pressures cannot be used without 
danger of pre-ignition. The effect of different timing on economy is 
shown in a test by J. R. Bibbins, reported by Carpenter and Diederichs, of 
an engine using natural gas of a lower heating value* of 934 B.T.U. per 
cu. ft., delivering 71 H.P. at 297 revs, per min. The maximum thermal 
efficiency, 23.3%, was obtained when the timing device was set for igni- 

* By "lower heating value" is meant the value computed after sub- 
tracting the latent heat of evaporation of 9 lbs. of water per pound of 
hydrogen contained in the gas. See page 533. 



1080 



INTERNAL-COMBUSTION ENGINES. 



tion 30° in advance of the dead center, while the efficiency with ignitioi? 
at the center was 19%, and with ignition 55° in advance 17.3%. 

Other things being equal, the hotter the walls of the cylinder the lest 
heat is transferred into them from the hot gases, and therefore the highei 
the efficiency. Cool walls, however, allow of higher compression without 
pre-ignition, and high compression is a cause of high efficiency. Cool 
walls also tend to give the engine greater capacity, since with hot walls 
the fuel mixture expands more on entering the cylinder, reducing the 
weight of charge admitted in the suction stroke. 

Heat Losses in the Gas Engine, — The difference between the thermal 
efficiency, which is the proportion of heat converted into work in the 
engine, and 100%, is the loss of heat, which includes the heat carried away 
in the jacket water, that carried away in the waste gases, and that lost 
by radiation. The relative amounts of these three losses vary greatly, 
depending on the size of the engine and on the amount of water used for 
cooling. Thurston, in Heat as a Form of Energy, reports a test in which 
the heat distribution was as follows: Useful work, 17.3% ;" jacket water, 
52%; exhaust gas, 16%; radiation, 15%. Carpenter and Diederichs 
quote the following, showing that the distribution of the heat losses 
varies with the rate of compression and with the speed. 



Ratio 

of 
Com- 
pres- 
sion. 


R.p.m. 


M.E.P. 

lbs. 
per sq. 

in. 


Ratio 
Air to 
Gas. 


Heat- 
ing 
Value 

of 
Charge, 
B.T.U. 


Work 

done 

by 1 

B.T.U. , 

Ft.-lbs. 


Ex- 
haust 
Temp. 
Deg. F. 


Heat Distribution, 
Per Cent. 


Work. 


Jacket 
Water. 


Ex- 

bausto 


2.67 
2.67 
4.32 
4.32 


187 
247 
187 
247 


54.3 
51.5 
69.3 
65.2 


7.11 
7.35 
7.43 
7.40 


18.5 
17.4 
17.0 
16.8 


140 
141 
190 
184 


1022 
1137 
867 
992 


18.0 
18.1 

24.4 
23.7 


51.2 
45.6 
53.8 
49.5 


30.8 
36.3 
21.8 
26.8 



In the long table of results of tests reported by Carpenter and Diede- 
richs, figures of the distribution of heat show that of the total heat re- 
ceived by the engines the heat lost in the jacket water ranged from 25.0 
to 50.4%, and that lost in the exhaust gases from 55 to 23.4%. 

In small air-cooled gasoline engines, such as those used in some auto- 
mobile engines, in which the cylinders are surrounded by thin metal 
ribs to increase the radiating surface, and air is propelled against them 
by a fan, the air takes the place of the jacket water, and the total loss 
of heat is that carried away by the air and by the exhaust gases. 

Economical Performance of Gas Engines. — The best performance 
of a gas engine using producer gas (1909) is about 30% better than the 
best recorded performance of a triple-expansion steam engine, or about 
0.71 lb. coal per I.H.P. hour, as compared with 1.06 lbs. for the steam 
engine. It is probable that the performance of the combination of a 
high-pressure reciprocating engine, using superheated steam generated in 
a well-proportioned boiler supplied with mechanical stokers and an econo- 
mizer, and a low-pressure steam turbine will ere long reduce the steam 
engine record to 0.9 lb. per I.H.P. hour. As compared with an ordinary 
steam engine, however, the gas engine with a good producer is far more 
economical than the steam engine. Where gas can be obtained cheaply, 
such as the waste-gas from blast furnaces, or natural gas, the gas-engine 
can furnish power much more cheaply than it can be obtained from the 
same gas burned under a boiler to furnish steam to a steam engine. 

In tests made for the U. S. Geological Survey at the St. Louis Exhibi- 
tion, 1904, of a 235-H.P. gas engine with different coals, made into gas 
in the same producer, the best result obtained was 1.12 lbs. of West 
Virginia coal per B.H.P. hour, and the poorest result 3.23 lbs. per B.H.P. 
hour, with North Dakota lignite. 

A 170-H.P. Crossley (Otto) engine tested in England in 1892, using 
producer gas, gave a consumption of 0.85 lb. coal per I.H.P. hour, or a 
thermal efficiency of engine and producer combined of 21.3%. 

Experiments on a Taylor gas producer using anthracite coal and a 



TESTS OF GAS AND OIL ENGINES. 1081 

100-H.P. Otto gas engine showed a consumption of 0.97 lb. carbon per 
I.H.P. hour. {Iron Age, 1893.) 

In a table in Carpenter and Diederichs on Internal Combustion Engines 
the lowest recorded coal consumption per B.H.P. hour is 0.71 lb., with 
a Tangye engine and a suction gas producer, using Welsh anthracite coal. 
Other tests show figures ranging from 0.74 lb. to 1,95, the last with a 
Westinghouse 500-H.P. engine and a Taylor producer using Colorado 
bituminous coal. 

In the same book are given the following figures of the thermal efficiency 
on brake H.P. with different gas and liquid fuels. Illuminating gas, 
6 tests, 16.1 to 31.0%; natural gas, 4 tests, 16.1 to 29.0%; coke-oven gas, 
1 test, 27.5%; Mond gas, 1 test, 23.7%; blast-furnace gas, 3 tests, 20.4 to 
28.2%; gasoline, 8 tests, 10.2 to 28%; kerosene, Diesel engine, 3 tests, 
25.8 to 31.9%; kerosene, other engines, 8 tests, 9.2 to 19.7%; crude oil, 
Diesel engine, 1 test, 28.1%; alcohol, 4 tests, 21.8 to 32.7%. 

Tests of Diesel engines operating centrifugal pumps in India are 
reported in Eng. News, Nov. 25, 1909. Using Borneo petroleum residue 
of 0.934 sp. gr., and a fuel value of 18,600 B.T.U. per lb., an average of 
151 B.H.P. during a season, for a total of 6003 engine hours, was obtained 
with a consumption of 0.462 lb. of fuel per B.H.P. hour, or one B.H.P. 
for about 8600 B.T.U. per hour, equal to a thermal efficiency of 29.5%. 
The pump efficiency at maximum lift of 14 to 16 ft. was 70%, and the 
fuel consumption per water H.P. hour at the same lift was 0.7 lb. 

Utilization of Waste Heat from Gas Engines. — The exhaust gases 
from a gas engine may be used to heat air by passing them across a nest 
of tubes through which air is flowing. A design of this kind, for heating 
the Ives library building, New Haven, Conn., by Harrison Engineering 
Co., New York, is illustrated in Heat, and Vent. Mag., Jan., 1910. 

The waste heat might also be used in a boiler to generate steam at or 
below atmospheric pressure, for use in a low pressure steam turbine. On 
account of the comparatively low temperature of the exhaust gases, 
however, the boiler would require a much greater extent of heating sur- 
face for a given capacity than a boiler with an ordinary coal-fired furnace. 

RULES FOR CONDUCTING TESTS OF GAS AND OIL 
ENGINES*. CODE OF 1903. 

(From the report of the committee of the A. S. M. E. on Engine Tests.) 
[Only a brief abstract is here given. The items, 1, Objects of the Tests; 
2, General Conditions of the Engine; 3, Dimensions; 5, Calibration of 
Instruments, are practically the same as in the report on Steam Engine 
Tests.] 

IV. Fuel. — Decide upon the gas or oil to be used, and if the trial is 
to be made for maximum efficiency, the fuel should be the best of its 
class that can readily be obtained, or one that shows the highest calorific 
power. 

VI. Duration of Test. — The duration of a test should depend largely 
upon the objects in view, and in any case the test should be continued until 
the successive readings of the rates at which oil or gas is consumed, 
taken at say half-hourly intervals, become uniform and thus verify each 
other. If the object is to determine the working economy, and the period 
of time during which the engine is usually in motion is some part of 
twenty-four hours, the duration of the test should be fixed for this number 
of hours. If the engine is one using coal for generating gas, the test 
should be of at least twenty-four hours' duration. 

VII. Storting a Test. — In a test for determining the maximum econ- 
omy of an engine, it should first be run a sufficient time to bring all 
the conditions to a normal and constant state. 

If a test is made to determine the performance under working condi- 
tions, the test should bej?in as soon as the regular preparations have 
been made for starting the engine in practical work, and the measurements 
should then commence and be continued until the close of the period 
covered by the day's work. 

VIII. Measurement of Fuel. — If the fuel used is coal furnished to a gas 

* Hot-air engines are not included in this code, those in the market 
being of comparatively small size, and seldom tested. 



1082 INTERNAI^COMBUSTION ENGINES. 

producer, the same methods apply for determining the consumption as 
are usea in steam-boiler tests. 

If the fuel used be gas, the only practical method of measurement is 
the use of a meter through which the gas is passed. The temperature 
and pressure of the gas should be measured, and the quantity of gas 
should be determined by reference to the calibration of the meter, taking 
into account the temperature and pressure of the gas. 

If the fuel is oil, this can be drawn from a tank which is filled to the 
original level at the end of the test, the amount of oil required for so 
doing being weighed ; or, for a small engine, the oil may be drawn from a 
calibrated vertical pipe. 

IX. Measurement of Heat- Units Consumed by the Engine. — The num- 
ber of heat-units used is found by multiplying the number of pounds of 
coal or oil or the cubic feet of gas consumed, by the total heat of combus- 
tion of the fuel as determined by a calorimeter test. In determining the 
total heat of combustion no deduction is made for the iatent heat of the 
water vapor in the products of combustion. 

It is sometimes desirable, also, to have a complete chemical analysis 
of the oil or gas. The total heat of combustion may be computed, if 
desired, from the results of the analysis, and should agree well with the 
calorimeter values. 

X. Measurement of Jacket Water. — The jacket water mny be meas- 
ured by passing it through a water meter or allowing it to flow from a 
measuring tank before entering the jacket, or by collecting it in tanks 
on its discharge. 

XI. Indicated Horse-power. — The directions given for determining 
the indicated horse-power for steam engines apply in all respects to inter- 
nal combustion engines. 

XII. Brake Horse-power. — The determination of the brake horse- 
power is the same for internal combustion as for steam engines. 

XIII. Speed. — The same directions apply to internal combustion 
engines as to steam engines for the determination of speed. 

In an engine which is governed by varying the number of explosions 
or working cycles, a record should be kept of the number of explosions 
per minute; or if the engine is running at nearly maximum load, by 
counting the number of times the governor causes a miss in the ex- 
plosions. 

XIV. Recording the Data. — The pressures, temperatures, meter 
readings, speeds, and other measurements should be observed every 20 
or 30 minutes when the conditions are practically uniform, and at more 
frequent intervals if they are variable. Observations of the gas or oil 
measurements should be taken with special care at the expiration of each 
hour, so as to divide the test into hourly periods, and reveal the uniform- 
ity, or otherwise, of the conditions and results as the test goes forward. 

XV. Uniformity of Conditions. — When the object of the test is to 
determine the maximum economy, all the conditions relating to the 
operation of the engine should be maintained as constant as possible 
during the trial. 

XVI. Indicator Diagrams. — Sample diagrams nearest to the mean 
should be selected from those taken during the trial and appended to the 
tables of the results. If there are separate compression or feed cylinders, 
the indicator diagrams from these should be taken and the power deducted 
from that, of the main cylinder. 

XVII. Standards of Economy and Efficiency. — The hourly consump- 
tion of heat, divided by the indicated or the brake horse-power, is the 
standard expression of engine economy recommended. 

In making comparisons between the standard for internal combustion 
engines and that for steam engines, it must be borne in mind that the 
steam engine standard does not cover the losses due to combustion, while 
the internal combustion engine standard, in cases where a crude fuel 
such as oil is burned in the cylinder, does cover these losess. 

The thermal efficiency ratio per indicated horse-power or per brake 
horse-power for internal combustion engines is expressed by the fraction 
2545 -*- B.T.U. per H.P. per hour. 

XVIII. Heat Balance. — For purposes of scientific research, a heat 
balance should be drawn which shows the manner in which the total 



TESTS OF GAS AND OIL ENGINES. 1083 

heat of combustion is expended in the various processes concerned in 
the working of the engine. It may be divided into three parts: first, 
the heat which is converted into the indicated or brake work; second, the 
heat rejected in the cooling water of the jackets; and third, the heat 
rejected in the exhaust gases, together with that lost through incomplete 
combustion and radiation. 

To determine the first item, the number of foot-pounds of work per-* 
formed by, say, one pound or one cubic foot of the fuel, divided by 778, 
gives the number of heat-units desired. The second item is determined 
by measuring the amount of cooling water passed through the jackets, 
equivalent to one pound or one cubic foot of fuel consumed, and multi- 
plying this quantity by the difference in the sensible heat of the water 
leaving the jacket and that entering. The third item is obtained by 
subtracting the sum of the first two items from the total heat supplied. 
The third item can be subdivided by computing the heat rejected in the 
exhaust gases as a separate quantity. The data for this computation 
are found by analyzing the fuel and the exhaust gases, or by measuring 
the quantity of air admitted to the cylinder in addition to that of the gas 
or oil. 

XIX. Report of Test. — The data and results of a test should be re- 
ported in the manner outlined in one of the following tables, the first of 
which gives a complete summary when all the data are determined, and 
the second is a shorter form of report in which some of the minor items 
are omitted. [The short form is given below.] 

Data and Results of Standard Heat Test of Gas or Oil Engine. 

Arranged according to the Short Form advised by the Engine Test 
Committee, American Society of Mechanical Engineers. Code of 
1902. 

1 Made by. . of 

on engine located at 

to determine 



2. Date of trial 

3. Type and class of engine . 



4. Kind of fuel used 

(a) Specific gravity deg Fahr. 

(b) Burning point 

(c) Flashing point 

5. Dimensions of engine: 

1st Cyl. 2d Cyl. 
(a) Class of cylinder (working or for com- 
pressing the charge) 

(&) Single or double acting 

(c) Cylinder dimensions: 

Bore in. 

Stroke ft. 

Diameter piston rod in. 

(d) Average compression space, or clear- 

ance, in per cent 

(e) Horse-power constant for one lb. M.E.P. 

and one revolution per minute 

Total Quantities. 

6. Duration of test hours 

7. Gas or oil consumed cu. ft. ( pr lbs. 

8. Cooling water supplied to jackets 

9. Calorific value of fuel by calorimeter test, determined 

by calorimeter B.T.U. 

Pressures and Temperatures. 

10. Pressure at meter (for gas engine) in inches of water . . . ins. 

11. Barometric pressure of atmosphere: 

(a) Reading of barometer 

(b) Reading corrected to 32 degs. Fahr 



1084 LOCOMOTIVES. 



12. Temperature of cooling water: 

(a) Inlet deg. Fahr. 

(6) Outlet 

13. Temperature of gas at meter (for gas engine) " 

14. Temperature of atmosphere: 

(a) Dry bulb thermometer •• 

(b) Wet bulb thermometer ♦' 

(c) Degree of humidity " 

15. Temperature of exhaust gases " 

Data Relating to Heat Measurement. 

16. Heat units consumed per hour (pounds of oil or cubic 

feet of gas per hour multiplied by the total heat of 
combustion) , B.T.U. 

17. Heat rejected in cooling water per hour 

Speed, etc. 

18. Revolutions per minute rev. 

19. Average number of explosions per minute 

Indicator Diagrams. 

20. Pressure in lbs. per sq. in. above atmosphere: 

1st Cyl. 2d Cyl. 

(a) Maximum pressure 

(6) Pressure just before ignition 

(c) Pressure at end of expansion 

(d) Exhaust pressure 

(e) Mean effective pressure 

Power. 

21. Indicated horse-power: 

First cylinder H.P. 

Second cylinder 

Total 

22. Brake horse-power 

23. Friction horse-power by friction diagrams 

24. Percentage of indicated horse-power lost in friction. . per cent. 

Standard Efficiency, and Other Results. 

25. Heat units consumed by the engine per hour: 

(a) Per indicated horse-power B.T.U. 

(6) Per brake horse-power 

26. Pounds of oil or cubic feet of gas consumed per hour: 

(a) Per indicated horse-power lbs. or cu. ft. 

(6) Per brake horse-power 

Additional Data. 
Add any additional data bearing on the particular objects of the test 
or relating to the special class of service for which the engine is to be 
used. Also give copies of indicator diagrams nearest the mean, and the 
corresponding scales. 

LOCOMOTIVES. 

Resistance of Trains. — Resistance due to Speed. — Various formula 
and tables for the resistance of trains at different speeds on a straight 
level track have been given by different writers. Among these are the 
following: 

By D. L. Barnes (Eng. Mag.), June, 1894: 

Speed, miles per hour 50 60 70 80 90 100 

Resistance, pounds per gross ton 12 12.4 13.5 15 17 20 

By Engineering News, March 8, 1894: 

Resistance in lbs. per ton of 2000 lbs. = ViV + 4. 

Speed 5 10 15 20 25 30 35 40 45 50 60 70 80 90 100 

Resistance. 31/4 4.5 53/ 4 7 8 1/4 9.5 103/ 4 12 13V* 14.5 17 19.5 22 24.5 27 



LOCOMOTIVES. 1085 

This formula seems to be more generally accepted than the others. 
It gives results too small, however, below 10 miles an hour. At starting, 
the resistance is about 17 lbs. per ton, dropping to 4 or 5 lbs. at 5 miles 
an hour. 

By Baldwin Locomotive Works: 

Resistance in lbs. per ton of 2000 lbs. = 3 + v h- 6. 

Speed 5 10 15 20 25 30 35 40 45 50 55 60 70 80 90 100 

Resistance. 3.8 4.7 5.5 6.3 7.2 8 8.8 9.7 10.5 11.3 12.2 13 14.7 16.3 18 19.7 

The resistance due to speed varies with the condition of the track, the 
number of cars in a train, and other conditions. 

For tables showing that the resistance varies with the area exposed to 
the resistance and friction of the air per ton of loads, see Dashiell, Trans. 
A. S. M. E., vol. xiii. p. 371. 

P. H. Dudley (Bulletin International Ry. Congress, 1900, p. 1734) 
shows ihat the condition of the track is an important factor of train 
resistance which has not hitherto been taken account of. The resist- 
ance of heavy trains on the N. Y. Central R. R. at 20 miles an hour is 
only about 31/2 lbs. per ton on smooth 80-lb. 51/s-in. rails. The resist- 
ance of an 80-car freight train, 60,000 lbs. per car, as given by indicator 
cards, at speeds between 15 and 25 miles per hour, is represented by the 
formula R = 1 + l/s F, in which R = resistance in lbs. per ton and 
V = miles per hour. These values are much below the average and 
should not be used in estimating the hauling power needed. 

New Formulae for Resistance. — The Amer. Locomotive Co. (Bulletin 
No. 1001, Feb., 1910) states that the figures obtained from the old formulae 
for train resistance are much too high for modern loaded freight cars 
of 40 to 50 tons capacity, and in some instances too low for very light 
or empty cars. The best data available show that the resistance varies' 
from about 2.5 to 3 lbs. per ton (of 2000 lbs.) for 72-ton cars (including 
weight of empty car) to 6 to 8 lbs. for 20-ton cars. From speeds between 
5 to 10 and 30 to 35 miles an hour, the resistance of freight cars is prac- 
tically constant. The resistance of the engine and tender is figured 
separately, and is composed of the following factors: (a) Engine friction = 
22.2 lbs. per ton, or 1.11% of the weight on drivers, (b) Head air resist- 
ance = cross-sectional area (taken at 120 sq. ft.) X 0.002 V 2 , V being 
the speed in miles per hour, (c) Resistance due to weight on engine 
trucks and trailing wheels, and to the tender, the same per ton as that 
due to the cars, (d) Grade resistance = 20 lbs. per ton for each per 
cent of grade, (e) Curve resistance, which varies with the wheel-base 
of the locomotive, and is taken as 0.4 + cD lbs. per ton, in which D is 
the degree of the curve and c a constant whose value is, 
For wheel-base, ft. 5 6 7 8 9 12 13 15 16 20 

Value of c 0.380 .415 .460 .485 .520 .625 .660 .730 .765 .905 : 

The sum of these resistances is to be deducted from the tractive force of 
the locomotive to obtain the available tractive force for overcoming the 
resistance of the cars. (See Tractive Force, below.) The maximum 
tractive force is taken for low speeds at 85% of that due to the boiler 
pressure; for piston speeds over 250 ft. per min. this is to be multiplied 
by a speed factor to obtain the actual force. Speed factors and percent- 
ages of maximum horse-power corresponding to different piston speeds 
are given below. S = piston speed, ft. per min., F = speed factor, 
P = % of maximum H.P. 

S 250 300 350. 400 450 500 550 600 650 700 750 

F 1.00 .954 .908 .863 .817 .772 .727 .680 .636 .592 .5.50 

P 60.4 69.177.2 83.7 89.0 93.5 96.8 98.7 99.7 100 100 

S ....800 850 900 950 1000 1100 1200 1300 1400 1500 1600 

F 0.517 .487 .460 .435 .412 .372 .337 .307 .283 .261 .241 

P 100 100 100 100 100 99 97.8 96.8 95.7 94.7 93.5 

The resistance of freight cars, according to experiments on the Penna 
R.R., varies with the weight in tons per car as follows: 

Tons per car 10 20 25 30 40 50 60 70 72 

Resistance, lbs. per ton 

13.10 7.84 6.62 5.78 4.66 3.94 3.44 3.06 3.00 



1086 LOCOMOTIVES. 

From plotted curves of resistances of trains of empty and loaded cars 
the following figures are derived. R — resistance in lbs. per ton. 

Wt. loaded, tons 75 70 65 60 55 50 

Wt. empty, tons 21 20.3 19.5 18.6 17.6 16.5 

Per cent of loaded wt 28 29 30 31 32 33 

R loaded 2.90 3.07 3.24 3.43 3.65 3.90 

R empty 5.63 5.82 6.00 6.26 6.50 6.85 

Wt. loaded, tons 45 40 35 30 25 20 15 

Wt. empty, tons 15.3 14.0 12.6 11.1 9.5 7.8 6.0 

Per cent of loaded wt. . . . 34 35 36 37 38 39 40 

R loaded 4.18 4.40 4.74 5.07 5.44 5.91 6.40 

R empty 7.26 7.65 8.05 «.45 9.05 9.60 10.3 

The resistance of passenger cars is derived from the formula R = 5.4 + 
0.002(F - 15) 2 + 100 ■*- (V + 2) 3 . V in miles per hour, R = resistance 
in lbs. per ton (2000 lbs.) H.P. = horse-power per ton. 

V = 5 10 15 20 25 30 35 

R = 5.89 5.51 5.42 5.46 5.60 5.85 6.20 

H.P. = 0.079.147 .217 .291 .374 .469 .578 

V = 40 45 50 60 70 80 90 

R = 6.65 7.20 7.85 9.45 11.45 13.85 16.65 

H.P.= 709 .864 1.047 1.515 2.135 2.95 4.00 

Resistance of Electric Railway Cars and Trains. — W. J. Davis, Jr. 
(Street Ry. Jour., Dec. 3, 1904), gives as a result of numerous experiments 
the following formulae : 

(A) For light open platform street cars, 8 tons to 20 tons; maximum 
speed, 30 miles per hour; cross-section, 85 sq. ft. 

R = 6 + 0.11 V + ^~ [1 + 0.1 (n - 1)]. 

(B) For standard interurban electric cars, 25 tons to 40 tons; maximum 
speed, 60 m.p.h.; cross section, 100 sq. ft. 

22 = 5+ 0.13 V+ 0.3V*/T[1 + 0.1 (n - 1)]. 

(C) For heavy interurban electric cars, or steam passenger coaches, 
40 tons to 50 tons; maximum speed, 75 m.p.h.; crosss-ection, 110 sq. ft. 

r = 4 + 0.13 V + 0.33 V*/T [1 + 0.1 (n - 1)]. 

(D) For heavy freight trains, cars weighing 45 tons loaded; maximum 
speed, 35 m.p.h.; average cross-section, 110 sq. ft. 

R - 3.5 +• . 13 V + 0.385 V 2 /T [1 + 0.1 (n - 1)]. 

R = resistance in lbs. per ton of 2000 lbs., F= speed in miles per hour 
T == Weight of train in tons, n — number of ears in train, including lead- 
ing motor car. The cross-section includes the space bounded by the wheels 
between the top of rails and the body. 

Resistance due to Grade. — The resistance due to a grade of 1 ft. per 
mile is, per ton of 2000 lbs., 2000 X 1/5280 = 0.3788 lb. per ton, or if 
R g = resistance in lbs. per ton due to grade and G = ft. per mile R g = 
0.3788 G. 

If the grade is expressed as a percentage of the length, the resistance is 
20 lbs. per ton for each per cent of grade. 

Resistance due to Curves. — Mr. G. P. Henderson in his book entitled 
"Locomotive Operation" gives the resistance due to curvature at 0.7 
lb. per ton of 2000 lbs. per degree of the curve. (For definition of 
degrees of a railroad curve see p. 55.) For locomotives, this factor is 
sometimes doubled, making the resistance in lbs. per ton = 0.7 c for cars 
and 1.4 c for locomotives, c being the number of degrees. 

The Baldwin Locomotive Works take the approximate resistance due 
to each degree of curvature as that due to a straight grade of 1 1/2 ft. per 
mile. This corresponds to R c = 0.5682 c. 

The Amer. Locomotive Co. takes 0.8 lb. per ton per degree of curva- 
ture for the resistance of cars on curves. 



LOCOMOTIVES. 1087 

For mine cars, with short wheel-bases and wheels loose on the axles, 
experiments quoted by the Baldwin Locomotive Works, 1904, lead to the 
formula, Resistance due to curvature, in pounds, = 0.20 X wheel-base X 
weight of loaded cars in pounds, -*• radius of curve in feet. 

Resistance due to Acceleration. — This may be calculated by the ordi- 
nary formula (see page 504), or reduced to common railroad units, and 
including the rotative energy of wheels and axles, which increases the 
effect of the weight of the cars by an equivalent of about 5%, we have 

F 2 V Vi 2 — Vi* 
P = 70 -s- =95.6 -. =70 ■ ^ , where P = the accelerating force in 

pounds per ton, V = the velocity in miles per hour, S = the distance 
in feet, and t = the time in seconds in which the acceleration takes 
place. Vi and V2 = the smaller and greater velocities, respectively, 
in miles per hour, for a change of speed. 

Total Resistance. — The total resistance in lbs. per ton of 2000 lbs. due 
to speed, to grade, to curves, and to acceleration is the sum of the resist- 
ances calculated above. 

The Baldwin Locomotive Works in their "Locomotive Data" take the 
total resistance on a straight level track at slow speeds at from 6 to 10 lbs. 
per ton, and in a communication printed in the fourth edition (1898) of 
this Pocket-book, p. 1076, say: "We know that in some cases, for in- 
stance in mine construction, the frictional resistance has been shown to 
be as much as 60 lbs. per ton at slow speed. The resistance should be 
approximated to suit the conditions of each individual case, and the 
increased resistance due to speed added thereto." 

Resistance due to Friction. — In the above formulae no account has been 
taken of the resistance due to the friction of the working parts. This is 
rather an obscure subject. Mr. Henderson estimates the percentage of 
the indicated power consumed by friction to be 0.15 V + r, where 
V = speed in miles per hour and c = a constant, whose value may 
vary from 2 to 8, the latter figure being the safest to use for heavy work 
at slow speeds. Ordinarily 8% of the indicated power is consumed by 
internal resistance under these conditions. Professor Goss gives the 
following formula, obtained from tests at the Purdue locomotive testing 
laboratory: 

Let d = diameter of cylinder: S = stroke of piston; D == diameter of 
drivers, all in inches. Then the internal friction= 3.8d 2 S/D,iu. pounds 
at the circumference of the drivers. 

Concerning the effect of increasing speed on tractive force, Mr. Hender- 
son says (1906): 

From a number of tests and information from various roads and au- 
thorities it seems as if, for ordinary simple engines, the coefficient 0.8 

8 Pd 2 s 
in the equation Actual tractive force = - 1 — j? — could be modified in ac- 
cordance with the speed in order to obtain the actual tractive force at 
various speeds about as follows: 

Revs, per min. = 20 40 60 80 100 120 140 160 

Coefficient = . 80 0.80 0.80 0.70 0.61 0.53 0.46 0.40 

Revs, per min. = 180 200 220 240 260 280 300 320 340 

Coefficient = . 35 0.31 0.28 0.26 0.24 0.23 0.21 0.20 0.19 

Efficiency of the Mechanism of a Locomotive. — Frank C.Wagner 
(Proc. A. A. A. S., 1900, p. 140) gives an account of some dynamometer 
tests which indicate that in ordinary freight service the power used to 
drive the locomotive and tender and to overcome the friction of the 
mechanism is from 10% to 35% of the total power developed in the steam- 
cylinder. In one test tho weight of the locomotive and tender was 16% 
of the total weight of the train, while the power consumed in the loco- 
motive and tender was from 30% to 33% of the indicated horse-power. 

Adhesion. — The limit of the hauling capacity of a locomotive is the 
adhesion due to the weight on the driving wheels. Holmes gives the 
adhesion, in English practice, as equal to 0.15 of the load on the driving 
wheels in ordinary dry weather, but only 0.07 in damp weather or when 
the rails are greasy. In American practice it is generally taken as from 
1/4 to 1/5 of the load on the drivers. 



1088 



LOCOMOTIVES. 



Tractive Force of a Locomotive. — Single Expansion. 
Let F = indicated tractive force in lbs. 

p = average effective pressure in cylinder in lbs. per sq. in. 

S = stroke of piston in inches. 
d = diameter of cylinders in inches. 
D = diameter of driving-wheels in inches. Then 
4 xd*pS = (1 2 pS 

4:7lD D 

The average effective pressure can be obtained from an indicator- 
diagram, or by calculation, when the initial pressure and ratio of expan- 
sion are known, together with the other properties of the valve-motion. 
The subjoined table from Auchincloss gives the proportion of mean 
effective pressure to boiler-pressure above atmosphere for various pro- 
portions of cut-off. 



Stroke, 
Cut-off at - 



M.E.P. 

(Boiler- 
pres. = 1). 



Stroke, 
Cut-off at- 



M.E.P. 

(Boiler- 

pres. = 1). 



Stroke, 
Cut-off at - 



M.E.P. 

(Boiler- 

pres. = 1). 



1/8 



0.1 
.125 
.15 
.175 
.2 

.25 = 1/4 
.3 



0.15 
.2 
.24 
.28 
.32 
.4 
.46 



0.333 = 1/3 
.375 = 3/ 8 
.4 
.45 

J5 =lh 



0.5 = 
.55 
.57 
.62 
.67 
.72 



0.625 = 5/ 8 
.666 = 2/3 
.7 

• 75 =3/ 4 
.8 
.875 = 7/ 8 



0.79 
.82 
.85 
.89 
.93 



These values were deduced from experiments with an English locomo- 
tive by Mr. Gooch. As diagrams vary so much from different causes, 
this table will only fairiy represent practical cases. It is evident that 
the cut-off must be such that the boiler will be capable of supplying 
sufficient steam at the given speed. 

We can, however, al'ow for wire drawing to the steam chest and drop in 
pressure due to expansion, and internal friction by writing the formula: 

Actual Tractive Force = — — =r , d, S, and D being a.3 before and P 

representing boiler pressure in lbs. per sq. in. 

Compound Locomotives. — The Baldwin Locomotive Works give the fol- 
lowing formulae for compound engines of the Vauclain four-cylinder type: 
C*S X 2/3 P C*S X 1/4 P 
D + D 

T= tractive force in lbs. C= diam. of high-pressure cylinder in Ins. 
c= diam. of low-pressure cylinder in ins. P= boiler-pressure in lbs. 
<S= stroke of piston in ins. D= diam. of driving-wheels in ins. 

For a two-cylinder or cross-compound engine it is only necessary to con- 
sider the high-pressure cylinder, allowing a sufficient decrease in boiler 
pressure to compensate for the necessary back-pressure. The formula is 

: c*sxyaP 



T= ■ 



T= - 



D 



The above formulae are for speeds of from 5 to 10 miles an hour, or 
less; above that the capacity of the boiler limits the cut-off which can be 
used, and the available tractive force is rapidly reduced as the speed 
increases. For a full discussion of this, see page 375 of Henderson's 
" Locomotive Operation." 

The Size of Locomotive Cylinders is usually taken to be such that 
the engine will just overcome the adhesion of its wheels to the rails under 
favorable circumstances. 

The adhesion is taken by a committee of the Am. Ry. Master Mechan- 
ics' Assn. as 0.25 of the weight on the drivers for passenger engines, 0.24 
for freight, and 0.22 for switching engines; and the mean effective pres- 
sure in the cylinder, when exerting the maximum tractive force, is taken 
at 0.85 of the boiler-pressure. 



LOCOMOTIVES. 



1089 



W=4:P= - 



Let W = weight on drivers in lbs.; P = tractive force in lbs., = say 
0.25 W; pi = boiler-pressure in lbs. per sq. in.; p = mean effective 
pressure, = 0.85 pv, d = diam. of cylinder, S = length of stroke, and 
D = diam. of driving-wheels, all in inches. Then 

4 d*pS _ 4:d 2 X0.85piS 
D D 

Whence d = 0.5 "\|^J= 0.542 \^J • 

Von Borries's rule for the diameter of the low-pressure cylinder of a 
compound locomotive is d- = 2ZD -5- ph, in which d= diameter of l.p. 
cylinder in inches; D = diameter of driving-wheel in inches; p = mean 
effective pressure per sq. in., after deducting internal machine friction; 
h = stroke of piston in inches; Z = tractive force required, usually 0.14 
to 0.16 of the adhesion. 

The value of p depends on the relative volume of the two cylinders, 
and from indicator experiments may be taken as follows: 

Ratio of Cylinder p in percent of p for Boiler-pres- 
Volumes. Boiler-pressure, sure of 176 lbs. 

Large-tender eng's. 1 : 2 or 1 : 2.05 42 74 

Tank-engines 1 : 2 or 1 : 2.2 40 71 

Horse-power of a Locomotive. — For each cylinder the horse-power 
is H.P. = pLaN ■*- 33,000, in which p = mean" effective pressure, L = 
stroke in feet, a = area of cylinder = 1/4 xd 2 , N = number of single 
strokes per minute, LN = piston speed, ft. per min. Let M = speed of 
train in miles per hour, 5 = length of stroke in inches, and D = diam- 
eter of driving-wheel in inches. Then LN = M X88 X 2 S -*• nD. 
Whence for the two cylinders the horse-power is 

2XpXV4^X176gXM pd 2 SM 
nD X 33,000 375 D ' 



Class of Engine. 



Revolutions 


per Minute for Various Diameters 


of Wheels 








and Speeds. 
















Miles per Hour 








Diameter 
of Wheel. 


































10 


20 


30 


40 


50 


60 


70 


80 


50 in. 


67 


134 


201 


268 


336 


403 


470 


538 


56 in. 


60 


120 


180 


240 


300 


360 


420 


480 


60 in. 


56 


112 


168 


.224 


280 


336 


392 


448 


62 in. 


54 


108 


162 


217 


271 


325 


379 


433 


66 in. 


51 


102 


153 


204 


255 


306 


357 


408 


68 in. 


49 


99 


148 


198 


247 


296 


346 


395 


72 in. 


47 


93 


140 


187 


233 


279 


326 


373 


78 in. 


43 


86 


129 


172 


215 


258 


301 


344 


80 in. 


42 


84 


126 


168 


210 


252 


294 


336 


84 in. 


40 


80 


120 


160 


200 


240 , 


280 


320 


90 in. 


37 


75 


112 


150 


186 


224 


261 


299 



The Size of Locomotive Boilers. (Forney's Catechism of the Loco- 
motive.) — They should be proportioned to the amount of adhesive 
weight and to the speed at which the locomotive is intended to work. 
Thus a locomotive with a great deal of weight on the driving-wheels 
could Dull a heavier load, would have a greater cylinder capacity than 
one with little adhesive weight, would consume more steam, and there- 
fore should have a larger boiler. 

The weight and dimensions of locomotive boilers are in nearly all 
cases determined by the limits of weight and space to which they are 
necessarily confined. It may be stated generally that within these limits 
a locomotive boiler cannot be made too large. In other words, boilers for 



1090 



LOCOMOTIVES. 



locomotives should always be made as large as is possible under the 
conditions that determine the weight and dimensions of the locomotives. 
(See also Holmes on the Steam-engine, pp. 371 to 377 and 383 to 389, 
and the Report of the Am. Ry. M. M. Ass'n. for 1897, pp. 218 to 232.) 
Holmes gives the following from English practice: 

Evaporation, 9 to 12 lbs. of water from and at 212°. 

Ordinary rate of combustion, 65 lbs. per sq. ft. of grate per hour. 

Ratio of grate to heating surface, 1 : 60 to 90. 

Heating surface per lb. of coal burnt per hour, 0.9 to 1.5 sq. ft. 
Mr. Henderson states the approximate heating surface needed per 
indicated horse-power as follows: 

Compound Locomotives 2 square feet. 

Simple Locomotives (cut-off 1/2 stroke or less) ........ 21/3 square feet. 

Simple Locomotives (cut-off 1/2 to 3/ 4 stroke) 22/3 square feet. 

Simple Locomotives (full stroke) 3 square feet. 

For the ratio of heating surface to grate area the Master Mechanics 
Ass'n Committee of 1902 advised as below: 



Fuel. 


Passenger. 


Freight. 


Simple. 


Com- 
pound. 


Simple. 


Com- 
pound. 




65 to 90 
50 to 65 
40 to 50 

35 to 40 

28 to 35 


75 to 95 
60 to 75 
35 to 60 

30 to 35 

24 to 30 


70 to 85 
45 to 70 
35 to 45 

30 to 35 

25 to 30 


65 to 85 




50 to 65 




45 to 50 


Bituminous slack and free burning. . 


40 to 45 


Low grade bituminous, lignite and 


30 to 40 







A. E. Mitchell, (Eng'g News, Jan. 24, 1891) says: Square feet of boiler- 
heating surface for bituminous coal should not be less than 4 times the 
square of the diameter in inches of a cylinder 1 inch larger than the 
cylinder to be used. One tenth of this should be in the fire-box. On 
anthracite locomotives more heating-surface is required in the fire-box, on 
account of the larger grate-area required, but the heating-surface of the 
flues should not be materially decreased. 

Wootten's Locomotive. (Clark's Steam-engine; see also Jour. 
Frank. Inst. 1891, and Modern Mechanism, p. 485.) — J. E. Wootten 
designed and constructed a locomotive boiler for the combustion of an- 
thracite and lignite, though specially for the utilization as fuel of the 
waste produced in the mining and preparation of anthracite. The special 
feature of the engine is the fire-box, which is made of great length and 
breadth, extending clear over the wheels, giving a grate-area of from 
64 to 85 sq. ft. The draught diffused over these large areas is so gentle 
as not to lift the fine particles of the fuel. A number of express-engines 
having this type of boiler are engaged on the fast trains between Phila- 
delphia and Jersey City. The fire-box shell is 8 ft. 8 in. wide and 10 ft. 
5 in. long; the fire-box is 8 X 91/2 ft., making 76 sq. ft. of grate-area. 
The grate is composed of bars and water-tubes alternately. The regular 
types of cast-iron shaking grates are also used. The height of the fire- 
box is only 2 ft. 5 in. above the grate. The grate is terminated by a 
bridge of fire-brick, beyond which a combustion-chamber, 27 in. long, 
leads to the flue-tubes, 'about 184 in number, 13/ 4 in. diam. The cylin- 
ders are 21 in. diam., with a stroke of 22 inches. The driving-wheels, 
four-coupled, are 5 ft. 8 in. diam. The engine weighs 44 tons, of which 
29 tons are on driving wheels. The heating-surface of the fire-box is 
135 sq. ft., that of the flue-tubes is 982 sq. ft.: together, 1117 sq. ft., or 
14.7 times the grate-area. Hauling 15 passenger-cars, weighing with 
passengers 360 tons, at an average speed of 42 miles per hour, over ruling 
gradients of 1 in 89, the engine consumes 62 lbs, of fuel per mile, or 
34V4 lfr s » P er sq. ft- °f g rate P er hour. 



LOCOMOTIVES. 



1091 



Grate-surface, Smoke-stacks, and Exhaust-nozzles for Locomo- 
motives. — A. E. Mitchell, Supt. of Motive Power of the Erie R. R., says 
(1895) that some roads use the same size of stack, 13 1/2 in. diam. at 
throat, for all engines up to 20 in, diam. of cylinder. 

The area of the orifices in the exhaust-nozzles depends on the quantity 
and quality of the coal burnt, size of cylinder, construction of stack, 
and the condition of the outer atmosphere. It is therefore impossible 
to give rules for computing the exact diameter of the orifices. All that 
can be done is to give a rule by which an approximate diameter can be 
found. The exact diameter can only be found by trial. Our experi- 
ence leads us to believe that the area of each orifice in a double exhaust- 
nozzle should be equal to 1/430 part of the grate-surface, and for single 
nozzles 1/200 of the grate-surface. These ratios have been used in finding 
the diameters of the nozzles given in the following table. The same 
sizes are often used for either hard or soft coal-burners. [These sizes are 
small at the present day (1909) as locomotives have enormously in- 
creased in size.] 











Double 


Single 


Size of 


Grate-area 
for Anthra- 
cite Coal, in 


Grate-area 
for Bitumin- 
ous Coal, in 


Diameter 
of Stacks, 
in inches. 


Nozzles. 


Nozzles. 


Cylinders, 
in inches. 


Diam. of 


Diam. of 




sq. in. 


sq. in. 




Orifices, in 
inches. 


Orifices, in 
inches. 


12x20 


1591 


1217 


91/2 


2 


213/ie 


13x20 


1873 


1432 


IOI/2 


21/8 


3 


14x20 


2179 


1666 


111/4 


25/16 


31/4 


15x22 


2742 


2097 


121/2 


29/i 6 


3*1/16 


16x24 


3415 


2611 


14 


27/8 


41/16 


17x24 


3856 


2948 


15 


31/16 


4->A6 


18x24 


4321 


3304 


153/ 4 


31/4 


4"V8 


19x24 


4810 


3678 


161/2 


37/16 


413/16 


20x24 


5337 


4081 


171/2 


35/ 8 


31/16 



Exhaust-nozzles in Locomotive Boilers. — A committee of the 
Am. Ry. Master Mechanics' Ass'n. in 1890 reported that they had, after 
two years of experiment and research, come to the conclusion that, 
owing to the great diversity in the relative proportions of cylinders and 
boilers, together with the difference in the quality of fuel, any rule which 
does not recognize each and all of these factors would be worthless. 

The committee was unable to devise any plan to determine the size 
of the exhaust-nozzle in proportion to any other part of the engine or 
boiler. The conditions desirable are: That it must create draught 
enough on the fire to make steam, and at the same time impose the least 
possible amount of work on the pistons in the shape of back pressure. 
It should be large enough to produce a nearly uniform blast without 
lifting or tearing the fire, and be economical in its use of fuel. The 
Annual Report of the Association for 1896 contains interesting data on 
this subject. 

Much important information regarding stacks and exhaust nozzles is 
embodied in the tests at Purdue University, reported to the Master 
Mechanics' Ass'n. in 1896 and in the tests reported in the American 
Engineer in 1902 and 1903. 

Fire-brick Arches in Locomotive Fire-boxes. — A committee of 
the Am. Ry. Master Mechanics' Ass'n. in 1890 reported strongly in favor 
of the use of brick arches in locomotive fire-boxes. They say: It is the 
unanimous opinion of all who use bituminous coal and brick arch, that 
it is most efficient in consuming the various gases composing black 
smoke, and by impeding and delaying their passage through the tubes, 
and mingling and subjecting them to the heat of the furnace, greatly 
lessens the volume ejected, and intensifies combustion, and does not in 
the least check but rather augments draught, with the consequent saving 
of fuel and increased steaming capacity that might be expected from 
such results, This in particular when used in connction with extension 
front, 



o 

o 


O 


Ob 


O'OO Oc 


o 


o 


o o 



1092 LOCOMOTIVES. 

Arches now (1909) are not quite so much in favor, largely on account 
of the difficulty and delay caused to workmen when flues must be calked, 
as occurs frequently in bad water districts, and some of their former 
advocates are now omitting them altogether. 

Economy of High Pressures. — Tests of a Schenectady locomotive 
with cylinders 16 X 24 ins., at the Purdue University locomotive testing 
plant, gave results as follows: (Eng. Digest, Mar., 1909; Bull. No. 26, Univ. 
of 111. Expt. Station). 

Boiler pressure, lbs. per sq. in. 120 140 160 180 200 220 210 
Steam per 1 H.P. hour, lbs. 29.1 27.7- 26.6 26. 25.5 25.1 24.7 
Coal per 1 H.P. hour, lbs. 4 3.77 3.59 3.50 3.43 3.37 3.31 

In the same series of tests the economy of the boiler at different rates of 
driving and different pressures was determined, the results leading to the 
formula E = 11 .305 — 0.221 H, in which E = lbs. evaporated from and 
at 212" per lb. of Youghiogheny coal, and H the equivalent evaporation 
_per sq. ft. of heating surface per hour, with an average error for any 
pressure which does not exceed 2.1%. 

Leading American Types of Locomotive for Freight and 
Passenger Service. 

1. The eight-wheel or " American" passenger type, having four coupled 
driving-wheels and a four-wheeled truck in front. 

2. The "ten-wheel" type, for mixed traffic, having six coupled drivers 
and a leading four-wheel truck. 

3; The "Mogul" freight type, having six coupled driving-wheels and 
a pony or two-wheel truck in front. 

4. The "Consolidation" type, for heavy freight service, having eight 
coupled driving-wheels and a pony truck in front. 

Besides these there is a great variety of types for special conditions of 
service, as four-wheel and six-wheel switching-engines, without trucks; 
the Forney type used on elevated railroads, with four coupled wheels 
under the engine and a four-wheeled rear truck carrying the water-tank 
and fuel; locomotives for local and suburban service with four coupled 
driving r wheels, with a two-wheel truck front and rear, or a two-wheel 
truck front and a four-wheel truck rear, etc. "Decapod" engines for 
heavy freight service have ten coupled driving-wheels and a two-wheel 
truck in front. 

n O O o O e 

OOP OF 

P P P o n o 
P DOC) o h 

Classification of Locomotives (Penna. R. R. Co., 1900). — Class A, 
two pairs of drivers and no truck. Class B, three pairs of drivers and no 
truck. Class C, four pairs of drivers and no truck. Class D, two pairs of 
drivers and four-wheel truck. Class E, two pairs of drivers, four-wheel 
truck, and trailing wheels. Class F, three pairs of driving-wheels and 
two-wheel truck. Class G, three pairs of drivers and four-wheel truck. 
Class H, four pairs of drivers and two-wheel truck. Class A is com- 
monly called a "four-wheeler"; B, a " six- wheeler " ; D, an "eight- 
wheeler," or "American" type; E, "Atlantic" type; F, "Mogul"; 
G, " ten- wheeler " ; H, "Consolidation." 

Modern Classification. — The classes shown above, lettered A, B, C, 
etc., are commonly represented respectively by the symbols 0-4-0; 
0-6-0; 0-8-0, 4-4-0; 4-4-2, 2-6-0; 4-6-0; 2-8-0; the first figure being 
the number of wheels in the truck, the second the driving-wheels, and the 
third the trailers. Other types are the "Pacific," 4-6-2; the "Prairie," 2-6-2; 



LOCOMOTIVES. 



1093 



and the "Santa Fe," 2-10-2. Engines on the Mallet system, with two 
locomotive engines under one boiler, are classified 0-8-8-0, 2-6-6-2, etc. 

Formulae for Curves. (Baldwin Locomotive Works.) 
Approximate Formula for Radius. Approximate Formula for Swing. 

R = 0.7646 W -v- 2 P. WT h- 2 R = S. 



O 



o o 



o 



o 



R = radius of min. curve in feet. W — rigid wheel-base. 

P = play of driving-wheels in T = total wheel-base. 

decimals of 1 ft. R = radius of curve. 

W = rigid wheel-base in feet. S — swing on each side of centre. 

Steam-distribution for High-speed Locomotives. 

(C. H. Quereau, Eng'g News, March 8, 1894. 

Balanced Valves. — Mr. Philip Wallis, in 1886, when Engineer of Tests 
for the C, B. & Q. R. R., reported that while 6 HP. was required to 
work unbalanced valves at 40 miles per hour, for the balanced valves 
2.2 HP. only was necessary. 

[Later tests were reported by the Master Mechanics' Committee in 1896. 
Unbalanced valves required from 3/ 4 to 21/2 per cent of the LHP. for 
their motion, balanced valves from 1/3 to 1/2 as much, and piston valves 
about 1/5 or i/e. Generally in balanced valves, the area of balance = 
area of exhaust port + area of two bridges + area of one steam port. J 

Effect of Speed on Average Cylinder-pressure. — Assume that a locomo- 
tive has a train in motion, the reverse lever is placed in the running 
notch, and the track is level; by what is the maximum speed limited? 
The resistance of the train and the load increase, and the power of the 
locomotive decreases with increasing speed till the resistance and power 
are equal, when the speed becomes uniform. The power of the engine 
depends on the average ^pressure in the cylinders. Even though the 
cut-off and boiler-pressure remain the same, this pressure decreases as 
the speed increases; because of the higher piston-speed and more rapid 
valve-travel the steam has a shorter time in which to enter the cylinders 
at the higher speed. The following table, from indicator-cards taken 
from a locomotive at varying speeds, shows the decrease of average 
pressure with increasing speed: 

Miles per hour 46 51 51 53 54 57 60 66 

Speed, revolutions 224 248 248 258 263 277 292 321 

Average pressure per sq. in.: 

Actual 51.5 44.0 47.3 43.0 41.3 42.5 37.3 36.3 

Calculated 46.5 46.5 44.7 43.8 41.6 39.5 35.9 

The "average pressure calculated" was figured on the assumption that 
the mean effective pressure would decrease in the same ratio that the 
speed increased. The main difference lies in the higher steam-line at 
the lower speeds, and consequent higher expansion-line, showing that 
more steam entered the cylinder. The back pressure and compression- 
lines agree quite closely for all the cards, though they are slightly better 
for the slower speeds. That the difference is not greater may safely be 
attributed to the large exhaust-ports, passages, and exhaust tip, which 
is 5 in. diameter. These are matters of great importance for high speeds. 

Boiler-pressure. — Assuming that the train resistance increases as the 
speed after about 20 miles an hour is reached, that an average of 50 lbs. 
per sq. in. is the greatest that can be realized in the cylinders of a given 
engine at 40 miles an hour, and that this pressure furnishes just sufficient 
power to keep the train at this speed, it follows that, to increase the 
speed to 50 miles, the mean effective pressure must be increased in the 
same proportion. To increase the capacity for speed of any locomotive 
its power must be increased, and at least by as much as the speed is to 
t>e increased, One way to accomplish this is to increase the boiler-» 



1094 LOCOMOTIVES. 

Eressure. That this is generally realized, is shown by the increase in 
oiler-pressure in the last ten years. For twenty-three single-expansion 
locomotives described in the railway journals this year the steam-pres- 
sures are as follows: 3, 160 lbs.; 4, 165 lbs.; 2, 170 lbs.; 13 180 lbs.; 
1, 190 lbs. 

Valve-travel. — An increased average cylinder-pressure may also be 
obtained by increasing the valve-travel without raising the boiler- 
pressure, and better results will be obtained by increasing both. The 
longer travel gives a higher steam-pressure in the cylinders, a later 
exhaust-opening, later exhaust-closure, and a larger exhaust-opening — 
all necessary for high speeds and economy. I believe that a 20-in. 
port and 61/2-in. (or even 7-in.) travel could be successfully used for 
high-speed engines, and that frequently by so doing the cylinders could 
be economically reduced and the counter-balance lightened. Or, better 
still, the diameter of the drivers increased, securing lighter counterbal- 
ance and better steam-distribution. 

Size of Drivers. — Economy will increase with increasing diameter of 
drivers, provided the work at average speed does not necessitate a cut-off 
longer than one fourth the stroke. The piston-speed of a locomotive 
with 62-in. drivers at 55 miles per hour is the same as that of one with 
68-in. drivers at 61 miles per hour. 

Steam-ports. — The length of steam-ports ranges from 15 in. to 23 in., 
and has considerable influence on the power, speed, and economy of the 
locomotive. In cards from similar engines the steam-line of the card 
from the engine with 23-in. ports is considerably nearer boiler-pressure 
than that of the card from the engine with 17V4-in- ports. That the 
higher steam-line is due to the greater length of steam-port there is little 
room for doubt. The 23-in. port produced 531 H.P. in an 181/2-in. 
cylinder at a cost of 23.5 lbs. of water per I. H.P. per hour. The 171/4 
in. port, 424 H.P., at the rate of 22.9 lbs. of water, in a 19-in. cylinder. 

Allen Valves. — There is considerable difference of opinion as to the 
advantage of the Allen ported- valve. (See Eng. News, July 6, 1893.) 

A Report on the advantage of Allen valves was made by the Master 
Mechanics' Committee of 1896. 

Speed of Railway Trains. — In 1834 the average speed of trains on 
the Liverpool and Manchester Railway was 20 miles an hour; in 1838 it 
was 25 miles an hour. But by 1840 there were engines on the Great 
Western Railway capable of running 50 miles an hour with a train and 
80 miles an hour without. {Trans. A. S. M. E., vol. xiii, 363.) 

The limitation to the increase of speed of heavy locomotives seems at 
present to be the difficulty of counterbalancing the reciprocating parts. 
The unbalanced vertical component of the reciprocating parts causes 
the pressure of the driver on the rail to vary with every revolution. 
Whenever the speed is high, it is of considerable magnitude, and its 
change in direction is so rapid that the resulting effect upon the rail is 
not inappropriately called a "hammer blow." Heavy rails have been 
kinked, and bridges have been shaken to their fall under the action of 
heavily balanced drivers revolving at high speeds. The means by 
which the evil is to be overcome has not yet been made clear. See 
paper by W. F. M. Goss, Trans. A. S. M. E., vol. xvi. 

Much can be accomplished, however, by carefully designing and 
proportioning the counter-balance in the wheels and by using light, but 
strong, reciprocating parts. Pages 41-74 of "Locomotive Operation," 
gives complete rules and results. 

Balanced compound locomotives, with 4 cylinders, the adjacent pis- 
tons and crossheads being connected 180° apart have also done much 
to reduce the disturbance of the moving parts. 

Engine No. 999 of the New York Central Railroad ran a mile in 32 
seconds equal to 112 miles per hour, May 11, 1893. 
Speed in) ^ circum. of driving-wheels in in. X no. of rev, per min. X 60 

hour ) 63,360 

= diam., of driving-wheels in in. X no. of rev. per min. X.003 
(approximate, giving result 8/10 of 1 per cent too great). 

Performance of a High-speed Locomotive. — The Baldwin com- 
pound locomotive No. 1027, on the Phila. & Atlantic City Ry., in 1897 
made a record as follows: 



LOCOMOTIVES. 



1095 



For the 52 days the train ran, from July 2d to August 31st, the average 
time consumed on the run of 551/2 miles from Camden to Atlantic City 
was 48 minutes, equivalent to a uniform rate of speed from start to stop 
of 69 miles per hour. On July 14th the run from Camden to Atlantic 
City was made in 461/2 min., an average of 71.6 miles per hour for the total 
distance. On 22 days the train consisted of 5 cars and on 30 days it was 
made up of 6, the weight of cars being as follows: combination car, 57,200 
lbs.; coaches, each, 59,200 lbs.; Pullman car, 85,500 lbs. 

The general dimensions of the locomotive are as follows: cylinders, 
13 and 22 X 26 in.; height of drivers, 841/4 in.; total wheel-base, 26 ft. 
7 in.; driving-wheel base, 7 ft. 3 in.; length of tubes, 13 ft.; diameter of 
boiler, 583/ 4 in.; diameter of tubes, 13/ 4 in.; number of tubes, 278; length 
of fire-box, 113 7/gin.; width of fire-box, 96 in.; heating-surface of fire- 
box, 136.4 sq. ft.; heating-surface of tubes, 1614.9 sq. ft.; total heating- 
surface, 1835.1 sq. ft.; tank capacity, 4000 gallons; boiler-pressure, 
200 lbs. per sq. in.; total weight of engine and tender, 227,000 lbs.; 
weight on drivers (about), 78,600 lbs. 

Fuel Efficiency of American Locomotives. — Prof. W. M. Goss, as 
a result of a series of tests run on the Purdue locomotive, finds the dis- 
position of the heat developed by burning coal in a locomotive fire-box 
to be on the average about as shown in the following table: 

Absorbed by steam in the boiler, 52 % ; by the superheater, 5 % ; 
total, 57 %. Losses: In vaporizing moisture in the coal, 5 %; discharge 
of CO., 1 %; high temperature of the products of combustion, 14 %; 
unconsumed fuel in the form of front-end cinders, 3 % ; cinders or sparks 
passed out of the stack, 9 %; unconsumed fuel in the ash, 4 %; radia- 
tion, leakage of steam and water, etc., 7 %. Total losses, 43 %. 

It is probable that these losses are considerably less than the losses 
which are experienced in the average locomotive in regular railway 
service. — (Bulletin No. 402, U.S. Geol. Survey, 1909.) 

Locomotive Link Motion. — Mr. F. A. Halsey, in his work on " Loco- 
motive Link Motion," 1898, shows that the location of the eccentric-rod 
pins back of the link-arc and the angular vibrations of the eccentric- 
rods introduce two errors in the motion which are corrected by the 
angula*r vibration of the connecting-rod and by locating the saddle-stud 
back of the link-arc. He holds that it is probable that the opinions of 
the critics of the locomotive link motion are mistaken ones, and that it 
comes little short of all that can be desired for a locomotive valve motion. 
The increase of lead from full to mid gear and the heavy compression at 
mid gear are both advantages and not defects. The cylinder problem of 
a locomotive is entirely different from that of a stationary engine. With 
the latter the problem is to determine the size of the cylinder and the dis- 
tribution of steam to drive economically a given load at a given speed. 
With locomotives the cylinder is made of a size which will start the 
heaviest train which the adhesion of the locomotive will permit, and the 
problem then is to utilize that cylinder to the best advantage at a greatly 
increased speed, but under a greatly reduced mean effective pressure. 

Negative lead at full gear has been used in the recent practice of some 
railroads. The advantages claimed are an increase in the power of the 
engine at full gear, since positive lead offers resistance to the motion of 
the piston; easier riding; reduced frequency of hot bearings; and a 
slight gain in fuel economy. Mr. Halsey gives the practice as to lead on 
several roads as follows, showing great diversity: 





Full Gear 
Forward, in. 


Full Gear 
Back, in. 


Reversing 
Gear, in. 


New York, New Haven & 


Vl6 pos. 


1/32 pos. 
1/16 neg. 


3 /l6 neg. 


V4 neg. 
1/4 neg. 


1/4 pos. 








abt 3/ 16 




9/64 neg. 





Chicago Great Western 

Chicago & Northwestern 


3 /l6 to 9/ie 
1/4 pos. 





1096 



LOCOMOTIVES. 



DIMENSIONS OF SOME LARGE AMERICAN 
LOCOMOTIVES, 1893 AND 1904. 

Of the four locomotives described in the table on the next page the first 
two were exhibited at the Chicago Exposition in 1893. The dimensions 
are from Engineering News, June, 1893. The first, or Decapod engine, 
has ten-coupled driving-wheels. - It is one of the heaviest and most power- 
ful engines built up to that date for freight service. The second is a sim- 
ple engine, of the standard American 8-wheel type, 4 driving-wheels, and 
a 4-wheel truck in front. This engine held the world's record for speed 
in 1893 for short distances, having run a mile in 32 seconds. 

The other two engines formed part of the exhibit of the Baldwin Loco- 
motive Works at the St. Louis Exposition in 1904. The Santa Fe type 
engine has five pairs of driving-wheels, and a two-wheeled truck at the front 
and at the rear. It is equipped with Vauclain tandem compound cylinders. 

Dimensions of Some American Locomotives. 

(Baldwin Loco. Wks., 1904-8.) 







Boilers. 


Tubes. 


Heating 
Surface. 


Driving 
Wheels 

Diam., 


Weight, lbs. 


S 03 

it 


firn 


a?*S 


No. 


Ln 








on 


Total 


"8?; 


<u 


o3 c 




.2 c 


a 


<D . 


-Srr 


ins. 


Drivers 


Engine 


rt 


GO 


w 


O m 




.-1 


fe m 


H M 




















ft. in. 










i 


150 


47 


9 


97 


2 


11 7 


41 


586 


37 


44,420 


52,720 


2 


160 


50 


14.6 


160 


2 


10 6 


75 


.873 


48 


72,150 


84,650 


3 


700 


60 


7.5 9 


287 


2 


11 7 


133 


1733 


69 


83,680 


124,420 


4 


700 


67. 


30 


272 


2 


16 1 


136 


2279 


68 


112,000 


159,000 


5 


700 


76 


37.2 


298 


21/4 


13 10 


200 


2414 


51 


164,000 


179,500 


6 


700 


68 


35 


306 


21/4 


14 6 


195 


2593 


56 


166,000 


186,000 


7 


700 


66 


49.5 


273 


21/4 


18 10 


190 


3015 


79 


101,420 


193,760 


8 


700 


70 


53.5 


318 


21/4 


19 


195 


3543 


79 


144,600 


209,210 


9 


7,10 


70 


55 


303 


21/4 


21 


190 


3772 


74 


151,290 


230,940 


10 


7.7.5 


78 


58.5 


463 


21/ 4 


19 


210 


5155 


57 


237,800 


267,800 


11 


200 


84 


68.4 


401 


21/4 


21 


232 


4941 


57 


394,150 


475,900 



Type and cylinder size: 1 Mogul, 13X18; 2, Mogul, 16X20; 3, American, 
18X24; 4, 10-wheel balanced compound, 16X26 and 26X28; 5. Consoli- 
dation, 22 X28; 6, Consolidation, 23 and 35X32; 7, Atlantic, 15 and 25 X 
26; 8, Prairie, 17 and 28X28; 9, Pacific, 22X28; 10, Decapod, 19 and 
32 X 32; 11, Mallet, two each 26 and 40 X 30. 

The Mallet Compound Locomotive. —The Mallet articulated loco- 
motive consists principally of two sets of engines flexibly connected under 
one boiler; the rear, which is a high-pressure engine of two cylinders, 
fixed rigid with the boiler and receiving the steam direct from the dome. 
The front or low-pressure engine, also provided with two cylinders, is 
capable of lateral movement to adjust itself to the curvature of the road 
on the same general principle as a radial truck. The high-pressure engine 
exhausts into a receiver flexibly connecting the cylinders of the two sets 
of engines, from which the low-pressure engine receives its steam supply 
and is exhausted from the latter through a flexible pipe to the stack. 
Each cylinder has its independent valve and gear connected to ana 
operated with a common reversing rigging. By this means the tractive 
power can be doubled over that of the ordinary engine for a given weipnt 
of rail with a substantial saving in fuel. (See paper by C. J. Melhn, Trans. 
A. S. M. E., 1909.) 

This type of locomotive is adapted to a wider range of service than per- 
haps any other design. It was originally intended for narrow-gauge roads 
of light construction, necessitating sharp curves and steep grades, in com- 
bination with light rails. The characteristics of this design are flexibility 
and uniform distribution of weight combined with the use of two separate 
engines which would not slip at the same time, and the total weight carried 
on the drivers, giving great tractive power. The first engine of this class 



LARGE AMERICAN LOCOMOTIVES 



1097 



Baldwin. 
N.Y., L.E. 
&W.R.R. 

Decapod 

Freight. 



N.Y. C. & 
H.R.R. 
Empire 

State 
Express. 
No. 999. 



Baldwin. 

Santa Fe 

Type 

2-10-2 

Freight. 



Baldwin. 

Pacific 

Type 4-6-2 

Passenger. 



Running-gear: 

Driving-wheels, diam. . 

Truck " " ... 

Journals, driving-axles 
truck- 
" tender- 
Wheel-base : 

Driving 

Total engine 

" tender 

eng. and tender. . 
Wt. in working-order: 

On drivers 

On truck-wheels 

Engine, total 

Tender " 

Eng. and tend., loaded 
Cylinders: 

h.p.(2) - 

1-P- (2) ....... 

Piston-rod, diam 

Connecting-rod, l'gth. . 

Steam-ports 

Exhaust-ports 

Valves, out. lap, h.p. . . 
Out. lap, l.p. . . . 

" in. lap, h.p 

" in. lap, l.p 

max. travel . . . 

lead, h.p 

" lead, l.p 

Boiler.— Type 

Diam. barrel inside .... 
Thickness of plates . . . 
Height from rail to 

center line 

Length of smoke-box . . 

Working pressure 

Firebox.— type 

Length inside 

Width " 

Depth at front 

Thickness side plates. . 
back plate . . 
crown-sheet, 
tube sheet.. . 

Grate-area 

Stay-bolts, U/8 in 

Tubes — iron.. 

Pitch 

Diam., outside 

Length 

Heating-surface : 

Tubes, exterior 

Fire-box. 

Miscellaneous: 

Exhaust-nozzle, diam . 

Stack, smal'st diam. . . 

height from 

rail to top 



50 in. 

30 " 
9 XlOin. 
5 X10" 
41/ 2 X 9 " 

18 ft. 10 in. 

27 " 3 " 

16 " 8 " 

53 " 4 " 

170,000 lbs. 
29,500 " 
192,500 " 
117,500 " 
310,000 " 

16X28 in. 
27X28 " 

4 in. 
9' 87/ 16 " 

281/2X2 in. 

281/2X8 " 

7/s in. 

5 /8 " 



86 in. 
40 " 

9 X 121/2 in 
6I/4XIO " 
41/sX 8 " 

8 ft. 6 in. 
23" 11 " 
15 "21/2 ' 
47 " 81/ 8 " 

84,000 lbs. 

40,000 " 
124,000 " 

80,000 " 
204,000 " 

19X24 in. 



33/s in. 
8 ft. IV2 in. 

U/ 2 Xl8in. 

23/4X18 " 

1 in. 



6 in. 

Vl6in. 

5/16 " 

Straight 

6 ft. 21/2 in. 

3/4 in. 

8 ft. in. 
5 " 77/8 " 

180 lbs. 

Wootten 

10' 1 1 9/ie" 

8 ft. 21/8 in. 

4 " 6 " 

5 /l6 in. 

5/16 " 

3/8" 

V2" 

89.6 sq. ft. 

pitch, 41/4 in. 

354 

23/4 in. 

2 

lift. 11 in. 

2,208.8 ft. 
234.3 " 

5 in. 
1 ft. 6 in. 

15ft.61/ 2 in. 



VlO in. 
"51/2 in'-' 



Wagon top 

4ft. 9in. 

9/16 in. 

7 ft. 11 1/2 in. 
4 " 8 

190 lbs. 

Buchanan 

9 ft. 63/ 8 in. 

3 " 47/8 " 

6 " II/4 " 

5/16 in. 

5/!6 " 

3/8" 

V2 " 

30.7 sq.ft. 

4 in. 

268 



57 in. 
29 1/4 & 40" 
1 1 X 12" 

6V2XIO" 
71/2X12"' 

19 ft. 9 in. 
35 " II " 



234,580 It 
52,660 
287,240 



19X32 in. 

32X32 " 



293/4X15/8' 

and 13/ 4 " 

293/4X63/4" 

7/8 in. 

3/4 " 
neg. 1/4 in. 
neg. 3/ 8 " 

6 in. 

" 

Vs " 
Wagon to 

783/4 in. 
7/8 & 1 Vie" 



225 lbs. 



108 in. 
78 " 
80 1/4 in. 
781/4 " 
3/8 " 



2 in. 
12 ft. in. 



1,697 g 
233 



31/2 in. 
1 ft. 3 1/4 in. 



14 ft. 10 in. 



21/4 in. 
20 ft. 



4,586 sq. ft. 
210 " 



* Back truck journals. 



1098 



LOCOMOTIVES. 



was built about 1887, and in 1909 there were approximately 500 running in 
Europe. They are now extensively in use in the United States for the 
heaviest service. The largest locomotive yet built is described in Eng. 
News, April 29, 1909. It was built by the Baldwin Locomotive Works 
for use on the heavy grades of the Southern Pacific R.R. The principal 
dimensions areas follows: Cylinders, 26 and 40 X 30 ins.; valves, balanced 
piston; boiler (steel): diameter, 84 ins.; thickness, i3/i6 and 27/ 32 ins.; work- 
ing pressure, 200 lbs. per sq. in.; fuel, oil; fire-tubes, 401, 2i/4ins. dia. X 
21 ft.; firebox: length, 126 ins., width, 781/4 ins., depth, front, 751/2 ins., 
depth, back, 701/2 ins.; water spaces, 5 ins.; grate area, 68.4 sq. ft.; 
feed-water heater: length, 63 ins., tubes, 401, 21/4 ins. dia.; heating sur- 
face: firebox, 232 sq. ft., fire-tubes, 4941 sq. ft., feed-water heater tubes, 
1220 sq. ft.; smokebox superheater, 655 sq. ft.; wheels: driving (16), 
57 ins. O. dia., main journals, 11 X 12 ins., other journals, 10 X 12 ins.; 
truck (4), 30 1/2 ins. dia., journals, 6 X 10 ins.; tender (8),33ty2 ins. dia., 
journals, 6X11 ins.; wheelbase: driving, 39 ft. 4 ins., rigid, 15 ft., total 
engine, 56 ft. 7 ins., total engine and tender, 83 ft. 6 ins.; length over all, 
93 ft. 6V2 ins.; weight: on drivers, 394,150 lbs., on front truck, 14,500 lbs., 
on back truck, 17,250 lbs., total engine 425,900 lbs., total engine and 
tender 596,000 lbs.; tender: water tank capy., 9000 gals., oil tank capy., 
2850 gals. 

Indicated Water Consumption of Single and Compound Loco- 
motive Engines at Varying Speeds. 

C. H. Quereau, Eng'g News, March 8, 1894. 



Two-cylinder Compound. 


Single-expansion 




Revolutions. 


Speed, 

miles per 

hour. 


Water per 

I.H.P. per 

hour. 


Revolu- 
tions. 


Miles per 
Hour. 


Water. 


100 to 150 
150 to 200 
200 to 250 
250 to 275 


21 to 31 
31 to 41 
41 to 51 
51 to 56 


18.33 lbs. 
18.9 lbs. 
19.7 lbs. 
21.4 lbs. 


151 
219 
253 
307 
321 


31 
45 
52 
63 
66 


21.70 
20.91 
20.52 
20.23 
20.01 



It appears that the compound engine is the more economical at low 
speeds, the economy decreasing as the speed increases, and that the 
single engine increases in economy with increase of speed within ordinary 
limits, becoming more economical than the compound at speeds of more 
than 50 miles per hour. 

The C, B. & Q. two-cylinder compound, which was about 30% less 
economical than simple engines of the same class when tested in passenger 
service, has since been shown to be 15% more economical in freight 
service than the best single-expansion engine, and 29% more economical 
than the average record of 40 simple engines of the same class on the 
same division. 

The water rate is also affected by the cut-off; the following table gives 
what we should consider very good results in practice, though better 
(i.e. lower results) have occasionally been obtained. (G. R. Henderson, 
1906.) 

Cut-off per cent of stroke 10 20 30 40 50 

Lbs. water per I.H.P. hour — simple. . 26 23 22 22 23 

Lbs. water per I.H.P. hour — compound .. .. 18 18 18 



Cut-off per cent of stroke . . . 
Lbs. water per I.H.P. hour - 
Lbs. water per I H.P. hour - 



60 

- simple ... 24 
■compound 18 1/2 



70 
26 

191/2 



80 90 100 

29 33 38 

201/2 221/2 25 



Indicator-tests of a Locomotive at High Speed. (Locomotive 
Eng'g, June, 1893.) — Cards were taken by Mr. Angus Sinclair on the 
locomotive drawing the Empire State Express. 







Results 


op Indicator-diagrams. 




Card No. 


Revs 


Miles 
per hour. 


I.H.P. 


Card No. 


Revs. 


Miles 
per hour 


1 


160 


37.1 


648 


7 


304 


70.5 


2 


260 


60.8 


728 


8 


296 


68.6 


3 


190 


44 


551 


9 


300 


69.6 


4 


250 


58 


891 


10 


304 


70.5 


5 


260 


60 


960 


11 


340 


78.9 


6 


298 


69 


983 


12 


310 


71.9 



LOCOMOTIVES. 1099 



I.H.P. 

977 
972 
1,045 
1,059 
1,120 
1,026 
The locomotive was of the eight-wheel type, built by the Schenectady 
Locomotive Works, with 19 X 24 in. cylinders, 78-in. drivers, and a 
large boiler and fire-box. Details of important dimensions are as fol- 
lows: Heating-surface of fire-box, 150.8 sq. ft.; of tubes. 1670.7 sq. ft.; 
of boiler, 1821.5 sq. ft. Grate area, 27.3 sq. ft. Fire-box: length, 
8 ft.; width, 3 ft. 47/ 8 in. Tubes, 268; outside diameter, 2 in. Ports: 
steam, 18 X 1 1/4 in.; exhaust, 18 X 23/4 in. Valve-travel, 51/2 in. Out- 
side lap, 1 in.; inside lap, V64 in. Journals: driving-axle, 8I/2X 10i/2in.; 
truck-axle, 6 X 10 in. 

The train consisted of four coaches, weighing, with estimated load, 
340,000 lbs. The locomotive and tender weighed in working order 200,000 
lbs., making the total weight of the train about 270 tons. During the 
time that the engine was first lifting the train into speed diagram No. 1 
was taken. It shows a mean cylinder-pressure of 59 lbs. According to 
this, the power exerted on the rails to move the train is 6553 lbs., or 24 
lbs. per ton. The speed is 37 miles an hour. When a speed of nearly 
60 miles an hour was reached the average cylinder-pressure is 40.7 lbs., 
representing a total traction force of 4520 lbs., without making deduc- 
tions for internal friction. If we deduct 10% for friction, it leaves 15 lbs. 
per ton to keep the train going at the speed named. Cards 6, 7, and 8 
represent the work of keeping the train running 70 miles an hour. They 
were taken three miles apart, when the speed was almost uniform. The 
average cylinder-pressure for the three cards is 47.6 lbs. Deducting 
10% again for friction, this leaves 17.6 lbs. per ton as the power exerted 
in keeping the train up to a velocity of 70 miles. Throughout the trip 
7 lbs. of water were evaporated per lb. of coal. The work of pulling 
the train from New York to Albany was done on a coal consumption of 
about 31/8 lbs. per H.P. per hour. The highest power recorded was at 
the rate of 1120 H.P. 

Locomotive-testing Apparatus at the Laboratory of Purdue Uni- 
versity. (W. F. M. Goss, Trans. A. S. M. K., vol. xiv, 826.) — The 
locomotive is mounted with its drivers upon supporting wheels which 
are carried by shafts turning in fixed bearings, thus allowing the engine 
to be run without changing its position as a whole. Load is supplied by 
four friction-brakes fitted to the supporting shafts and offering resistance 
to the turning of the supporting wheels. Traction is measured by a 
dynamometer attached to the draw-bar. The boiler is fired in the 
usual way, and an exhaust-blower above the engine, but not in pipe 
connection with it, carries off all that may be given out at the stack. 

A Standard Method of Conducting Locomotive-tests is given in a report by 
a Committee of the A. S. M. E. in vol. xiv of the Transactions, page 1312. 
Locomotive Tests of the Penna. R. R. Co. — Eight locomotives were 
tested in the dynamometer testing plant built by the P. R. R. Co. at the 
St. Louis Exhibition in 1903. Among the principal results obtained and 
conclusions derived are the following: 

Boiler Performance. 
Coal per sq. ft. grate per hour, lbs. 

20 40 60 80 100 120 

Equiv. evap. per sq. ft. H. S. per hour 

3-5 5-7.5 7-10 8.2-12 10.4-14 11.4-15.3 
Coal per sq. ft. H. S. per hour 

0.6 0.8 1.0 1.2 1.4 1.6 1.8 

Equiv. evap. per lb. dry coal 

10-11.5 9-10.5 8.2-9.7 7.7-9.1 7.1-8.5 6.6-8.1 6.2-7.7 
Equiv. evap. per sq. ft. H. S. per hour 

4 6 8 10 12 14 

Equiv. evap. per lb. dry coal 

9.7-12.1 8.8-11.3 7.8-10.5 6.8-9.6 5.8-8.8 5.5-8 



1100 



LOCOMOTIVES, 



The coal used in these tests was a semi-bituminous, containing 16.25% 
volatile combustible, 7.00% ash and 0.90% moisture. 

The maximum boiler capacity ranged from 8 1/2 to more than 16 lbs. 
of water evaporated per hour per sq. ft. of heating surface. Little or no 
advantage was found in the use of Serve or ribbed tubes. 

The boiler efficiency decreases" as the rate of power developed increases. 

Furnace losses due to excess air are no greater with large grates properly 
fired than with smaller ones. The boilers with small grates were inferior 
in capacity to those with la^ge grates. 

No special advantage is derived from large fire-box heating surface; the 
tube heating surface is effective in absorbing heat not taken up by the 
fire-box. 

Engine Performance. 

Maximum I.H.P., four freight locomotives, 1041, 1050, 1098, 1258 

Maximum I.H.P., four passenger locomotives, 816, 945, 1622, 1641 





Kind of Locomotive. 




Simple 
Freight. 


Com- 
pound 
Freight. 


Com- 
pound 
Passen- 
ger. 




23.67 
23.83 
28.95 


20.26 
22.03 
25.31 


18.86 


Water per I.H.P. hr. at maximum load 

Water per I.H.P. hr. at max. consumption. .. 


21.39 
24.41 



The steam consumption of simple locomotives operating at all speeds 
and cut-offs commonly employed on the road falls between the limits 
of 23.4 and 28.3 lbs. per I.H.P. hour; compound locomotives between 
18.6 and 27 lbs.; and with superheating the minimum steam consumption 
was reduced to 16.6 lbs. of superheated steam. 

Comparing a simple and a compound locomotive, the simple enerine 
used 40% more steam than the compound at 40 revs, per min., 27% more 
at 80 revs., and only 7% more at 160 revs, per min. 

The frictional resistance of the engines snowed an extreme variation 
ranging from 6 to 38% of the indicated horse-power. The frictional 
losses increased rapidly at speeds in excess of 160 revs, per min. It 
appears that the matter of machine friction is closely related to that of 
lubrication. With oil lubrication a stress at the draw-bar of approxi- 
mately 500 lbs. is required to overcome the friction of each coupled axle, 
while with grease the required force is from 800 to 1100 lbs. 

The lowest figures for dry coal consumed per dynamometer H.P. hour 
were approximately as follows: 
Revs, per min. 40 80 160 240 

Compound freight engine, {§?h°P? 500° fof 80C? "ll 
Compound passenger engine, {^jj ^ 1 /;;; |q| j^ ^5% 

A complete report of the St. Louis locomotive tests is contained in a 
book of 734 pages and over 800 illustrations, published by the Penna. R.R. 
Co., Philadelphia, 1906. See also pamphlet on Locomotive Tests, pub- 
lished by Amer. Locomotive Co., New York, 1906, and Trans. A. S. M. E., 
xxvii, 610. 

Weights and Prices of Locomotives, 1885 and 1905. 
(Baldwin Loco. Wks.) 



Type. 


W'gt 


Price 


Price 
per 
lb. 

$ 0828 
.0912 
.0892 
.0854 


2 


American. . . . 

Mogul 

Ten wheel . . . 
Consolidation 


80,857 
72,800 
85,000 
92,400 


$6,695 
6,662 
7.583 
7,888 



Type. 



American 

Atlantic 

Pacific 

Ten wheel 
Consolidation 



Price 
W'ght Price per 



102,000 
187,200 
227,000 
156,000 
192,460 



$9,410 
15,750 
15,830 
13,690 
14,500 



$.092 
083 
070 



" 



LOCOMOTIVES. 



1101 



The price per pound is figured from the weight of the engine in working 
order, without the tender. 

Depreciation of Locomotives. — (Baldwin Loco. Wks.) — It is suggested 
that for the first five years the full second-hand value of the locomotive 
(75% of first cost) be taken; for the second five years 85% of this value; 
forthe third five years, 70%; after 15 years, 50% of the second-hand value; 
and after 20 years, and as long as the engine remains in use, 25% of the 
first cost. 

The Average Train Loads of 14 railroads increased from 229 tons of 
2000 lbs. in 1895 to 385 tons in 1904. On the Chicago, Milwaukee & St. 
Paul Ry. the average load increased from 152 tens in 1895 to 281 tons in 
1903, and on the Lake Shore & Michigan Southern Ry. from 318 tons in 
1895 to 615 tons in 1903. In the same time the average cost of transpor- 
tation per ton mile on the C, M. & St. P. Ry. decreased from 0.67 to 0.58 
cent; and on the L. S. & M. S. Ry. increased from 0.39 to 0.41 cent, the 
decrease in cost due to heavier train loads being offset by higher cost for 
labor and material. 

Tractive Force of Locomotives, 1893 and 1905. 

(Baldwin Loco. Wks.) 



Passenger, 1893. 



Weight Trac- 

on tive Passenger, 1905. 

Driver. Force. 



Weight Trac- 

on tive 

Driver. Force. 



American, single-ex. 
American, comp .... 
American, single-ex.. 
American, comp 
Ten-wheel type, com 

Average 



75,210 
83,860 
64,560 
78,480 
93,850 



17,270 
12,900 
15,550 
14,050 
16,480 

15,250 



Atlantic, comp. .. . 
Atlantic, single-ex.. 
Pacific, single-ex. . 
Pacific, single-ex. . 
Atlantic, single-ex. 



101,420 
103,600 
141,290 
114,890 
80,930 



22,180 
23,800 
29,910 
25,610 
21,740 



Freight, 1893. 



Freight, 1905. 



24,648 



Consolidation, comp. 
Ten-wheel, s'gle-ex.. 

Mogul, single-ex 

Decapod, compound 



120,600 
101,000 
91,340 
172,000 



21,190 
23,310 
21,030 
35,580 



Sante Fe type, comp. 
Consol., 2-cyl. comp.. 



Consol , 
Consol., s 
Consol., s 



ngle-ex.. 
ngle-ex.. 
ngle-ex. . 



234,580 
166,000 
151,490 
171,560 
165,770 



Average . , 



62,740 
40,200 
40,150 
44,080 
45,170 



46,468 



"Waste of Fuel in Locomotives. — In American practice economy 
of fuel is necessarily sacrificed to obtain greater economy due to heavy 
train-loads. D. L. Barnes, in Eng. Mag., June, 1894, gives a diagram 
showing the reduction of efficiency of boilers due to high rates of com- 
bustion, from which the following figures are taken: 
Lbs. of coal per sq. ft. of grate per hour. 
Per cent efficiency of boiler 



12 


40 


80 


120 


160 


200 


80 


75 


67 


59 


51 


43 



A rate of 12 lbs. is given as representing stationary-boiler practice, 40 
lbs. English locomotive practice, 120 lbs. average American, and 200 
lbs. maximum American, locomotive practice. 

Pages 473 and 475 of Henderson's " Locomotive Operation" give 
diagrams of evaporation per lb. of various kinds of coal for different 
rates of combustion per sq. ft. grate area and heating surface. 

Advantages of Compounding. — Report of a Committee of the 
American Railwav Master Mechanics' Association on Compound Loco- 
motives (Am. Mach., July 3, 1890) gives the following summary of the 
advantages gained by compounding: (a) It has achieved a saving in the 
fuel burnt averaging 18% at reasonable boiler-pressures, with encourag- 
ing possibilities of further improvement in pressure and in fuel and water 
economy. (&) It has lessened the amount of water (dead weight) to be 



1102 LOCOMOTIVES. 

hauled, so that (c) the tender and its load are materially reduced in 
weight, (d) It has increased the possibilities of speed far beyond 60 
miles per hour, without unduly straining the motion, frames, axles, or 
axle-boxes of the engine, (e) It has increased the haulage-power at 
full speed, or, in other words, has increased the continuous H.P. devel- 
oped, per given weight of engine and boiler. (/) In some classes has 
increased the starting-power, (g) It has materially lessened the slide- 
valve friction per H.P. developed, (h) It has equalized or distributed 
the turning force on the crank-pin, over a longer portion of its path, 
which, of course, tends to lengthen the repair life of the engine, (i) In 
the two-cylinder type it has decreased the oil consumption, and has even 
done so in the Woolf four-cylinder engine, (j) Its smoother and steadier 
draught on the fire is favorable to the combustion of all kinds of soft 
coal; and the sparks thrown being smaller and less in number, it lessens 
the risk to property from destruction by fire. (&) These advantages 
and economies are gained without having to improve the man handling 
the engine, less being left to his discretion (or careless indifference) than 
in the simple engine. (I) Valve-motion, of every locomotive type, can 
be used in its best working and most effective position, (m) A wider 
elasticity in locomotive design is permitted; as, if desired, side-rods can 
be dispensed with or articulated engines of 100 tons weight, with inde- 
pendent trucks, used for sharp curves on mountain service, as suggested 
by Mallet and Brunner. 

Of 27 compound locomotives in use on the Phila. and Reading Rail- 
road (in 1892), 12 are in use on heavy mountain grades, and are designed 
to be the equivalent of 22 X 24 in. simple consolidations; 10 are in some- 
what lighter service and correspond to 20 X 24 in. consolidations; 5 are 
in fast passenger service. The monthly coal record shows: 

Gain in Fuel 
Class of Engine. No. Economy. 

Mountain locomotives , 12 25% to 30% 

Heavy freight service 10 12% to 17% 

Fast passenger 5 9% to 11% 

(Report of Com. A. R. M. M. Assn. 1892.) For a description of the 
various types of compound locomotive, with discussion of their relative 
merits, see paper by A. Von Borries, of Germany, the Development of 
the Compound Locomotive, Trans. A. S. M. E., 1893, vol. xiv, p. 1172. 

As a rule compounds cost considerably more for repairs, and require 
a better class of engineers and machinists to obtain satisfactory results. 
(Henderson.) 

Balanced Compound Locomotives. — There are two high-pressure 
cylinders placed between the frames and two low-pressure cylinders 
outside. The inside crank shaft has cranks 90° apart, and each outside 
crank pin is 180° from the inside crank pin on the same side, so that the 
engine on each side is perfectly balanced. The balanced piston valve is 
so made that high-pressure steam may be admitted to the low-pressure 
cylinder for starting. See circular of the Baldwin Loco. Wks., No. 62, 1907. 

Superheating in Locomotives. (R. R. Age Gazette, Nov. 20, 1908.) — 
Superheating steam in locomotives has been found to effect a saving of 
10 to 15% in the fuel consumption of a locomotive, and 8 to 12% of the 
water used, or with the same fuel to increase the horse-power and the 
tractive force. The Baldwin Locomotive Works builds a superheater in 
the smoke-box, where it utilizes part of the heat of the waste gases in 
drying the steam and superheating it 50 to 100° F. The heating surface 
of the superheater is from 1 2 to 22 % of the heating surface in the tubes and 
fire-box of the boiler. It is recommended to use a boiler pressure of about 
160 lbs. when a superheater is used, and to have cylinders of larger dimen- 
sions than when ordinary steam of 200 lbs. pressure is used. For an illus- 
trated and historical description of the use of superheating in locomotives, 
see paper by H. H. Vaughan, read before the Am. Ry. Mast. Mechs.' Assn., 
Eng. News, June 22, 1905. 

Counterbalancing Locomotives. — Rules for counterbalancing, 
adopted by different locomotive-builders, are quoted in a paper by Prof. 
Lanza (Trans. A. S. M. E., x, 302.) See also articles on Counterbalan- 
cing Locomotives, in R. R. & Eng. Jour., March and April, 1890; Trans. 
A. S. M. E„ vol. xvi, 305; and Trans. Am. Ry. Master Mechanics* Assn., 



LOCOMOTIVES. 1103 

1897. W. E. Dalby's book on the "Balancing of Engines" (Longmans 
Green & Co., 1902) contains a very full discussion of this subject. See 
also Henderson's "Locomotive Operation" {The Railway Age, 1904). 

Narrow-gauge Railways in Manufacturing Works. — A tramway 
of 18 inches gauge, several miles in length, is in the works of the Lan- 
cashire and Yorkshire Railway. Curves of 13 feet radius are used. 
The locomotives used have the following dimensions (Pror. Inst. M. E„ 
July, 1888): The cylinders are 5 in. in diameter with 6 in. stroke, and 
2 ft. 31/4 in. centre to centre. Wheels 16i/4in. diameter, the wheel-base 
2 ft. 9 in.; the frame 7 ft. 41/4 in. long, and the extreme width of the 
engine 3 feet. Boiler, of steel, 2 ft. 3 in. outside diam. and 2 ft. long 
between tube-plates, containing 55 tubes of 13/ 8 in. outside diam.; fire- 
box, of iron and cylindrical, 2 ft. 3 in. long and 17 in. inside diam. Heat- 
ing-surface 10.42 sq. ft. in the fire-box and 36.12 in the tubes, total 46.54 
sq. ft.; grate-area, 1.78 sq. ft.; capacity of tank, 26V2 gallons; working- 
pressure, 170 lbs. per sq. in. tractive power, say, 1412 lbs., or 9.22 lbs. per 
lb. of effective pressure per sq. in., on the piston. Weight, empty, 2.80 
tons; full and in working order, 3.19 tons. 

For description of a system of narrow-gauge railways for manufac- 
tories, see circular of the C. W. Hunt Co., New York. 

Light Locomotives. — For dimensions of light locomotives used for 
mining, etc., and for much valuable information concerning them, see 
catalogue of H. K. Porter Co., Pittsburgh. 

Petroleum-burning Locomotives. (From Clark's Steam-engine.) — 
The combustion of petroleum refuse in locomotives has been success- 
fully practised by Mr. Thos. Urquhart, on the Grazi and Tsaritsin Rail- 
way, Southeast Russia. Since November, 1884, the whole stock of 143 
locomotives under his superintendence has been fired with petroleum 
refuse. The oil is injected from a nozzle through a tubular opening in 
the back of the fire-box, by means of a jet of steam, with an induced 
current of air. 

A brickwork cavity or "regenerative or accumulative combustion- 
chamber" is formed in the fire-box, into which the combined current 
breaks as spray against the rugged brickwork slope. In this arrange- 
ment the brickwork is maintained at a white heat, and combustion is 
complete and smokeless. The form, mass, and dimensions of the brick- 
work are the most important elements in such a combination. 

Compressed air was tried instead of steam for injection, but no appre- 
ciable reducticn in consumption of fuel was noticed. 

The heating-power of petroleum refuse is given as 19,832 heat-units, 
equivalent to the evaporation of 20.53 lbs. of water from and at 212° F., 
or to 17.1 lbs. at 8 1/2 atmospheres, or 125 lbs. per sq. in., effective pres- 
sure. The highest evaporative duty was 14 lbs. of water under 8V2 
atmospheres per lb. of the fuel, or nearly 82% efficiency. 

There is no probability of any extensive use of petroleum as fuel for 
locomotives in the United States, on account of the unlimited supply of 
coal and the comparatively limited supply of petroleum. Texas and 
California oils are now (1902) used in locomotives of the Southern Pacific 
Railway and the Santa Fe System. 

Self-propelled Railway Cars. — The use of single railway cars con- 
taining a steam or gasolene motor has become quite common in Europe. 
For a description of different systems see a paper on European Railway 
Motor Cars by B. D. Gray in Trans A. S. M. E., 1907. 

Fireless Locomotive. — The principle of the Francq locomotive is 
that it depends for the supply of steam on its spontaneous generation 
from a body of heated water in a reservoir. As steam is generated and 
drawn off the pressure falls; but by providing a sufficiently large volume 
of water heated to a high temperature, at a pressure correspondingly 
high, a margin of surplus pressure may be secured, and means may thus 
be provided for supplying the required quantity of steam for the trip. 

The fireless locomotive designed for the service of the Metropolitan 
Railway of Paris has a cylindrical reservoir having segmental ends, 
about 5 ft. 7 in. in diameter, 261/4 ft. in length, with a capacity of about 
620 cubic feet. Four-fifths of the capacity is occupied by water, which 
is heated by the aid of a powerful jet of steam supplied from stationary 
boilers. The water is heated until equilibrium is established between 
the boilers and the reservoir. The temperature is raised to about 390° F., 
corresponding to 225 lbs. per sq. in. The steam from the reservoir is 



1104 



LOCOMOTIVES, 



passed through a reducing-valve, by which the steam is reduced to the 
required pressure. It is then passed through a tubular superheater 
situated within the receiver at the upper part, and thence through the 
ordinary regulator to the cylinders. The exhaust-steam is expanded to 
a low pressure, in order to obviate noise of escape. In certain cases the 
exhaust-steam is condensed in closed vessels, which are only in part 
filled with water. 

In working off the steam from a pressure of 225 lbs. to 67 lbs., 530 
cubic feet of water at 390° F. is sufficient for the traction of the trains, 
for working the circulating-pump for the condensers, for the brakes, 
and for electric-lighting of the train. At the stations the locomotive 
takes from 2200 to 3300 lbs. of steam — nearly the same as the weight 
of steam consumed during the run between two consecutive charging 
stations. There is 210 cubic feet of condensing water. Taking the 
initial temperature at 60° F., the temperature rises to about 180° F. 
after the longest runs underground. 

The locomotive has ten wheels, on a base 24 ft long, of which six are 
coupled, 41/2 ft. in diameter. The extreme wheels are on radial axles. 
The cylinders are 231/2 in. in diameter, with a stroke of 231/2 in. 

The engine weighs, in working order, 53 tons, of which 35 tons are on 
the coupled wheels. The speed varies from 15 miles to 25 miles per hour. 
The trains weigh about 140 tons. 

Compressed-air Locomotives. — A compressed-air locomotive con- 
sists essentially of a storage tank mounted upon driving wheels, with two 
engines similar to those of a steam locomotive. One or more reservoirs or 
storage tanks are located on the line, from which the locomotive tank is 
charged. These reservoirs are usually riveted steel cylinders, designed 
for about 1000 lbs. working pressure; but sometimes seamless steel cylinders 
of small diameter, designed for a working pressure of 2000 lbs. or upwards, 
are used. The customary maximum pressure in the locomotive tank is 
800 lbs. gauge, and the working pressure in the cylinders is from 130 to 
140 lbs. The following table is condensed from one in a circular of the 
Baldwin Locomotive Works, No. 45, 1GG1. 
See account of the Mekarski compressed-air locomotives, page 624 ante. 

Dimensions and Tractive Power of Four Coupled Compressed- Air 
Locomotives Having Two Storage Tanks. 



Class 

Cylinders, inches 

Diam. of drivers 

Wheel base 

Approx. weight, lbs.. 

Inside dia. of tanks. . 

Aggregate tank vol., 
cu. ft 

App. height , 

App. width over 
tanks 

App. width over cyl- 
inders 

App. length over 
bumpers 

g h Full stroke...... 

•43 I 3/4 Stroke cut-off 

rt o V2 Stroke cut-off 

£Ph 1/4 Stroke cut-off 



4-4-C 


4-6-C 


4-8-C 


4-10-C 


4-1 2-C 


4-16-C 


4-18-C 


5X10 
22" 
4 r 0" 
10,000 
26" 


6X10 

24" 
4' 3" 
14,000 

28" 


7X12 
24" 
4' 6" 
18,000 
30" 


8X14 

26" 

5' 3" 

23,000 

32" 


9X14 
28" 
5' 5" 
27,000 
34" 


11X14 

28" 

5' 6" 

37,000 

38" 


12X16 
30" 
6' 0" 

44,000 
40" 


75 

4' 5" 


100 
4' 10" 


130 

5' 0" 


170 

5' 4" 


200 
5' 8" 


280 
6' 0" 


320 

6' 4" 


if 10" 

Gauge 
+ 24" 


5' 2" 
Gauge 
+ 26" 


5' 6" 
Gauge 
+ 27" 


5' 10" 

Gauge 
+ 28" 


6' 3" 
Gauge 
+30" 


7 0" 
Gauge 
+ 32" 


7' 4" 
Gauge 
+33" 


12' 0" 
1350 
1290 
940 
510 


14' 0" 
1785 
1700 
1240 
670 


15' 0" 
2915 
2780 
2025 
1100 


17' 0" 

4100 
3900 
2840 
1540 


18' 0" 
4820 
4580 
3345 
1815 


20' 0" 
7200 
6860 
4995 
2710 


2W 6" 
9140 
8705 
6340 
3440 



Draw-bar pull on any grade = tractive power - (.0075 + % of grade) 
X weight of engine. 

Working pressure in cylinders 140 lbs.; tank storage pressure, 800 lbs. 

Other sizes of engines are 51/2 X 10 in., 6X12 in., and 8 X12in„ 24-in. 
diam. of drivers; 9 X14 in., 26-in. drivers, and 10 X 14 in., 28-in. drivers. 



COMPRESSED-AIR LOCOMOTIVES. 




1105 


Cubic Feet of Air, at Different Storage Pressures, Required to 


Haul One Ton One Mile at Half Stroke Cut-off, with 20, 30 


and 40 lbs. Frictional Resistance per Ton. (Baldwin Loco. Wks.) 


Storage pressure 




600 


700 


800 




600 


700 


800 


600 


700 


800 


Cylinder working 






























130 


135 


140 




130 


135 


140 




130 


135 


140 










Grade. 


R 


V 


V 


V 


R 


V 


V 


V 


R 


V 


V 


V 


Level 


20.0 


1.16 


0.99 


87 


30.0 


1 74 


1 50 


1 31 


40.0 


2 33 


1 99 


1 74 


V2% 


31.2 


1.81 


1.56 


1.36 


41.2 


2 40 


2 05 


1 79 


51.2 


2.98 


2 56 


2 23 


1% 


42.4 


2 47 


2 12 


1 85 


52.4 


i 05 


2 61 


2 28 


62.4 


3.643.11 


2 73 


2% 


64.8 


3,78 


3 24 


2 83 


74.8 


4 35 


3 73 


3 26 


84.8 


4 94 


4 24 


3 70 


3% 


87.2 


5.08 


4 35 


3 81 


97.2 


5 67 


4 86 


4 25 


107.2 


6 25 


5 35 


4 69 


US:::::::::::::: 


109.6 


6.39 


5.48 


4.79 


119.6 


6 97 


5 97 


5 22 


129.6 


7 56 


6 47 


5 67 


132.0 


7.69 


6.60 


5.77 


142.0 


8.27 


7.09 


6.20 


152.0 


8.86 


7.60 


6.64 



R= resistance per ton of 2240 lbs. in pounds. V = cubic feet of air. 

Air Locomotives with Compound Cylinders and Atmospheric Interheaters 
are built by H. K. Porter Co. The air enters the high-pressure cylinder 
at 250 lbs. gauge pressure and is expanded down to 50 lbs., overcoming 
resistance, while the temperature drops about 140° F. This loss of heat 
is practically all restored in the atmospheric interheater, which is a 
cylindrical reservoir filled with brass tubes located in the passage-way 
from the high- to the low-pressure cylinder. The air enters the low- 
pressure cylinder at 50 lbs. gauge and a temperature within 10 or 20° of 
that of the surrounding atmosphere. The exhaust is used to induce a 
draught of atmospheric air through the tubes of the interheater. This 
combination permits of expanding the air from 250 lbs. down to atmos- 
phere without unmanageable refrigeration. 

The following calculation shows the relative economy of a single- cylinder 
locomotive using air at 150 lbs. and of a compound using air at 250 lbs. 
in the high-pressure and 50 lbs. in the low-pressure cylinder, non-expan- 
sive working being assumed in both cases. 

11.2 cu. ft. of free air at 150 lbs. gauge and atmospheric temperature 
would fill a cylinder of 1 cu. ft. capacity, and in moving a piston of 1 sq. 
ft. area one foot would develop 144 X 150 = 21,600 ft. lbs. of energy. 

11.2 cu. ft. of free air at 250 lbs. gauge if used in a cylinder 0.623 sq. ft. 
area and 1 ft. stroke would develop 0.623 X 144 X 250= 22,425 ft lbs. 

If expanded in two cylinders with a ratio of 4 to 1 the energy developed 
would be 0.623 X 144 X 200 plus 4 X 0.623 X 144 X 50 = 35,880 ft. lbs., if 
the heat is restored between the two cylinders. Gain by compounding 
with interheating, over simple cylinders with 150 lbs. initial pressure, 
35,880 ± 21,600 = 1.66. 

These results are about the best that can be obtained with either 
simple or compound locomotives, as any improvement due to expansive 
working just about balances the losses due to clearance and initial refrig- 
eration. The work done per cubic foot of free air in the two systems is: 
with simple cylinders, 21,600 -*■ 11.2 = 1840 ft. lbs.; with compound 
cylinders and atmospheric interheater, 35,880 ■*- 11.2 = 3205 ft. lbs. 

The above calculations have been practically confirmed by actual 
tests, which show 1900 ft. lbs. of work per cubic foot of free air with the 
simple locomotive and 3000 ft. lbs. with the compound, the gain due to 
expansive working and the losses due to internal friction being some- 
what greater in the compound than in the simple machine. 

In the operation of compressed-air locomotives the air compressor is 
generally delivering compressed air at a pressure fluctuating between 
800 and 1000 lbs. per sq. in. into the storage reservoir, and it requires an 
average of about 12,000 ft. lbs. per cubic foot of free air to compress and 
deliver it at these pressures. The efficiency of the two systems then is: 
1900 + 12000 = 16% for the simple locomotive, and 3000 + 12000 = 
25% for the compound with atmospheric interheater. 



1106 



SHAFTING. 

(See also Torsional Strength; also Shafts of Steam Engines.) 
For shafts subjected to torsion only, let d = diam. of the shaft in ins., 
P = a force in lbs. applied on a lever arm at a distance =~ a ins. from 
the axis, <S = shearing resistance at the outer fiber, in lbs. per sq. in., then 

If R = revolutions per minute, then the horse-power transmitted = 

H p = Pa2 *R = *&S X2nR = RSd 3 . 
33,000X12 16X33,000X12 321,000' 



7321,000 H. P. .VCXH.P. 

d= V RS = V ~R 

In practice, empirical values are given to S and to the coefficients 
K = 5.1/5 and C = 321,000/S, according to the factor of safety assumed, 
depending on the material, on whether the shaft is subjected to steady, 
fluctuating, bending, or reversed strains, on the distance between bear- 
ings, etc. Kimball and Barr (Machine Design) state that the following 
factors of safety are indicated by successful practice: For head shafts, 
15; for line shafts carrying pulleys, 10; for small short shafts, counter- 
shafts, etc., 7. For steel shafting the allowable stress, S, for the above 
factors would be about 4000, 6000 and 8500 lbs. respectively, whence 



for head shafts d = 



\/W 



V80H.P. , .. . .. . ,753 EU 

a/ — r> — ; for line shafts d= 4/ — ^- 



Jones & Laughlin Steel Co. gives the following for steel shafts: 

Turned. Cold-rolled. 

For simply transmitting power ) 

and short countershafts, bear- \ H.P. = d s R ■+■ 50 H.P = d 3 R * 40 
ings not more than 8 ft. apart ) 

A teSg s Tfr&art' neSha ' tS :} Hp -' is ' J - 9 ° H.P.-« + 70 

As prime movers or head shafts! 

carrying main driving pulley I H p = wsp ^ 105 H P = d*R ■* 100 
or gear, well supported by( nr - an ' vzo atr - aK ' 1UU 
bearings J 

Jones & Laughlins give the following notes: Receiving and transmit- 
ting pulleys should always be placed as close to bearings as possible; 
and it is good practice to frame short "headers" between the main tie- 
beams of a mill so as to support the main receivers, carried by the head 
shafts, with a bearing close to each side as is contemplated in the for- 
mulae. But if it is preferred, or necessary, for the shaft to span the full 
width of the "bay" without intermediate bearings, or for the pulley to 
be placed away from the bearings towards or at the middle of the bay, 
the size of the shaft must be largely increased to secure the stiffness 
necessary to support the load without undue deflection. 

Diameter of sha ft D to carry load at center of bays from 2 to 12 ft. 



D '\/i<"- 



span, D = %/ - d\ in which d is the diameter derived from the formula 

for head shafts, Ci= length of bay in inches, and Ci = distance in inches 
between centers of bearings in accordance with the formula for horse- 



1107 



power of head shafts. (Jones & Laughlin Steel Co.) Values of Ci for 
different diameters d are as follows: 



d c x 


d c x 


d c x 


d 


Cl 


d Cx 


d c x 


1 to 13/ 8 15 


213/ie 25 


315/ie & 4 37 


5 1/4 & 5 3/ 8 


55 


63/ 8 71 


73/8 88 


Hl/16 & l 3 /4 16 


27/8 to 3 26 


43/ie 40 


51/2 


5/ 


61/2 73 


71/2 91 


U3/16 & 17/8 17 


3 1/8 to 3 1/4 28 


41/4 41 


55/8 


59 


65/8 75 


75/8 93 


U5/16 to 21/8 18 


33/8 30 


47/ie & 41/2 44 


53/4 


61 


63/ 4 77 


73/4 96 


23/ie & 21/ 4 19 


3 7/i6 & 3 1/2 31 


43/4 47 


57/8 


63 


67/8 79 


77/8 99 


2-3/16 to 27/ie 20 


39/16 & 35/ 8 33 


413/i 6 49 


6 


65 


7 81 


8 101 


21/2 to 25/8 24 


3 H/16 & 3 3/4 34 


5 51 


61/8 


6/ 


71/8 84 


8I/2 112 


211/16 & 23/4 22 


3 7/8 36 


51/ 8 52 


61/4 


69 


71/4 86 


9 123 



Should the load be applied near one end of the span or bay instead of 
at the center, multiply the fourth power of the diameter of the shaft 
required to carry the load at the center of the span or bay by the prod- 
uct of the two parts of the shaft when the load is near one end, and 
divide this product by the product of the two parts of the shaft when 
the load is carried at the center. The fourth root of this quotient will 
be the diameter required. 

The shaft in a line which carries a receiving-pulley, or which carries a 
transmitting-pulley to drive another line, should always - be considered a 
head-shaft, and should be of the size given by the rules for shafts carrying 
main pulleys or gears. 

The greatest admissible distance between bearings of shafts subject to 
no transverse strain except from their own weight is for cold-rolled shafts, 
L = -<y 330,608 X D 2 , and for turned shafts, L = ^319,586 X Z> 2 . D = 
diam. and L = length of shaft, in inches. These formulae are based on 
an allowable deflection at the center of Vso in. per foot of length, weight 
of steel 490 lbs. per cu. ft., and modulus of elasticity = 29,000,000 for 
turned and 30,000,000 for cold-rolled shafting. [In deriving these formulae 
the weight of the shaft has been taken as a concentrated instead of a dis- 
tributed load, giving additional safety.] 

Kimball and Barr say that the lateral deflection of a shaft should not 
exceed 0.01 in. per 100 ft. of length, to insure proper contact at the bear- 
ings. For ordinary small shafting they give_the following as the allow- 
able distance between the hangers: L = 7 \J d 2 , for shaft without pulleys; 
L = 5 ^d 2 , for shaft carrying pulleys. (L in ft., d in ins.) 

Deflection of Shafting. (Pencoyd Iron Works.) — For continuous 
line-shafting it is considered good practice to limit the deflection to a 
maximum of 1/100 of an inch per foot of length. The weight of bare shaft- 
ing in pounds = 2.6 d 2 L = W, or when as fully loaded with pulleys as is 
customary in practice, and allowing 40 lbs. per inch of width for the 
vertical pull of the belts, experience shows the load in pounds to be about 
13 d 2 L = W. Taking the modulus of transverse elasticity at 26,000,000 
lbs., we derive from authoritative formulae the following: 



L = -\/873 d 2 , d = ^1,3/873, for bare shafting; 

L = ^/l75d 2 , d = VL3/175, f or shafting carrying pulleys, etc.; 

L being the maximum distance in feet between bearings for continuous 
shafting subjected to bending stress alone, d = diam. in inches. 

The torsional stress is inversely proportional to the velocity of rota- 
tion, while the bending stress will not be reduced in the same ratio. It 
is therefore impossible to write a formula covering the whole problem 
and sufficiently simple for practical application, but the following rules 
are correct within the range of velocities usual in practice. 

For continuous shafting §0 proportioned as to deflect not more than 



1108 



SHAFTING. 



1/100 of an inch per foot of length, allowance being made for the weaken- 
ing effect of key-seats, 

d = ^50 H.P. -f- R, L = ^720 d 2 , for bare shafts; 

d = ZJ70 H.P. -*■ R, L = ^140 d 2 , for shafts carrying pulleys, etc. 

d = diam. in inches, L = length in feet, R = revs, per min. 

The following are given by J. B. Francis as the greatest admissible dis- 
tances between the bearings of continuous steel shafts subject to no trans- 
verse strain except from their own weight, as would be the case were the 
power given off from the shaft equal on all sides, and at an equal distance 
from the hanger-bearings. 

Diam. of shaft, in. ... 2345 6-789 

Dist. bet. bearings, ft. 15.9 18.2 20.0 21.6 22.9 24.1 25.2 26.2 

These conditions, however, do not usually obtain in the transmission of 
power by belts and pulleys, and the varying circumstances of each case 
render it impracticable to give any rule which would be of value for 
universal application. 

For example, the theoretical requirements would demand that the 
bearings be nearer together on those sections of- shafting where most 
power is delivered from the shaft, while considerations as to the location 
and desired contiguity of the driven machines may render it impracti- 
cable to separate the driving-pulleys by the intervention of a hanger at 
the theoretically required location. (Joshua Rose.) 

Horse-Power Transmitted by Cold-rolled Steel Shafting at Different 
Speeds as Prime Movers or Head Shafts Carrying Main Driving 
Pulley or Gear, well Supported by Bearings. 

Formula H.P. = d*R + 100. 



Revolutions per minute. 




Revolutions 


per minute. 




Diam. 


100 


200 


300 


400 


500 


Diam. 


100 


200 


300 


400 


500 


n/ 2 


3.4 


6.7 


10.1 


13.5 


16.9 


27/8 


24 


48 


72 


95 


119 


19/16 


3.8 


7.6 


11.4 


15.2 


19. G 


215/16 


25 


51 


76 


101 


127 


15/8 


4.3 


8.6 


12.8 


17.1 


21 


3 


27 


54 


81 


108 


135 


1 n /l6 


4.8 


9.6 


14.4 


19.2 


24 


31/8 


31 


61 


91 


122 


152 


13/4 


5.4 


10.7 


16.1 


21 


27 


33/16 


32 


65 


97 


129 


162 


1 !3/l6 


5.9 


11.9 


17.8 


24 


30 


31/4 


34 


69 


103 


137 


172 


t7/ 8 


6.6 


13.1 


19.7 


26 


33 


33/8 


38 


77 


115 


154 


192 


I 15/16 


7.3 


14.5 


22 


29 


36 


37/16 


41 


81 


122 


162 


203 


2 


8.0 


16.0 


24 


32 


40 


31/, 


43 


86 


128 


171 


214 


21/16 


8.8 


17.6 


26 


35 


44 


39/16 


45 


90 


136 


180 


226 


21/8 


9.6 


19.2 


29 


38 


48 


35/ 8 


48 


95 


143 


190 


238 


23/ie 


10.5 


21 


31 


42 


52 


3H/16 


50 


100 


150 


200 


251 


21/4 


11.4 


23 


34 


45 


57 


33/4 


55 


105 


158 


211 


264 


2">/l6 


12.4 


25 


37 


49 


62 


37/ 8 


58 


116 


174 


233 


291 


23/s 


13.4 


27 


40 


54 


67 


315/ie 


61 


122 


183 


244 


305 


27/ie 


14.5 


29 


43 


58 


72 


4 


64 


128 


192 


256 


320 


21/2 


15.6 


31 


47 


62 


78 


43/16 


74 


147 


221 


294 


367 


29/16 


16.8 


34 


50 


67 


84 


41/4 


77 


154 


230 


307 


383 


25/8 


18.1 


36 


54 


72 


90 


47/16 


88 


175 


263 


350 


438 


2H/16 


19.4 


39 


58 


77 


97 


41/2 


91 


182 


273 


365 


456 


23/4 


21 


41 


62 


•83 


104 


43/4 


107 


214 


322 


429 


537 


213/is 


22 


44 


67 


89 


111 


5 


125 


250 


375 


500 


625 



For H.P. transmitted by turned steel shafts, as prime movers, etc., 
multiply the figures by 0.8. 

For shafts, as second movers or line shafts, i 
bearings 8 ft. apart, multiply by ] 

For simply transmitting power, short counter- 
shafts, etc., bearings not over 8 ft. apart, multi- 
ply by 



Cold-rolled Turned 
1.43 1.11 



1109 



The horse-power is directly proportional to the number of revolutions 
per minute. 

Speed of Shafting. — Machine shops 120 to 240 

Wood-working 250 to 300 

Cotton and woollen mills . . 300 to 400 

Flange Couplings. — The bolts should be designed so that their 
combined resistance to a torsional moment around the axis of the shaft 
is at least as great as the torsional strength of the shaft itself; and the 
bolts should be accurately fitted so as to distribute the load evenly 
; among them. Let D = diam. of the shaft, d = diam. of the bolts, 
radius of bolt circle, in inches, n = number of bolts, S = allowab le shear - 
ing stress per sq. in., then ^rd 3 5-f-16 = i/4 nd 2 rS, whence d= 0.5 ^D 3 /(nr)- 
Kimball and Barr give n = 3 +D/2, but this number may be modified for 
convenience in spacing, etc. 

Effect of Cold Rolling. — Experiments by Prof. R. H. Thurston in 
jl902 on hot-rolled and cold-rolled steel bars (Catalogue of Jones & 
(Laughlin Steel Co.) showed that the cold-rolled steel in tension had its 
lelastic limit increased 15 to 97%; tensile strength increased 20 to 45%; 
ductility decreased 40 to 69%. In transverse tests the resistance in- 
creased 11 to 30% at the elastic limit and 13 to 69% at the yield point. 
In torsion the resistance at the yield point increased 31 to 64%, and at 
the point of fracture it decreased 4 to 10%. The angle of torsion at 
the elastic limit increased 59 to 103%, while the ultimate angle de- 
creased 19 to 28%. Bars turned from 13/4 in. diam. to various sizes 
down to 0.35 in. showed that the change in quality produced by cold 
rolling extended to the center of the bar. The maximum strength of 
the cold-rolled bar of full size was 82,200 lbs. per sq. in., and that of the 
smallest bar 73,600 lbs. In the hot-rolled steel bars the maximum 
strength of the full-sized bar was 62,900 lbs. and that of the smallest bar 
58,600 lbs. per sq. in. 

Hollow Shafts. — Let d be the diameter of a solid shaft, and d t d 2 the 
external and internal diameters of a hollow shaft of the same material. 

Then the shafts will be of equal torsional strength when d 3 = * ~ — - • 

«i 
A 10-inch hollow shaft with internal diameter of 4 inches will weigh 16% 
less than, a solid 10-inch shaft, but its strength will be only 2.56% less. 
If the hole were increased to 5 inches diameter the weight would be 
25% less than that of the solid shaft, and the strength 6.25% less. 

Table for Laying Out Shafting. — The table on the opposite page 
(from the Stevens Indicator, April, 1892) is used by Wm. Sellers & Co. to 
facilitate the laying out of shafting. 

The wood-cuts at the head of this table show the position of the hangers 
and position of couplings, either for the case of extension in both direc- 
tions from a central head-shaft or extension in one direction from that 
head-shaft. 

Sizes of Collars for Shafting, Wm. Sellers & Co., Am. Mach. Jan. 28, 
1897. — D, diam. of collar; T, thickness; d, diam. of set screw; I, length. 
All in inches. 

















Loose Collars. 














Shaft 


D 
13/4 

17/8 

21/4 
25/8 

23/ 4 
3 


T 

3/4 

13/16 

15/16 

1 

11/16 

H/8 


d 

7/16 

7/16 
7/16 
7/16 
1/2 
5/8 


I 
5/16 
3/8 
7/16 
7/16 
9/16 
9/16 


Shaft 


D 

33/8 

3 3/4 

4 

41/2 

47/s 

53/ie 


T 

13/16 
H/4 
15/16 
17/16 
15/8 
13/4 


d 

~5/8 
5/8 
■>/8 
5/8 
3/4 
3 /4 


I 

5/8 
H/16 
H/16 
13/16 
13/16 
15/16 


Shaft 


D 


t 

17/8 

17/8 

17/8 

2 

2 


d 

3/4 
3/4 
3/4 
3/4 
3/4 


I 


1 

H/4 

U/2 

15/8 

13/ 4 

2 


21/4 

21/2 

23/4 

3 

31/4 

31/2 


4 

41/2 
5 

51/2 
6 


513/16 

67/16 

615/ie 

71/2 

8 


1 
1 
1 
1 

1 


Fast Collars. 


Shaft 


D 


T 


Shaft 


D 


T 


Shaft 


D 


T 


Shaft 


D 


T 


U/2 
13/4 
2 

21/4 


2 

21/4 
25/8 
3 


1/2 
1/2 
1/2 
9/16 


21/2 
23/4 
3 
31/4 


31/4 
35/8 
4 

41/4 


9/16 
5/8 
H/16 
11/16 


31/2 
4 

41/2 


45/8 
53/8 
6 
7 


7/8 

15/16 
1 
H/8 


51/2 
6 

61/2 
7 


75/8 
81/4 
9 
93/ 4 


13 

13 
H 


16 

4 
8 
2 



1110 



SHAFTING, 





'aa^euiBtQ 


CA ^T IPl IT* \© tXi Is 




^j^» » -. s 




•satput 
'q^Bubq; 


ifnOIMWao-Nm^vOoOO^-mmoOoo 


•sm 'xog jo 'Sui 
-j^ag jo q^Sdaq; 


\Ot>»0»0'-Nm'*>Ci»0 


N^ vCaOON 






00 


C 
cj 

bfl 
£ 

CO 

oi 
c 

*a 

a 

o 

1 

m 
*S 

O 
M 

m 

'o, 

6 

a 

o 

a 
J 

5 


8 a «-l -isj 

•d«" g^H- 

,£ B J= 13 3 *• 
"| &! ^ « 

1 n . u g £^ 


"6 2 S+^-o 

CO m B 


^ p 


^ 


c*-* 


- 


lis 


\C 


»0-N 


o 


jogjog 


^ 


^r5«N*^rn 




<s r>i ™ rs rs rs r^ 


T 


NNNNNNNN 


n- 


00 £ © £j rq JT JO £j w 


^ 




Sr 


m^oiNoo-— * J3<Q 


& 


jn^-ot^oo^^-jQ 


r>l 


^ *T in IT\ ^O PS 00 


^S 






rq 


r^^'T^inS^S 


B «j ^~ ~ "S 


M 


rq(V!r^n^T-«3-irivO 




'$ 


— NNKMAtin 




S 


S-O — — M 


S 2 


»0*0 




■S °| • 

SnUQB 


i.^.(sjfqc^^fi^fAt<> 1 Tr , <riiMn , ovor>.t>.oo 


u 

lb 


bfljS-o oi r 


£r!«!lf 











PULLEYS. 1111 

PULLEYS. 

Proportions of Pulleys. (See also Fly-wheels, page 1031.) — Let 
= number of arms, D = diameter of pulley, S = thickness of belt, 
it = thickness of rim at edge, T = thickness in middle, B = width of rim, 
/? = width of belt, h = breadth of arm at hub, hi = breadth of arm at 
rim, e = thickness of arm at hub, ei = thickness of arm at rim, c = 
amount of crowning; dimensions in inches. 

Unwin. Reuleaux. 

B = width of rim 9/ 8 (# + o .4) 9/s /? to 5/ 4 /? 

t = thickness at edge of rim 0.75+0 .005 D j ( $ffc to */!?? 1 '* 

T = thickness at middle of rim ... 2t+ c 

I For single . BD 

belts = 0.6337V IT K n 

h = breadth of arm at hub < ' . — i/. in + £ + _±L 

For double . * BD /iU1 ' ^ 4 r 20 n 
[belts = 0.798 V ~£ 

hi = breadth of arm at rim 2/ 3 h .8 h 

e = thickness of arm at hub 0.4 h .5 h 

e\ = thickness of arm at rim .4 h x .5 hi 

n = number of arms, for a single set 3 + j=~ 1/2 ( 5 + ^-^ | 

IB for sin.-arm 
pulleys. 
2 B for double- 
arm pulleys. 

M = thickness of metal in hub hto^/ih 

c = crowning of pulley 1/24 B 

The number of arms is really arbitrary, and may be altered if necessary, 
(Unwin.) 

Pulleys with two or three sets of arms may be considered as two or three 
separate pulleys combined in one, except that the proportions of the arms 
should be .8 or .7 that of single-arm pulleys. (Reuleaux.) 

Example. — Dimensions of a pulley 60 in. diam., 16 in. face, for double 
belt 1/2 in. thick. 

Solution by n h hi e ei t T L M c 

Unwin 9 3.792.531.521.010.651.9710.73.80.67 

Reuleaux 4 5.0 4.0 2.5 2.0 1.25 16 5 

The following proportions are given in an article in the Amer. Machinist 
authority not stated: 

h = .0625 D + .5 in., hi = .04 D + .3125 in., e = .025 D + .2 
in., €i = .016 D + .125 in. 

These give for the above example: h = 4.25 in., hi = 2.71 in., e = 
1 .7 in., ei = 1 .09 in. The section of the arms in all cases its taken as 
elliptical. 

The following solution for breadth of arm is proposed by the author: 
Assume a belt pull of 45 lbs. per inch of width of a single belt, that the 
whole strain is taken in equal proportions on one-half of the arms, and that 
the arm is a beam loaded at one end and fixed at the other. We have 
the formula for a beam of elliptical section fP = .0982 Rbd 2 -r-l, in which 
P = the load, R ■= the modulus of rupture of the cast iron, b = breadth, 
d = depth, and I = length of the beam, and / = factor of safety. Assume 
a modulus of rupture of 36,000 lbs., a factor of safety of 10, and an addi- 
tional allowance for safety in taking I = 1/2 the diameter of the pulley 
instead of 1/2 D less the radius of the hub. 

Take d = h, the breadth of the arm at the hub, and b = e = OAh 

the thickness. We then have/P - 10 X -^A; = 900 - = 3535X0.4ft» t 

n ■*- 2 n 1/2 D 

3/ qr»rj nn ^/rD 

whence h = 4 / - — = 0.6331/ , which is practically the same as 

the value reached by Unwin from a different set of assumptions. 



1112 



Convexity of Pulleys. — Authorities differ. Morin gives a rise equal 
to 1/10 of the face; Molesworth, 1/24; others from i/s to 1/96. Scott A. 
Smith says the crown should not be over 1/8 inch for a 24-inch face. 
Pulleys for shifting belts should be "straight," that is, without crowning. 

CONE OR STEP PUIXEYS. 

To find the diameters for the several steps of a pair of cone-pulleys: 
1. Crossed Belts. — Let D and d be the diameters of two pulleys 
connected by a crossed belt, L = the distance between their centers, 
and /? = the angle either half of the belt makes with a line joining the 



- 2 L cos / 



? = angle whose sine is 



D+ d 
2L 



LCos / 



V"-m- 



The length of the belt is constant when D + d is constant; that is, in ai 
pair of step-pulleys the belt tension will be uniform when the sum of the 
diameters of each opposite pair of steps is constant. Crossed belts are 
seldom used for cone-pulleys, on account of the friction between the; 
rubbing parts of the belt. 

To design a pair of tapering speed-cones, so that the belt may fit 
equally tight in all positions: When the belt is crossed, use a pair of equal 
and similar cones tapering opposite ways. 

2. Open Belts. — When the belt is uncrossed, use a pair of equal 
and similar conoids tapering opposite ways, and bulging in the middle, 
according to the following formula: Let L denote the distance between 
the axes of the conoids; R the radius of the larger end of each; r the radius 
of the smaller end; then the radius in the middle, r , is found as follows: 
R + r (R - r) 2 ._, .'. , 
ro = ~2-t T28T' (Rankxne.) 

If Do = the diameter of equal steps of a pair of cone-pulleys, D and 
d = the diameters of unequal opposite steps, and L = distance between 

D + d , (D - d) 2 
the axes, D = 



- r, be assumed, then 



12.566 L 
If a series of differences of radii of the steps, R ■ 
R + t (R — r) 2 

for each pair of steps — - — = r — ' R ' , and the radii of each may 

be computed from their half sum and half difference, as follows: 
R+ r , R - r R + r R - r 

*=— + -2T- ; r = —2 2— 

A. J. Frith (Trans. A. 8. M. E., x, 298) shows the following application 
of Rankine's method: If we had a set of cones to design, the extreme 
diameters of which, including thickness of belt, were 40 ins. and 10 ins., 
and the ratio desired 4, 3, 2, and 1, we would make a table as follows, 
L being 100 ins.: 



Trial 

Sum of 


Ratio. 


Trial Diams. 


Values of 

{D-dY- 


D 


d 


D+ d 


12.56 L 


50 
50 
50 
50 


4 
3 
2 
1 


40 

37.5 
33.333 
25 


10 

12.5 
16.666 
25 


0.7165 

.4975 
.2212 
.0000 



Amount 
to be 
Added. 



1 

0.0000 
.2190 
.4953 
.7165 



Corrected Values. 



40 
37.7190 

33.8286 
25.7165 



10 
12.7190 
17.1619 
25.7165 



The above formulae are approximate, and they do not give satisfactory 
results when the difference of diameters of opposite steps is large and 
when the axes of the pulleys are near together, giving a large belt-angle. 
Two more accurate solutions of the problem, one by a graphical method, 
and another by a trigonometrical method derived from it, are given by C. 
A. Smith (Trans. A. S. M. E., x, 269). These were copied in earlier edi- 
tions of this Pocket-book, but are now replaced by the more recent graphi- 
cal solution by Burmester, given below, and by algebraic formulae deduced 



CONE OR STEP PULLEYS 



1113 



from it by the author, which give results far more accurate than are required 
in practice. 

In all cases 0.8 of the thicknessof the belt should be subtracted from the 
calculated diameter to obtain the actual diameter of the pulley. This 
should be done because the belt drawn tight around the pulleys is not the 
same length as a tape-line measure around them. — (C. A. Smith.) 

Burmester's Method, Dr. R. Burmester, in his " Lehrbuch der 
Kinematik" (Machinery's Reference Series, No. 14, 1908), gives a graphi- 
cal solution of the cone-pulley problem, which while not theoretically 
exact is much more accurate than practice requires. 

From A on a horizontal line AB, Fig. 170, draw a 45° line, AC. Lay off 
AS on AC equal, on any convenient scale, the larger the better, to the 
distance between centers of the" 
shafts, and from S draw ST per- 
pendicular to AC. Make SK = 
1/2 AS, and with radius AK draw 
an arc of a circle, XY. From a 
convenient point D on AC draw 
a vertical line FDE, and make 
DE equal the given radius of a 
step on one cone, and EF equal 
the given radius of the corre- 
sponding step on the other cone. 
Draw FG and EH parallel to AC. 
From the point G on the arc drop 
a vertical line cutting EH in H. 
Through H draw a horizontal 
line MO, touching AC at M. 
Then if horizontal distances are 
measured from M, as Ma, MH, 
MP, to equal the radii of the 
pulleys or steps on one cone, the 
corresponding vertical distances 
ab, HG and PN will be the radii 
of the corresponding steps on the 
other cone. 

If the radii of the two steps of any pair are to bear a certain ratio, as 
ab -s- Ma, from M draw a line at an angle with MO whose tangent equals 
that ratio, and from the point where it cuts the arc, as b, drop a vertical, 
ba. Ma and ba will be the radii required. 

Using Burmester's diagram the author has devised an algebraic solution 
of the problem (Indust. Eng., June, 1910) which leads to the following 
equations: 

Let L— distance between the centers, = AS on the diagram. 

r = radius of the steps of equal diameter on the two cones, = MP 
= PN. 
n, r 2 = Ma, ab, radii of any pair of steps. 

a = co-ordinates of M, referred to A, = 0.79057 L - r . 




Fig. 170. 



If r t is given, r 2 = Vi.25 L 2 - (0.79057 L - 
If the ratio r 2 -=- r x is given, let r 2 /r x = c: r 2 : 



r + n) 2 - 

= CTx. 



0.79057 L + r . 



We then have a + cr-i = v'.fi! 2 — (a + ri) 2 , which reduces to 

(1 + c 2 ) r x 2 + 2 a (1 + c) n = 1.25 L 2 - 2 a 2 , a quadratic equation, in 
which a = 0.79057 L — r . Substituting the value of a we have 

(l + c 2 )rx2+ (1.58114 L - 2 r ) (1+ c)r x = 3.16228 Lr - 2r 2 , 
in which L, r and c are given and r x is to be found. 

Let L = 100, c = 4, r = 12.858 as in Mr. Frith's example, page 1112. 

Then 17ri 2 + 10ar x , = 12,500 -8764.62, from which n =5.001, r? = 20.004. 

If c = 3, r x = 6.304, r 2 = 18.912. If c = 2, r t = 8.496, r 2 = 16.992. 

Checking the results by the approximate formula for length of belt, 
page 1125, viz, Length = 2L + !t(r 1 +r 2 )+ (r 2 - n) 2 -h d, we have 
for C = 1, 200 + 80.79 +0 = 280.79 

2, 200 + 80.07 + 0.72 = 280.79 

3, 200+79.22+ 1.59 = 280.81 

4, 200 + 78.56 + 2.25 = 280.81 
The maximum difference being only 1 part in 14,000. 



1114 



J. J. Clark (Indust. Eng., Aug., 1910) gives the following solution: 
Using the same notation as above, 

(c 2 1)2 y,i2+?r(c+1)ri=27rro (1) 

«(c+l)r 1 + Lx(^£)=2«r (2) 

x = (r 2 -rtf + L* (3 ) 

The quadratic equation (1) gives the value of r\ with an approximation 
to accuracy sufficient for all practical purposes. If greater accuracy is for 
any reason desired it may be obtained by (2) and (3), using in (3) the values 
of r, and r 2 , = cr x , already found from (1). Taking n = 3.1415927, the re- 
sult will be correct to the seventh figure. 

Speeds of Shaft with Cone Pulleys. — If S = speed (revs, per min.) 
of the driving shaft, 

Si, «2, so, s n = speeds of the driven shaft, 
D u Di, D3, D n = diameters of the pulleys on the driving cone, 

di, rf?, d 3 , d ft = diams. of corresponding pulleys on the driven cone, 
£Di = Mi; SDz =s 2 d2, etc. 
s 1 /S^Dx/d 1 = rn s n /S = D n /d n , = r n . 

The speed of the driving shaft being constant, the several speeds of 
the driven shaft are proportional to the ratio of the diameter of the 
driving pulley to that of the driven, or to D/d. 

Speeds in Geometrical Progression. — If it is desired that the speed 
ratios shall increase by a constant percentage, or in geometrical progres-f 
sion, thenr 2 /ri = rz/r 2 = r n /r n _ 1 = c, a constant. 

r n ■* r i = c n_1 ; c = n ~ 1 vV n - r x 

Example. If the speed ratio of the driven shaft at its lowest speed, 

to the driving shaft be 0.76923, and at its highest speed 2.197, the speeds 

being in geometrical progression, what is the constant multiplier if n=5? 

Log 2.197 = 0.341830 

Log 0.76923 = 1.886056 

0.455774 

Divide by n- 1,= 4, 0.113943 = log of 1.30. 

If Di/di = 1, then AM = 1 -> 1.3 = 0.769; D 3 d 3 = 1.30; DJdv 
1.69; ZVds = 2.197. 



1115 



BELTING. 



Theory of Belts and Bands. — A pulley is driven by a belt by means 
of the friction between the surfaces in contact. Let Tx be the tension on 
the driving side of the belt, Ti the tension on the loose side; then S, = Tx 
— Ti, is the total friction between the band and the pulley, which is 
equal to the tractive or driving force. Let / = the coefficient of friction, 
6 the ratio of the length of the arc of contact to the length of the radius, 
a = the angle of the arc of contact in degrees, e = the base of the Nape- 
rian logarithms = 2.71828, m= the modulus of the common logarithms = 
0.434295. The following formulas are derived by calculus (Rankine's 
Mach'y and Millwork, p. 351; Carpenter's Exper. Eng'g, p. 173): 

fi=e/<> ; r 2 =-%; Tx-T 2 =Tx-^ = Tx(l-e-f e ). 
Tx-T 2 = Tx (1 - e~f e ) = Tx (1 - \^~f Qm ) = Tx (1 -10~°- 00758 »; 

Tx = 10 0.00758 >; Ti = To _ x 10 0.00758 >;:r2 = Tx . 

If the arc of contact between the band and the pulley expressed in 
turns and fractions of a turn == n, 6 = 2im; ef e = io 2 - 7288 -/"; that is, ef d is 
the natural number corresponding to the common logarithm 2.7288/n. 

The value of the coefficient of friction /depends on the state and mate- 
rial of the rubbing surfaces. For leather belts on iron pulleys, Morin 
found f = .56 when dry, .36 when wet, .23 when greasy, and .15 
when oily. In calculating the proper mean tension for a belt, the smallest 
value, / = .15, is to be taken if there is a probability of the belt becom- 
ing wet with oil. The experiments of Henry R. Towne and Robert 
Briggs, however (Jour. Frank. Inst., 1868), show that such a state of 
lubrication is not of ordinary occurrence; and that in designing machinery 
we may in most cases safely take / = .42. Reuleaux takes / = .25. 
Later writers have shown that the coefficient is not a constant quantity, 
but is extremely variable, depending on the velocity of slip, the condition 
of the surfaces, and even on the weather. 

The following table shows the values of the coefficient 2.7288 /, by 
winch n is multiplied in the last equation, corresponding to different 
values of /; also the corresponding values of various ratios among the 
forces, when the arc of contact is half a circumference: 



Let i 



2 S = 1.5. This corresponds to / = 0.22 nearly. 

For a wire rope on cast iron / may be taken as .15 nearly; and if the 
groove of the pulley is bottomed with gutta-percha, .25. (Rankine.) 

Centrifugal Tension of Belts. — When a belt or band runs at a high 
velocity, centrifugal force produces a tension in addition to that existing 
when the belt is at rest or moving at a low velocity. This centrifugal 
tension diminishes the effective driving force. 

Rankine says: If an endless band, of any figure whatsoever, runs at a 
given speed, the centrifugal force produces a uniform tension at each 
cross-section of the band, equal to the weight of a piece of the band whose 
length is twice the height from which a heavy body must fall in order 
to acquire the velocity of the band. (See Cooper on Belting, p. 101.) 
If T c = centrifugal tension; 

V= velocity in feet per second; 
<7= acceleration due to gravity = 32.2; 
W= weight of a piece of the belt 1 ft. long and 1 sq. in. sectional 
area, — 
Leather weighing 56 lbs. per cubic foot gives W = 56 -5- 144 = .388. 
T c = WV 2 +• g = 0.388 F 2 -^- 32.2 = .012F 2 . 



/= 0.15 


0.25 




0.42 


0.56 


2.7288/= 0.41 


0.68 




1.15 


1.53 


7r and n = 1/2, then 










Ti + T 2 = 1.603 


2.188 




3.758 


5.821 


Ti -f- 5 = 2.66 


1.84 




1.36 


1.21 


1 + T2 + 25= 2.16 


1.34 




0.86 


0.71 


ary practice it is usual to 


assume 


To 


= S; Tx -- 


= 2S; Tx + T 2 



1116 BELTING. 

Belting Practice. Handy Formulae for Belting. — Since in the 
practical application of the above formulae the value ot the coefficient of 
friction must be assumed, its actual value varying within wide limits 
(15% to 135%), and since the values of T\ and Ti also are fixed arbi- 
trarily, it is customary in practice to substitute for these theoretical 
formulae more simple empirical formulae and rules, some of which are 
given below. 

Let d = diam. of pulley in inches; 7rd = circumference; 

V = velocity of belt in ft. per second; v = vel. in ft. per minute; 
a = angle of the arc of contact: 

I/ = length of arc of contact in feet = nda -4- (12 X 360); 
F = tractive force per square inch of sectional area of belt; 
w = width in inches; t = thickness; 
*S = tractive force per inch of width = F -s- t; 
r.p.m.=revs. per minute; r.p.s. = revs, per second = r.p.m. -f- 60. 

F ^ X , p ,..g x ^ =0 .004363 d X,p. m .= ^^ ; 

ird 
v= jTj X r.p.m.; = .2618 d X r.p.m. 

„ TT _, Svw SVw SwdX r.p.m. 

Horse-power, H.P. = 33^- = -^ = 126Q5Q • 

If F = working tendon per square inch = 275 lbs., and t = 7/ 32 inch, 
S = 60 lbs. nearly, then 

H.P. = ||=0 .109 Vw = .000476 wd X r.p.m. = wd **£ m ' ■ (1) 

If F = 180 lbs. per square inch, and t = Ve inch, S = 30 lbs., then 

H.P.= ^ = 0.055 Vw = 0. 000238 wdX r.p.m. = wd ^o™' ' (2) 

If the working strain is 60 lbs. per inch of width, a belt 1 inch wide 
traveling 550 ft. per minute will transmit 1 horse-power. If the working 
strain is 30 lbs. per inch of width, a belt 1 inch wide traveling 1100 ft. 
per minute will transmit 1 horse-power. Numerous rules are given by 
different writers on belting which vary between these extremes. A rule 
commonly used is: 1 inch wide traveling 1000 ft. per min. = I. H.P. 

H.P. = ^ =0.06 Vw = .000262 wd X r.p.m. = wd ^g' 1 "' • (3) 

This corresponds to a working strain of 33 lbs. per inch of width. 

Many writers give as safe practice for single belts in good condition a 
working tension of 45 lbs. per inch of width. This gives 

H.P.= ^ = .0818 Vw = .000357 wd X r.p.m. = Wd i5 r '*?' m ' • (4) 

For double belts of average thickness, some writers say that the trans- 
mitting efficiency is to that of single belts as 10 to 7, which would give 

= 0.1169 Fw = 0.00051 wtfXr.p.m. = wd *J']? — 
\ 19ou 

(■ r >) 
Other authorities, however, make the transmitting power of double belts 
twice that of single belts, on the assumption that the thickness of a double 
belt is twice that of a single belt. 

Rules for horse-power of belts are sometimes based on the number of 
square feet of surface of the belt which pass over the pulley in a minute. 
Sq. ft. per min. = wv h- 12. The above formulae translated into this 
form give: 

(1) For S = 60 lbs. per inch wide; H.P. = 46 sq. ft. per minute. 

(2) " S = 30 " " " H.P. = 92 

(3) " S = 33 " " " H.P. = 83 

(4) " S = 45 " " " H.P. = 61 

(5) " S = 64.3" " " H.P. = 43 " " (double belt). 



1117 



The above formulae are all based on the supposition that the arc of con- 
tact is 180°. For other arcs, the transmitting power is approximately 
proportional to the ratio of the degrees of arc to 180°. 

Some rules base the horse-power on the length of the arc of contact in 
t nda ' TT _ Svw Sw w nd w w a 

feet. Since L = -^^ and H.P. = ^q = 33^ X - X r.p.m. X ^ 

we obtain by substitution H.P. = _--„ XLX r.p.m., and the five for- 

lboUU 
mul£e then take the following form for the several values of S: 



H.P.= wLX 27 r f m - (l) 



H.P. (double belt) 



wL X r.p.m. wL X r.p.m . wL X r.p.m 

550 Uj: 500 W; 367 { ); 



_ wL X r.p.m. 

~ 257 



(5). 



None of the handy formulae take into consideration the centrifugal 
tension of belts at high velocities. When the velocity is over 3000 ft. 
per minute the effect of this tension becomes appreciable, and it should 
be taken account of, as in Mr. Nagle's formula, which is given below. 

Horse-power of a Leather Belt One Inch wide. (Nagle.) 

Formula: H.P. = CVtw (5-0 .012 7 2 ) -h 550. 

For/ = .40, a = 180°, C = .715, w = I. 



Laced Belts, S = 275. 


Riveted Belts, S = 400. 


0) 


Thickness in inches = t. 


CD 

~ .-- 
>^ 

15 


Thickness in inches = t. 




1/7 
51 


1/6 
0.59 


3/16 

63 


7/32 

0.73 


1/4 

84 


Vie 

1.05 


1/3 

1.18 


7/32 
1 69 


V4 

1 94 


5/16 


Vs 


3/8 


7/16 
3 39 


1/2 


10 


2.42 


2 58 


2 91 


3.87 


15 


75 


0,88 


1.00 


1.16 


1.32 


1.66 


i.yy 


20 


2 24 


?. 57 


3.21 


3 42 


3 85 


4,49 


5.13 


20 


1.00 


1.17 


1.32 


1.54 


1.75 


2.19 


2.34 


25 


2.79 


3 19 


3.98 


4.25 


4 78 


5 57 


6.37 


75 


1 23 


1 43 


1 61 


1 88 


2 16 


2 69 


2 86 


SO 


i 31 


3 79 


4 74 


5 05 


5 67 


6.62 


7.58 


30 


1 47 


1 72 


1 93 


2 25 


2 58 


y U 


3 44 


35 


3 82 


4 37 


5 46 


5 83 


6 56 


7 65 


8 75 


35 


1 69 


1 97 


2 22 


2 59 


2 96 


3 70 


3 94 


40 


4 33 


4 95 


6 19 


6.60 


7 47. 


8.66 


9.90 


40 


1 90 


2 22 


2 49 


2,90 


y 32 


4.15 


4 44 


45 


4 85 


5 49 


6 86 


7 32 


8 43 


9.70 


10.98 


45 


2 09 


2 45 


2 75 


3.21 


3.6/ 


4,58 


4 89 


50 


5 26 


6 01 


7 51 


8 02 


9 07 


10 57. 


12.03 


50 


2 27 


2.65 


2 98 


3.48 


3.98 


4,97 


5 30 


55 


5 68 


6 50 


8 12 


8.66 


9 74 


11.36 


13.00 


55 


2 44 


2.84 


3 19 


3.72 


4.26 


5.32 


5 69 


60 


6 09 


6 96 


8 70 


9 7.8 


10 43 


17. 17 


13.91 


60 


2 58 


3,01 


3.38 


3.95 


4 51 


5.64 


6 02 


65 


6 45 


7 37 


9 22 


9 83 


11 06 


12.90 


14.75 


65 


2 71 


3,16 


3.55 


4.14 


4,74 


5.92 


6 32 


70 


6 78 


7 75 


9.69 


10 33 


11 62 


13.56 


15.50 


70 


2 81 


3.27 


3.68 


4.29 


4.91 


6.14 


6 54 


75 


7 09 


8 11 


10 13 


10 84 


12 16 


14.18 


16.21 


75 


2,89 


3.37 


3.79 


4.42 


5.05 


6.31 


6.73 


80 


7 36 


8 41 


10 51 


11 21 


12 61 


14 71 


16.81 


80 


2.94 


3.43 


3.86 


4.50 


5.13 


6.44 


6 86 


85 


7 58 


8 66 


10 82 


11 55 


13 00 


15.16 


17.32 


85 


2.97 


3.47 


3.90 


4.55 


5.20 


6.50 


6.93 


90 


7 74 


8 85 


11.06 


11 80 


13 27 


15 48 


17.69 


90 


2.97 


3.47 


3.90 


4.55 


5.20 


6.50 


6.93 


100 


7.96 


9.10 


11.37 


12.13 


13.65 


15.92 


18.20 


The H.P. becomes a maximum 


The H.P. becomes a maximum at 


at 87.41 ft. per sec, = 5245 ft. p. min. 


105.4 ft. per sec. = 6324 ft. per min. 



In the above table the angle of subtension, 

Should it be 

Multiply above 

values by J .65| 

A. F. Nagle's Formula (Trans. A. S. M. E., vol 
Tables published in 1882). 



is taken at 180°. 

200° 



1100° 


110° 


120° 


130° 


140° 


150° 


160° 


170° 


180°. 


1 .70 


.75 


.79 


.83 


.87 


'.91 


.94 


.97 


1 1 



1.05 
1881, p. 91. 



H.P.= CVtw 

C = 1 - 10 -0-00758 fa; 

a = degrees of belt contact; 
/ = coefficient of friction; 
w = width in inches ; 



- .012 F 2 \ 



< 550 J' 

t= thickness in inches; 
v= velocity in feet per second; 
S== stress upon belt per square inch. 



1118 



BELTING. 



Taking S at 275 lbs. per sq. in. for laced belts and 400 lbs. per so. in, 
for lapped and riveted belts, the formula becomes 

H.P.= CVtw (0 .50 - .0000218 V*) for laced belts; 
H.P. = CVtw (0 .727 - .00002J8 F 2 ) for riveted belts. 
Values ofC= 1- 10-o.oo758/ a . (Nagle.) 





Degrees of contact = a. 
































90° 


100" 


II0 U 


120° 


130° 


I40 u 


150° 


160° 


170° 


180° 


200° 


0.15 


0.210 


0.230 


0.250 


0.270 


0.288 


0.307 


0.325 


342 


359 


376 


0.408 


.20 


.270 


.295 


.319 


.342 


.364 


.386 


.408 


428 


.448 


467 


.503 


.25 


.325 


.354 


.381 


.407 


.432 


.457 


.480 


.503 


524 


.544 


.582 


.30 


.376 


.408 


.438 


.467 


.494 


.520 


.544 


.567 


.590 


.610 


.649 


.35 


.423 


.457 


.489 


.520 


.548 


.575 


600 


,624 


.646 


667 


.705 


.40 


.467 


.502 


.536 


.567 


.597 


.624 


.649 


673 


695 


715 


.753 


.45 


.507 


.544 


.579 


.610 


.640 


.667 


692 


715 


737 


757 


.792 


.55 


578 


.617 


.652 


.684 


.713 


.739 


,763 


785 


805 


.822 


.853 


.60 


610 


.649 


.684 


.715 


.744 


.769 


,792 


813 


.832 


848 


.877 


1.00 


.792 


.825 


.853 


.877 


.897 


.913 


.927 


.937 


.947 


.956 


.969 



The following table gives a comparison of the formulae already given 
for the case of a belt one inch wide, with arc of contact 180°. 



Horse-power 


of a Belt One Inch wide, Arc of Contact 180°. 






Comparison of Different Formulae. 






.9 w 


•3d 


«m fl 


Form. 1 


Form .2 


Form. 3 


P\)rm. 4 


Form. 5 
double 


Nagle's 


Form. 


In, 


o * 


. S 


H.P. = 

wv 


H.P. = 
wv 


H.P. = 

wv 


H.P. = 

wv 


belt 
H.P.= 


7 /32-in. single 
belt. 






*2 


550 


1100 


1000 


733 


wv 
513 


Laced. 


Riv't'd 


10 


600 


50 


1.09 


0.55 


0.60 


0.82 


1.17 


0.73 


1.14 


20 


1200 


100 


2.18 


1.09 


1.20 


1.64 


2.34 


1.54 


2.24 


30 


1800 


150 


3.27 


1.64 


1.80 


2.46 


3.51 


2.25 


3.31 


40 


2400 


200 


4.36 


2.18 


2.40 


3.27 


4.68 


2.90 


4.33 


50 


3000 


250 


5.45 


2.73 


3.00 


4.09 


5.85 


3.48 


5.26 


60 


3600 


300 


6.55 


3.27 


3.60 


4.91 


7.02 


3.95 


6.09 


70 


4200 


350 


7.63 


3.82 


4.20 


5.73 


8.19 


4.29 


6.78 


80 


4800 


400 


8.73 


4.36 


4.80 


6.55 


9.36 


4.50 


7.36 


90 


5400 


450 


9.82 


4.91 


5.40 


7.37 


10.53 


4.55 


7.74 


100 


6000 


500 


10.91 


5.45 


6.00 


8.18 


11.70 


4.41 


7.96 


110 


6600 
7200 


550 
600 












4.05 
3.49 


7.97 


120 












7.75 

















Width of Belt for a Given Horse-power. — The width of belt 
required for any given horse-power may be obtained by transposing the 
formulae for horse-power so as to give the value of w. Thus: 

. „ x 550 H.P. 9.17 H.P. 2101 H.P. 275 H.P. 

From formula (1), w = 

From formula (2), w = 

From formula (3), w = 

From formula (4), w = 

From formula (5),* w = 

* For double belts. 



v V (IX r.p.m. 
1100 H.P. 18. 33 H.P. 4202 H.P. 


L Xr.p.m." 
530 H.P. 


v V d X r.p.m. 
1000 H.P. 16.67 H.P. 3820 H.P. 


L Xr.p.m. 
500 H.P. 


v V d X r.p.m. 
733 H.P. 12.22 H.P. 2800 H.P. 


L X r.p.m. 
360 H.P. 


v V dXr.p.Tn. 
513 H.P. 8.56 H.P. 1960 H.P. 


L Xr.p.m.' 
257 H.P. 


v V dX r.p.m. 


L Xr.p.m." 



BELTING. 



1119 



Many authorities use formula (1) for double belts and formula (2) or 
(3) for single belts. 

To obtain the width by Nagle's formula, Wm ' ny t fo_ Q qi' 2 vzy or 

divide the given horse-power by the figure in the table corresponding to 
the given thickness of belt and velocity in feet per second. 

The formula to be used in any particular case is largely a matter of judg- 
ment. A single belt proportioned according to formula (1), if tightly 
stretched, and if the surface is in good condition, will transmit the horse- 
power calculated by the formula, but one so proportioned is objectionable, 
first, because it requires so great an initial tension that it is apt to stretch, 
sip, and require frequent restretching and relacing; and second, because 
this tension will cause an undue pressure on the pulley-shaft, and therefore 
an undue loss of power by friction. To avoid these difficulties, formula 
(2), (3), or (4), or Mr. Nagle's table, should be used; the latter especially 
in cases in which the velocity exceeds 4000 ft. per min. 

The following are from the notes of the late Samuel Webber. (Am. 
Mach. May 11, 1909.) 

Good oak-tanned leather from the back of the hide weighs almost 
exactly one avoirdupois ounce for each one-hundredth of an inch in thck- 
ness, in a piece of leather one foot square, so that 





Lbs. 

per Sq. 

Ft. 


Approx. 
Thick- 
ness. 


Actual 
Thick- 
ness. 


Vel. per 
Inch for 
1 H.P. 


Safe Strain 
per Inch 
Width. 




16 oz. 
24 " 
28 " 
33 " 
45 " 


V6in. 

V4" 
5/16 " 

1/3 " 
9/16 " 


0.16 in. 
0.24 " 
0.28 " 
0.33 " 
0.45 " 


625 ft. 
417 " 
357 " 
303 " 
222 " 


52.8 lbs. 




78.1 " 




92.5 " 




109 '• 


3-ply 


148 " 







The rule for velocity per inch width for 1 H.P. is: 

Multiply the denominator of the fraction expressing the thickness of 
the belt in inches by 100, and divide it by the numerator; 

Good, well-calendered rubber belting made with 30-ounce duck and 
new (i. e., not reclaimed vulcanized) rubber will be as follows: 



Nomenclature. 


Approximate 
Thickness. 


Safe Working 
Strain for I Inch 
Width. 


Velocity per Inch for 
for 1 H.P. 


3-ply 

4 " 

5 " 

6 " 

7 •« 

8 " 


0.18 in. 
0.24 " 
0.30 " 
0.35 " 
0.40 " 
0.45 " 


45 pounds 

65 " 

85 " 
105 " 
125 " 
145 " 


735 ft. per min. 
508 " " " 
388 " " " 
314" " " 
264 " " " 
218 " " " 



The thickness of rubber belt does not necessarily govern the strength, 
but the weight of duck does, and with 30-ounce duck, the safe working 
strains are as above. 

Belt Factors. W. W. Bird (Jour. Worcester Polyt. Inst., Jan. 1910.) 
— The factors given in the table below, for use in the formula H.P. = 
vw ■*■ F, in which F is an empirical factor, are based on the following 
assumptions: A belt of single thickness will stand a stress on the tight 
side, 2\, of 60 lbs. per inch of width, a double belt 105 lbs., and a 
triple belt 150 lbs., and have a fairly long life, requiring only occasional 
taking up; the ratio of tensions T/T 2 should not exceed 2 on small, 
2 5 on medium and 3 on large pulleys; the creep (travel of the belt 
relative to the surface of the pulley due to the elasticity of the belt 
and not to slip) should not exceed 1% — this requires that the differ- 



1120 



ence in tensions T t — To should not be greater than 40 lbs. per inch of 
width for single, 70 for double and 100 for triple belts. 



Pulley diam, 


Under 
8 in. 


8 to 
36 in. 


Over 
3 ft. 


Under 
14 in. 


14 to 
60 in. 


Over 

5 ft. 


Under 
21 in. 


21 to 

84 in. 


Over 
7 ft. 


Belt thick- 
ness. 


Single. 


S'gle. 


S'gle. 


Dbl. 


Dbl. 


Dbl. 


Triple. 


Triple. 


Triple. 


Factor 

T x - T 2 

Creep, %.... 

T t + T 2 

T t 


1100 

30 
0.74 
2 

60 


920 
36 

0.89 

2.5 
60 


830 
40 

0.99 

3 
60 


630 
52.5 
0.74 
2 
105 


520 
63 
0.89 
2.5 
105 


470 
70 
0.99 
3 
105 


440 
75 
0.74 
2 
150 


370 
90 
0.89 
2.5 
150 


330 

100 

0.99 

3 

150 



These factors are for an arc of contact of 180°. For other arcs they 
are to be multiplied by the figures given below. 

Arc 220° 210° 200° 190° 170° 160° 150° 140° 130° 120° 

Multiply by... 0.89 0.92 0.95 0.97 1.04 1.07 1.11 1.16 1.21 1.27 

Taylor's Rules for Belting. — F. W. Taylor (Trans. A. S. M. E., 
xv, 204) describes a nine years' experiment on belting in a machine shop, 
giving results of tests of 42 belts running night and day. Some of these 
belts were run on cone pulleys and others on shifting, or fast-and-loose, 
pulleys. The average net working load on the shifting belts was only 
0.4 of that of the cone belts. 

The shifting belts varied in dimensions from 39 ft. 7 in. long, 3.5 in. 
wide, .25 in. thick, to 51 ft. 5 in. long, 6 .5 in. wide, .37 in. thick. The 
cone belts varied in dimensions from 24 ft. 7 in. long, 2 in. wide, .25 in. 
thick, to 31 ft. 10 in. long, 4 in. wide, .37 in. thick. 

Belt-clamps were used having spring-balances between the two pairs 
of clamps, so that the exact tension to which the belt was subjected was 
accurately weighed when the belt was first put on, and each time it was 
tightened. 

The tension under which each belt was spliced was carefully figured so 
as to place it under an initial strain — while the belt was at rest immedi- 
ately after tightening — of 71 lbs. per inch of width of double belts. This 
is equivalent, in the case of 

Oak tanned and fulled belts, to 192 lbs. per sq. in. section; 
Oak tanned, not fulled belts, to 229 " " " " 
Semi-raw-hide belts, to 253 " " " " " 

Raw-hide belts to 284 " •' " " 

From the nine years' experiment Mr. Taylor draws a number of con- 
clusions, some of which are given in an abridged form below. 

In using belting so as to obtain the greatest economy and the most 
satisfactory results, the following rules should be observed: 





Oak Tanned 

and Fulled 

Leather Belts. 


Other Types 

of Leather 

Belts and 

6- to 7-ply 

Rubber Belts. 


A double belt, having an arc of contact of 
180°, will give an effective pull on the face 

of a pulley per inch of width of belt of 

Or, a different form of same rule: 
The number of sq. ft. of double belt passing 
around a pulley per minute required to 


35 lbs. 

80 sq. f to 

950 ft. 
30 H.P. 


30 lbs. 
90 sq. ft. 


Or: The number of lineal feet of double 
belting 1 in. wide passing around a pulley 
per minute required to transmit one horse- 


1100 ft. 


Or: A double belt 6 in. wide, running 4000 to 
5000 ft. per min., will transmit 


25 H.P. 



The terms "initial tension," "effective pull," etc., are thus explained 
by Mr, Taylor: When pulleys upon which belts are tightened are at rest, 



BELTING. 1121 

both strands of the belt (the upper and lower) are under the same stress 
per in. of width. By "tension," "initial tension," or "tension while at 
rest," we mean the stress per in. of width, or sq. in. of section, to which 
one of the strands of the belt is tightened, when at rest. After the belts 
are in motion and transmitting power, the stress on the slack side, or 
strand, of the belt becomes less, while that on the tight side — or the side 
which does the pulling — becomes greater than when the belt was at rest. 
By the term "total load" we mean the total stress per in. of width, or 
sq. in. of section, on the tight side of belt while in motion. 

The difference between the stress on the tight side of the belt and its 
slack side, while in motion, represents the effective force or pull which is 
transmitted from one pulley to another. By the terms "working load," 
"net working load," or "effective pull," we mean the difference in the 
tension of the tight and slack sides of the belt per in. of width, or sq. in. 
section, while in motion, or the net effective force that is transmitted from 
one pulley to another per in. of width or sq. in. of section. 

The discovery of Messrs. Lewis and Bancroft (Trans. A. S. M. E., 
vii, 749) that the "sum of the tension on both sides of the belt does not 
remain constant," upsets all previous theoretical belting formulae. 

The belt speed for maximum economy should be from 4000 to 4500 ft. 
per minute. 

The best distance from center to center of shafts is from 20 to 25 ft. 

Idler pulleys work most satisfactorily when located on the slack side 
of the belt about one-quarter way from the driving-pulley. 

Belts are more durable and work more satisfactorily made narrow and 
thick, rather than wide and thin. 

It is safe and advisable to use: a double belt on a pulley 12 in. diameter 
or larger; a triple belt on a pulley 20 in. diameter or larger; a quadruple 
belt on a pulley 30 in. diameter or larger. 

As belts increase in width they should also be made thicker. 

The ends of the belt should be fastened together by splicing and cement- 
ing, instead of lacing, wiring, or using hooks or clamps of any kind. 

A V-splice should be used on triple and quadruple belts and when 
idlers are used. Stepped splice, coated with rubber and vulcanized in 
place, is best for rubber belts. 

For double belting the rule works well of making the splice for all belts 
up to 10 in. wide, 10 in. long; from 10 in. to 18 in. wide the splice should 
be the same width as the belt, 18 in. being the greatest length of splice 
required for double belting. 

Belts should be cleaned and greased every five to six months. 

Double leather belts will last well when repeatedly tightened under 
a strain (when at rest) of 71 lbs. per in. of width, or 240 lbs. per sq. in. 
section. They will not maintain this tension for any length of time, 
however. 

Belt-clamps having spring-balances between the two pairs of clamps 
should be used for weighing the tension of the belt accurately each time 
it is tightened. 

The stretch, durability, cost of maintenance, etc., of belts proportioned 

(A) according to the ordinary rules of a total load of 111 lbs. per inch of 
width, corresponding to an effective pull of 65 lbs. per inch of width, and 

(B) according to a more economical rule of a total load of 54 lbs., corre- 
sponding to an effective pull of 26 lbs. per inch of width, are found to be 
as follows: 

When it is impracticable to accurately weigh the tension of a belt in 
tightening it, it is safe to shorten a double belt one-half inch for every 
10 ft. of length for (A) and one inch for every 10 ft. for (B), if it requires 
tightening. 

Double leather belts, when treated with great care and run night and 
day at moderate speed, should last for 7 years (A); 18 years (B). 

The cost of all labor and materials used in the maintenance and repairs 
of double belts, added to the cost of renewals as they give out, through a 
term of years, will amount on an average per year to 37% of the original 
cost of the belts (A); 14% or less (B). 

In figuring the total expense of belting, and the manufacturing cost 
chargeable to this account, by far the largest item is the time lost on the 
machines while belts are being relaced and repaired. 

The total stretch of leather belting exceeds 6% of the original length. 



1122 BELTING. 

The stretch during the first six months of the life of belts is 36% of 
their entire stretch (A); 15% (B). 

A double belt will stretch 0.47% of its length before requiring to be 
tightened (A); 0.81% (B). 

The most important consideration in making up tables and rules for the 
use and care of belting is how to secure the minimum of interruptions to 
manufacture from this source. 

The average double belt (A), when running night and day in a machine- 
shop, will cause at least 26 interruptions to manufacture during its life, 
or 5 interruptions per year, but with (B) interruptions to manufacture 
will not average oftener for each belt than one in sixteen months. 

The oak-tanned and fulled belts showed themselves to be superior in 
all respects except the coefficient of friction to either the oak-tanned 
not fulled, the semi-raw-hide, or raw-hide with tanned face. 

Belts of any width can be successfully shifted backward and forward 
on tight and loose pulleys. Belts running between 5000 and 6000 ft. 
per min. and driving 300 H.P. are now being daily shifted on tight and 
loose pulleys, to throw lines of shafting in ana out of use. 

The best form of belt-shifter for wide belts is a pair of rollers twice the 
width of belt, either of wnicn can be pressed onto the flat surface of the 
belt on its slack side close to the driven pulley, the axis of the roller 
making an angle of 75° with the center line of the belt. ' 

Remarks on Mr. Taylor's Rules. (W. Kent, Trans. A. S. M. E., xv, 
242.) — The most notable feature in Mr. Taylor's paper is the great dif- 
ference between Ms rules for proper proportioning of belts and those 
given by earlier writers. A very commonly used rule is, one horse-power 
may be transmitted by a single belt 1 in. wide running x ft. per min., sub- 
stituting for x various values, according to the ideas of different engineers, 
ranging usually from 550 to 1100. 

The practical mechanic of the old school is apt to swear by the figure 
600 as being thoroughly reliable, while the modern engineer is more apt 
to use the figure 1000. Mr. Taylor, however, instead of using a figure 
from 550 to 1100 for a single belt, uses 950 to 1100 for double belts. If 
we assume that a double belt is twice as strong, or will carry twice as much 
power, as a single belt, then he uses a figure at least twice as large as that 
used in modern practice, and would make the cost of belting for a given 
shop twice as large as if the belting were proportioned according to the 
most liberal of the customary rules. 

This great difference is to some extent explained by the fact that the 
problem which Mr. Taylor undertakes to solve is quite a different one 
from that which is solved by the ordinary rules with their variations. Tho 
problem of the latter generally is, " How wide a belt must be used, or how 
narrow a belt may be used, to transmit a given horse-power?" Mr. 
Taylor's problem is: " How wide a belt must be used so that a given horse- 

f)ower may be transmitted with the minimum cost for belt repairs, the 
ongest life to the belt, and the smallest loss and inconvenience from stop- 
ping the machine while the belt is being tightened or repaired?" 

The difference between the old practical mechanic's rule of a 1-in.- 
wide single belt, 600 ft. per min., transmits one horse-power, and the rule 
commonly used by engineers, in which 1000 is substituted for 600, is due 
to the belief of the engineers, not that a horse-power could not be trans- 
mitted by the belt proportioned by the older yule, "but that such a pro- 
portion involved undue strain from overtightening to prevent slipping, 
which strain entailed too much journal friction, necessitated frequent 
tightening, and decreased the length of the life of the belt. 

Mr. Taylor's rule substituting 1100 ft. per min. and doubling the belt, 
Is a further step, and a long one, in the same direction. Whether it will 
be taken in any case by engineers will depend upon whether they appre- 
ciate the extent of the losses due to slippage of belts slackened by use 
under overstrain, and the loss of time in tightening and repairing belts, 
to such a degree as to induce them to allow the first cost of the belts to 
be doubled in order to avoid these losses. 

It should be noted that Mr. Taylor's experiments were made on rather 
narrow belts, used for transmitting power from shafting to machinery, 
and his conclusions may not be applicable to heavy and wide belts, such 
as engine "fly-wheel belts. 



MISCELLANEOUS NOTES ON BELTING . 1123 

Earth's Studies on Beltingo (Trans. A. S. M. E., 1909.) — Mr. 
Carl G. Barth has made an extensive study of the work of earlier writers 
on the subject of belting, and has derived several new formulae and dia- 
grams showing the relation of the several variables that enter into the 
belt problem. He has also devised a slide rule by which calculations of 
belts may easily be made. He finds that the coefficient of friction de- 
pends on the velocity of the belt, and may be expressed by the formula 
/ = 0.54 A — 140 -^-(500 + V), in which A is the sum of the tension on 
the tight side and one-half the tension on the slack side of the belt, and 
V is the velocity in feet per minute. 

Taking Mr. Taylor's data as a starting point, Mr Barth has adopted 
the rule, as a basis for use of belts on belt-driven machines, that for the 
driving belt of a machine the minimum initial tension must be such 
that when the belt is doing the maximum amount of work intended, the 
sum of the tension in the tight side of the belt and one-half the tension in 
the slack side will equal 240 lbs. per square inch of cross-section for all 
belt speeds; and that for a belt driving a countershaft, or any other belt 
inconvenient to get at for retightening or more readily made of liberal 
dimensions, this sum will equal 160 lbs. Further, the maximum initial 
tension, that is, the initial tension under which a belt is to be put up in 
the first place, and to which it is to be retightened as often as it drops 
to the minimum, must be such that the sum defined above is 320 lbs. 
for a machine belt, and 240 lbs. for a counter-shaft belt or a belt simi- 
larly circumstanced. 

From a set of curves plotted by Mr. Barth from his formula the follow- 
ing tables are derived. The figures are based upon the conditions named 
in the above rule, and on an arc of contact = 180°. 

Belts on Machines. Tension ^n tight side + 1/2 tension in slack side 
= 240 lbs. 
Velocity, ft. per min... 500 1000 2000 3000 4000 5000 6000 

Initial tension, t 124 120 121 128 136 144 152 

Centrifugal tension t c . 0+ 3 13 31 56 86 124 

Difference, t - t c 123 117 108 ,97 80 58 28 

Tensionontightside.il 210 212 211 207 198 187 173 
Tension on slack side, fa 60 54 57 68 84 107 134 
Effective pull. t± - fa . . 150 158 154 139 114 80 39 
Sum of tensions fa + fa 270 268 269 274 282 294 307 
H.P. per sq. in. of sec- 
tion 2.27 4.79 9.33 12.64 13.82 12.12 7.09 

H.P. per in. width, 5/ie 

in. thick 0.71 1.50 2.82 3.95 4.32 3.71 2.22 

Belts driving countershafts, fa + V2 fa = 160 lbs. 

Velocity of belt, ft. per min 500 1000 2000 3000 4000 5000 

Initial tension, to 82 81 83 89 96 102 

Tension on tight side, fa 140 141 140 134 125 114 

. Tension on slack side, tt 40 38 41 53 69 92 

Effective pull, fa - fa 100 103 99 81 56 22 

Sum of tensions 180 179 181 187 194 206 

H.P. per sq. in. of section 1.51 3.12 6.04 7.36 6.79 3.33 

H.P. per in. width, 5/ 16 in. thick 3.47 0.97 1.87 2.30 2.12 1.04 

MISCELLANEOUS NOTES ON BELTING. 

Formulae are useful for proportioning belts and pulleys, but they fur- 
nish no means of estimating how much power a particular belt may be 
transmitting at any given time, any more than the size of the engine is a 
measure of the load it is actually drawing, or the known strength of a 
horse is a measure of the load on the wagon. The only reliable means of 
determining the power actually transmitted is some form of dynamometer. 
(See Trans. A. S. M. E., vol. xii, p. 707.) 

If we increase the thickness, the power transmitted ought to increase 
in proportion; and for double belts we should have half the width required 
for a single belt under the same conditions. With large pulleys and 
moderate velocities of belt it is probable that this holds good. With 
small pulleys, however, when a double belt is used, there is not such per- 



i 



1124 BELTING. 

feet contact between the pulley-face and the belt, due to the rigidity of 
the latter, and more work is necessary to bend the belt-fibers than when a 
tninner and more pliable belt is used. The centrifugal force tending to 
throw the belt from the pulley also increases with the thickness, ana for 
these reasons the width of a double belt required to transmit a given 
horse-power when used with small pulleys is generally assumed not less 
than seven-tenths the width of a single belt to transmit the same power. 
(Flather on "Dynamometers and Measurement of Power.") 

F. W. Taylor, however, finds that great pliability is objectionable, and 
favors thick belts even for small pulleys. The power consumed in bending 
the belt around the pulley he considers inappreciable. According to 
Rankine's formula for centrifugal tension, this tension is proportional to 
the sectional area of the belt, and hence it does not increase with increase 
of thickness when the width is decreased in the same proportion, the 
sectional area remaining constant. 

Scott A. Smith (Trans. A. S. M. E., x, 765) says: The best belts are made 
from all oak-tanned leather, and curried with the use of cod oil and 
tallow, all to be of superior quality. Such belts have continued in use 
thirty to forty years when used as simple driving-belts, driving a proper 
amount of power, and having had suitable care. The flesh side should 
not be run to the pulley-face, for the reason that the wear from contact 
with the pulley should come on the grain side, as that surface of the belt 
is much weaker in its tensile strength than the flesh side; also as the grain 
is hard it is more enduring for the wear of attrition; further, if the grain is 
actually worn off, then the belt may not suffer in its integrity from a 
ready tendency of the hard grain side to crack. 

The most intimate contact of a belt with a pulley comes, first, in the 
smoothness of a pulley-face, including freedom from ridges and hollows 
left by turning-tools; second, in the smoothness of the surface and even- 
ness in the texture or body of a belt ; third, in having the crown of the driv- 
ing and receiving pulleys exactly alike, — as nearly so as is practicable 
in a commercial sense; fourth, in having the crown of pulleys not over 
1/8 in. for a 24-in. face, that is to say, that the pulley is not to be over 
1/4 in. larger in diameter in its center; fifth, in having the crown other 
than two planes meeting at the center; sixth, the use of any material 
on or in a belt, in addition to those necessarily used in the currying 
process, to keep them pliable or increase their tractive quality, should 
wholly depend upon the exigencies arising in the use of belts; non-use is 
safer than over-use; seventh, with reference to the lacing of belts, it 
seems to be a good practice to cut the ends to a convex shape by using a 
former, so that there may be a nearly uniform stress on the lacing through 
the center as compared with the edges. For a belt 10 ins. wide, the center 
of each end should recede i/io in. 

Lacing of Belts. — In punching a belt for lacing, use an oval punch, 
the longer diameter of the punch being parallel with the sides of the belt. 
Punch two rows of holes in each end, placed zigzag. In a 3-in. belt there 
should be four holes in each end — two in each row. In a 8-in. belt, 
seven holes — four in the row nearest the end. A 10-in. belt should have 
nine holes. The edge of the holes should not come nearer than 3/ 4 in. 
from the sides, nor 7/ 8 in. from the ends of the belt. The second row 
should be at least l°/4 ins. from the end. On wide belts these distances 
should be even a little greater. 

Begin to lace in the center of the belt and take care to keep the ends 
exactly in line, and to lace both sides with equal tightness. The lacing 
should not be crossed on the side of the belt that runs next the pulley. 
In taking up belts, observe the same rules as in putting on new ones. 

Setting a Belt on Quarter-twist. — A belt must run squarely on to 
the pulley. To connect with a belt two horizontal shafts at right angles 
with each other, say an engine-shaft near the floor with a line attached to 
the ceiling, will require a quarter-turn. First, ascertain the central point 
on the face of each pullev at the extremity of the horizontal diameter 
where the belt will leave the pullev, and then set that point on the driven 
Dulley plumb over the corresponding point on the driver. This will cause 
the belt to run squarely on to each pulley, and it will leave at an angle 
greater or less, according to the size of the pulleys and their distance from 
eanh other. 

In quarter-twist belts, in order that the belt may remain on the pulleys, 



MISCELLANEOUS NOTES ON BELTING. 1125 



the central plane on each pulley must pass through the point of delivery 
of the other pulley. This arrangement does not admit of reversed 
motion. 

To And the Length of Belt required for two given Pulleys. — 

When the length cannot be measured directly by a tape-line, the follow- 
ing approximate rule may be used: Add the diameter of the two pulleys 
together, divide the sum by 2, and multiply the quotient by 31/4, and 
add the product to twice the distance between the centers of the shafts. 
(See accurate formula below.) 

To find the Angle of the Arc of Contact of a Belt. — Divide the 
difference between the radii of the two pulleys in inches by the distance 
between their centers, also in inches, and in a table of natural sines find 
the angle most nearly corresponding with the quotient. Multiply this 
angle by 2, and add the product to 180° for the angle of contact with the 
larger pulley, or subtract it from 180° for the smaller pulley. 
Or, let R = radius of larger pulley, r = radius of smaller; 
L = distance between centers of the pulleys; 
a = angle whose sine is (R — r) -s- L. 

Arc of contact with smaller pulley = 180° — 2 a; 
Arc of contact with larger pulley = 180° + 2 a. 

To find the Length of Belt in Contact with the Pulley. — For the 

larger pulley, multiply the angle a, found as above, by .0349, to the 
product add 3.1416, and multiply the sum by the radius of the pulley. 
Or length of belt in contact with the pulley 

= radius X U + .0349 a) = radius X *(1 + a/90). 
For the smaller pulley, length=radius X Or— .0349 a) 
= radius X f(l — a) -*-90. 

The above rules refer to Open Belts. The accurate formula for length 
of an open belt is, 

Length = ttR(1 + a/90) + nr(l -a/90) + 2 L cos a. 

= R (tt+ 0.0349 a) + r (tt-O .0349 a) + 2 Z, cos a, 
in which R = radius of larger pulley, r = radius of smaller pulley, 

L = distance between centers of pulleys, and a = angle whose 
sine is 
(R - r) h- L; cos a = ^U - (R - r) 2 -*- L. 
An approximate formula is 
Length = 2 L + n (R + r) + (R - r) 2 /L 

For L = 4, R = 2, r = 1, this formula gives length = 17.6748, the 
accurate formula giving 17.6761 
For Crossed Belts the formula is 

Length of belt = ir R(l 4-/3/90) + nr (1 + j8/90) + 2 L cos /S 
= (R + r) X (tt + 0.0349 J3) + 2 L cos j8, 

in which /3 = angle whose sine is (R + r) -f- L\ cos )3 = "^L 2 — (R + r) 2 -*■ L. 

To find the Length of Belt when Closely Rolled. — The sum of the 

diameter of the roll, and of the eve in inches, X the number of turns made 
by the belt and by 1309, = length of the belt in feet. 

To find the Approximate Weight of Belts. — Multiply the length 
of belt, in feet, by the width in inches, and divide the product by 13 for 
single and 8 for double belt. 

Relations of the Size and Speeds of Driving and Driven Pulleys. 
— The driving pulley is called the driver, D, and the driven pulley the 
driven, d. If the number of teeth in gears is used instead of diameter, 
in these calculations, number of teeth must be substituted wherever 
diameter occurs. R = revs, per min. of driver, r = revs, per min. of 
driven. 

D = dr -^ R; 

Diam. of driver = diam. of driven X revs, of driven -*- revs, of driver. 
d = DR -h r; 

Diam. of driven = diam. of driver X revs, of driver -4- revs, of driven. 



1126 



BELTING . 



R = dr -*• D; 
Revs, of driver = revs, of driven X diam. of driven + diam. of driver. 

r = DR ■+■ d; 
Revs, of driven = revs, of driver X diam. of driver ■+■ diam. of driven. 

Evils of Tight Belts. (Jones and Laughlins.) — Clamps with power- 
ful screws are often used to put on belts with extreme tigntness, and with 
most injurious strain upon tne leather. They should be very judiciously 
used for horizontal belts, which should be allowed sufficient slackness 
to move with a loose undulating vibration on the returning side, as a test 
that they have no more strain imposed than is necessary simply to trans- 
mit the power. 

On this subject a New England cotton- mill engineer of large experience 
says: I believe that three-quarters of the trouble experienced in broken 
pulleys, hot boxes, etc., can be traced to the fault of tight belts. The 
enormous and useless pressure thus put upon pulleys must in time break 
them, if they are made in any reasonable proportions, besides wearing 
out the whole outfit, and causing heating and consequent destruction of 
the bearings. Below are some figures showing the power it takes, in 
average modern mills with first-class shafting, to drive the shafting 
alone: 



Mill 


Whole 
Load, 
H.P. 


Shaftin 


I Alone. 


Mill 
No. 


Whole 
Load, 
H.P. 


Shafting Alone. 


Wo. 


Horse- 
power. 


Per cent 
of whole. 


Horse- 
power. 


Per cent 
of whole. 


1 
2 
3 
4 


199 
472 
486 
677 


51 

111.5 
134 
190 


25.6 
23.6 
27.5 
28.1 


5 
6 

7 
8 


759 
235 
670 
677 


172.6 

84.8 
262.9 
182 


22.7 
36.1 
39.2 
26.8 



These may be taken as a fair showing of the power that is required in 
many of our best mills to drive shafting. It is unreasonable to think that 
all that power is consumed by a legitimate amount of friction of bearings 
and belts. I know of no cause for such a loss of power but tight belts. 
These, when there are hundreds or thousands in a mill, easily multiply 
the friction on the bearings, and would account for the figures. 

Sag of Belts. Distance between Pulleys. — In the location of shafts 
that are to be connected with each other by belts, care should be taken 
to secure a proper distance one from the other. This distance should be 
such as to allow of a gentle sag to the belt when in motion. 

A general rule may be stated thus: Where narrow belts are to be run 
over small pulleys 15 feet is a good average, the belt having a sag of 
1 1/2 to 2 inches. 

For larger belts, working on larger pulleys, a distance of 20 to 25 feet 
does well, with a sag of 21/2 to 4 inches. 

For main belts working on very large pulleys, the distance should be 25 
to 30 feet, the belts working well with a sag of 4 to 5 inches. 

If too great a distance is attempted, the belt will Jhave an unsteady 
flapping motion, which will destroy both the belt and machinery. 

Arrangement of Belts and Pulleys. — If possible to avoid it, con- 
nected shafts should never be placed one directly over the other, as in 
such case the belt must be kept very tight to do the work. For this 
purpose belts should be carefully selected of well-stretched leather. 

It is desirable that the angle of the belt with the floor should not exceed 
45°. It is also desirable to locate the shafting and machinery so that 
belts should run off from each shaft in opposite directions, as this arrange- 
ment will relieve the bearings from the friction that would result when 
the belts all pull one way on the shaft. 

In arranging the belts leading from the main line of shafting to the 
counters, those pulling in an opposite direction should be placed as near 



MISCELLANEOUS NOTES ON BELTING. 1127 

each other as practicable, while those pulling in the same direction should 
be separated. This can often be accomplished by changing the relative 
positions of the pulleys on the counters. By this procedure much of the 
friction on the journals may be avoided. 

If possible, machinery should be so placed that the direction of the belt 
motion shall be from the top of the driving to the top of the driven pulley, 
when the sag will inc p ease the arc of contact. 

The pulley should be a little wider than the belt required for the work. 

The motion of driving should run with and not against the laps of the 
belts. 

Tightening or guide pulleys should be applied to the slack side of belts 
and near the smaller pulley. 

Jones and Laughlins, in their Useful Information, say: The diameter of 
the pulleys should be as large as can be admitted, provided they will not 
produce a speed of more than 4750 feet of belt motion per minute. 

They also say: It is better to gear a mill with small pulleys and run 
them at a high velocity, than with large pulleys and to run them slower. 
A mill thus geared costs less and has a much neater appearance than with 
large heavy pulleys. 

M. Arthur Achard (Proc. Inst. M. E., Jan., 1881, p. 62) says: When the 
belt is wide a partial vacuum is formed between the belt and the pulley 
at a high velocity. The pressure is then greater than that computed from 
the tensions in the belt, and the resistance to slipping is greater. This 
has the advantage of permitting a greater power to be transmitted by a 
given belt, and of diminishing the strain on the shafting. 

On the other hand, some writers claim that the belt entraps air between 
itself and the pulley, which tends to diminish the friction, and reduce 
the tractive force. On this theory some manufacturers perforate the 
belt with numerous holes to let the air escape. 

Care of Belts. — Leather belts should be well protected against water, 
loose steam, and all other moisture, with which they should not come in 
contact. But where such conditions prevail fairly good results are 
obtained by using a special dressing prepared for the purpose of water- 

E roofing leather, though a positive water-proofing material has not yet 
een discovered. 

Belts made of coarse, loose-fibered leather will do better service in dry 
and warm places, but if damp or moist conditions exist then the very 
finest and firmest leather should be used. (Fayerweather & Ladew.) 

Do not allow oil to drip upon the belts. It destroys the life of the leather. 

Leather belting cannot safely stand above 110° of heat. 

Strength of Belting. — The ultimate tensile strength of belting does 
not generally enter as a factor in calculations of power transmission. 

The strength of the solid leather in belts is from 2000 to 5000 lbs. per 
square inch; at the lacings, even if well put together, only about 1000 to 
1500. If riveted, the joint should have half the strength of the solid 
belt. The working strain on the driving side is generally taken at not 
over one-third of the strength of the lacing, or from one-eighth to one- 
sixteenth of the strength of the solid belt. Dr. Hartig found that the 
tension in practice varied from 30 to 532 lbs. per sq. in., averaging 273 lbs. 

Adhesion Independent of Diameter. (Schultz Belting Co.) — 
1. The adhesion of the belt to the pulley is the same — the arc or number 
of degrees of contact, aggregate tension or weight being the same — 
without reference to width of belt or diameter of pulley. 

2. A belt will slip just as readily on a pulley four feet in diameter as it 
will on a pulley two feet in diameter, provided the conditions of the faces 
of the pulleys, the arc of contact, the tension, and the number of feet 
the belt travels per minute are the same in both cases. 

3. To obtain a greater amount of power from belts the pulleys may be 
covered with leather; this will allow the belts to run very slack and give 
25% more durability. 

Endless Belts. — If the belts are to be endless, they should be put on 
and drawn together by "belt clamps" made for the purpose. If the belt 
is made endless at the belt factory, it should never be run on to the pulleys, 
lest the irregular strain spring the belt. Lift out one shaft, place the 
belt on the pulleys, and force the shaft back into place. 

Belt Data. — A fly-wheel at the Amoskeag Mfg. Co., Manchester, N.H., 
30 feet diameter, 110 inches face, running 61 revs, per min., carried two 



1128 



heavy double-leather belts 40 inches wide each, and one 24 inches wide. 
The engine indicated 1950 H.P., of which probably 1850 H.P. was trans- 
mitted by the belts. The belts were considered to be heavily loaded, but 
not overtaxed. (30 X 3.14 X 104 X 61) + 1850 = 323 ft. per min. for 
1 H.P. per inch of width. 

Samuel Webber (Am. Mach., Feb. 22, 1894) reports a case of a belt 30 
ins. wide, 3/ 8 in. thick, running for six years at a velocity of 3900 ft. per 
min., on to a pulley 5 ft. diameter, and transmitting 556 H.P. This gives 
a velocity of 210 ft. per min. for 1 H.P. per in. of width. By Mr. Nagle's 
table of riveted belts this belt would be designed for 332 H.P. By Mr. 
Taylor's rule it would be used to transmit only 123 H.P. 

The above may be taken as examples of what a belt may be made to 
do, but they should not be used as precedents in designing. It is not 
stated how much power was lost by the journal friction due to over- 
tightening of these belts. 

Belt Dressings. — We advise that no belt dressing should be used 
except when the belt becomes dry and husky, and in such instances we 
recommend the use of a dressing. Where this is not used beef tallow at 
blood-warm temperature should be applied and then dried in either by 
artificial heat or the sun. The addition of beeswax to the tallow will be 
of some service if the belts are used in wet or damp places. Our expe- 
rience convinces us that resin should never be used on leather belting. 
(Fayerweather & Ladew.) 

Belts should not be soaked in water before oiling, and penetrating ods 
should but seldom be used, except occasionally when a belt gets very 
dry and husky from neglect. It may then be moistened a little, and 
have neat's-foot oil applied. Frequent applications of such oils to a new 
belt render the leather soft and flabby, thus causing it to stretch, and 
making it liable to run out of line. A composition of tallow and oil, with 
a little resin or beeswax, is better to use. Prepared castor-oil dressing is 
good, and may be applied with a brush or rag while the belt is running. 
(Alexander Bros.) 

Some forms of belt dressing, the compositions of which have not been 
published, appear to have the property of increasing the coefficient of 
friction between the belt and the pulley, enabling a given power to be 
transmitted with a lower belt tension than with undressed belts. C. W. 
Evans (Power, Dec, 1905), gives a diagram, plotted from tests, which 
shows that three of these compositions gave increased transmission for 
a given tension, ranging from about 10% for 90 lbs. tension per inch of 
width to 100% increase with 20 lbs. tension. 

Cement for Cloth or Leather. (Molesworth.) — 16 parts gutta- 
percha, 4 india-rubber, 2 pitch, 1 shellac, 2 linseed-oil, cut small, melted 
together and well mixed. 

Rubber Belting. — The advantages claimed for rubber belting are 
perfect uniformity in width and thickness; it will endure a great degree of 
heat and cold without injury; it is also specially adapted for use in damp 
or wet places, or where exposed to the action of steam; it is ^ery durable, 
and has great tensile strength, and when adjusted for service it has the 
most perfect hold on the pulleys, hence is less liable to slip than leather. 

Never use animal oil or grease on rubber belts, as it will greatly injure and 
soon destroy them. 

Rubber belts will be improved, and their durability increased, by 
putting on with a painter's brush, and letting it dry, a composition made 
of equal parts of red lead, black lead, French yellow, and litharge, mixed 
with boiled linseed-oil and japan enough to make it dry quickly. The 
effect of this will be to produce a finely polished surface. If, from dust 
or other cause, the belt should slip, it should be lightly moistened on the 
side next the pulley with boiled linseed-oil. (From circulars of manufac- 
turers.) 

The best conditions are large pulleys and high speeds, low tension and 
reduced width of belt. 4000 ft. per min. is not an excessive speed on 
proper sized pulleys. 

H.P. of a 4-ply rubber belt = (length of arc of contact on smaller pulley 
in ft. X width of belt in ins. X revs, per min.) -4- 325. For a 5-ply belt 
multiplv bv It's, for a 6-plv by 12/ 3 , for a 7-ply by 2, for an 8-pIv by 21 '3. 
When the proper weight of duck is used a 3- or 4-ply rubber belt is equal 
to a single leather belt and a 5- or 6-ply rubber to a double leather belt. 



ROLLER CHAIN AND SPROCKET DRIVES. 



1129 



When the arc of contact is 180°, H.P. of a 4-ply belt = width in ins. X 
velocity in ft. per min. -s- 650. (Boston Belting Co.) 

Steel Belts. — The Eloesser-Kraftband-Gesellschaft, of Berlin, has 
introduced a steel belt for heavy power transmission at high speeds 
(Am. Mach., Dec. 24, 1908). It is a thin flat band of tempered steel. 
The ends are soldered and then clamped by a special device consisting of 
two steel plates, tapered to thin edges, which are curved to the radius 
of the smallest pulley to be used, and joined together by small screws 
which pass through holes in the ends of the belt. It is stated that the 
slip of these belts is less than 0.1%; they are about one-fifth the width 
of a leather belt for the same power, and they are run at a speed of 10,000 ft. 
per minute or upwards. The following figures give a comparison of a 
rope drive with six ropes 1.9 ins. diam,, a leather belt 9.6 ins. wide and a 
steel belt 4 ins wide, for transmitting 100 H.P. on pulley 3 ft. diam., 
30 ft. apart at 200 r.p.m. 





Rope 
Drive. 


Leather 
Belt. 


Steel Belt. 




2200 
530 

$335 
13 


1120 
240 

$425 
6 


460 




30 




$250 




0.5 







ROLLER CHAIN ANI> SPROCKET DRIVES. 

The following is abstracted from an article by A. E. Michel, in Machy, 
Feb., 1905. 

Steel chain of accurate pitch, high tensile strength, and good wearing 
qualities, possesses, when used within proper limitations, advantages 
enjoyed by no other form of transmission. It is compact, affords a posi- 
tive speed ratio, and at slow speeds is capable of transmitting heavy 
strains. On short transmissions it is more efficient than belting and will 
operate more satisfactorily in damp or oily places. There is no loss of 
power from stretch, and as it allows of a low tension, journal friction is 
minimized. 

Roller chain has been known to stand up at a speed of 2,000 ft. per min., 
and transmit 25 H.P. at 1,250 ft. per min.; but speeds of 1,000 ft. per 
min. and under give better satisfaction. Block chain is adapted to 
slower speeds, say 700 ft. per min. and under, and is extensively used on 
bicycles, small motor cars and machine tools. Where speed and pull are 
not fixed quantities, it is advisable to keep the speed high, and chain 
pull low, yet it should be borne in mind that high speeds are more de- 
structive to chains of large than to those of small pitch. 

The following table of tensile strengths, based on tests of "Diamond " 
chains taken from stock, may be considered a fair standard: 

Roller Chain. 

Pitch, in 1/2 5/ 8 3/4 1 ll/ 4 11/2 13/4 2 

Tens, strength, lbs. 1,200 1,200 4,000 6,000 9,000 12,000 19,000 25,000 
Block chain linch, 1,200 to 2,500; li/2inch, 5,000. 

The safe working load of a chain is dependent on the amount of rivet 
bearing surface, and varies from 1/5 to 1/40 of the tensile strength, accord- 
ing to the speed, size of sprockets, and other conditions peculiar to each 
case. The tendency now is to use the widest possible chain in order to 
secure maximum rivet bearing surface, thus insuring minimum wear 
from friction. Manufacturers are making heavier chains than heretofore 
for the same duty. As short pitch is always desirable, special double and 
even triple width chains are now made to conform to the requirements 
when a heavy single width chain of greater pitch is not practical. A 
double chain has twice the rivet bearing surface and half again as much 
tensile strength as the similar single one. 

The length of chain for a given drive may be found by the following 
formula: 



1130 • BELTING. 

All dimensions in inches. D = Distance between centers of shafts. 
A = Distance between limiting points of contact. R = Pitch radius of 
large sprocket, r = Pitch radius of small sprocket. N = Number of 
teeth of large sprocket, n = Number of teeth of small sprocket. P = 
Pitch of chain and sprockets. (180° + 2 a) = angle of contact on large 
sprocket. (180° — 2 a) = angle of contact on small sprocket, a = angle 
whose sine is (R — r)/D. A = D cos a. 

Length of chain required: 

For block chain, the total length specified in ordering should be in 
multiples of the pitch. For roller chain, the length should be in multiples 
of twice the pitch, as a union of the ends can be effected only with an out- 
side and an inside link. 

Wherever possible, the distance between centers of shafts should permit 
of adjustment in order to regulate the sag of the chain. A chain should 
be adjusted, in proportion to its length, to show slack when running, care 
being taken to have it neither too tight nor too loose, as either conoition 
is destructive. If a fixed center distance must be used, and roults in 
too much sag, the looseness should be taken up by an idler, and when 
there is any considerable tension on the slack side, this idler must be 
a sprocket. Where an idler is not practical, another combination of 
sprockets giving approximately the same speed ratio may be tried, and 
in this manner a combination giving the proper sag may always be 
obtained. 

In automobile drives, too much sag or too great a distance between 
shafts causes the chain to whip up and down — a condition detrimental 
to smooth running and very destructive to the chain. In this class of 
work a center distance of over 4 ft. has been used, but greater efficiency 
and longer life are secured from the chain on shorter lengths, say 3 ft. and 
under. 

Sprocket Wheels. Properly proportioned and machined sprockets are 
essential to successful chain gearing. The important dimensions of a 
sprocket are the pitch diameter and the bottom and outside diameters. 
For block chain these are obtained as follows: 

N = No. of teeth, b = Diameter of round part of chain block. B = 
Center to center of holes in chain block. A = Center to center of holes 
in side links. a= 180°/ N. Tan /?= sin a -?■ (B/A + cos a). 
Pitch diameter = A/Sin 0. 

Bottom diam.=pitch diam.— &. Outside diam.=pitch diam. + b. 

For roller chain: N = Number of teeth. P = Pitch of chain. D ~ 
Diameter of roller. a= 180°/ N. Pitch diameter = P/sin a. 

Bottom diam. = pitch diam. — D. 

For sprockets of 17 teeth and over, outside diam = pitch diam. + D. 

The outside diameters of small sprockets are cut down so that the teeth 
will clear the roller perfectly at high speeds. 

Outside diam. = pitch diam. 4- D - E. 



8 to 12 
Teeth. 



13 to 16 
Teeth. 



1/2 in. to 3/ 4 in. 
1 in. to 2 ins... . 



0.062 in. 
0.125 in. 



0.031 in. 
0.062 in. 



Sprocket diameters should be very accurate, particularly the base ; 
diameter, which should not vary more than 0.002 in. from the calculated i 
values. Sprockets should be gauged to discover thick teeth and inaccurate I 
diameters. A poor chain may operate on a good sprocket, but a bad 
sprocket will ruin a goOd chain. Sprockets of 12 to 60 teeth give best 



ROLLER CHAIN AND SPROCKET DRIVES. 1131 

results. Fewer may De used, but cause undue elongation in the chain, 
wear the sprockets and consume too much power. Eight-tooth sprockets 
ruin almost every roller chain applied to them, and ten and eleven teeth 
are fitted only for medium and slow speeds with other conditions unusu- 
ally favorable. 

Sprocket teeth seldom break from insufficient strength, but the tooth 
must be properly shaped. A chain will not run well unless the sprockets 
have sidewise clearance and teeth narrowed at the ends by curves begin- 
ning at the pitch line. 

Calling W the width of the chain between the links, 

A = 1/2 W = width of tooth at top. B = uniform width below pitch line. 
B = W — V64 in. when W = 1/4 in. or less. 

= W— 1/32 in. when W = 5/ 16 to 5/ 8 in. inclusive. 

= w— 1/16 in. when W = 3/ 4 in. or over. 

If the sprocket is flanged the chain must seat itself properly without the 
side bars coming into contact with the flange. 

The principal cause of trouble within the chain is elongation. It is 
the result of stretch of material or natural wear of rivets and their bearings. 
To guard against the former, chain makers use special materials of high 
tensile strength, but a chain subjected to jars and jolts beyond the limit 
of elasticity of the material may be put in worse condition in an instant 
than in months of natural wear. If for any reason a link elongates 
unduly it should be replaced at once, as one elongated link will eventually 
ruin the entire chain. Such elongation frequently results from all the 
.load being thrown on at once. 

To minimize natural wear, chains should be well greased inside and 
out, protected from mud and heavy grit, cleaned often and replaced to 
run in the same direction and same side up. A new chain should never 
be applied to a much-worn sprocket. 

Importance of pitch line clearances: In a sprocket with no clearances 
a new chain fits perfectly, but after natural wear the pitch of chain and 
sprocket become unlike. The chain is then elongated and climbs the 
teeth, which act as wedges, producing enormous strain, and it quickly 
wrecks itself. With the same chain on a driven sprocket, cut with 
clearances, all rollers seat against their teeth. After long and useful life, 
the working roller shifts to the top, and the other rollers still seat with 
the same ease as when new. Theoretically, all the rollers share the load. 
This never occurs in practice, for infinitesimal wear within the chain 
causes one, and only one, roller to bear perfectly seated against the 
working face of the sprocket tooth at any one time. Clearance alone on 
the driver will not provide for elongation. To operate properly the 
pitch of the driver must be lengthened, which is done by increasing the 
pitch diameter by an amount dependent upon the clearance allowed. 
For theoretical reasoning on this subject see " Roller Chain Gear," a 
treatise on English practice, by Hans Renold. 

When the load reverses, each sprocket becomes alternately driver and 
driven. This happens in a motor car during positive and negative accel- 
eration, or in ascending or descending a hill. In this event, the above 
construction is not applicable, for a driven sprocket of longer pitch than 
the chain will stretch it. No perfect method of equalizing the pitch of a 
roller chain and its sprockets under reversible load and at all periods of 
chain elongation has been found. This fault is eliminated in the " silent " 
type of chain; hence it runs smooth at a very much greater speed than 
roller chain will stand. 

In practice there are comparatively few roller chain drives with chain 
pull always in the same direction, so manufacturers generally cut the 
driver sprockets for these with normal pitch diameter, same as the 
driven. Recent experiments have proven that the difficulties are greatly 
lessened by cutting both driver and driven with liberal pitch line clear- 
ance. Accordingly, chain makers now advise the following pitch line 
clearance for standard rollers: 



Pitch, in., 


1/2 


3/4 


1 


1V4 


1V2 


13/4 


2 


Clearance, in., 


V32 


Vie 


3 /32 


3/16 


7/32 


V8 


5 /32 



Cutters may be obtained from Brown & Sharpe Mfg. Co. with this 
clearance. 



1132 BELTING. 

Belting versus Chain Drives. — Chains are suitable for positive 
transmissions of very heavy powers at slow speed. They are properly 
used for conveying ashes, sand, chemicals and liquids which would cor- 
rode or destroy belting. Chains of this kind are generally made of 
malleable iron. For conveyers for clean substances, flour, wheat and 
other grains, belts are preferable, and in the best installations leather is 
preferred to cotton or rubber, being more durable. Transmission 
chains have to be carefully made. If the chain is to run smoothly, noise- 
lessly, and without considerable friction, both the links and the sprockets 
must be mathematically correct. This perfection of design is found only 
in the highest and best makes of steel chain. 

Deterioration of chains starts in with the beginning of service. Even 
in such light and flexible duty as bicycle transmission, a chain is sub- 
jected to sudden severe strains, which either stretch the chain or distort 
the bearing surfaces. Either mishap is fatal to smooth frictionless 
running. If the transmission is positive, as from motor or shaft to a 
machine tool, sudden variations in strain become sledge-hammer blows, 
and the chain must either break or the parts yield. To avoid the evils 
arising from the stretching of the chain, self-adjusting forms of teeth have 
been invented, of which the Renold silent-chain gear is one of the best. 

The makers of the Morse rocker chain, also an excellent chain, recom- 
mend it for use under the following conditions: (1) Where room is lack- 
ing for the proper sized pulleys for belts. (2) Where the centers between 
shafts are too short for belts. (3) Where a positive speed ratio is desired. 
(4) Where there is moisture, heat or dust that would prevent a belt 
working properly. (5) Where a maximum power per inch of width is 
desired. 

The Renold silent chain and the Morse rocker chain find springs 
necessary in the sprocket wheel. This springiness the belt naturally 
possesses, and where maximum power is not necessary at a low speed 
under service conditions of moisture and dirt, as in automobile trans- 
mission, the belt will be cheaper to install, cheaper to maintain, cheaper 
to repair in case of breakdown, and more efficient than any chain. A 
leather belt will run on very short centers and transmit very high powers, 
but it should be run at higher speed than a long belt. 

For slow service, for positive transmission, for rough service, gears 
are rivals of chain .transmission. For fast service, for springy transmis- 
sion, for clean, dry work, leather belts are still the best. — Harrington 
Emerson, Am. Mach., April 6, 1909. 

It is to be regretted that there is no standard among chain manufac- 
turers for the correct outline of sprocket cutters and amount of clearance 
for various sizes of chain. If it is clearly understood that the high quality 
roller and block chains now on the market require correctly cut sprockets 
properly proportioned for the particular conditions of service they are 
to work under, there will be a large increase in their use for power trans- 
mission, and the troubles now incident to incorrect installations could be 
wholly obviated. — C. C. Myers, Am. Mach., Aug. 5, 1909. 

A 350-H.P. Silent Chain Drive has been built by the Link Belt Co. 
The gears are 12 ft. apart, centers. The drive consists of two strands, 
each 12 ins. wide, of Renold silent chain of 2-in. pitch. The pinion is 
of forged steel, about 16 1/2 in. diameter, 27-in. face, 26 teeth, bore 29 in. 
■ long 10 in. diameter. The main gear is made of two cast-iron wheels, 
side by side, each 76i/2-in. diameter, 131/2-in. face, 120 teeth. Each 
wheel is provided with steel flanges and a special hub containing a series 
of stiff coiled springs in compression through which the driving force is 
transmitted from the hub to the wheel. The object of this device is to 
provide an equalizing factor between the power shaft and the teeth of 
the wheel, so that any unevenness in the rotation and consequent shock 
will be absorbed by the device. The pinion is mounted on the armature 
of a motor running' 300 r.p.m., and the speed of the driven gear is 65 r.p.m. 
The speed of the chain belt is 780 ft. per minute. Three of these drives 
have been constructed to transmit power for wire' drawing. — (Power, 
Dec. 28, 1909.) 




TOOTHED- WHEEL GEARING. 



1133 



GEARING. 

TOOTHED-WHEEL GEARING. 

Pitch, Pitch-circle, etc. — If two cylinders with parallel axes are 
pressed together and one of them is rotated on its axis, it will drive the 
other by means of the friction between the surfaces. The cylinders may 
be considered as a pair of spur-wheels with an infinite number of very small 
teeth. If actual teeth are formed upon the cylinders, making alternate 
elevations and depressions in the cylindrical surfaces, the distance between 
the axes remaining the same, we have a pair of gear-wheels which will 
drive one another by pressure upon the faces of the teeth, if the teeth are 
properly shaped. In making the teeth the cylindrical surface may 
entirely disappear, but the position it occupied may still be considered as 
a cylindrical surface, which is called the "pitch-surface," and its trace 
on the end of the wheel, or on a plane cutting the wheel at right angles to 
its axis, is called the "pitch-circle" or "pitch-line." The diameter of 
this circle is called the pitch-diameter, and the distance from the face 
of one tooth to the corresponding face of the next tooth on the same 
wheel, measured on an arc of the pitch-circle, is called the "pitch of the 
tooth," or the circular pitch. 

If two wheels having teeth of the same pitch are geared together so 
that their pitch-circles touch, it is a property of the pitch-circles that 
their diameters are proportional to the number of teeth in the wheels, 
and vice versa; thus, if one wheel is twice the diameter (measured on the 
pitch-circle) of the other, it has twice as many teeth. If the teeth are 
properly shaped the linear velocities of the two wheels are equal, and the 
angular velocities, or speeds of rotation, are inversely proportional to the 
number of teeth and to the diameter. Thus the wheel that has twice as 
many teeth as the other will revolve 
just half as many times in a minute. 

The "pitch," or distance meas- 
ured on an arc of the pitch-circle 
from the face of one tooth to the 
face of the next, consists of two 
oarts — the "thickness" of the 
tooth and the "space" between it 
and the next tooth. The space is 
larger than the thickness by a small 
amount called the "backlash," 
which is allowed for imperfections 
of workmanship. In finely cut 
gears the backlash may be almost 
nothing. 

The length of a tooth in the 
direction of the radius of the wheel . ., • 

is called the "depth," and this is divided into two parts: First, the 
"addendum : ' the height of the tooth above the pitch line; second, the 
"dedendum " the depth below the pitch-line, which is an amount equal to 
the addendum of the mating gear. The depth of the space is usually 
given a little "clearance" to allow for inaccuracies of workmanship, 

eS Referring 1 1? Fig 6 17i, pi, pi are the pitch-lines, al the addendum-line, 
rl the root line or dedendum-line, cl the clearance-line, and b the back- 
lash. The addendum and dedendum are usually made equal to each 
other. „ ■'■*■. i„ 

No of teeth 3.1416 

Diametral pitch ■■ 




Fig, 171. 



Circular pitch 



= diam. of pitch-circle in inches circular pitch 
diam.X 3.1416 3.1416 

No. of teeth diametral pitch' 



diam. 



Some writers use the term diametral pitch to mean No of teet h = 

circular pitch ^ but tfae first definit i on j s the more common and the more 
3.1416 



1134 



GEARING. 



convenient. A wheel of 12 in. diam. at the pitch-circle, with 48 teeth, is 
48 /i2 = 4 diametral pitch, or simply 4 pitch. The circular pitch of the 
same wheel is 12 X 3.1416-5- 48= 0.7854, or 3.1416-s- 4= 0.7854 in. 





Relation of Diametral to Circular Pitch. 




Diame- 
tral 
Pitch. 


Circular 
Pitch. 


Diame- 
tral 
Pitch. 


Circular 
Pitch. 


Cir- 
cular 
Pitch. 


Diame- 
tral 
Pitch. 


Circular 
Pitch. 


Diame- 
tral 
Pitch. 


1 


3. 142 in. 


11 


0.286 in. 


3 


1.047 


15/16 


3.351 


U/2 


2.094 


12 


.262 


21/2 


1.257 


7/8 


3.590 


2 


1. 571 


14 


.224 


2 


1.571 


13/16 


3.867 


21/4 


1.396 


16 


.196 


17/8 


1.676 


3/4 


4.189 


21/2 


1.257 


18 


.175 


13/ 4 


1.795 


11/16 


4.570 


23,4 


1.142 


20 


.157 


l 5 /8 


1.933 


5/8 


5.027 


3 


1.047 


22 


.143 


H/2 


2.094 


9 /l6 


5.585 


31/2 


.898 


24 


.131 


17/16 


2.185 


1/2 


6.283 


4 


.785 


26 


.121 


13/8 


2.285 


7/16 


7.181 


5 


.628 


28 


.112 


15/16 


2.394 


3/8 


8.378 


6 


.524 


30 


.105 


11/4 


2.513 


5/16 


10.053 


7 


.449 


32 


.098 


13/16 


2.646 


1/4 


12.566 


8 


.393 


36 


.087 


U/8 


2.793 


3/16 


16.755 


9 


.349 


40 


.079 


H/16 


-2.957 


1/8 


25.133 


10 


.314 


48 


.055 


1 


3.142 


Vl6 


50.266 



Since circ. pitch 



diam. X 3.1416 
No. of teeth ' 



diam. = 



circ. pitch X No. of teeth 
3.1416 



which always brings out the diameter as a number with an inconvenient 
fraction if the pitch is in even inches or simple fractions of an inch. By 
the diametral-pitch system this inconvenience is avoided. The diameter 
may be in even inches or convenient fractions, and the number of teeth 
is usually an even multiple of the number of inches in the diameter. 



Diameter of Pitch-line of Wheels from 10 to 100 Teeth of 1 In. 












Circular Pitch. 






.-d 


c3.£ 


.A 
£1 


i.s 


$ 

S2j 


is 


.A 
£1 


i.s 




l.s 


.A 

Z a) 


is 


H 


Q 


H 


5 


H 


Q 


H 


Q 


H 


Q 


H 


5 


to 


3.183 


26 


8.276 


41 


13.051 


56 


17.825 


71 


22.600 


86 


27.375 


11 


3.501 


27 


8.594 


42 


13.369 


57 


18.144 


72 


22.918 


87 


27.693 


12 


3.820 


28 


8.913 


43 


13.687 


58 


18.462 


73 


23.236 


88 


28.011 


13 


4.138 


29 


9.231 


44 


14.006 


59 


18.781 


74 


23.555 


89 


28.329 


14 


4.456 


30 


9.549 


45 


14.324 


60 


19.099 


75 


23.873 


90 


28.648 


15 


4.775 


31 


9.868 


46 


14.642 


61 


19.417 


76 


24.192 


91 


28.966 


16 


5.093 


32 


10.186 


47 


14.961 


62 


19.735 


77 


24.510 


92 


29.285 


17 


5.411 


33 


10.504 


48 


15.279 


63 


20.054 


78 


24.878 


93 


29.603 


18 


5.730 


34 


10.823 


49 


15.597 


64 


20.372 


79 


25.146 


94 


29.921 


19 


6.048 


35 


11.141 


50 


15.915 


65 


20.690 


80 


25.465 


95 


30.239 


20 


6.366 


36 


11.459 


51 


16.234 


66 


21.008 


81 


25.783 


96 


30.558 


21 


6.685 


37 


11.777 


52 


16.552 


67 


21.327 


87, 


26.101 


97 


30.876 


??. 


7.003 


38 


12.096 


53 


16.870 


68 


21.645 


83 


26.419 


98 


31.194 


23 


7.321 


39 


12.414 


54 


17.189 


69 


21.963 


84 


26.738 


99 


31.512 


74 


7.639 


40 


12.732 


55 


17.507 


70 


22.282 


85 


27.056 


100 


31.831 


75 


7.958 













































For diameter of wheels of any other pitch than 1 in., multiply the figures 
in the table by the pitch. Given the diameter and the pitch, to find the 
number of teeth. Divide the diameter by the pitch, look in the table 
under diameter for the figure nearest to the quotient, and the number 
of teeth will be found opposite. 



TOOTHED-WHEEL GEARING. 



1135 



Proportions of Teeth 


Circular 


Pitch 


= 1. 








1. 


2. 


3. 


4. 


5. 


6. 


Depth of tooth above pitch-line 

Depth of tooth below pitch-line 


0.35 
.40 
.70 
.75 
.05 
.45 
.54 
.09 


0.30 
.40 
.60 
.70 
.10 
.45 
.55 
.10 


0.37 
.43 
.73 
.80 
.07 
.47 
.53 
.06 
.47 


0.33 

'M 
.75 


0.30 

.40 


0.30 
.35 




.70 


.65 








.45 
.55 
.10 

.45 


.475 
.525 
.05 
.70 


485 




515 




03 




.65 











7. 


8. 


9. 


10.* 


Depth of tooth above pitch- 


0.25 to 0.33 
.35 to .42 


0.30 
.35+. 08" 


0.318 

.369 

.637 

.687 

.04 to .05 

.48 to .5 { 

.52 to .5 { 
.0 to .04 


1+ P 


Depth of tooth below pitch- 
line 


1.157 + P 
2-P 


Total depth of tooth 


.6 to .75 


.65 +.08" 


2.157-P 
0.I57+P 


Thickness of tooth 

Width of space 

Backlash 


.48 to .485 

.52 to .515 
.04 to .03 


.48 -.03" 

.52 +.03" 
.04+. 06" 


1.51 -s-Pto 
1.57 +P 
1.57 -hPto 
1.63 + P 

.Oto .06-rP 



* In terms of diametral pitch. 

Authorities. — 1. Sir Wm. Fairbairn. 2, 3. Clark, R. T. D.; "used 
by engineers in good practice. " 4. Molesworth. 5,6. Coleman Sellers: 
5 for cast, 6 for cut wheels. 7, 8. Unwin. 9, 10. Leading American 
manufacturers of cut gears. 

The Chordal Pitch (erroneously called "true pitch" by some authors) 
is the length of a straight line or chord drawn from center to center of two 
adjacent teeth. The term is now but little used, except in connection 
with chain and sprocket gearing. 

Chordal pitch = diam. of pitch-circle X sine of = j— — -r- Chordal 

No. of teeth 
pitch of a wheel of 10 in. pitch diameter and 10 teeth, 10 X sin 18° = 
3.0902 in. Circular pitch of same wheel = 3.1416. Chordal pitch is 
used with chain or sprocket wheels, to conform to the pitch of the chain. 

Gears with Short Teeth. — There is a tendency in recent years to 
depart widely from the proportions of teeth given in the above and to 
use much shorter teeth, especially for heavy machinery. C. W. Hunt 
gives addendum and dedendum each = 0.25, and the clearance 0.05 of 
the circular pitch, making the total depth of tooth 0.55 of the circular 
pitch. The face of the tooth is involute in form, and the angle of action 
is 14V2 , C. H. Logue uses a 20° involute with the following proportions: 
Addendum 0.25P' = 0.7854 -e-P; dedendum 0.30 P' = 0.9424 -^ P; 
clearance, 0.05P' = 0.157P: whole depth 0.55P' = 1.7278 -^ P. P' = 
circular pitch, P = diametral pitch. See papers by R. E. Flanders and 
Norman Litchfield in Trans. A. S. M. E., 1908. 

John Walker (Am. Mach., Mar. 11, 1897) says: For special purposes of 
slow-running gearing with great tooth stress I should prefer a length of 
tooth of 0.4 of the pitch, but for general work a length of 0.6 of the pitch. 
In 1895 Mr. Walker made two pairs of cut steel gears for the Chicago 
cable railway with 6-in. circular pitch, length = 0.4 pitch. The pinions 
had 42 teeth and the gears 62, each 20-in. face. The two pairs were 
set side by side on their shafts, so as to stagger the teeth, making the 
total face 40 ins. The gears transmitted 1500 H.P. at 60 r.p.m. replac- 
ing cast-iron gears of 7V2 in. pitch which had broken in service. 



1136 



Formulae for Determining the Dimensions of Small Gears. 

(Brown & Sharpe Mfg. Co.) 

P = diametral pitch, or the number of teeth to one inch of diameter of 
pitch-circle; 



D' '— diameter of iDitch-circle.. 

D = whole diameter 

N = number of teeth 

V = velocity 



d' = diameter of pitch-circle. . 

d = whole diameter. 

n = number of teeth 

u = velocity 



Larger 
Wheel. 



Smaller 
Wheel. 



These 
wheels run 
together. 



a = distance between the centers of the two wheels; 

b = number of teeth in both wheels; 

t = thickness of tooth or cutter on pitch-circle; 

s = addendum; 
D" = working depth of tooth; 

/ = amount added to depth of tooth for rounding the corners and for 
clearance; 
D" + f = whole depth of tooth; 

ir = 3.1416. 

P' = circular pitch, or the distance from the center of one tooth to the 
center of the next measured on the pitch-circle. 



Formulae 


for a single w 


heel: 




N+2 
D ' 


"-£& 


D"=|=2s 


s=~= ^ = 0.3183 P'; 


N 
D''' 


»-§>• 


N = PD-2; 
N = PD'\ 


D' D 

S N N+2' 


IT 


D=»p; 


J 10' 


S + ^W + 2^)= & - 


7T 


D = D> +| 


' l P 


1/2 P*. 


Formulas for a pair of wheels: 






b = 2aP; 


PD'V 

v ' 


D 2a{N+2)_ 
b ' 






PD'V 


rl 2 a (n+2) 
a b 




_ NV m 

v ' 


n ' 


b 

fl= 2P ; 




iV v + V 


N' 


D'+d' 
a= -2—' 




bV 

v + V 


u v + V 


„ 2aV 

d== V+v' 




Width of Teeth. — The width of the faces of teeth is generally made 
from 2 to 3 times the circular pitch, that is from 6.28 to 9.42 divided by 
the diametral pitch. There is no standard rule for width. 

The following sizes are given in a stock list of cut gears in "Grant's 
Gears:" 

Diametral pitch.. 3 4 6 8 12 16 

Face, inches 3 and 4 2i/ 2 13/ 4 and 2 1 1/4 and H/2 3/ 4 and 1 1/2 and 5/ 8 

The Walker Company gives: 
Ci r cular pitch, in. . 1/2 5 /8 



3/4 7/ 8 1 
13/4 2 21/2 



H/2 
41/2 



2 21/2 3 4 5 6 
6 71/2 9 12 16 20 



TOOTHED-WHEEL GEARING. 



1137 



The following proportions of gear-wheels are recommended by Prof. 
Coleman Sellers. (Stevens Indicator, April, 1892.) 





Proportions 


of Gear-wheels. 








Circular 

Pitch. 

P 


Outside of 
Pitch-line. 
P X 0.3. 


Inside of Pitch-line. 


Width of Space. 


Diametral 
Pitch. 


For Cast 

or Cut 
Bevels or 


For Cut 
Spurs. 
P X 0.35 


For Cast 
Spurs or 


For Cut 
Bevels or 






for Cast 


Bevels. 


Spurs. 








Spurs. 


P x 0.525. 


PX0.5I. 








P x 0.4. 










1/4 


0.075 


0.100 


0.088 


0.131 


0.128 


12 


0.2618 


.079 


.105 


.092 


.137 


.134 


10 


0.31416 


.094 


.126 


.11 


.165 


.16 




3/8 


.113 


.150 


.131 


.197 


.191 


8 


0.3927 


.118 


.157 


.137 


.206 


.2 


7 


0.4477 


.134 


.179 


.157 


.235 


.228 




1/2 


.15 


.20 


.175 


.263 


.255 


6 


0.5236 


.157 


.209 


.183 


.275 


.267 




9/16 


.169 


.225 


.197 


.295 


.287 




5/8 


.188 


.25 


.219 


.328 


.319 


5 


0.62832 


.188 


.251 


.22 


.33 


.32 




3/4 


.225 


.3 


.263 


.394 


.383 


4 


0.7854 


.236 


.314 


.275 


.412 


.401 




7/8 


.263 


.35 


.307 


.459 


.446 




1 


.3 


.4 


.35 


.525 


.51 


3 


1.0472 


.314 


.419 


.364 


.55 


.534 




U/8 


.338 


.45 


.394 


.591 


.574 


2S/4 


1.1424 


.343 


.457 


.40 


.6 


.583 




H/4 


.375 


.5 


.438 


.656 


.638 


21/2 


1.25664 


.377 


.503 


.44 


.66 


.641 




13/8 


.413 


.55 


.481 


.722 


.701 




H/2 


.45 


.6 


.525 


.788 


.765 


2 


1.5708 


.471 


.628 


.55 


.825 


.801 




13/4 


.525 


.7 


.613 


.919 


.893 




2 


.6 


.8 


.7 


1.05 


1.02 


BV2 


2.0944 


.628 


.838 


.733 


1.1 


1.068 




21/4 


.675 


.9 


.788 


1.181 


1.148 




21/2 


.75 


1.0 


.875 


1.313 


1.275 




23/4 


.825 


1.1 


.963 


1.444 


1.403 




3 


.9 


1.2 


1.05 


1.575 


1.53 


1 


3.1416 


.942 


1.257 


1.1 


1.649 


1.602 




31/4 


.975 


1.3 


1.138 


1.706 


1.657 




31/2 


1.05 


1.4 


1.225 


1.838 


1.785 



Thickness of rim below root = depth of tooth. 

Rules for Calculating the Speed of Gears and Pulleys. — The 

relations of the size and speed of driving and driven gear-wheels are the 
same as those of belt pulleys. In calculating for gears, multiply or 
divide by the diameter of the pitch-circle or by the number of teeth, as 
may be required. In calculating for pulleys, multiply or divide by their 
diameter in inches. 

If D = diam. of driving wheel, d = diam. of driven, R = revolutions 
per minute of driver, r = revs, per min. of driven, RD = rd; 
R = rd + D; r = RD + d; D = dr + R; d = DR + r. 

It N = No. of teeth of driver and n = No. of teeth of driven, NR = nr; 
N = nr + R; n = NR + r; R = rn + AT; r= RN ■*■ n. 

To find the number of revolutions of the last wheel at the end of a 
train of spur-wheels, all of which are in a line and mesh into one another, 
when the revolutions of the first wheel and the number of teeth or the 



1138 GEARING. 

diameter of the first and last are given: Multiply the revolutions of the 
first wheel by its number of teeth or its diameter, and divide the product 
by the number of teeth or the diameter of the last wheel. 

To find the number of teeth in each wheel for a train of spur-wheels, 
each to have a given velocity: Multiply the number of revolutions of 
the driving-wheel by its number of teeth, and divide the product by the 
number of revolutions each wheel is to make. 

To find the number of revolutions of the last wheel in a train of wheels 
and pinions, when the revolutions of the first or driver, and the diameter, 
the teeth, or the circumference of all the drivers and pinions are given; 
Multiply the diameter, the circumference, or the number of teeth of all 
the driving-wheels together, and this continued product by the number 
of revolutions of the first wheel, and divide this product by the contin- 
ued product of the diameter, the circumference, or the number of teeth 
of all the driven wheels, and the quotient will be the number of revolutions 
of the last wheel. 

Example. — 1. A train of wheels consists of four wheels each 12 in. 
diameter of pitch-circle, and three pistons 4, 4, and 3 in. diameter. The 
large wheels are the drivers, and the first makes 36 revs, per min. Re- 
quired the speed of the last wheel. 

"^^" -"■"■^ 

2. What is the speed of the first large wheel if the pinions are the 
drivers, the 3-in. pinion being the first driver and making 36 revs, per min.? 

36X3X4X4 , ■ 

12X12X12 = lr -P- m ° Ans - 

Milling Cutters for Interchangeable Gears. — The Pratt & 
Whitney Co. makes a series of cutters for cutting epicycloidal teeth. 
The number of cutters to cut from a pinion of 12 teeth to a rack is 24 for 
each pitch coarser than 10. The Brown & Sharpe Mfg. Co. makes a 
similar series, and also a series for involute teeth, in which eight cutters 
are made for each pitch, as follows: 

No 1. 

Will cut from..... 135 
to Rack 

FORMS OF THE TEETH, 

In order that the teeth of wheels and pinions may run together smoothly 
and with a constant relative velocity, it is necessary that their working 
faces shall be formed of certain curves called odontoids. The essential 
property of these curves is that when two teeth are in contact the com- 
mon normal to the tooth curves at their point of contact must pass through 
the pitch-point, or point of contact of the two pitch-circles. Two such 
curves are in common use — the cycloid and the involute. 

The Cycloidal Tooth. — In Fig. 172 let PL and pi be the pitch- 
circles of two gear-wheels; GC and gc are two equal generating-circles, 
whose radii should be taken as not greater than one-half of the radius 
of the smaller pitch-circle. If the circle gc be rolled to the left on the 
larger pitch-circle PL, the point will describe an epicycloid, Oefgh. If 
the other eenerating-eircle GC be rolled to the right on PL, the point 
will describe a hvpocycloid Oabcd. These two curves, which are tanerent 
at 0, form the two parts of a tooth curve for a gear whose pitch-circle is 
PL. The uoper part Oh is called the face and the lower part Od is called 
the flank. If the same circles be rolled on the other pitch-circle vl, they 
will describe the curve for a tooth of the gear pi, which will work properly 
with the tooth on PL. 

The cycloidal curves may be drawn without actually rolling the gen- 
erating-circle, as follows: Oh the line PL, from 0, step off and mark eauar 
distances, as 1, 2, 3, 4, etc. From 1, 2, 3, etc., draw radial lines toward 
the center of PL, and from 6, 7, 8, etc., draw radial lines from the same 



2 


3. 


4. 


5. 


6. 


7. 


8. 


55 


35 


26 


21 


17 


14 


12 


134 


54 


34 


25 


20 


16 


13 



FORMS OF THE TEETH. 



1139 



center, but beyond PL. With the radius of the generating-circle, and 
with centers successively placed on these radial lines, draw arcs of circles 
tangent to PL at 1, 2, 3, 6, 7, 8, etc. With the dividers set to one of the 
equal divisions, as 01, step off on the generating circle go the points a', V, 
c', d', then take suceessivelv the chordal distances 0a, Ob', Oe , 0a, 
and lay them off on the several arcs 6e, If, 8g, 9h, and la, 2b, 3c, 4d; 
through the points efgh and abed draw the tooth curves. 




Fig. 172. 



The curves for the mating tooth on the other wheel may be found in 
like manner by drawing arcs of the generating-circle tangent at equidistant 
points on the pitch-circle pi. 

The tooth curve of the face Oh is limited by the addendum-line r or r lt 
and that of the flank OH by the root curve R or R t . R and r represent 
the root and addendum curves for a large number of small teeth, and R^r 
the like curves for a small number of large teeth. The form or appearance 
of the tooth therefore varies according to the number of teeth, while the 
pitch-circle and the generating-circle may remain the same. 

In the cycloidal system, in order that a set of wheels of different diam- 
eters but equal pitches shall all correctly work together, it is necessary 
that the generating-circle used for the teeth of all the wheels shall be 
the same, and it should have a diameter not greater than half the diam- 
eter of the pitch-line of the smallest wheel of the set. The customary 
standard size of the generating-circle of the cycloidal system is one having 
a diameter equal to the radius of the pitch-circle of a wheel having 12 
teeth. (Some erear-makers adopt 15 teeth.) This circle gives a radial 
flank to the teeth of a wheel having 12 teeth. A pinion of 10 or even a 
smaller number of teeth can be made, but in that case the flanks will be 
undercut, and the tooth will not be as strong as a tooth with radial flanks. 
If in any case the describing circle be half the size of the pitch-circle, the 
flanks will be radial; if it be less, they will spread out toward the root of 
the tooth, giving a stronger form; but if greater, the flanks will curve in 
toward each other, whereby the teeth become weaker and difficult to 
make. 

In some cases cycloidal teeth for a pair of gears are made with the 
generating-circle of each gear having a radius equal to half the radius 
of its pitch-circle. In this case each of the gears will have radial flanks. 



1140 



This method makes a smooth working gear, but a disadvantage is that 
the wheels are not interchangeable with other wheels of the same pitch 
but different numbers of teeth. 

■ The rack in the cycloidal system is equivalent to a wheel with an 
infinite number of teeth. The pitch is equal to the circular pitch of the 
mating gear. Both faces and hanks are cycloids formed by rolling the 
generating-circle of the mating gear-wheel on each side of the straight 
pitch-line' of the rack. 

Another method of drawing the cycloidal curves is shown in Fig. 173. 
It is known as the method of tangent arcs. The generating-circles, as 
before, are drawn with equal radii, the length of the radius being less 
than half the radius of pi, the smaller pitch-circle. Equal divisions 1, 2, 




Fig. 173. 



3, 4, etc., are marked off on the pitch-circles and divisions of the same 
length stepped off on one of the generating-circles, as 0, a, b, c. From the 
points 1, 2, 3, 4, 5 on the line pO, with radii successively equal to the chord 
distances a, Ob, c, Od, Oe, draw the five small arcs F. A line drawn 
through the outer edges of these small arcs, tangent to them all, will be 
the hypocycloidal curve for the flank of a tooth below the pitch-line pi. 
From the points 1, 2, 3, etc., on the line 01, with radii as before, draw the 
small arcs G. A line tangent to these arcs will be the epicycloid for the 
face of the same tooth for which the flank curve has already been drawn. 
In the same way, from centers on the line P0, and t 0Z/, with the same 
radii, the tangent arcs H and K may be drawn, which will give the tooth 
for the gear whose pitch-circle is PL. 

If the generating-circle had a radius just one-half of the radius of pi, 
the hypocycloid F would be a straight line, and the flank of the tooth 
would have been radial. 

The Involute Tooth. — In drawing the involute-tooth curve, Fig. 174, 
the angle of obliquity, or the angle which a common tangent to the teeth, 
when they are in contact at the pitch-point, makes with a line joining 
the centers of the wheels, is first arbitrarily determined. It is customary 
to take it at 15°. The pitch-lines pi and PL being drawn in contact at 6, 
the line of obliquity AB is drawn through O normal to a common tangent 



FORMS OF THE TEETH. 



1141 



to the tooth curves, or at the given angle of obliquity to a common tan- 
gent to the pitch-circles. In the cut the angle is 20°. From the centers 
ol the pitch-circles draw circles c and d tangent to the line AB. These 
circles are called base-lines or base-circles, from which the involutes F 
and K are drawn. By laying off convenient distances, 0, 1, 2, 3, which 
should each be less than i/io of the diameter of the base-circle, small arcs 
can be drawn with successively increasing radii, which will form the 
involute. The involute extends from the points F and K down to their 




Fig. 174. 

respective base-circles, where a tangent to the involute becomes a radius 
of the circle, and the remainders of the tooth curves, as G and H, are 
radial straight lines. 

In the involute system the customary standard form of tooth is one 
having an angle of obliquity of 15° (Brown and Sharpe use 141/2°) an 
addendum of about one-third the circular pitch, and a clearance of about 
one-eighth of the addendum. In this system the smallest gear of a set 
has 12 teeth, this being the smallest number of teeth that will gear together 
when made with this angle of obliquity. In gears with less than 30 teeth 
the points of the teeth must be slightly rounded over to avoid interference 
(see Grant's Teeth of Gears). All involute teeth of the same pitch and 
with the same angle of obliquity work smoothly together. The rack to 
gear with an involute-toothed wheel has straight faces on its teeth, which 
make an angle with the middle line of the tooth equal to the angle of 
obliquity, or in the standard form the faces are inclined at an angle of 
30° with each other. 

To draw the teeth of a rack which is to gear with an involute wheel (Fig. 
175). — Let AB be the pitch-line of the rack and AI = 77' = the pitch. 
Through the pitch-point / draw EF at the given angle of obliquity. 




Fig. 175. 



Draw AE and I'F perpendicular to EF. Through E and F draw lines 
EGG' and FH parallel to the pitch-line. EGG' will be the addendum- 
line and HF the flank-line. From / draw IK perpendicular to AB equal 
to the greatest addendum in the set of wheels of the given pitch and 
obliquity plus an allowance for clearance equal to l/g of the addendum 
Through K, parallel to AB, draw the clearance-line. The fronts of the 
teeth are planes perpendicular to EF, and the backs are planes inclined 
at the same angle to AB in the contrarv direction. The outer half of the 
working, face AE may be slightly curved, Mr. Grant makes it a circular 




1142 GEARING. 

arc drawn from a center on the pitch-line with a radius = 2.1 inches 
divided by the diametral pitch, or .67 in. X circular pitch. 

To Draw an Angle of 15° without using a Protractor. — From C, on the 
line AC, with radius AC, draw an arc AB, and from A, with the same 
radius, cut the arc at B. Bisect 
the arc BA by drawing small arcs 
at D from A and B as centers, 
with the same radius, which must 
be greater than one-half of AB. 
Join DC, cutting BA at E. The 
angle EGA is 30°. Bisect the arc 
AE in like manner, and the angle 
FCA will be 15°. 

A property of involute-toothed 
wheels is that the distance between 
the axes of a pair of gears may be 
altered to a considerable extent 
without interfering with their ac- 
tion. The backlash is therefore 
variable at will, and may be ad- 
Fig. 176. justed by moving the wheels farther 

from or nearer to each other, and 
may thus be adjusted so as to be no greater than is necessary to prevent 
jamming of the teeth. 

The relative merits of cycloidal and involute-shaped teeth are a 
subject of dispute, but there is an increasing tendency to adopt the 
involute tooth for all purposes. 

Clark (R. T. D., p. 734) says: Involute teeth have the disadvantage of 
being too much inclined to the radial line, by which an undue pressure is 
exerted on the bearings. 

Unwin (Elements of Machine Design, 8th ed., p. 265) says: The obliquity 
of action is ordinarily alleged as a serious objection to involute wheels. 
Its importance has perhaps been overrated. 

George B. Grant {Am. Mach., Dec. 26, 1885) says: 

1. The work done by the friction of an involute tooth is always less 
than the same work for any possible epicycloidal tooth. 

2. With respect to work done by friction, a change of the base from a 
gear of 12 teeth to one of 15 teeth makes an improvement for the epicycloid 
of less than one-half of one per cent. 

3. For the 12-tooth system the involute has an advantage of 11/5 per 
cent, and for the 15-tooth system an advantage of 3/ 4 per cent. 

4. That a maximum improvement of about one per cent can be accom- 
plished by the adoption of any possible non-interchangeable radial flank 
tooth in preference to the 12-tooth interchangeable system. 

5. That for gears of very few teeth the involute has a decided advan- 
tage. 

6. That the common opinion among millwrights and the mechanical 
public in general in favor of the epicycloid is a prejudice that is founded 
on long-continued custom, and not on an intimate knowledge of the 
properties of that curve. 

Wilfred Lewis (Proc. Engrs. Club of Phila., vol. x, 1893) says a strong 
reaction in favor of the involute system is in progress, and he believes 
that an involute tooth of 221/2° obliquity will finally supplant all other 
forms. 

Approximation by Circular Arcs. — Having found the form of the 
actual tooth-curve on the drawing-board, circular arcs may be found by 
trial which will give approximations to the true curves, and these may be 
used in completing the drawing and the pattern of the gear-wheels. The 
root of the curve is connected to the clearance by a fillet, which should 
be as lar^e as possible to give increased strength to the tooth, provided 
it is not large enough to cause interference. 

Molesworth gives the following method of construction by circular! 
arcs: 

From the radial line at the edge of the tooth on the pitch-line, lay off the 
line HK at an angle of 75° with the radial line; on this line will be the 
centers of the root AB and the point EF. The lines struck from these' 
centers are shown in thick lines. Circles drawn through centers thus^ 



FORMS OF THE TEETH. 



1143 



found will give the lines in which the remaining centers will be. The 
radius DA for striking the root AB is the pitch 4- the thickness of the 
tooth. The radius CE for striking the point of the tooth EF = the pitch. 




one slightly in advance of 




Fig. 177. 

George B. Grant says: It is sometimes attempted to construct the curve 
by some handy method or empirical rule, but such methods are generally 
worthless. 

Stepped Gears. — Two gears of the same pitch and diameter mounted 
side by side on the same shaft will act as a single gear. If one gear is 
keyed on the shaft so that the teeth of the two wheels are not in line, 
but the teeth of one wheel slightly in advance of the other, the two gears 
form a stepped gear. If mated with a similar stepped gear on a parallel 
shaft the number of teeth in contact will be twice ; 
great as h\ a •: J -" n * 1 ' ~" r,T - which will incree«» U 
strength 

Twist ' 
gears w< e | togeth< 

the othe 
tinuing 
separate 

instead ol being _ steps take form ot a spiral oi 

twisted surface, and we have a twisted gear. The twist 
may take any shape, and if it is in one direction for half 
the width of the gear and in the opposite direction for 
the other half, we have what is known as the herring- 
bone or double helical tooth. The obliquity of the 
twisted tooth if twisted in one direction causes an end 
thrust on the shaft, but if the herring-bone twist is Fig. 178. 
used, the opposite obliquities neutralize each other. This form of tooth 
is much used in heavy rolling-mill practice, where great strength and 
resistance to shocks are necessary. They are frequently made of steel 
castings (Fig. 178). The angle of the tooth with a line parallel to the 
axis of the gear is usually 30°. 

Spiral or Helical Gears. — If a twisted gear has a uniform twist it 
becomes what is commonly called a spiral gear (properly a helical gear). 
The line in which the pitch-surface intersects the face of the tooth is part 
of a helix drawn on the pitch-surface, A spiral wheel may be made with 
only one helical tooth wrapped around the cylinder several times, in 
which it becomes a screw or worm. If it has two or three teeth so 
wrapped, it is a double- or triple-threaded screw or worm. A spiral-gear 
meshing into a rack is used to drive the table of some forms of planing- 
machine. For methods of laying out and producing spiral gears see 
Brown and Sharpe's treatise on Gearing and Halsey's Worm and Spiral 
Gearing, also Machy., May 1906 and Machy's Reference Series No. 20. 

Worm- gearing. — When the axes of two spiral gears are at right 
angles, and a wheel of one, two, or three threads works with a larger wheel 
of many threads, it becomes a worm-gear, or endless screw, the smaller 
wheel or driver being called the worm, and the larger, or driven wheel, 
the worm-wheel. With this arrangement a high velocity ratio may be 
obtained with a single pair of wheels. For a one-threaded wheel the veloc- 
ity ratio is the number of teeth in the worm-wheel. The worm and wheel 
are commonly so constructed that the worm will drive the wheel, but the 
wheel will not drive the worm. 




1144 



To find the diameter of a worm-wheel at the throat, number of teeth and 
pitch of the worm being given: Add 2 to the number of teeth, multiply 

the sum by 0.3183, and 
by the pitch of the worm 
in inches. 

To find the number of 
teeth, diameter at throat 
and pitch of worm being 
given: Divide 3.1416 
times the diameter by the 
pitch, and subtract 2 
from the quotient. 

In Fig. 179 ab is the 
diam. of the pitch-circle, 
cd is the diam. at the 
throat. 

Example. — Pitch of 
worm 1/4 in., number of teeth 70; required the diam. at the throat. (70 
+ 2) X .3183 X .25 = 5 .73 in. 

For design of worm gearing see Kimball and Barr's Machine Design. 
For efficiency of worm gears see page . 

The Hindley Worm. — In the Hind ley worm-gear the worm, in- 
stead of being cylindrical in outline, is of an hour-glass shape, the pitch 
line of the worm being a curved line corresponding to the pitch line of the 
gear. It is claimed that there is surface contact between the faces of 
the teeth of the worm and gear, instead of only line contact as in the case 
of the ordinary worm gear, but this is denied by some writers. For 
discussion of the Hindley worm see Am. Mach., April 1, 1897 and 
Mad*, 1., Dec. 1908. The Hindley gear is made by the Albro-Clem 
Elevator Co., Philadelphia. 

Teeth of Bevel-wheels. (Rankine's Machinery and Millwork.) — 
The teeth of a bevel-wheel have acting surfaces of the conical kind, gen- 
erated by the motion of a line traversing the ppex of the conical pitch- 
surface, while a point in it is carried round the traces of the teeth upon 
a spherical surface described about that apex. 

The operations of drawing the traces of the teeth of bevel-wheels exactly, 
whether by involutes or by rolling curves, are in every respect analogous 
to those for drawing the traces of the teeth of spur-wheels; except that in 
the case of bevel-wheels all those operations are to be performed on the 
surface of a sphere described about the apex, instead of on a plane, sub- 
stituting poles for centers and great circles for straight lines. 

In consideration of the practical difficulty, especially in the case of 
large wheels, of obtaining an accurate spherical surface, and of drawing 
upon it when obtained, the follow- 
ing approximate method, proposed 
originally by Tredgold, is generally 
used: 

Let O, Fig. 180, be the common 
apex of the pitch-cones, OBI, OB' I, 
of a pair of bevel-wheels; OC, OC , 
the axes of those cones; OI their 
line of contact. Perpendicular to ., 
OI draw AIA', cutting the axes in B« 
A, A'; make the outer rims of the 
patterns and of the wheels portions 
of the cones ABI, A'B'I, of which 
the narrow zones occupied by the 
teeth will be sufficiently near for 
practical purposes to a spherical 

surface described about O. As the p IG i§0 

cones ABI, A'B'I cut the pitch- ' " 

cones at right angles in the outer pitch-circles IB, IB', they may be called 
the normal cones. To find the traces of the teeth upon the normal cones, 
draw on a flat surface circular arcs, ID, ID', with the radii AI, A'l; those 
arcs will be the developments of arcs of the pitch-circles IB, IB' when the 
conical surfaces ABI, A'B'I are spread out flat. Describe the traces of 
teeth for the developed arcs as for a pair of spur-wheels, then wrap the 




FORMS OF THE TEETH. 1145 

developed arcs on the normal cones, so as to make them coincide with 
the pitch-circles, and trace the teeth on the conical surfaces. 

For formulae and instructions for designing bevel-gears, and for much 
other valuable information on the subject of gearing, see " Practical 
Treatise on Gearing," and "Formulas in Gearing," published by Brown 
& Sharpe Mfg. Co.; and "Teeth of Gears, " by George B. Grant, Lexington, 
Mass. The student may also consult llankine's Machinery and Millwork, 
Reuleaux's Constructor, and Unwin's Elements of Machine Design. See 
also article on Gearing, by C. W. MacCord in App. Cyc. Mech., vol. ii. 

Annular and Differential Gearing. (S. W. Balch, Am. Mach., 
Aug. 24, 1893.) — In internal gears the sum of the diameters of the dtsciib- 
ing circles for faces and flanks should not exceed the difference in the 
pitch diameters of the pinion and its internal gear. The sum may be 
equal to this difference or it may be less; if it is equal, the faces of the 
teeth of each wheel will drive the faces as well as the flanks of the teeth of 
the other wheel. The, teeth will therefore make contact with each other 
at two points at the same time. 

Cycloidal tooth-curves for interchangeable gears are formed with de- 
scribing circles of about 5/ 8 the pitch diameter of the smallest gear of the 
series. To admit two such circles between the pitch-circles of the pinion 
and internal gear the number of teeth in the internal gear should exceed 
the number in the pinion by 12 or more, if the teeth are of the customary 
proportions and curvature used in interchangeable gearing. 

Very often a less difference is desirable, and the teeth may be modified 
in several ways to make this possible. 

First. The tooth curves resulting from smaller describing circles may 
be employed. These will give teeth which are more rounding and nar- 
rower at their tops, and therefore not as desirable as the regular forms. 

Second. The tips of the teeth may be rounded until they clear.. This 
is a cut-and-try method which aims at modifying the teeth to such out- 
lines as smaller describing circles would give. 

Third. One of the describing circles may be omitted and one only 
used, which may be equal to the difference between the pitch-circles. 
This will permit the meshing of gears differing by six teeth. It will usu- 
ally prove inexpedient to put wheels in inside gears that differ by much 
less than 12 teeth. 

If a regular diametral pitch and standard tooth forms are determined 
on, the diameter to which the internal gear-blank is to be bored is calcu- 
lated by subtracting 2 from the number of teeth, and dividing the re- 
mainder by the diametral pitch. 

The tooth outlines are the match of a spur-gear of the same number 
of teeth and diametral pitch, so that the spur-gear will fit the internal 
gear as a punch fits its die, except that the teeth of each should fail to 
bottom in the tooth spaces of the other by the customary clearance of one- 
tenth the thickness of the tooth. 

Internal gearing is particularly valuable when employed in differential 
action. This is a mechanical movement in which one of the wheels is 
mounted on a crank so that its center can move in a circle about the center 
of the other wheel. Means are added to the device which restrain the 
wheel on the crank from turning over and confine it to the revolution of 
the crank. 

The ratio of the number of teeih in the revolving wheel compared with 
the difference between the two will represent the ratio between the revolv- 
ing wheel and the crank-shaft by which the other is carried. The advan- 
tage in accomplishing the change of speed with such an arrangement, as 
compared with ordinary spur-gearing, lies in the almost entire absence of 
friction and consequent wear of the teeth. 

But for the limitation that the difference between the wheels must not 
be too small, the possible ratio of speed might be increased almost indefi- 
nitely, and one pair of differential gears made to do the service of a whole 
train of wheels. If the problem is properly worked out with bevel-gears 
this limitation may be completely set aside, and external and internal 
bevel-gears, differing by but a single tooth if need be, made to mesh per- 
fectly with each other. 

Differential bevel-gears have been used with advantage in mowing- 
machines. A description of their construction and operation is given by 
Mr. Balch in the article from which the above extracts are taken. 



1146 



EFFICIENCY OF GEARING. 

An extensive series of experiments on the efficiency of gearing, chiefly 
worm and spiral gearing, is described by Wilfred Lewis in Trans. A. S. 
M. E., vii, 273. The average results are shown in a diagram, from which 
the following approximate average figures are taken: 

Efficiency of Spur, Spiral, and Worm Gearing. 



Gearing. 



Spur pinion. . . 
Spiral pinion. 



Spiral pinion or worm. , 



45° 
30 
20 
15 
10 

7 

5 



Velocity at pitch-line in feet per min. 



3 



0.90 
.81 
.75 
.67 
.61 
.51 
.43 
,34 



10 


40 


100 


0.935 


0.97 


0.98 


.87 


.93 


.955 


.815 


.89 


.93 


.75 


.845 


.90 


.70 


.805 


.87 


.615 


.74 


.82 


.53 


.72 


.765 


.43 


.60 


.70 



200 



0.985 
.965 
.945 
.92 
.90 
.86 
.815 
.765 



The experiments showed the advantage of spur-gearing over all other 
kinds in both durability and efficiency. The variation from the mean 
results rarely exceeded 5% in either direction, so long as no cutting 
occurred, but the variation became much greater and very irregular as 
soon as cutting began. The loss of power varies with the speed, the 
pressure, the temperature, and the condition of the surfaces. The excess- 
ive friction of worm and spiral gearing is largely due to the end thrust on 
the collars of the shaft. This may be considerably reduced by roller- 
bearings for the collars. 

When two worms with opposite spirals run in two spiral worm-gears 
that also work with each other, and the pressure on one gear is opposite 1 
that on the other, there is no thrust on the shaft. Even with light loads 
a worm will begin to heat and cut if run at too high a speed, the limit for 
safe working being a velocity of the rubbing surfaces of 200 to 300 ft. 
per minute, the former being preferable where the gearing has to work 
continuously. The wheel teeth will keep cool, as they form part of a 
casting having a large radiating surface; but the worm itself is so small 
that its heat is dissipated slowly. Whenever the heat generated increases 
faster than it can be conducted and radiated away, the cutting of the 
worm may be expected to begin. A low efficiency for a worm-gear means 
more than the loss of power, since the power which is lost reappears as 
heat and may cause the rapid destruction of the worm. 

Unwin (Elements of Machine Design, p. 294) says: The efficiency is j 
greater the less the radius of the worm. Generally the radius of the j 
worm = 1 .5 to 3 times the pitch of the thread of the worm or the circular j 
pitch of the worm-wheel. For a one-threaded worm the efficiency is j 
only 2/ 5 to 1/4: for a two-threaded worm, 4/7 to 2/5; for a three-threaded j 
worm, 2/3 to 1/2. Since so much work is wasted in friction it is not sur- j 
prising that the wear is excessive. The following table gives the calcu- I 
lated efficiencies of worm-wheels of 1, 2, 3, and 4 threads and ratios of 
radius of worm to pitch of teeth of from 1 to 6, assuming a coefficient of 
friction of .15: 



No. of 


Radius of Worm ■*■ Pitch. 


Threads. 


1 


11/4 


U/ 2 


13/4 


2 


21/2 


3 


4 


6 


1 


0.50 


0.44 


0.40 


0.36 


0.33 


0.28 


0.25 


0.20 


0.14 


2 


.67 


.62 


.57 


.53 


.50 


.44 


.40 


.33 


.25 


3 


.75 


.70 


.67 


.63 


.60 


.55 


.50 


.43 


.33 


4 


.80 


.76 


.73 


.70 


.67 


.62 


.57 


.50 


.40 



EFFICIENCY OF GEARING. 



1147 



Efficiency of Worm Gearing. — Worm gearing as a means of trans- 
mitting power has generally been looked upon with suspicion, its efficiency 
being considered necessarily low and its life short. When properly pro- 
portioned, however, it is both durable and reasonably efficient. Mr. F. 
A. Halsey discusses the subject in Am. Machinist, Jan. 13 and 20, 1898. 
He quotes two formulas for the efficiency of worm gearing: 



t ana' (1 -/tana;) 
tan a + / ' 

In which E = efficiency; 



• (1) E = 



tana (1 — /tan a) 



approx., 



(2) 



tan a+ 2/ 

angle of thread, being angle between thread 

and a line perpendicular to the axis of the worm:/ = coefficient of friction. 

Eq. (1) applies to the worm thread only, while (2) applies to the worm 
and step combined, on the assumption that the mean friction ra dius o f the 
two is equal. Eq. (1) gives a maximum for E wh en tan a = v'l +/ 2 — / 
... (3) and eq. (2) a maximum when tan a = V2 + 4/ 2 — 2/ . . . . (4) 
Using 0.05 for /gives a in (3) = 43° 34' and in (4) = 52° 49'. 

On plotting equations (1) and (2) the curves show the striking influence 
of the pitch-angle upon the efficiency, and since the lost work is expended 
in friction and wear, it is plain why worms of low angle should be short- 
lived and those of high angle long-lived. The following table is taken 
from Mr. Halsey's plotted curves: 

Relation between Thread-angle Speed and Efficiency of Worm 
Gears. 















Velocity of 












Pitch-line, 
feet per 


5 


,0 


20 1 30 


40 


« 


minute. 






Efficiency. 






3 


35 


52 


66 


73 


76 


77 


5 


40 


56 


69 


76 


79 


80 


10 


47 


62 


74 


79 


82 


82 


20 


52 


67 


78 


83 


85 


86 


40 


60 


74 


83 


87 


88 


88 


100 


70 


82 


88 


91 


91 


91 


200 


76 


85 


91 


92 


92 


92 



The experiments of Mr. Wilfred Lewis on worms show a very satisfac- 
tory correspondence with the theory. Mr. Halsey gives a collection of 
data comprising 16 worms doing heavy duty and having pitch-angles 
ranging between 4° 30' and 45°, which show that every worm having an 
angle above 12° 30' was successful in regard to durability, and every worm 
below 9° was unsuccessful, the overlapping region being occupied by 
worms some of which were successful and some unsuccessful. In several 
cases worms of one pitch-angle had been replaced by worms of a different 
angle, an increase in the angle leading in every case to better results and a 
decrease to poorer results. He concludes with the following table from 
experiments by Mr. James Christie, of the Pencoyd Iron Works, and gives 
data connecting the load upon the teeth with the pitch-line velocity of 
the worm. 

Limiting Speeds and Pressures of Worm Gearing. 





Single-thread 
Worm 1 " Pitch, 
21 Pitch Diam. 


Double- 
thread 
Worm 2" 
Pitch, 2\ 
Pitch Diam. 


Double- 
thread 
Worm 2\" 

Pitch, 4£ 
Pitch Diam. 


Revolutions per minute 

Velocity at pitch-line, feet per 


128 

96 
1700 


201 

150 
1300 


272 

205 
1100 


425 

320 
700 


128 

96 
1100 


201 

150 
1100 


272 

205 
1100 


201 

235 
1100 


272 

319 

700 


425 

498 


Limiting pressure, pounds 


400 



1148 



GEARING . 



Efficiency of Automobile Gears. (G. E. Quick, Horseless Age, Feb. 12, 
1908.) — A set of slide gears was tested by an electric-driven absorption 
dynamometer. The following approximate results are taken from a 
series of plotted curves: 







2 


1 4 


1 6 


1 8 


1 10 


1 14 


1 18 








r.p.m. 


Efficiency, per cent. 


Direct driven, third speed 


800 


89 


95 


97 


97.5 


97.5 


97.5 


96 


Direct driven, third speed 


1,500 


80 


89 


93 


93 


96.3 


97 


97 


Second speed, ratio 1 . 76 to 1 ... 


800 


87 


92.5 


94 


93 


94 


93 




Second speed, ratio 1 . 76 to 1 ... 


1,500 


79 


88 


92.5 


94 


95 


93 


94 


First speed, ratio 3.36 to 1 


800 


75 


87.5 


93 


94 


94 


93.5 


92.5 


First speed, ratio 3.36 to 1 


1,500 


70 


84 . 


89 


92 


93 


92 




Reverse speed, ratio 4.32 to 1.. . 


800 


73 


84 


67 


87 


86 


82.5 


Reverse speed, ratio 4.32 to I... 


1,500 




70 


B 


83 


86 


87 


85 


Worm-gear axle, ratio 6.83 to 1.. 


400 


85 


8/ 


86.5 


83.3 


84 


80 


Jb 


Worm-gear axle, ratio 6.83 to I.. 


800 


83 


87 


88.5 


89 


89 


88 


87 


Worm-gear axle, ratio 6.83 to 1 .. 


1,500 


80 


85 


87.5 


88.3 


89 


89 


89 



Two bevel-wheel axles were tested, one a floating type, ratio 15 to 32, 
14V2° involute; the other a solid wheel and axle type, ratio 13 to 54, 20° 
involute. Both gave efficiencies of 95 to 96 % at 800 to 1500 r.p.rn., 
and 10 to 26 H.P., with lower efficiencies at lower power and at lower 
speed. The friction losses include those of the journals and thrust ball 
bearings. 

The worm was 6-threaded, lead, 4.69 in.; pitch diam., 2.08 in.; the 
gear had 41 teeth; pitch diam., 10.2 in. The worm was of hardened 
steel and the gear of phosphor-bronze. A test of a steel gear and steel 
worm gave somewhat lower efficiencies. In both tests the heating was 
excessive both in the gears and in the thrust bearings, the balls in which 
were 7/i6 in. diam. 

STRENGTH OF GEAR-TEETH. 

The strength of gear-teeth and the horse-power that may be transmitted 
by them depend upon so many variable and uncertain factors that it is 
not surprising that the formulas and rules given by different writers 
show a wide variation. In 1879 John H. Cooper {Jour. Frank. Inst., 
July, 1879) found that there were then in existence about 48 well-estab- 
lished rules for horse-power and working strength, differing from each 
other in extreme cases about 500%. In 1886 Prof. Wm. Harkness 
(Proc. A. A. A. S., 1886), from an examination of the bibliography of the 
subject, beginning in 1796, found that according to the constants and 
formulae used by various authors there were differences of 15 to 1 in the 
power which could be transmitted by a given pair of geared wheels. 
The various elements which enter into the constitution of a formula to 
represent the working strength of a toothed wheel are the following: 
1. The strength of the metal, usually cast iron, which is an extremely 
variable quantity. 2. The shape of the tooth, and especially the relation 
of its thickness at the root or point of least strength to the pitch and to 
the length. 3. The point at which the load is taken to be applied, 
assumed by some authors to be at the pitch-line, by others at the extreme 
end, along the whole face, and by still others at a single outer corner. 
4. The consideration of whether the total load is at any time received 
by a single tooth or whether it is divided between two teeth. 5. The 
influence of velocity in causing a tendency to break the teeth by shock. 
6. The factor of safety assumed to cover all the uncertainties of the 
other elements of the problem. 

Prof. Harkness, as a result of his investigation, found that all the 
formula? on the subject might be expressed in one of three forms, viz.s 
Horse-power = CVpf, or CVp 2 , or CVp*/; 

in which C is a coefficient, V = velocity of pitch-line in feet per second. 
V = pitch in inches, and / = face of tooth in inches. 



STRENGTH OF GEAR-TEETH. 



1149 



From an examination of precedents he proposed the following formula 
for cast-iron wheels: 

0.910 Vpf 



H.P. = 



Vl + 0.65 V 

He found that the teeth of chronometer and watch movements were 
subject to stresses four times as great as those which any engineer would 
dare to use in like proportion upon cast-iron wheels of large size. 

It appears that all of the earlier rules for the strength of teeth neglected 
the consideration of the variations in their form; the breaking strength, as 
said by Mr. Cooper, being based upon the thickness of the teeth at the 
pitch-line or circle, as if the thickness at the root of the tooth were the 
same in all cases as it is at the pitch-line. 

Wilfred Lewis (Proc. Eng'rs Club, Phila., Jan., 1893; Am. Mach., 
June 22, 1893) seems to t ive been the first to use the form of the tooth 
in the construction of a working formula and table. He assumes that 
in well-constructed machinery the load can be more properly taken as 
well distributed across the tooth than as concentrated in one corner, but 
that it cannot be safely taken as concentrated at a maximum distance 
from the root less than the extreme end of the tooth. He assumes that 
the whole load is taken upon one tooth, and considers the tooth as a 
beam loaded at one end, and from a series of drawings of teeth of the 
involute, cycloidal, and radial flank systems, determines the point of 
weakest cross-section of each, and the ratio of the thickness at that section 
to the pitch. He thereby obtains the general formula, 

W = spfy; 
in which W is the load transmitted by the teeth, in pounds; s is the safe 
working stress of the material, taken at 8000 lbs. for cast iron, when the 
working speed is 100 ft. or less per minute; p = pitch; / = face, in 
inches ; y = a factor depending on the form of the tooth, whose value for 
different cases is given in the following table: 



No. of 


Factor for Strength, y. 


No. of 


Factor for Strength, y. 














Teeth. 


Involute 
20° Ob- 
liquity. 


Involute 

15° and 

Cycloidal 


Radial 
Flanks. 


Teeth. 


Involute 
20° Ob- 
liquity. 


Involute 

15° and 

Cycloidal 


Radial 
Flanks. 


12 


0.078 


0.067 


0.052 


27 


0.111 


0.100 


0.064 


13 


.083 


.070 


.053 


30 


.114 


.102 


.065 


14 


.088 


.072 


.054 


34 


.118 


.104 


.066 


15 


.092 


.075 


.055 


38 


.122 


.107 


.067 


16 


.094 


.077 


.056 


43 


.126 


.110 


.068 


17 


.096 


.080 


.057 


50 


.130 


.112 


.069 


18 


.098 


.083 


.058 


60 


.134 


.114 


.070 


19 


.100 


.087 


.059 


75 


.138 


.116 


.071 


20 


.102 


.090 


.060 


100 


.142 


.118 


.072 


21 


.104 


.092 


.061 


150 


.146 


.120 


.073 


23 


.106 


.094 


.062 


300 


.150 


.122 


.074 


25 


.108 


.097 


.063 


Rack. 


.154 


.124 


.075 



Safe Working Stress, s 


FOR 


Different Speeds. 




Speed of Teeth in 
ft. per minute. 


100 or 
less. 


200 


300 


600 


900 


1200 


1800 


2400 




8000 
20000 


6000 
15000 


4800 
12000 


4000 
10000 


3000 
7500 


2400 
6000 


2000 
5000 


1700 


Steel........ 


4300 



The values of s in the above table are given by Mr. Lewis tentatively, In 
the absence of sufficient data upon which to base more definite values, 
but they have been found to give satisfactory results in practice. 




1150 GEARING. 

Mr. Lewis gives the following example to illustrate the use of the tables: 
Let it be required to find the working strength of a 12-toothed pinion of 
1-inch pitch, 21/2-inch face, driving a wheel of 60 teeth at 100 feet or less 
per minute, and let the teeth be of the 20-degree involute 
form. In the formula W= spfy we have for a cast-iron 
pinion s = 8000, pf =2.5, and y = .078; and multiply- 
7 ing these values together, we have \v =1560 pounds. For 
[ the wheel we have y = .134 and J/ = 2680 pounds. 
The cast-iron pinion is, therefore, the measure of 
strength; but if a steel pinion be substituted we have 
s = 20,000 and W= 3900 pounds, in which combination 
the wheel is the weaker, and it therefore becomes the 
measure of strength. 

For bevel-wheels Mr. Lewis gives the following, refer- 
ring to Fig. 181: D= large diameter of bevel; d = small 
diameter of bevel; p = pitch at large diameter; n = actual 
number of teeth; /= face of bevel; N = formative number 
of teeth = n X secant a, or the number corresponding 
; y = factor depending upon shape of teeth and formative 
number N; W = working load on teeth. 

D 3 — d 3 d 

W = spfy 3 D2 , D _ d y or, more simply, W = spfy ^ , 

which gives almost identical results when d is not less than 2/3 D, as is the 
case in good practice. 

In Am. Mach., June 22, 1893, Mr. Lewis gives the following formulas 
for the working strength of the three systems of gearing, which agree 
very closely with those obtained by use of the table: 

(0 912\ 
0.154 ^— J; 

For involute 15°, and cycloidal, W = spf (o.l24 - ~^) '• 

(0 276 \ 
0.075 '- — ■ J; 

in which the factor within the parenthesis corresponds to y in the general 
formula. For the horse-power transmitted, Mr. Lewis's general formula 

W = spfy = 33 - 000HP - , may take the form H.P. = *ffi^ , in which 

V 06, (JUL) 

v = velocity in feet per minute; or since v = dn X r.p.m. -s- 12 = 
.2618 d X r.p.m., in which d = diameter in inches, 

"• - 3^0 - spfv iz;r- = - ~™ r* >< **^ 

It must be borne in mind, however, that in the case of machines which 
consume power intermittently, such as punching and shearing machines, 
the gearing should be designed with reference to the maximum load W, 
which can be brought upon the teeth at any time, and not upon the 
average horse-power transmitted. 

Comparison of the Harkness and Lewis Formulas. — Take an 
average case in which the safe working strength of the material, s = 6000, 
v = 200 ft. per min.. and y = .100, the value in Mr. Lewis's table for an 
involute tooth of 15° obliquity, or a cycloidal tooth, the number of teeth 
in the wheel being 27. 

"-^- M00 g- 100 -t- 1 ^^ 

if V is taken in feet per second. 

Prof. Harkness gives H.P. = °- 910 y ^/ _ . If the y in t he denominator 
Vi + 0.65 V 
be taken at 200 -4- 60 = 31/3 ft. per sec, H.P. = 0.571 pfV, or about 
52% of the result given by Mr. Lewis's formula. This is probably as 
close an agreement as can be expected, since Prof. Harkness derived his 
formula from an investigation of andent precedents and rule-of-thumb 
practice, largely with common cast gears, while Mr. Lewis's formula was 



STRENGTH OF GEAR-TEETH. 



1151 



derived from considerations . of modern practice with machine-molded 
and cut gears. 

Mr. Lewis takes into consideration the reduction in working strength 
of a tooth due to increase in velocity by the figures in his table of the 
values of the safe working stress s for different speeds. Prof. Harkness 
gives expressio n to the sam e reduction by means of the denominator of 
his formula, Vl + O-Go V. The decrease in strength as computed by 
this formula is somewhat less than that given in Mr. Lewis's table, and as 
the figures given in the table are not based on accurate data, a mean 
between the values given by the formula and the table is probably as 
near to the true value as may be obtained from our present knowledge. 
The following table gives the values for different speeds according to Mr. 
Lewis's table and Prof, Harkness's formula, taking for a basis a working 
stress s, for cast-iron 8000, and for steel 20,000 lbs. at speeds of 100 ft. 
per minute and less: 



v = speed of teeth, ft. per min.. 
V = speed of teeth, ft. per sec. 



Safe stress s, cast iron, Lewis . . 

Relati ve do., a ± 8000 

1 h- V\ +0.65 V 

Relative val. c + 0.693 

Sl = 8000 X (c +0.693).. 

Mean of s and s lt cast-iron = S2. 
Mean of s and s lt for steel = S3.. 
Safe stress for steel, Lewis 



8000 
1 

6930 

1 
8000 
8000 
20000 
20000 



31/3 



6000 
0.75 
5621 



6200 
15500 
15003 



4800 
0.6 

4850 
0.700 

5600 

5200 
13000 
12000 



4000 
0.5 

3650 
0.526 
4208 
4100 
10300 
10000 



900 1200 
15 20 



3000 
0.375 
.3050 
0.439 
3512 
3300 
8100 
7500 



2400 

0.3 
2672 

0.385 
3080 
2700 
6800 
6000 



2000 
0.25 

2208 
0.318 
2544 

2300 
5700 
5000 



2400 
40 



1700 
0.2125 
.1924 - 
0.277 

2216 

2000 

4900 

4300 



In Am. Mach., Jan. 30, 1902, Mr. Lewis says that 8,000 lbs. was given 
as safe for cast-iron t.eeth, either cut or cast, and that 20,000 lbs. was 
intended for any steel suitable for gearing whether cast or forged. 
These were the unit stresses for static loads. 

The iron should be of good quality capable of sustaining about a ton 
on a test bar 1 in. square between supports 12 in. apart, and the steel 
should be solid and of good quality. The value given for steel was in- 
tended to include the lower grades, but when the quality is known to be 
high, correspondingly higher values may be assigned. 

Comparing the two formulae for the case of s = 8000, corresponding to 
a speed of 100 ft. per min., we have 

Harkness: H.P. = 1 -f- Vi + o.65 VX .910 Vpf= 1 .053 pf, 

Lewis- HP = spfyv = spfyV = 800Q X 1 2 /3 Pfv 
550 



33,000 



550 



24.24 pfy, 



in which y varies according to the shape and number of the teeth. 
For radial-flank gear with 12 teeth y = 0.052; 24.24 pfy = 1.260pf; 

For 20° inv., 19 teeth, or 15° inv., 27 teeth y = 0.100; 24.24 pfy = 2.424p/; 
For 20° involute, 300 teeth y *» 0.150; 24.24 pfy = 3.636p/. 

Thus the weakest-shaped tooth, according to Mr. Lewis, will transmit 
20 per cent more horse-power than is given by Prof. Harkness's formula, 
in which the shape of the tooth is not considered, and the average-shaped 
tooth, according to Mr. Lewis, will transmit more than double the horse- 
power given by Prof. Harkness's formula. 

Comparison of Other Formulae. — Mr. Cooper, in summing up his 
examination, selected an old English rule, which Mr. Lewis considers as 
a passably correct expression of good general averages, viz.: X = 2000 pf, 
X = breaking load of tooth in pounds, p = pitch, / = face. If a factor 
of safety of 10 be taken, this would give for safe working load W =200 pf. 

George B. Grant, in his Teeth of Gears, page 33, takes the breaking 
load at 3500 pf, and, with a factor of safety of 10, gives W = 350 pf. 

Nystrom's Pocket-Book, 20th ed., 1891, savs: "The strength and dura- 
bility of cast-iron teeth require that they shall transmit a force of 80 lbs. 



1152 GEARING. 

per inch of pitch and per inch breadth of face." This is equivalent to 
W = 80 pf, or only 40% of that given by the English rule. 

F. A. Halsey (Clark's Pocket-Book) gives a table calculated from the 
formula H.P. = pfd X r.p.m. -h 850. 

Jones & Laughlins give H.P. = pfd X r.p.m. •*- 550. 

These formulae transformed give W = 128 pf and W = 218 pf, respec- 
tively. 

Unwin, on the assumption that_the load acts on the corners of the 
teeth, derives a formula p = K "^W , in which K is a coefficient derived 
from existing wheels, its values being: for slowly moving gearing not sub- 
ject to much vibration or shock K = .04; in ordinary mill-gearing, 
running at greater speed and subject to considerable vibration, K = .05; 
and in wheels subjected to excessive vibration and shock, and in mortise 
gearing, K = 0.06. Reduced to the form W = Cpf, assuming that/ = 
2 p, these values of K give W = 262 pf, 200 pf. and 139 pf, respectively. 

Unwin also give the following, based on the assumption that th e pres- 
sure is distributed along the edge of the tooth: p = K x "^p/f^W, where 
Ki = about .0707 for iron wheels and .0848 for mortise wheels when 
the breadth of face is not less than twice the pitch. For the case of /= 
2 p and the given values of K x this reduces to W = 200 pf and W = 139 pf, 
respectively. 

Box, in his Treatise on Mill Gearing, gives H.P. = 12 p 2 f v'dn ■*■ 1000, 
in which n = number of revolutions per minute. This formula differs 
from the more modern formulae in making the H.P. vary as p 2 f, instead 
of as pf, and in this respect itjs no doubt incorrect. 

Making the H.P. vary as v ' dn or as "^v, instead of directly as v, makes 
the velocity a factor of the working strength as in the Harkness and 
Lewis formulae, the relative strength varying as l/^v, which for different 
velocities is as follows : 

Speed of teeth in £t. per J j 0Q 2QQ 30Q 600 900 120Q 1800 2 400 

Relative strength = 1 0.707 0.574 0.408 0.333 0.289 0.236 0.20 

showing a somewhat more rapid reduction than is given by Mr. Lewis. 

For the purpose of comparing different formulae they may in general 
be reduced to either of the following forms: 

.P. = Cpfv, H.P. = dpfd X r.p.m., W = cpf, 

in which p = pitch, / = face, d = diameter, all in inches; v = velocity 
in feet per minute, r.p.m. revolutions per minute, and C, Ci and c coeffi- 
cients. The formulae for transformation are as follows: 

H.P. = Wv -*• 33,000 = WX dX r.p.m. -h 126,050; 
w 33,000 H.P . 126,050 H.P. 00 nnA ^ - , H.P. H.P. W 

W ~ v = dX r.p.m. =33 - 000 W; g/ — cT- ftdXr.p.m. -T 

C, = 0.2618 C; c = 33,000 C; C = 3.82 '&, 

In the Lewis formula C varies with the form of the tooth and with the 
speed, and is equal to sy -e- 33,000, in which y and s are the values taken 
from the table, and c = sy. 

In the Harkness formula C varies with .the speed and is equal to 

910 / ■ 

- (F being in feet per second), = 0.01517 -*- vi + 0.011 v. 



Vl + 0.65 V 

In the Box for mula C vari es with the pitch and also with the velocity; 

and equals 12 p ^f * r - p " m - = .02345 '-*- , c - 33,000 C = 774 *~ 

For v — 100 ft. per min. C = 77.4 p\ for v = 600 ft. per min., c = 31.6 p. 
In the other formulae considered C, Ci, and c are constants. Reducing 
the several formulae to the form W = cpf, we have the following; 



STRENGTH OF GEAR-TEETH. 1153 



Compaeison or Different Formula for Strength of Gear-teeth. 

Safe working pressure per inch pitch and per inch of face, or value of 
c in formula W = cpf: 

v = ft. per min. 100 600 

Lewis: Weak form of tooth, radial flank, 12 teeth c = 416 208 

Medium tooth, inv. 15°, or cycloid, 27 teeth .c = 800 400 

Strong form of tooth, inv. 20°, 300 teeth, .c = 1200 600 

Harkness: Average tooth c = 347 184 

Box: Tooth of 1 inch pitch c= 77.4 31.6 

Box: Tooth of 3 inches pitch c = 232 95 

The Gleason Works gives for ft. per min. 500 1000 1500 2000 2500 

working stress in pounds = p.f. X 480 400 340 290 240 

These are for cut gears, 18 teeth or more, rigidly supported, for average 
steady loads. Hammering loads, as in rolling mills and saw mills, require 
heavier gears. 

C. W. Hunt, Trans. A.S.M.E., 1908, gives a table of working loads of 
cut cast gears with a strong shoot form of tooth, which is practically 
equivalent to W= 700 pf. 

Various, in which c is independent of form and speed: Old English 
rule, c = 200; Grant, c = 350; Nystrom, c = 80; Halsey, c = 128; Jones 
& Laughlins, c = 218; Unwin, c = 262, 200, or 139, according to speed, 
shock, and vibration. 

The value given by Nystrom and those given by Box for teeth of small 
pitch are so much smaller than those given by the other authorities that 
they may be rejected as having an entirely unnecessary surplus of strength. 
The values given by Mr. Lewis seem to rest on the most logical basis, the 
form of the teeth as well as the velocity being considered; and since they 
are said to have proven satisfactory in an extended machine practice, 
they may be considered reliable for gears that are so well made that 
the pressure bears along the face of the teeth instead of upon the corners. 
For rough ordinary work the old English rule W = 200 pf is probably 
as good as any, except that the figure 200 may be too high for weak forms 
of tooth and for high speeds. 

The formula W= 200 p/is equivalent to H.P. = p/cZ X r.p.m. -i-630 = pfv 
h-165 or, H.P. = 0.0015873 pfd X r.p.m. = .006063 pfv. 

Raw-hide Pinions. — Pinions of raw-hide are in common use for 
gearing shafts driven by electric motors to other shafts which carry 
machine-cut cast-iron or steel gears, in order to reduce vibration, noise 
and wear. A formula for the maximum horse-power to be transmitted 
by such gears, given by the New Process Raw-Hide Co., Syracuse, N. Y., 
is H.P. = pitch diam. X circ. pitch X face X r.p.m. tt- 850, or pfd X 
r.p.m. -f- 850. This is about 3/ 4 of the H.P. for cast-iron teeth by the old 
English rule. The formula is to be used only when the circular pitch 
does not exceed 1.65 ins. 

Composite gears also are made, consisting of alternate sheets of raw- 
hide or fibre and steel or bronze, so that a high degree of strength is 
combined with the smooth-running quality of the fibre. 

Maximum Speed of Gearing. — A. Towler, Eng'g, April 19, 1889, 
p. 388, gives the maximum speeds at which it was possible under favor- 
able conditions to run toothed gearing safely as follows, in ft. per min.: 
Ordinary cast-iron wheels, 1800; Helical, 2400; Mortise, 2400; Ordinary 
cast-steel wheels, 2600; Helical, 3000: special cast-iron machine-cut 
wheels, 3000. 

Prof. Coleman Sellers (Stevens Indicator, April, 1892) recommends that 
gearing be not run over 1200 ft. per minute, to avoid great noise. The 
Walker Company, Cleveland, Ohio, say that 2200 ft. per min. for iron 
gears and 3000 ft. for wood and iron (mortise gears) are excessive, and 
should be avoided if possible. The Corliss engine at the Philadelphia 
Exhibition (1876) had a fly-wheel 30 ft. in diameter running 35 r.p.m. 
geared into a pinion 12 ft. diam. The speed of the pitch-line was 3300 ft. 
per min. 

A Heavy Machine-cut Spur-gear was made in 1891 by the Walker 
Company, Cleveland, Ohio, for a diamond mine in South Africa, with 
dimensions as follows: Number of teeth, 192; pitch diameter, 30 ft. 
6.66 ins.; face, 30 ins.; pitch, 6 ins.; bore, 27 ins.: diameter of hub, 9 ft. 
2 ins.; weight of hub, 15 tons; and total weight of gear, 663/ 4 tons. The 



1154 GEARING. 



rim was made in 12 segments, the joints of the segments being fastened 
with two bolts each. The spokes were bolted to the middle of the seg- 
ments and to the hub with four bolts in each end. 

Frictional Gearing. — In frictional gearing the wheels are toothless, 
and one wheel drives the other by means of the friction between the two 
surfaces which are pressed together. They may be used where the power 
to be transmitted is not very great; when the speed is so high that toothed 
wheels would be noisy; when the shafts require to be frequently put into 
and out of gear or to have their relative direction of motion reversed; 
or when it is desired to change the velocity-ratio while the machinery 
is in motion, as in the case of disk friction-wheels for changing the feed 
in machine tools. 

Let P = the normal pressure in pounds at the line of contact by which 
two wheels are pressed together, T = tangential resistance of the driven 
wheel at the line of contact, / = the coefficient of friction, V the veloc- 
ity of the pitch-surface in feet per second, and H.P. = horse-power; then 
T may be equal to or less than/P; H.P. = TV -*- 550. The value of/ 
for metal on metal may be taken at 0.15 to 0.20; for wood on metal, 
0.25 to 0.30; and for wood on compressed paper, 0.20. The tangential 
driving force T may be as high as 80 lbs. per inch width of face of the 
driving surface, but this is accompanied by great pressure and friction on 
the journal-bearings. 

In frictional grooved gearing circumferential wedge-shaped grooves are 
cut in the faces of two wheels in contact. If P = the force pressing the 
wheels together, and N = the normal pressure on all the grooves, P = N 
(sin a + /cos a), in which 2 a = the inclination of the sides of the grooves, 
and the maximum tangential available force T = fN. The inclination 
of the sides of the grooves to a plane at right angles to the axis is usually 
30°. 

Frictional Grooved Gearing. — A set of friction-gears for trans- 
mitting 150 H.P. is on a steam-dredge described in Proc. Inst. M. E., 
July, 1888. Two grooved pinions of 54 in. diam., with 9 grooves of 13/ 4 in. 
pitch and angle of 40° cut on their face, are geared into two wheels of 
1271/2 in. diam. similarly grooved. The wheels can be thrown in and out 
of gear by levers operating eccentric bushes on the large wheel-shaft. 
The circumferential speed of the wheels is about 500 ft. per min. Allow- 
ing for engine friction, if half the power is transmitted through each set 
of gears the tangential force at the rims is about 3960 lbs., requiring, if 
the angle is 40° and the coefficient of friction 0.18, a pressure of 7524 lbs. 
between the wheels and pinion to prevent slipping. 

The wear of the wheels proving excessive, the gears were replaced by 
spur-gear wheels and brake-wheels with steel brake-bands, which arrange- 
ment has proven more durable than the grooved wheels. Mr. Daniel 
Adamson states that if the frictional wheels had been run at a higher 
speed the results would have been better, and says they should run at 
least 30 ft. per second. 

Power Transmitted by Friction Drives. (W. F. M. Goss, Trans. 
A. S. M. E., 1907.) — A friction drive consists of a fibrous or somewhat 
yielding driving wheel working in rolling contact with a metallic driven 
wheel. Such a drive may consist of a pair of plain cylinder wheels 
mounted upon parallel shafts, or a pair of beveled wheels, or of any 
other arrangement which will serve in the transmission of motion by 
rolling contact. 

Driving wheels of each of the materials named in the table below were 
tested in peripheral contact with driving wheels of iron, aluminum and 
type metal. All the wheels were 16 in. diam.; the face of the driving 
wheels was 13/ 4 in., and that of the driven wheels 1/2 In. Records were 
made of the pressure of contact, of the coefficient of friction developed, 
and of the percentage of slip resulting from the development of the said 
coefficient of friction. Curves were plotted showing the relation of the 
coefficient and the slip for pressures of 150 and 400 lbs. per inch width 
of face in contact. Another series of tests was made in which the slip 
was maintained constant at 2% and the pressures were varied. In most 
of the combinations it was found that with constant slip the coefficient 
of friction diminished very slightly as the pressure of contact was in- 
creased, so that it may be considered practically constant for all pres- 
sures between 150 and 400 lbs. per sq. in. 



STRENGTH OF GEAR-TEETH. 



1155 



The crushing strength of each material under the conditions of the 
test was determined by running each combination with increasing loads 
until a load was found under which the wheel failed before 15,000 revo- 
lutions had been made. The results showed the failure of the several 
fiber wheels under loads per inch of width as follows: Straw fiber 
750 lbs.; leather fiber, 1,200 lbs.: tarred fiber, 1,200 lbs.; leather, 750 lbs.; 
sulphite fiber, 700 lbs. One-fifth of these pressures is taken as a safe 
working load. The coefficient of friction approaches its maximum 
value when the slip between driver and driven wheel is 2%. The safe 
working horse-power of the drive is calculated on the basis of 60% the 
coefficient developed at a pressure of 150 lbs. per inch of width, a re- 
duction of 40% being made to cover possible decrease of the coefficient 
in actual service and to cover also loss due to friction of the journals. 
From these data the following table is constructed showing the H.P. 
that may be transmitted by driving wheels of the several materials 
named when in frictional contact with iron, aluminum and type metal. 

„, , ,'*■"'». . nTJ rf u WPN X 0.6/ 

The formula for horse-power is H.P. = — n X — 



= KdWN, in 
= safe work- 



12 33000 

which d = diam. in inches, W = width of face in inches, P - „. 
ing pressure in lbs. per in. of width, N = revs, per min., / = coefficient 
of friction, 0.6 a factor for the decrease of the coefficient in service and 
for the loss in journal friction, K a coefficient including P, / and the 
numerical constants. 

Coefficients of Friction and Horse-power of Friction Drives. 





On iron. 


On aluminum. 


On type metal. 




/ 


k 


/ 


k 


/ 


k 




0.255 
0.309 
0.150 
0.330 
0.135 


0.00030 
0.00059 
0.00029 
0.00037 
0.00016 


0.273 
0.297 
0.183 
0.318 
0.216 


0.00033 
0.00057 
0.00035 
0.00035 
0.00026 


0.186 
0.183 
0.165 
0.309 
0.246 


0.00022 


Leather fiber 

Tarred fiber 

Sulphite fiber 


0.00035 
0.00031 
0.00034 
0.00029 







Horse-power = K x dWN. 

Friction Clutches. — Much valuable information on different forms of 
friction clutches is given in a paper by Henry Souther in Trans. A. S. M. 
E., 1908, and in the discussion on the paper. All friction clutches contain 
two surfaces that rub on each other when the clutch is thrown into gear, 
and until the friction between them is increased, by the pressure with 
which they are forced together, to such an extent that the surfaces bind 
and enable one surface to drive the other. The surfaces may be metal 
on metal, metal on wood, cork, leather or other substance, leather on 
leather or other substance, etc. The surfaces may be disks, at right 
angles to the shaft, blocks sliding on the outer or inner surface, or both, 
of a pulley rim, or two cones, internal and external, one fitting in the 
other, or a band or ribbon around a pulley. The driving force which is 
just sufficient to cause one part of the clutch to drive the other is the 
product, of the total pressure, exerted at right angles to the direction of 
sliding, and the coefficient of friction. The latter is an exceedingly 
variable quantity, depending on the nature and condition of the sliding 
surfaces and on their lubrication. The surfaces must have sufficient 
area so that the pressure per square inch on that area will not be suffi- 
cient to cause undue heating and wear. The total pressure on the parts 
of the mechanism that forces the surfaces together also must not cause 
undue wear of these parts. 

For cone clutches, Reuleaux states that the angle of the cone should 
not be less than 10°, in order that the parts may not become wedged 
together. He gives the coefficient of cast iron on cast iron, for such 
clutches, at 0.15. 

For clutches with maple blocks on cast iron Mr. Souther gives a coeffi- 
cient of 0.37, and for a speed of 100 r.p.m. he gives the following table of 
capacity of such clutches, made by the Dodge Mfg. Co. 



1156 



Horse- 
power. 


Block 
Area. 


Diam. at 
Block, Ins. 


Circumferen- 
tial Pull at 
Block Center. 


Total 
Pressure. 


Total Pres- 
sure per 
sq. in. 


25 
32 
50 
98 


Ins. 
120 
141 
208 
280 


16 
18 

21.5 
27.5 


Lbs. 
1,960 
2,240 
2,900 
4,500 


5,300 
6,000 
7,800 
12,000 


44 
44.5 
37.5 
43.5 



Prof. I. N. Hollis has found the coefficient of cork on cast iron to be 
from 0.33 to 0.37, or about double that of cast iron on cast iron or on 
bronze. A set of cork blocks outlasted a set of maple blocks in the ratio 
of five to one. Prof. C. M. Allen has found the torque for cork inserts 
to be nearly double that of a leather-faced clutch for a given dimension. 

Disk clutches for automobiles are made with frictional surfaces of 
leather, bronze, or copper against iron or steel. The Cadillac Motor Car 
Co. give the following: Mean radius of leather frictional surface 4Vi6 ins; 
area of do., 36V2 sq. ins.; axial pressure, 1000 to 1200 lbs.; H.P. capacity 
at 400 r.p.m., 51/2 H.P.: at 1400 r.p.m., 10 H.P. 

C. H. Schlesinger (Horseless Age, Oct. 2, 1907) gives the following 
formula for the ordinary cone clutch: 

H.P. = PfrR -h 63,000 sin. 6, 

in which P = assumed pressure of engaging spring in lbs., / = coeff. of 
friction, which in ordinary practice is about 0.25; r = mean radius of 
the cone, ins.; R = v.p.m. of the motor; = angle of the cone with the 
axis. Mr. Souther says the value of / = 0.25 is probably near enough 
for a properly lubricated leather-iron clutch. 

The Hele-Shaw clutch, with V-shaped rings struck up in the surfaces 
of disks, is described in Proc. Inst. M. E., 1903. A clutch of this form 
18 ins. diam. between theV's transmitted 1000 H.P. at 700 or 800 r.p.m. 

Coil Friction Clutches. (H. L. Nachman, Am. Mach., April 1, 1909.) 
— Friction clutches are now in use which will transmit 1000, and even 
more, horse-power. A type of clutch which is satisfactory for the trans- 
mission of large powers is the coil friction clutch. It consists of a steel 
coil wound on a chilled cast-iron drum. At each end of the coil a head 
is formed. The head at one end is attached to the pulley or shaft that is 
to be set in motion, while that at the other end of the coil serves as a 
point of application of a force which pulls on the coil to wind it on the 
drum, thus gripping it firmly. 

The friction of the coil on the drum is the same as that of a rope or 
belt on a pulley. That is, the relation of the tensions at the two ends of 
the coil may be found from the equation P/Q=e? ia where P = pull at fixed 
end of coil; Q=pull at free end of coil; e= base of natural iogarithms = 
2.718; fi = coefficient of friction between coils and drum; and a= Angle 
subtended by coil in radian measure, = 6.283 for each turn of coil. 

Values of P/Q for different numbers of turns are as follows, assuming 
N = 0.05 for steel on cast iron, lubricated: 
No. of turns 1234567 8 

P/Q = 1.37 1.87 2.57 3.51 4.81 6.58 8.60 12.33 



If D = diam. of drum in ins., N = 
(12 X 33,000) = 0.00000793 DNP. 



revs., per min., then H.P. =nDNP-* 



HOISTING AND CONVEYING. 



1157 



HOISTING AND CONVEYING. 

Strength of Ropes and Chains. — For the weight and strength of rope 
for hoisting see notes and tables on pages 386 to 391. For strength of 
chains see page 251. 



Working Strength of Blocks. 

(Boston and Lockport Block Co., 1908.) 
REGULAR BLOCKS WITH LOOSE HOOKS— LOADS IN POUNDS. 



Size, Inches. 


5 


6 


8 


10 


12 

H/8 
4000 
8000 
12000 


14 




9 /l6 
150 
250 
400 


3/ 4 
250 
400 
650 


7/8 
700 
1200 
1900 


1 

2000 
4000 
6000 


M/4 
7000 






12000 




19000 







LOADS IN TONS. 





Wide Mortise with 
Loose Hooks. 


Extra Heavy with 

Shackles. 


Size, inches 

Rope, diam., in . 


8 
1 
1/2 

1 
2 


10 

11/4 
2 
3 
4 


12 
15/16 

4 

6 

8 


14 

8 
10 


16 

13/4 

10 

12 

14 


18 

2 


20 

21/ 4 


22 

21/2 


24 
3 


2 double blocks. . . . 
2 triple blocks 


25 
30 
40 


30 
35 
45 


35 
40 
55 


40 
50 
70 

















WORKING LOADS FOR A PAIR OF WIRE-ROPE BLOCKS— TONS. 



Loose Hooks. 


Shackles. 


Sheave 

Diam., 

In. 


Two 


Two 


Two 


Two 


Two 


Two 


Singles. 


Doubles. 


Triples. 


Singles. 


Doubles. 


Triples. 


8 


3 


4 


5 


4 


5 


6 


10 


4 


5 


6 


6 


8 


10 


12 


5 


6 


7 


8 


10 


12 


14 


6 


7 


8 


10 


12 


15 


16 


7 


8 


10 


12 


15 


20 


18 


8 


10 


12 


15 


20 


25 



Chain Blocks. — Referring to the table on the next page, the speed 
of a chain block is governed by the pull required on the hand chain 
and the distance the hand chain must travel to lift the load the re- 
quired distance. The speeds are given for short lifts with men ac- 
customed to the work; for continuous easy lifting two-thirds of these 
speeds are attainable. The triplex block lifts rapidly, and the speed 
increases for light loads because the length of hand chain to be overhauled 
is small. This fact also enables the operator to lower the load very 
quickly with the triplex block. The 12- to 20-ton triplex blocks are 
provided with two separate hand wheels, thus permitting two men to 
hoist simultaneously, thereby securing double speed. In the triplex 
block the power is transmitted to the hoisting-chain wheel by means of a 
train of spur gearing operated by the hand chain. In the duplex block 



1158 



HOISTING AND CONVEYING. 



Chain Block Hoisting Speeds. 

(Yale & Towne Mfg. Co., 1908.) 





Pull 
in Pounds re- 
quired on 
Hand-Chain 

to Lift 
Full Loads. 


Feet of Hand- 


Hoisting Speeds. Feet per Minute 
Attainable and No. of Men re- 




Chain to be 




Pullea by 


quired for Hoisting Full Loads 


a 


Operator to 

Lift Load 

One Foot 

High. 


without Pulling over 80 Lb. 


^03 


Triplex. 


Duplex. 


Differ- 
ential. 


ftH 












i i 






73 




T3 




o 


CD 


X 


<d_; 


X 

CD 


X 

CD 


S 




h3 


ia^ 


CD~ 


o . 


Hi 


*s . 


h-5 


°fl 




ft 


a 

3 


<d-2 


a 


a 

3 


JC~ 


3 


^ 


2^ 


£§ 


"3 


O CD 


3 


£S 




H 


Q 


2 


H 


a 


a 


l*i 




Of 


*■ 


ta 




6~ 
6 


h— 


V4 
V2 






72 
122 






18 
24 










1 


62 


68 


21 


40 


8. 


16. 


24. 


1 


4. 


1 


2 


1 


82 


87 


216 


31 


59 


30 


4. 


8. 


12. 


1 


2. 


1 


3 70 


3 


H/2 


110 


94 


246 


35 


80 


36 


4.8 


9.6 


14.4 


2 


2.40 


2 


2 50 


3 


2 


12a 


115 


308 


42 


93 


42 


3.6 


7.2 


10.8 


2 


1.80 


2 


2 30 


4 


3 


114 


132 


557 


69 


126 


38 


2 3 


4,6 


6 9 


2 


1 10 


?. 


2 30 


7 


4 


124 
110 
130 
135 
140 
130* 
135* 
143* 


142 
145 
145 
160 
160 




84 
125 
126 
168 
210 
125* 
168* 
210* 


155 
195 
252 
310 
390 




1.7 
1.3 

1.1 

0.8 
0.6 
1.1 
0.8 
0.6 


3.3 

2.6 
2.2 
1.6 
1.2 

2.2 
1.6 
1.2 


5.2 
3.9 
3.3 
2.4 
1.8 
3.3 
2.4 
1.8 


2 
2 
2 
2 
2 
4 
4 
4 


0.80 
0.65 
0.50 
0.35 
0.30 


2 
2 
2 
2 
2 






5 






6 






8 






10 






12 






16 


















20 



















* On each of the two hand-chains. 

t The number of men is based on each man pulling not over 80 lb. 
One man pulling 160 lb. or less, as given in the first two columns, can lift 
the full capacity of any Triplex or Duplex Block. 

the power is transmitted through a worm wheel and screw. In the dif- 
ferential block the power is applied by pulling on the slack part of the 
load chain and the force is multiplied by means of a differential sheave. 
(See page 513.) The relative efficiency and durability of the three types 
are as follows: 





Differen- 
tial. 


Duplex. 


Triplex. 




35 

20 
40 


50 
80 
80 


100 




100 




too 






Efficiency of Hoisting 

11, 1903. 


Tackle. — (S. L. Wonson, Eng. News, June 


1 1/4 to 2-in. Manila rope. 




2 


3 


4 


5 


6 


7 


8 


9 














1.91 
96 


2.64 

88 


3.30 

83 


3.84 
77 


4.33 

72 


4.72 
67 


5 08 


5 37 






Efficiency, per cent 


64 


60 






3/4-in. Wire rope. 


Parts of line. 


3 


4 1 5 


6 


7 


8 


9 


10 


11 


12 

7.08 
59 


13 


Ratio load to pull 

Efficiency, per cent 


2.73 
91 


3.474.11 
87 1 82 


4.70 
78 


5.20 5.68 

74 1 71 


6.08 
68 


6.46 
65 


6.78 
62 


7.34 
56 



HOISTING AND CONVEYING. 



1159 



Proportions of Hooks. — The following formulae are given by Henry 
R. Towne, in his Treatise on Cranes, as a result of an extensive experi- 
mental and mathematical investiga- 
tion. They apply to hooks of capaci- 
ties from 250 lb. to 20,000 lb. Each 
size of hook is made from some com- 
mercial size of round iron. The basis in 
each case is, therefore, the size of iron of 
which the hook is to be made, indicated 
by A in the diagram. The dimension D 
is arbitrarily assumed. The other di- 
mensions, as given by the formulae, are 
those which, while preserving a proper 
bearing-face on the interior of the hook 
for the ropes or chains which may be 
passed through it, give the greatest re- 
sistance to spreading and to ultimate 
rupture, which the amount of material 
in the original bar admits of. The 
symbol A is used to indicate the nom- 
inal capacitv of the hook in tons of 
2000 lb. The formulae which deter- 
mine the lines of the other parts of the 
hooks of the several sizes are as follows, 
the measurements being all express'ed 
in inches: 




Fig. 182. 



H = 1.08 A; L = 1.05.4; 
; / = 1.33 A; M = 0.50 4; 
; J = 1.20 A; N = 0.85 5 - 



0.16; 



Z) = 0.5A +1.25; G = 0.75 D ; 

E = 0.64 A + 1.60 ; O = 0.363 A + 0.6 

F = 0.33 A + 0.85 ; Q = 0.64 A +1.60 '; 

K = 1.13-4; U = 0.866 4. 

The dimensions A are necessarily based upon the ordinary merchant 
sizes of round iron. The sizes which it has been found best to select are 
the following: 
Capacity of hook: 

V8 V4 1/2 1 H/2 2 3 4 5 6 8 10 tons. 
Dimension A: 

5/8 "/IB 3/4 H/16 H/4 1 3/g 13/4 2 21/4 21/ 2 27/ 8 31/4 In. 

Experiment has shown that hooks made according to the above formu- 
lae will give way first by opening of the jaw, which, however, will not occur 
except with a load much in excess of the nominal capacity of the hook. 
This yielding of the hook when overloaded becomes a source of safety, as 
it constitutes a signal of danger which cannot easily be overlooked, and 
which must proceed to a considerable length before rupture will occur 
and the load be dropped. 

Iron versus Steel Hooks. — F. A. Waldron, for over fifteen years con- 
nected with the manufacturing of hooks, in the works of the Yale & Towne 
Mfg. Co., after careful observation of hooks made of different materials and 
in different forms, says that the only proper material from which hooks 
can be made and be perfectly reliable is a high-grade puddled iron. 
While a steel hook, properly made, may stand from 25 to 50% greater 
load than a wrought-iron hook, it does not follow that the steel hook is 
better and more reliable than the iron hook. 

Iron hooks, made in accordance with the Towne formula, having serious 
surface defects, have been tested to destruction, and none of them, in. 
spite of these defects, have broken at less than 2 1/2 times the working load, 
while several steel hooks broke at the working load, without a moment's 
warning. (Trans. A. S. M. E., 1903.) 

Heavy Crane Hooks. — A. E. Holcomb, vice-pres. of the Earth Moving 
Machinery Co., contributes the following (1908). Seven years ago, while 
engaged in the design of a 100-ton crane. I made a study of the variations 
in strength with the different sectional forms for hooks in most common 
use. As a result certain values which gave the best results were sub- 
stituted in "Gordon's" formula and a formula was thereby obtained which 
was srood for hooks of any size desired, provided the proper allowable fiber 
stress per square inch was made use of when designing. From this 



1160 



HOISTING AND CONVEYING. 



formula the enclosed table was made up and was published in the American 
Machinist of Oct. 31, 1901. Since that time hundreds of hooks of cast 
or hammered steel have been designed and made according to my formula, 
and 'not one of them, so far as I know, has ever failed. 

The Industrial Works, Bay City, Michigan, manufacturers of heavy 
cranes, in December, 1904, made the following test under actual working 
conditions: 

A hook was made of hammered steel having an elastic limit or yield 
point at approximately 36,000 lbs. per sq. in. fiber stress and having the 
following important dimensions: d = 75/gin.; r = 4l/2in.; D = 207/igin. 

When the applied load reached 150,000 lbs. the hook straightened out 
until the opening at the mouth of the hook was 21/2 in. larger than 
formerly, and the distance from center of action line of load to center of 
gravity of section was found to have decreased 1/2 in., at which point the 
hook held the load. Upon increasing the load still further, the hook 
opened still more. From the dimensions of the hook as originally formed, 
we find from the formula or table that the fiber stress with a load of 
150,000 lbs.' was 37,900 lbs. per sq. in., or in excess of the yield point, 
whereas making use of the dimensions obtained from the hook when it 
held we find that the fiber stress per square inch was reduced to 35,940 lbs., 
or under the yield point. 

The designer must use his own judgment as to the selection of a proper 
allowable fiber stress, being governed therein by the nature of the material 
to be used and the probability of the hook being overloaded at some time. 
Under average conditions I have made use of the following values for (/): 





Values of (/) in pounds for a load of — 




1,000 to 
5000 
lbs. 


5,000 to 
15,000 
lbs. 


15,000 
. to 
30,000 
lbs. 


30,000 

to 
60,000 
lbs. 


60,000 

to 
100,000 

lbs. 


100,000 

lbs. 
and up. 




.2,000 
6,000 
12,000 


2,500 
8,000 
16,000 












10,666 

20,000 


11,250 
22,500 


12,500 
25,000 




Hammered steel 


27,500 



Mr. Holcomb's formula and his table in condensed form are given 
below: 

DiKECTioNS. — P and / being known, assume r to suit the requirements 
for which the hook is to be designed. Divide P by /and find the quotient 
in the column headed by the required r. At the side of the Table, in the 
same row, will be found the necessary depth of section, d. 

Notation. — P = load. S = area of section. R 2 = square of the radius 
of gyration. / = allowable fiber stress in lbs. per sq. in., 20,000 lbs. for 
hammered steel. For other letters see Fig. 183. 

P S 




f 



1 + 



2/02/1 
R 2 



General formula. 



(1) 



Vx = - 



d 2 (b 2 + 4 be + c 2 ) 
~~ 18(b 2 + 2 be + c 2 ) ' 
b+ 2 c w d 



. (2) 
. (3) 



r**l 

Fig. 183. 



(b + 2 c „ d\ 
yo = KTTe- X 3) + r - 
Assuming b = 0.66 d; 1 

_i \__ we have: 

P_ d* 

f _ 7.44d+ 12.393 r = 

di = 0.5 d. 

D = 2r+ 1.5d. 



. . (4) 
= 0.22d, 



K. (5) 






HOISTING AND CONVEYING. 
Values of K. 



1161 



d. 


r. 


0.50 

0.379 

.496 

.629 

.778 

.944 

1.143 

1.342 

1.558 

1.790 

2.038 

2.304 

2.586 

2.884 

3.214 

3.532 


0.75 

0.331 

.437 

.559 

.697 

.852 

1.039 

1.226 

1.429 

1.649 

1.886 

2.138 

2.408 

2.694 

3.008 

3.315 

3.651 

4.003 

4.757 

5.578 


1.00 


1.50 


2.00 


2.50 


3.00 


3.50 


4.00 


5.00 


6.00 


2.00 


0.292 

.391 

.504 

.632 

.776 

.953 

1.129 

1.321 

1.530 

1.754 

1.995 

2.253 

2.527 

2.828 

3.124 

3.447 

3.787 

4.516 

5.311 

6.173 

7.102 

8.096 

9.158 


0.240 

.329 

.420 

.532 

.659 

.801 

.957 

1.148 

1.336 

1.544 

1.760 

1.996 

2.248 

2.525 

2.801 

3.101 

3.418 

4.100 

4.848 

5.661 

6.540 

7.485 

8.496 

9.574 

10.788 

12.098 

13.374 

14.717 

16.126 

17.601 


0.203 

.275 

.360 

.460 

.572 

.700 

.841 

.998 

1.187 

1.373 

1.575 

1.793 

2.072 

2.281 

2.538 

2.818 

3.115 

3.754 

4.459 

5.227 

6.061 

6.960 

7.924 

8.954 

10.220 

11.381 

12.608 

13.901 

15.261 

16.686 

18.178 

19.735 

21.359 

23.050 

24.807 

26.630 

28.520 


0.176 

.239 

.316 

.404 

.506 

.621 

.750 

.893 

1.067 

1.239 

1.426 

1.627 

1.843 

2.081 

2.321 

2.583 

2.861 

3.463 

4.128 

4.855 

5.648 

6.504 

7.424 

8.409 

9.460 

10.746 

11.922 

13.173 

14.485 

15.862 

17.305 

18.814 

20.389 

22.031 

23.738 

25.511 

27.351 


0.155 

.212 

.281 

.360 

.454 

.559 

.677 

.808 

.953 

1.129 

1.321 

1.490 

1.691 

1.913 

2.140 

2.385 

2.646 

3.213 

3.842 

4.533 

5.287 

6.104 

6.984 

7.928 

8.932 

10.008 

11 316 

12.518 

13.785 

15.117 

16.514 

17.976 

19.504 

21.098 

22.758 

24.483 

26.274 










2.25 










2.50 










2.75 










3.00 


0.411 

.508 

.617 

.738 

.873 

1.038 

1.214 

1.374 

1.563 

1.770 

1.983 

2.215 

2.461 

2.998 

3.594 

4.252 

4.970 

5.750 

6.593 

7.498 

8.467 

9.499 

10.766 

11.926 

13.150 

14.442 

15.792 

17.210 

18.694 

20.242 

21.846 

23.535 

25.388 








3.25 








3.50 








3.75 








4.00 


0.805 

0.943 

1.124 

1.275 

1.453 

1.647 

1.849 

2.067 

2.300 

2.809 

3.377 

4.003 

4.689 

5.436 

6.243 

7.113 

8.044 

9.039 

10.267 

11.388 

12.572 

13.820 

15.-132 

16.508 

17.948 

19.453 

21.023 

22.658 

24.358 






4.25 






4.50 






4.75 






5.00 






5 25 






5.50 
5.75 
6.00 
6.50 
7.00 
7.50 


1.628 
1.825 
2.035 
2.496 
3.012 
3.584 
4.213 
4.900 
5.645 
6.450 
7.316 
8.241 
9.228 
10.448 
11.558 
12.730 
13.965 
15.263 
16.624 
18.049 
19.536 
21.088 
22.704 


'2/246 
2.719 
3.244 


8 00 






3.825 


8.50 






4,460 


9.00 






5.152 


9.50 






5.901 


10.00 








6.708 


10 50 








7.573 


11.00 








8.498 


11.50 








9.482 


12.00 








10.697 


U2.50 








11.802 


13.00 








12.967 


13.50 










14.195 


14 00 










15.484 


14 50 










16.835 


15 00 










18.248 


15.50 










19.724 


16.00 










21.262 




1 











For values of K and r intermediate to those given in the table approx- 
imate values of d may be found by interpolation. Thus, for K = 3.700, 
r = 2.75. 

r = 2.5 3.0 Int. for 2.75 

K = 3.462 3.213 3.338 

K = 4.128 3.842 3.985 

* (3.700 - 3.338) \ _ 

(3.985-3.338)/ X (7 -° " 6>5) ~ 6 - 78 ' 



Tabular values, 

d = 6.50 
d = 7.00 

Vhence: d= 6.5 + 



In like manner, if d and r are given the value of K and the corresponding 
safe load may be found. 

Strength of Hooks and Shackles. (Boston and Lockport Block Co., 
1908.) — Tests made at the Watertown arsenal on the strength of hooks 
and shackles showed that they failed at the loads given in the table below. 
In service they should be subjected to only 50% of the figures in the table. 
Ordinarily the hook of a block gives way first, and where heavy weights 
are to be handled shackles are superior to hooks and should be used 
wherever possible. 



1162 HOISTING AND CONVEYING. 

Strength of Hooks and Shackles. 



Hooks.* 


Shackles. 


Hooks.* 


Shackles. 




£ 


j,- 






J3 


J=J - 






















M 


M 






M 


M 






R • 








C . 


C • 




8 




£"3 


Description of 




CD 02 


OQ S 


Description of 


o 

£3 


<D Q 


«i 3 


Fracture. 




WJ 3 


0>„° 


Fracture. 




:§fc 


T^ 






~Ph 


rS^ 




<D 


s 


§ 




a> 


O 


§ 




co 


H 


H 




CO 


H 


EH 




V-> 


1,890 






13/8 


17310 


103,750 




9 /lB 


2.560 






20,940 


1 19,800 


Eye of shackle. 


5/8 


3,020 






mi* 


23,670 


125,900 


Eye of shackle. 


3/ 4 


4,470 


20,700 


Eye of shackle. 


13/4 


27,420 


146,804 


Sheared shackle 


V* 


6,280 


38,100 


Eye of shackle. 








pin. 


1 


12,600 


51,900 


Eye of shackle. 


17/8 


36,120 


162,700 


Eye of shackle. 


•1/8 


13,520 


62,900 


Sheared shackle 
pin. 


2 


38,100 


196,600 


Shackle at neck 
of eye. 


H/4 


16,800 


75,200 


Eye of shackle. 


2l/ 2 


55.380 


210,400 


Eye of shackle. 



* All the hooks failed by straightening the hook. 
Horse-power Required to Raise a Load at a Given Speed. — H.P. = 

Gy ° SS 33^00 t mlb X Speed in ft- Per min ' T ° thiS add 25% t0 5 ° % f ° r 
friction,' contingencies, etc. The gross weight includes the weight of 
cage, rope, etc. In a shaft with two cages balancing each other use the 
net load 4- weight of one rope, instead of the gross weight. 

To find the load which a given pair of engines will start. ■ — Let A = area 
of cylinder in square inches, or total area of both cylinders, if there are 
two; P = mean effective pressure in cylinder in lb. per sq. in.; S = stroke 
of cylinder, inches; C = circumference of hoisting-drum, inches; L = 
load lifted by hoisting-rope, lb.; F = friction, expressed as a diminution 

of the load. Then L = A X ^ X 2S - F. 

An example in Coll'y Engr., July, 1891, is a pair of hoisting-engines 
24" X 40", drum 12 ft. diam., average steam-pressure in cylinder = 
59.5 lb.; A = 904.8; P = 59.5; S = 40; C = 452.4. Theoretical load, 
not allowing for friction, AXPX2S + C = 9589 lb. The actual load 
that could just be lifted on trial was 7988 lb., making friction loss F = 
1601 lb., or 20 + per cent of the actual load lifted, or 162/ 3 % of the theo- 
retical load. 

The above rule takes no account of the resistance due to inertia of 
the load, but for all ordinary cases in which the acceleration of speed of 
the cage is moderate, it is covered by the allowance for friction, etc. The 
resistance due to inertia is equal to the force required to give the load the 
velocity acquired in a given time, or, as shown in Mechanics, equal to the 

WV 
product of the mass by the acceleration, or R = — „- ' in which R = 

resistance in lb. due to inertia; W = weight of load in lb.; V = maximum 
velocity in ft. per second; T = time in seconds taken to acquire the 
velocity V; g = 32.16. 

Effect of Slack Rope upon Strain in Hoisting. — A series of tests 
with a dynamometer are published by the Trenton Iron Co., which show 
that a dangerous extra strain may be caused by a few inches of slack rope. 
In one case the cage and full tubs weighed 11,300 lb.: the strain when the 
load was lifted gently was 11,525 lb.; with 3 in. of slack chain it was 
19,025 lb.; with 6 in. slack 25,750 lb., and with 9 in. slack 27,950 lb. 

Limit of Depth for Hoisting. — Taking the weight of a cast-steel 
hoisting-rope of li/sin. diameter at 2 lb. per running foot, and its break- 



HOISTING AND CONVEYING. 1163 

ing strength at 84,000 lb., it should, theoretically, sustain itself until 
42,000 feet long before breaking from its own weight. But taking the 
usual factor of safety of 7, then the safe working length of such a rope 
would be only 6000 ft. If a weight of 3 tons is now hung to the rope, 
which is equivalent to that of a cage of moderate capacity with its loaded 
cars, the maximum length at which such a rope could be used, with the 
factor of safety of 7, is 3000 ft., or 

2 x + 6000 = 84,000 -4- 7; .\ x = 3000 feet. 

This limit may be greatly increased by using special steel rope of higher 
strength, by using a smaller factor of safety, and by using taper ropes. 
(See paper by H. A. Wheeler, Trails. A. I. M. E., xix. 107.) 

Large Hoisting Records. — At a colliery in North Derbyshire during 
the first week in June, 1890, 6309 tons were raised from a depth of 509 
yards, the time of winding being from 7 a.m. to 3.30 p.m. 

At two other Derbyshire pits, 170 and 140 yards in depth, the speed of 
winding and changing has been brought to such perfection that tubs are 
drawn and changed three times in one minute. (Proc. Inst. M. E., 1890.) 

At the Nottingham Colliery near Wilkesbarre, Pa., in Oct., 1891, 70,152 
tons were shipped in 24.15 days, the average hoist per day being 1318 mine 
cars. The depth of hoist was 470 feet, and all coal came from one opening. 
The engines were fast motion, 22 X 48 inches, conical drums 4 feet 1 inch 
long, 7 feet diameter at small end and 9 feet at large end. (Eng'g News, 
Nov., 1891.) 

The 31ost Powerful Hoisting Engines ever built are said to be two 
32 X 72 duplex double-drum units built in 1906 for the Boston and 
Montana Co., at Butte, Mont. Each is designed to lift a dead load, 
unbalanced, of 17 tons out of a 3,500-ft. vertical shaft, at the rate of 
2,500 ft. per minute. Each hoist has two drums, 12 ft. diameter and 5 ft. 
6 ins. face, mounted on the same shaft and driven by 12-ft. diameter flat- 
disk reversible friction clutches. 

Pneumatic Hoisting. (H. A. Wheeler, Trails. A. I. M. E., xix, 107.) 
— A pneumatic hoist was installed in 1876 at Epinac, France, consisting 
of two continuous air-tight iron cylinders extending from the bottom to 
the top of the shaft. Within the cylinder moved a piston from which was 
hung the cage. It was operated by exhausting the air from above the 
piston, the lower side being open to the atmosphere. Its use was dis- 
continued on account of the failure of the mine. Mr. Wheeler gives a 
description of the system, but criticises it as not being equal on the whole 
to hoisting by steel ropes. 

Pneumatic hoisting-cylinders using compressed air have been used at 
blast-furnaces, the weighted piston counterbalancing the weight of the 
cage, and the two being connected by a wire rope passing over a pulley- 
sheave above the top of the cylinder. In the more modern furnaces 
steam-engine or electric hoists are generally used. 

Electric 31ine-Hoists. — An important paper on this subject, by 
D. B. Rushmore and K. A. Paulv, will be found in Trans. A. 1. M. E., 1910. 

Counterbalancing of Winding-engines. (H. W. Hughes, Columbia 
Coll. Qly.) — Engines running unbalanced are subject to enormous 
variations in the load; for let W = weight of cage and empty tubs, say 
6270 lb.: c = weight of coal, say 4480 lb.; r = weight of hoisting rope, 
sav 6000 lb.; r' = weight of counterbalance rope hanging down pit, say 
6000 lb. The weight to be lifted will be: 

If weight of rope is unbalanced. If weight of rope is balanced. 
At beginning of lift: -\ 

W+c+r-W or 10,480 lb. W + c + r - (W + r'), 

At middle of lift: f I or 

W+c+^- (iF 4-^) or 4480 lb. W + c 4- | 4- ^- (w + | + ^V M480 

At end of lift: " f 

W + c - (IP 4- r) or minus 1520 lb. W + c + r' - (W + r), J 
That counterbalancing materially affects the size of winding-engines is 
shown by a formula given by Mr. Robert Wilson, which is based on the 
fact that the greatest work a winding-engine has to do is to get a given 
mass into a certain velocity uniformly accelerated from rest, and to raise 
a load the distance passed over during the time this velocity is being 
obtained. 



1164 HOISTING AND CONVEYING. 



Let W = the weight to be set in motion: one cage, coal, number of empty 
tubs on cage, one winding rope from pit head-gear to bottom, 
and one rope from banking level to bottom. 
v = greatest velocity attained, uniformly accelerated from rest; 

g = gravity = 32.2; 

t = time in seconds during which v is obtained; 

L = unbalanced load on engine; 

R = ratio of diameter of drum and crank circles; 

P = average pressure of steam in cylinders; 

N = number of cylinders; 

S = space passed over by crank-pin during time t; 

C = 2/3, constant to reduce angular space passed through by crank to 
the distance passed through by the piston during the time t; 

A — area of one cylinder, without margin for friction. To this an 
addition for friction, etc., of engine is to be made, varying 
from 10 to 30% of A. 

1st. Where load is balanced, 

(Wv* 



A ■ 



KITH^)}* 



PNSC 



2d. Where load is unbalanced : 

The formula is the same, with the addition of another term to allow for 
the variation in the lengths of the ascending and descending ropes. In 
this case 

hi = reduced length of rope in t attached to ascending cage; 
h 2 = increased length of rope in t attached to descending cage; 
w = weight of rope per foot in pounds. Then 



V(Wv 2 \ , < ( T vt\ hiw + h,2iv)l _ 



PNSC 

Applying the above formula when designing new engines, Mr. Wilson 
found that 30 in. diameter of cylinders would produce equal results, when 
balanced, to those of the 36-in. cylinder in use; the latter being unbalanced. 

Counterbalancing may be employed. in the following methods: 

(a) Tapering Rove. — At the initial stage the tapering rope enables us 
to wind from greater depths than is possible with ropes of uniform section. 
The thickness of such a rojpat any point should only be such as to safely 
bear the load on it at thfiJmmmi:^^ 

With tapering ropes \ve Qfrfain a smaller difference between the initial 
and final load, but the difterence is still considerable, and for perfect 
equalization of the load we^w&ust rely on some other resource. The theory 
of taper ropes is to obtain a rope of uniform strength, thinner at the cage 
end where the weight is least, and thicker at the drum end where it is 
greatest. 

(6) The Counterpoise System consists of a heavy chain working up and 
down a staple pit, the motion being obtained by means of a special small 
drum placed on the same axis as the winding drum. It is so arranged 
that the chain hangs in full length down the staple pit at the commence- 
ment of the winding; in the center of the run the whole of the chain rests 
on the bottom of the pit, and, finally, at the end of the winding the counter- 
poise has been rewound upon the small drum, and is in the same con- 
dition as it was at the commencement. 

(c) Loaded-wagon System. — A plan, formerly much employed, was to 
have a loaded wagon running on a short incline in place of this heavy 
chain; the rope actuating this wagon being connected in the same manner 
as the above to a subsidiary drum. The incline was constructed steep 
at the commencement, the inclination gradually decreasing to nothing. 
At the beginning of a wind the wagon was at the top of the incline, and 
during a portion of the run gradually passed down it till, at the meet of 
cages, no pull was exerted on the engine — the wagon by this time being 
at the bottom. In the latter part of the wind the resistance was all 
against the engine, owing to its having to pull the wagon up the incline, 






CRANES. 1165 

and this resistance increased from nothing at the meet of cages to its 
greatest quantity at the conclusion of the lift. 

(d) The Endless-rope System is preferable to all others, if there is suffi- 
cient sump room and the shaft is free from tubes, cross timbers, and other 
impediments. It consists in placing beneath the cages a tail rope, similar 
in diameter to the winding rope, and, after conveying this down the pit, 
it is attached beneath the other cage. 

(e) Flat Ropes Coiling on Reels. — This means of winding allows of a 
certain equalization, for the radius of the coil of ascending rope continues to 
increase, while that of the descending one continues to diminish. Conse- 
quently, as the resistance decreases in the ascending load the leverage 
increases, and as the power increases in the other, the leverage diminishes. 
The variation in the leverage is a constant quantity, and is equal to the 
thickness of the rope where it is wound on the drum. 

By the above means a remarkable uniformity in the load may be ob- 
tained, the only objection being the use of flat ropes, which weigh heavier 
and only last about two-thirds the time of round ones. 

(/) Conical Drums. — Results analogous to the preceding may be 
obtained by using round ropes coiling on conical drums, which may either 
be smooth, with the successive coils lying side by side, or they may be 
provided with a spiral groove. The objection to these forms is, that 
perfect equalization is not obtained with the conical drums unless the sides 
are very steep, and consequently there is great risk of the rope slipping; 
to obviate this, scroll drums were proposed. They are, however, very 
expensive, and the lateral displacement of the winding rope from the 
center line of pulley becomes very great, owing to their necessary large 
width. 

(g) The Koepe System of Winding. ■ — An iron pulley with a single cir- 
cular groove takes the place of the ordinary drum. The winding rope 
passes from one cage, over its head-gear pulley, round the drum, and, after 
passing over the other head-gear pulley, is connected with the second cage. 
The winding rope thus encircles about half the periphery of the drum in the 
same manner as a driving-belt on an ordinary pulley. There is a balance 
rope beneath the cages, passing round a pulley in the sump; the arrange- 
ment may be likened to an endless rope, the two cages being simply points 
of attachment. 

CRANES. 

Classification of Cranes. (Henry R. Towne, Trans. A. S. M. E., iv. 

288. Revised in Hoisting, published by The Yale & Towne Mfg. Co.) 

A Hoist is a machine for raising and lowering weights. A Crane is a 
hoist with the added capacity of moving the load in a horizontal or lateral 
direction. 

Cranes are divided into two classes, as to their motions, viz., Rotary and 
Rectilinear, and into four groups, as to their source of motive power, viz.: 

Hand. — When operated by manual power. 

Power. — When driven by power derived from line shafting. 

Steam, Electric, Hydraulic, or Pneumatic. — When driven by an engine 
or motor attached to the crane, and operated by steam, electricity, water, 
or air transmitted to the crane from a fixed source of supply. 

Locomotive. — When the crane is provided with its own boiler or other 
generator of power, and is self-propelling; usually being capable of both 
rotary and rectilinear motions. 

Rotary and Rectilinear Cranes are thus subdivided: 

Rotary Cranes. 

(1) Swing-cranes. — Having rotation, but no trolley motion. 

(2) Jib-cranes. — Having rotation, and a trolley traveling on the jib. 

(3) Column-cranes. — Identical with the jib-cranes, but rotating around 
a fixed column (which usually supports a floor above). 

(4) Pillar-cranes. — Having rotation only; the pillar or column being 
supported entirely from the foundation. 

(5) Pillar Jib-cranes. — Identical with the last, except in having a jib 
and trolley motion. 

(6) Derrick-cranes. — Identical with jib-cranes, except that the head of 
the mast is held in position by guy-rods, instead of by attachment to a 
roof or ceiling. 



trolle 



1166 HOISTING AND CONVEYING. 

(7) Walking-cranes. — Consisting of a pillar or jib-crane mounted on 
wheels and arranged to travel longitudinally upon one or more rails. 

(8) Locomotive-cranes. — Consisting of a pillar-crane mounted on a 
truck, and provided with a steam-engine capable of propelling and rotating 
the crane, and of hoisting and lowering the load. 

Rectilinear Cranes. 

(9) Bridge-cranes. — Having a fixed bridge spanning an opening, and a 
olley moving across the bridge. 

(10) Tram-cranes. — Consisting of a truck, or short bridge, traveling 
longitudinally on overhead rails, and without trolley motion. 

(11) Traveling-cranes. — Consisting of a bridge moving longitudinally 
on overhead tracks, and a trolley moving transversely on the bridge. 

(12) Gantries. — Consisting of an overhead bridge, carried at each end 
by a trestle traveling on longitudinal tracks on the ground, and having 
a trolley moving transversely on the bridge. 

(13) Rotary Bridge-cranes. — Combining rotary and rectilinear move- 
ments and consisting of a bridge pivoted at one end to a central pier or 
post, and supported at the other end on a circular track; provided with a 
trolley moving transversely on the bridge. 

For descriptions of these several forms of cranes see Towne's " Treatise 
on Cranes." 

Stresses in Cranes. — See Stresses in Framed Structures, p. 515, ante. 

Position of the Inclined Brace in a Jib-crane. — The most econom- 
ical arrangement is that in which the inclined brace intersects the jib at 
a distance from the mast equal to four-fifths the effective radius of the 
crane. {Hoisting.) 

Electric Overhead Traveling Cranes. (From data supplied by 
Alliance Machine Co., Alliance, O., and Pawling & Harnischfeger, Mil- 
waukee.) — Electric overhead traveling cranes usually have 3 motors, for 
hoisting, traversing the hoist trolley on the bridge and for moving the 
bridge, respectively. The usual range of motor sizes is as follows: Hoist, 
15-50 H.P.; trolley, 3-15 H.P.; bridge, 15-50 H.P. The speeds at which 
the various motions are made range as follows, the figures being feet per 
minute: Hoist, 8-60; trolley traverse, 75-200; bridge travel, 200-600. 
These speeds are varied in the same capacity of crane to suit each par- 
ticular installation. In general, the speed of the bridge in feet per minute 
should not exceed (length of runway + 100). If the runway is long and 
covered by more than one crane, the speed may be made equal to the 
average distance between cranes 4- 100. Usually 300 ft. per min. is a 
good speed. For small cranes in special cases, the speeds may be increased, 
but for cranes of over 50 tons capacity the speed should be below 300 ft. 
per min. unless the building is made especially strong to stand the strains 
incident to starting and stopping heavv cranes geared for high speeds. 
Cranes of over 15 tons capacity usuallv'have an auxiliary hoist of 1/5 the 
capacity of the main hoist, and usually operated by the same motor. 
Wire rope is now almost exclusively used for hoisting with cranes. The 
diameter of the drums and sheaves should be not less than 30 times 
the diameter of the hoisting rope, and should have a factor of safety of 5. 
Cranes are equipped with automatic load brakes to sustain the load when 
lifted and to regulate the speed when lowering, it being necessary for the 
hoist to drive the load down. 

The voltage now standard for crane service is 220 volts at the crane 
motor, although 110 volts for small cranes is not objectionable. Voltages 
of 500-600 are inadvisable, especiallv in foundries and steel works, where 
dust and metallic oxides cover many parts of the crane and necessitate 
frequent cleaning to avoid grounds. On account of the danger from the 
higher voltages, the operators are apt to neglect this part of their work. 
Power Reouirod to Drive Cranes. (Morgan Engineering Co., 
Alliance, O., 1909.) — The power required to drive the different parts of 
cranes is determined by allowing a certain friction percentage over th-; 
power required to move the dead load. On hoist motions 331/3% is 
allowed for friction of the moving parts, thus giving a motor of 1/3 greate- 
capacity than if friction were neglected. For bridge and trolley motions, 
a journal friction of the track wheel axles of 10% of the total weight of 
the crane and load is allowed. There is then added an allowance of 331/3% 
of the horse-power required to drive the crane and load plus the trac h wheel 



CRANES. 



1167 



axle friction, to cover friction of the gearing. In selecting motors, the 
most important consideration is the maximum starting torque which 
the motor can exert. With alternating-current motors, this is less than 
with direct-current motors, requiring a larger motor, particularly on the 
bridge and trolley motions which require tne greatest starting torque. 

Walter G. Stephan says {Iron 'iraae Rev,, Jan. 7, 1909) that the bridge 
girders should be made of two plates latticed, or box girders, their depth 
varying from Vio to 1/20 of the span. Ihe important feature of crane 
girder design is ample strength and stiffness, both vertically and laterally. 
Especial attention should be given to the transverse strain on the bridge 
due to sudden stopping or starting of heavy loads. The wheel base on 
the end trucks should have a ratio to the crane span of 1 to 6, although 
for long spans this ratio must necessarily be reduced to 1 to 8. Quick- 
traveling cranes should have as long a wheel base as possible, since the 
tendency to twist increases with the speed. Where several wheels are 
necessary at each end to support the crane, equalizing means should be 
used. 

A recent development in cranes is the four- or six-girder crane for han- 
dling ladles of molten metal in steel works. The main trolley runs on the 
outer girders, with the hoist ropes depending between the outer and inner 
girders. The auxiliary trolley runs on the inner girders, thus being able 
to pass between the main ropes, and tilt the ladle in either direction. 

Dimensions and Wheel Loads of Electric Traveling Cranes. 

Based on 60-ft. span and 25-ft. lift; wire rope hoist. 
(Alliance Machine Co., 1908.) 



Capacity, 

Tons (2000 

Lb.). 



Distance Run- 
way Rail to 
Highest Point. 



Ft. 
6 
6 
7 



Distance 

Center of 

Rail to Ends 

of Crane. 



In. 



Wheel Base of 
End Truck. 



Ft. 
9 
10 
II 
12 
12 



Maximum 
Load per 
Wheel; Trol- 
ley at End of 
Bridge. 



Pounds. 
20,000 
27,000 
51,000 
82,000 
48,000* 



* Has 8 track wheels on bridge. 

Standard cranes are built in intermediate sizes, varying by 5 tons, up 
to 40 tons. 



Standard Hoisting and Traveling Speeds of Electric Cranes. 

(Pawling & Harnischfeger, 1908.) 



Capacity, 


Hoisting 


Bridge Travel 


Capacity 


Speed Aux. 


Tons (2000 


Speed, Ft. per 


Speed, Ft. per 


Aux. Hoist, 


Hoist, Ft. per 


Lb.). 


Min. 


Min. 


Tons. 


Min. 


5 

10 


25-100 
20-75 


300-450 
300-450 






3 


30-75 


25 


10-40 


250-350 


f.J 


50-125 ) 
25-60 ( 


40 


9-30 


250-350 


\i 


40-100 1 
25-60 \ 


50 


8-30 


200-300 


u 


40-100 ) 
25-60 j 


75 


6-25 


200-250 


15 


20-50 


125 


5-15 


200-250 


25 


20-50 


150 


5-15 


200-250 


25 


20-50 



Trolley travel speed from 100-150 ft. per min. in all cases. 



1168 



HOISTING AND CONVEYING. 



Notable Crane Installations. (1909.) 



^ 






A 


H.P.of 


>> 


S. 


l'« 


L 


, 


a 






§ 




1 




Hoist 


jv 


M 

3 


1.9 


gifi 


!§ 






£ 


a 


"o 
H 
o 

6 


Motor. 




"3 o 


as 
.S ft 


02^ 
as a 




^2 


^3 




"S 

a 




6 oj 


03 


o 


m 


£ 


O " 


3 


<1S 


w 


w 


w 


PQ 


H 


Q 


^ 


a 




Ft. In. 




















Ft.In. 






150 


65 


1 


25 


75f 


s 


30 


75 


8-24 


150-200 


100-150 


7 


4 


i 


150 


55 


1 


30 


120 


35 


50 


8 


150-200 


75-100 




5 


3 


150 


65 


2 


15 


75f 


30t 


18f 


75 


10-25 


150-200 


100-150 


7 "6" 


4 


1 


125* 




2 




110 


J50| 
130J 


63 


100| 


10 


200 


f 801 
1125/ 
100-150 


5 10 


6 


2 

1 


120 


56 7 


2 


10 


50f 


18 


iot 


52+ 


10-25 


150-300 


5 5 


7 




100 


65 


2 


10 


sot 


18 


iot 


50 


10-25 


200-250 


100-150 


5 5 


8 


J 


80 


74 


2 


10 


40f 


18f 


iot 


40 


10-25 


200-250 


100-150 


5 101/2 


9 


' 


50 


129 III/4 


1 


15 


50 


25 


71/ 2 


50 


10 


100-150 


80-100 


8 6 


10 


3 


50 


125 10 


1 


15 


50 


25 


71/2 


50 


10 


100-150 


80-100 


8 6 


11 


3 


50 


121 2 


1 


5 


75 


15 


15 


75 


111/2 


225 


125 


8 4 


12 


2 



* Four-girder ladle crane, t On each trolley. 

% Divided equally between 2 motors for series-parallel control. 

1. Pawling & Harnischfeger; 2. Alliance Mach. Co.; 3. Morgan En>- 
gineering Co.; 4. Midvale Steel Co., Phila.; 5. Homestead Steel Works, 
Munhall, Pa.; 6. Indiana Steel Co., Gary, Ind.; 7. Oregon Ry. & Nav. 
Co., Portland, Ore.; 8. El Paso & S. W. Ry., El Paso, Tex.; 9. C. & E. I 
Ry., Danville, 111.; 10. 3d Ave. Ry., N. Y. City; 11. United Rys. Co., 
Baltimore; 12. Carnegie Steel Co., Youngstown, Ohio. 

A 150-ton Pillar-crane was erected in 1893 on Finnieston Quay, 
Glasgow. The jib is formed of two steel tubes, each 39 in. djam. and 90 
ft. long. The radius of sweep for heavy lifts is 65 ft. The jib and its load 
are counterbalanced by a balance-box weighted with 100 tons of iron and 
steel punchings. In a test a 130-ton load was lifted at the rate of 4 ft. per 
minute, and a complete revolution made with this load in 5 minutes. 
Eng'g News, July 20, 1893. 

Compressed-air Traveling-cranes.— Compressed-air overhead travel- 
ing-cranes have been built by the Lane & Bodley Co., of Cincinnati. 
They are of 20 tons nominal capacity, each about 50 ft. span and 400 ft. 
length of travel, and are of the triple-motor type, a pair of simple reversing- 
engines being used for each of the necessary operations, the pair of engines 
for the bridge and the pair for the trolley travel being each 5-inch bore by 
7-inch stroke, while the pair for hoisting is 7-inch bore by' 9-inch stroke. 
The air-pressure when required is somewhat over 100 pounds. The air- 
compressor is allowed to run continuously without a governor, the speed 
being regulated by the resistance of the air in a receiver. An auxiliary 
receiver is placed on each traveler, whose object is to provide a supply 
of air near the engines for immediate demands and independent of the 
hose connection. Some of the advantages said to be possessed by this 
type of crane are: simplicity; absence of all moving parts, excepting 
those required for a particular motion when that motion is in use; no 
danger from fire, leakage, electric shocks, or freezing; ease of repair; 
variable speeds and reversal without gearing; almost entire absence of 
noise; and moderate cost. 

Quay-cranes. — An illustrated description of several varieties of sta- 
tionary and traveling cranes, with results of experiments, is given in a 
paper on Quay-cranes in the Port of Hamburg by Chas. Nehls, Trans. 
A. S. C. E., 1893. 

Hydraulic Cranes, Accumulators, etc. — See Hydraulic Pressure 
Transmission, page 779, ante. ] 

Electric versus Hydraulic Cranes for Docks. — A paper by V. L. j 
Raven, in Trans. A. S. M. E., 1904, describes some tests of capacity and ; 



CRANES. 1169 

efficiency of electric and hydraulic power plants for dock purposes at Mid- 
dlesbrough, Eng. In loading two cargoes of rails, weighing respectively 
1210 and 1225 tons, the first was done with a hydraulic crane, in 7 hours, 
with 3584 lbs. of coal burned in the power station, and the second with 
an electric crane in 51/4 hours, with 2912 lbs. of coal. The total cost in- 
cluding labor, per 100 tons, was 327 pence with the hydraulic and 245 
pence for the electric crane, a saving by the latter of 25 %. 

Loading and Unloading and Storage Machinery for coal, ore, etc., 
is described by G. E. Titcomb in Trans. A. S. M. E., 1908. The paper 
illustrates automatic ore unloaders for unloading ore from the hold of a 
vessel and loading it onto cars, and car-dumping machinery, by which 
a 50-ton car of coal is lifted, turned over and its contents discharged 
through a chute into a vessel. Methods of storage of coal and of re- 
loading it on cars are also described. 

Power Required for Traveling-Cranes and Hoists. — Ulrich Peters. 
in Machy, Nov. 1907, develops a series of formulae for the power re- 
quired to hoist and to move trolleys on cranes. The following is a brief 
abstract. Resistance to be overcome in moving a trolley or crane- 
bridge. Pi = rolling friction of trolley wheels, Pi = journal friction 
of wheels or axles, P3 = inertia of trolley and load. P = sum of these 

resistances = Pi + Pi+P 3 = (T+L) ( fr~yv*^ '+ rr|^) in which r = weight 

of trolley, L = load, f t = coeff. of rolling frictionrabout 0.002, (0.001 to 
0.003 for cast iron on steel); / 2 = coeff. of journal friction, = 0.1 for start- 
ing and 0.01 for running, assuming a load on brasses of 1000 to 3000 lb. 
per sq. in.; f/ 2 is more apt to be 0.05 unless the lubrication is perfect. See 
Friction and Lubrication, W. K.l d = diam. of journal; D = diam. of 
wheels; v = trolley speed in ft. per min.; t = time in seconds in which 
the trolley under full load is required to come to the maximum speed. 
Horse-power = sum of the resistances X speed, ft. per min. -J- 33,000. 

Force required for hoisting and lowering: Fh = actual hoisting force, 
F = theoretical force or pull, L = load, v = speed in ft. per min. of 
the rope or chain, c = hoisting speed of the load L, c/v = transmission 
ratio of the hoist, e = efficiency = F /Fh. The actual work to raise 
the load per minute = Fhv = Lc = F v -s- e. The efficiency e is the 
product of the efficiencies of all the several parts of the hoisting mech- 
anism, such as sheaves, windlass, gearing, etc. Methods of calculating 
these efficiencies, with examples, are given at length in the original paper 
by Mr. Peters. 

Lifting Magnets. — (From data furnished by the Electric Controller 
and Mfg. Co., Cleveland, and the Cutler-Hammer Clutch Co., Milwaukee). 
Lifting magnets first came into use about 1898. They have had wide 
application for handling pig iron, scrap, castings, etc. A lifting magnet 
comprises essentially a magnet winding, a pole-piece, a shoe and a pro- 
tecting case, which is ribbed to afford ample radiating surface to dissi- 
pate the heat generated in operation. The winding usually consists of 
coils, each wound with copper ribbon and insulated with asbestos. The 
insulation must be designed to withstand a higher voltage than the line 
voltage, due to the inductive kick when the circuit is opened. The wear- 
ing plate, which takes the shocks incident to picking up the load, is usualljr 
made of manganese steel. The shape of the pole piece or lifting surface.of 
the magnet must be varied, as the same shape is not usually applicable 
to all classes of materials. For handling pig iron, scrap, etc., a concave 
pole surface is usually superior to a flat one, which is adapted to hand- 
ling plates or flat material of similar character, and which bear equally 
on the piece to be lifted at both the edge and center. A test of a lift- 
ing magnet made at the works of the Youngstown Sheet and Tube Co., 
in 1907, showed the following results: 

Total pig iron unloaded. 109,350 pounds; weight of average lift, 785 
pounds; time required, 2 hours. 15 minutes; current on magnet, 1 hour 
15 minutes; current required, 30 amperes. 

The No. 3 and No. 4 magnets are particularly fitted for use on steam- 
iriven locomotive cranes, and when so used are usually supplied with 
Current from a small steam-driven generator set mounted on the crane, 
;team being drawn from the boiler of the crane. Nos. 5 and 6 are adapted 
"or use with overhead electric traveling cranes in cases wheje large lifts 
;ind high speed of handling are essential. 



1170 



HOISTING AND CONVEYING. 



zes and Capacities of the Electric Controller & Mfg. Co. 'a 
Type S-A Lifting Magnets. (1909). 



Weight. 



Lb. 
2,100 
3,200 
4,800 
6,600 



Average 
current at 
220 volts. 



Amp. 
11 
27 
35 
45 



Lifts in machine cast pig 
iron. 


Maximum 
lift. 


Average 
lift. 


Lb. 
1,405 
2,180 
3,087 
4,589 


Lb. 
750 
1,250 
1,800 
2,600 



Sizes and Capacities of Lifting Magnets (Cutler-Hammer), 1908. 



10 
35 
50 



Weight 
lb. 



75 
1,650 
5,000 



Maximum* 

Lifting 

Capacity, 

lb. 



800 
5,000 
20,000 



Average 

Lifting 

Capacity, 

lb. 



100-300 

500-1,000 

1,000-2,000 



Current 

Required 

at 220 volts, 

amperes. 



1 
15-18 
30-35 



Head room- 
required , 
ft. 



♦This capacity can be obtained only under the most favorable con- 
ditions, with complete magnetic contact between the magnet and the 
piece to be lifted. 

The capacity of a lifting magnet in service depends on many other 
factors than the design of the magnet. Most important is the character 
of the material handled. Much more can be handled at a single lift 
with material like billets, ingots, etc.,. than with scrap, wire, pig iron 
etc The speed of the crane, from which the magnet is suspended, and 
the' distance it must transport the material are also important factors to 
De considered in calculating the capacity of a given magnet under given 
conditions The following results have been selected from a great num- 
be? of tests of the Electric Controller and Mfg. Co.'s No. 2 Type S magnets 
in commercial service, and represent what is probably average practice 
It should be borne in mind that the average lift is determined from a large 
number of lifts including lifts made from a full car of sa y w .iron, 
where the magnetic conditions are very favorable, and also the lean 
lifts where the car is nearly empty, and magnetic conditions unfavorable; 
the magnet can reach only a few pigs at one time ^on ^e tean^j. wghjj 
consequent heavv decrease in the size of the load. The average lilt is 
therefore less than the maximum lift in handling a given lot of material. 

mS?^tSftom an ordinary electric overhead traveling crane a 
magnet of the type used in these trials will handle from 20 to 30 tons 
per hour of the scrap used by open-hearth furnaces, If operated from 
a special fast crane, the amount may be somewhat increased. Average 
lifts in pounds for various materials are as follows: 

Skull P cracker balls up to 20,000; ingot (or if ground man places 
magnet two) each, 6,000; billet slabs, 900-6,000 . A 

The above weights depend on dimensions and whether in pile or 
stacked evenly. , . . ., 1 _„ 

Machine cast pig iron, 1,250; sand cast pig iron, 1,150. . 

These are values obtained in unloading railway cars, including lean 

1 Machine cast pfg iron, 1,350; sand cast pig iron, 1,200. 
The above are average lifts from stockpile. . , 

Heavy melting stock (billets, crop ends of billets, rails or structural 
shan's 1250- boiler plate scrap, 1,100; farmers' scrap (harvesting 
mafhfnery parts, plow Joints, etc..), 900; small risers from steel castings 
1 600- fine wire scrap, scrap tubing not over 3 ft. long, loose even or 
laminati?? Jcrap, 500; bundled scrap, 1,200; miscellaneous junk deal- 
ers' scrap, 4.00-80>'\ 



TELPHERAGE. 



1171 



Commercial Results with a 52-inch, 5,000 pound Magnet. 
(Electric Controller & Mfg. Co., 1908.) 




* 1. Machine cast pig handled from stock pile to charging boxes. 2. 
Bull heads, ditto. 3. Sand cast pig unloaded from car to stock pile. 
4. Baled tin and wire unloaded from car to stock pile. 5. Boiler plate 
scrap handled from stock pile to charging boxes. 6. Farmers' scrap, com- 
prising knotters and butters from threshing and binding machines, sections 
of cutter bars from mowers, broken steel teeth from hay rakes, plow points, 
etc., from stock pile to charging boxes. 7. Small risers from steel castings, 
handled from stock pile to charging boxes. 8. Laminated plates from 
armatures and transformers, mixed sizes, from stock pile to charging 
boxes. 9. Cast iron sewer pipe, 3 feet diameter, weighing 2,000 pounds 
each, lifted from cars to flat boat. Each pipe had to be blocked and 
lashed to prevent washing overboard. 10. Pensylvania Railroad East 
River tunnel section castings, convex on one side, concave on other, 
weighing 4,000 pounds each. Handled from local float to barge for ship- 
ment. 11. Steel plate 1/2-inch X 10 inches X 6 feet inches handled 
from car to float. 12. Steel rails, 40 pounds per yard, 25 feet long. 
Handled from car to lighter, about 8 rails per lift. 

The above results of tests relate to the Electric Controller & Mfg. 
Co.'s No. 2 Type " S " magnet, 52 in. diameter and weighing 5200 lbs. 
and are the average of a large number of tests made at various plants 
between the years 1905 and 1908. This type of magnet is being super- 
seded by the No. 4 Type S-A magnet which is 43 in. diameter, weighs 
3200 lbs. and gives substantially the same average lift. 



TELPHERAGE. 

Telpherage is a name given to a system of transporting materials in 
which the load is suspended from a trolley or small truck running on a 
cable or overhead rail, and in which the propelling force is obtained 
from an electric motor carried on the trolley. The trolley, with its 
motor, is called a "telpher." A historical and illustrated description 
of the system is given in a paper by C. M. Clark, in Trans. A. I. E. E., 
(1902. A series of circulars of the United Telpherage Co., New York, 
ishow numerous illustrations of the system in operation for handling 
different classes of materials. Telpherage is especially applicable for 
moving packages in warehouses, on wharfs, etc. The moving machin- 
ery consists of the telpher or the conveying power, with accompanying 
trailers; the portable electric hoist or the vertical elevating power, and 
ihe carriers containing the load. Among the accessories are brakes, 
Switches and controlling devices of many kinds. 



1172 HOISTING AND CONVEYING. 

An automatic line is controlled by terminal and intermediate switches 
which are operated by the men who do the loading and unloading, no 
additional labor being required. A non-automatic line necessitates a 
boy to accompany the telpher. The advisability of using the non- 
automatic rather than the automatic line is usually determined by the 
distance between stations. 

COAL-HANDLING MACHINERY. 

The following notes and tables are supplied by the Link-Belt Co. 

In large boiler-houses coal is usually delivered from hopper-cars into 
a track-hopper, about 10 feet wide and 12 to 16 feet long. A feeder set 
under the track-hopper feeds the coal at a regular rate to a crusher, which 
reduces it to a size suitable for stokers. 

After crushing, the coal is elevated or conveyed to overhead storage- 
bins. Overhead storage is preferred for several reasons: 

1. To avoid expensive wheeling of coal in case of a breakdown of the 
coal-handling machinery. 

2. To avoid running the coal-handling machinery continuously. 

3. Coal kept under cover indoors will not freeze in winter and clog the 
supply-spouts to the boilers. 

4. It is often cheaper to store overhead than to use valuable ground- 
space adjacent to the boiler-house. 

5. As distinguished from vault or outside hopper storage, it is cheaper 
to build steel bins and supports than masonry pits. 

Weight of Overhead Bins. — Steel bins of approximately rectangular 
cross-section, say 10 X 10 feet, will weigh, exclusive of supports, about 
one-sixth as much as the contained coal. Larger bins, with sloping 
bottoms, may weigh one-eighth as much as the contained coal. Bag 
bottom bins of the Berquist type will weigh about one-twelfth as much as 
the contained coal, not including posts, and about one-ninth as much, 
including posts. 

Supply-pipes from Bins. — The supply-pipes from overhead bins to 
the boiler-room floor, or to the stoker-hoppers, should not be less than 12 
inches in diameter. They should be fitted at the top with a flanged cast- 
ing and a cut-off gate, to permit removal of the pipe when the boilers are 
to be cleaned or repaired. 

Types of Coal Elevators. — Coal elevators consist of buckets of 
various shapes attached to one or more strands of link-belting or chain, or 
to rubber belting. The buckets may either be attached continuously or 
at intervals. The various types are as follows: 

Continuous bucket elevators consist usually of one strand of chain and 
two sprocket-wheels with buckets attached continuously to the chain. 
Each bucket after passing the head wheel acts as a chute to direct the 
flow from the next bucket. This type of elevator will handle the larger 
sizes of coal. It runs at slow speeds, usually from 90 to 1.76 feet per min- 
ute, and has a maximum capacity of about 120 tons per hour. 

Centrifugal discharge elevators consist usually of a single strand of chain, 
with the buckets attached thereto at intervals. They are used to handle 
the smaller sizes of coal in small quantities. They run at high speeds, 
usually 34 to 40 revolutions of the head wheel per minute, and have a 
capacity up to 40 tons per hour. 

Perfect discharge elevators consist of two strands of chain, with buckets 
at intervals between them. A pair of idlers set under the head wheels 
cause the buckets to be completely inverted, and to make a clean delivery 
into the chutes at the elevator head. This type of elevator is useful in 
handling material which tends to cling to the buckets. It runs at slow 
speeds, usually less than 150 feet per minute. The capacity depends on 
the size of the buckets. 

Combined Elevators and Conveyors are of the following types: 

Gravity discharge elevators, consisting of two strands of chain, with 
spaced V-shaped buckets fastened between them. After passing the head 
wheels the buckets act as conveyor-flights and convey the coal in a trough 
to any desired point. This is the cheapest type of combined elevator and 
conveyor, and is economical of power. A machine carrying 100 tons of 
coal per hour, in buckets 20 inches wide, 10 inches deep, and 24 inches long, 



COAL-HANDLING MACHINERY. 1173 

spaced 3 feet apart, requires 5 H.P. when loaded and 1 1/2 H.P. when empty 
for each 100 feet of horizontal run, and 1/9 H.P. for each foot of vertical lift. 

Rigid bucket-carriers consist of two strands of chain with a special 
bucket rigidly fastened between them. The buckets overlap and are so 
shaped that they will carry coal around three sides of a rectangle. The 
coal is carried to any desired point and is discharged by completely 
inverting the bucket over a turn-wheel. 

Pivoted bucket-carriers consist of two strands of long pitch steel chain to 
which are attached, in a pivotal manner, large malleable iron or steel 
buckets so arranged that their adjacent lips are close together or overlap. 
Overlapping buckets require special devices for changing the lap at the 
corner turns. Carriers in which the buckets do not overlap should be 
fitted with auxiliary pans or buckets, arranged in such a manner as to 
catch the spill which falls between the lips at the loading point, and so 
shaped as to return the spill to the buckets at the corner turns. Pivoted 
bucket-carriers will carry coal around four sides of a rectangle, the buckets 
being dumped on the horizontal run by striking a cam suitably placed. 
Buckets for these carriers are usually of 2 ft. pitch, and range in width 
from 18 in. to 48 in. They run at low speeds, usually not over 50 ft. per 
minute, 40 ft. per minute being most usual. At the latter speed, the 
capacities when handling coal vary from 40' tons per hour for the 18 in. 
width to 120 tons for the 48 in. width. On account of the superior con- 
struction of these carriers and the slow speed at which they .run, they are 
economical of power and durable. The rollers mounted on the chain • 
joints are usually 6 in. diameter, but for severe duty 8-in. rollers are often 
used. It is usual to make these hollow to carry a quantity of oil for 
internal lubrication. 

Coal Conveyors. — Coal conveyors are of four general types, viz., 
scraper or flight, bucket, screw, and belt conveyors. 

The flight conveyor consists of a trough of any desired crots-section and 
a single or double strand of chain carrying scrapers or flights of approxi- 
mately the same shape as the trough. The flights push the coal ahead of 
them in the trough to any desired point, where it is discharged through 
openings in the bottom of the trough. 

• For short, low-capacity conveyors, malleable link hook-joint chains 
are used. For heavier service, malleable pin-joint chains, steel link chains, 
or monobar, are required. For the heaviest service, two strands of steel 
link chain, usually with rollers, are used. 

Flight conveyors are of three types: plain scraper, suspended flight, and 
roller flight. 

In the plain scraper conveyor, the flight is suspended from the chain 
and drags along the bottom of the trough. It is of low first cost and is 
useful where noise of operation is not objectionable. It has a maximum 
capacity of about 30 tons per hour, and requires more power than either 
of the other two types of flight conveyors. 

Suspended flight conveyors use one or two strands of chain. The flights 
are attached to cross-bars having wearing-shoes at each end. These wear- 
ing-shoes slide on angle-iron tracks on each side of the conveyor trough. 
The flights do not touch the trough at any point. This type of conveyor 
is used where quietness of operation is a consideration. It is of higher 
first cost than the plain scraper conveyor, but requires one-fourth less 
power for operation. It is economical up to a capacity of about 80 tons 
per hour. 

The roller flight conveyor is similar to the suspended flight, except that 
the wearing-shoes are replaced by rollers. It is highest in first cost of all 
the flight conveyors, but has the advantages of low power consumption 
(one-half that of the scraper), low stress in chain, long life of chain, trough, 
and flights, and noiseless operation. It has an economical maximum 
capacity of about 120 tons per hour. 

The following formula gives approximately the horse-power at the head 
wheel required to operate flight conveyors: 

H.P. = (ATL + BWS) + 1000. 

T = tons of coal per hour; L = length of conveyor in feet, center to 
center; W = weight of chain, flights, and shoes (both runs) in pounds; 
<S = speed in feet per minute; A and B constants depending on angle of 
incline from horizontal. See example below. 



1174 



HOISTING AND CONVEYING. 



Values of A and B. 



Angle, 
Deg. 


A 


B 


Angle, 
Deg. 


A 


B 


Angle, 
Deg. 


A 


B 





0.343 


0.01 


10 


0.50 


0.01 


30 


0.79 


0.009 


2 


0.378 


0.01 


14 


0.57 


0.01 


34 


0.84 


0.008 


4 


0.40 


0.01 


18 


0.63 


0.009 


38 


0.88 


0.008 


6 


0.44 


0.01 


22 


0.69 


0.009 


42 


0.92 


0.007 


8 


0.47 


0.01 


26 


0.74 


0.009 


46 


0.95 


0.007 



For suspended flight conveyors take B as 0.8, and for roller flights as 0.6, 
of the values given in the table. 

Weight of Chain in Pounds per Foot. 



Link-belting. 


Monobar. 


Chain 
No. 


Pitch of Flights, 
Inches. 


Chain 

No.* 


Pitch of Flights, Inches. 


12 

~2T4 
2.8 
3.1 
4.6 
4.9 
5.6 
6.3 
8.1 
8.9 


18 

2.3 
2.7 
2.8 
4.4 
4.7 
5.2 
6.0 
7.7 
8.4 


24 

2.26 
2.6 
2.7 
4.3 
4.4 
4.9 
5.9 
7.4 
8.2 


36 

~~2l 

2.5 
2.6 
4.2 

4.1 
4.7 
5.7 
7.2 
7.9 


12 


18 


24 
T6 

4.9 

'9.6 

14.7 


36 

~X5 
2.8 
5.5 

ib'j' 

"\\'.8 


48 


54 


72 


78 


612 
618 
818 
824 
1018 
1024 
1224 
1236 
1424 




88 


3 

5 


.0 
.7 




2.7 
5.3 




85 






103 


4.7 


4.6 


108 




11 


.5 


10.4 


110 


9.07 
14.04 


8.8 
13.8 
11.34 
19.4 


114 










122 










124 








20.5 


19.7 




* In monobar the first one or two figures in the number of the chain 
denote the diameter of the chain in eighths of an inch. The last two fig- 
ures denote the pitch in inches. 


Pin Chains. 


Roller Chains. 


No. 


Pitch of Flights, 
Inches. 




No. 


Pitch of Flights, Inches. 




12 


18 


24 


3 


12 


18 


24 


36 






— 


720 
730 
825 


5.9 
6.9 
9.6 


5.6 
6.6 
9.3 


5.4 
6.4 
9.1 


5.3 
6.3 

8.9 


1112 
1113 
1130 


7.7 
9.5 
10.5 


6.9 
8.8 
9.5 


6.2 
8.0 
9.0 


5.7 
7.5 
7.8 






Weight of Flights with Wearing-shoes and Bolts. 


Size, Inches. 


' Steel. 


Malleable Iron. 


Suspended Flights. 


Size. 


Y 


height, Lb. 


4x10 
4x12 
5x10 
5x12 
5x15 
6x18 
8x18 
8x20 
8x24 
10x24 


3.5 
3.9 
4.1 
4.6 
5.8 
8.1 
10.1 
11.0 
12.6 
15.2 


4.3 
4.7 
5.2 
5.7 
5.9 
9.2 
12.7 
13.4 
14.4 
17.4 


6x14 
8x19 
10x24 
10x30 
10x36 
10x42 


12.37 
15.55 
25.57 
29.37 
33.17 
34.97 



COAL-HANDLING MACHINERY. 



1175 



Example. — Required the H.P. for a rnonobaf conveyor 200 ft. center 
to center carrying 100 tons of coal per hour, up a 10° incline at a speed 
of 100 feet per minute. Conveyor has No. 818 chain and 8X19 suspended 
flights, spaced 18 inches apart. 

0.5 X 100 X 200 + 0.008 (400 X 5.7 + 267 X 15.55) X 100 . 
1000 

The following table shows the conveying capacities of various sizes of 
flights at 100 feet per minute in tons, of 2000 lb., per hour. The values 
are true for continuous feed only. 



H.P. 



= 15.15. 





Horizontal Conveyors. 


Inclined Conveyors. 


Size of 
Flight. 


Flight 

Every 

16". 


Flight 

Every 

18". 


Flight 

Every 
24". 


Pounds 
Coal per 
Flight. 


10° 

Flights 
Every 

24". 


20° 

Flights 

Every 

24". 


30° 

Flights 

Every 

24". 


6x14 
8x19 


Tons. 
69.75 


Tons. 
62 
130 


Tons. 
46.5 
97.5 

172.5 

220 

268 

315 


31 
65 
115 
147 
179 
210 


Tons. 

40.5 

78 
150 
184 
225 
264 


Tons. 

31.5 

62 
120 
146 
177 
210 


Tons. 
22.5 
52 


10x24 




90 


10x30 






116 


10x36 






142 


!0x42 






167 



















Bucket Conveyors. — Rigid bucket-carriers are used to convey large 
quantities of coal over a considerable distance when there is no inter- 
mediate point of discharge. These conveyors are made with two strands 
of steel roller chain. They are built to carry as much as 10 tons of coal 
per minute. 

Screw Conveyors. — Screw conveyors consist of a helical steel flight, 
either in one piece or in sections, mounted on a pipe or shaft, and running 
in a steel or wooden trough. These conveyors are made from 4 to 18 
inches in diameter, and in sections 8 to 12 feet long. The speed ranges 
from 20 to 60 revolutions per minute and the capacity from 10 to 30 tons 
of coal per hour.,, It is not advisable to use this type of conveyor for coal, 
as it will only handle the smaller sizes and the flights are very easily dam- 
aged by any 'foreign substance of unusual size or shape. 

Belt Conveyors. — Rubber and cotton belt conveyors are used for 
handling coal, ore, sand, gravel etc., in all sizes. They combine a high 
carrying capacity with low power consumption. 

In some cases the belt is flat, the material being fed to the belt at its 
Center in a narrow stream. In the majority of cases, however, the belt 
is troughed by means of idler pulleys set at an angle from the horizontal 
and placed at intervals along the length of the belt. Rubber belts are 
often made more flexible for deep troughing by removing some of the 
layers of cotton from the belt and substituting therefor an extra thickness 
of rubber. 

Belt conveyors may be used for elevating materials up to about 23° 
incline. On greater inclines the material slides back on the belt and spills. 
With many substances it is important to feed the belt steadily if the con- 
veyor stands at or near the limiting angle. If the flow is interrupted 
the material may slide back on the belt. 

Belt conveyors are run at any speed from 200 to 800 feet per minute, 
and are made in widths varying from 12 inches to 60 inches. 

Capacity of Belt Conveyors in Tons of Coal per Hour. 



Width 
of 


Velocity, Feet per 
Minute. 


Width 

of 
Belt, 
ins. 


Velocity, Feet per Minute. 


Belt, 
Ins. 


300 


350 


400 


300 


35G 


400 


450 


500 


12 
14 
16 

18 


34 

47 
62 
78 


72 
91 


82 
104 


20 
24 
30 
36 


96 
139 
218 
315 


112 
162 
254 
368 


128 
186 
290 
420 


210 
326 

472 


520 



1176 



HOISTING AND CONVEYING. 



For materials other than coal, the figures in the above table should be 
multiplied by the coefficients given in the table below: 



Material. 


Coefficient. 


Material. 


Coefficient. 




0.86 
1.76 
1.26 
0.60 


Earth 

Sand 

Stone (crushed) 


1.4 




1.8 


Clay 


2.0 


Coke 





Belt Conveyor Construction. (C. K. Baldwin, Trans. A. S. M. E., 
1908.) — The troughing idlers should be spaced as follows, depending 
on the weight of the material carried: 



Belt width 
Spacing, ft. 



12-16 in. 
41/2-5 



18-22 in. 
4-41/2 



24-30 in. 
31/2-4 



32-36 in. 
3-31/2 



The stress in the belt should not exceed 18 to 20 lb. per inch of width 
per ply with rubber belts. This may be increased about 20% with belts 
in which 28 oz. duck is used. Where the power required is small the stiff- 
ness of the belt fixes the number of plies. The minimum number of plies 
is as follows: 



Belt width, in. 
Minimum plies 



12-14 
3 



16-20 
4 



22-28 
5 



30-36 
6 



Pulleys of small diameter should be avoided on heavy belts, or the con- 
stant bending of the belt under heavy stress will cause the friction to lose 
its hold and destroy the belt. In many cases it is advisable to cover the 
driving pulley with a rubber lagging to increase the tractive power, 
particularly in dusty places. The minimum size of driving pulleys to be 
used is shown in the table below. 



Smallest Diameter of Driving Pulleys for Belt Conveyors. 



Width of 
Belt. 


Diameter 
of Pulley. 


Width of 
Belt. 


Diameter of 
Pulley. 


Width of 
Belt'. 


Diameter of 
Pulley. 


In. 
12 
14 
16 
18 


In. 

16-18 

16-18 

20-24 

20-24 

20-24 


In. 

22 
24 
26 
28 
30 


In. 

20-30 

24-30 

24-30 

24-30 

30-36 


In. 
32 
34 
36 


In. 
30-36 
30-42 
30-48 


20 







Horse-power to Drive Belt Conveyors. (C. K. Baldwin, Tra^s. 
A. S. M. E., 1908.) — The power required to drive a belt conveyor de- 
pends on a great variety of conditions, as the spacing of idlers, type of 
drive, thickness of belt, etc. In' figuring the power required, the belt 
should run no faster than is necessary to carry the desired load. If it 
should be necessary to increase the speed, the load should be increased 
in proportion and the power figured accordingly. 

For level conveyors 

HP. = CX TX L + 1000. 
For inclined conveyors 

H.P. = (C X T X L -5- 1000) + (TX H -*■ 1000). 

C = power constant from table below; T = load, tons per hour; L = 
length of conveyor, center to center, ft.; H= vertical height material is , 
lifted, ft.; S = belt speed, ft per minute: B = width of belt, in. 

For each movable or fixed tripper add horse-power in column 3 of table, i 
Add 20% to horse-power for each conveyor under 50 ft. long. Add 10% to | 
horse-power for each conveyor between 50 ft. and 100 ft. long. The for- i 
mulse above do not include gear friction, should the conveyor be gear- ! 
driven. 



WIRE-ROPE HAULAGE. 



1177 



Constants for Formulae Above. 





1 


2 


3 


4 


5 


Width of 
Belt. 


C for Mate- 
rial Weigh- 
ing from 25 
Lb. to 75 Lb. 
per Cu. Ft. 


C for Mate- 
rial Weigh- 
ing from 75 
Lb. to 125 Lb. 
per Cu. Ft. 


H.P. Re- 
quired for 
Each Mov- 
able or 
Fixed 
Tripper. 


Minimum 

Plies of 

Belt. 


Maximum 
Plies of 
Belt. 


In. 
12 
14 
16 
18 
20 
22 
24 
26 
28 
30 
32 
34 
36 


0.234 
0.226 
0.220 
0.209 
0.205 
0.199 
0.195 
0.187 
0.175 
0.167 
0.163 
0.161 
0.157 


0.147 
0.143 
0.140 
0.138 
0.136 
0.133 
0.131 
0.127 
0.121 
0.117 
0.115 
0.114 
0.112 


1/2 
1/2 
3/ 4 
I 

11/4 
U/2 
13/4 
2 

21/4 
21/2 
23/ 4 
3 
31/4 


3 
3 
4 
4 
4 
5 
5 
5 
5 
6 
6 
6 
6 


4 
4 
5 
5 
6 
6 
7 
7 
8 
8 
9 
10 
10 



When horse-power and speed are known the stress in the belt in pounds 
per inch of width is 

Stress - H - P - X 33,000 

Stress g^^ 

From this the number of plies can be found, using 20 lb. per ply per 
inch of width as a maximum for rubber belts. 

Relative Wearing; Power of Conveyor Belts. (T. A. Bennett, 
Trans. A. S. M. h\, 1908.) —Different materials used in the construction 
of conveyors were subjected to the uniform action of a sand blast for 45 
minutes, and the relative abrasive resisting qualities were found to be as 
follows, taking the volume of rubber belt worn away as 1.0: 

Rubber belt 1.0 Woven cotton belt, high grade 6.5 

Rolled steel bar 1.5 Stitched duck, high grade 8.0 

Cast iron 3.5 Woven cotton belt, low grade, 9.0 to 

Balata belt, including gum cover 5.0 15.0 

A Symposium on Hoisting and Conveying was presented at the Detroit 
meeting of the A. S. M. E, 1908 (Trans., vol. xxx.), in papers by G. E. 
Titcomb, S. B. Peck, C. K. Baldwin, C. J Tomlinson and E. J. Haddock. 
Among the subjects discussed are the loading and unloading of cargo 
steamers; car unloaders; storing of ore and coal; continuous conveying of 
merchandise; conveying in a Portland cement plant, and suspension 
cableways. 

WIRE-ROPE HAULAGE. 

Methods for transporting coal and other products by means of wire rope, 
though varying from each other in detail, may be grouped in five classes: 
I. The Self-acting or Gravity Inclined Plane. 
II. The Simple Enefine-plane. 

III. The Tail-rope System. 

IV. The Endless-rope Svstem. 
V. The Cable Tramway. 

The following brief description of these systems is abridged from a 
pamphlet on Wire-rope Haulage, by Wm. Hildenbrand, C.E., published 
by John A. Roebling's Sons Co., Trenton, N. J. 

I. The Self-acting: Inclined Plane. — The motive power for the 
self-actins: inclined plane is gravity: consequently this mode of transport- 
ins: coal finds application only in places where the coal is conveyed from a 
higher to a lower point and where the plane has sufficient grade for the 
loaded descending cars to raise the empty cars to an upper level. 



1178 HOISTING AND CONVEYING. 

At the head of the plane there is a drum, which is generally constructed 
of wood, having a diameter of seven to ten feet. It is placed high enough 
to allow men and cars to pass under it. Loaded cars coming from the pit 
are either singly or in sets of two or three' switched on the track of the 
plane, and their speed in descending is regulated by a brake on the drum. 

Supporting rollers, to prevent the rope dragging on the ground, are 
generally of wood, 5 to 6 in. in diameter and 18 to 24 in. long, with 
3 /4 to 7/ 8 in. iron axles. The distance between the rollers varies from 15 to 
30 ft., steeper planes requiring less rollers than those with easy grades. 
Considering only the reduction of friction and what is best for the preserva- 
tion of rope, a general rule may be given to use rollers of the greatest 
possible diameter, and to place them as close as economy will permit. 

The smallest angle of inclination at which a plane can be made self- 
acting will be when the motive and resisting forces balance each other. 
The motive forces are the weights of the loaded car and of the descending 
rope. The resisting forces consist of the weight of the empty car and 
ascending rope, of the rolling and axle friction of the cars, and of the axle 
friction of the supporting rollers. The friction of the drum, stiffness of 
rope, and resistance of air may be neglected. A general rule cannot be 
given, because a change in the length of the plane or in the weight of the 
cars changes the proportion of the forces; also, because the coefficient of 
friction, depending on the condition of the road, construction of the cars, 
etc., is a very uncertain factor. 

For working a plane with a 5/8-in. steel rope and lowering from one to 
four pit cars weighing empty 1400 lb. and loaded 4000 lb., the rise in 100 ft. 
necessary to make the plane self-acting will be from about 5 to 10 ft., 
decreasing as the number of cars increase, and increasing as the length of 
plane increases. . . 

A gravity inclined plane should be slightly concave, steeper at the top 
than at the bottom. The maximum deflection of the curve should be at 
an inclination of 45 degrees, and diminish for smaller as well as for steeper 
inclinations. 

II. The Simple Engine-plane. — The name " Engine-plane" is given 
to a plane on which a load is raised or lowered by means of a single wire 
rope and stationary steam-engine. It is a cheap and simple method of 
conveying coal underground, and therefore is applied wherever circum- 
stances permit it. Under ordinary conditions such as prevail in the 
Pennsylvania mine region, a train of twenty-five to thirty loaded cars will 
descend, with reasonable velocity, a straight plane 5000 ft. long on a 
grade of 13/4 ft. in 100, while it would appear that 21/4 ft. in 100 is neces- 
sary for the same number of empty cars. For roads longer than 5000 ft. 
or containing sharp curves, the grade should be correspondingly larger. 

III. The Tail-rope System. — Of all methods for conveying coal 
underground by wire rope, the tail-rope system has found the most appli- 
cation. It can be applied under almost any condition. The road may be 
straight or curved, level or undulating, in one continuous line or with side 
branches. In general principle a tail-rope plane is the same as an engine- 
plane worked in both directions with two ropes. One rope, called the 
" main rope," serves for drawing the set of full cars outward; the other, 
called the " tail-rope," is necessary to take back the empty set, which on 
a level or undulating road cannot return by gravity. The two drums may 
be located at the opposite ends of the road, and driven by separate engines, 
but more frequently they are on the same shaft at one end of the plane. 
In the first case each rope would require the length of the plane, but in the 
second case the tail rope must be twice as long, being led from the drum 
around a sheave at the other end of the plane and back again to its starting- 
point. When the main rope draws a set of full cars out, the tail-rope drum 
runs loose on the shaft, and the rope, being attached to the rear car, un- 
winds itself steadily. Going in, the reverse takes place. Each drum is 
provided with a brake to check the speed of the train on a down grade and 
prevent its overrunning the forward rope. As a rule, the tail rope is 
strained less than the main rope, but in cases of heavy grades dipping out- 
ward it is possible that the strain in the former may become as large, or 
even larger, than in the latter, and in the selection of the sizes reference 
should be had to this circumstance. 

IV. The Endless-rope System. — The principal features of this 
system are as follows: 

1. The rope, as the name indicates, is endless. 2. Motion is given to 



WIRE-ROPE HAULAGE. 



1179 



the rope by a single wheel or drum, and friction is obtained either by a 
grip-wheel or by passing the rope several times around the wheel. 3. The 
rope must be kept constantly tight, the tension to be produced by artificial 
means. It is done in placing either the return-wheel or an extra tension 
wheel on a carriage and connecting it with a weight hanging over a 
pulley, or attaching it to a fixed post by a screw which occasionally can be 
shortened. 4. The cars are attached to the rope by a grip or clutch, 
which can take hold at any place and let go again, starting and stopping 
the train at will, without stopping the engine or the motion of the rope. 
5. On a single-track road the rope works forward and backward, but on a 
double track it is possible to run it always in the same direction, the full 
cars going on one track and the empty cars on the other. 

This method of conveying coal, as a rule, has not found as general an in- 
troduction as the tail-rope system, probably because its efficacy is not so 
apparent and the opposing difficulties require greater mechanical skill and 
more complicated appliances. Its advantages are, first, that it requires 
one-third less rope than the tail-rope system. This advantage, however, 
is partially counterbalanced by the circumstance that the extra tension in 
the rope requires a heavier size to move the same load than when a main 
and tail rope are used. The second and principal advantage is that it is 
possible to start and stop trains at will without signaling to the engineer. 
On the other hand, it is more difficult to work curves with the endless sys- 
tem, and still more so to work different branches, and the constant stretch 
of the rope under tension or its elongation under changes of temperature 
frequently causes the rope to slip on the wheel, in spite of every attention, 
causing delay in the transportation and injury to the rope. 

Stress in Hoisting-ropes on Inclined Planes. 

(Trenton Iron Co., 1906.) 



^ 












.j 






fa 


■J. 


A® 


£_• 


■J. 


A§ 


fa . 


■J; 


J*g 


2T5 
Si 


c • 
»-H a 

u o 
0'£ 


J2 


t* o 


e>V3 


•-a e 


© c 
~~ o 


"3 




ftN 


a 
< 


02 t-,° 
£ 5 § 




c 
< 


||1 




1 

< 


III 

CO 


Ft. 






Ft. 






Ft. 






5 


2° 52' 


140 


55 


28° 49' 


1003 


no 


47° 44' 


1516 


10 


5° 43' 


240 


60 


30° 58' 


1067 


120 


50° 12' 


1573 


15 


8° 32' 


336 


65 


33° 02' 


1128 


130 


52° 26' 


1620 


20 


11° 10' 


432 


70 


35° 00' 


1185 


140 


54° 28' 


1663 


25 


14° 03' 


527 


75 


36° 53' 


1238 


150 


56° 19 7 


1699 


30 


16° 42' 


613 


80 


38° 40' 


1287 


160 


58° 00' 


1730 


35 


19° 18' 


700 


85 


40° 22' 


1332 


170 


59° 33' 


1758 


40 


21° 49' 


782 


90 


42° 00' 


1375 


180 


60° 57' 


1782 


45 


24° 14' 


860 


95 


43 o 32 / 


1415 


190 


62° 15' 


1804 


50 


26° 34' 


933 


100 


45° 00' 


1450 


200 


63° 27' 


1822 



The above table is based on an allowance of 40 lb. per ton for rolling 
friction, but an additional allowance must be made for stress due to the 
weight of the rope proportional to the length of the plane. A factor of 
safety of 5 to 7 should be taken. 

In hoisting the slack-rope should be taken up gently before beginning 
the lift, otherwise a severe extra strain will be brought on the rope. 

V. Wire-rope Tramways. — The methods of conveying products on 
a suspended rope tramway find especial application in places where a mine 
is located on one side of a river or deep ravine and the loading station on 
the other. A wire rope suspended between the two stations forms the 
track on which material in properly constructed " carriages " or " buggies" 
is transported. It saves the construction of a bridge or trestlework and is 
practical for a distance of 2000 feet without an intermediate support. 

There are two distinct classes of rope tramways: 



1180 HOISTING AND CONVEYING. 

1. The rope is stationary, forming the track on which a bucket holding 
the material moves forward and backward, pulled by a smaller endless 
wire rope. 2. The rope is movable, forming itself an endless line, which 
serves at the same time as supporting track and as pulling rope. 

Of these two the first method has found more general application, and is 
especially adapted for long spans, steep inclinations, and heavy loads 
The second method is used for long distances, divided into short spans 
and is only applicable for light loads which are to be delivered at regular 
intervals. 

For detailed descriptions of the several systems of wire-rope transporta- 
tion, see circulars of John A. Roebling's Sons Co., The Trenton Iron Co., 
A. Leschen & Sons Rope Co. See also paper on Two-rope Haulage Sys- 
tems, by R. Van A. Norris, Trans. A. S. M. E., xii. 626. 

In the Bleichert System of wire-rope tramways, in which the track rope 
is stationary, loads up to 2000 lb. are carried at a speed cf 3 to 4 miles per 
hour. While the average spans on a level are from 150 to 200 ft., in cross- 
ing rivers, ravines, etc., spans up to 1500 ft. are frequently adopted. In a 
tramway on this system at Bingham, Utah, the total length of the line is 
12,700 ft. with a fall of 1120 ft. The line operates by gravity and carries 
35 tons per hour. The cost of conveying on this carrier is 73/4 cents per 
ton of 2000 lb. for labor and repairs, without any apparent deterioration 
in the condition of track cables and traction rope. 

The Aerial Wire-rope Tramway of A. Leschen & Sons Co. is of the 
double-rope type, in which the buckets travel upon stationary track 
cables and are propelled by an endless traction rope. The buckets are 
attached to the traction rope by means of clips — spaced according to 
the desired tonnage. The hold on the rope is positive, but the clip is 
easily removable. The bucket is held in its normal position in the frame 
by two malleable iron latches — one on each side. A tripping bar 
engages these latches at the unloading terminal when the bucket dis- 
charges its material. This operation is automatic and takes place while 
the carriers are moving. At the loading terminal, the bucket is auto- 
matically returned to its normal position and latched. Special carriers 
are provided for the accommodation of any class of material. At each 
of the terminal stations is alO-ft. sheave wheel around which the trac- 
tion rope passes, these wheels being provided with steel grids for the 
control of the traction rope. When the loaded carriers travel down 
grade and the difference in elevation is sufficient; this tramway will 
operate by the force due to gravity, otherwise the power is applied to 
the sheaves through bevel gearing. Numerous modifications of the 
system are in use to suit different conditions. 

An Aerial Tramway 21.5 miles long, with an elevation of the loading 
end above the discharging end of 11,500 ft., built by A. Bleichert & Co. 
for the government of the Argentine Republic, connecting the mines of 
La Mejicana with the town of Chilecito, is described by Wm. Hewitt in 
Indust. Eng., Aug. 15, 1909. Some of the inclinations are as much as 
45 deg., there are some spans nearly 3000 ft. long, and there is a tunnel 
nearly 500 ft. long. The line is divided into eight sections, each with 
an independent traction rope. The gravity of the descending loaded 
carriers is sufficient to make the line self-operating when it is once set 
in motion, but in order to ensure full control, and to provide for carrying 
four tons upward while the descending carriers are empty, four steam 
engines are installed, one for each two sections. The carriers hold 10 cu. 
ft., or about 1100 lbs. of ore. The speed is 500 ft. per minute, and the 
interval between carriers 45 seconds. The stress in the traction rope is 
as high as 11,000 lbs. in some sections. 

General Formulae for Estimating the Deflection of a Wire Cable 
Corresponding to a Given Tension. 

(Trenton Iron Co., 1906.) 

Let s = distance between supports or span AB; m and n = arms into 
which the span is divided by a vertical through the required point of 
deflection x, m representing the arm corresponding to the loaded side; 
y = horizontal distance from load to point of support corresponding with 
m; w — wt. of rope per ft.; g = load; t = tension; h = required deflection 
at any point z; all measures being in feet and pounds. 



WIEE-ROPE HAULAGE. 1181 



h\ 

Fig. 184. 
For deflection due to rope alone, 

. mnw , ws 2 . . . 

ft = . at x, or -~- at center of span. 

For deflection due to load alone, 

h = —~ at x, or — . at center of span. 

If V = V2 s, ft = —, at .r, or j- at center of span. 

^at:r,orf fi 
ts ' 4t 



If // = ?», ft = —7 — at a*, or —. at center of span. 



For total deflection, 

, wmns + 2 gny , ws 2 + 4 gy . , . 

ft = —, — - — at x, or - — —7 — - at center of span. 

T , , . , wmn + gn , ws 2 + 2 gs . . 

If y = V2 s, ft = —, — - at x, or ^-7 at center of span. 

_. . wmns + 2 gmn . ids 2 + 2 gs , . . 

If y = m, ft = —: — - — at x, or — -, at center of span. 

2 is St 

If the tension is required for a given deflection, transpose t and ft in 
above formulae. 

Suspension Cableways or Cable Hoist-conveyors. 

(Trenton Iron Co.) 

In quarrying, rock-cutting, stripping, piling, dam-building, and many 
other operations where it is necessary to hoist and convey large individual 
loads economically, it frequently happens that the application of a system 
of derricks is impracticable, by reason of the limited area of their effi- 
ciency and the room which they occupy. To meet such conditions cable 
hoist-conveyors are adopted, as they can be operated in clear spans up to 
1500 ft., and in lifting individual loads up to 15 tons. Two types are 
made — ■ one in which the hoisting and conveying are done by separate 
running ropes, and the other applicable only to inclines in which the 
carriage descends by gravity, and but one running rope is required. The 
moving of the carriage in the former is effected by means of an endless 
rope, and these are commonly known as " endless-rope " hoist-conveyors 
to distinguish them from the latter, which are termed " inclined " hoist- 
conveyors. 

The general arrangement of the endless-rope hoist-conveyors consists 
of a main cable passing over towers, A-frames or masts, as may be most 
convenient, and anchored firmly to the ground at each end, the requisite 
tension in the cable being maintained by a turnbuckle at one anchorage. 

Upon this cable travels the carriage, which is moved back and forth 
over the line by means of the endless rope. The hoisting is done by a 
separate rope, both ropes being operated by an engine specially designed 
for the purpose, which may be located at either end of the line, and is 
constructed in such a way that the hoisting-rope is coiled up or paid out 
automatically as the carriage is moved in and out. Loads may be picked 
up or discharged at any point along the line. Where sufficient inclination 
can be obtained in the main cable for the carriage to descend by gravity, 
and the loading and unloading are done at fixed points, the endless rope can 
be dispensed with. The carriage, which is similar in construction to the 
carriage used in the endless-rope cableways, is arrested in its descent by a 



1182 



HOISTING AND CONVEYING. 



stop-block, which may be clamped to the main cable at any desired point, 
the speed of the descending carriage being under control of a brake on the 
engine^drum. 

A Double-suspension Cableway, carrying loads of 15 tons, erected near 
Williamsport, Pa., by the Trenton Iron Co., is described by E. G. Spilsbury 
in Trans. A. I. M. E t( xx. 766. The span is 733 ft., crossing the Susque- 
hanna River. Two steel cables, each 2 in. diam^ are used. On these 
cables runs a carriage supported on four wheels and moved by an endless 
cable 1 inch in diam. The load consists of a cage carrying a railroad-car 
loaded with lumber, the latter Weighing about 12 tons. The power is 
furnished by a 50-H.P. engine, and the trip across the river is made in 
about three minutes. 

A hoisting cableway on the endless-rope system, erected by the Lidger- 
wood Mfg. Co., at the Austin Dam, Texas, had a single span 1350 ft. in 
length, with main cable 21/2 in. diam., and hoisting-rope 13/ 4 in. diam. 
Loads of 7 to 8 tons were handled at a speed of 600 to 800 ft. per minute. 

Another, of still longer span, 1650 ft., was erected by the same company 
at Holyoke, Mass., for use in the construction of a dam. The main cable 
is the Elliott or locked-wire cable, having a smooth exterior. In the con- 
struction of the Chicago Drainage Canal twenty cableways 1 , of 700 ft. span 
and 8 tons capacity, were used, the towers traveling on rails, 

Tension required to Prevent Slipping of Rope on Drum. (Trenton 
Iron Co., 1906.) — The amount of artificial tension to be applied in an 
endless rope to prevent slipping on the driving-drum depends on the char- 
acter of the drum, the condition of the rope and number of laps which it 
makes. If T and S represent respectively the tensions in the taut and 
slack lines of the rope; W, the necessary weight to be applied to the tail- 
sheave; R, the resistance of the cars and rope, allowing for friction; n, the 
number of half-laps of the rope on the driving-drum; and /, the coefficient 
of friction, the following relations must exist to prevent slipping: 



: St/ nn , W = T+ S, and R -- 



from which we obtain W ■■ 



efnn_ 



-R, 



in which e = 2.71828, the base of the Naperian system of logarithms. 
The following are some of the values of /: 

Dry. Wet. 
Wire-rope on a grooved iron drum. ... 0. 120 0.085 

Wire-rope on wood-filled sheaves 0. 235 0. 170 

Wire-rope on rubber and leather filling 0.495 0.400 
The importance of keeping the rope dry is evident from these figures. 
e fnrr j j 

The values of the coefficient — : . corresponding to the above values 

e fnn_ t 

off, for one up to six half-laps of the rope on the driving-drum or sheaves, 
are as follows: 



Greasy. 
0.070 
0.140 
0.205 



/ 


n - Number of Half-laps on Driving-wheel. 


\ 


2 


3 


4 


5 


6 


0.070 


9.130 


4.623 


3.141 


2.418 


1.999 


1.729 


0.085 


7.536 


3.833 


2.629 


2.047 


1.714 


1.505 


0.120 


5.345 


2. 777 


1.953 


1.570 


1.358 


1.232 


0.140 


4.623 


2.418 


1.729 


1.416 


1.249 


1.154 


0.170 


3.833 


2.047 


1.505 


1.268 


1.149 


1.085 


0.205 


3.212 


1.762 


1.338 


1.165 


1.083 


1.043 


0.235 


2.831 


1.592 


1.245 


1.110 


1.051 


1.024 


0.400 


1.795 


1.176 


1.047 


1.013 


1.004 


1.001 




1.538 


1.093 


1.019 


1.004 


r .001 









TRANSMISSION OF POWER BY WIRE ROPE. 1183 

r When the rope is at rest the tension is distributed equally on the two 
lines of the rope, but when running there will be a difference in the tensions 
of the taut and slack lines equal to the resistance, and the values of T and S 
may be readily computed from the foregoing formulae. 

The increase in tension in the endless rope, compared with the main rope 
of the tail-rope system, where the stress in the rope is equal to the resist- 
ance, is about as follows: 

n= 12 3 4 5 6 

Increase in tension in endless rope, 
compared with direct stress % 40 9 21/3 2/3 1/5 1/ 10 

These figures are useful in determining the size of rope. For instance, 
if the rope makes two half-laps on the driving drum, the strength of the 
rope should be 9% greater than a main rope in the tail-rope syste.n. 

Taper Ropes of Uniform Tensile Strength. — The true form of rope 
is not a regular taper but follows a logarithmic curve, the girth rapidly 
increasing toward the upper end. Mr. Chas. D. West gives the following 
formula, based on a breaking strain of 80,000 lb. per sq. in. of the rope, 
core included, and a factor of safety of 10: log G = i^-^3680 -f log g, in 
which F = length in fathoms, and G and g the girth in inches at any two 
sections F fathoms apart. The girth g is first calculated for a safe strain 
of 8000 lb. per sq. in., and then G is obtained bv the formula. For a 
mathematical investigation see The Engineer, April, 1880, p. 267. 



TRANSMISSION OF POWER BY 
WIRE ROPE. 

The following notes have been furnished to the author by Mr. Wm, 
Hewitt, Vice-President of the Trenton Iron Co, (See also circulars of the 
Trenton Iron Co. and of the John A. Roebling's Sons Co., Trenton, N. J.; 
" Transmission of Power by Wire Ropes," by A. W. Stahl, Van Nostrand's 
Science Series, No. 28; and Reuleaux's Constructor.) 

The load stress or working tension should not exceed the difference 
between the safe stress and the bending stress as determined by the table 
on page 1185. 

The approximate strength of iron-wire rope composed of wires hav- 
ing a tensile strength of 75,000 to 90,000 lbs. per sq. in. is half that of 
cast-steel rope composed of wires of a tensile strength of 150,000 to 
190,000 lbs. per sq. in. Extra strong steel wires have a tensile strength 
of 190,000 to 225,000 and plow-steel wires 225,000 to 275,000 lbs. per 
sq. in. 

The 19-wire rope is more flexible than the 7-wire, and for the same 
load stress may be run around smaller sheaves, but it is not as well 
adapted to withstand abrasion or surface wear. 

The working tension may be greater, therefore, as the bending stress 
is less; but since the tension in the slack portion of the rope cannot be 
less than a certain proportion of the tension in the taut portion, to avoid 
slipping, a ratio exists between the diameter of sheave and the wires 
composing the rope corresponding to a maximum safe working tension. 
This ratio depends upon the number of laps that the rope makes about 
the sheaves, and the kind of filling in the rims or the character of the 
material upon which the rope tracks. 

For ordinary purposes the maximum safe stress should be about one- 
third the ultimate, and for shafts and elevators about one-fourth the ulti- 
mate. In estimating the stress due to the load for shafts and elevators 
allowance should be made for the additional stress due to acceleration in 
starting. For short inclined planes not used for passengers a factor of 
safety as low as 2 1/2 is sometimes used, and for derricks, in which large 
sheaves cannot be used, and long life of the rope is not expected, the 
factor of safety may be as low as 2. 



1184 TRANSMISSION OF POWER BY WIRE ROPE. 



The Seale wire rope is made of six strands of 19 wires, laid 9 around 9 
around 1, the intermediate layer being smaller than the others. It is 
intermediate in flexibility between the 7-wire and the ordinary 19-wire 
rope. 

Approximate Breaking Strength of Steel-Wire Ropes. 



6 strands of 19 


wires each. 




6 strands of 7 


wires each. 


a 

o 

ni • 




Approximate breaking 


fi? 




Approximate breaking 


Wt. 




stress, lbs 




O 

r 

s 


Wt. 


stress, lbs. 


. a 


















ft., 

lbs. 


Cast 
steel. 


Extra 
strong 
steel. 


Plow 
steel. 


ft., 

lbs. 


Cast 
steel. 


Extra 
strong 
steel. 


Plow 
steel. 


21/4 


8.00 


312,000 


364,000 


416,000 


H/9 


3.55 


136,000 


158,000 


182,000 


2 


6.30 


248,000 


288,000 


330,000 


1 3/8 


3.00 


116,000 


136,000 


156,000 


N/ 4 


4.85 


192,000 


224,000 


256,000 


U/4 


2.45 


96,000 


112,000 


128,000 


l>/8 


4.15 


168,000 


194,000 


222,000 


U/8 


2.00 


80,000 


92,000 


106,000 


IV? 


3.55 


144,000 


168,000 


192,000 


1 


1.58 


64,000 


74,000 


84,000 


N/8 


3.00 


124,000 


144,000 


164,000 


Vh 


1.20 


48,000 


56,000 


64,000 


U/4 


2.45 


100,000 


116,000 


134,000 


3/ 4 


0.89 


37,200 


42,000 


48,000 


iVs 


2.00 


84,000 


98,000 


112,0 i 


U/18 


0.75 


31,600 


36,800 


42,000 


l 


1.58 


68,000 


78,000 


88,000 


5/8 


0.62 


26,400 


30,200 


34,000 


V/8 


1.20 


52,000 


60,000 


68,000 


»/lfl 


0.50 


21,200 


24,600 


28,000 


V4 


0.89 


38,800 


44,000 


50,000 


l/o 


0.39 


16,800 


19,400 


22,000 


W8 


0.62 


27,200 


31,600 


36,000 


7/1 ft 


0.30 


13,200 


15,000 


17,100 


»/l« 


0.50 


22,000 


25,400 


29,000 


3/8 


0.22 


9,600 


11,160 


12,700 


V2 
7/6 
3/8 


39 


17,600 
13,600 


20,200 
15,600 


22,800 
17,700 
13,100 


5/16 
9 /32 


15 


6,800 
5,600 


7,760 
6,440 




0.30 


125 




0.22 


10,000 


11,500 






■Vifi 


0.15 


6,800 


8,100 














V4 


0.10 


4,800 


5,400 















The sheaves (Fig. 185) are usually of cast iron, and are made as light 
as possible consistent with the requisite strength. Various materials 

+ sfit'-^-o nave been used for fillm g tne bottom of the 

't \ I a Section groove, such as tarred oakum, jute yarn, 

J a ! a ofRim hard wood, India-rubber, and leather. The 

filling which gives the best satisfaction, how- 
^ ever, in ordinary transmissions consists of 
m J|a segments of leather and blocks of India- 
jr j§^3§L of Arm 111 rubber soaked in tar and packed alternately 

T i f Mm M ' W in tne g roove - Where the working tension 

v is very great, however, the wood filling is 
to be preferred, as in the case of long-dis- 
tance transmissions where the rope makes 
several' laps about the sheaves, and is run 
at a comparatively slow speed. 

The Bending Stress is determined by 
the formula 

*- Ea 




Fig. 185. 



' 2.06 (R -s- d)+ C 



k = bending stress in lbs.; E = modulus of elasticity = 28,500,000: 
=» aggregate area of wires, sq. ins.; R = radius of bend; d = diam, of 
/ires, ins. 

For 7-wire rope d=i/9 diam. of rope; C = 9.27. 

" 19-wire " d = Vi5 " " " ; C = 15.45. 

" the Seale cabled = 1/12 " " " ; C = 12.36. 
From this formula the tables below have been calculated. 



TRANSMISSION OF POWER BY WIRE ROPE. 



1185 



Bending Stresses, 7-wire Rope. 



Diam. bend. 


24 


36 


48 


60 


72 


84 


96 


108 


120 


132 


Diam. Rope. 






















Hi 


826 


553 


412 


333 


277 


238 


208 


185 


166 


151 


9 /32 


1,120 


750 


563 


451 


376 


323 


282 


251 


226 


206 


5/16 


1,609 


1,078 


810 


649 


541 


464 


406 


361 


325 


296 


3/8 


2,774 


1,859 


1,398 


1,120 


934 


801 


702 


624 


562 


511 


7/16 


4,385 


2,982 


2,217 


1,777 


1,482 


1,272 


1,113 


990 


892 


811 


V2 


6,200 


4,161 


3,131 


2,510 


2,095 


1,797 


1,574 


1,400 


1,260 


1,146 


9 /l6 


9,072 


6,095 


4,589 


3,679 


3,071 


2,635 


2,308 


2,053 


1,848 


1,681 


5/8 




8,547 


6,438 


5,164 


4,310 


3,699 


3,240 


2,882 


2,595 


2,360 


U /l6 




10,922 


8,230 


6,603 


5,513 


4,731 


4,144 


3,687 


3,320 


3,020 


3/4 




14,202 


10,706 


8,591 


7,174 


6,158 


5,394 


4,799 


4,322 


3,931 


7/8 




22,592 


17,045 


13,685 


11,431 


9,815 


8,599 


7,651 


6,892 


6,269 


1 






25,476 


20,464 


17,100 


14 686 


12 869 


11 452 


10 317 


9,386 


'Vs 






36,289 


29,165 


24,416 


20,942 


18,355 


16 336 


14 718 


13,391 


11/ 4 








40,020 


33,464 


28,754 


25,206 


22,437 


20,216 


18,396 


13/8 










44,551 


38,290 


33,571 


29,888 


26,933 


24,510 


U/ 2 










57,835 


49,718 


43,599 


38,821 


34,987 


31,842 















Bending Stresses, 19-wire Rope. 



Diam. Bend. 


12 


24 


36 


48 


60 


72 


84 


96 


108 


120 


Diam. Rope. 


















V4 


993 


502 


336 


252 


202 


168 


144 


126 


112 


101 


5/16 


1,863 


944 


632 


475 


380 


317 


272 


238 


212 


191 


3/8 


2 771 


1,406 


942 


708 


567 


473 


406 


355 


316 


285 


7/16 


4 859 


2,473 


1,658 


1,247 


1,000 


834 


716 


627 


557 


502 


V2 


7,125 


3,635 


2,440 


1,836 


1,472 


1,228 


1,054 


923 


821 


739 


9 /l6 




5,319 


3,573 


2,690 


2,157 


1,800 


1,545 


1,353 


1,203 


1,084 


5/8 




7,452 


5,011 


3,774 


3,027 


2,526 


2,169 


1,900 


1,690 


1,522 


U/16 




9,767 


6,572 


4,953 


3,973 


3,317 


2,847 


2,494 


2,219 


1,998 


3/4 




12,512 


8,427 


6,352 


5,098 


4,257 


3,654 


3,201 


2,848 


2,565 


7/8 




19,436 


13,111 


9,891 


7,941 


6,633 


5,696 


4,990 


4,440 


3,999 


1 




29,799 


20,136 


15,205 


12,214 


10,206 


8,766 


7,681 


6,836 


'6,158 


U/8 

11/4 






28,153 


21,276 


17,099 


14,293 


12,278 


10,761 


9,578 


8,689 






38,034 


28,766 


23,130 


19,340 


16,618 


14,567 


12,967 


11,(83 


J 3/8 






51,609 


39,067 


31,430 


26,290 


22,594 


19,811 


17,637 


15,893 


M/2 
15/8 
13/4 
17/8 
2 






66,065 


50,049 


40,284 


33,707 


28,976 


25,410 


22,625 


20,390 








62,895 


50,647 


42,391 


36,450 


31,969 


28,470 


25,661 








79,749 


64,252 


53,798 


46,270 


40,590 


36,152 


32,589 








97,018 


78,202 


65,500 


56,347 


49,438 


44,039 


39,701 










94,016 


78,769 


67,778 


59,478 


52,989 


47,777 


21/4 










134,319 


112,611 


96,943 


85,103 


75,F40 


68,396 


2V2 












154,870 


133,386 


117,137 


104,417 


94,189 

















Horse-Power Transmitted. — The general formula for the amount 
of power capable of being transmitted is as follows: 

H.P. = [cd 2 - 0.000006 (w+ g t + g 2 )]v; 

in which d = diameter of the rope in inches, v = velocity of the rope in 
feet per second, w = weight of the rope, <7i = weight of the terminal 
sheaves and shafts, gi = weight of the intermediate sheaves and shafts 
(all in lbs.), and c = a constant depending on the material of the rope, 
the filling in the grooves of the sheaves, and the number of laps about 
the sheaves or drums, a single lap meaning a half-lap at each end. The 
values of c for one up to six laps for steel rope are given in the following 
table: 



1186 TRANSMISSION OF POWER BY WIRE ROPE. 





Number of laps about sheaves or drums. 


c = for steel rope on 


1 


2 


3 


4 


5 


6 




5.61 
6.70 
9.29 


8.81 
9.93 
11.95 


10.62 
11.51 

12.70 


11.65 
12.26 
12.91 


12.16 
12.66 
12.97 


12 56 


Wood 


12 83 


Rubber and leather.. 


13.00 



The values of c for iron rope are one half the above. 

When more than three laps are made, the character of the surface in 
contact is immaterial as far as slippage is concerned. 

From the above formula we have the general rule, that the actual 
horse-power capable of being transmitted by any wire rope approximately 
equals c times the square of the diameter of the rope in inches, less six mil- 
lionths the entire weight of all the moving parts, multiplied by the speed of 
the rope, in feet per second. 

Instead of grooved drums or a number of sheaves, about which the 
rope makes two or more laps, it is sometimes found more desirable, 
especially where space is limited, to use grip-pulleys. The rim is fitted 
with a continuous series of steel jaws, which bite the rope in contact by 
reason of the pressure of the same against them, but as soon as relieved 
of this pressure they open readily, offering no resistance to the egress of 
the rope. 

In the ordinary or " flying " transmission of power, where the rope 
makes a single lap about sheaves lined with rubber and leather or wood, 
the ratio between the diameter of the sheaves and the wires of the rope, 
corresponding to a maximum safe working tension, is: For 7-wire rope, 
steel, 79.6; iron, 160.5. For 12-wire rope, steel, 59.3; iron, 120. For 19- 
wire rope, steel, 47.2; iron, 95.8. 

Diameters of Minimum Sheaves in Inches, Corresponding to a 
Maximum Safe Working Tension. 



Diameter 




Steel. 






Iron. 




of Rope, 














In. 


7-Wire. 


12-Wire. 


I9-Wlre. 


7-Wire. 


12-Wire. 


19-Wire. 


-V4 


20 


15 


12 


40 


30 


24 


¥*6 


25 


19 


15 


50 


38 


30 


3/8 


30 


22 


18 


60 


45 


36 


7 /l6 


35 


26 


21 


70 


53 


42 


V2 


40 


30 


24 


80 


60 


48 


»/l6 


45 


33 


27 


90 


68 


54 


5/8 


50 


37 


30 


100 


75 


60 


U/16 


55 


41 


32 


110 


83 


66 


3/ 4 


60 


44 


35 


120 


90 


72 


7/8 


70 


52 


41 


140 


105 


84 


t 


80 


59 


47 


160 


120 


96 



Assuming the sheaves to be of equal diameter, and of the sizes in the 
above table, the horse-power that may be transmitted by a steel rope making 
a single lap on wood-filled sheaves is given in the table on the next page. 

The transmission of greater horse-powers than 250 is impracticable 
with filled sheaves, as the tension would be so great that the filling would 
quickly cut out, and the adhesion on a metallic surface would be insuffi- 
cient where the rope makes but a single lap. In this case it becomes 
necessary to use the Reuleaux method, in which the rope is given more 
than one lap, as referred to below, under the caption " Long-distance 
Transmissions." 



TRANSMISSION OF POWER BY WIRE ROPE. 1187 
Horse-power Transmitted by a Steel Rope on Wood-filled Sheaves. 









Veloci 


ty of Rope in Feet 


per Second 






of Rope, 






















In. 


10 


20 


30 


40 


50 


60 


70 


80 


90 


100 


Vi 


4 


8 


13 


17 


21 


25 


28 


32 


37 


40 


5 /l6 


7 


13 


20 


26 


33 


40 


44 


51 


57 


62 


3/8 


10 


19 


28 


38 


47 


56 


64 


73 


80 


89 


7/16 


13 


26 


38 


51 


63 


75 


88 


99 


109 


121 


V 3 


17 


34 


51 


67 


83 


99 


115 


130 


144 


159 


9 /l6 


22 


43 


65 


86 


106 


128 


147 


167 


184 


203 


5 /8 


27 


53 


79 


104 


130 


155 


179 


203 


225 


247 


%6 


32 
38 
52 
68 


63 
76 
104 
,35 


95 
103 
156 
202 


126 
150 
206 


157 
186 


186 
223 


217 


245 






3/4 






7 /8 










1 































The horse-power that may be transmitted by iron ropes is one-half of the 
above. 

This table gives the amount of horse-power transmitted by wire ropes 
under maximum safe working tensions. In using wood-lined sheaves, 
therefore, it is well to make some allowance for the stretching of the 
rope, and to advocate somewhat heavier equipments than the above table 
would give; that is, if it is desired to transmit 20 horse-power, for in- 
stance, to put in a plant that would transmit 25 to 30 horse-power, avoid- 
ing the necessity of having to take up a comparatively small amount of 
stretch. On rubber and leather filling, however, the amount of power 
capable of being transmitted is 40 per cent greater than for wood, so that 
this filling is generally used, and in this case no allowance need be made 
for stretch, as such sheaves will likely transmit the power given by the 
table, under all possible deflections of the rope. 

Under ordinary conditions, ropes of seven wires to the strand, laid 
about a hemp core, are best adapted to the transmission of power, but 
conditions often occur where 12- or 19-wire rope is to be preferred, as 
stated below, under " Limits of Span." 

Deflections of the Rope. — The tension of the rope is measured by 
the amount of sag or deflection at the center of the span, and the deflec- 
tion corresponding to the maximum safe working tension is determined 
by the following formulae, in which S represents the span in feet: 

Steel Rope. Iron Rope. 
Def. of still rope at center, in feet . .h = .00004 ,S 2 h = .00008 S 2 
driving " M " ...hi =. 000025 S* h t = .00005 S 2 

slack " " "...//•> = .0000875 ,S 2 h% = .00017 5S 2 

limits of Span. — On spans of less than sixty feet, it is impossible to 
splice the rope to such a degree of nicety as to give exactly the required 
deflection, and as the rope is further subject to a certain amount of 
stretch, it becomes necessary in such cases to apply mechanical means 
for producing the proper tension in order to avoid frequent splicing, 
which is very objectionable: but care should always be exercised in using 
such tightening devices that they do not become the means, in unskilled 
hands, of overstraining the rope. The rope also is more sensitive to 
every irregularity in the sheaves and the fluctuations in the amount of 
power transmitted, and is apt to sway to such an extent beyond the 
narrow limits of the required deflections as to cause a jerking motion, 
which is very injurious. For this reason on very short spans it is found 
desirable to use a considerably heavier rope than that actually required 
to transmit the power: or in other words, instead of a 7-wire rope cor- 
responding to the conditions of maximum tension, it is better to use a 
19-wire rope of the same size wires, and to run this under a tension con- 
siderably below the maximum. In this way are obtained the advantages of 
increased weight and less stretch, without having to use larger sheaves, 
while the wear will oe greater in proportion to the increased surface. 



1188 TRANSMISSION OF POWER BY WIRE ROPE. 

In determining the maximum limit of span, the contour of the ground 
and the available height of the terminal sheaves must be taken into con- 
sideration. It is customary to transmit the power through the lower 
portion of the rope, as in this case the greatest deflection in this portion 
occurs when the rope is at rest. When running, the lower portion rises 
and the upper portion sinks, thus enabling obstructions to be avoided 
which otherwise would have to be removed, or make it necessary to erect 
very high towers. The maximum limit of span in this case is determined 
by the maximum deflection that may be given to the upper portion of 
the rope when running, which for sheaves of 10 ft. diameter is about 
600 feet. 

Much greater spans than this, however, are practicable where the con- 
tour of the ground is such that the upper portion of the rope may be the 
driver, and there is nothing to interfere with the proper deflection of the 
under portion. Some very long transmissions of power have been 
effected in this way without an intervening support, one at Lockport, 
N.Y., having a clear span of 1700 feet. 

Long-distance Transmissions. — When the distance exceeds the 
limit for a clear span, intermediate supporting sheaves are used, with 
plain grooves (not filled), the spacing and size of which will be governed 
by the contour of the ground and the special conditions involved. The 
size of these sheaves will depend on the angle of the bend, gauged by the 
tangents to the curves of the. rope at the points of inflection. If the cur- 
vature due to this angle and the working tension, regardless of the size of 
the sheaves, as determined by the table on the next page, is less than 
that of the minimum sheave (see table p. 1186), the intermediate sheaves 
should not be smaller than such minimum sheave, but if the curvature is 
greater, smaller intermediate sheaves may be used. 

In very long transmissions of power, requiring numerous intermediate 
supports, it is found impracticable to run the rope at the high speeds 
maintained in " flying transmissions." The rope therefore is run under 
a higher working tension, made practicable by wrapping it several times 
about grooved terminal drums, with a lap about a sheave on a take-up or 
counter-weighted carriage, which preserves a constant tension in the slack 
portion. 

Inclined Transmissions. — When the terminal sheaves are not on 
the same elevation, the tension at the upper sheave will be greater than 
that at the lower, but this difference is so slight, in most cases, that it 
may be ignored. The span to be considered is the horizontal distance 
between the sheaves, and the principles governing the limits of span will 
hold good in this case, so that for very steep inclinations it becomes 
necessary to resort to tightening devices for maintaining the requisite 
tension in the rope. The limiting case of inclined transmissions occurs 
when one wheel is directly above the other. The rope in this case pro- 
duces no tension whatever on the lower wheel, while the upper is sub- 
ject only to the weight of the rope, which is usually so insignificant that 
it may be neglected altogether, and on vertical transmissions, therefore, 
mechanical tension is an absolute necessity. 

Bending Curvature of Wire Ropes. — The curvature due to any 
bend in a wire rope is dependent on the tension, and is not always the 
same as the sheave in contact, but may be greater, which explains how 
it is that large ropes are frequently run around comparatively small 
sheaves without detriment, since it is possible to place these so close that 
the bending angle on each will be such that the resulting curvature will 
not overstrain the wires. This curvature may be ascertained from the 
formula and table on the next page, which give the theoretical radii of 
curvature in inches for various sizes of ropes and different angles for one 
pound tension in the rope. Dividing these figures by the actual tension 
in pounds, gives the radius of curvature assumed by the rope in cases 
where this exceeds the curvature of the sheave. The rigidity of the rope 
or internal friction of the wires and core has not been taken into account 
in these figures, but the effect of this is insignificant, and it is on the safe 
side to ignore it. By the " angle of bend " is meant the angle between 
the tangents to the curves of the rope at the points of inflection. When 
the rope is straight the angle is 180°. For angles less than 160° the 
radius of curvature in most cases will be less than that corresponding to 
the safe working tension, and the proper size of sheave to use in such 



ROPE-DRIVING. 



1189 



cases will be governed by the table headed " Diameters of Minimum 
Sheaves Corresponding to a Maximum Safe Working Tension " on page 
1186. 

Radius of Curvature of Wire Ropes in Inches for 1-lb. Tension. 

Formula: R= Ed^n -s- 5.25 t cos 1/2 <?; in which R = radius of curvature; 
E = modulus of elasticity = 28,500,000; <J = diameter of wires; n = no. 
of wires; = angle of bend; t = working stress (lbs. and ins.). 
Divide by stress in pounds to obtain radius in inches. 



Diam. 
















of 


160° 


165° 


170° 


172° 


174° 


176° 


178° 


Wire. 
















a; f 1/2 


4,226 


5,623 


8,421 


10,949 


14,593 


21,884 


43,762 


& 5 /8 


11,090 


14,753 


22,095 


26,731 


35,628 


53,429 


106,841 


«| 3 /4 


22,274 


29,633 


45,412 


54,417 


72,530 


108,767 


217,500 


©1 7/ 8 


43,184 


57,451 


86,040 


102,688 


136,869 


205,251 


410,440 


£ ' 


71,816 


95,541 


143,085 


175,182 


233,492 


350,150 


700,193 


£ 1 Vs 


112,763 


150,016 


224,667 


280,607 


374 010 


560,872 


1,121,574 


0U11/4 


169,135 


225,012 


336,982 


427,689 


570,050 


854,858 


1,709,459 


of V2 


12,914 


17,179 


25,727 


31,125 


41,485 


62,212 


124,405 


ft 5 /8 


29,762 


39,594 


59,297 


75,988 


101,282 


151,884 


303,723 


7 /8 


62,313 


82,899 


124,151 


157,570 


210,018 


314,948 


629,800 


116,239 


154,641 


231,593 


291,917 


389,085 


583,479 


1 164,099 


.a I' 


199,323 


265,173 


397,129 


497,998 


663,767 


995,390 


1 ,990,478 


£ 1 1/8 


320,556 


426,459 


638,674 


797,697 


1,063,217 


1,594,422 


3,188,359' 


£ln/ 4 


504,402 


671,041 


1,004,965 


1,215,817 


1,620,513 


2,430,151 


4,859,561 



ROPE-DRIVING. 

The transmission of power by cotton or manila ropes is a competitor 
with gearing and leather belting when the amount of power is large, or 
the distance between the power and the work is comparatively great. 
The following is condensed from a paper by C. W. Hunt, Trans. A. S. 
M. E., xii, 230: 

But few accurate data are available, on account of the long period 
required in each experiment, a rope lasting from three to six years. 
Installations which have been successful, as well as those in which the 
wear of the rope was destructive, indicate that 200 lbs. on a rope one 
inch in diameter is a safe and economical working strain. When the 
strain is materially increased, the wear is rapid. 
In the following equations 

C = circumference of rope, inches; g = gravity; 
D = sag of the rope in inches; H = horse-power; 

F = centrifugal force in pounds; L = distancebetweenpulleys.it.; 

P = pounds per foot of rope; w = working strain in pounds; 

R = force in pounds doing useful work; 
S = strain in pounds on the rope at the pulley; 
T = tension in pounds of driving side of the rope; 
t = tension in pounds on slack side of the rope; 
v = velocity of the rope in feet per second; 
W = ultimate breaking strain in pounds. 
W = 720 C 2 ; P = 0.032 C 2 ; w = 20 C 2 . 

This makes the normal working strain equal to 1/36 of the breaking 
strength, and about 1/25 of the strength at the splice. The actual strains 
are ordinarily much greater, owing to the vibrations in running, as well 
as from imperfectly adjusted tension mechanism. 

For this investigation we assume that the strain on the driving side 
of a rope is equal to 200 lbs. on a rope one inch in diameter, and an 
equivalent strain for other sizes, and that the rope is in motion at vari- 
ous velocities of from 10 to 140 ft. per second. 

The centrifugal force of the rope in running over the pulley will reduce 



1190 



ROPE-DRIVING. 



the amount of force available for the transmission of power. The cen- 
trifugal force F = Pv 2 -*- g. 

At a speed of about 80 ft. per second, the centrifugal force increases 
faster than the power from increased velocity of the rope, and at about 
140 ft. per second equals the assumed allowable tension of the rope. 
Computing this force at various speeds and then subtracting it from the 
assumed maximum tension, we have the force available for the trans- 
mission of power. The whole of this force cannot be used, because a 
certain amount of tension on the slack side of the rope is needed to give 
adhesion to the pulley. What tension should be given to the rope for 
this purpose is uncertain, as there are no experiments which give accurate 
data. It is known from considerable experience that when the rope runs in 
a groove whose sides are inclined toward each other at an angle of 45° 
there is sufficient adhesion when the ratio of the tensions T -e- t = 2. 

For the present purpose T can be divided into three parts: 1. Tension 
doing useful work; 2. Tension from centrifugal force; 3. Tension to 
balance the strain for adhesion. 

The tension t can be divided into two parts: 1. Tension for adhesion; 
2. Tension from centrifugal force. 

It is evident, however, that the tension required to do a given work 
should not be materially exceeded during the life of the rope. 

There are two methods of putting ropes on the pulleys; one in which 
the ropes are single and spliced on, being made very taut at first, and 
less so as the rope lengthens, stretching until it slips, when it is re- 
spliced. The other method is to wind a single rope over the pulleys 
as many turns as needed to obtain the necessary horse-power and put a 
tension pulley to give the necessary adhesion and also take up the wear. 
The tension t on one of the ropes required to transmit the normal horse- 
power for the ordinary speeds and sizes of rope is computed by formula 
(1). below. The total tension T on the driving side of the rope is 
assumed to be the same at all speeds. The centrifugal force, as well as 
an amount equal to the tension for adhesion on the slack side of the 
rope, must be taken from the total tension T to ascertain the amount of 
force available for the transmission of power. 

It is assumed that the tension on the slack side necessary for giving 
adhesion is equal to one half the force doing useful work on the driving 































































10 
38 
36 
34 
32 
30 
28 
26 
24 


40 
38 
36 
34 
32 
30 
28 
H 26 
| 24 

cS 28 

o20 

2 18 

ffiW 

H 


ROPE DRIVING 

Horse Power of manila 
rope at various speeds 








S 
































































































































































tf 
























































* 






















x 










































d$> 


















S 


































































\ 
























„ 




























\ 






\ 




















V 














l*p 


o 


















\ 














20 
18 
16 
14 
























^ 


^~ 














^s 








\ 




\ 












f/ 




| 






























\ 




\ 




















































X 




\ 






12 
10 
8 


z 








■$, 


-' 




■V 


w 


y 






























\ 


\ 






12 

10 

8 
6 
4 
2 






Q 


































N 








\ 


1 




/ 


/ 












































N 




\ 


\ 






// 


/ 




' 














































\ 




£ 


/ 


s 


















































vo 




, 



























































.. 100 110 120 1.30 140. 
Velocity of Driving Rope in feet per second 
Fig. 186. 
side of the rope; hence the force for useful work is R = 2/ 3 (T — F); and 
the tension on the slack side to give the required adhesion is 1/3 (T — F). 

Hence t = (T - F)/Z + F (1) 

The sum of the tensions T and t is not the same at different speeds, as 
the equation (1) indicates. As F varies as the square of the velocity, 
there is, with an increasing speed of the rope, a decreasing useful force, 
and an increasing total tension, t, on the slack side. 



ROPE-DRIVING. 



1191 



With these assumptions of allowable strains the horse-power will be 



H= 2v (r-F)-i-(3X 550) 



(2) 



Transmission ropes are usually from 1 to 2 inches in diameter. A 
computation of the horse-power for four sizes at various speeds and 
under ordinary conditions, based on a maximum strain equivalent to 
200 lbs. for a rope one inch in diameter, is given in Fig. 186. The 
horse-power of other sizes is readily obtained from these. The maxi- 
mum power is transmitted, under the assumed conditions, at a speed of 
about 80 feet per second. 

The wear of the rope is both internal and external; the internal is 
caused by the movement of the fibers on each other, under pressure in 
bending over the sheaves, and the external is caused by the slipping and 
the wedging in the grooves of the pulley. Both of these causes of wear 
are, within the limits of ordinary practice, assumed to be directly pro- 
portional to the speed. 

The rope is supposed to have the strain T constant at all speeds on 
the driving side, and in direct proportion to the area of the cross-section; 
hence the catenary of the driving side is not affected by the speed or by 
the diameter of the rope. 

The deflection of the rope between the pulleys on the slack side varies 
with each change of the load or change of the speed, as the tension equa- 
tion (1) indicates. 

The deflection of the rope is computed for the assumed value of T and 

t by the parabolic formula S = ~-=- + PD, S being the assumed strain 

T on the driving side, and t, calculated by equation (1), on the slack 
side. The tension t varies with the speed. 

Horse-power of Transmission Rope at Various Speeds. 

Computed from formula (2) given above. 





Speed of the Rope in feet per minute. 
























l«d 


& 


1500 


2000 


2500 


3000 


3500 


4000 


4500 


5000 


6000 


7000 


8000 




l/o 


1.45 


1.9 


2.3 


2,7 


3 


3.2 


3.4 


3.4 


3.1 


2.2 





20 


5/8 


2.3 


3.2 


3.6 


4.2 


4.6 


5.0 


5.3 


5.3 


4.9 


3.4 





24 


3/J 


3.3 


4.3 


5 2 


5.8 


6.7 


7 2 


7,7 


7 7 


7.1 


4.9 





30 


7/S 


4.5 


5.9 


7.0 


8.2 


9.1 


9 8 


10.8 


10,8 


9.3 


6.9 





36 


1 ™ 


5.8 


7.7 


9.2 


10.7 


11.9 


12,8 


13.6 


13.7 


12.5 


8.8 





42 


niA 


9.2 


12.1 


14.3 


16.8 


18.6 


20,0 


21.2 


21.4 


19.5 


13.8 





54 


i# 


13.1 


17.4 


20.7 


23.1 


26.8 


28.8 


30.6 


30.8 


28.2 


19.8 





60 


13/ 4 


18 


23.7 


28.2 


32.8 


36.4 


39 2 


41,5 


41 8 


37.4 


27,6 





72 


2 


23.2 


30.8 


36.8 


42.8 


47.6 


51.2 


54.4 


54.8 


50 


35.2 





84 



The following notes are from the circular of the C. W. Hunt Co.: 

For a temporary installation, it might be advisable to increase the work 
to double that given in the table. 

For convenience in estimating the necessary clearance on the driving 
and on the slack sides, we insert a table showing the sag of the rope at 
different speeds when transmitting the horse-power given in the pre- 
ceding table. When at rest the sag is not the same as when running, 
being greater on the driving and less on the slack sides of the rope. The 
sag of the driving side when transmitting the normal horse-power is the 
same no matter what size of rope is used or what the speed driven at, 
because the assumption is that the strain on the rope shall be the same 
at all speeds when transmitting the assumed horse-power, but on the 
slack side the strains, and consequently the sag, vary with the speed of 
the rope and also with the horse-power. The table gives the sag for 
three speeds. If the actual sag is less than given in the table, the rope 
is strained more than the work requires. 

This table is only approximate, and is exact only when the rope is 
running at its normal speed, transmitting its full load and strained to the 
assumed amount. All of these conditions are varying in actual work. 



1192 



ROPE-DRIVING. 



Sag op the Rope Between Pulleys. 



Distance 
between 


Driving Side. 




Slack Side of Rope. 


Pulleys 
in feet. 


All Speeds. 


80 ft. per sec. 


60 ft. per sec. 


40 ft. per sec. 


40 
60 
80 
100 
120 
140 
160 


feet 4 inches 

" 10 

, .... 5 .. 

2 " " 

2 " 11 " 

3 " 10 " 
5 " 1 


feet 7 inches 

1 " 5 " 

2 " 4 " 

3 " 8 " 
5 " 3 " 
7 " 2 " 
9 " 3 " 


feet 9 inches 

1 " 8 " 

2 " 10 " 
4 " 5 " 
6 " 3 " 
8 " 9 " 

11 " 3 " 


feet 1 1 inches 

1 " 11 " 
3 " 3 " 
5 " 2 " 
7 " 4 " 
9 " 9 " 

14 " " 



The size of the pulleys has an important effect on the wear of the rope — 
the larger the sheaves, the less the fibers of the rope slide on each other, 
and consequently there is less internal wear of the rope. The pulleys 
should not be less than forty times the diameter of the rope for economical 
wear, and as much larger as it is possible to make them. This rule applies 
also to the idle and tension pulleys as well as to the main driving-pulley. 

The angle of the sides of the grooves in which the rope runs varies, 
with different engineers, from 45° to 60°. It is very important that the 
sides of these grooves should be carefully polished, as the fibers of the 
rope rubbing on the metal as it comes from the lathe tools will gradually 
break fiber by fiber, and so give the rope a short life. It is also neces- 
sary to carefully avoid all sand or blow holes, as they will cut the rope 
out with surprising rapidity. 

Tension on the Slack Part of the Rope. 



Speed of 
Rope, in feet 


Diameter of the Rope and Pounds Tension on the Slack Rope. 
















per second. 


V2 


5/8 


3/4 


7/8 


1 


U/4 


M/2 


l3/ 4 


2 


20 


10 


27 


40 


54 


71 


110 


162 


216 


283 


30 


14 


29 


42 


56 


74 


115 


170 


226 


296 


40 


15 


31 


45 


60 


79 


123 


181 


240 


315 


50 


16 


33 


49 


65 


85 


132 


195 


259 


339 


60 


18 


36 53 


71 


93 


145 


214 


285 


373 


70 


19 


39 59 


78 


101 


158 


236 


310 


406 


80 


21 


43 64 


85 


111 


173 


255 


340 


445 


90 


24 


48 70 


93 


122 


190 


279 


372 


487 



Much depends also upon the arrangement of the rope on the pulleys, 
especially where a tension weight is used. Experience shows that the 
increased wear on the rope from bending the rope first in one direction 
and then in the other is similar to that of wire rope. At mines where 
two cages are used, one being hoisted and one lowered by the same 
engine doing the same work, the wire ropes, cut from the same coil, are 
usually arranged so that one rope is bent continuously in one direction 
and the other rope is bent first in one direction and then in the other, in 
winding on the drum of the engine. The rope having the opposite bends 
wears much more rapidly than the other, lasting about three quarters 
as long as its mate. This difference in wear shows in manila rope, both 
in transmission of power and in coal-hoisting. The pulleys should be 
arranged, as far as possible, to bend the rope in one direction. 
Diameter of' Pulleys and Weight of Rope. 



Diameter of 


Smallest Diameter 


Length of Rope to 


Approximate 


Rope, 


of Pulleys, in 


allow for Splicing, 


Weight, in lbs. per 


in inches. 


inches. 


in feet. 


foot of rope. 


V2 


20 


6 


0.12 


5/8 


24 


6 


0:18 


3/ 4 


30 


7 


0.24 


7/8 


36 


8 


0.32 


1 


42 


9 


0.49 


11/4 


54 


10 


0.60 


U/2 


60 


12 


0.83 


13/4 


72 


13 


1 .10 


2 


84 


14 


1.40 



ROPE-DRIVING. 



1193 



For large amounts of power it is common to use a number of ropes 
lying side by side in grooves, each spliced separately. For lighter drives 
some engineers use one rope wrapped as many times around the pulleys 
as is necessary to get the horse-power required, with a tension pulley to 
take up the slack as the rope wears when first put in use. The weight 
put upon this tension pulley should be carefully adjusted, as the over- 
straining of the rope from this cause is one of the most common errors 
in rope-driving. We therefore give a table showing the proper strain on 
the rope for the various sizes, from which the tension weight to transmit 
the horse-power in the tables is easily deduced. This strain can be still 
further reduced if the horse-power transmitted is usually less than the 
nominal work which the rope was proportioned to do, or if the angle of 
groove in the pulleys is acute. 

With a given velocity of the driving-rope, the weight of rope required 
for transmitting a. given horse-power is the same, no matter what size 
rope is adopted. The smaller rope will require more parts, but the 
weight will be the same. 

Data of Manila Transmission Rope. 

From the " Blue Book " of The American Mfg. Co., New York. 













Length of 
















Splice, ft. 




ft 

ill 

9— 


ft 
o 

"3 


a 

Q 


S <B 

IS 

g* 


.9 M 


a 

H 

|l 

9& 


a 


a 




is 


a 
5 


3 

& 

in 


< 






m 


ffi 


02 


1*™ 

0-8 

02 


■RP5."9 


3/ 4 


0.5625 


0.20 


3,950 


112 


6 


8 




28 


760 


7/8 


0.7656 


0.26 


5,400 


153 


6 


8 




32 


650 


1 


1. 


0.34 


7,000 


200 


7 


10 


Ya 


36 


570 


H/8 


1.2656 


0.43 


8,900 


253 


7 


10 


16 


40 


510 


M/4 


1 . 5625 


0.53 


10,900 


312 


7 


10 


16 


46 


460 


13/8 


1.8906 


0.65 


13,200 


378 


8 


12 


15 


50 


415 


1V2 


2.25 


0.77 


15.700 


450 


8 


12 


18 


54 


380 


15/8 


2. 6406 


0.90 


18,500 


528 


8 


12 


18 


60 


344 


13/ 4 


3.0625 


1.04 


21,400 


612 


8 


12 


18 


64 


330 


2 


4. 


1.36 


28,000 


800 


9 


14 


20 


72 


290 


21/4 


5.0625 


1.73 


35,400 


1,012 


9 


14 


20 


82 


255 


21/2 


6.25 


2.13 


43,700 


1,250 


10 


16 


22 


90 


230 



Weight of transmission rope = 0.34 X diam. 2 

Breaking strength = 7,000 X diam. 2 

Maximum allowable tension = 200 X diam. 2 
Diam. smallest practicable 

sheave, = 36 X diam. 

Velocity of rope (assumed) = 5,400 ft. per min. 

Miscellaneous Notes on Rope-Driving. — Reuleaux gives formulae 
for calculating sources of loss in hemp-rope transmission due to (1) journal 
friction, (2) stiffness of ropes, and (3) creep of ropes. The constants in 
these formlu33 are, however, uncertain from lack of experimental data. 
He calculates an average case giving loss of power due to journal friction 
= 4%, to stiffness 7.8%, and to creep 5%, or 16.8% in all, and says this 
is not to be considered higher than the actual loss. 

Spencer Miller, in a paper entitled "A Problem in Continuous Rope- 
driving " (Trans. A. S. C. E., 1897), reviews the difficulties which occu~ in 
rope-driving, with a continuous rope from a large to a small pulley. He 
adopts the angle of 45° as a minimum angle to use on the smaller pulley, 
and recommends that the larger pulley be grooved with a wider angle to a 
degree such that the resistance to slipping is equal in both wheels. 



1194 FRICTION AND LUBRICATION. 

Mr. Miller refers to a 250-H.P. drive which has been running ten years, 
the large pulley being grooved 60° and the smaller 45°. This drive was 
designed to use a li/4-in. manila rope, but the grooves were made deep 
enough so that a 7/ 8 -in. rope would not bottom. In order to determine the 
value of the drive a common 7/g-in. rope was put in at first, and lasted six 
years, working under a factor of safety of only 14. He recommends, how- 
ever, for continuous rope-driving a factor of safety of not less than 20. 

A heavy rope-drive on the separate, or English, rope system is described 
and illustrated in Power, April, 1892. It is in use at the India Mill at Dar- 
wen, England, and is driven by a 2000-H.P. engine at 54 revs, per min. 
The fly-wheel is 30 ft. diameter, weighs 65 tons, and is arranged with 30 
grooves for 13/ 4 -in. ropes. These ropes lead off to receiving-pulleys upon 
the several floors, so that each floor receives its power direct from the fly- 
wheel. The speed of the ropes is 5089 ft. per min., and five 7-ft. receivers 
are used. Lambeth cotton ropes are used. (For much other information 
on this subject see " Rope-Driving," by J. J. Flather, John Wiley & Sons.) 

Cotton Ropes are advantageously used as bands of cords on the 
smaller machine appliances; the fiber, being softer and more flexible 
than manila hemp, gives good results for small sheaves; but for large 
drives, where power transmitted is in considerable amounts, cotton rope, 
as compared with manila, is hardly to be considered, on account of 
the following disadvantages: It is less durable; it is injuriously affected 
by the weather, so that for exposed drives, paper-mill work, or use in 
water-wheel pits, it is absolutely unsatisfactory; it is difficult, if not 
impossible, to splice uniformly; even the best quality cotton fope is 
much inferior to manila in strength, the breaking strain of the highest 
grade being but 4000 X diam. 2 as against 7000 X diam. 2 for manila; while, 
for the transmission of equal powers, the cost of a cotton rope varies 
from one-third to one-half more than manila. — (" Blue Book " of the 
Amer. Mfg. Co.) 

A different opinion is found in a paper by E. Kenyon in Proc. Inst. 
Engrs. and Shipbuilders of Scotland, 1904. He says: Evidences of the 
progress of cotton in the manufacture of driving-ropes are so far-reaching 
that its superiority may be considered as much an accepted principle in 
enhanced power-transmitting value, its immunity from frequent atten- 
rope transmission as the law of gravitation is in science. As to the longevity 
of cotton ropes, 24 cotton ropes 13/4-in. diam. are transmitting 820 H.P. at a 
peripheral speed of 4396 ft. per min., from a driving pulley 28 ft. diam. 
All the card-room ropes in this drive have been running since 1878, a 
period of 26 years, without any attention whatever. 



FRICTION AND LUBRICATION. 

Friction is defined by Rankine as that force which acts between two 
bodies at their surface of contact so as to resist their sliding on each 
other, and which depends on the force with which the bodies are pressed 
together. 

Coefficient of Friction, — The ratio of the force required to slide a 
body along a horizontal plane surface to the weight of the body is called 
the coefficient of friction. It is equivalent to the tangent of the angle of 
repose, which is the angle of inclination to the horizontal of an inclined 
plane on which the body will just overcome its tendency to slide. The 
angle is usually denoted by d, and the coefficient by /. / = tan 0. 

Friction of Rest and of Motion. — The force required to start a 
body sliding is called the friction of rest, and the force required to con- 
tinue its sliding after having started is called the friction of motion. 

Rolling Friction is the force required to roll a cylindrical or spheri- 
cal body on a plane or on a curved surface. It depends on the nature of 
the surfaces and on the force with which they are pressed together, but 
is essentially different from ordinary, or sliding, friction. 

Friction of Solids. — Rennie's experiments (1829) on friction of solids, 
usually unlubricated and dry, led to the following conclusions: 



FRICTION AND LUBRlCATiON. 



1195 



1. The laws of sliding friction differ with the character of the bodies 
rubbing together. 

2. The friction of fibrous material is increased by increased extent of 
surface and by time of contact, and is diminished by pressure and speed. 

3. With wood, metal, and stones, within the limit of abrasion, friction 
varies only with the pressure, and is independent of the extent of surface, 
time of contact, and velocity. 

4. The limit of abrasion is determined by the hardness of the softer of 
the two rubbing parts. 

5. Friction is greatest with soft and least with hard materials. 

6. The friction of lubricated surfaces is determined by the nature of 
the lubricant rather than by that of the solids themselves. 

Friction of Rest. (Rennie.) 



Pressure, 
lbs. 




Values of /. 










per square 


Wrought iron on 


Wrought on 


Steel on 


Brass on 


inch. 


Wrought Iron. 


Cast Iron. 


Cast Iron. 


Cast IrOn. 


187 


0.25 


0.28 


0.30 


0.23 


224 


.27 


.29 


.33 


.22 


336 


.31 


.33 


.35 


.21 


448 


.38 


.37 


.35 


.21 


560 


.41 


.37 


.36 


.23 


672 


Abraded 


.38 


.40 


.23 


784 




Abraded 


Abraded 


.23 



Law of TJnlnbricated Friction. — A. M. Wellington, Eng'g News, 
April 7, 1888, states that the most important and the best determined of 
all the laws of unlubricated friction may be thus expressed: 

The coefficient of unlubricated friction decreases materially with 
velocity, is very much greater at minute velocities of + , falls very 
rapidly with minute increases of such velocities, and continues to fall 
much less rapidly with higher velocities up to a certain varying point, 
following closely the laws which obtain with lubricated friction. 

Friction of Steel Tires Sliding on Steel Rails. (Westinghouse & 
Galton.) 

Speed, miles per hour 10 15 25 38 45 50 

Coefficient of friction 0.110 .087 .080 .051 .047 .040 

Adhesion, lbs. per gioss ton 246 195 179 128 114 90 

Rolling Friction is a consequence of the irregularities of form and 
the roughness of surface of bodies rolling one over the other. Its laws 
are not yet definitely established in consequence of the uncertainty which 
exists in" experiment as to how much of the resistance is due to roughness 
of surface, how much to original and permanent irregularity of form, 
and how much to distortion under the load. (Thurston.) 

Coefficients of Rolling Friction. — If R = resistance applied at the 
circumference of the wheel, W = total weight, r = radius of the wheel, 
and / = a coefficient, R = fW + r. f is very variable. Coulomb gives 
0.06 for wood, 0.005 for metal, where W is in pounds and r in feet. Tred- 
gold made the value of / for iron on iron 0.002. 

For wagons on soft soil Morin found / = 0.065, and on hard smooth 
roads 0.02. 

A Committee of the Society of Arts (Clark, R. T. D.) reported a loaded 
omnibus to exhibit a resistance on various loads as below: 

Pavement. Speed per hour. Coefficient. Resistance. 

Granite 2.87 miles. 0.007 17.41 per ton. 

Asphalt 3.56 " 0.0121 27.14 

Wood 3.34 " 0.0185 41.60 

Macadam, graveled 3.45 " 0.0199 44.48 

Macadam, granite, new.... 3.51 " 0.0451 101.09 



1196 



FRICTION AND LUBRICATION. 



Thurston gives the value of / for ordinary railroads, 0.003; well-laid 
railroad track, 0.002; best possible railroad track, 0.001. 

The few experiments that have been made upon the coefficients of 
rolling friction, apart from axle friction, are too incomplete to serve as a 
basis for practical rules. (Trautwine.) 

Laws of Fluid Friction. — For all fluids, whether liquid or gaseous, 
the resistance is (1) independent of the pressure between the masses in 
contact; (2) directly proportional to the area of rubbing-surface; (3) pro- 
portional to the square of the relative velocity at moderate and high 
speeds, and to the velocity nearly at low speeds; (4) independent of the 
nature of the surfaces of the solid against which the stream may flow, but 1 
dependent to some extent upon their degree of roughness; (5) proportional 
to the density of the fluid, and related in some way to its viscosity. 
(Thurston.) 

The Friction of Lubricated Surfaces approximates to that of solid fric- 
tion as the journal is run dry, and to that of fluid friction as it is flooded 
with oil. 

Angles of Repose and Coefficients of Friction of Building Materials. 

(From Rankine's Applied Mechanics.) 



/=ta: 



Dry masonry and brickwork. . . 
Masonry and brickwork with 

damp mortar 

Timber on stone 

Iron on stone 

Timber on timber 

Timber on metals 

Metals on metals 

Masonry on dry clay 

Masonry on moist clay 

Earth on earth 

Earth on earth, dry sand, clay, 

and mixed earth 

Earth on earth, damp clay 

Earth on earth, wet clay 

Earth on earth, shingle and 

gravel 



31° to 35° 

361/2° 

22° 

35° to I62/3 

26 1/ 2 ° to 11 1/ 3 ° 

31° to III/3 

14° to 81/ 2 ° 

27° 

181/4° 

14° to 45° 

21° to 37° 
45° 
17° 



0.6 to 0.7 

0.74 
about 0.4 
0.7 to 0.3 
0.5 to 0.2 
0.6 to 0.2 
0.25 to 0.15 

0.51 

0.33 
0.25 to 1.0 

0.38 to 0.75 



1.67 to 1.4 

1.35 

2.5 
1.43 to 3.3 

2 to 5 
1.67 to 5 
4 to 6.67 

1.96 

3. 
4 to 1 

2.63 to 1.33 



Coefficients of Friction of Journals. (Morin.) 



Material. 


Unguent. 


Lubrication. 


Intermittent 


Continuous. 


Cast iron on cast iron j 

Cast iron on bronze j 

Cast iron on lignum vitse . . . 
Wrought iron on cast iron . ) 
Wrought iron on bronze. . J 
Iron on lignum vitse j 


Oil, lard, tallow. 
Unctuous and wet 
Oil, lard, tallow. 
Unctuous and wet 
Oil, lard. 

Oil, lard, tallow. 

Oil, lard. 

Unctuous. 
Olive oil. 
Lard. 


0.07 to 0.08 

0.14 
0.07 to 0.08 

0.16 


0.03 to 0.054 
0.03 to 0.054 

0.09 
0.03 to 0.054 


0.07 to 0.08 
0.11 
0.19 
0.10 
0.09 




Prof. Thurston says con 
results are probably obtains 
Those here given are so grea 
and temperature, that they c 


^erning the above 
d in good practice 
tly modified by va 
annot be taken as c 


figures that 
with ordinar 
riations of sp< 
orrect for gent 


much better 
y machinery, 
ed, pressure, 
,ral purposes. 



FRICTION AND LUBRICATION. 



1197 



Friction of Motion. — The following is a table of the angle of repose 
0, the coefficient of friction / = tan 0, and its reciprocal, 1 -J- /, for the 
materials of mechanism — condensed from the tables of General Morin 
(1831) and other sources, as given by Rankine: 



No. 



Surfaces. 



Wood on wood, dry 

" " " soa] 

Metals on oak, dry 

" " wet 

" " soapy 

" elm, dry 

Hemp on oak, dry 

" " " wet 

Leather on oak 

" metals, dry 

metals, wet 

greasy . . 

oily 

Metals on metals, dry 

" " " wet 

Smooth surfaces, occasion- 
ally greased 

Smooth surfaces, continu- 
ously greased 

Smooth surfaces, best results 
Bronze on lignum vitse, con- 
stantly wet 



14° to 261/2° 
1 1 1/ 2 ° to 2° 
261/2° to 31° 
131/2° to 14° 

1 1 1/2° 

111/2° to 14° 

28° 

181/2° 

15° to 191/2° 

291/ 2 ° 

20° 

13° 

81/2° 
81/ 2 ° to 11° 

161/2° 

4° to 4 1/ 2 ° 



1 3/ 4 ° to 2° 
3°? 



0.25 to 0.5 
0.2 to 0.04 
0.5 to 0.6 
0.24 to 0.26 

0.2 
0.2 to 0.25 

0.53 

0.33 
0.27 to 0.38 

0.56 

0.36 

0.23 

n 15 
0.15 to 0.2 



0.05 
0.03 to 0.036 



>-/• 



4 to 2 

5 to 25 
2 to 1.67 

4.17 to 3.85 

5 

5 to 4 

1.89 

3 

3.7 to 2.86 

1.79 

2.78 

4.35 

6.67 

6.67 to 5 

3.33 

14.3 to 12.5 

20 



Average Coefficients of Friction. — Journal of cast iron in bronze 
bearing; velocity 720 feet per minute; temperature 70° F.; intermittent 
feed through an oil-hole. (Thurston on Friction and Lost Work.) 





Pressures, pounds per square inch. 


Oils. 


8 


16 


32 


48 


Sperm, lard, neat's-f t., etc. . 
Olive, cotton-seed, rape, etc. 


.159 to .250 
.160 to .283 
.248 to .278 
.154 to .261 


.138 to .192 
.107 to .245 
.124 to .167 
.145 to .233 


.086 to .141 
.101 to .168 
.097 to .102 
.086 to .178 


.077 to .144 
.079 to .131 
.081 to 122 


Mineral lubri eating-oils 


.094 to .222 



With fine steel journals running in bronze bearings and continuous 
lubrication, coefficients far below those above given are obtained. Thus 
with sperm-oil the coefficient with 50 lbs. per square inch pressure was 
0.0034; with 200 lbs., 0.0051; with 300 lbs., 0.0057. 

For very low pressures, as in spindles, the coefficients are much higher. 
Thus Mr. Woodbury found, at a temperature of 100° and a velocity of 
600 feet per minute, 

Pressures, lbs. per sq. in. 1 2 3 4 5 

Coefficient 0.38 0.27 0.22 0.18 0.17 

These high coefficients, however, and the great decrease in the coefficient 
at increased pressures are limited as a practical matter only to the smaller 
pressures which exist especially in spinning machinery, where the pressure 
is so light and the film of oil so thick that the viscosity of the oil is an 
important part of the total frictional resistance. 

Experiments on Friction of a Journal Lubricated by an Oil- 
bath (reported by the Committee on Friction, Proc. In$t. M. E. 
Nov., 1883) show that the absolute friction, that is, the absolute tan- 



1198 FRICTION AND LUBRICATION. 



gential force per square inch of bearing, required to resist the tendency 
of the brass to go round with the journal, is nearly a constant under all 
loads, within ordinary working limits. Most certainly it does not in- 
crease in direct proportion to the load, as it should do according to the 
ordinary theory of solid friction. The results of these experiments 
seem to show that the friction of a perfectly lubricated journal follows 
the laws of liquid friction much more closely than those of solid friction. 
They show that under these circumstances the friction is nearly inde- 
pendent of the pressure per square inch, and that it increases with the 
velocity, though at a rate not nearly so rapid as the square of the velocity. 

The experiments on friction at different temperatures indicate a great 
diminution in the friction as the temperature rises. Thus in the case of 
lard-oil, taking a speed of 450 r.p.m., the coefficient of friction at a tem- 
perature of 120° is only one-third of what it was at a temperature of 60°. 

The journal was of steel, 4 ins. diameter and 6 ins. long, and a gun- 
metal brass, embracing somewhat less than half the circumference of the 
journal, rested on its upper side, on which the load was applied. When 
the bottom of the journal was immersed in oil, and the oil therefore carried 
under the brass by rotation of the journal, the greatest load carried with 
rape-oil was 573 lbs. per sq. in., and with mineral oil 625 lbs. 

In experiments with ordinary lubrication, the oil being fed in at the 
center of the top of the brass, and a distributing groove being cut in the 
brass parallel to the axis of the journal, the bearing would not run cool 
with only 100 lbs. per sq. in., the oil being pressed out from the bearing- 
surface and through the oil-hole, instead of being carried in by it. On 
introducing the oil at the sides through two parallel grooves, the lubrica- 
tion appeared to be satisfactory, but the bearing seized with 380 lbs. 
per sq. in. 

When the oil was introduced through two oil-holes, one near each end 
of the brass, and each connected with a curved groove, the brass refused 
to take its oil or run cool, and seized with a load of only 200 lbs. per sq. in. 

With an oil-pad under the journal feeding rape-oil, the bearing fairly 
carried 551 lbs. Mr. Tower's conclusion from these experiments is that 
the friction depends on the quantity and uniformity of distribution of the 
oil, and may be anything between the oil-bath results and seizing, accord- 
ing to the perfection or imperfection of the lubrication. The lubrication 
may be very small, giving a coefficient of Vioo; but it appeared as though 
it could not be diminished and the friction increased much beyond this 
point without imminent risk of heating and seizing. The oil-bath prob- 
ably represents the most perfect lubrication possible, and .the limit 
beyond which friction cannot be reduced by lubrication; and the experi- 
ments show that with speeds of from 100 to 200 feet per minute, by 
properly proportioning the bearing-surface to the load, it is possible to 
reduce the coefficient of friction to as low as Viooo. A coefficient of 1/1500 
is easily attainable, and probably is frequently attained, in ordinary 
engine-bearings in which the direction of the force is rapidly alternating 
and the oil given an opportunity to get between the surfaces, while the 
duration of the force in one direction is not sufficient to allow time for 
the oil film to be squeezed out. 

Observations on the behavior of the apparatus gave reason to believe 
that with perfect lubrication the speed of minimum friction was from 
100 to 150 feet per minute, and that this speed of minimum friction tends 
to be higher with an increase of load, and also with less perfect lubrica- 
tion. By the speed of minimum friction is meant that speed in approach- 
ing which from rest the friction diminishes, and above which the friction 
increases. 

Coefficients of Friction of Motion and of Rest of a Journal. — 
A cast-iron journal in steel boxes, tested by Prof. Thurston at a speed of 
rubbing of 150 feet per minute, with lard and with sperm oil, gave the 
following: 

Press, per sq. in., lbs. 50 100 250 500 750 1000 

Coeff., with sperm ... 0.013 0.008 0.005 0.004 0.0043 0.009 
Coeff., with lard 0.02 0.0137 0.0085 0.0053 0066 0.125 

The coefficients at starting were: 

With sperm 0.07 0.135 0.14 0.15 0.185 0.18 

Withlard 0.07 0.11 0.U 0.10 0.12 0-12 



FRICTION AND LUBRICATION. 



1199 



The Coefficient at a speed of 150 feet per minute decreases with increase 
Of pressure until 500 lbs. per sq. in. is reached; above this it increases. 
The coefficient at rest or at starting increases with the pressure through- 
out the range of the tests. 

Coefficients of Friction of Journal with Oil-bath. — Abstract of 
results of Tower's experiments on friction (Proc. Inst. M. E., Nov., 1883). 
Journal, 4 in. diam., 6 in. long; temperature, 90° F. 





Nominal Load, in lbs. per sq. in. 


Lubricant in Bath. 


625 


520 


415 


310 


205 


153 


100 




Coefficient of Friction. 






.0009 
.0017 
.0014 
.0022 
seiz'd 


.0012 
.0021 
.0016 
.0027 
.0015 
.0021 

.0009 
.0016 
.0012 
.002 


.0014 
.0029 
.0022 
.004 
.0011 
.0019 

.0008 
.0016 
.0014 
.0024 

0056 


.0020 
.0042 
.0034 
.0066 
.0016 
.0027 

.0014 
.0024 
.0021 
.0035 

.0098 
.0077 

.0105 
.0078 


.0027 
.0052 
.0038 
.0083 
.0019 
.0037 

.002 
.004 


.0042 


" "471 " " 




.009 


Mineral crease: 157 ft. per min.. . . 
471 " " .... 


.001 
.002 


.0076 
.0151 

.003 


" "* 47i "" " ' :;::::; 




0064 




(5731b. 
.001 


.001 
.0015 
.0012 
.0018 


004 


" " 471 " " 


.007 


Mineral-oil: 157 ft. per min 

"471 " " 


,0013 


.004 
.007 


Rape-oil fed by 




0125 


siphon lubricator: j ^. V<^ .. 
Rape-oil, pad 








0068 


.0152 








0099 


.0099 


under journal: j^ 7.^ «« 








0099 


.0133 















Comparative friction of different lubricants under same circumstances, 
temperature 90°, oil-bath: sperm-oil, 100; rape-oil, 106; mineral oil, 129; 
lard, 135; olive oil, 135; mineral grease, 217. 

Value of Anti-friction Metals. (Denton.) — The various white 
metals available for lining brasses do not afford coefficients of friction 
lower than can be obtained with bare brass, but they are less liable to 
"overheating," because of the superiority of such material over bronze 
in ability to permit of abrasion or crushing, without excessive increase of 
friction. 

Thurston (Friction and Lost Work) says that gun-bronze, Babbitt, 
and other soft white alloys have substantially the same friction; in other 
words, the friction is determined by the nature of the unguent and not 
by that of the rubbing-surfaces, when the latter are in good order. The 
soft metals run at higher temperatures than the bronze. This, however, 
does not necessarily indicate a serious defect, but simply deficient con- 
ductivity. The value of the white alloys for bearings lies mainly in their 
ready reduction to a smooth surface after any local or general injury by 
alteration of either surface or form. 

Cast Iron for Bearings* (Joshua Rose.) — Cast iron appears to be an 
exception to the general rule, that the harder the metal the greater the 
resistance to wear, because cast iron is softer in its texture and easier to 
cut with steel tools than steel or wrought iron, but in some situations it 
is far more durable than hardened steel; thus when surrounded by steam 
it will wear better than will any other metal. Thus, for instance, ex- 
perience has demonstrated that piston-rings of cast iron will wear smoother, 
better, and equally as long as those of steel, and longer than those of 
either wrought iron or brass, whether the cylinder in which it works be 
composed of brass, steel, wrought iron, or cast iron; the latter being the 
more noteworthy, since two surfaces of the same metal do not, as a rule, 
wear or work well together. So also slide-valves of brass are not found 
to wear so long or so smoothly as those of cast iron, let the metal of which 
the seating is composed be whatever it may; while, on the other hand, a 



1200 FRICTION AND LUBRICATION. 



cast-iron slide-valve will wear longer of itself and cause less wear to 
its seat, if the latter is of cast iron, than if of steel, wrought iron, or 
brass. 

Friction of Metals under Steam-pressure. — The friction of brass 
upon iron under steam-pressure is double that of iron upon iron. (G. H. 
Babcock, Trans. A. S. M. E., i, 151.) 

Morin's "Laws of Friction." — 1. The friction between two bodies 
is directly proportioned to the pressure; i.e., the coefficient is constant 
for all pressures. 

2. The coefficient and amount of friction, pressure being the same, are 
independent of the areas in contact. 

3. The coefficient of friction is independent of velocity, although static 
friction (friction of rest) is greater than the friction of motion. 

Eng'g News, April 7, 1S88, comments on these "laws" as follows: 
From 1831 till about 1876 there was no attempt worth speaking of to 
enlarge our knowledge of the laws of friction, which during all that period 
was assumed to be complete, although it was really worse than nothing, 
since it was for the most part wholly false. In the year first mentioned 
Morin began a series of experiments which extended over two or three 
years, and which resulted in the enunciation of these three "funda- 
mental laws of friction," no one of which is even approximately true. 

For fifty years these laws were accepted as axiomatic, and were quoted 
as such without question in every scientific work published during that 
whole period. Now that they are so thoroughly discredited it has been 
attempted to explain away their defects on the ground that they cover 
only a very limited range of pressures, areas, velocities, etc., and that 
Morin himself only announced them as true within the range of his con- 
ditions. It is now clearly established that there are no limits or con- 
ditions within winch any one of them even approximates to exactitude, 
and that there are many conditions under which they lead to the wildest 
kind of error, while many of the constants were as inaccurate as the laws. 
For example, in Morin's "Table of Coefficients of Moving Friction of 
Smooth Plane Surfaces, perfectly lubricated," which may be found in 
hundreds of text-books now in use, the coefficient of wrought iron on 
brass is given as 0.075 to 0.103, which would make the rolling friction of 
railway trains 15 to 20 lbs. per ton instead of the 3 to 6 lbs. which.it 
actually is. 

General Morin, in a letter to the Secretary of the Institution of Mechan- 
ical Engineers, dated March 15, 1879, writes as follows concerning his 
experiments on friction made more than forty years before: "The results 
furnished by my experiments as to the relationsbetween pressure, surface, 
and speed on the one hand, and sliding friction on the other, have always 
been regarded by myself, not as mathematical laws, but as close approxi- 
mations to the truth, within the limits of the data of the experiments 
themselves. The same holds, in my opinion, for many other laws of 
practical mechanics, such as those of rolling resistance, fluid resistance, 
etc." 

Prof. J. E. Denton (Stevens Indicator, July, 1890) says: It has been 
generally assumed that friction between lubricated surfaces follows the 
/' simple law that the amount of the friction is some fixed fraction of I 
' the pressure between the surfaces, such fraction being independent of the 
intensity of the pressure per square inch and the velocity of rubbing, 
between certain limits of practice, and that the fixed fraction referred to 
is represented by the coefficients of friction given by the experiments of j 
Morin or obtained from experimental data which represent conditions of 
practical lubrication, such as those given in Webber's Manual of Power. 

By the experiments of Thurston, Woodbury, Tower, etc., however, it 
appears that the friction between lubricated metallic surfaces, such as 
machine bearings, is not directly proportional to the pressure, is not 
independent of the speed, and that the coefficients of Morin and Webber 
are. about tenfold too great for modern journals. 

Prof. Denton offers an explanation of this apparent contradiction of 
authorities by showing, with laboratory testing-machine data, that 
Morin's laws hold for bearings lubricated by a restricted feed of lubricant, 
such as is afforded by the oil-cups common to machinery; whereas the! 
modern experiments have been made with a surplus feed or superabun-j 



FRICTION AND LUBRICATION. 1201 

dance of lubricant, such as is provided only in railroad-car journals, and 
a few special cases of practice. 

That the low coefficients of friction obtained under the latter conditions 
are realized in the case of car-journals, is proved by the fact that the 
temperature of car-boxes remains at 100° at high velocities; and experi- 
ment shows that this temperature is consistent only with a coefficient of 
friction of a fraction of one per cent. Deductions from experiments on 
tram resistance also indicate the same low degree of friction. But these 
low coefficients do not account for the internal friction of steam-engines 
as well as do the coefficients of Morin and Webber. 

In American Machinist, Oct. 23, 1890, Prof. Denton says: Morin's 
measurements of friction of lubricated journals did not extend to light 
pressures. They apply only to the conditions of general shafting and 
engine work. 

He clearly understood that there was a frictional resistance, due solely 
to the viscosity of the oil, and that therefore, -for very light pressures, 
the laws which he enunciated did not prevail. 

He applied his dynamometers to ordinary shaft-journals without 
special preparation of the rubbing-surfaces, and without resorting to 
artificial methods of supplying the oil. 

Later experimenters have with few exceptions devoted themselves 
exclusively to the measurement of resistance practically due to viscosity 
alone. They have eliminated the resistance to which Morin confined his 
measurements, namely, the friction due to such contacts of the rubbing- 
surfaces as prevail with a very thin film of lubricant between compara- 
tively rough surfaces. 

Prof. Denton also says {Trans. A. S. M. E., x, 518): "I do not believe 
there is a particle of proof in any investigation of friction ever made, 
that Morin's laws do not hold for ordinary practical oil-cups or restricted 
rates of feed." 

Laws of Friction of Well-lubricated Journals. — John Goodman 
(Trans. Inst. C. E., 1886, Eng'g News, April 7 and 14, 1888), reviewing 
the results obtained from the testing-machines of Thurston, Tower, and 
Stroudley, arrives at the following laws: 

Laws of Friction: Well-lubricated Surfaces. 
(Oil-bath.) 

1. The coefficient of friction with the surfaces efficiently lubricated is 
from i/e to Vio that for dry or scantily lubricated surfaces. 

2. The coefficient of friction for moderate pressures and speeds varies 
approximately inversely as the normal pressure; the frictional resistance 
varies as the area in contact, the normal pressure remaining constant. 

3. At very low journal speeds the coefficient of friction is abnormally 
high; but as the speed of sliding increases from about 10 to 100 ft. per 
min., the friction diminishes, and again rises when that speed is exceeded, 
varying approximately as the square root of the speed. 

4. The coefficient of friction varies approximately inversely as the 
temperature, within certain limits, namely, just before abrasion takes 
place. 

The evidence upon which these laws are based is taken from various 
modern experiments. That relating to Law 1 is derived from the "First 
Report on Friction Experiments," by Mr. Beauchamp Tower. 



Method of Lubrication. 


Coefficient of 
Friction. 


Comparative 
Friction. 


Oil-bath 


0.00139 
0.0098 
0.0090 


1.00 




7.06 




6.48 







With a load of 293 lbs. per sq. in. and a journal speed of 314 ft. per 
nin. Mr. Tower found the coefficient of friction to be .0016 with an oil- 
Dath, and 0.0097, or six times as much, with a pad. The very low co- 
efficients obtained by Mr. Tower will be accounted for by Law 2, as he 
i'ound that the frictional resistance per square inch under varying loads 

nearly constant, as below: 



1202 



FRICTION AND LUBRICATION. 



Load in lbs. per sq. in. 529 468 415 363 310 258 205 153 100 
F sq U in nal IeS1St ' Per } 0-416 0.514 0.498 0.472 0.464 0.438 0.43 0.458 0.45 

The frictional resistance per square inch is the product of the coefficient 
of friction into the load per square inch on horizontal sections of the brass. 
Hence, if this product be a constant, the one factor must vary inversely 
as the other, or a high load will give a low coefficient, and vice versa. 

For ordinary lubrication, the coefficient is more constant under varying 
loads; the frictional resistance then varies directly as the load, as shown 
by Mr. Tower in Table VIII of his report (Proc. Inst. M. E., 1883). 

With respect to Law 3, A. M. Wellington (Trans. A. S. C. E., 1884), in 
experiments on journals revolving at very low velocities, found that the 
faction was then very great, and nearly constant under varying condi- 
tions of the lubrication, load, and temperature. But as the speed in- 
creased the friction fell slowly and regularly, and again returned to the 
original amount when the velocity was reduced to the same rate. This is 
shown in the following table: 

Speed, feet per minute: 

0+ 2.16 3.33 4.86 8.82 21.42 35.37 53.01 89.28 106.02 

Coefficient of friction: 
0.118 0.094 0.070 0.069 0.055 0.047 0.040 0.035 0.030 0.026 

It was also found by Prof. Kimball that when the journal velocity was 
increased from 6 to 110 ft. per minute, the friction was reduced 70%; 
in another case the friction was reduced 67% when the velocity was 
increased from 1 to 100 ft. per minute; but after that point was reached 
the coefficient varied approximately with the square root of the velocity. 

The following results were obtained by Mr. Tower: 



Feet per minute. . . . 


209 


262 


314 


366 


419 


471 


Nominal Load 
per sq. in. 


Coeff. of friction 


0.001C 
.0013 
.0014 


0.0012 
.0014 
.0015 


0.0013 
.0015 
.0017 


0.0014 
.0017 
.0019 


0.0015 
.0018 
.0021 


0.0017 
.002 
.0024 


520 lbs. 
468 lbs. 
415 lbs. 


The variation of 
inverse ratio, Law 4. 
per minute: 


friction with temperature is approximately in the 
Take, for example, Mr. Tower's results, at 262 ft. 


Temp. F. 


110° 


100° 


90° 


80° 


70° 60° 




0.0044 
0.00451 


0.0051 


006 


0.0073 
00733 


0.0092 
00964 


0.0119 

0.01252 




0.005181 00608 

























This law does not hold good for pad or siphon lubrication, as then the 
coefficient of friction diminishes more rapidly for given increments of 
temperature, but on a gradually decreasing scale, until the normal tem- 
perature has been reached; this normal temperature increases directly 
as the load per sq. in. This is shown in the following table taken from 
Mr. Stroudley's experiments with a pad of rape-oil: 



Temp. F 


105° 


110° 


115° 


120° 


125° 


130° 


135° 


140° 


145° 








0.022 


0.0180 
0.0040 


0.0160 
0.0020 


0.0140 
0.0020 


0.0125 
0.0015 


0.01150 0110 


0.0106 
0.0004 


0.0102 


Decrease of coeff . . 


0.0010 


0.0005 


0.0002 



In the Galton-Westinghouse experiments it was found that with 
velocities below 100 ft. per min., and with low pressures, the frictional 
resistance varied directly as the normal pressure; but when a velocity of 
100 ft. per min. was exceeded, the coefficient of friction greatly diminished; 



FRICTION AND LUBRICATION. 1203 

from the same experiments Prof. Kennedy found that the coefficient of 
friction for high pressures was sensibly less than for low. 

Allowable Pressures on Bearing-surfaces. {Proc. Inst. M. E., 
May, 1888.) — The Committee on Friction experimented with a steel 
ring of rectangular section, pressed between two cast-iron disks, the 
annular bearing-surfaces of which were covered with gun-metal, and were 
12 in. inside diameter and 14 in. outside. The two disks were rotated 
together, and the steel ring was prevented from rotating by means of a 
lever, the holding force of which was measured. When oiled through 
grooves cut in each face of the ring and tested at from 50 to 130 revs, 
per min., it was found that a pressure of 75 lbs. per sq. in. of bearing- 
surface was as much as it would bear safely at the highest speed without 
seizing, although it carried 90 lbs. per sq. in. at the lowest speed. The 
coefficient of friction is also much higher than for a cylindrical bearing, 
and the friction follows the law of the friction of solids much more nearly 
than that of liquids. This is doubtless due to the much less perfect 
lubrication applicable to this form of bearing compared with a cylindrical 
one. The coefficient of friction appears to be about the same with the 
same load at all speeds, or, in other words, to be independent of the 
speed; but it seems to diminish somewhat as the load is increased, and 
may be stated approximately as 1/20 at 15 lbs. per sq. in., diminishing to 
1/30 at 75 lbs. per sq. in. 

The high coefficients of friction are explained by the difficulty of lubri- 
cating a collar-bearing. It is similar to the slide-block of an engine, 
which can carry only about one-tenth the load per sq. in. that can be 
carried by the crank-pins. 

In experiments on cylindrical journals it has been shown that when a 
cylindrical journal was lubricated from the side on which the pressure 
bore, 100 lbs. per sq. in. was the limit of pressure that it would carry; 
but when it came to be lubricated on the lower side and was allowed to 
drag the oil in with it, 600 lbs. per sq. in. was reached with impunity; 
and if the 600 lbs. per sq. in., which was reckoned upon the full diameter 
of the bearing, came to be reckoned on the sixth part of the circle that was 
taking the greater proportion of the load, it followed that the pressure 
upon that part of the circle amounted to about 1200 lbs. per sq. in. 

In connection with these experiments Mr. Wicksteed states that in 
drilling-machines the pressure on the collars is frequently as high as 336 
lbs. per sq. in., but the speed of rubbing in tins case is lower than it was 
in any of the experiments of the Research Committee. In machines 
working very slowly and intermittently, as in testing-machines, very 
much higher pressures are admissible. 

Mr. Adamson mentions the case of a heavy upright shaft carried upon 
a small footstep-bearing, where a weight of at least 20 tons was carried 
on a shaft of 5 in. diameter, or, say, 20 sq. in. area, giving a pressure of 
1 ton per sq. in. The speed was 190 to 200 revs, per min. It was neces- 
sary to force the oil under the bearing by means of a pump. For heavy 
horizontal shafts, such as a fly-wheel shaft, carrying 100 tons on two jour- 
nals, his practice for getting oil into the bearings was to flatten the journal 
along one side throughout its whole length to the extent of about an 
eighth of an inch in width for each inch in diameter up to 8 in. diameter; 
above that size rather less flat in proportion to the diameter. At first 
sight it appeared alarming to get a continuous flat place coming round 
in every revolution of a heavily loaded shaft; yet it carried the oil effec- 
tually into the bearing, which ran much better in consequence than a 
truly cylindrical journal without a flat side. 

In thrust-bearings on torpedo-boats Mr. Thornycroft allows a pressure 
of never more than 50 lbs. per sq. in. 

Prof. Thurston (Friction end Lost Work, p. 240) says 7000 to 9000 lbs. 
pressure per square inch is reached on the slow-working and rarely 
moved pivots of swing bridges. 

Mr. Tower says (Proc. Inst.M.E., Jan., 1884): In eccentric-pins of punch- 
ing and shearing machines very high pressures are sometimes used with- 
out seizing. In addition to the alternation in the direction, the pressure 
is applied for only a very short space of time in these machines, so that 
the oil has no time to be squeezed out. 

In the discussion on Mr. Tower's paper (Proc. Inst. M. E., 1885) it was 
stated that it is well known from practical experience that with a con- 



1204 FRICTION AND LUBRICATION. 

stant load on an ordinary journal it is difficult and almost impossible 
to have more than 200 lbs. per square inch, otherwise the bearing would 
get hot and the oil go out of it ; but when the motion was reciprocating, 
so that the load was alternately relieved from the journal, as with crank- 
pins and similar journals, much higher loads might be applied than even 
700 or 800 IDs. per square inch. 

Mr. Goodman (Proc. Inst. C. E., 1886) found that the total frictional 
resistance is materially reduced by diminishing the width of the brass. 

The lubrication is most efficient in reducing the friction when the brass 
subtends an angle of from 120° to 60°. The film is probably at its best 
between the angles 80° and 110°. 

In the case of a brass of a railway axle-bearing where an oil-groove is 
cut along its crown and an oil-hole is drilled through the top of the brass 
into it, the wear is invariably on the off side, which is probably due to 
the oil escaping as soon as it reaches the crown of the brass, and so leaving 
the off side almost dry, where the wear consequently ensues. 

In railway axles the brass wears always on the forward side. The 
same observation has been made in marine-engine journals, which always 
wear in exactly the reverse way to what might be expected. Mr. Stroud- 
ley thinks this peculiarity is due to a film of lubricant being drawn in 
from the under side of the journal to the aft part of the brass, which 
effectually lubricates and prevents wear on that side; and that when the 
lubricant reaches the forward side of the brass it is so attenuated down 
to a wedge shape that there is insufficient lubrication, and greater wear 
consequently follows. 

C. J. Field (Power, Feb., 1893) says: One of the most vital points of an 
engine for electrical service is that of main bearings. They should have 
a surface velocity of not exceeding 350 feet per minute, with a mean 
bearing-pressure per square inch of projected area of journal of not more 
than 80 lbs. This is considerably within the safe limit of cool perform- 
ance and easy operation. If the bearings are designed in this way, it 
would admit the use of grease on all the main wearing-surface, which in 
a large type of engines for this class of work we think advisable. 

Oil-pressure in a Bearing. — Mr. Beauchamp Tower (Proc. Inst. 
M. E., Jan., 1885) made experiments with a brass bearing 4 ins. diameter 
by 6 ins. long, to determine the pressure of the oil between the brass and 
the journal. The bearing was half immersed in oil, and had a total 
load of 8008 lbs. upon it. The journal rotated 150 r.p.m. The pressure 
of the oil was determined by drilling small holes in the bearing at different 
points and connecting them by tubes to a Bourdon gauge. It was found 
that the pressure varied from 310 to 625 lbs. per sq. in., the greatest 
pressure being a little to the "off" side of the center line of the top of the 
bearing, in the direction of motion of the journal. The sum of the up- 
ward force exerted by these pressures for the whole lubricated area was 
nearly equal to the total pressure on the bearing. The speed was re- 
duced from 150 to 20 r.p.m., but the oil-pressure remained the same, 
showing that the brass was as completely oil-borne at the lower speed as 
at the higher. The following was the observed friction at the lower speed : 

Nominal load, lbs. per sq. in... . 443 333 211 89 

Coefficient of friction .00132 .00168 .00247 .0044 

The nominal load per square inch is the total load divided by the 
product of the diameter and length of the journal. At the low speed 
of 20 r.p.m. it was increased to 676 lbs. per sq. in. without any signs of 
heating or seizing. 

Friction of Car- journal Brasses. (J. E. Denton, Trans. A. S. M. E., 
xii, 405.) — A new brass dressed with an emery-wheel, loaded with 5000 
lbs., may have an actual bearing-surface on the journal, as shown by the 
polish of a portion of the surface, of only 1 square inch. With this pressure 
of 5000 lbs. per sq. in., the coefficient of friction may be 6%, and the 
brass may be overheated, scarred and cut, but, on the contrary, it may 
wear down evenly to a smooth bearing, giving a highly polished area of 
contact of 3 sq. ins., or more, inside of two hours of running, gradually 
decreasing the pressure per square inch of contact, and a coefficient of 
friction of less than 0.5%. A reciprocating motion in the direction of the 
axis is of importance in reducing the friction. With such polished sur- 
faces any oil will lubricate, and the coefficient of friction then depends 



FRICTION AND LUBRICATION. 1205 



on the viscosity of the oil. With a pressure of 1000 lbs. per sq. in., revo- 
lutions from 170 to 320 per min., and temperatures of 75° to 113° F., witli 
botn sperm and paraffine oils, a coefficient of as low as 0.11% has been 
obtained, the oil being fed continuously by a pad. 

Experiments on Overheating of Bearings. — Hot Boxes. (Denton.) 
— Tests witn car brasses loaded from 1100 to 4500 lbs. per sq. in. gave 
7 cases of overlieating out of 32 trials. The tests show how purefy a 
matter of chance is tne overheating, as a brass which ran hot at 5000 lbs. 
load on one day would run cool on a later date at the same or higher 
pressure. The explanation of this apparently arbitrary difference of 
behavior is that tne accidental variations of tne smoothness of the sur-' 
faces, almost infinitesimal in their magnitude, cause variations of friction 
which are always tending to produce overheating, and it is solely a matter 
of chance when these tendencies preponderate over the lubricating 
influence of the oil. There is no appreciable advantage shown by sperm- 
oil, when there is no tendency to overheat — that is, paraffine can lubri- 
cate under the highest pressures which occur, as well as sperm, when the 
surfaces are within the conditions affording the minimum coefficients of 
friction. 

Sperm and other oils of high heat-resisting qualities, like vegetable oil 
and petroleum cylinder stocks, differ from the more volatile lubricants, 
like paraffine, only in their ability to reduce the chances of the continual 
accidental infinitesimal abrasion producing overheating. 

The effect of emery or other gritty substance in reducing overheating 
of a bearing is thus explained: 

The effect of the emery upon the surfaces of the bearings is to cover the 
latter with a series of parallel grooves, and apparently after such grooves 
are made the presence of the emery does not practically increase the 
friction over its amount when pure oil only is between the surfaces. 
The infinite number of grooves constitute a very perfect means of insuring 
a uniform oil supply at every point of the bearings. As long as grooves 
in the journal match with those in the brasses the friction appears to 
amount to only about 10% to 15% of the pressure. But if a smooth 
journal is placed between a set of brasses which are grooved, and pres- 
sure be applied, the journal crushes the grooves and becomes brazed 
or coated with brass, and then the coefficient of friction becomes upward 
of 40%. If then emery is applied, the friction is made very much less by 
its presence, because the grooves are made to match each other, and a 
uniform oil supply prevails at every point of the bearings, whereas before 
the application of the emery many spots of the bearing receive no oil 
between them. 

Moment of Friction and Work of Friction of Sliding-surfaces, etc. 

Moment of Friction, Energy lost by Fric- 
inch-lbs. tioninft.-lbs. 

per min. 

Flat surfaces fWS 

Shafts and journals 1/2 fWd 0.2618 fWdn 

Flat pivots 2/3/TFr 0.349 fWrn 

Collar-bearing 2 /3/TT r2 ?~ ri ? 0.349 fWn r ''~ ri ' 

r 2 z-ri 2 r 2 2 -r 1 2 

Conical pivot 2 /3fWr cosec a 0.349 fWrn cosec a 

Conical journal 2 /sfWr sec a 0.349 fWrn sec a 

Truncated-cone pivot 2/3 fw T2 ~ Tl 0.349 fW r2 ~ n 

r 2 sin a r 2 sin a 

Hemispherical pivot fWr 0.5236 fWrn 

Tractrix, or Schiele's "anti- 
friction" pivot fWr 0.5236 fWrn 

In the above/ = coefficient of friction; 

W = weight on journal or pivot in pounds; 
r = radius, d = diameter, in inches; 
S = space in feet through which sliding takes place; 
r 2 = outer radius, r t = inner radius; 
n = number of revolutions per minute; 
a = the half-angle of the cone, i.e., the angle of the slope 
with the axis. 



i206 FRICTION AND LUBRICATION, 

To obtain the horse-power, divide the quantities in the last column 
by 33,000. Horse-power absorbed by friction of a shaft = <£.— "- 



126,050 

The formula for energy lost by shafts and journals is approximately 
true for loosely fitted bearings. Prof. Thurston shows that the correct 
formula varies according to the character of fit of the bearing; thus for 
loosely fitted journals, if U = the energy lost, 

tT 2firr TT7 . , j 0.2618 fWdn . . lfc 

U = . Wn inch-pounds = — — . foot-lbs. 

V1+/2 V1+/2 

For perfectly fitted journals U = 2.54 fnrWn inch-lbs. = 0.3325 fWdn 
ft. -lbs. 

For a bearing in which the journal is so grasped as to give a uniform 
pressure throughout, U = fir 2 rWn inch-lbs. = 0A112fWdn ft.-lbs. 

Resistance of railway trains and wagons due to friction of trains: 

Pull on draw-bar — /X 2240 4= R pounds per gross ton, 

in which R is the ratio of the radius of the wheel to the radius of journal. 

A cylindrical journal, perfectly fitted into a bearing, and carrying a 
total load, distributes the pressure due to this load unequally on the 
bearing, the maximum pressure being at the extremity of the vertical 
radius, while at the extremities of the horizontal diameter the pressure 
is zero. At any point of the bearing-surface at the extremity of a radius 
which makes an angle 8 with the vertical radius the normal pressure is 
proportional to cos 8. If p = normal pressure on a unit of surface, 
w = total ioad on a unit of length of the journal, and r = radius of journal, 
w cos 8 = 1.57 rp, p = w Cos 8 -4 s 1.57 r. 

Tests of Large Shaft Bearings are reported by Albert Kingsbury 
in Trans. A. S. M. E., 1905. A horizontal shaft was supported in two 
bearings 9 X 30 ins., and a third bearing 15 X 40 ins., midway between the 
other two, was pressed upwards against the shaft by a weighed lever, so 
that it was subjected to a pressure of 25 to 50 tons. The journals were 
flooded with oil from a supply tank. The shaft was driven by an electric 
motor, and the friction H.P. was determined by measuring the current 
supplied. Following are the principal results: 
Load, tons* 

25 25 25 25 25 

Load per sq. in.* 

83 83 83 83 83 

Speed, r.p.m. 

309 506 180 179 301 
Speed, ft. per min.* 
1215 1990 708 704 1180 
Friction H.P.f 

12.6 21.7 6.43 5.12 10.1 16 17.9 41.9 47.8 52.3 

Cceff. of frictionf 

.0045 .0048 .0040 .0037 .0037 .0029 .0024 .0025 .0022 .0022 
* On the large bearing; t Three bearings. 

The last three tests were with paraffin oil; the others with heavy machine 
oil. 

Clearance between Journal and Bearing. — John W. Upp, in 
Trans. A. S. M. E., 1905 gives a table showing the. diameter of bore 
of horizontal and vertical bearings according to the practice of one of the 
leading builders of electrical machinery. The maximum diameter of the 
journal is the same as its nominal diameter, with an allowable variation 
below maximum of 0.0005 in. up to 3 in. diam., 0.001 in. from 3V2 to 9 in., 
and 0.0015 in. from 10 to 24 in. The maximum bore of a horizontal bear- 
ing is larger than the diam. of the journal bv from 0.002 in. for a 1/2-m. 
journal to 0.009 for 6 in., for journals 7 to 15 in. it is 0.004 + 0.001 X 
diam., and for 16 to 24 in. it is uniformly 0.02 in. Fof vertical journals the 
clearance is less by from 0.001 to 0.004 in. according to the diameter. The 
allowable variation above the minimum bore is from 0.001 to 0.005. 

Allowable Pressures on Bearings. — J. T. Nicholson, in a paper 
read before the Manchester Assoc, of Engrs. (Am. Mach., Jan. 16, 1908, 



33.6 


42.3 


47 


47 


50.5 


112 


141 


157 


157 


168 


454 


480 


946 


1243 


1286 


1785 


1890 


3720 


4900 


5050 



FRICTION AND LUBRICATION. 1207 

Eng. Digest, Feb., 1908), as a result of a theoretical study of the lubrication 
of bearings and of their emission of heat, obtains the formula p = P/ld — 
40 (dN) /■*, in which p = allowable pressure per sq. in. of projected area, 
P = total pressure, I = length and d = diam. of journal, N = revs, per 
min. It appears from this formula that the greater the speed the greater 
the allowable pressure per sq. in., so that for a 1-in. journal the allowable 
pressure per sq. in. is 126 lbs. at 100 r.p.m. and 189 lbs. at 500 r.p.m., and 
for a 5-in. journal 189 lbs. at 100 and 283 lbs. at 500 r.p.m. W. H. Scott 
(Eng. Digest, Feb., 1908) says this is contrary to the teaching of practical 
experience, and therefore the formula is inaccurate. Mr. Scott, from a 
study of the experiments of Tower, Lasche, and Stribeck, derives the 
following formulae for the several conditions named : 

For main bearings of double-acting vertical engines, p = 750 D^^/N 1 ^ 
" horizontal " ..p= 660 dVw/N 1 /* 
" single-acting four-cycle gas en- : , 

gines p = 1350 #Vi3/jvV4 

For crank pins of. vert, and hor. double-acting engines, p = 1560 dV^/N 1 /* 
" " " " single-acting four-cycle gas engines, p = 3000 D^^/N 1 /* 

For dead loads with ordinary lubrication p = 400 iV -1 /.5 

" forced " p = 1600 jV _1 /4 

p = allowable pressure in lbs. per sq. in. of projected area; D = diam. 
in ins.; N = revs. per. min. 

F. W. Taylor (Trans. A. S. M. E., 1905), as the result of an investigation 
of line shaft and mill bearings that were running near the limit of dura- 
bility and heating yet not dangerously heating, gives the formula PV = 
400. P = pressure in lbs. per sq. in. of projected area, V = velocity of 
circumference of bearing in ft. per sec. 

The formula is applicable to bearings in ordinary shop or mill use on 
shafting which is intended to run with the care and attention which such 
bearings usually receive, and gives the maximum or most severe duty to 
which it is safe to subject ordinary chain or oiled ball and socket bearings 
which are babbitted. It is not safe for ordinary shafting to use cast-iron 
boxes, with either sight feed, wick feed, or grease-cup oiling, under as severe 
conditions as P X V = 200. 

Archbutt and Deeley's "Lubrication and Lubricants" gives the follow- 
ing table of allowable pressures in lbs. per sq. in. of projected area of 
different bearings: 

Crank-pin of shearing and punching machine, hard steel, inter- 
mittent load bearing 3000 

Bronze crosshead neck journals 1200 

Crank pins, large slow engine 800-900 

Crank pins, marine engines 400-500 

Main crankshaft bearing, fast marine 400" 

Same, slow marine 600 

Railway coach journals 3Q0-400 

Flywheel shaft journals 150-200 

Small engine crank pin . .' 150-200 

Small slide block, marine engine 100 

Stationary engine slide blocks 25-125 

Same, usual case 30- 60 

Propeller thrust bearings 50- 70 

Shafts in cast-iron steps, high speed 15 

Bearing Pressures for Heavy Intermittent Loads. (Oberlin Smith, 
Trans. A. S. M. E., 1905.) — In a punching press of about 84 tons capa- 
city, the pressure upon the front journal of the main shaft is about 
2400 lbs. per sq. in. of projected area. Upon the eccentric the pressure 
against the pitman driving the ram is. some 7000 lbs. per sq. in. — both 
surfaces being of cast iron, and sometimes running at a surface speed of 
140 feet per minute. Such machines run year in and year out with but 
little trouble in the way of heating or " cutting." An instance of excessive 
pressure may be cited in the case of a Ferracute toggle press, where the 
whole ram pressure of 400 tons is brought to bear upon hardened steel 



1208 FRICTION AND LUBRICATION. 

toggle-pins, running in cast iron or bronze bearings, 3 in. in diam. by nearly 
14 in. long. These run habitually, for maximum work, under a load of 
20,000 lbs. per sq. in. 

Bearings for Very High Rotative Speeds. (Proc. Inst. M. E., 
Oct., 1888, p. 482.) — In the Parsons steam-turbine, which has a speed as 
high as 18,000 rev. per min., as it is impossible to secure absolute accuracy 
of balance, the bearings are of special construction so as to allow of a 
certain very small amount of lateral freedom. For this purpose the 
bearing is surrounded by two sets of steel washers Vi6 in. thick and of 
different diameters, the larger fitting close in the casing and about 1/32 in. 
clear of the bearing, and the smaller fitting close on the bearing and about 
V32 in. clear of the casing. These are arranged alternately, and are 
pressed together by a spiral spring. Consequently any lateral movement 
of the bearing causes them to slide mutually against one another, and by 
their friction to check or damp any vibrations that may be set up in the 
spindle. The tendency of the spindle is then to rotate about its axis of 
mass, and the bearings are thereby relieved from excessive pressure, and 
the machine from undue vibration. The allowing of the turbine itself 
to find its own center of gyration is a well-known device in other branches 
of mechanics: as in the instance of the centrifugal hydro-extractor, where 
a mass very much out of balance is allowed to find" its own center of 
gyration; the faster it runs the more steadily does it revolve and the less 
is the vibration. Another illustration is to be found in the spindles of 
spinning machinery which run at about 10,000 or 11,000 revs, per min.: 
although of very small dimensions, the outside diameter of the largest 
portion or driving whorl being perhaps not more than 11/4 in., it is found 
impracticable to run them at that speed in what might be called a hard- 
and-fast bearing. They are therefore run with some elastic substance 
surrounding the bearing, such as steel springs, hemp, or cork. Any 
elastic substance is sufficient to absorb the vibration, and permit of 
absolutely steady running. 

Thrust Bearings in Marine Practice. (G. W. Dickie, Trans. A. S- 
M. E., 1905.) — The approximate pressure on a thrust bearing of a propeller 
shaft assuming two thirds of the indicated horse-power to 'be effective 

on the propeller is P = I.H.P. X 2 *™ 3 x 6080° = ^li^ X 217 " 1 ' in 

which S = speed of ship in knots per hour, P = total thrust in lbs. The 
following are data of water-cooled bearings which have given satisfactory 
service: 

Speed in knots 22 221/2 28 21 

Thrust-ring surface, horse-shoe type, 

sq. ins 1188 891 581 2268 

Horse-power, one engine, I.H.P 11,500 6,800 4,200 15,000 

Indicated pressure on bearing, lbs,.. . 112,700 89,000 33,600 154,000 

Pressure per sq. in. of surface, lbs 95 100 58 68.1 

Mean speed of bearing surfaces, ft. per 

min. 642 610 827 504 

Bearings for Locomotives. (G. M. Basford, Trans. A. S. M. E., 
1905.) — Bearing areas for locomotive journals are determined chiefly 
by the possibilities of lubrication. On driving journals the -following 
figures of pressure in lbs. per sq. in. of projected area give good service: 
passenger, 190; freight, 200; switching, 220 lbs. Crank pins may be 
loaded from 1500 to 1700 lbs.; wrist pins to 4000 lbs. per sq. in. Car and 
tender bearings are usually loaded from 300 to 325 lbs. per sq. in. 

Bearings of Corliss Engines. (P. H. Been, 'Trans, A. S. M. E., 
1905.) — In the practice of one of the largest builders the greatest pressure 
allowed per sq. in. of projected area for all shafts is 140 lbs. On most 
engines the pressure per sq. in. multiplied by the velocity of the bearing 
surface in ft. per sec. lies between 1000 and 1300. 

Edwin Reynolds says that a main engine bearing to be safe against 
undue heating should be of such a size that the. product of the square root 
of the speed of rubbing-surface in feet per second multiplied by the pounds 
per square inch of projected area, should not exceed 375 for a horizontal 
engine, or 500 for a vertical engine when the shaft is lifted at every revo- 
lution. Locomotive driving boxes in some cases give the product as high 



!:; 



PIVOT-BEARINGS. 1209 

as 585, but this is accounted for by the cooling action of the air. (Am. 
Mach., Sept. 17, 1903.) 

Temperature of Engine Bearings. (A. M. Mattice, Trans. A. S. M. 
E., 1905.) — An examination of the temperature of bearings of a large num- 
ber of engines of various makes showed more above 135° F. than below 
that figure. Many bearings were running with a temperature over 150°, 
and in one case at 180°, and in all of these cases the bearings were giving 
no trouble. 

PIVOT-BEARING S . 

The Schiele Curve. — W. H. Harrison (Am. Mach., 1891) says t"ie 
Schiele curve is not as good a form for a bearing as the segment of % 
sphere. He says: A mill-stone weighing a ton frequently bears its whc 3 
weight upon the flat end of a hard-steel pivot 1 Vs in. diam., or 1 sq. in. 
area of bearing; but to carry a weight of 3000 lbs. he advises an end 
bearing about 4 ins. diam., made in the form of a segment of a sphere 
about 1/2 in. in height. The die or fixed bearing should be dished to fit 
the pivot. This form gives a chance for the bearing to adjust itself, 
which it does not have when made flat, or when made with the Schiele 
curve. If a side bearing is necessary it can be arranged farther up the 
shaft. The pivot and die should be of steel, hardened: cross-gutters 
should be in the die to allow oil to flow, and a central oil-hole should be 
made in the shaft. 

The advantage claimed for the Schiele bearing is that the pressure is 
uniformly distributed over its surface, and that it therefore wears uni- 
formly. Wilfred Lewis (Am. Mach., April 19, 1894) says that its merits 
as a thrust-bearing have been vastly overestimated; that the term 
"anti-friction" applied to it is a misnomer, since its friction is greater 
than that of a flat step or collar of the same diameter. He advises that 
flat thrust-bearings should always be annular in form, having an inside 
diameter one-half of the external diameter. 

Friction of a Flat Pivot-bearing. — The Research Committee on 
Friction (Proc. Inst. M. E., 1891) experimented on a step-bearing, flat- 
tended, 3 in. diam., the oil being forced into the bearing through a hole 
in its center and distributed through two radial grooves, insuring thorough 
lubrication. The step was of steel and the bearing of manganese-bronze. 

At revolutions per min. 50 128 194 290 353 

The coefficient of frictionl 0.0181 0.0053 0.0051 0.0044 0.0053 
varied between /and 0.0221 0.0113 0.0102 0.0178 0.0167 

With a white-metal bearing at 128 revs, the coefficient of friction was 
a little larger than with the manganese-bronze. At the higher speeds 
the coefficient of friction was less, owing to the more perfect lubrication, 
as shown by the more rapid circulation of the oil. At 128 revs, the 
bronze-bearing heated and seized on one occasion with a load of 260 lbs., 
and on another occasion with 300 lbs. per sq. in. The white-metal bear- 
ing under similar conditions heated and seized with a load of 240 lbs. 
per sq. in. The steel footstep on manganese-bronze was afterwards 
tried, lubricating with three and with four radial grooves: but the friction 
was from one and a half times to twice as great as with only the two 
grooves. 

Mercury-hath Pivot. — A nearlv frictionless step-bearing may be 
obtained by floating the bearing with its superincumbent weight upon 
mercury. Such an apparatus is used in the lighthouses of La Heve, 
Havre. It is thus described in Eng'a, July 14, 1893. p. 41: 

The optical apparatus, weighing; about 1 ton. rests on a circular cast- 
iron table, which is supported bv a vertical shaft of wrought iron 2.36 in. 
diameter. This is kept in position at the top by a bronze ring and outer 
iron supDort, and at the bottom in the same way. while it rotates on a 
removable steel pivot resting in a steel socket, which is fitted to the base 
of the support. To the vertical shaft there is riridly fixed a floating cast- 
iron ring 17.1 in. diameter and 11.8 in. in depth, which is plunged into 
and rotates in a mercury bath contained in a fixed outer drum or tank, 
the clearance between the vertical surfaces of the drum and ring being 
only 0.2 in., so as to reduce as much as possible the volume of mercury 
(about 220 lbs.), while the horizontal clearance at the bottom is 0.4 in. 



1210 



FRICTION AND LUBRICATION. 



BALL-BEARINGS, ROLLER-BEARINGS, ETC. 

Friction-rollers. — If a journal instead of revolving on ordinary 
. bearings be supported on friction-rollers the force required to make the 
journal revolve will be reduced in nearly the same proportion that the 
diameter of the axles of the rollers is less than the diameter of the rollers 
themselves. In experiments by A. M. Wellington with a journal 31/2 in. 
diam. supported on rollers 8 in. diam., whose axles were 13/ 4 in. d\am., the 
friction in starting from rest was 1/4 the friction of an ordinary 31/2-in. 
bearing, but at a car speed of 10 miles per hour it was 1/2 that of the ordi- 
nary bearing. The ratio of the diam. of the axle to diam. of roller was 
13/ 4 : 8, or as 1 to 4.6. 

Coefficients of Friction of Roller Bearings. C. H. Benjamin, Machy. 
Oct., 1905. — Comparative tests of plain babbitted, McKeel plain roller, 
and Hyatt roller bearings gave the following values of the coefficient of 
friction at a speed of 560 r.p.m.: 



Diameter 


Hyatt Bearing. 


McKeel Bearing. 


Babbitt Bearing. 


of 
Journal. 


Max. 


Min. 


Ave. 


Max. 


Min. 


Ave. 


Max. 


Min. 


Ave. 


1 15/16 
23/16 


.032 
.019 
.042 
.029 


.012 
.011 
.025 
.022 


.018 
.014 
.032 
.025 


.033 


.017 


.022 


.074 
.088 
.114 
.125 


.029 
.078 
.083 
.089 


.043 
082 


27/ie 
215/16 ' 


.028 
.039 


.015 
.019 


.02J 
.027 


.096 
.107 



The friction of the roller bearing is from one-fifth to one-third that of a 

J)lain bearing at moderate loads and speeds. It is noticeable that as the 
oad on a roller bearing increases the coefficient of friction decreases. 

A slight change in the pressure due to the adjusting nuts was sufficient 
to increase the friction considerably. In the McKeel bearing the rolls 
bore on a cast-iron sleeve and in the Hyatt on a soft-steel one. If roller 
bearings are properly adjusted and not overloaded a saving of from 2-3 
to 3-4 of the friction may be reasonably expected. 

McKeel bearings contained rolls turned from solid steel and guided by 
spherical ends fitting recesses in cage rings at each end. The cage rings 
were joined to each other by steel rods parallel to the rolls. 

Lubrication is absolutely necessary with ball and roller bearings, 
although the contrary claim is often advanced. Under favorable con- 
ditions an almost imperceptible film is sufficient; a sufficient quantity 
to immerse half the lowest ball should always be provided as a rust 
preventive. Rust and grit must be kept out of ball and roller bearings. 
Acid or rancid lubricants are as destructive as rust. (Henry Hess.) 

Both ball and roller bearings, to give the best satisfaction, should be 
made of steel, hardened and ground; accurately fitted, and in proper 
alignment with the shaft and load: cleaned and oiled regularly, and fitted 
with as large-size balls or rollers as possible, depending upon the revolutions 
per minute and load to be carried. Oil is absolutely necessary on both 
ball and roller bearings, to prevent rust. (S. S. Eveland.) 

Roller Bearings. — The Mossberg roller bearings for journals are made 
in the sizes given in the table below. D = diam. of journal; d = diam. of 
roll; N = number of rolls; P = safe load on journals, in lbs. The rolls 
are enclosed in a bronze supporting cage. (Trans. A. S. M. E., 1905.) 



D 


d 


N 


P 


D 


d 


N 


P 


D 


d 


N 


P 


2 
21/2 

4 
5 


1/4 

5/16 
3/8 

7/16 
9 /l6 


20 

22 
22 
24 
24 


3,500 

7,000 
13,000 
24,000 
37,000 


6 
7 
8 
9 
12 


H/16 

13/16 
7/8 
1 
11/4 


24 

22 
22 
24 
26 


50,000 
70, COO 
90,000 
115,000 
175,000 


15 
18 
20 

24 


13/8 
13/8 

11/2 
11/2 


28 
32 
34 
38 


255,000 
325,000 
400,000 
576,000 













BALL-BEARINGS, ROLLER-BEARINGS,' ETC. 1211 



Surface speed of journal to 50 ft. per min. Length of journal 11/2 
diameters. The rolls are made of tool steel not too high in carbon, and of 
spring temper. The journal or shaft should be made not above a medium 
spring temper. The box should be made of high carbon steel and tem- 
pered as hard as possible. 

Conical Roller Thrust Bearings. — The Mossberg thrust bearing is 
made of conical rollers contained in a cage, and two collars, one being 
stationary and the other fixed to the shaft and revolving with it. One 
side of each collar is made conical to correspond with the rollers which 
bear on it. The apex of the cones is at the center of the shaft. The 
angle of the cones is 6 to 7 degrees. Larger- angles are objectionable, 
giving excessive end thrust. The following sizes are made: 



Diameter 

of Shaft. 

Ins. 


Outside 

Diameter 

of Ring. 

Ins. 


No. of 
Rolls. 


Safe Pressure on Bearing. 


Area of 

Pressure 

Plate. 

Sq. ins. 


Speed 
75 Rev. 

Lbs. 


Speed 
150 Rev. 
Lbs. 


21/16-21/4 
3 1/16-3 1/4 
4 l/i 6 -4 1/4 
5 1/16-5 1/4 
6 1/16-6 1/2 
8I/16-8V2 
9 1/16-9 1/2 


59/16 

8 

105/i 6 
123/ 8 
147/s 
183/ 4 
201/2 


30 
30 
30 
30 
30 
32 
32 


10 
20 
35 
54 
78 
132 
162 


19,000 
40,000 
70,000 
108,000 
125,000 
200,000 
300,000 


9,500 

20,000 
35,000 
56,000 
62,000 
100,000 
150,000 



Plain Roller Thrust Bearings. — S. S. Eveland, of the Standard 
Roller Bearing Co., contributes the following data of plain roller thrust 
bearings in use in 1903. The bearing consists of a large number of short 
cylindrical rollers enclosed in openings in a disk placed between two 
hardened steel plates. He says "our plain roller bearing is theoretically 
wrong, but in practice it works perfectly, and has replaced many thou- 
sand ball-bearings which have proven unsatisfactory." 



Size of 

Bearing. 

ins. 


Number and 
Size of Rollers, 
ins. 


R.p.m. 


Weight 

on 
Bear- 
ings, lbs. 


Lineal 
inches. 


Weight 
per lin. 
in., lbs. 


Weight 
on each 

roll, 

lbs. 


43/4X 6H/i 6 

43/4 X 71/4 
51/2X 8 1/2 

7 X 103/8 
71/2X1 15/ 16 

8 x 151/2 


36 5/ 8 x5/ 16 
32 3/ 4 x5/8 
54 3/4X5/8 
48 1 xl/2 
54 1 x 1/2 
70 H/4X5/8 


500 
470 
420 
370 
325 
300 


6,000 
10,000 
15,000 
20,000 
25,000 
60,000 


111/4 

12 

201/4 

24 

27 

45 


546 
833 
750 
833 
988 
1334 


167 
312 
279 
417 
463 
833 



The Hyatt Roller Bearing. (A. L. Williston, Trans. A. S. M. E., 
1905.) — The distinctive feature of the Hyatt roller bearing is a flexible 
roller, made of a strip of steel wound into a coil or spring of uniform diam- 
eter. A roller of this construction insures a uniform distribution of the 
load along the line of contact of the roller and the surfaces on which it 
operates. It also permits any slight irregularities in either journal or box 
without causing excessive pressure. The roller is hollow and serves as 
an oil reservoir. For a heavy load, a roller of heavy stock can be made, 
while for a high-speed bearing under light pressure a roller of light weight, 
made from thin stock, can be used. Following are the results of some tests 
of the Hvatt bearing in comparison with other bearings: 

A shaft 152 ft. long, 2i5/i6 in. diam. supported by 20 bearings, belt- 
driven from one end, gave a friction load of 2.28 H.P. with babbitted 
bearings, and 0.80 H.P. with Hyatt bearings. With 88 countershafts 
running in babbitted bearings, the H.P. required was 8.85 when the main 
shaft was in babbitted bearings and 6.36 H.P. when it was in Hyatt bearings. 



1212 FRICTION AND LUBRICATION. 

Comparative tests of solid rollers and of Hyatt rollers were made in 
1898 at the Franklin Institute by placing two sets of rollers between three 
flat plates, putting the plates under load in a testing machine and measur- 
ing the force required to move the middle plate. All the rollers were 
3/4 in. diam., 10 ins. long. The Hyatt rollers were made of 1/2 X 1/8 in. 
steel strip. With 2000 lbs. load and plain rollers it took 26 lbs. to move 
the plate, and with the Hyatt rollers 9 lbs. With 3000 lbs. load and 
plain rollers the resistance was 34 lbs., with Hyatt rollers 17 lbs. 

In tests with a pendulum friction testing machine at the Case Scientific 
School, with a bearing 115/16 in. diam. the coefficient of friction with the 
Hyatt bearing was from 0S)362 down to 0.0196, the loads increasing from 
64 to 264 lbs.; with cast-iron bearings and the same loads the coefficient 
was from 0.165 to 0.098. 

In tests at Purdue University with bearings 4 X IV2 ins. and loads 
from 1900 to 8300 lbs., the average coefficients with different bearings and 
different speeds were as follows: 

Hyatt bearing 130 r.p.m. 0.0114 302 r.p.m. 0.0099 585 r.p.m. 0.0147 
Cast-iron bearing 128 " 0.0548 302 " 0.0592 410 " 0.0683 
Bronze bearing 130 " 0.0576 320 " 0.0661 582 " 0.140 

The cast-iron bearing at 128 r.p.m. seized with 8300 lbs., and at 410 
r.p.m. with 5900 lbs. The bronze bearing seized at 130 r.p.m. with 3500 lbs., 
at 320 r.p.m. with 5100 lbs., and at 582 r.p.m. with 2700 lbs. 

The makers have found that the advantages of roller bearings of the 
type described are especially great with either high speeds or heavy loads. 
Generally, the best results are obtained for line-shaft work up to speeds of 
600 rev. per min., when a load of 30 lbs. per square inch of projected area 
is allowed. For heavy load at slow speed, such as in crane and truck 
wheels, a load of 500 lbs. gives the best results. 

The Friction Coefficient of a well-made annular ball-bearing is 0.001 
and 0.002 of the load referred to the shaft diameter and is independent 
of the speed and load. The friction coefficient of a good roller bearing 
is from 0.0035 to 0.014; it rises very much if the load is light. It in- 
creases also when the speeds are very low, though not so much as with 
plain bearings. (Henry Hess.) 

Notes on Ball Bearings. — The following notes are contributed by 
Mr. Henry Hess, 1910. Ball bearings in modern use date from the bi- 
cycle. That brought in the adjustable cup and cone and three-point 
contact type. Under the demands for greater load resistance and relia- 
bility the two-point contact type, without adjustability, was evolved; 
that is now used under loads from a few pounds to many tons. Such a 
bearing consists of an inner race, an outer race and the series of balls 
that roll in tracks of curved cross section. Various designs are used, 
differing chiefly in the devices for separating the balls and in the arrange- 
ment for introducing the balls between the races. The most widely 
used type has races that are of the same cross section throughout, un- 
broken by any openings for the introduction of balls. To introduce 
the balls the two races are first excentrically placed; the balls will fill 
slightly more than a half circumference ; elastic separators or solid cages 
are used to space the balls. 

Another type has a filling opening of sufficient depth cut into one race; 
the race continuity is restored by a small piece that is let in. This type 
is usually filled with balls, without cages or separators. The filling 
opening is always placed at the unloaded side of the bearing, where the 
weakening of the race is not important. This type has been almost en- 
tirely discarded in favor of the one above described. 

A third type has a filling opening cut into each race not quite deep 
enough to tangent the bottom of the ball track. As this weakened 
section necessarily comes under the load during each revolution, the 
carrying capacity is reduced. After slight wear there develops an inter- 
ference of the balls with the edges of these openings, which seriously 
reduces the speeds and load capacity. This interference precludes the 
use of this type to take end thrust. 

The carrying capacity of a ball-bearing is directly proportional to the 
number of 'balls and to the square of the ball diameter. 



BALL-BEARINGS, ROLLEIt-BEARINGS, ETC. 1213 

It may be written as: 

L = Knd 2 , in which L = load capacity in pounds; n = number of 
bails; d = ball diameter in eighths of an inch. K varies with the condition 
and type of bearing, as also with the material and speed. 

For a certain special sh-H that hardens throughout and is also unusu- 
ally tough, employed by " DWF" or "HB" (the originators of the modern 
two-point type), the following values apply. For other steels lesser values 
must be used. 

I. For Radial Bearings : 
K = 9 for uninterrupted race track, cross-section curvature = 0.52 

and 9/i6 in. ball diameter respectively for inner and outer races, 

separated balls, uniform load, and steady speed up to 3000 

revs, per min. 
K = 5 for full ball type, filling opening in one race at the unloaded 

side, otherwise as above. 
K = 2.5 for both ball tracks interrupted by filling openings, inelastic 

cage separators for balls, or full ball, speeds not above 2000 

revs, per min., Uniform load. 
K = 0.9 for thrust on a radial bearing of the first type, as above. The 

larger the balls the smaller K. The type with filling openings 

in each race is not suitable for end thrust. 

The radial load bearing is, up to high speeds, practically unaffected by 
speed, as to carrying capacity. 

1 1 . Thrust B earing s : 

With the thrust type, consisting of one flat plate and one seat plate 
with grooved ball races, the load capacity decreases with speed or 

L _ K 1 nd? 

</R ' 

Ki= constant for material and race cross-section, etc., R = revolu- 
tions per minute. R ranges from about 3000 revs, per min. down to 1 rev. 
per min. as for crane hooks and similar elements. 

Ki = 25 to 40 for material used by the DWF or HB, and race cross- 
section radius = approx. 1.66 ball radius. 

K x = 0.5 for unhardened steel, occasionally used for very large races; 
a steel that is fairly hard without tempering must be used, and then only 
when there is no hammering or sharp load variation. 

Balls must be carefully selected to make sure that all that are used 
in the same bearing do not vary among one another by more than 0.0001 
inch. A ball that is more than that larger than its fellows will sustain 
more than its proportion of the load, and may therefore be overloaded 
and will in turn overload the races. 

The usual test of ball quality, which consists in compressing a ball 
between flat plates and noting the load at rupture, gives the quality of 
the plates, but not of the balls. It is the ability of the ball to resist 
permanent deformation that is of importance. As the deformations 
involved are very small the test is a difficult one to carry out. Of even 
greater importance than a small deformation under load is uniformity of 
such deformation between the balls employed; a hard ball will deform 
less than its softer mate and so will carry more than its share of the 
load, and will therefore be overloaded and in turn overload the races. 

Coned bearings for balls are objectionable. The defect in all these 
forms of bearings is their adjustable feature. A bearing properly propor- 
tioned with reference to a certain load may be enormously overloaded by 
a little extra effort applied to the wrench, or on the other hand the bear- 
ing may be adjusted with too little pressure, so that the balls will rattle, 
and the results consequently be unsatisfactory. The prevalent idea that 
coned ball-bearings can be adjusted to compensate for wear is erroneous. 

Mr. Hess's paper, in Trans. A.S.M. E., 1907, contains a great deal of 
useful information on the practical design of ball-bearings, including dif- 
ferent forms of raceways. He prefers a two-point bearing, in which the 
ball races have a curved section, with sustaining surfaces at right angles 
with the direction of the load. 

Formulae for Number of Balls in a Bearing. (H. Rolfe, Am. Mach., 
Dec. 3, 1896. "> — Let D = diam, of ball circle (the circle passing through 



1214 



FRICTION AND LUBRICATION. 



the centers of the balls) ; d = diam. of balls; n= number of balls; s = aver- 
age clearance space between the balls. Then D = (d + s) -s- sin (180°/n); 
d = D sin (1807ft) - s; s = D sin (180°/ft) - d: n = 180° -*■ angle whose 
sine is (d + s) -s- D. The clearance s should be about 0.003 in. 







Values of 


1807ft 


AND OF SIN 1807ft. 










8 






8 






,8 






£ 


n. 


.8 


o 
2 


n. 


4 


1 


n. 


8* 


1 


n. 


8* 


I 




1 


_c 




1 


a 




1 


,a 




1 


# c 




"~ 


CO 




"" 


<a 




"" 


CQ 




""" 


Hi 


3 


60 


0.86603 


15 


12 


0.20791 


27 


6.667 


0.11609 


39 


4.615 


0.08047 


4 


45 


.70711 


16 


11.250 


. 19509 


28 


6.429 


.11197 


40 


4.500 


.07846 


5 


36 


.58799 


17 


10.588 


.18375 


29 


6.207 


.10812 


41 


4.390 


.07655 


6 


30 


.50000 


18 


10 


.17365 


30 


6 


.1Q453 


42 


4.286 


.07473 


7 


25.714 


.43388 


19 


9.474 


. 16454 


31 


5.806 


.10117 


43 


4.186 


.07300 


8 


22.500 


.38268 


20 


9. 


.15643 


32 


5.625 


.09801 


44 


4.091 


.07134 


9 


20 


.34202 


21 


8.571 


.14904 


33 


5.455 


.09506 


45 


4 


.06976 


10 


18 


.30902 


22 


8.182 


.14233 


34 


5.294 


.09227 


46 


3.913 


.06825 


11 


16.364 


.28173 


23 


7.826 


.13616 


35 


5.143 


.08963 


47 


3.830 


.06679 


12 


15 


.25882 


24 


7.500 


.13053 


36 


5 


.08716 


48 


3.750 


.06540 


13 


13.846 


.23931 


25 


7.200 


. 12533 


37 


4.865 


.08510 


49 


3.673 


.06407 


14 


12.857 


.22252 


26 


6.923 


.12055 


38 


4.737 


.08258 


50 


3.600 


.06279 



Grades of Balls for Bearings. (S. S. Eveland, Trans. A. S. M. E., 
1905.) — "A" grade balls vary about 0.0025 in. in diameter; "B" grade, 
0.001 to 0.002 in.; while " high-duty" or special balls are furnished varying 
not over 0.0001 in. The crushing strength of balls is of little importance 
as to the load a bearing will carry, the revolutions per minute being quite 
as important as the load. 

Saving of Power by Use of Bali-Bearings. — Henry Hess {Tram. 
A. S. M. E., 1909) describes a series of tests made by Dodge and Day on a 
2!5/i6 in. line shaft 72 ft. long, alternately equipped with plain ring-oiling 
babbitted boxes and with Hess-Bright ball-bearings. Eight countershafts 
were driven from pulleys on the line shaft. The countershaft pulleys had 
plain bearings. The conclusions from the tests made under normal belt 
conditions of 44 and 57 lbs. per inch width of angle of single belt are as 
follows: 

a. Savings due to the substitution of ball-bearings for plain bearings on 
line shafts may be safely calculated by using 0.0015 as the coefficient of 
ball-bearing friction, 0.03 as the coefficient of line shaft friction, and 0.08 
as the coefficient of countershaft friction. 

b. When the belts from line shaft to countershaft pull all in one direc- 
tion and nearly horizontally the saving due to the substitution of ball- 
bearings for plain bearings on the line shaft may be safely taken as 35% 
of the bearing friction. 

c. When ball-bearings are used also on the countershafts the savings 
will be correspondingly greater and may amount to 70% or more of the 
bearing friction. 

d. These percentages of savings are percentages of the friction work 
lost in the plain bearings; they are not percentages of the total power 
transmitted. The latter will depend upon the ratio of the total power 
transmitted to that absorbed in the line and countershafts. 

e. The power consumed in the plain line and countershafts varies, as 
is well known, from 10 to 60% in different industries and shops. The 
substitution of ball-bearings for plain bearings on the line shaft only, under 
conditions of paragraph "<7," will thus result in saving of total power of 
35 X 0.10 = 3.5% to 35 X 0.60 = 21%. By using ball-bearings on the 
countershafts also, the saving of total power will be from 70 X 0.10 = 7% 
to 70 X 0.60 = 42%. 

KNIFE-EDGE BEARINGS. 
Allowable loads on knife-edges vary with the manner in which the 
pivots or knife-edges are held in the lever and the pivot supports or 
seats secured to the base of weighing machines. The extension of the 



FRICTION OF STEAM-ENGINES. 1215 

pivot beyond the solid support is practically worthless. A high-grade uni- 
form tool steel with carbon 0.90% to 1.00% should be used. The temper 
of the seats should be drawn to a very light straw color; that of the pivots 
should be slightly darker. The angle of 90° for the knife-edge has given 
good results for heavy loads. For ordinary weighing machinery and most 
testing machinery 5000 lbs. per inch of length is ample. Loads of 10,000 
lbs. per inch of length are permissible, but the pivot must be flat at its 
upper portion, normal to the load and supported its whole length, with a 
minimum deflection of parts to secure reasonable accuracy. The edge may 
be made perfectly sharp, for loads up to 1000 lbs. per inch of length. For 
greater loads the sharp edge is rubbed with an oilstone, so that a smooth- 
ness is just visible. A pronounced radius of knife-edge will decrease the 
sensibility of the apparatus. (Jos. W. Bramwell, Eng. News, June 14, 
1906.) 

FRICTION OF STEA3I-ENGINES. 
Distribution of the Friction of Engines. — Prof. Thurston, in his 
" Friction and Lost Work," gives the following: 

Main bearings 

Piston and rod 

Crank-pin 

Cross-head and wrist-pin 

Valve and rod 

Eccentric strap 

Link and eccentric 



1. s 


2. 


3. 


47.0 


35.4 


35.0 


32.9 


25.0 


21.0 


6.8 
5.4 


5.1) 
4.1} 


13.0 


2.5 


26.4) 


22.0 


5.3 


4.0) 






9.0 


100.0 


100.0 


100.0 



Total 

No. 1, Straight-line, 6 x 12 in., balanced valve; No. 2, Straight-line, 
6 x 12 in., unbalanced valve; No. 3, 7 x 10 in., Lansing traction, locomo- 
tive valve-gear. 

Prof. Thurston's tests on a number of different styles of engines indicate 
that the friction of any engine is practically constant under all loads. 
(Trans. A. S. M. E., viii, 86; ix, 74.) 

In a straight-line engine, 8 x 14 in., I.H.P. from 7.41 to 57.54, the 
friction H.P. varied irregularly between 1.97 and 4.02, the variation 
being independent of the load. With 50 H.P. on the brake the I.H.P. 
was only 52.6, the friction being only 2.6 H.P., or about 5%. 

A compound condensing-engine, tested from to 102.6 brake H.P., gave 
I.H.P. from 14.92 to 117.8 H.P., the friction H.P. varying only from 
14 92 to 17.42. At the maximum load the friction was 15.2 H.P., or 
12.9%. 

The friction increases with increase of the boiler-pressure from 30 to 70 
lbs., and then becomes constant. The friction generally increases with 
increase of speed, but there arc exceptions to this rule. 

Prof. Denton (Stevens Indicator, July, 1890), comparing the calculated 
friction of a number of engines with the friction as determined by measure- 
ment, finds that in one case, a 75-ton ammonia ice-machine, the friction of 
the compressor, 17 1/2 H.P., is accounted for by a coefficient of friction 
of 71/2% on all the external bearings, allowing 6% of the entire friction 
of the machine for the friction of pistons, stuffing-boxes, and valves. In 
the case of the Pawtucket pumping-engine, estimating the friction of the 
external bearings with a coefficient of friction of 6% and that of the 
pistons, valves, and stuffing-boxes as in the case of the ice-machine, we 
have the total friction distributed as follows: 

Horse- Per cent 

power, of whole. 

Crank-pins and effect of piston-thrust on main shaft .71 11 .4 

Weight of fly-wheel and main shaft 1 .95 32 .4 

Steam-valves .23 3.7 

Eccentric 0.07 1.2 

Pistons 0.43 7.2 

Stuffing-boxes, six altogether .72 11.3 

Air-pump. . 2 .10 32 .8 

Total friction of engine with load 6 .21 100 .0 

Total friction per cent of indicated power. 4.27 



1216 FRICTION AND LUBRICATION. 

The friction of this engine, though very low in proportion to the indi- 
cated power, is satisfactorily accounted for by Morin's law used with a 
coefficient of friction of 5%. In both cases the main items of friction are 
those due to the weight of the fly-wheel and main shaft and to the piston- 
thrust on crank-pins and main-shaft bearings. In the ice-machine the 
latter items are the larger owing to the extra crank-pin to work the pumps, 
while in the Pawtucket engine the former preponderates, as the crank- 
thrusts are partly absorbed by the pump-pistons, and only the surplus- 
effect acts on the crank-shaft. 

Prof. Denton describes in Trans. A, S. M. E., x. 392, an apparatus by 
which he measured the friction of the piston packing-ring. When the 
parts of the piston were thoroughty devoid of lubricant, the coefficient 
of friction was found to be about 7 1/2%; with an oil-feed of one drop in 
two minutes the coefficient was about 5%; with one drop per minute it 
was about 3%. These rates of feed gave unsatisfactory lubrication, the 
piston groaning at the ends of the stroke when run slowly, and the flow of 
oil left upon the surfaces was found by analysis to contain about 50% of 
iron. A feed of two drops per minute reduced the coefficient of friction 
to about 1%, and gave practically perfect lubrication, the oil retaining its 
natural color and purity. 

FRICTION BRAKES AND FRICTION CLUTCHES. 

Friction Brakes are used for slowing down or stopping a moving 
machine by converting its energy of motion into heat, or for controlling 
the speed of a descending load. The simplest form is the block brake, 
commonly used for railway car wheels, which resists the motion of the 
wheei not only with the force due to ordinary sliding friction, but with 
that due to cutting or grinding away the surface of the metals in contact. 
If P = total pressure acting normal to the sliding surface, / = coefficient 
of friction, and v = velocity in feet per minute, then the energy absorbed, 
in foot-pounds per minute, is Pfv. If the surface is lubricated and the 
pressure per square inch not great enough to squeeze out the lubricant, 
then the value of / for different materials may be taken from Morin's 
tables for friction of motion, page 1196, but if the pressure is great enough 
to force out the lubricant, then the coefficient becomes much greater 
and the surface or surfaces will cut and wear, with a rapid rise of tempera- 
ture. 

Other forms of brakes are disk brakes and cone brakes, in which a 
disk or cone is carried by the rotating shaft and a mating disk or cone 
is pressed against it by a lever or other means; and band brakes, also 
called strap or ribbon brakes, in which a flexible band encircles the 
cylindrical surface of a rotating drum or wheel, and tension applied 
to one end of the band brings it in contact with that surface. For band 
brakes the theory of friction of belts applies. See page 1115. For much 
information on the theory and practice of friction brakes see articles by 
C. F. Blake in Mach'y, Jan., 1901, Mar., 1905, and Aug., 1906, and by 
E. R. Douglas, Am. Mach., Dec. 26, 1901, and R. B. Brown, Mach'y, 
April, 1909. For friction brake dynamometers see Dynamometers. 

Friction Clutches are used for putting shafts in motion gradually, 
without shock. If two shafts, in line with each other, one in motion and 
the other at rest, each having a disk keyed to the end, and the disks 
almost touching, are moved toward each other so that the disks are 
brought in contact with some pressure, the shaft at rest will be put in 
motion gradually, while the disks rub on each other, until it acquires the 
velocity of the driving shaft, when the friction ceases and the disks may 
then be locked together. This is an elementary form of friction clutch. 
A great variety of styles are made in which the sliding surfaces may be 
disks, cones, and gripping blocks of various forms. The work done by a 
clutch while the surfaces are in sliding contact, and before thev are locked 
together, is the overcoming of the inertia of the driven shaft and of all 
the mechanism driven by it, and giving it the velocity of the driving 
shaft. The principles of friction brakes apply to friction clutches. The 
sliding surfaces must be of sufficient area to keep the normal pressure 
below that at which they will overheat, cut and wear, and to dissipate 
the heat generated by friction. The following values of the coefficient 
of friction to be used in designing clutches are given by C. W. Hunt: 
cork on iron, 0.35; leather on iron, 0,3; wood on iron, 0.2; iron on iron, 



FRICTION OF HYDRAULIC PLUNGER PACKING. 



1217 



0.25 to 0.3. Lower values than these should be assumed for velocities 
exceeding 400 ft. per minute. The pressure per square inch in disk 
clutches should not exceed 25 or 30 lbs., and wooden surfaces should 
not be loaded beyond 20 to 25 lbs. per sq. in. See Kimball and Barr on 
Machine Design, also Trans. A.S. M.E., 1903 and 1908. 

Electrically Operated Brakes are discussed by H. A Steen in a 
paper read before the Engrs. Socy. of W. Penna., reprinted in Iron Trade 
Rev., Dec. 24, 1908. Formulae are given for the time required for stop- 
ping, for the heat generated and the temperature rise, for different types 
of brakes. 

Magnetic and Electric Brakes. — For braking the load on electric 
cranes a band brake is used which is held off the drum by the action of 
a magnet or solenoid, and is put on by the action of a spring or weight. 
The solenoid usually consists of a coil of wire connected in series with the 
motor, and a plunger working inside of the coil. It should be so pro- 
portioned that its action is not delayed by residual magnetism when the 
current is cut off. Too rapid action is prevented by making the end of 
the solenoid an air dash-pot. 

For electric-driven machinery an electric motor makes a most efficient 
brake by reversing the direction of the electric current, causing the motor 
to become a generator supplying current to a rheostat in which it is con- 
verted into heat and dissipated. In some cases the electric current 
generated, instead of being absorbed in a rheostat, is fed into the main 
electric circuit. In this case the energy of the rotating mass, instead of 
being wasted in friction or in electrical heating, is converted into electric 
energy and thus conserved for further use. 

Design of Band Brakes. (R. A. Greene, Am. Mach., Oct. 8, 1908.) — 
In the practice of the Browning Engineering Co., Cleveland, O., in 
regard to the design of band brakes the equations are: 

T= PX, t= T -P,S = p^ F , *= S X D X 0.262 X revolutions per 

minute, in which T = the greater tension on the band, t = the lesser 
tension on the band, P = equivalent load on the brake drum, X = factor 

N 
from the accompanying table, X = „__ in which log. N = 10 2-7288 /c, 

where / = the coefficient of friction and c the length of arc of contact in 
degrees divided by 360. D == diam. of brake drum, F = width of face 
of brake drum, S = a checking factor which has a maximum limit of 65, 
# = a checking factor which has a limit of 54,000 (Yale & Towne practice) 
or 60,000 (Brown hoist practice). 

Example. — A band brake is to be designed having an arc of contact 
of 260°, coefficient of friction = 0.2, drum diameter 30 ins., face 4 ins., 
speed 100 r.p.m., and a load of 3000 lbs. acting on a diameter of 20 ins. 

Then 

P= 3000 X 20-^30 = 2000 pounds, X = 1.68 (from table), T = 2000 X 
1.68 = 3360 pounds, t = 3360 - 2000 = 1360 pounds, S = 2X3360-^ 
(30 X4) = 56 (within the limit), & = 56 X30 X0.62 X100 = 44,000 (within 
the limit). 





Values of X. 




Values of X. 


Degrees. 






Degrees. 
















7=0.2. 


/=0.3. 


7=0.4. 




f=0.2. 


/=0.3. 


/=0.4. 


180 


2.14 


1.64 


1.40 


260 


1.68 


1.35 


1.19 


195 


2.03 


1.56 


1.35 


270 


1.64 


1.32 


1.18 


210 


1.93 


1.50 


1.30 


280 


1.60 


1.30 


1.17 


240 


1.76 


1.40 


1.23 


290 


1.57 


1.28 


1.15 


250 


1.72 


1.37 


1.21 


300 


1.54 


1.26 


1.14 



FRICTION OF HYDRAULIC PLUNGER PACKING. 

The " Taschenbuch der Hutte " (15th edition, vol. 1, p. 202) says: "For 
stuffing boxes with hemp, cotton or leather packing, with water pressures 
between 1 and 50 atmospheres, the frictional loss is dependent upon the 
water pressure, the circumference of the packed surface, and a coefficient 



1218 FRICTION AND LUBRICATION. 



ju, which is constant for this range of pressure. The loss is independent 
of the depth of stuffing-box or leather ring, and is given by the formula 
F = Kpd, in which F = total frictional loss in pounds, p = pressure in pounds 
per sq. in., d = diameter of plunger in inches. 

K is a coefficient, which depends on the kind and condition of the pack- 
ing, and is given as follows for various cases. 

For cotton or hemp, loose or braided, dipped in hot tallow; plungers 
smooth, glands not pulled down too tight, packing therefore retaining 
its elasticity; dimensions such as usually occur, K = 0.072. 

Same conditions, after packing is some months old, K = 0.132. 

Materials the same, but with hard packing, unfavorable conditions, 
etc., i£ = as much as 0.299. 

Leather packing; soft leather, well made, etc., K = 0.036 to 0.084. 

Hard, stiffly tanned leather, K = 0.12 to 0.156. 

Unfavorable conditions; rough plungers, gritty water, etc., i£ = as much 
as 0.239. 

Weisbach-Hermann, " Mechanics of Hoisting Machinery," gives a 
formula which when translated into the same notation as the one in 
" Hutte " is 

F = 0.0312 pd to 0.0767 pd. 

Since the total pressure on a plunger is V47rd 2 p, the ratio of the loss of 
pressure to the total pressure is Kpd^- x UTzd?p, or, using the extreme values 
of K, 0.0312 and 0.299, the ratio ranges from 0.04 n-d to 0.38 + d, or from 
4 to 38 per cent divided by the diameter in inches. 

Walter Ferris {Am. Mach., Feb. 3, 1898) derives from the formula 
given above the following formula for the pressure produced by a hemp- 
packed hydraulic intensifier made with two plungers of different diameters: 
A-KD 

in which P2 = pressure per sq. in. produced by the intensifier, pi= initial 
pressure, A=area and £> = diam. of the larger plunger, a==area and rf = 
diam. of the smaller plunger, and K an experimental coefficient. He gives 
the following results of tests of an intensifier with a small plunger 8 ins. 
diam. and two large plungers, 14V4 and 17 3 /4 ins., either one of which could 
be used as desired. 

Diam. of large plunger, in. 14V4 14V4 173/4 173/4 

Initial pressure, lbs. per sq. in. 285 475 335 350 

Intensified pressure, lbs. per sq. in. 750 1450 1450 1510 

Intensified if there were no friction 905 1505 1650 1725 

Intensified calculated by formula* 806 1433 1572 1643 

Efficiency of machine 0.83 0.965 0.88 0.875 

LUBRICATION. 

Measurement of the Durability of Lubricants. — (X E. Denton, 
Trans. A. S. M. E., xi, 1013.) — Practical differences of durability of 
lubricants depend not on any differences of inherent ability to resist 
being "worn out" by rubbing, but upon the rate at which they flow 
through and away from the bearing-surfaces. The conditions which 
control this flow are so delicate in their influence that all attempts thus 
far made to measure durability of lubricants may be said to have failed 
to make distinctions of lubricating value having any practical significance. 
In some kinds of service the limit to the consumption of oil depends upon 
the extent to which dust or other refuse becomes mixed with it, as in 
railroad-car lubrication and in the case of agricultural machinery. The 
economy of one oil over another, so far as the quality used is concerned — 
that is, so far as durability is concerned — is simply proportional to the 
rate at which it can insinuate itself into and flow out of minute orifices or 
cracks. Oils will differ in their ability to do this, first, in proportion to 
their viscosity, and, second, in proportion to the capillary properties which 
they may possess by virtue of the particular ingredients used in their 
composition. Where the thickness of film between rubbing-surfaces 
must be so great that large amounts of oil pass through bearings in a given 
time, and the surroundings are such as to permit oil to be fed at high 

♦Assuming K = 0.2. The efficiency calculated by the formula in each 
case was 0.953. 



LUBRICATION. 1219 

temperatures or applied by a method not requiring a perfect fluidity, it is 
probable that the least amount of oil will be used when the viscosity is as 
great as in the petroleum cylinder stocks. When, however, the oil must 
flow freely at ordinary temperatures and the feed of oil is restricted, as in 
the case of crank-pin bearings, it is not practicable to feed such heavy 
oils in a satisfactory manner. Oils of less viscosity or of a fluidity 
approximating to lard-oil must then be used. 

Relative Value of Lubricants. (J. E. Denton, Am. Mack., Oct. 30, 
1890.) — The three elements which determine the value of a lubricant 
are the cost due to consumption of lubricants, the cost spent for coal to 
overcome the frictional resistance caused by use of the lubricant, and the 
cost due to the metallic wear on the journal and the brasses. 

The Qualifications of a Good Lubricant, as laid down by W. H. 
Bailey, in Proc. Inst. C. E., vol. xlv, p. 372, are: 1. Sufficient body to 
keep the surfaces free from contact under maximum pressure. 2. The 
greatest possible fluidity consistent with the foregoing condition. 3. The 
lowest possible coefficient of friction, which in bath lubrication would be 
for fluid friction approximately. 4. The greatest capacity for storing 
and carrying away heat. 5. A high temperature of decomposition. 
6. Power to resist oxidation or the action of the atmosphere. 7. Freedom 
from corrosive action on the metals upon which the lubricant is used. 

The Examination of Lubricating Oils. (Prof. Thos. B. Stillman, 
Stevens Indicator, July, 1890.) — The generally accepted conditions of 
a good lubricant are as follows: 

1. "Body" enough to prevent the surfaces to which it is applied from 
coming in contact with each other. (Viscosity.) 

2. Freedom from corrosive acid, of either mineral or animal origin. 

3. As fluid as possible consistent with "body." 

4. A minimum coefficient of friction. 

5. High "flash" and burning points. 

6. Freedom from all materials liable to produce oxidation or "gum- 
ming." 

The examinations to be made to verify the above are both chemical and 
mechanical, and are usually arranged in the following order: 

1. Identification of the oil, whether a simple mineral oil, or animal oil, 
or a mixture. 2. Density. 3. Viscosity. 4. Flash-point. 5. Burning- 
point. 6. Acidity. 7. Coefficient of friction. 8. Cold test. 

Detailed directions for making all of the above tests are given in Prof. 
Stillman's article. See also Stillman's Engineering Chemistry, p. 366. 

Notes on Specifications for Petroleum Lubricants. (C. M. Everest, 
Vice-Pres. Vacuum Oil Co., Proc. Engineering Congress, Chicago World's 
Fair, 1893.) — The specific gravity was the first standard established for 
determining quality of lubricating oils, but it has long since been dis- 
carded as a conclusive test of lubricating quality. However, as the 
specific gravity of a particular petroleum oil increases the viscosity also 
increases. 

The object of the fire test of a lubricant, as well as its flash test, is the 
prevention of danger from fire through the use of an oil that will evolve 
inflammable vapors. The lowest fire test permissible is 300°, which gives 
a liberal factor of safetv under ordinary conditions. 

The cold test of an oil, i.e., the temperature at which the oil will congeal, 
should be well below the temperature at which it is used; otherwise the 
coefficient of friction would be correspondingly increased. 

Viscosity, or fluidity, of an oil is usually expressed in seconds of time in 
which a given quantity of oil will flow through a certain orifice at the tem- 
perature stated, comparison'sometimes being made with water, sometimes 
with sperm-oil, and again with rape-seed oil. It seems evident that 
within limits the lower the viscosity of an oil (without a too near approach 
to metallic contact of the rubbing surfaces) the lower will be the coefficient 
of friction. But we consider that each bearing in a mill or factory would 
probably require an oil of different viscosity from any other bearingin the 
mill, in order to give its lowest coefficient of friction, and that slight 
variations in the condition of a particular bearing would change the re- 
quirements of that bearing; and further, that when nearing the "danger 
point" the question of viscosity alone probably does not govern. 

The requirement of the New England Manufacturers' Association, that 
an oil shall not lose over 5% of its volume when heated to 140° Fahr. for 
12 hours, is to prevent losses by evaporation, with the resultant effects. 



1220 



FRICTION AND LUBRICATION. 



The precipitation test gives no indication of the quality of the oil itself, 
as the free carbon in improperly manufactured oils can be easily removed. 

It is doubtful whether oil buyers who require certain given standards 
of laboratory tests are better served than those who do not. Some of 
the standards are so faulty that to pass them an oil manufacturer must 
supply oil he knows to be faulty; and the requirements of the best stand- 
ards can generally be met by products that will give inferior results in 
actual serivce. 

Penna. R. R. Specifications for Petroleum Products, 1900. — 
Five different grades of petroleum products will be used. 

The materials desired under this specification are the products of the 
distillation and refining of petroleum unmixed with any other substances. 

150° Fire-test Oil. — This grade of oil will not be accepted if sample 
(1) is not "water-white" in color; (2) flashes below 130° Fahrenheit; 
(3) burns below 151° Fahrenheit; (4) is cloudy or shipment has cloudy 
barrels when received, from the presence of glue or suspended matter; 
(5) becomes opaque or shows cloud when the sample has been 10 minutes 
at a temperature of 0° Fahrenheit. 

300° Fire-test Oil. — This grade of oil will not be accepted if sample 
(1) is not "water-white" in color; (2) flashes below 249° Fahrenheit; 
(3) burns below 298° Fahrenheit; (4) is cloudy or shipment has cloudy 
barrels when received, from the presence of glue or suspended matter; 
(5) becomes opaque or shows cloud when the sample has been 10 minutes 
at a temperature of 32° Fahrenheit; (6) shows precipitation when some 
of the sample is heated to 450° F. The precipitation test is made by 
having about two fluid ounces of the oil in a six-ounce beaker, with a 
thermometer suspended in the oil, and then heating slowly until the 
thermometer shows the required temperature. ' The oil changes color, 
but must show no precipitation. 

Paraffine and Neutral Oils. — These grades of oil will not be accepted 
if the sample from shipment (1) is so dark in color that printing with 
long-primer type cannot be read with ordinary daylight through a layer of 
the oil V? inch thick: (2) flashes below 298° F.: (3) has a gravity at 
60° F., below 24° or above 35° Baume; (4) from October 1st to May 1st 
has a cold test above 10° F., and from May 1st to October 1st has a cold 
test above 32° F. 

The color test is made by having a layer of the oil of the prescribed 
thickness in a proper glass vessel, and then putting the printing on one 
side of the vessel and reading it through the layer of oil with the back 
of the observer toward the source of light. 

Well Oil. — This grade of oil will not be accepted if the sample from 
shipment (1) flashes, from May 1st to October 1st, below 298° F., or 
from October 1st to May 1st, below 249° F.; (2) has a gravity at 60° F., 
below 28° or above 31° Baume; (3) from October 1st to May 1st has 
a cold test above 10° F., and from May 1st to October 1st has a cold test 
above 32° F.; (4) shows any precipitation when 5 cubic centimeters are 
mixed with 95 c.c. of gasoline. The precipitation test is to exclude tarry 
and suspended matter. It is made by putting 95 c.c. of 88° B. gasoline, 
which must not be above 80° F. in temperature, into a 100 c.c. graduate, 
then adding the prescribed amount of oil and shaking thoroughly. Allow 
to stand ten minutes. With satisfactory oil no separated or precipitated 
J material can be seen. 



500° Fire-test Oil. — This grade of oil will not be accepted if sample 
flashes below 494° F.; (2) shows precipitation with 



from shipment (1) 

gasoline when tested as described for well oil. 

Printed directions for determining flashing and burning tests and for 
making cold tests and taking gravity are furnished by the railroad company. 

Penna. R. R. Specifications for Lubricating Oils (1894). (In 
force in 1902.) 



Constituent Oils. 


Parts by volume. 










1 








1 








1 
I 
4 


i i 

1 2 

2 1 


1 
1 


I 

1 


1 

2 




500° fire-test oil 




1 


4 








Well oil . . . 


1 




4 


2 


1 














Used for 


A 


B 


Ci 1 c 2 1 c 3 


Dt 


Do 


D s 


E 



LUBRICATION. 



1221 



A, freight cars; engine oil on shifting-engines; miscellaneous greasing 
in foundries, etc. B, cylinder lubricant on marine equipment and on 
stationary engines. C, engine oil; all engine machinery; engine and 
tender truck boxes; shafting and machine tools; bolt cutting; general 
lubrication except cars. D, passenger-car lubrication. E, cylinder 
lubricant for locomotives. Ci, Di, for use in Dec, Jan., and Feb.; Ci, 
Z>2, in March, April, May, Sept., Oct., and Nov.; C3, Dz, in June, July, 
and August. Weights per gallon, A, 7.4 lbs.; B, C, D, E, 7.5 lbs. 

Grease Lubricants. — Tests made on an Olsen lubricant testing machine 
at Cornell University are reported in Power, Nov. 9, 1909. It was found 
that some of the commercial greases stood much higher pressures than 
the oils tested, and that the coefficients of friction at moderate loads were 
often as low as those of the oils. The journal of the testing machine 
was 33/4 in. diam., 3 1/2 in. long, and the babbitt bearing shoe had a projected 
area of 5.8 sq. in. The speed was 240 r.p.m. and each test lasted one 
hour, except when the bearing showed overheating. The following are 
the coefficients of friction obtained in the tests: 



Lbs. 

per 

sq. in. 


Min- 
eral 
Grease. 


Ani- 
mal 
Grease. 


Graph- 
ite 
Grease. 


Min- 
eral 
Grease. 


Engine 
Oil. 


Engine 
Oil. 


Grease. 


Grease. 


86.2 
172.4 
258.6 
344.8 


0.024 
0.021 
0.021 
0.025 
0.050 


0.023 

0.023 
0.023 
0.025 
0.035 


0.04 
0.05 


0.023 
0.018 
0.018 
0.019 
0.028 


0.019 
0.04 
0.06 


0.015 
0.022 
0.037 


0.020 
0.015 
0.014 
0.017 
0.026 


0.025 
0.022 
0.020 
020 


431.0 






0.019 











Testing Oil for Steam Turbines. (Robert Job, Trans. Am. Soc. for 
Testing Matls., 1909.) — 

In some types of steam-turbines, the bearings are very closely adjusted 
and, if the oil is not clear and free from waxy substances, clogging and 
heating quickly results. A number of red engine and turbine oils some 
of which had given good service and others bad service were tested and 
it was found that clearness and freedom from turbidity were of importance, 
but mere color, or lack of color, seemed to have little influence, and good 
service results were obtained with oils which were of a red color, as well 
as with those which were filtered to an amber color. 

Heating Test. — It was found that on heating the oils to 450° F. all 
which had given" bad service showed a marked darkening of color, while 
those which had proved satisfactory showed little change. With oils 
that had been filtered or else had been chemically treated in such manner 
that the so-called " amorphous waxes " had been completely removed, 
on applying the heating test only a slight darkening of color resulted. 
It is of advantage in addition to other requirements to specify that an 
oil for steam turbines on being heated to 450° F. for five minutes shall 
show not more than a slight darkening of color. The test is that com- 
monly used in test of 300° oil for burning purposes. 

Separating Test. — It is known that elimination of the waxes causes an 
increase in the ease with which the oil separates from hot water when 
thoroughly shaken with it. This condition can be taken advantage of 
by prescribing that when one ounce of the oil is placed in a 4-oz. bottle 
with two ounces of boiling water, the bottle corked and shaken hard for 
one minute and let stand, the oil must separate from the water within a 
specified time, depending upon the nature of the oil, and that there must 
be no appearance of waxy substances at the line of demarcation between 
the oil and the water. 

Quantity of Oil needed to Run an Engine. — The Vacuum Oil Co. in 
1892, in response to an inquirv as to cost of oil to run a 1000-H.P. Corliss 
engine, wrote: The cost of running two engines of equal size of the same 
make is not always the same. Therefore, while we could furnish figures 
showing what it is costing some of our customers having Corliss engines 
of 1000 H.P., we could only give a general idea, which in itself might be 
considerably out of the way as to the probable cost of cylinder- and 
engine-oils per year for a particular engine. Such an engine ought to 



1222 FRICTION AND LUBRICATION. 



run readily on less than 8 drops of 600 W oil per minute. If 3000 drops 
are figured to the quart, ana 8 drops used per minute, it would take about 
two and one half barrels (52.5 gallons) of 600 W cylinder-oil, at 65 cents 
per gallon, or about $85 for cylinder-oil per year, running 6 days a week 
and 10 hours a day. Engine-oil would be even more difficult to guess at 
what the cost would be, because it would depend upon the number of 
cups required on the engine, which varies somewhat according to the 
style of the engine. It would doubtless be safe, however, to calculate 
at the outside that not more than twice as much engine-oil would be 
required as of cylinder-oil. 

The Vacuum Oil Co. in 1892 published the following results of practice 
with "600 W" cylinder-oil: 

Torli^ rnmnmind pnHnP \ 20 and 33 X 48 = 83 reVS - P er min - ; X dr0 P of 

Corliss compound engine, j oil per min to 1 drop in two minutes , 

* triple exp. " 20, 33, and 46 x 48; 1 drop every 2 minutes. 

f 20 and 36 x 36; 143 revs, per min.; 2 drops 
Porter-Allen " ] of oil per min., reduced afterwards to 1 drop 

( per min. 
R ,. .. (15 and 25 x 16; 240 revs, per min.; 1 drop 

I every 4 minutes. 

Results of tests on ocean-steamers communicated to the author by 
Prof. Denton in 1892 gave: for 1200-H.P. marine engine, 5 to 6 English 
gallons (6 to 7.2 U. S. gals.) of engine-oil per 24 hours for external lubri- 
cation; and for a 1500-H.P. marine engine, triple expansion, running 
75 revs, per min., 6 to 7 English gals, per 24 hours. The cylinder-oil 
consumption is exceedingly variable, — from 1 to 4 gals, per day on 
different engines, including cylinder-oil used to swab the piston-rods. 

Cylinder Lubrication. — J. H. Spoor, in Power, Jan. 4. 1910, has made 
a study of a great number of records of the amount of oil used for lubri- 
cating cylinders of different engines, and has reduced them to a sys- 
tematic basis of the equivalent number of pints of oil used in a 10-hour 
day for different areas of surface lubricated. The surface is determined 
in square inches by multiplying the circumference of the cylinder by the 
length of stroke. The results are plotted in a series of curves for different 
types of engines, and approximate average figures taken from these curves 
are given below : 

Compound Engines. 

Sq. ins. lubricated 2,000 4,000 6,000 8,000 10,000 12,000, 18,000 

Pints of oil used in 10 hrs. 2 3.5 4.3 5 5.5 6 6.5 

Corliss Engines. 

Sq. ins. lubricated 1,000 2,000 3,000 4,000 

Pints of oil in 10 hrs. Avge 0.9 1.65 2.25 3.75 

Max 1.2 2.25 

Min 1.00 

Automatic high-speed engines, about 2 pints per 1,000 sq. in. 

Simple slide-valve engines, about 0.5 pints per 1,000 sq. ins. 

As shown in the figures under 2.000, Corliss, a certain engine may take 
21/4 times as much oil as another engine of the same size. The difference 
may be due to smoothness of cylinder surface, kind and pressure of piston 
rings, quality of oil, method of introducing the lubricant, etc. Variations 
in speed of a given type of engine and in steam pressure do not appear to 
make much difference, but the small automatic high-speed engine takes 
more oil than any other type. Vertical marine engines are commonly run 
without any cylinder oil, except that used occasionally to swab the piston 
rods. 

Quantity of Oil used on a Locomotive Crank-pin. — Prof. Denton, 
Trans. A. S. M. E., xi, 1020, says: A very economical case of practical 
oil-consumption is when a locomotive main crank-pin consumes about 
six cubic inches of oil in a thousand miles of service. This is equivalent 
to a consumption of one milligram to seventy square inches of surface 
rubbed over. 



SOLID LUBRICANTS. 1223 

Soda Mixture for Machine Tools. (Penna. R. R. 1894.) — Dissolve 
5 lbs. of common sal-soda in 40 gallons of water and stir thoroughly. 
When needed for use mix a gallon of this solution with about a pint of 
engine oil. Used for the cutting parts of machine tools instead of oil. 

Water as a Lubricant. (C. W. Naylor, Trans. A. S. M. E., 1905.) — 
Two steel jack-shafts 18 ft. long with bearings 5 X 14 ins. each receiving 
175 H.P. from engines and driving 5 electric generators, with six belts all 
pulling horizontally on the same side of the shaft, gave trouble by heating 
when lubricated with oil or grease. Water was substituted, and the shafts 
ran for 1 1 years, 10 hours a day, without serious interruption. Oil was fed 
to the shaft before closing down for the night, to prevent rusting. The 
wear of the babbitted bearings in 11 years was about 1/4 in., and of the shalt 
nil. 

Acheson's " Deflocculated " Graphite. (Trans. A. I. E. E., 1907; 
Eng. News, Aug. 1, 1907.) — In 1906, Mr. E. G. Acheson discovered a 
process of producing a fine, pure, unctuous graphite in the electric fur- 
nace. He calls it deflocculated graphite. By treating this graphite 
in the disintegrated form with a water solution of tannin, the amount 
of tannin being from 3% to 6% of the weight of the graphite treated, 
he found that it would be retained in suspension in water, and that it 
was in such a fine state of subdivision that a large part of it would run 
through the finest filter paper, the filtrate being an intensely black liquid 
in which the graphite would remain suspended for months. The addition 
of a minute quantity of hydrochloric acid causes the graphite to floccu- 
late and group together so that it will no longer flow through filter paper. 
The same effect has been obtained with alumina, clay, lampblack and 
siloxicon, by treatment with tannin. The graphite thus suspended in 
water, known as "aquedag," has been successfully used as a lubricant 
for journals with sight-feed and with chain-feed oilers. It also prevents 
rust in iron and steel. The deflocculated graphite has also been sus- 
pended in oil, in a dehydrated condition, making an excellent lubricant 
known as "oildag." Tests by Prof. C. H. Benjamin of oil with 0.5% 
of graphite showed that it had a lower coefficient of friction than the oil 
alone. 

SOLID LUBRICANTS. 

Graphite in a condition of powder and used as a solid lubricant, so 
called, to distinguish it from a liquid lubricant, has been found to do well 
where the latter has failed. 

Rennie, in 1829, says: "Graphite lessened friction in all cases where it 
was used." General Morin, at a later date, concluded from experiments 
that it could be used with advantage under heavy pressures; and Prof. 
Thurston found it well adapted for use under both light and heavy pres- 
sures when mixed with certain oils. It is especially valuable to prevent 
abrasion and cutting under heavy loads and at low velocities. 

For comparative tests of various oils with and without graphite, see 
paper on lubrication and lubricants, by C. F. Mabery, Jour. A.S.M.E., 
Feb., 1910. 

Soapstone, also called talc and steatite, in the form of powder and 
mixed with oil or fat, is sometimes used as a lubricant. Graphite or 
soapstone, mixed with soap, is used on surfaces of wood working against 
either iron or wood. 

Metaline is a solid compound, usually containing graphite, made in the 
form of small cylinders which are fitted permanently into holes drilled 
in the surface of the bearing. The bearing thus fitted runs without any 
other lubrication. 



1224 



THE FOUNDRY. 



THE FOUNDRY. 

(See also Cast-iron, pp. 414 to 429, and Fans and Blowers, pp. 626 to 643.) 

Cupola Practice. 

The following table and the notes accompanying it are condensed from 
an article by Simpson Bolland in Am. Mach., June 30, 1892: 

84 
16 
3000 
9000 
1310 
11,790 
26 
31 



Diam. of lining, in 

Height to char'g door, ft 

Fuel used in bed, lbs 

First charge of iron, lbs. 
Other fuel charges, lbs... 
Other iron charges, lbs.. 

Diam. blast pipe, in 

No. of 6-in. round tuyeres. . 

Equiv. No. flat tuyeres 

Width of flat tuyeres, in... 
Height of flat tuyeres, in. . 

Blast pressure, oz 

Size of Root blower, No... . 

Revs, per min 

Engine for blower, H.P — 

Sturtevant blower, No 

Engine for blower, H.P.. . . 
Melting cap., lbs. per hr. . . 



36 


48 


54 


60 


66 


72 


12 


13 


14 


15 


15 


16 


840 


1380 


1650 


1920 


2190 


2460 


2520 


4140 


4950 


5760 


6570 


7380 


302 


554 


680 


806 


932 


1058 


2718 


4986 


6120 


7254 


8388 


9522 


14 


18 


20 


22 


22 


24 


3.7 


6.8 


10.7 


13.7 


15.4 


19 


4 


6 


8 


8 


8 


10 


2 


2.5 


2.5 


3 


3 


3 


13.5 


13.5 


15.5 


16.5 


18.5 


18.5 


8 


12 


14 


14 


14 


16 


2 


4 


4 


5 


5 


6 


241 


212 


277 


192 


240 


163 


2.5 


10 


14 


18 V, 


23 


33 


4 


6 


7 


8 


8 


9 


3 


93/4 


16 


22 


22 


35 


4820 


10,760 


13,850 


16,940 


21,200 


26,070 



16 
3.5 

16 

16 

7 

160 

47 

10 

48 
37,530 



Mr. Bolland says that the melting capacities in the table are not sup- 
posed to be all that can be melted in the hour by some of the best cupolas, 
but are simply the amounts which a common cupola under ordinary 
circumstances may be expected to melt in the time specified. 

By height of cupola is meant the distance from the base to the bottom 
side of the charging door. The distance from the sand-bed, after it has 
been formed at the bottom of the cupola, up to the under side of the 
tuyeres is taken at 10 ins. in all cases. 

All the amounts for fuel are based upon a bottom of 10 ins. deep. The 
quantity of fuel used on the bed is more in proportion as the depth is 
increased, and less when it is made shallower. 

The amount of fuel required on the bed is based on the supposition that 
the cupola is a straight one all through, and that the bottom is 10 ins. 
deep. If the bottom be more, as in those of the Colliau type, then addi- 
tional fuel will be needed. 

First Charge of Iron. — The amounts given are safe figures to work upon 
in every instance, yet it will always be in order, after proving the ability 
of the bed to carry the load quoted, to make a slow and gradual increase 
of the load until it is fully demonstrated just how much burden the bed 
will carry. 

Succeeding Charges of Fuel and Iron. — The highest proportions are 
not favored, for the simple reason that successful melting with any greater 
proportion of iron to fuel is not the rule, but, rather, the exception. 

Diameter of Main Blast-pipe. — The sizes given are of sufficient area 
for all lengths up to 100 feet. 

Tuyeres. — Any arrangement or disposition of tuyeres may be made, 
which shall answer in their totality to the areas given in the table. On no 
consideration must the tuyere area be reduced; thus, an 84-inch cupola 
must have tuyere area equal to 31 pipes 6 ins. diam., or 16 flat tuyeres 
16 X 31/2 ins. The tuyeres should be arranged in such a manner as will 
concentrate the fire at the melting-point into the smallest possible com- 
pass, so that the metal in fusion will have less space to traverse while 
exposed to the oxidizing influence of the blast. 

To accomplish this, recourse has been had to the placing of additional 
rows of tuyeres in some instances — the "Stewart rapid cupola" having 
three rows, and the " Colliau cupola furnace" having two rows, of tuyeres. 



THE FOUNDRY. 1225 



[Cupolas as large as 84 inches in diameter are now (1906) built without 
boshes. The most recent development with this size cupola is to place a 
center tuyere in the bottom discharging air vertically upwards.] 

Blast-pressure. — About 30,000 cu. ft. of air are consumed in melting a 
ton of iron, which would weigh about 2400 pounds, or more than both 
iron and fuel. When the proper quantity -of air is supplied, the com- 
bustion of the fuel is perfect, and carbonic-acid gas is the result. When 
the supply of air is insufficient, the combustion is imperfect, and car- 
bonic-oxide gas is the result. The amount of heat evolved in these two 
cases is as 15 to 4 1/2, showing a loss of over two-thirds of the heat by 
imperfect combustion. [Combustion is never perfect in the cupola except 
near the tuyeres. The CO2 formed by complete combustion is largely 
reduced to CO in passing through the hot coke above the fusion zone.] 

It is not always true that we obtain the most rapid melting when we are 
forcing into the cupola the largest quantity of air. Too much air absorbs 
heat, reduces the temperature, and retards combustion, and the fire in the 
cupola may be extinguished with too much blast. 

Slag in Cupolas. — A certain amount of slag is necessary to protect the 
molten iron which has fallen to the bottom from the action of the blast ; if 
it was not there, the iron would suffer from decarbonization. 

When slag from any cause forms in too great abundance, it should be 
led away by inserting a hole a little below the tuyeres, through which it 
will find its way as the iron rises in the bottom. 

With clean iron and fuel, slag seldom forms to any appreciable extent 
in small heats; but when the cupola is to be taxed to its utmost capacity 
it is then incumbent on the melter to flux the charges all through the heat, 
carrying it away in the manner directed. 

The best flux for this purpose is the chips from a white-marble yard. 
About 6 pounds to the ton of iron will give good results when all is clean. 
[Fluor-spar is now largely used as a flux.] 

When fuel is bad, or iron is dirty, or both together, it becomes imperative 
that the slag be kept running all the time. 

Fuel for Cupolas. — The best fuel for melting iron is coke, because it 
requires less blast, makes hotter iron, and melts faster than coal. When 
coal must be used, care should be exercised in its selection. All anthra- 
cites which are bright, black, hard, and free from slate, will melt iron 
admirably. For the best results, small cupolas should be charged with 
the size called ''egg,' 1 a still larger grade for medium-sized cupolas, and 
what is called "lump" will answer for all large cupolas, when care is taken 
to pack it carefully on the charges. 

31elting Capacity of Different Cupolas. — The following figures 
are given by W. B. Snow, in The Foundry, Aug., 1908, showing the 
records of capacity and the blast pressure of several cupolas: 
Diam. of lining, 

ins 44 44 47 49 54 54 54 60 60 60 74 

Tons per hour . . 6.7 7.3 8.4 9.1 7.7 8.8 10.2 12.4 14.8 13.8 13.0 
Pressure, oz. per 

sq. in 12.9 16.4 17.5 11.8 13.6 11.0 20.8 15.5 16.8 12.6 8.7 

From plotted diagrams of records of 46 tests of different cupolas the 
following figures are obtained: 

Diam. of lining, ins 30 36 42 48 54 60 66 72 

Max. tons per hour 3 5 7.3 9.5 12 15 18 21 

Avge. " " " 2.5 4 5.5 7.5 9 11 13 16 

Max. pressure, oz 11 12 13.5 14 14.6 15.2 15.7 16 

For a given cupola and blower the melting rate increases as the square 
root of the pressure. A cupola melting 9 tons per hour with 10 ounces 
pressure will melt about 10 tons with 12.5 ounces, and 11 tons with 15 
ounces. The power required varies as the cube of the melting rate, so 
that it would require (11/9) 3 = 1.82 times as much power for 11 tons as 
for 9 tons. Hence the advantage of large cupolas and blowers with light 
pressures. 

Charging a Cupola. — Chas. A. Smith (Am. Mach., Feb. 12, 1891) 
gives the following: A 28-in. cupola should have from 300 to 400 lbs. of 
coke on bottom bed; a 36-in. cupola, 700 to 800 lbs.; a 48-in. cupola, 
1500 lbs.; and a 60-in. cupola should have one ton of fuel on bottom bed. 



1226 



THE FOUNDRY. 



To every pound of fuel on the bed, three, and sometimes four pounds of 
metal can be added with safety, if the cupola has proper blast; in after- 
charges, to every pound of fuel add 8 to 10 pounds of metal; any well- 
constructed cupola will stand ten. 

F. P. Wolcott (Am. Mach., Mar. 5, 1891) gives the following as the 
practice of the Col well Iron-works, Carteret, N. J.: "We melt daily from 
twenty to forty tons of iron, with an average of 11.2 pounds of iron to 
one of fuel. In a 36-in. cupola seven to nine pounds is good melting, 
but in a cupola that lines up 48 to 60 inches, anything less than nine 
pounds shows a defect in arrangement of tuyeres or strength of blast, . 
or in charging up." 

"The Molder's Text-book," by Thos. D. West, gives forty-six reports 
in tabular form of cupola practice in thirty States, reaching from Maine 
to Oregon. 

Improvement of Cupola Practice. — The following records are given 
by J. R. Fortune and H. S. Wells (Proc. A. S. M. E., Mar., 1908) showing 
how ordinary cupola practice may be improved by making a few changes. 
The cupola is 13 ft. 4 in. in height from the top of the sand bottom to 
the charging door, and of three diameters, 50 in. for the first 3 ft. 6 in., 
then 54 in. for the next 2 ft. 4 in., then 60 in. to the top. When driven 
with a No. 8 Sturtevant blower, the maximum melting rate, from iron 
down to blast off, was 8.5 tons per hour. A No. 11 high-pressure blower 
was then installed. Test No. 1 in the table below gives the result with 
cupola charges as follows in pounds: Bed, 590 coke, followed by 826 coke, 
2000 iron; 400 coke, 2000 iron; 300 coke, 2000 iron; and thereafter all 
charges were 200 coke, 2000 iron. The time between starting fire and start- 
ing blast was 2 hr. 30 min., and the time from blast on to iron down, 
11 min. The melting rate, tons per hour, is figured for the time from 
iron down to blast off. The tuyeres were eight rectangular openings 
11 1/4 in. high and of a total area of 1/9.02 of the area of the 54-in. circle. 



No. of Test. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


Total tons. . . 


22.7 


24. 


22.15 


24.25 


24.25 


22.65 


24. 


20.30 


23.85 


22.35 


Tons per hr.. 


9.45 


8.88 


8.86 


9.15 


9.66 


10.24 


10.43 


10.91 


11.35 


11.17 


Lbs. per min* 


19.81 


18.61 


18.55 


19.17 


20.25 


21.44 


21.82 


22.95 


23.77 


23 39 


Iron -r- cokef 


7.54 


7.40 


7.28 


8.58 


8.94 


8.71 


9.02 


9.02 


10.02 


9.49 


Blast, oz 


11.60 


10.63 


10.00 


9.47 


9.80 


9.86 


10.00 


10.13 


10.55 


10.55 



* Per sq. ft. cupola area at 54 in. diam. from iron down to blast off. 
t Including bed. 

The tuyeres were then enlarged, making their area 1/5.98 of the cupola 
(54 in.) area, and the results are shown in tests No. 2 and 3 of the table. 
The iron was too hot, and the coke charge was decreased to a ratio of 
1/13.33 instead of 1/10, the bed of coke being increased. The result, 
test No. 4, was an increased rate of melting, a decrease in the amount of 
coke, and a decrease in the blast pressure. Tests 5, 6, 7, 8 and 9 were 
then made, the coke being decreased, while the blast pressure was in- 
creased, resulting in a decided increase in the melting speed. In tests 
5, 6 and 7 the iron layer was 13.33 times the weight of the coke layer; 
in test 8, 14.28 times; and in test 9, 15.38 times. In test 9 it was noticed 
that the iron was not at the proper temperature, and in test 10 the coke 
layer was increased to a ratio of 1 to 14.28 without altering the blast 
pressure; this resulted in a decreased melt per hour. It has been found 
that a coke charge of 150 lbs. to 2000 lbs. of iron, with a blast pressure 
of 10.5 ounces, results in a melt of 11.5 tons per hour, the iron coming 
down at the proper temperature. 

An excess of coke decreases the melting rate. Iron in the cupola is 
melted in a fixed zone, the first charge of iron above the bed being melted 
by burning coke in the bed. As this iron is melted, the charge of coke 
above it descends and restores to the bed the amount which has been 
burned away. If there is too much coke in the charge, the iron is held 
above the melting zone, and the excess coke must be burned away before 
it can be melted, and this of course decreases the economy and the melting 
speed. 



THE FOUNDRY. 



1227 



Cupola Charges in Stove-foundries. (Iron Age, April 14, 1892.) — 
No two cupolas are charged exactly the same. The amount of fuel on 
the bed or between the charges differs, while varying amounts of iron are 
used in the charges. Below will be found charging-lists from some of the 
prominent stove-foundries in the country: 



lbs. 

A— Bed of fuel, coke 1 ,500 

First charge of iron 5,000 

All other charges of iron 1 ,000 

First and second charges of 
coke, each 200 



Four next charges of coke, 

each 

Six next charges of coke, each 

Nineteen next charges of coke, 

each 



lbs 



Thus for a melt of 18 tons there would be 5120 lbs. of coke used, giving 
a ratio of 7 to 1. Increase the amount of iron melted to 24 tons, and a 
ratio of 8 pounds of iron to 1 of coal is obtained . 



lbs. 

B— Bed of fuel, coke 1 ,600 

First charge of iron 1,800 

First charge of fuel 150 

All other charges of iron, 

each 1.00C 

For an 18-ton melt 5060 lbs. of coke would be necessary, giving a ratio 
of 7.1 lbs. of iron to 1 pound of coke, 
lbs. 

C— Bed of fuel, coke 1,600 

First charge of iron 4,000 

First and second charges of 

coke 200 

In a melt of 18 tons 4100 lbs. of coke would be used, or a ratio of 8.5 to 1. 
lbs. 1 lbs. 

D— Bed of fuel, coke 1,800 All charges of coke, each 200 

First charge of iron 5,600 | All other charges of iron 2,900 

In a melt of 18 tons, 3900 lbs. of fuel would be used, giving a ratio of 
9.4 pounds of iron to 1 of coke. Very high, indeed, for stove-plate. 

lbs. lbs. 

E— Bed of fuel, coal 1 ,900 

First charge of iron 5,000 

First charge of coal 200 

In a melt of 18 tons 4700 lbs. of coal would be used, giving a ratio of 
7.7 lbs. of iron to 1 lb. of coal. 

These are sufficient to demonstrate the varying practices existing 
among different stove-foundries. In all these places the iron was proper 
for stove-plate purposes, and apparently there was little or no difference 
in the kind of work in the sand at the different foundries. 

Foundry Blower Practice. (W. B. Snow, Trans. A. S. M. E., 
1907.) — The v elocity of air produced by a blower is expressed by the 
formula V = ^2 gp/d. If p, the pressure, is taken in ounces per sq. in., 
and d, the density, in pounds per cu. ft. of dry air at 50° and atmospheric 
pressure o f 14.69 lbs, or 235 oun ces, = 0.77884 lb., the formula reduces 
to V = Vi ,746,700 p/(235 + p), no allowance being made for change of 
temperature during discharge. From this formula the following figures 
are obtained. Q = volume discharged per min. through an orifice of 
1 sq. ft. effective area, H.P = horse-power required to move the given 
volume under the given conditions, p = pressure in ounces per sq. in. 



lbs- 
Second and third charges of 

fuel 130 

All other charges of fuel, 

each 100 



lbs. 

All other charges of iron 2,000 

All other charges of coke 150 



All other charges of iron, each 2,000 
All other charges of coal, each 175 



P 1 Q 


H.P. 


P 


Q 


H.P. 


V 


Q 


H.P. 


]> 


Q 


H.P. 


1 35.85 


0.00978 


6 


86.89 


0.1422 


11 


116.45 


0.3493 


16 


139.03 


0.6067 


2 


50.59 


0.02759 


7 


93.66 


0.1788 


12 


121.38 


0.3972 


17 


143.03 


0.6631 


3 


61.83 


0.05058 


8 


99.92 


0.2180 


13 


126.06 


0.4470 


18 


146.88 


0.7211 


4 


71.24 


0.07771 


9 


105.76 


0.2596 


14 


130.57 


0.4986 


19 


150.61 


0.7804 


5 


79.48 


0.1084 


10 


111.25 


0.3034 


15 


134.89 


0.5518 


20 


154.22 


0.8412 



The greatest effective area over which a fan will maintain the maximum 
velocity of discharge is known as the "capacity area" or "square inches 
of blast." As originally established by Sturtevant it is represented by 
DW/3, D = diam. of wheel in ins., W = width of wheel at circumference, 



1228 



THE FOUNDRY. 



in inches. For the ordinary type of fan at constant speed maximum 
efficiency and power are secured at or near the capacity area; the power 
per unit of volume and the pressure decrease as the discharge area and 
volume increase; with closed outlet the power is approximately one-third 
of that at capacity area. 

The following table is calculated on these bases: Capacity area per inch 
of width at periphery of wheel = 1/3 of diam. Air, 50° F. Velocity 
of discharge = circumferential speed of the wheel. Power = double the 
theoretical. In rotary positive blowers, as well as in fans, the velocity 
and the volume vary as the number of revolutions, the pressure varies 
as the square, and the power as the cube of the number of revolutions. 
In the fan, however, increase of pressure can be had only by increasing 
the revolutions, while in the rotary blower a great range of pressure is 
obtainable with constant speed by merely varying the resistance. With a 
rotary blower at constant speed, theoretically, and disregarding the effect 
of changes in temperature and density, the volume is constant ; the velocity 
varies inversely as the effective outlet area; the pressure varies inversely 
as the square of the outlet area, hence as the square of the velocity; 
and the power varies directly as the pressure. The maximum power is 
required when a fan discharges against the least, and when a rotary 
blower discharges against the greatest resistance. 

Performance of Cupola Fan Blowers at Capacity Area per Inch 
of Peripheral Width. 



as 
5£ 



r.p.m. 
cu. ft. 
h.p. 

r.p.m. 
cu. ft. 
h.p. 



h.p. 

r.p.m 
cu. ft 
h.p. 

r.p.m 
cu. ft 
h.p. 



Total Pressure in Ounces per Square Inch. 



2660.0 

520.0 

1.7 

2000.0 

700.0 

2.3 

1590.0 

870.0 

2. 

1330.0 
1040.0 

3.4 

1140.0 

1220.0 

3.9 



2860.0 

560.0 

2.1 

2150.0 

750.0 

2.9 

1720.0 

940.0 

3.6 

1430.0 

1120.0 

4.3 

1230.0 

1310.0 

5.0 



3050.0 

600.0 

2.6 

2290.0 

800.0 

3.5 

1830.0 
1000.0 

4.4 

1530.0 

1200.0 

5.2 

1310.0 

1400.0 

6.1 



3230.0 

640.0 

3.1 

2420.0 

850.0 

4.2 

1940.0 

1060.0 

5.2 

1620.0 
1270.0 



1380.0 

1480.0 

7.3 



10 11 12 13 14 15 16 



3400.0 

670.0 

3.6 

2550.0 

890.0 

4.9 

2040.0 
1110.0 



1700.0 

1340.0 

7.3 

1460.0 
1560.0 
5 



r.p.m. 1000.0 1070.0 1150.0 1210.0 1270.0 1330.Q 1390.0 1450.0 1500.0 1550.0 1590.0 

48 \ cu. ft. 1390.0 1500.0 1600.0 1690.0 1780.0 1860.0 1940.0 2020.0 2090.0 2160.0 2230.0 

h.p. 4.5 5.7 7.0 8.3 9.7 11.2 12.7 14.3 15.9 17.7 21.0 



3560.0 

700.0 

4.2 

2670.0 

930.0 

5.6 

2140.0 

1160.0 

7.0 

1780.0 
1400.0 



1530.0 

1630.0 

9.8 



3710.0 

730.0 

4.8 

2780.0 

970.0 

6.4 

2230.0 

1210.0 

7.9 

1850.0 

1460.0 

9.5 

1590.0 

1700.0 

11.1 



3850.0 

760.0 

5.4 

2890.0 

1010.0 

7.1 

2310.0 
1260.0 



1930.0 

1510.0 

10.7 

1650.0 

1770.0 

12.5 



3990.0 
780.0 



2990.0 

1040.0 

8.0 

2390.0 

1310.0 

10.0 

2000.0 

1570.0 

11.9 

1710.0 

1830.0 

13.9 



4120.0 

810.0 

6.6 

3090.0 
1080.0 



2470.0 

1350.0 

11.0 

2060.0 

1620.0 

13.2 

1770.0 

1890.0 

15.4 



4250.0 

830.0 

7.3 

3190.0 

1110.0 

9.7 

2550.0 

1390.0 

12.1 

2120.0 

1670.0 

14.5 

1820.0 

1950.0 

17.0 



The air supply required by a cupola varies with the melting ratio, the 
density of the charges, and the incidental leakage. Average practice is 
represented by the following: 

Lbs. iron per lb. coke 6 '! 7 8 9 10 

Cu. ft. air per ton of iron 33,000 31,000 29,000 27,000 25,000 

It is customary to provide blower capacity on a basis of 30,000 cu. ft., 
which corresponds to 75 to 80% of the chemical requirements for complete 
combustion with average coke, and a melting ratio of 7.5 to 1. 

In comparative tests with a 54-inch lining cupola under identical con- 
ditions as to contents, alternately run with a No. 10 Sturtevant fan and 
a 33 cu. ft. Connersville rotary, with the fan the pressure varied between 
I2V2 and 14V8 ounces in the wind box, the net power from 25 to 38.5 H.P., 
while with the rotary blower the pressure varied between 10 1/2 and 25 
ounces, and the power between 19 and 45 H.P. ' With the fan 28.84 tons 



THE FOUNDRY. 



1229 



were melted in 3.77 hours, or 7.65 tons per hour, while with the rotary 
blower 2.82 hours were required to melt 31.5 tons, an hourly rate of 10.6 
tons, an increase of nearly 40 per cent in output. This reduces to a net 
input of 4.09 H.P. per ton melted per hour with the fan, and 2.98 H.P. 
with the rotary blower; an apparent advantage of 27% in favor of the 
rotary. Had the rotary been of smaller capacity such excessive pressures 
would not have been necessary, the power would have been decreased, 
and the duration of the heat prolonged, with probable decrease in the 
H.P. hours per ton. Had the fan been run at higher speed the H.P. 
would have increased, the time decreased and the power per ton per hour 
would have more closely approached that required by the rotary blower. 
• Theoretically, for otherwise constant conditions, the following relations 
hold for cupolas and melting rates within the range of practical operation: 

For a givenjcupolaj For a given melting rate: For a given volume; 

M oc F,Vp. or^ITR 

v* m 

Poo V 2 __ 

H.P. oc M3 or Vp3 



D 2 



Foe 1 ■ 
Poc d 
H.P. oc P or 1 h- D i 
E oc M , P, or 1 -h D* 



M oc D 
For a given cupola 
E oc M 2 , or P 
Duration of beat 
oc l -- Vp 

M = melting rate; V = volume; P = pressure; H.P. = horse-power; 
D = diam. of lining; E = operating efficiency = power per ton per hour; 
d = depth of the charge; oc, varies as. 

These relations might be the source of formulae for practical use were 
it possible to establish accurate coefficients. But the variety in cupolas, 
tuyere proportions, character of fuel and iron, and difference in charging 
practice are bewildering and discouraging. Maximum efficiency in a 
given case can only be assured after direct experiment. Something short 
of the maximum is usually accepted in ignorance of the ultimate possi- 
bilities. 

The actual melting range of a cupola is ordinarily between 0.6 and 
0.75 ton per hour per sq. ft. of cross section. The limits of air supply 
per minute per sq. ft. are roughly 2500 and 4000 cu. ft. The possible 
power required varies even more widely, ranging from 1.5 to 3.75 H.P. 
per sq. ft., corresponding to 2.5 and 5 H.P. per ton per hour for the melting 
rates specified. The power may be roughly calculated, from the theoreti- 
cal requirement of 0.27 H.P. to deliver 1000 cu. ft. per minute against 
1 oz. pressure. The power increases directly with the pressure, and de- 
pends also on the efficiency of the blower. Current practice can only be 
expressed between limits as in the following table. 

Range of Performance of Cupola Blowers. 



Pressure 
per sq. 
in., oz. 





Diameter inside 
Lining, in. 


Capacity per 
Hour, tons. 


18 


0.25- 0.5 


24 


1.00- 1.5 


30 


2.00- 3.5 


36 


4.00- 5.0 


42 


5.00- 7.0 


48 


8.00-10.0 


54 


9.00-12.0 


60 


12.00-15.0 


66 


14.00-18.0 


72 


17.00-21.0 


78 


19.00-24.0 


84 


21.00-27.0 



Volume of Air 
permin., cu. ft. 



5- 7 
7- 9 
8-11 
8-12 
8-13 
8-13 
9-14 
9-14 
9-15 
10-15 
10-16 
10-16 



150- 300 
600- 900 
1,200- 2,000 
2,200- 2,800 
2,700- 3,700 
4,000- 5,000 
4,500- 6,000 
6,000- 7,500 
7,000- 9,000 
8,500-10,500 
9,500-12,000 
10,500-13,500 



Horse- 
power. 



0.5- 1.5 
2.0- 6.0 
5.0- 15.0 
10.0-23.0 
12.0- 32.0 
18.0- 45.0 
22.0- 60.0 
30.0- 75.0 
35.0- 90.0 
45.0-110.0 
52.0-130.0 
60.0-150.0 



Results of Increased Driving. (Erie City Iron- works, 1891.) — 
May-Dec, 1890: 60-in. cupola, 100 tons clean castings a week, melting 
8 tons per hour; iron per pound of fuel, 7V2 lbs.; per cent weight of good 
castings to iron charged, 753/ 4 . Jan-May, 1891: Increased rate of melt- 
ing to 111/2 tons per hour; iron per lb. fuel, 9V2; per cent weight of good 
castings, 75; one week, 13V4 tons per hour, 10.3 lbs. iron per lb. fuel; 
per cent weight of good castings, 75.3. The increase was made by putting 
in an additional row of tuyeres and using stronger blast, 14 ounces. Coke 
was used as fuel. (W. O. Webber, Trans. A. S. M. E. t xii, 1045.) 



1230 



THE FOUNDRY. 



Power Required for a Cupola Fan. (Thos. D. West, The Foundry, 
April, 1904.) — -The power required when a fan is connected with a cupoia 
depends on the length and diameter of the piping, the number of bends, 
valves, etc., and on the resistance to the passage of blast through the 
cupola. The approximate power required in everyday practice is the 
difference between the power required to run the fan with the outlet open 
and with it closed. Another rule is to take 75% of the maximum power 
or that with the outlet open. A fan driving a cupola 66 ins. diam., 
1800 r.p.m., driven by an electric motor required horse-power and gave 
pressures as follows : Outlet open, 146.6; outlet closed, 37.2, pressure 
15 oz.; attached to cupola, with no fuel in it, 120.5, 5 oz.; after kindling 
and coke had been fired, 101.0, 10 oz.; during the run 70.8 to 76.7, 11 to 
13 oz., the variations being due to changes in the resistances to the passage 
of the blast. 

Utilization of Cupola Gases. — Jules De Clercy, in a paper read 
before the Amer. Foundrymen's Assn., advises the return of a portion of 
the gases from the upper part of the charge to the tuyeres, and thus 
utilizing the carbon monoxide they contain. He says that A. Baillot 
has thereby succeeded in melting 15 lbs. of iron per lb. of coke, and at the 
same time obtained a greater melting speed and a superior quality of 
castings. 

Loss in Melting Iron in Cupolas. — G. O. Vair, Am. Mach., March 
5, 1891, gives a record of a 45-in. Colliau cupola as follows: 
Ratio of fuel to iron, 1 to 7-42. 

Good castings 21,314 lbs. 

New scrap 3,005 " 

Millings 200 " 

Loss of metal 1 ,481 " 

Amount melted 26,000 lbs. 

Loss of metal, 5.69%. Ratio of loss, 1 to 17.55. 

Use of Softeners in Foundry Practice. (W. Graham, Iron Age, 
June 27, 1889.) — In the foundry the problem is to have the right pro- 
portions of combined and graphitic carbon in the resulting casting; this 
is done by getting the proper proportion of silicon. The variations in 
the proportions of silicon afford a reliable and inexpensive means of 
producing a cast iron of any required mechanical character which is 
possible with the material employed. In this way, by mixing suitable 
irons in the right proportions, a required grade of casting can be made 
more cheaply than by using irons in which the necessary proportions are 
already found. 

Hard irons, mottled and white irons, and even steel scrap, all containing 
low percentages of silicon and high percentages of combined carbon, 
could be employed if an iron having a large amount of silicon were mixed 
with them in sufficient amount. This would bring the silicon to the 
proper proportion and would cause the combined carbon to be forced into 
the graphitic state, and the resulting casting would be soft. High-silicon 
irons used in this way are called "softeners." 

Mr. Keep found that more silicon is lost during the remelting of pig of 
over 10% silicon than in remelting pig iron of lower percentages of silicon. 
He also points out the possible disadvantage of using ferro-silicons con- 
taining as high a percentage of combined carbon as 0.70% to overcome 
the bad effects of combined carbon in other irons. 

The Scotch irons generally contain much more phosphorus than is 
desired in irons to be employed in making the strongest castings. It is a 
mistake to mix with strong low-phosphorus irons an iron that would 
increase the amount of phosphorus for the sake of adding softening 
qualities, when softness can be produced by mixing irons of the same low 
phosphorus. 

(For further discussion of the influence of silicon see pages 415 and 422.) 

Weakness of Large Castings. (W. A. Bole, Trans. A. S. M. E., 
1907.) — Thin castings, by virtue of their more rapid cooling, are almost 
certain to be stronger per unit section than would be the case if the same 
metal were poured into larger and heavier shapes. Many large iron castings 
are of questionable strength, because of internal strains and lack of har- 
raony between their elements, even though the casting is poured out of iron 
of the best quality. This may be due to lack of experience on the part of 



THE FOUNDRY. 



1231 



the designer, especially in the cooling and shrinking of the various parts 
ot a large casting after being poured. 

Castings are often designed with a useless multiplicity of ribs, walls, 
gussets, brackets, etc., which, by their asynchronous cooling and their 
inharmonious shrinkage and contraction, may entirely defeat the intention 
of the designer. 

There are some castings which, by virtue of their shapes, can be specially 
treated by the foundryman, and artificial cooling of certain critical parts 
may be effected in order to compel such parts to cool more rapidly than 
they would naturally do, and the strength of the casting may by such 
means be beneficially affected. As for instance in the case of a fly-wheel 
with heavy rim but comparatively light arms and hub; it may be bene- 
ficial to remove the flask and expose the rim to the air so as to hasten its 
natural rate of cooling, while the arms and hub are still kept muffled up 
in the sand of the mold and their cooling retarded as much as possible. 

Large fillets are often highly detrimental to good results. Where two 
walls meet and intersect, as in the. shape of a 7\ if a large fillet is swept 
at the juncture, there will be a pool of liquid metal at this point which will 
remain liquid for a longer time than either wall, the result being a void, 
or "draw," at the juncture point. 

Risers and sink heads should often be employed on iron castings. In 
large iron-foundry work interior cavities may exist without detection, 
and some of these may be avoided by tne use of suitable feeding devices, 
risers and sink heads. 

Specimens from a casting having at one point a tensile strength as high 
as 30,250 lbs. per sq. in. have shown as low as 20,500 in another and 
heavier section. Large sections cannot be cast to yield the high strength 
of specimen test pieces cast in smaller sections. 

The paper describes a successful method of artificial cooling, by means of 
a coil of pipe with flowing water, of portions of molds containing cylinder 
heads with ports cast in them. Before adopting this method the internal 
ribs in these castings always cracked by contraction. 

Shrinkage of Castings. — The allowance necessary for shrinkage 
varies for different kinds of metal, and the different conditions under 
which they are cast. For castings where the thickness runs about one 
inch, cast under ordinary conditions, the following allowance can be made: 

For .cast iron, 1/8 inch per foot. For zinc, 5/ 16 inch per foot. 

" brass, 3/ 16 " " " " tin, V12 " 

" steel, 1/4 " " " " aluminum, 3/ 16 " " " 

" mal. iron, Vs " " " " britannia, 1/32 " 

Thicker castings, under the same conditions, will shrink less, and thinner 
ones more, than this standard. The quality of the material and the man- 
ner of molding and cooling will also make a difference. (See also 
Shrinkage of Cast Iron, page 423.) 

Mr. Keep (Trans. A. S. M. E., vol. xvi) gives the following "approxi- 
mate key for regulating foundry mixtures" so as to produce a shrinkage 
of 1/8 in. per ft. in castings of different sections: • 

Size of casting 1/2 1 2 3 4 in. sq. 

Silicon required, per cent 3.25 2.75 2.25 1.75 1.25 per cent. 

Shrinkage of a 1/2-in. test-bar. . 0.125 .135 .145 .155 .165 in per. ft. 

Growth of Cast Iron by Heating. (Proc. I. and S. Inst., 1909.) — 
Investigations by Profs. Rugan and Carpenter confirm Mr. Outerbridge's 
experiments. (See page 425.) They found: 1. Heating white iron causes 
it to become gray, and it expands more than sufficient to overcome the 
original shrinkage. 2. Iron when heated increases in weight, probably 
due to absorption of oxygen. 3. The change in size due to heating is 
not only a molecular change, but also a chemical one. 4. The growth of 
one bar was shown to be due to penetration of gases. When heated in 
vacuo it contracted. 

Hard Iron due to Excessive Silicon. — W. J. Keep in Jour. Am. 
Foundrymen's Assn., Feb., 1898, reports a case of hard iron containing 
graphite, 3.04; combined C, 0.10; Si, 3.97; P, 0.61; S, 0.05; Mn, 0.56. He 
says: For stove plate and light hardware castings it is an advantage to 
have Si as high as 3.50. When it is much above that the surface of the 
castings often become very hard, though the center will be very soft. 



1232 



THE FOUNDRY. 



The surface of heavier parts of a casting having 3.97 Si will be harder than 
the surface of thinner parts. Ordinarily if a casting is hard an increase 
of silicon softens it, but after reaching 3.00 or 3.50 per cent, silicon hardens 
a casting. 

Ferro-Alloys for Foundry Use. E. Houghton (Iron Tr. Rev., 
Oct. 24, 1907.) — The objects of the use of ferro-alloys in the foundry are: 
1, to act as deoxidizers and desulphurizers, the added element remaining 
only in small quantities in the finished casting; 2, to alter the composition 
of the casting and so to control its mechanical properties. Some of these , 
alloys are made in the blast furnace, but the purest grades are made in 
the electric furnace. The following table shows the range of composition 
of blast furnace alloys made by the Darwen & Mostyn Iron Co. Ail of 
these alloys may be made of purer quality in the electric furnace. 





Ferro- 


Spiegel- 


Silicon 


Ferro- 


Ferro- 


Ferro- 




Mn. 


eisen. 


Spiegel. 


sil. 


phos. 


Chrome. 


Mn 


41.5- 87.9 


9.25-29.75 


17.50-20.87 


1.17- 2.20 


3.00- 5.90 


1.55- 2.30 


Si 


0.10- 0.63 


0.42- 0.95 


9.45-14.23 


8.10-17.00 


0.50- 0.84 


0.13-0.36 


P 


0.09- 0.20 


0.06- 0.09 


0.07- 0.10 


0.06- 0.08 


15.71-20.50 


0.04- 0.07 


C 


5.62- 7.00 


3.94- 5.20 


1.05- 1.89 


0.90- 1.75 


0.27- 0.30 


5.34- 7.12 


S 


nil 


nil-trace 


nil 


0.02- 0.05 


0.16- 0.33 


Cr, 13.50-41.39 



The following are typical analyses of other alloys made in the electric 
furnace: 





Si 


Fe 


Mn 


Al 


Ca 


Mg 


C 


S 


P 


Ti 




1.21 
45.65 
69.80 






0.30 
9.45 
2.55 






3.28 
0.55 
1.14 


0.03 
0.01 
0.01 


0.02 
0.03 
0.04 


53 


Ferro-aluminum-silicide 

Ferro-calcium-silicide 


44.15 
11.15 


tr. 

0.22 


nil 
15.05 


nil 

0.26 





Ferro-aluminum, Al, 5, 10 and 20%. Metallic manganese, Mn, 95 to 
98; Fe, 2 to 4; C, under 5. Do. refined, Mn, 99; Fe, 1; C, 0. 

Dangerous Ferro-silicon. — Phosphoretted and arseniuretted hvdro- 
gen, highly poisonous gases, are said to be disengaged in a humid atmos- 
phere from ferro-silicon containing between 30 and 40% and between 47 
and 65% of Si, and there is therefore danger in transporting it in passenger 
steamships. A French commission has recommended the abandonment 
of the manufacture of FeSi of these critical percentages. (La Lumiere 
Electrique, Dec. 11, 1909. Elep. Rev., Feb. 26, 1910.) 

Quality of Foundry Coke. (R. Moldenke, Trans. A. S. M. E., 
1907.) — Usually the sulphur, ash and fixed carbon are sufficient to give 
a fair idea of the value of coke, apart from its physical structure, specific 
gravity, etc. The advent of by-product coke will necessitate closer 
attention to moisture Beehive coke, when shipped in open cars, may, 
through inattention, cause the purchase of from 6 to 10 per cent of water 
at coke prices. 

Concerning sulphur, very hot running of the cupola results in less sulphur 
m the iron. In good coke, the amount of S should not exceed 1.2 per 
cent; but, unfortunately, the percentage often runs as high as 2.00. If 
the coke has a good structure, an average specific gravity, not over 11 per 
cent of ash and over 86 per cent of fixed carbon, it does not matter much 
whether it be of the "72 hour" or "24 hour" variety. Departure from 
the normal composition of a coke of any particular region should place the 
foundryman on his guard at once, and sometimes the plentiful use of 
limestone at the right moment may save many castings. 

Castings made in Permanent Cast-iron Molds. — E. A. Custer, in 
a paper before the Am. Foundrymen's Assn. (Eng. News, May 27, 1909), 
describes the method of making castings in iron molds, and the quality 
of these castings. Very heavy molds are used, no provision is made 
against shrinkage, and the casting is removed from the mold as soon as 
it has set, giving it no time to chill or to shrink by cooling. Over 6000 
pieces have been cast in a single mold without its showing any signs of 



THE FOUNDRY. 



1233 



failure. The mold should be so heavy that it will not become highly 
heated in use. Casting a 4-in. pipe weighing 65 lbs. every seven min- 
utes in a mold weighing 6500 lbs. did not raise the temperature above 
300° F. In using permanent molds the iron as it comes from the cupola 
should be very hot. The best results in casting pipe are had with iron 
containing over 3% carbon and about 2% silicon. Iron when cast in 
an iron mold and removed as soon as it sets, possesses some unusual prop- 
erties. It will take a temper, and when tempered will retain magnetism. 
If the casting be taken from the mold at a bright heat and suddenly 
quenched in cold water, it has the cutting power of a good high-carbon 
steel, whether the iron be high or low in silicon, phosphorus, sulphur or 
manganese. There is no evidence of "chill"; no white crystals are shown. 

Chilling molten iron swiftly to the point of setting, and then allowing 
it to cool gradually, produces a metal that is entirely new to the art. It 
has the chemical characteristics of cast iron, with the exception of com- 
bined carbon, and it also possesses some of the properties of high-carbon 
steel. A piece of cast iron that has 0.44% combined, and over 2% free 
carbon, has been tempered repeatedly and will do better service in a lathe 
than a good non-alloy steel. Once this peculiar property is imparted to 
the casting, it is impossible to eliminate it except by remelting. A bar of 
iron so treated can be held in a flame until the metal drips from the end, 
and yet quenching will restore it to its original hardness. 

The character of the iron before being quenched is very fine, close- 
grained, and yet it is easily machined. If permanent molds can be used 
with success in the foundry, and a system of continuous pouring be 
inaugurated which in duplicate work would obviate the necessity of having 
molders, why is it necessary to melt pig iron in the cupola? What could 
be more ideal than a series of permanent molds supplied with molten iron 
practically direct from the blast furnace? The interposition of a reheating 
ladle such as is used by the steel makers makes possible the treatment of 
the molten iron. 

The molten iron from the blast furnace is much hotter than that ob- 
tained from the cupola, so that there is every reason to believe that the 
castings obtained from a blast furnace would be of a better quality than 
when the pig is remelted in the cupola. 

It is immaterial whether an iron contains 1.75 or 3% silicon, so long as 
the molten mass is at the proper temperature, so that the high tempera- 
tures obtained from the blast furnace would go far toward offsetting the 
variations in the impurities. 

R. H. Probert (Castings, July, 1909) gives the following analysis of 
molds which gave the best results: Si, 2.02; S, 0.07; P, 0.89: Mn, 0.29: 
CO, 0.84: G.C., 2.76. Molds made from iron with the following analysis 
were worthless: Si, 3.30; S, 0.06; P, 0.67; Mn, 0.12; CO, 0.19; G.C., 2.98. 

Weight of Castings determined from Weight of Pattern. 

(Rose's Pattern-makers' Assistant.) 



A Pattern weighing One 
Pound, made of — 


Will weigh when cast in 


Cast 
Iron. 


Zinc. 


Copper. 


Yellow 
Brass. 


Gun 
metal. 




lbs. 
10.7 
12.9 
8.5 
12.5 
16.7 
14.1 


lbs. 
10.4 
12.7 
8.2 
12.1 
16.1 
13.6 


lbs. 
12.8 
15.3 
10.1 
14.9 
19.8 
16.7 


lbs. 
12.2 
14.6 
9.7 
14.2 
19.0 
16.0 


lbs. 
12.5 


Honduras 

Spanish 


15. 
9.9 




14.6 


" ' white 


19.5 




16.5 







Molding Sand. (Walter Bagshaw, Proc. Inst. M. E., 1891.)— The 
chemical composition of sand will affect the nature of the casting, no 
matter what treatment it undergoes. Stated generally, good sand is 
composed of 94 parts silica, 5 parts alumina, and traces of magnesia and 
oxide of iron. Sand containing much of the metallic oxides, and especially 



1234 



THE FOUNDRY. 



lime, is to be avoided. Geographical position is the chief factor governing 
the selection of sand; and whether weak or strong, its deficiencies are made 
up for by the skill of the inolder. For this reason the same sand is often 
used for both heavy and light castings, the proportion of coal varying 
according to the nature of the casting. A common mixture of facing- 
sand consists of six parts by weight of old sand, four of new sand, and one 
of coal-dust. Floor-sand requires only half the above proportions of new 
sand and coal-dust to renew it. German founders adopt one part by 
measure of new sand to two of old sand; to which is added coal-dust in 
the proportion of one-tenth of the bulk for large castings, and one-twen- 
tieth for small castings. A few founders mix street-sweepings with the 
coal in order to get porosity when the metal in the mold is likely to be 
a long time in setting. Plumbago is effective in preventing destruction 
of the sand; but owing to its refractory nature, it must not be dusted 
on in such quantities as to close the pores and prevent free exit of the 
gases. Powdered French chalk, soapstone, and other substances are 
sometimes used for facing the mold; but next to plumbago, oak charcoal 
takes the best place, notwithstanding its liability to float occasionally and 
give a rough casting. 

For the treatment of sand in the molding-shop the most primitive 
method is that of hand-riddling and treading. Here the materials are 
roughly proportioned by volume, and riddled over an iron plate in a flat 
heap, where the mixture is trodden into a cake by stamping with the feet; 
it- is turned over with the shovel, and the process repeated. Tough 
sand can be obtained in this manner, its toughness being usually tested 
by squeezing a handful into a ball and then breaking it; but the process 
is slow and tedious. Other things being equal, the chief characteristics 
of a good molding-sand are toughness and porosity, qualities that depend 
on the manner of mixing as well as on uniform ramming. 

Toughness of Sand. — In order to test the relative toughness, sand 
mixed in various ways was pressed under a uniform load into bars 1 in. sq. 
and about 12 in. long, and each bar was made to project further and 
further over the edge of a table until its end broke off by its own weight. 
Old sand from the shop floor had very irregular cohesion, breaking at all 
lengths of projections from 1/2 in. to 1 1/2 in. New sand in its natural state 
held together until an overhang of 23/4 in. was reached. A mixture of old 
sand, new sand, and coal-dust 

Mixed under rollers broke at 2 to 2V4 in. of overhang. 

in the centrifugal machine .. . " " 2 " 21/4 " " 

through a riddle " " 13/ 4 " 21/8 " " 

showing as a mean of the tests only slight differences between the last 
three methods, but in favor of machine-work. In many instances the 
fractures were so uneven that minute measurements were not taken. 

Heinrich Piles (Castings, July, 1908) says that chemical analysis gives 
little or no information regarding the bonding power, texture, permea- 
bility or use of sand, the only case in which it is of value being in the 
selection of a highly silicious sand for certain work such as steel casting. 

Dimensions of Foundry Ladles. — The following table gives the 
dimensions, inside the lining, of ladles from 25 lbs. to 16 tons capacity. 
All the ladles are supposed to have straight sides. (Am. Mach., Aug. 4, 
1892.) 



Cap'y- 


Diam. 


Depth. 


Cap'y- 


Diam. 


Depth. 


Cap'y. 


Diam. 


Depth. 




in 


in. 




in. 


in. 




in. 


in. 


16 tons 


54 


56 


3 tons 


31 


32 


300 lbs. 


f Hi/2 


1U/2 


14 " 


52 


53 


2 " 


27 


28 


250 " 


103/ 4 


11 


12 " 


49 


50 


1 Va" 


241/2 


25 


200 " 


10 


IOV2 


10 " 


46 


48 


1 ton 


22 


22 


150 " 


9 


91/ 2 


8 " 


43 


44 


3/4" 


20 


20 


100 " 


8 


81/2 


6 " 


39 


40 


V2" 


17 


17 


75 " 


7 


71/2 


4 " 


34 


35 


V4" 


131/2 


131/2 


50 *' 


6V2 


6V2 



THE MACHINE-SHOP. 



1235 



THE MACHINE-SHOP. 



SPEED OF CUTTING-TOOLS IN LATHES, MILLING 
3IACHINES, ETC. 

Relation of diameter of rotating tool or piece, number of revolutions 
and cutting-speed: 

Let d = diam. of rotating piece in inches, n = No. of revs, per min.; 
S = speed of circumference in feet per minute; 
c ndn n „ fi ,oj S 3.82 5 . 3.82 5 

S = IT =0-2«18dn; n- ^-^ = -j- ; d .- ^-- 

Approximate rule: Number of revolutions per minute = 4 X speed in 
feet per minute -e- diameter in inches. 









Table of 


Cutting-speeds. 








In 

c3 G 


Feet per minute. 


> 


10 


15 


20 


25 


30 


35 


40 


45 


50 


s"" 


Revolutions per minute. 


■ V4 


76.4 


152.8 


229.2 


305.6 


382.0 


458.4 


534.8 


611.2 


687.6 


764.0 


3 /8 


50 9 


101.9 


152.8 


203.7 


254.6 


305.6 


356.5 


407.4 


458.3 


509.3 


i/ 2 


38.2 


76.4 


114.6 


152.8 


191.0 


229.2 


267.4 


305.6 


343.8 


382.0 


5/8 


30.6 


61.1 


91.7 


122.2 


152.8 


183.4 


213.9 


244.5 


275.0 


305.6 


3/4 


25.5 


50.9 


76.4 


101.8 


127.3 


152.8 


178.2 


203.7 


229.1 


254.6 


7/8 


21.8 


43.7 


65.5 


87.3 


109.1 


130.9 


152.8 


174.6 


196.4 


218.3 


1 


19.1 


38.2 


57.3 


76.4 


95.5 


114.6 


133.7 


152.8 


171.9 


191.0 


U/8 


17.0 


34.0 


50.9 


67.9 


84.9 


101.8 


118.8 


135.8 


152.8 


169.7 


H/4 


15.3 


30.6 


45.8 


61.1 


76.4 


91.7 


106.9 


122.2 


137.5 


152.8 


13/8 


13.9 


27.8 


41.7 


55.6 


69.5 


83.3 


97.2 


111.1 


125.0 


138.9 


H/2 


12.7 


25.5 


38.2 


50.9 


63.6 


76.4 


89.1 


101.8 


114.5 


127.2 


13/4 


10.9 


21.8 


32.7 


43.7 


54.6 


65.5 


76.4 


87.3 


98.2 


109.2 


2 


9.6 


19.1 


28.7 


38.2 


47.8 


57.3 


66.9 


76.4 


86.0 


95.5 


21/4 


8.5 


17.0 


25.5 


34.0 


42.5 


50.9 


59.4 


67.9 


76.4 


84.9 


21/2 


7.6 


15.3 


22.9 


30.6 


38.2 


45.8 


53.5 


61.1 


68.8 


76.4 


23/4 


6.9 


13.9 


20.8 


27.8 


34.7 


41.7 


48.6 


55.6 


62.5 


69.5 


3 


6.4 


12.7 


19.1 


25.5 


31.8 


38.2 


44.6 


50.9 


57.3 


63.7 


31/2 


5.5 


10.9 


16.4 


21.8 


27.3 


32.7 


38.2 


43.7 


49.1 


54.6 


4 


4.8 


9.6 


14.3 


19.1 


23.9 


28.7 


33.4 


38.2 


43.0 


47.8 


41/2 


4.2 


8.5 


12.7 


17.0 


21.2 


25.5 


29.7 


34.0 


38.2 


42 5 


5 


3.8 


7.6 


11.5 


15.3 


19.1 


22.9 


26.7 


30.6 


34.4 


38.1 


51/2 


3.5 


6.9 


10.4 


13.9 


17.4 


20.8 


24.3 


27.8 


31.2 


34.7 


6 


3.2 


6.4 


9.5 


12.7 


15.9 


19.1 


22.3 


25.5 


28.6 


31.8 


7 


2.7 


5.5 


8.2 


10.9 


13.6 


16.4 


19.1 


21.8 


24.6 


27.3 


8 


2.4 


4.8 


7.2 


9.6 


11.9 


14.3 


16.7 


19.1 


21.5 


23.9 


9 


2.1 


4.2 


6.4 


8.5 


10.6 


12.7 


14.8 


17.0 


19.1 


21.2 


10 


1.9 


3.8 


5.7 


7.6 


9.6 


11.5 


13.3 


15.3 


17.2 


19.1 


11 


1.7 


3.5 


5.2 


6.9 


8.7 


10.4 


12.2 


13.9 


15.6 


17.4 


12 


1.6 


3.2 


4.8 


6.4 


8.0 


9.5 


11.1 


12.7 


14.3 


15.9 


13 


1.5 


2.9 


4.4 


5.9 


7.3 


8.8 


10.3 


11.8 


13.2 


14.7 


14 


1.4 


2.7 


4.1 


5.5 


6.8 


8.2 


9.5 


10.9 


12.3 


13.6 


15 


1.3 


2.5 


3.8 


5.1 


6.4 


7.6 


8.9 


10.2 


11.5 


12.7 


16 


1.2 


2.4 


3.6 


4.8 


6.0 


7.2 


8.4 


9.5 


10.7 


11.9 


18 


1.1 


2.1 


3.2 


4.2 


5.3 


6.4 


7.4 


8.5 


9.5 


106 


20 


1.0 


1.9 


2.9 


3.8 


4.8 


5.7 


6.7 


7.6 


8.6 


9.6 


22 


.9 


\.7 


2.6 


3.5 


4.3 


5.2 


6.1 


6.9 


7.8 


8.7 


24 


.8 


1.6 


2.4 


3.2 


4.0 


4.8 


5.6 


6.4 


7.2 


8.0 


26 


.7 


1.5 


2.2 


2.9 


3.7 


4.4 


5.1 


5.9 


6.6 


7.3 


28 


.7 


1.4 


2.0 


2.7 


3.4 


4.1 


4.8 


5.5 


6.1 


6.8 


30 


.6 


1.3 


1.9 


2.5 


3.2 


3.8 


4.5 


5.1 


5.7 


6.4 


36 


.5 


1.1 


1.6 


2.1 


2.7 


3.2 


3.7 


4.2 


4.8 


5.3 


42 


.5 


.9 


1.4 


1.8 


2.3 


2.7 


3.2 


3.6 


4.1 


4.5 


48 


.4 


.8 


1.2 


1.6 


2.0 


2.4 


2.8 


3.2 


3.6 


4.0 


54 


.4 


.7 


1.1 


1.4 


1.8 


2.1 


2.5 


2.8 


3.2 


3.5 


60 


.3 


.6 


1.0 


1.3 


1.6 


1.9 


2.2 


2.5 


2.9 


3.2 



1236 



THE MACHINE-SHOP. 



The Speed of Counter-shaft of the lathe is determined by an 
assumption of a slow speed with the back gear, say 6 feet per minute, 
on the largest diameter that the lathe will swing. 

Example. — A 30-inch lathe will swing 30 inches =, say, 90 inches 
circumference = 7 feet 6 inches; the lowest triple gear should give a 
speed of 5 or 6 feet per minute. 

Spindle Speeds of Lathes. — The spindle speeds of lathes are usu- 
ally in geometric progression, being obtained either by a combination of 
cone-pulley and back gears, or by a single pulley in connection with a 
gear train. Either of these systems may be used with a variable speed 
motor, giving a wide range of available speeds. 

It is desirable to keep work rotating at a rate that will give the most 
economical cutting speed, necessitating, sometimes, frequent changes in 
spindle speed. A variable speed motor arranged for 20 speeds in geometric 
progression, any one of which can be used with any speed due to the 
mechanical combination of belts and back gears, gives a tine gradation of 
cutting speeds. The spindle speeds obtained with the higher speeds of 
the" motor in connection with a certain mechanical arrangement of belt 
and back gears may overlap those obtained with the lower- speeds avail- 
able in the motor in connection with the next higher speed arrangement 
of belt and gears, but about 200 useful speeds are possible. E. R^- Douglas 
{Elec. Rev., Feb. 10, 1906) presents an arrangement of variable speed 
motor and geared head lathe, with 22 speed variations in the motor and 3 in 
the head. The speed range of the spindle is from 4.1 to 500 r.p.m. By 
the use of this arrangement, and taking advantage of the speed changes 
possible for different diameters of the work, a saving of 35.4 per cent was 
obtained in the time of turning a piece ordinarily requiring 289 minutes. 
Rule for Gearing Lathes for Screw-cutting. (Garvin Machine 
Co.) — Read from the lathe index the number of threads per inch cut 
by equal gears, and multiply it by any number that will give for a pro- 
duct a gear on the index; put this gear upon the stud, then multiply the 
number of threads per inch to be cut by the same number, and put the 
resulting gear upon the screw. 

Example. — To cut 11 3^ threads per inch. We find on the index 
that 48 into 48 cuts 6 threads per inch, then 6 X 4 = 24, gear on stud, 
and 11 K X 4 = 46, gear on screw. Any multiplier may be used so long 
as the products include gears that belong with the lathe. For instance, 
instead of 4 as a multiplier we may use 6. Thus, 6 X 6 = 36, gear upon 
stud, and 11 3^ X 6 = 69, gear upon screw. 

Rules for Calculating Simple and Compound Gearing where 
there is no Index. {Am. Mach.) — If the lathe is simple-geared, 
and the stud runs at the same speed as the spindle, select some 
gear for the screw, and multiply its number of teeth by the number 
of threads per inch in the lead-screw, and divide this result by the num- 
ber of threads per inch to be cut. This will give the number of teeth in 
the gear for the stud. If this result is a fractional number, or a number 
which is not among the gears on hand, then try some other gear for the 
screw. Or, select the gear for the stud first, then multiply its number of 
teeth by the number of threads per inch to be cut, and divide by the 
number of threads per inch on the lead-screw. This will give the num- 
ber of teeth for the gear on the screw. If the lathe is compound, select 
at random all the driving-gears, multiply the numbers of their teeth 
together, and this product by the number of threads to be cut. Then 
select at random all the driven gears except one; multiply the numbers 
of their teeth together, and this product by the number of threads per 
inch in the lead-screw. Now divide the first result by the second, to 
obtain the number of teeth in the remaining driven gear. Or, select 
at random all the driven gears. Multiply the numbers of their teeth 
together, and this product by the number of threads per inch in the 
lead-screw. Then select at random all the driving-gears except one. 
Multiply the numbers of their teeth together, and this result by the num- 
ber of threads per inch of the screw to be cut. Divide the first result by 
the last, to obtain the number of teeth in the remaining driver. When 
the gears on the compounding stud are fast together, and cannot be 
changed, then the driven one has usually twice as many teeth as the 
other, or driver, in which case in the calculations consider the lead-screw 
to have twice as many threads per inch as it actually has, and then ignore 



GEARING OF LATHES. 



123' 



the compounding entirely. Some lathes arc so constructed that the stud 
on which the first driver is placed revolves only half as fast as the spindle. 
This can be ignored in the calculations by doubling the number of threads 
of the lead-screw. If both the last conditions are present ignore them 
in the calculations by multiplying the number of threads per inch in the 
lead-screw by four. If the thread to be cut is a fractional one, or if the 
pitch of the lead-screw is fractional, or if both are fractional, then reduce 
the fractions to a common denominator, and use the numerators of these 
fractions as if they equaled the pitch of the screw to be cut, and of the 
lead-screw, respectively. Then use that part of the rule given above 
which applies to the lathe in question. For instance, suppose it is desired 
to cut a thread of 25/ 32 -irich pitch, and the lead-screw has 4 threads per 
inch. Then the pitch of the lead-screw will be 1/4 inch, which is equal to 
8/32 inch. We now have two fractions, 25/ 32 and 8/ 32i and the two screws 
will be in the proportion of 25 to 8, and the gears can be figured by the 
above rule, assuming the number of threads to be cut to be 8 per inch, 
and those on the lead-screw to be 25 per inch. But this latter number 
may be further modified by conditions named above, such as a reduced 
speed of the stud, or fixed compound gears. In the instance given, if 
the lead-screw had been 2 i/ 2 threads per inch, then its pitch being 4/ 10 
inch, we have the fractions 4/ 10 and 25/ 32i which, reduced to a common 
denominator, are 64/ 160 and 125/ 160 , and the gears will be the same as if the 
lead-screw had 125 threads per inch, and the screw to be cut 64 threads 
per inch. 

On this subject consult also "Formulas in Gearing," published by 
Brown & Sharpe Mfg. Co., and Jamieson's Applied Mechanics. 

Change-gears for Screw-cutting Lathes. — There is a lack of 
uniformity among lathe-builders as to the change-gears provided for 
screw-cutting. W. R. Macdonald, in Am. Mach., April 7, 1892, pro- 
posed the following series, by which 33 whole threads (not fractional) 
may be cut by changes of only nine gears: 







Spindle. 








fcs 










Whole Threads. 


ZQ 


20 


30 


40 


50 


60 


70 


110 


120 


130 




20 




8 


6 


4 4/5 


4 


3 3/ 7 


2 2/ii 


2 


1 11/13 


2 


11 


22 


44 


30 


18 




9 


7 1/5 


6 


5 1/7 


3 3/n 


3 


2 IO/13 


3 


12 


24 


48 


40 


24 


16 


12 


9 3/5 


8 


6 6/ 7 


4 4/n 


4 


3 9/13 


4 


13 


26 


52 


50 


30 


20 


l!> 




10 


8 4/7 


5 5/11 


5 


4 8/13 


5 


14 


28 


66 


60 


36 


24 


18 


14 2/5 




IO2/7 


6 6/n 


6 


5 7/i3 


6 


15 


30 


72 


yo 


42 


28 


21 


16 4/s 


14 




7 7/ii 


7 


68/13 


7 


16 


33 


78 


no 


66 


44 


33 


26 2/5 


22 


18 6/7 




II 


102/ 13 


8 


18 


36 




120 


il 


48 


36 


28 4/5 


24 


20 4/7 


13 1/u 




1 1 VIS 


9 


20 


39 




130 


76 


bl 


39 


31 1/5 


26 


22 3/7 


142/n 


13 




10 


21 


42 





Ten gears are sufficient to cut all the usual threads, with the exception 
of perhaps IIV2, the standard pipe-thread; in ordinary practice any 
fractional thread between 11 and 12 will be near enough for the custom- 
ary short pipe-thread; if not, the addition of a single gear will give it. 

In this table the pitch of the lead-screw is 12, and it may be objected 
to as too fine for the purpose. This may be rectified by making the real 

gitch 6 or any other desirable pitch, and establishing the proper ratio 
etween the lathe spindle and the gear-stud. 

"Quick Change Gears." — About 1905, lathe manufacturers began 
building "quick change" lathes in which gear changing for screw 
cutting is eliminated. The lead-screw carries a cone of gears, one of which 
is in mesh with a movable gear in a nest of gears driven from the spindle. 
By changing the position of this movable gear, in relation to the cone of 
gears, the proper ratio of speeds between the spindle and lead-screws is 
obtained for cutting any desired thread usual in the range of the machine. 
About 16 different numbers of threads per inch can usually be cut by 
means of the "quick change" gear train. Different threads from those 
usually available can be cut by means of change gears between the spindle 



THE MACHINE-SHOP. 



and "quick change" gear train. The threads per inch usually available 
range from 2 to 46 in a 12-inch lathe to 1 to 24 in a 30-inch lathe. Catalogs 
of lathe manufacturers should be consulted for constructional details. 

Shapes of Tools. — For illustrations and descriptions of various forms 
of cutting-tools, see Taylor's Experiments, below; also see articles on 
Lathe Tools in Appleton's Cyc. Mech., vol. ii. and in Modern Mechanism. 

Cold Chisels. — Angle of cutting-faces (Joshua Rose): For cast steel, 
about 65 degrees; for gun-metal or brass, about 50 degrees; for copper 
and soft metals, about 30 to 35 degrees. 

Metr'c Screw-threads may be cut on lathes with inch-divided lead- 
ing-screws, by the use of change- wheels with 50 and 127 teeth; since 127 
centimeters = 50 inches (127 X 0.3937 = 49.9999 in.). 

Rule for Setting the Taper in a Lathe. (Am. Mach.) — No rule 
can be given which will produce exact results, owing to the fact that 
the centers enter the work an indefinite distance. If it were not for 
this circumstance the following would be an exact rule, and it is an approx- 
imation as it is. To find the distance to set the center over: Divide the 
difference in the diameters of the large and small ends of the taper by 2, 
and multiply this quotient by the ratio which the total length of the shaft 
bears to the length of the tapered portion. Example: Suppose a shaft 
three feet long is to have a taper turned on the end one foot long, the large 
end of the taper being two inches and the small end one inch diameter, 

2 — 1 3 

— s — Xt= 1^ inches. 



TAYLOR'S EXPERIMENTS. 

Fred W. Taylor directed a series of experiments, extending over 26 
years, on feeds, speeds, shape of tool, composition of tool steel, and heat 
treatment. His results are given in Trans. A. S. M. E., xxviii, "The Art 
of Cutting Metals." The notes below apply mainly to tools of high 
speed steel and to heavy work requiring tools not less than 1/2 by 3/ 4 
inch in cross-section. 

Proper Shape of Lathe Tool. — Mr. Taylor discovered the best 
shape for lathe tools to be as shown in Fig. 187 with the angles 
given in the following table, when used on materials of the class shown. 
The exact outline of the nose of the tool is shown in Fig. 188. The 
actual dimensions of a 1-inch roughing tool are shown in Fig. 189. 
Let R = radius of point of tool, A = width of tool, L = length of shank, 
and H = height of shank, all in inches. Then L = 14 A + 4; H = 1.5 A; 
R = 0.5 A — 0.3125 for cutting hard steel and cast iron; R = 0.5 A — 
0.1875 for soft steel. The meaning of the terms back slope, etc., is shown 
in Fig. 187. 

Angles for Tools. 



* Material cut. 


a = clearance. 


b = back slope. 


c = side slope. 


Cast iron; Hard steel. 


6 degrees. 


8 degrees. 


14 degrees. 


Medium steel; Soft 
steel. 


6 degrees. 


8 degrees. 


22 degrees. 


Tire steel. 


6 degrees. 


5 degrees. 


9 degrees. 



* As far as the shape of the tool is concerned, Taylor divides metals to 
be cut into general classes: (a) cast iron and hard steel, steel of 0.45-0.50 
percent carbon, 100,000 pounds tensile strength, and 18 per cent stretch, 
being a low limit of hardness ; (6) soft steel, softer than above; (c) chilled 
iron; (d\ tire steel; (e) extremely soft steel of carbon, say, 0.10-0.15 per 
cent. 

The table presupposes the use of an automatic tool grinder. If tools 
are ground by hand the clearance angle should be 9 degrees. The lip 
angles for tools cutting hard steel ar-4 cast iron should be 68 degrees; 



1240 



THE MACHINE-SHOP. 



for soft steel, 61 degrees; for chilled iron, 86 to 90 degrees; for tire steel, 
74 degrees; for extremely soft steel, keener than 61 degrees. A tool 
should be given more side than back slope; it can then be ground more 
times without weakening, the chip does not strike the tool post or clamps, 



h If" — +tf'l3S — i 




Fig. 189. 

and it is also easier to feed. The nose of the tool should be set to one 
side, as in Fig. 189 above, to avoid any tendency to upset. To use 
a tool of this shape, lathe tool posts should be set lower below the 
center of the work than is now (1907) customary. 

Forging and Grinding Tools. — The best method of dressing a tool 
is to turn one end up nearly at right angles to the shank, so that the 
nose will be high above the top of the body of the tool. Dressing can 
be thus done in two heats. Tools should leave the smith shop with 
a clearance angle of 20 degrees. Detailed directions for dressing a tool 
are given in Mr. Taylor's paper. To avoid overheating the tool in grind 
ing, a stream of water, of at least five gallons a minute, should be thrown 
at low velocity on the nose of the tool where it is in contact with the 
emery wheel. In hand grinding, tools should not be held firmly against 
the wheel, but should be moved over its surface. It is of the utmost 
importance that high speed steel tools should not be heated above 1200° F. 
in grinding. Automatic tool grinders are economical, even in a small 
shop. Grinding machines should have some means for automatically 
adjusting the pressure of the tool against the grinding wheel. Each size 
of tool should have adapted to it a pressure, automatically adjusted, and 
which is just sufficient to grind rapidly without overheating the tooL 
Standard shapes should be adopted, to which all tools should be ground, 
there being no economy in automatic grinding without standard shapes, 

Best Grinding Wheel. — The best grinding wheel was found to be 
a corundum wheel, of a mixture of 24 and 30 grit. 



TAYLORS EXPERIMENTS. 1241 

Pressure of Tool, etc. — Mr. Taylor found that there is no definite 
relation between the cutting speed of tools and the pressure with which 
the chip bears on the lip surface of the tool. He found, however, that 
the pressure per square inch of sectional area of the chip increases 
slightly as the thickness of the chip decreases. The feeding pressure of 
the tool is sometimes equal to the entire driving pressure of the chip against 
the lip surface of the tool, and the feed gears should be designed to deliver 
a pressure of this magnitude at the nose of the tool. 

Chatter. — Chatter is caused by: too small lathe dogs; imperfect 
bearing at the points where the face plate drives the dogs ; badly made or 
badly fitted gears; shafts in the machine of too small diameter, or of too 
great length; loose fits in bearings. A tool which chatters must be run 
at a cutting speed about 15 per cent slower than can be used if the tool 
does not chatter, irrespective of the use or non-use of water on the tool. 
A higher cutting speed can be used with an intermittent cut, as occurs 
on a planer, or shaper, or in turning, say, the periphery of a gear, than 
with a steady cut. To avoid chatter, tools should have curved cutting 
edges, or two or more tools should be used at the same time in the same 
machine. The body of the tool should be greater in height than width, 
and should have a true, solid bearing on the tool support, which latter 
should extend to almost beneath the cutting edge of the tool. Machines 
should be made massive beyond the metal needed for strength alone, 
and steady rests should be used on long work. It is advisable to use a 
steady rest, when turning any cylindrical piece of diameter D, when the 
length exceeds 12 D. 

Use of Water on Tool. — With the best high speed steel tools, a 
gain of 16 per cent in cutting speed can be made in cutting cast iron, 
steel or wrought iron by throwing a heavy stream of water directly on 
the chip at the point where it is being removed from the forging by the 
tool. Not less than three gallons a minute should be used for a 2 X 21/2- 
inch tool. The gain is practically the same for all qualities of steel, 
regardless of hardness and whether thick or thin chips are being cut. 

Interval between Grindings. — Mr. Taylor derived a table showing 
how long various sizes of tools should run without regrinding to give the 
maximum work for the lowest all-around cost. Time a tool should run 
continuously without regrinding equals 7 X (time to change tool + 
proper portion of time for redressing + time for grinding + time equi- 
valent to cost of the tool steel ground off). 

Interval Between Grindings, at Maximum Economical 
Cutting Speeds. 

Size of tool. 

Inches. 1/2 X3/ 4 5/ 8 xl 3/ 4 X 1 l/ 8 7/ 8 X I % lXl 1/2 

Hours. 1.25 1.25 1.25 1.5 1.5 

Size of tool. 

Inches. 1 V4X 1 7/ 8 U/2X2 1/4 13/4X2 3/4 2x3 

Hours. 1.75 2.0 2.5 2.75 

If the proper cutting speed (A) is known for a cut of given duration, 
the speed for a cut (B) of different duration can be obtained by multiply- 
ing (A) by the factor given in the following table: 

Duration of cut in minutes: 

At known speed (A) 20 40 20 40 80 80 

At derived speed (B) 40 80 80 20 40 20 

Factor 0.92 0.92 0.84 1.09 1.09 1.19 

For cutting speeds of high-speed lathe tools to last 11/2 hours, see 
tables on pages 1244 and 1245. 

Effect of Feed and Depth of Cut on Cutting Speed. — With a given 
depth of cut, metal can be removed faster with a coarse feed and slow 
speed, than with fine feed arid high speed. With a_given depth of cut, a 
cutting speed of S, and a feed of F, S varies as l/^F. With tools of the 
best high speed steel, varying the feed and depth of cut varies the 
cutting speed in the same ratio when cutting hard steel as when cutting 
soft steel. 



1242 THE MACHINE-SHOP. 



Best High Speed Tool Steel — Composition — Heat Treatment. 

— Mr. Taylor and Maunsel White developed a number of high speed 
steels, the one showing the best all-around qualities having the following 
chemical composition: Vanadium, 0.29; tungsten, 18.19; chromium, 
5.47; carbon, 0.674; manganese, 0.11; silicon, 0.043. The use of 
vanadium materially improves high speed steel. The following method 
of treatment is described as the best for this or any other composition of 
high speed steel. The tool should be forged at a light yellow heat, and, 
after forging slowly and uniformly, heated to a bright cherry red, allowing 
plenty of time for the heat to penetrate to the center of the tool, in order 
to avoid danger of cracking due to too rapid heating. The tool should 
then be heated from a bright cherry red to practically its melting-point as 
rapidly as possible in an intensely hot fire; if the extreme nose of the tool 
is slightly fused no harm is done. Time should be allowed for the tool 
to become uniformly hot from the heel to the lip surface. 

After the high heat has been given the tools, as above described, they 
should be cooled rapidly until they are below the " breaking-down point, " 
or, say, down to or below 1550° F. The quality of the tool will be but 
little affected whether it is cooled rapidly or slowly from this point down 
to the temperature of the air. Therefore, after all parts of a tool from 
the outside to the center have reached a uniform temperature below the 
breaking-down point, it is the practice sometimes to lay it down in any 
part of the room or shop which is free from moisture, and let it cool in 
the air, and sometimes to cool it in an air blast to the temperature of the 
air. 

The best method of cooling from the high heat to below the breaking- 
down point is to plunge the tools into a bath of red-hot molten lead below 
the temperature of 1550° F. They should then be plunged into a lead 
bath maintained at a uniform temperature of 1150° F., because the same 
bath is afterward used for reheating the tools to give them their second 
treatment. This bath should contain a sufficiently large body of the lead 
so that its temperature can be maintained uniform; and for this purpose 
should be used preferably a lead bath containing about 3600 lb. of lead. 

Too much stress cannot be laid upon the importance of never allowing 
the tool to have its temperature even slightly raised for a very short 
time during the process of cooling down. The temperature must either 
remain absolutely stationary or continue to fall after the operation of 
cooling has once started, or the tool will be injured. Any temporary rise 
of temperature during cooling, however small, will injure the tool. This, 
however, applies only to cooling the tool to the temperature of about 
1240° F. Between the limits of 1240 degrees and the temperature of 
the air, the tool can be raised or lowered in temperature time after time 
and for any length of time without injury. And it should also be noted 
that during the rirst operation of heating the tool from its cold state to 
the melting-point, no injury results from allowing it to cool slightly and 
then reheating. It is from reheating during the operation of cooling 
from the high heat to 1240° F. that the tool is injured. 

The above-described operation is commonly known as the first or high- 
heat treatment. 

To briefly recapitulate, the first or high-heat treatment consists of 
heating the tool — 

(a) slowly to 1500° F.; 

(6) rapidly from that temperature to just below the melting-point. 

(c) cooling fast to below the breaking-down point, i.e., 1550°F. 

(d) cooling either fast or slowly from 1550° F. to temperature of the air. 

Second Treatment, Reheating the Cooled Tool. — After air- 
temperature has been reached the tool should be reheated to a temperature 
of from 700 to 1240° F., preferably by plunging it in the before-mentioned 
lead bath at 1150° F. and kept at that temperature at least five minutes. 
To avoid danger of fire cracks, the tool should be heated slowly before 
immersing in the bath. The above tool heated in this fashion possesses 
a high degree of "red hardness" (ability to cut steel with the nose of the 
tool at red heat), while it is not extraordinarily hard at ordinary tem- 
peratures. It is difficult to injure it by overheating on the grindstone or 
in the lathe. It will operate at 90 per cent of its maximum cutting speed, 
even without the second or low-heat treatment. A coke fire is prefer- 
able for giving the first heat, and it should be made as deep as possible. 



taylor's experiments. 1243 

Cooling the tool by plunging it in on or water, renders it liable to fire 
cracks and to brittfeness in the body. Next to the lead bath an air blast 
is preferable for cooling. 

Best Method of Treating Tools in Small Shops. — For small 
shops, in treating high-speed tools, Mr. Taylor considers the best method 
to be as follows for the blacksmith who is equipped only with the 
apparatus ordinarily found in a smith-shop. 

After the tools have been forged and before starting to give them their 
heat, fuel should be added to the smith's fire so as to give a good deep 
bed either of coke about the size of a walnut or of first-class blacksmiths' 
soft coal. A number of tools should then be laid with their noses at a 
slight distance from the hotter portion of the fire, so that they may all 
be pre-heating while the fire is being blown up to its proper intensity. 
After reaching its proper intensity, the tools should be heated one at a time 
over the hottest part of the fire as rapidly as practicable up to just below 
their melting-point. During this operation they should be repeatedly 
turned over and over so as to insure a uniform high heat throughout the 
whole end of the tool. As soon as each tool reaches its high heat, it 
should be placed with its nose under a heavy air blast and allowed to 
cool to the temperature of the air before being removed from the blast. 

Unfortunately, however, the blacksmith's fire is so shallow that it is 
incapable of maintaining its most intense heat for more than a com- 
paratively few minutes, and, therefore, it is only through these few min- 
utes that first-class high-speed tools can be properly heated in the smith's 
fire. Great numbers of high-speed tools are daily turned out from 
smiths' fires which are not sufficiently intense in their heat, and they are 
therefore inferior in red hardness and produce irregular cutting tools. 

On the whole, a blacksmith's fire made from coke may be regarded as 
better for giving the high heat to tools than a soft-coal fire, merely 
because a coke fire can be more easily made by the smith which will 
remain capable for a longer period of heating the tools quickly to their 
melting-points. 

Quality of Different Tool Steels. — Mr. Taylor in a letter to the 
author, Dec. 30, 1907, says : 

First. Any of a half dozen makes of high speed tools now on the market 
are amply good, and but little attention need be paid to the special direc- 
tions for heating and cooling high speed tools given by the makers of the 
tool steel. The most important matter is that an intensely hot fire should 
be used for giving the tools their high heat, and that they should not be 
allowed to soak a long time in this fire. They should be heated as fast 
as possible and then cooled in an air blast. 

Second. The greatest number of tools are ruined on the emery wheel 
through overheating, either because a wheel whose surface is glazed is 
used, or because too small a stream of water is run upon the nose of the 
tool. The emery wheel should be kept sharp through frequent dress- 
ings with a diamond tool. 

Third. Uniformity is the most important quality in high speed tools. 
For this reason, only one make of high speed tool steel should be used 
in each shop. 

Economical Cutting Speeds. — Tools shaped as in Fig. 189, 
and of the chemical composition and heat treatment given in the pre- 
ceding paragraphs, should be run at the cutting speeds given in the tables 
on pages 1244 and 1245 in order to last one hour and 30 minutes without 
re-grinding. 

Cutting Speed of Parting and Thread Tools. — To find the 
economical cutting speed of a parting tool of the best high speed 
steel, find the proper value for the size of tool in the tables below and 
divide by 2.7. The economical speed for a thread tool is similarly found 
by dividing by 4. The thickness of chip in the latter case is the advance 
in inches per revolution of the tool toward the center of the work. 

Durability of Cutting Tools. — E. G. Herbert (Am. Mach., June 24, 
1909) shows that the durability of a tool depends mainly on the tem- 
perature to which its extreme edge is raised, and that the rate of evolu- 
tion of heat and consequently the durability is proportional to the thick- 
ness and to the area of the chip and to the cube of the cutting speed. 
Or if U= thickness or feed, d = depth of cut, a x = area of the cut and 
«i= cutting speed, for any given set of working conditions, and ticiai and 
S2 values for another set of conditions, then the durability of the tool 



1244 



THE MACHINE-SHOP. 





1 


1 


•2 


64.2 
49.4 
35.7 
29.1 
25.2 
20.5 


58.9 
45 4 
328 
26.8 
232 
18.8 


52.0 
40.1 
29 
23 7 
20.5 
166 


47.7 
36.7 
26.5 
21 6 
187 
15.2 


23.4 

16 5 
134 


JgSg-'j 


Ui 


*J 


o^-am^ 


552553 


»eoo>em"od 


£53533 


£•35 


ssiSs ; 


■3 

a 


«J 


0008»- 

© o' r>i <> %d © 


jg|S2S 


qoto-e 
foj^'g — oo 


mm 


OOOm*«) 


llSSi j 


e 
1 

3 


n 


1 


1 


Irs* 


ES52-2 : 


ov^auj : 


i*U j ; 


15S 


52 




|||l y 


© © •© 0> * . 


©©.©■«© 


SS3S j ■ 


©C4 — - 


11 


s 


iill i i 


ooooo 

s*a««jj : 

3S2 — — • 


ooooo 


5552 : 


111;:; 


°°- : : : : 


1 


j 


I 

J 




I^rS55 


JJ5g5§ 


»mmqis.r« 


iSSagi 


5555^3 


SSgg&i 


o 

o 

<S 

H 




*J 


i&ss 


liSi53 


SS^^S® 


SSSSREi" 


SSSSSw 


2-5-;-- 


1 


OOOOBN 




555555; 


00»*'0if| 


55*555 


S 

\ 

o 


J 
QQ 


1 

X 


55^5 : : 


KISS •' 


sis'SIS 


-£5£5 : 


£*5i<3 | ; 


SiSSsi ^ 


4 


Opqir, . . 


HISS : 


555555 


mm \ 


sas j : 


-§R ■ • 


i 


to 


iii 1 1 


5S5.5.5 


qooooo 1 ooooo - 


llii • ; 


555 


1 


1 




S£*m°S 


5SSSSS 


OvOr- 








* 

55 


?.S2S;;2: 


s&rsse: 


*SSS23 


OONOiOm 


© 

3 

1 

fa 

a 
a 
I 


*l 


mm 


ONOT.^t 




-NO;>qm* 


SS3SSS 


ssSSS'S 


1 


oooooo 


OOOO'tB 


igSEi 


1II3SS 


oo-o;eio 


55 5 52 2 


l 




SmS* I \ 


55S-S : 


ssaaa 


jA-'jOOjtn'o 


§3253 : 


3255 : : 




§5SS •' : 


52522 "" 


||S2ss 


5S552S 4 


RSSR* j 


oo>om^ : 


a 

1 


I 


S;I;Q8 ' ■ 


ooooo '. 

S— SSIri • 


©ooooo 
©' ©' e\ » <?>' g 


ooooo* 


52553 : 


o«g*'g< ; ; 


H 


6 

"3 

'C 

1 


1-s 


.3 8.3 8.2 


S8SS ff S 


s s a 8 » 3 


S S3 8.« 3 


.3 8 3.8 » 2 


*ISf& 






3 

* 


ff 


1 


* 


•" 


=? 



taylor's experiments. 



1245 



4 

a 


I 
1 


es 

a 


60.O 
42.8 
28.5 
22.2 
18.7 


OO'ls'j; 


IN • 


piv— vq . . 

<*■! r>» «■* on •' ' 
■A<r\N— ; ; 


0«n<r\ - • 


1 








©•".cop — - 1 omift-» • 


qq-ts • • j mop • • 








O 1 o^rar>\D : 


9 9 ""."". 9 • 1 oo-^. • • 


999 _■ : 




v : 




1 

CO 


3 


S2?S j i 


Boasq 


• I* 1 * 




p 




1 








OOlst • • | poo 

M TcOMO . . ONQ 


; : 1 9°. 




p 










1 


pppp • • 


pop 




po 


ill 


o 
6 










a 
4 


I 
3 


"2 




p-rfpcq • | — "o»««q • 


1 <rcqo> 






OOONts . I ©©OOPICO • 

eoo'irlf'f*; • 0'>t— ■ — •* ; 
© eo >n *r <*\ ; orsmtm * 


vqvtprsN . 


INN»,N • • 

cosS-*S : 


j cocoa 




1 


SOOtt • 
— *o~cot>. ; 


OOO'O'O • 

8333$ ; 


OOO 'T to • 
COrnOM^sO 1 


pOoq'T . • 


©Or>. 
•6 -6 »' 

1A— t^ 




1 

03 


S3 1 — 


aso-rm : : 


rsico.evi • • • 

co«r\«"> : : : 


'*•« .'11! 


1 9 ; • 

S : : 






ppoo • • 


©Otnoo • • 

SSSS : ; 


99*. • • • 


oo • • ■ ■ 
■*» > > 1 '. ■'. '. 
£2 • ■ • 


9 •• 




1 


pppp • • 


pppp • • 


999 • ■ • 


pp . . . . 


© • • 

oo . : 




a 


2 


fci ) in a T CO T a 


co\qp»moo 


OOiASSt-scO 


op nO >o •■ CO 


j 00 — >q - ; • • 

tmN- : : 




Of^C0«TM»»(S I ©MOT— T I •0<As>OI>.— . 1 «N*mif\ . 

— ^a'co'— ' t*\ t4<6v\vfo6ei o'op'oo'v>«Xt»" ] m'mu-iso'— ' ; 
-emttn ©t>.ir\*rc*\m ao^-mmfs i a0>O^-<*\««v : 


iri«'o"<s ; ; 


1 


OOOOt'T 1 OOO.0N'O| I OOIsOmN 1 OOfflrsCs • 
cs^OMtroovO lorn — cor** I eo «n &• t-s >0 >ri >©<scPt^>o ; 


©p©«A . • 


55 


•2 


OTmq • • 


-mNNO • 


■*«p>-q«>. • • 

—■■*>o'oo" : 


r^ccr^ • • • 

S'*» : : : 


ts,© • 

39 ; 






pppoq • • 

<N — — . t 


ooNme • | qqmts 
— *rat>-o . t^tMsoNO ; ; 


oo© • • • 

©"i"»<s : : : 

ooi>i ; ; . 


©T -. 

eo'gj : 




"3 

CO 


pppp ; • 


ooopp • 1 pppp • • 
tn^rO'-oo '. e'd-'is I ; 


OO© • • • 

©in-* r ; '. 


99 : 




1 


i 

s 


i- 


3828,2 


3S28«2 


3 S 2^ . 2 


^8 2 8^ 2 


£ft£g^3 


jjs 


y 


* 








5 


1 


«~ 





1246 



THE MACHINE-SHOP. 



will be the same when tid 1 s 1 s = hats??, or for constant durability S2 — 

«l-y/(*r%l + (WCz). 

New High-Speed Steels. — Am. Mach., April 8, May 20 and 27, 1909, 
describes the operations of some new varieties of high-speed steel made 
by Sheffield manufacturers, which show results superior to those of the 
earlier high-speed steels in endurance of tool, ability to cut very hard 
metals, and higher speeds. The following are the results of some of the 
tests in lathe-work. 



Tool 
size. 



Material Cut. 



Diam. Depth. Feed £ p *f d Length of 
cutin. in. f *;.P ei ' Cut. 



H/4 
11/4 
U/4 

7/8 
7/8 
7/8 
11/4 
U/2 
U/4 
1x2 
1x2 
U/4 
U/4 



Steel, 2.00 C 

Steel, 0.70 C 

Steel, 0.70 C... 

Steel, 0.40C 

Steel, 0.40 C 

Cast iron 

Cast iron 

Cast iron 

Steel, 0.40 C 

Steel 

Nickel steel 

Steel casting, 0.45 C. 
Steel, 0.60 C 



4 

4 
5 ft. 
5 ft. 
5 ft. 
53/ 8 in. 
93/ 4 in. 
31/2 in. 
20 in. 
71/2 in. 



V4 
3/16 
1/8 
1/8 
V8to3/ 16 

5 /l6 

1/8 
V8 
3 /8 
1/2 

m 

9 /64 



Vl6 

Vl6 
Vl6 
Vl6 
1/32 
VlO 
V32 
1/8 ■ 

Vio 

1/8 
0.072 
1/8 
1/26 



43/ 4 in.* 
13 in.t 

87/ 8 in. 
28 ins., t 
28 ins., § 

41/2 ins. 

6 ins. 

8 ins. 
54 ins. 
72 ins. 
124 ins. 
15 to 20 min.|| 
18 in. 



* Then 1 3/4 in. at 50 ft. per min. t Then 1 1/8 in. at 65 ft. per min. 
t Then 28 ins. at 98 ft. § Then 22 ins. at 160 ft. || Required 28 H.P. 
Chilled rolls, too hard for ordinary high-speed steel, were cut at a speed 
of 80 ft. per min., with 5/ 16 in. depth of cut and Vs in. feed. 

The following results were obtained in drilling: 



Drill 
size. 


Material. 


Rev. 
per 
min. 


Feed 

per 

rev. 


Speed 
per 
min. 


Drilled without Re- 
grinding. 


3/4 in. 
3/4 
3/4 
13/16 


Close cast iron 

Steel, 0.25 C 


466 

247 
526 
400 


0.018 
0.011 


8 1/2 in. 

6 in. 

31/2 


70 holes, 3 ins. deep. 
60 holes, 23/4 ins. deep. 
12 holes, 21/2 ins. deep. 
14 in. at one operation. 




Steel 





A milling cutter 5 in. diam., with 54 teeth, milling teeth in saw-blanks, 
at a cutting speed of 56 ft. per min. and a feed of 1 in. per min., cuts 
80 blanks (three or more together), each 32 in. diam., 3/ 8 in. thick, 240 
teeth, before re-grinding. 

Use of a Magnet to Determine the Hardening Temperature. 
(Catalogue of Firth-Sterling Steel Co.) — At the proper hardening heat a 
piece of regular tool steel loses its power to attract a magnet. By touch- 
ing a magnet against the tool as it heats up in the furnace, the magnet 
will take hold until the proper heat for quenching is reached, and then it 
will not take hold at any point. This determines the lowest heat at which 
it can be hardened. 

By heating slowly, trying with a magnet frequently, and dipping the 
tool when the magnet will not take hold, an extremely hard tool will be 
secured and one which will do excellent work. The magnet should not 
be allowed to become heated. In order to guard against the loss of 
magnetism in a horseshoe magnet an electro-magnet may be made by 
passing an electric current through a coil of wire wound on an iron rod. 

CASE-HARDENING, ETC. 

Case-hardening of Iron and Steel, Cementation, Harveyizing. — 

When iron or soft steel is heated to redness or above in contact with 
charcoal or other carbonaceous material, the carbon gradually penetrates 



MILLING CUTTERS. 1247 

the metal, converting it into high carbon steel. The depth of penetra- 
tion and the percentage of carbon absorbed increase with the temperature 
and with the length of time allowed for the process. In the old cementa- 
tion process for converting wrought iron into "blister steel" for re-melting 
.in crucibles flat bars were packed with charcoal in an oven which was 
kept at a red heat for several days. In the Harvey process of hardening 
the surface of armor plate, the plate is covered with charcoal and heated 
in a furnace for a considerable time, and then rapidly cooled by a spray 
of water. 

In case-hardening, a very hard surface is given to articles of iron or 
soft steel by covering them or packing them in a box or oven with a ma- 
terial containing carbon, heating them to redness while so covered, and 
then chilling them. Many different substances have been used for the 
purpose, such as wood or bone charcoal, charred leather, sugar, cyanide 
of patassium, bichromate of potash, etc. Hydrocarbons, such as illu- 
minating gas, gasolene or naphtha, are also used. Amer. Machinist, 
Feb. 20, 1908, describes a furnace made by the American Gas Furnace 
Company of Elizabeth, N. J., for case-hardening by gas. The best results 
are obtained with soft steel, 0.12 to 0.15 carbon, and not over 0.35 man- 
ganese, but steel of 0.20 to 0.22 carbon may be used. The carbon begins 
to penetrate the steel at about 1300° F., and 1700° F. should never be 
exceeded with ordinary steels. A depth of carbonizing of V64 in, is 
obtained with gas in one hour, and 1/4 in. in 12 hours. After carbonizing 
the steel should be annealed at about 1625° F. and cooled slowly, then 
re-heated to about 1400° F. and quenched in water. Nickel-chrome steels 
may be carbonized at 2000° F. and tungsten steels at 2200° F. 

Change of Shape due to Hardening and Tempering. — J. E. Storey, 
Am. Mack., Feb. 20, 1908, describes some experiments on the change of 
dimensions of steel bars 4 in. long, 7/g in. diam. in hardening and temper- 
ing. On hardening the length increased in different pieces .0001 to 
.0014 in., but in two pieces a slight shrinkage, maximum .00017, was found. 
The diameters increased .0003 to .0036 in. On tempering the length 
decreased .0017 to .0108 in. as compared with the original 4 ins. length, 
while the diameter was increased .0003 to .0029; a few samples showing 
a decrease, max. 0009 in. The general effect of hardening is a slight 
increase in bulk, which increase is reduced by tempering. The distortion 
is more important than the increase in bulk. 

MILLING CUTTERS. 

George Addy (Proc. Inst. M. E., Oct., 1890, p. 537) gives the following: 
Analyses of Steel. — The following are analyses of milling cutter 
blanks, made from best quality crucible cast steel and from self-harden- 
ing "Ivanhoe" steel: 

C Si P 

Crucible Steel, 1.2 0.112 0.018 
Ivanhoe Steel, 1.67 0.252 0.051 

The first analysis is of a cutter 14 in. diam., 1 in. wide, which gave 
very good service at a cutting-speed of 60 ft. per min. Large milling 
cutters are sometimes built up, the cutting-edges only being of tool steel. 
A cutter 22 in. diam. by 5 1/2 in. wide has been made in this way, the teeth 
being clamped between two cast-iron flanges. Mr. Addy recommends 
for this form of tooth one with a cutting-angle of 70°, the face of the 
tooth being set 10° back of a radial line on the cutter, the clearance-angle 
being thus 10°. At the Clarence Iron Works, Leeds, the face of the tooth 
is set 10° back of the radial line for cutting wrought iron and 20° for steel. 

Pitch of Teeth. — For obtaining a suitable pitch of teeth for 
milling-cutters of various diameters there exists no standard rule, the 
pitch being usually decided in an arbitrary manner according to individual 
taste. For estimating the pitch of teeth in a cutter of any diameter from 
4 in. to 15 in., Mr. Addy has worked out the following rule, which he has 
found capable of givin g good results in pra ctice: 

Pitch in inches = \/(diam. in inches X 8) X 0.0625 = 0.177 Vdiam. 

J. M. Gray gives a rule for pitch as follows: The number of teeth in a 
milling cutter ought to be 100 times the pitch in inches; that is, if there 
were 27 teeth, the pitch ought to be 0.27 in. The rules are practically 



Mn S Tungsten c 


iron, D] 
ifferenc 


0.36 0.02 

2.56 0.01 4.65 


98.29 
90.81 



1248 



THE MACHINE-SHOP. 



the same, for if d ■ 
f erence, c = pn; d ■ 



diam., 
pn _ 



n = no. of teeth, p = pitch, c = circum- 
^^ = 31.83p 2 ; p=Vo.0314d = 0.177 Vd; 



No. of teeth, n. = 3.14d ^- p. 

Teeth of Plain or Spiral Milling Cutters. (Mach'y, April, 1907.) — 
Plain milling cutters are usually manufactured in sizes from 2 to 5 
in. diameter, and up to 6-in. face. The use of solid plain milling cutters 
of over 5-in. face is not advised, and cutters over 5-in. face should be 
made in two or more interlocking sections. 

Number of Teeth and Amount of Spiral of Plain Milling Cutters. 
No. of teeth = 5X diam ' + 24 ; Length of Spiral = 9 X diam. + 4. 

Diameter of cutter, 

2 21/4-21/2 23/4 3 3V 3 4 41/2 5 ,51/ 2 6 61/ 2 7 7l/ 2 8 
Number of teeth, 

16 18 18 18 20 20 22 24 24 26 26 28 30 30 32 
Length oT one turn of spiral, inches, 

22 241/4 261/2 283/ 4 31 35i/ 2 40 441/2 49 53l/ 2 58 62l/ 2 67 71 1/ 2 76. 

A cutter with an included angle of 60° (12° on one side and 48° on the 
other) is recommended for fluting plain milling cutters, although cutters 
of 52° (12° and 40°) are commonly furnished by manufacturers. The 
angle of relief of milling cutters should be between 5° and 7°. 

Nicked Cutters. — -Cutters for milling broad surfaces, whether of the 
spiral or straight type, usually have nicks cut in the teeth, the nicks 
being staggered in consecutive teeth. These afford relief from jam- 
ming the teeth with chips. 

Side Milling Cutters. (Mach'y, April, 1907.) — The teeth of side 
milling cutters should have the same general form as those of plain 
milling cutters, excepting that the cutter used to form them should have 
an included angle of about 75°. 

Number of Teeth in Side Milling Cutters. 
Number of teeth = 3.1 diam. + 11. 
Diam. of cutter, 

2 21/4 21/2 23/4 3 3V 2 4 4i/ 2 5 5i/ 2 6 6 1/2 7 71/2 8 9 
Number of teeth, 
18 18 18 20 20 22 24 24 26 28 30 32 32 34 36 38 

Milling Cutters with Inserted Teeth. — When it is required to use 
milling cutters of a greater diameter than about 8 in., it is preferable 
to insert the teeth in a disk or head, so as to avoid the expense of 
making solid cutters and the difficulty of hardening them, not merely 
because of the risk of breakage in hardening them, but also on account 
of the difficulty in obtaining a uniform degree of hardness or temper. 

Keyways in 31illing Cutters. — A number of manufacturers have 
adopted the keyways shown below, as standards. The dimensions in 
inches are given in the tables. 




Fig. 190.— Square Key way. 



Diam. 
Hole, 


3/8-9/16 


5/8-7/8 


15/16-1 1/8 


13/16-13/s 


1 7/16-1 3/4 


1 13/16-2 


2 V16-2 1/2 


29/16-3 


Width 
W 


3 /32 


1/8 


5/32 


3/16 


1/4 


5/16 


3/8 


7/16 


Depth, 
D 


3/64 


1/16 


5/64 


3/32 


1/8 


5/32 


3/16 


3 /l6 


Radius, 
R 


0.020 


0.030 


0.035 


0.040 


0.050 


0.060 


0.060 


0.060 



MILLING CUTTERS 



1249 








Fig. 191. — Half-round Keyway 






Diam. 
Hole, H 


3/8-5/8 


H/16-13/16 


7/8-1 3/16 


1 1/4-1 7/ 16 


1 1/2-2 


21/l6-2 7/i 6 


2 1/2-3 


Width 
W 


1/8 


3/16 


1/4 


5 /l6 


3/8 


7/16 


1/2 


Depth, 
D 


Vie 


3/32 


1/8 


5 /32 


3/16 


7/32 


1/4 



Power Required for Milling. (Mech. Engr., Oct. 26, 1907.) — 
Mr. S. Strieff made a series of experiments to determine the power 
required to drive milling cutters of high-speed steel. The results are 
shown in the table below. A proportionately higher amount of power 
is required for light than heavy milling, as the power to drive the machine 
is the same at all loads. The table also shows that the depth of cut does 
not increase the power required in the same proportion as the width, arid 
that work with a quick feed and a deep but comparatively narrow cut 
requires less power than a wide cut of moderate depth with slow feed, 
the amount of metal removed being the same in both cases. 

Power Required for Milling. 



*s 


Feed. 


u . 












a 












73 




T3 








































0) 




O <d' 


A 


J3 


3 


CD 


'3 ^ 


<3 o> 


c 

3 
C 


fi 


la 


a 
6 


3 

o 




a . 
cu 2 

gP-4 


erg 

fSfM 


§0 


§ 


3 


a 


-a 


o 


"Shh 


o a ' 


£ 


Oh 


£ 


o 


Q 


$ 


w 


§ 


w 


24 


2.46 


0.10 


37 


0.26 


23.6 


25 


245 


0.102 


24 


3.50 


0.15 


37 


0.26 


10.2 


17 


150 


0.113 


24 


4.35 


0.18 


37 


0.14 


9.8 


17 


97 


0.175 


24 


3.50 


0.15 


37 


0.49 


9.8 


27 


490 


0.055 


19 


4.33 


0.23 


29.5 


0.28 


9.3 


17 


331 


0.051 


23 


4.17 


0.18 


36 


0.28 


20.5 


27 


386 


0.070 


23 


4.17 


0.18 


36 


0.28 


9.8 


20 


183 


0.109 


40 


1.89 


0.05 


64 


0.24 


10.2 


17 


74 


0.230 


40 


3.94 


0.10 


64 


0.37 


13.8 


21 


331 


0.063 


40 


5.79 


0.14 


64 


0.16 


16.5 


17 


123 


0.138 



Extreme Results with Milling Machines. — Horace L. Arnold (Am. 
Mach., Dec. 28, 1893) gives the following results in flat-surface milling, 
obtained in a Pratt & Whitney milling machine: The mills for the flat 
cut were 5 in. diam., 12 teeth, r 40 to 50 r.p.m. and 47/g in. feed per min. 
One single cut was run over this piece at a feed of 9 in. per min., but 
the mills showed plainly at the end that this rate was greater than they 
could endure. At 50 r.p.m. for these mills the figures are as follows, with 
47/ 8 in. feed: Surface speed, 64 ft., nearly; feed per tooth, 0.00812 in.; 
cuts per in., 123. And with 9-in. feed per min.: Surface speed, 64 ft. 
per min.; feed per tooth, 0.015 in.; cuts per in., 662/3. 



1250 THE MACHINE-SHOP. 

At a feed of 47/g in. per min., the mills stood up well in this job of 
cast-iron surfacing, while with a 9-in. feed they required grinding after 
surfacing one piece; in other words, it did not damage the mill-teeth to 
do this job with 123 cuts per in. of surface finished, but they would not 
endure 662/3 cuts per in. In this cast-iron milling the surface speed 
of the mills does not seem to be the factor of mill destruction; it is 
the increase of feed per tooth that prohibits increased production of 
finished surface. This is precisely the reverse of the action of single- 
pointed lathe and planer tools in general; with such tools there is a sur- 
face-speed limit which cannot be economically exceeded for dry cuts, 
and so long as this surface-speed limit is not reached, the cut per tooth 
or feed can be made anything up to the limit of the driving power of the 
lathe or planer, or to the safe strain on the work itself, which can in many 
cases be easily broken by a too great feed. 

In wrought metal extreme figures were obtained in one experiment 
made in cutting keyways 5/ 16 in. wide by Vs in. deep in a bank of 
8 shafts 1 1/4 in. diam. at once, on a Pratt & Whitney, No. 3 column 
milling machine. The 8 mills were successfully operated with 45-ft. 
surface speed and 19 1/2 in. per min. feed; the cutters were 5-in. diam., 
with 28 teeth, giving the following figures, in steel: Surface speed, 45 
ft. per minute; feed per tooth, 0.02024 in.; cuts per inch, 50, nearly. 
Fed with the revolution of mill. Flooded with oil, that is, a large 
stream of oil running constantly over each mill. Face of tooth radial. 
The resulting keyway was described as having a heavy wave or cutter- 
mark in the bottom, and it was said to have shown no signs of 
being heavy work on the cutters or on the machine. As a result of the 
experiment it was decided for economical steady work to run at 17 r.p.m., 
with a feed of 4 in. per min., flooded cut, work fed with mill revolution, 
giving the following figures: Surface speed, 221/4 ft. per min.; feed per 
tooth, 0.0084 in.; cuts per in., 119. 

The Cincinnati Milling Machine Co. (1906) gives the following exam- 
ples of rapid milling machine work: Gray iron castings 10 1/4 in. wide, 
14 in. long X l 3 /4 in. thick, finished all over, and a slot 5/ 8 x 1 in. cut 
from the solid. A gang of five cutters was used, two of 8 in., two of 
31/2 in. and one of 53/ 4 in. diameter, respectively. These took a cut 
3/is in. deep across the top and two edges, and milled the slot in one 
operation. The table travel was 4.2 in. per minute. The average time, 
including chucking, was 15.6 minutes. 

Gray iron castings 3 in. and 6V2 in. wide X 251/4 in. long, 11/4 in. 
thick, were surfaced by a face mill 8 in. diameter at a surface speed of 
80 feet per minute. The cut was 3/ 16 in., and the table travel 11.4 in. 
per minute in the 3-in. part and 8 in. per minute in the 6 1/2-in. part. 
The total time for finishing, including chucking, was seven minutes. The 
planer required 23 minutes for the same operation. In finishing the 
opposite side of these castings, two castings are milled at one setting, 
s/16 in. of stock being removed all over and two slots 5/ 8 x 5 /s in. milled 
from the solid. A gang of seven cutters, 3 of 3 in., 2 of 4 1/4 in., and 1 
of 8 1/4 in. diameter, was used at 38 revolutions per minute and a feed of 
0.1 in., giving a table travel of 3.8 in. per minute. These two castings 
were finished in 18 minutes, including chucking, the actual milling time 
being eight minutes on each piece. A planer working at 55 ft. cutting 
speed finished the same job in 36 minutes. 

An inserted -tooth face mill 12 in. diameter took a 9-in. cut, Vs in. 
deep across the entire face of a gray iron casting at a table travel of 5 in. 
per minute. The length of cut was 18 inches and the time required ■ 
6 1/2 minutes. 

The following table summarizes a number of typical jobs of milling: 



MILLING CUTTERS 



1251 



Typieal Milling Jobs. 

(Cincinnati Milling Mach. Co.; Brown & Sharpe Mfg. Co., 1907.) 







Cut, 
Inches . 


Cutter. 


fl - 


83 

a 


a 


s "»? 


3 

O 

3 






> 

U 


13 
> 

83 fl 


-S-2 


o 
"o 






_fl 


fl 


^fl 

0,1 

w. u 


I* 

a> a; 
«■§ 
— fl 


3 




ft 


6 


g 






t3 




eSrs 


1 




Q 


-a 


| 

Q 


> 




83 
83 


3*8 




Spline (R) . . . 


Steel .... 


5 /32 


3 /l6 


21/2 


166 


108 


0.05 


8.3 


0.243 


Keyseat (R) . . 


Gray iron . . 


3 /ie 


3 / 8 


2 1/2 


166 


108 


0.108 


17.9 


1.04 


Keyseat (R) . . 


Lumen metal 


1/8 


•Vl« 


2 


211 


110 


0.15 


31.6 


0.74 


Surfacing (F) . 


Brass .... 


0.01 


2 l/o 


31 


100 


78 


0.25 


25.0 


0.675 


Surfacing (F) . 


Tool steel . . 


Vl6 


21/o 


31 


37 


29 


0.05 


1.85 


0.289 


Face Milling (F) 


Gray iron . . 


0.015 


8 


10 


47 


123 


0.30 


\4.\ 


1.692 


Face Milling (R) 


Gray iron . . 


V8 


6 


8 


26 


54 


0.168 


4.36 


3.27 


Surfacing (R) . 


Gray iron . . 


1/8 


21/2 


32 


100 


78 


0.30 


30.0 


9.375 


Surfacing (F) . 


Bronze casting 


1/64 


3 


32 


166 


130 


0.05 


8.3 


0.389 


T-slotting . . . 


Gray iron . . 


See Note 3 


11/16 


252 


75 


0.05 


12.6 


6.693 


Surfacing . . . 


Gray iron . . 


0.10 112 


4.5 4 


45 


52 


0.266 


12. 


14.4 


Surfacing . . . 


Gray iron . . 


1/8 12 


3.5* 


53 


55 


0.226 


12. 


18.0 


Surfacing . . . 


Gray iron . . 


0.20 12 


4 4 


61 


65 


0.148 


9.02 


21.6 



(F) Finishing cut; (R) Roughing cut. 

1 End mill; 2 spiral mill with nicked teeth; work done by peripheral 
teeth. 3 Both sides of cutter engaged, making slot width equal to 
cutter diameter; slot Vie* 1/2 inch. * Carbon steel nicked spiral cutter. 

Tests with a Helical Milling Cutter, 3 in. diam., 6 in. long; 8 teeth; 
pitch of helix, 183/ 4 in.; notched teeth; on cast iron and on mild steel, 
are reported by P. V. Vernon in Am. Mach., June 3, 1909. The cutter 
was run at a constant speed, 84 turns per minute, cutting speed 66 ft. 
per min. In the tests on cast iron the depth of cut was varied from 
0.14 to 1.10 in., and the feed per min. from 109/ie in. to 127/ 32 in. The 
material removed per minute ranged from 7.39 to 15.23 cu. in., and the 
cu. in. per min. per net machine horse-power from 1.06 to 1.52, averaging 
about 1.30. 

In the tests on steel the depth of cut was 0.10 to 1.10 in. and the feed 
103/g to 05/g in. per min. ; the material removed per min. from 2.88 to 6.27 
cu. in. per min. ; and the cu. in. per min. per net H.P. from 0.47 to 0.71, aver- 
aging about 0.57. No regular relation appears between the rate of feed 
and the metal removed per min., but the maximum output on cast iron 
was obtained with a cut 5/ 8 in. deep and a feed of 4"/s in. per min.; and 
on mild steel with a cut 0.12 in. deep and a feed of 91/2 in. per min. 

Milling "with" or "against" the Feed. — Tests made with the 
Brown & Sharpe No. 5 milling-machine (described by H. L. Arnold, 
in Am. Mach. x Oct. 18, 1884) to determine the relative advantage of 
running the milling cutter with or against the feed — "with the feed" 
meaning that the teeth of the cutter strike on the top surface or 
" scale " of cast-iron work in process of being milled, and "against the 
feed " meaning that the teeth begin to cut in the clean, newly cut surface 
of the work and cut upwards toward the scale — showed a decided advan- 
tage in favor of running the cutter against the feed. The result is 
directly opposite to that obtained in tests of a Pratt & Whitney machine 
by experts of the Pratt & Whitney Co. 

In the tests with the Brown & Sharpe machine the cutters used were 6 
inches face by 41/2 and 3 inches diameter, respectively, 15 teeth in each 
mill, 42 revolutions per minute in each case, or nearly 50 feet per minute 
surface speed for the 41/2-inch and 33 feet per minute for the 3-inch mill. 
The revolution marks were 6 to the inch, giving a feed of 7 inches per 



1252 THE MACHINE-SHOP. 

minute, and a cut per tooth of 0.011 inch. When the machine was forced 
to the limit of its driving the depth of cut was H/32 inch when the cutter 
ran in the " old " way, or against the feed, and only 1/4 inch when it ran 
in the "new "way, or with the feed. The endurance of the milling 
cutters was much greater when they were run in the "old" way. The 
Brown & Sharpe Co. says that it is sometimes advisable to mill with 
the feed, as in surfacing two sides of a piece with straddle mills, the 
cutters will then tend to hold the work down. In milling deep slots or 
cutting off stock with thin cutters or saws milling with the feed is less 
likely to crowd the cutter sidewise and make a crooked slot. 

Modern Milling Practice. (Cincinnati Milling Machine Co., 1907.) — 
The limit of milling operations is determined by the strength and dura- 
bility of the cutter. A rigid frame on the machine and powerful 
feed mechanism increase these. The chief causes of low output are: 
Improperly constructed cutters; insufficient rigidity in the machine; and 
timidity, due to lack of experience, of both builders and operators. The 
principal cause of cutter failures is insufficient space for chips between 
the cutter teeth. Fixed rules cannot be laid down for proper feeds and 
speeds of milling cutters, these depending on the character and hardness 
of the metal being cut. On roughing cuts it is desirable to run the cutter 
at a speed well within its limit, and use as heavy a feed as the machine 
can pull. The size of chip taken by each tooth of the cutter with the 
heaviest feeds is comparatively light, and with properly sharpened 
cutters there is little danger of breaking the cutter by giving too great 
a feed. It is considered better practice, however, to break an occasional 
cutter than to run machines at a low rate. It is not considered desirable 
to run even high speed steel cutters at excessive speeds. The great 
value of these cutters is their long life and ability to hold a cutting edge 
as compared with carbon steel cutters. It is important to keep the 
cutters sharp, as accurate or fast work is impossible with dulled teeth. 
The clearance angle should be kept low; about 3 degrees for steel, and not 
more than 5 degrees for gray iron. 

The following speeds in feet per minute are a good basis for roughing 
the materials indicated: 

Carbon steel cutters. 

Cast Iron. Machinery Steel. Tool Steel. Brass and Bronze. 
40 40 20 60 

High speed steel cutters. 

80 80 40 120 

On cast-iron work a jet of air delivered to the cutter with sufficient 
force to blow the chips away as fast as made permits faster feeds and 
prolongs the cutter's life. A stream of oil fed under heavy pressure to 
wash the chips away has the same effect when cutting steel. On finish- 
ing cuts the rate of feed used determines the grade of the finish. If a 
spiral mill is used the feed should range from 0.036 in. to 0.05 in. per 
revolution of a 3-in. diameter cutter. As such cuts are light the speed 
of cutting can be much higher than used for roughing cuts. The nature of 
the cut is a factor in determining speeds; a saw can run twice as fast as 
a surface mill. Keyseating and similar work can be best done with a 
plain cutter rather than a side mill. 

In general small cutters are preferable to large ones, and the hole 
should be as small as the strength of the arbor will permit. It is 
advisable in surface milling to have the cutter wider than the work. 

Lubricant for Milling Cutters. (Brown & Sharpe Mfg. Co., 1907.) — 
An excellent lubricant, to use with a pump, for milling cutters is made 
by mixing together and boiling for one half hour, 1/4 lb. sal soda, 1/2 pint 
lard oil, 1/2 pint soft soap and water enough to make 10 quarts. 

Milling Machine versus Planer. — For comparative data of work 
done by each see paper by J. J. Grant, Trans. A. S. M. E., ix, 259. 
He says: The advantages of the milling machine over the planer are 
many, among which are the following: Exact duplication of work; 
rapidity of production — the cutting being continuous; lower cost of 

Eroduction, as several machines can be operated by one workman, and 
e not a skilled mechanic; and lower cost of tools for producing a given 
amount of work. 



DRILLS. 



1253 



Constant for Finding Speeds of Drills. — For finding the speed in 
feet when the number of revolutions is given; or the number of revolu- 
tions, when the speed in feet is given. 

Constant = 12 -f- (size of drill X 3.1416). 
Number of revolutions = Constant X speed in feet. 
Speed in feet = Number of revolutions ■*■ constant. 



Size 


Con- 


Size 


Con- 


Size 


Con- 


Size 


Con- 


Size 


Con- 


Drill. 


stant. 


Drill. 


stant. 


Drill. 


stant. 


Drill. 


stant. 


Drill. 


stant. 


In. 


In. 


In. 


In. 


In. 


In. 


In. 


In. 


In. 


In. 


V8 


30.55 


3/4 


5.09 


13/s 


2.78 


2 


1.91 


25/ 8 


1.45 


a /l« 


20.38 


13/lfi 


4.70 


17/16 


2.66 


21/16 


1.85 


2H/16 


1.42 


V4 


15.28 


V* 


4.36 


H/7 


2.55 


21/8 


1.80 


23/4 


1.39 


Wi« 


12.22 


15/16 


4.07 


19/16 


2.44 


23/16 


1.75 


213/ie 


1.36 


3/8 


10.19 


1 


3.82 


15/8 


2.35 


21/4 


1 70 


27/g 


1.33 


7/16 


8.73 


H/1R 


3.59 


1 H/16 


2.26 


25/tfi 


1.65 


215/16 


1.30 


V? 


7.64 


I 1/8 


3.39 


13/ 4 


2.18 


23/ 8 


1.61 


3 


1.27 


9/16 


6.79 


13/1R 


3.22 


1 13/16 


2.11 


27/ie 


1.57 


31/16 


1.25 


5/8 


6.11 


1 1/4 


3.06 


IV/8 


2.04 


21/, 


1.53 


31/8 


1.22 


U/16 


5.56 


10/16 


2.91 


1 15/16 


1.97 


29/16 


1.49 


31/4 


1.18 



Speed of Drills. — The Cleveland Twist Drill Co. (1907) gives the 
following speeds in r.p.m. for drilling wrought iron, machinery steel or 
soft tool steel, with high speed and carbon steel drills. 



1, 




■ai 


a 




T3 


£ 


h 


frl 


£ 


o • 




S3 


o3 ® 
002 


grc 


S3 


O02 


ftm 


S3 


OM 


Mm 


S3 


OOl 


aft 


1/16 


1834 


3057 


13/16 


141 


235 


19/16 


73.4 


122 


2 5/! 6 


49.5 


82.7 


VS 


917 


1528 


7/8 


131 


218 


I 5/ 8 


70.5 


117 


23/s 


48.2 


80.5 


3/16 


611 


1020 


15/16 


122 


204 


Hl/16 


67.9 


113 


27/ib 


47.0 


78.5 


1/4 


458 


765 


I 


115 


191 


I 3/4 


65.5 


109 


2V ? 


45.8 


76.5 


5/16 


367 


612 


H/16 


108 


180 


U3/16 


63.2 


105.3 


2 9/! fi 


44.7 


74.6 


3/8 


306 


510 


I 1/8 


102 


170 


I 7/8 


61.1 


102 


25/ 8 


43.7 


72.8 


7/16 


262 


437 


13/iR 


96.5 


160 


U5/16 


59.2 


98.7 


2U/16 


42.6 


71.1 


lh 


229 


382 


H/4 


91.8 


153 


2 


57.3 


95.6 


23/4 


41.7 


69.5 


9/16 


204 


340 


15/16 


87.3 


145 


21/16 


55.6 


92.7 


213/i 6 


40.7 


68.0 


5/8 


184 


306 


13/8 


83.3 


139 


21/8 


54.0 


90.0 


27/s 


39.8 


66.5 


H/16 


167 


277 


17/16 


79.8 


133 


23/lfi 


52.4 


87.4 


2 15/ t 6 


39.0 


65.1 


3/4 


153 


255 


H/2 


76.3 


127 


21/4 


51.0 


85.0 


3 


38.2 


63.6 



The feed per revolution recommended for drills smaller than 1/2-in. 
is from 0.004 to 0.007 in.; and from 0.005 to 0.01 in. for drills larger 
than 1/2-in. 

High Speed Steel Drills. — The Cleveland Twist Drill Co. says 
that a high speed steel drill should be started with a peripheral 
speed between 50 and 60 ft. per minute, and a feed of 0.005 to 0.010 • 
in. per revolution for drills over 1/2-in. A drill with a tendency 
to wear away on the outside is running too fast ; if it breaks or chips on 
the cutting edges it has too much feed. When used in steel or wrought 
iron, the drill should be flooded with a good lubricant. For brass, paraffine 
oil is recommended, and for cast iron, an air blast. 

Power Required to Drive High Speed Steel Drills. — The American 
Tool Works Co. (1907) obtained some remarkable results with drills of 
high-speed steel as shown in the tables below. The machine used was 
a triple-geared radial, and the drill was of the " Celfors " type, a flat bar of 
steel, twisted, affording ease of lubrication, and a free escape for the chips. 



1254 



THE MACHINE-SHOP. 



Power Required to Drill Steel with High Speed Steel Drills. 



Size of 
Drill. 


R.P.M. 


Cutting 
Speed, 


Feeds. 


H.P. Re- 






quired. 


Inches. 




Ft. per Min- 


In. per Rev. 


In. per Min. 


9/16 


356 


52.3 


.012 


4.27 


4.2 


3/ 4 


313 


61.5 


.012 


3.75 


10.8 


U/32 


188 


50.9 


.024 


4.51 


9.0 


15/32 


188 


56.9 


.024 


4.51 


9.3 


1 23/3 2 


128 


57.6 


.024 


3.07 


8.4 


1 31/32 


167 


86.2 


.012 


2.00 


7.8 



Power Required to Drill Cast Iron 3 in. thick with High Speed 
Steel Drill. 



Size of 




Cutting 


Feeds. 




Drill, 


R.P.M. 


Speed, 






H.P. 






Inches. 




Ft. per Mm. 


In. per Rev. 


In. per Min. 




1 1/32 


313 


84.5 


.046 


14.4 


13.2 


17/32 


313 


99.8 


.046 


14.4 


15.3 


1 15/32 


216 


83.1 


.033 


7.1 


12.6 


1 23/3 2 


216 


97.0 


.033 


7.1 


16.8 


1 31/32 


128 


66.0 


.033 


4.22 


15.6 


31/2 


60 


55.0 


.024 


1.44 


10.2 



Extreme Results with Radial Drills. (F. E. Bocorselski, Am. 
Mach., Mar. 17, 1910.) — Three different radial drilling machines, de- 
signed to drive high-speed steel drills of the twisted type to the limit 
of their endurance, were tested by drilling steel billets of about 0.70 
carbon at speeds and feeds which caused the drills to break after drill- 
ing holes from 2 to 1 1 ins. deep. The following are a few of the results 
obtained with different sizes of drill. 



Drill 


Revs, 
per 
min. 


Cutting 
speed, 
ft. per 
min. 


Feed. 


Metal removed. 


Max. 
H.P. 


H.P. 

per lb. 

per 

min. 


size, 
ins. 


Per rev. 
in. 


Ins. per 
min. 


Cu. ins. 
per min. 


Lbs. per 
min. 


11/2 

H/2 
U/4 
H/8 
H/16 


290 
312 
330 
208 
330 


113 
123 
107 
61.3 
91 


0.0207 
0.0323 
0.0207 
0.022 
0.0207 


6 

10.08 
6.83 
4.58 
6.83 


10.56 
17.23 
8.33 
4.54 
6. 


2.95 
4.97 
2.33 J 
1.27 
1.68 


25 

56.0 

24.8 

22.6 

24.8 


8.48 
11.4 
10.6 
17.8 
14.8 



The H.P. of one of the machines running light at full speed was 4.4; 
running light at slow speed 2 H.P. 

It was concluded from these tests, which were destructive to the 
drills, that for maximum production and considering the life of the drills, 
it is best to run a 1-in. drill at about 300 r.p.m. with a feed of 0.015 in. 
per rev., and a 11/2-in. drill 225 r.p.m. with a feed of 0.02 in. per revolu- 
tion, 

Some Data on High-Speed Drilling are given by G. E. Hallenbeck 
in Iron Tr. Rev., April 29, 1909. A Baker high-speed drilling machine 
was used. Holes lVsin. diam. were drilled through 41/4-in. blocks of 
cast iron in 82/3 seconds per hole, or at the rate of 29 in. per min. Holes 
15/ie in- diam. were drilled through 3/ 4 in. steel plate in 31/2 seconds. 

Experiments on Twist Drills. — An extensive series of experiments 
on the forces acting on twist drills of high-speed steel when operating 



DRILLS. 



1255 



on cast-iron and steel is reported by Dempster Smith and A. Poliakoff, in 
Proc. Inst. M. E., 1909. Abstracted in Am. Mach., May, 1909, and 
Indust. Eng., May, 1909. Approximate equations derived from the 
first set of experiments are as follows: 

Torque in pounds-feet, / =(1800 1 + 9)d 2 , for medium cast-iron; 
T = (3200 4 + 20) J 2 , for medium steel. End thrust, lbs., P = 115,000 
t — 200, for medium cast-iron; P = 160,000(d - 0.5)4 +• 1000, for 
medium steel; d = diam., t = feed per revolution of drill, both in inches. 
The steel was of medium hardness, 0.29 C, 0.625 Mn. 

The end thrust in enlarging holes in medium steel from one size to 
a larger was as follows: 3/ 4 in. to 1 in., P = 15,200 t - 60; 1 in. to 11/2 in., 
P = 25,500 4 +; 3/4 in. to ll/ 2 in., P = 30,000 4 + 200. 

A second series of experiments, with soft cast-iron of C.C., 0.2; G.C., 
2.9; Si, 1.41; Mn, 0.68; S, 0.035; P, 1.48, and medium steel of C, 0.31; 
Si, 0.07; Mn, 0.50; S, 0.018; P, 0.033: tensile strength, 72,600 lbs. per 
sq. in., gave results from which were derived the following approximate, 
equations: 

Torque, lbs.-ft./ T = 740 d^t ' 7 , or Wd 2 + 100 4(14 d 2 + 3) for cast-iron, 
T = 1640 di*8fo.7 f or 28 d 2 (l + 100 4) for medium steel, 

End thrust, lbs. P = 35,500 d°-7 4°- 75 , or 200 d+ 10,000 t for cast iron, 
P = 35,500 d°-U°- 6 , or 750 d + 1000 4(75 d + 50) for 
medium steel, 

and for different sizes of drill the following equations: 



Drill. 


3/ 4 


1 


M/2 




5+ 1,100* 
125 + 82,000 * 
7.5+3,350* 
550+ 109,000 * 


10+1,750* 
200 + 89,000* 
17.5 + 4,400* 
750+131,000* 


25+3,700 * 
350+103,000* 




Steel T = 


40 + 9,000 * 


Steel P = 


1,250+162,000* 








Drill. 


2 


21/2 


3 




40+ 580 * 

500+110,000* 

75+12,500* 

1,500+181,250* 


60 + 8,800* 
600+126,000* 
112.5+19,050* 
1,725 + 224,375* 


90+12,900* 


Cast ironP = 


850+140,000* 


Steel T - 


175 + 26,250* 


Steel P = 


2,350+280,000* 







The tests above referred to were made without lubricants. When 
lubricants were used in drilling steel the average torque varied from 
72% with 1/400 in. feed to 92% with 1/35 in. feed of that obtained when 
operating dry. The thrust for soft, medium and hard steel is 26%, 
37% and 12% respectively less than when operating dry, no marked 
difference being found, as in the torque, with different feed. The horse- 
power varies as t ' 7 and as d°- 8 for a given drill and speed. The torque 
and horse-power when drilling medium steel is about 2.1 times that 
required for cast iron with the same drill speed and feed. The horse- 
power per cu. in. of metal removed is inversely proportional to d 0-2 4 ' 3 , 
and is independent of the revolutions. 

While the chisel point of the drill scarcely affects the torque it is account- 
able for about 20% of the thrust. Tests made with a preliminary hole 
drilled before the main drill was used to enlarge the hole showed that the 
work required to drill a hole where only one drill is used is greater than 
that required to drill the hole in two operations, with drills of different 
diameter. 

For economy of power a drill with a larger point angle than_120° is to 
be preferred, but the increased end thrust strains the machine in propor- 
tion, and there is more danger of breaking the drill. 

Taking the average recommended speed of 48 ft. per minute for cast 
iron and 60 ft. for mild steel, and the results obtained in these tests, the 
figures given in the following table are derived. 



1256 



THE MACHINE-SHOP. 



Revolutions per Minute, Feed per Revolution, Cubic Inches Re- 
moved per Minute, and Horse-power when Drilling Soft 
Cast-iron and Medium Hard Steel. 



Soft Cast Iron. 


Medium Hard Steel. 






u '£ 


&.S 


0> 




. 


^ftl 


u 


& a 




fiici 


T3 


goo X 

Cl o>-- 


•S.2 ^ 

.S3 « 


if 5 

.2 > 

■° 2 


o 

o 


il 


-5 


•H.3 ii 


2 a °°- 

.S-d - 

.2 > 

-° 2 


O 
ft 
h 

o 
A 

o 
H 


° ce- o> 
(-,-£ ft 

ftS is 


Vi 


735 


0.0075 


0.27 


0.295 


1.092 


l /4 


920 


0.0063 


0.284 


0.721 


2.54 


3/8 


490 


0.0086 


0.462 


0.4405 


0.954 


2/8 


614 


0.0072 


0.485 


1.078 


2.22 


V2 


368 


0.0094 


0.682 


0.586 


0.862 


1/2 


460 


0.00795 


0.716 


1.426 


1.99 


••5/4 


245 


0.0109 


1.17 


0.8766 


0.748 


3 /4 


306 


0.0091 


1.23 


2.152 


1.75 


1 


184 


0.0119 


1.715 


1.167 


0.681 


1 


230 


0.01 


1.8 


2.863 


1.59 


H/4 


147 


0.0129 


2.32 


1.457 


0.628 


M/ 


184 


0.0108 


2.44 


3.574 


1.47 


n/2 


122 


0.0136 


2.92 


1.748 


0.598 


I 1 / 


153 


0.0114 


3.08 


4.285 


1.39 


1 3/4 


105 


0.0144 


3.63 


2.038 


0.563 


13/ 


131 


0.0121 


3.81 


5.005 


1.31 


2 


92 


0.015 


4.32 


2.328 


0.539 


2 


115 


0.0126 


4.54 


5.715 


1.26 


21/4 


81.7 


0.0156 


5.05 


2.619 


0.519 


21/4 


102 


0.0131 


5.3 


6.436 


1.21 


2i/ 2 


73.5 


0.0162 


5.82 


2.909 


0.500 


21/2 


92 


0.0136 


6.12 


7.136 


1.165 


23/4 


66.75 


0.0167 


6.6 


3.199 


0.486 


23/4 


83.5 


0.014 


6.92 


7.857 


1.135 


3 


61.3 


0.0172 


7.4 


3.489 


0.472 


3 


76.5 


0.0144 


7.76 


8.567 


1.105 


31/4 


56.5 


0.0176 


8.22 


3.78 


0.46 


31/ 4 


70.5 


0.0148 


8.66 


9.267 


1.07 


3l/ 2 


52.5 


0.0181 


9.05 


4.07 


0.45 


31/2 


65.6 


0.0151 


9.5 


9.998 


1.05 


33/4 


49 


0.0185 


10.0 


4.36 


0.436 


33/4 


61.25 


0.0155 


10.48 


10.718 


1.024 


4 


46 


0.019 


10.8 


4.65 


0.431 


4 


57.5 


0.0158 


11.4 


11.42 


1.0 



POWER REQUIRED FOR MACHINE TOOLS. 

Resistance Overcome in Cutting Metal. (Trans. A. S. M. E., 
viii. 308.) — Some experiments made at the works of William Sellers 
& Co. showed that the resistance in cutting steel in a lathe would vary 
from 180,000 to 700,000 pounds per square inch of section removed, 
while for cast iron the resistance is about one third as much. The power 
required to remove a given amount of metal depends on the shape of the 
cut and on the shape and the sharpness of the tool used. If the cut is 
nearly square in section, the power required is a minimum; if wide and 
thin, ia maximum. The dullness of a tool affects but little the power 
required for a heavy cut. 

Heavy Work on a Planer. — Wm. Sellers & Co. write as follows 
to the American Machinist: The 120-inch planer table is geared to run 
18 feet per minute under cut, and 72 feet per minute on the return, 
which is equivalent, without allowance for time lost in reversing, to con- 
tinuous cut of 14.4 feet per minute. Assuming the work to be 28 feet 
long, we may take 14 feet as the continuous cutting speed per minute, 
the 0.8 of a foot being much more than sufficient to cover time loss in 
reversing and feeding. The machine carries four tools. At Vs inch feed 
per tool, the surface planed per hour would be 35 square feet. The sec- 
tion of metal cut at 3/ 4 inch depth would be 0.75 inch X 0.125 inches X 4 = 
0.375 square inch, which would require approximately 30,000 pounds 
pressure to remove it. The weight of metal removed per hour would be 
14X12X0.375X0.26 X 60 = 1082.8 lb. Our earlier form of 36 in. planer 
has removed with one tool on 3/ 4 in. cut on work 200 lb. of metal Der hour, 
and. the 120 in. machine has more than five times its capacity. The total 
pulling power of the planer is 45,000 lb. 

Horse-power Required to Run Eathes. — The power required 
to 4o useful work varies with the depth and breadth of chip, with the 



POWER REQUIRED FOR MACHINE TOOLS. 1257 



shape of tool, and with the nature and density of metal operated upon; 
and the power required to run a machine empty is often a variable 
quantity. For instance, when the machine is new, and the working parts 
have not become worn or fitted to each other as they will be after running 
a few months, the power required will be greater than will be the case after 
the running parts have become better fitted. 

Another cause of variation of the power absorbed is the driving-belt; 
a tight belt will increase the friction. 

A third cause is the variation of journal-friction, due to slacking up or 
tightening the cap-screws, and also the end-thrust bearing screw. 

Hartig's investigations show that it requires less total power to turn 
off a given weight of metal in a given time than it does to plane off the 
same amount; and also that the power is less for large than for small 
diameters. (J. J. Flather, Am. Mach., April 23, 1891.) 

Horse-power Required to Remove Metal in Lathes. 

(Lodge & Shipley Mach. Tool Co., 1906.) 
20-Inch Cone-Head Lathe. 





Cutting 
Speed, 
ft. per 


Cut, In. 


Diam. 


Cu. in. 


Lb. 


H.P. used 
by Lathe. 


Cu.in. 






of 
work, 


remov- 
ed per 


remov- 
ed per 








Cut. 










ed per 




nun. 


Depth. 


Feed. 


in. 


nun. 


hour. 


Idle. 


With 
Cut. 


H.P. 


Crucible 


C 35 


0.109 


1/8 


227/3 2 


5.74 


96 


0.48 


3.90 


1.471 


Steel 


) 65 


0.055 


1/8 


35/ 8 


5.33 


90 


0.74 


4.60 


1.158 


0.60 


) 62.5 


0.109 


Vlfi 


3 5/ie 


5.125 


86 


0.49 


4.65 


1.102 


Carbon 


( 32.5 


0.094 


VlO 


35/ie 


3.656 


62 


0.49 


2.64 


1.384 




( 62.5 


0.273 


Vn 


35/32 


17.09 


266 


0.66 


5.44 


3.141 


Cast 


) 60 


0.430 


Vl9 


221/ 64 


16.27 


253 


0.59 


4.77 


3.410 


Iron 


) 37.5 


0.334 


1/16 


221/32 


10.76 


167 


0.45 


3.91 


2.751 




C 115 


0.086 


1/12 


155/64 


9.88 


153 


0.21 


2.54 


3.889 


Open- 
hearth 
Steel 
0.30 

Carbon 


( 50 


0.109 


1/8 


223/32 


8.2 


138 


0.69 


5.34 


1.535 


) 45 


0.117 


1/8 


21/2 


7.91 


134 


0.53 


5.11 


1.547 


) 45 


0.217 


Vl9 


217/64 


6.439 


109 


0.69 


4.10 


1.570 


t 32.5 


0.109 


1/8 


223/64 


5.33 


90 


0.36 


4.04 


1.319 



Average H.P. running idle 0.53; average H.P. with cut 4.25. 
20-Inch Geared-Head Lathe, 















H.P. used 






Cutting 


Cut, in. 


Diam. 


Cu. in. 


Lb. 


by Lathe. 


Cu. in. 




Speed, 
ft. per 




of 
work 


remov- 
ed per 


remov- 
ed per 






Cut. 










ed per 
H.P. 




min. 


Depth. 


Reed. 


in. 


mm. 


hour. 


Idle. 


With 
Cut. 


0.50 


( 40 


0.266 


VlO 


227/32 


12.75 


215 


2.11 


11.1 


1.142 


Carbon 


\ 50 


0.281 


1/15 


227/32 


11.25 


190 


1.58 


8.35 


1.347 


Crucible 


) 75 


0.281 


1/15 


227/32 


16.87 


285 


1.58 


12.69 


1.329 


Steel. 


( 85 


0.109 


Vl5 


2 1/4 


7.43 


126 


1.28 


8.98 


0.827 




( 45 


0.609 


Vl6 


721/32 


20 57 


320 


1.34 


694 


2.963 


Cast 


) 62.5 


0.609 


Vl6 


721/32 


28.56 


445 


1.35 


9.50 


3.006 


Iron 


) 85 


0.641 


1/16 


721/32 


40.82 


636 


1.64 


12.69 


3.216 




( 80 


0.281 


1/8 


3 3/ 3 2 


33.75 


526 


1.18 


10.49 


3.217 


Open- 
hearth 
Steel 
0.15 

Carbon 


( 125 


0.250 


V->8 


421/32 


13.4 


226 


1.62 


10.60 


1.265 


) 105 


0.188 


Vl2 


4 5/32 


19.68 


33? 


0.94 


11.56 


1.702 


) 40 


0.172 


1/6 


327/32 


13.75 


232 


1.75 


12.49 


1.100 


( 180 


0.094 


1/16 


3 Vie 


12.65 


213 


2.15 


11.20 


1.129 



Average H.P. running idle 1.543; average H.P. with cut 10.55. 



1258 



THE MACHINE-SHOP. 



Owing to the demand imposed by high speed tool steels stouter machines 
are more necessary than formerly; these possess more rigid frames and 
powerful driving gears. The most modern (1907) forms of lathes obtain 
all speed changes by means of geared head-stocks, power being delivered 
at a single speed by a belt, or by a motor. If a motor drive is used, a 
speed variation may be obtained in addition to those available in the 
head, by using a variable speed motor, whose range usually is about 
3:1. The Lodge & Shipley Co. (1906) made an exhaustive series of 
tests to determine the power required to remove metal, using both the 
cone-head lathe and the more modern geared-head lathe. The table on 
page 1257 shows the results obtained with 20-in. lathes of each type. 

Power Required to Drive Machine Tools. — The power required 
to drive a machine tool varies with the material to be cut. There 
is considerable lack of agreement among authorities on the power required. 
Prof. C. H. Benjamin (Mach'y, Sept., 1902) gives a formula H.P. = cW, 
c being a constant and W the pounds of metal removed per hour, c varies 
both with the quality of metal and the type of machine. 





Values of c. 










Lathe. 


Planer. 


Shaper. 


Milling 
Machine. 




0.035 
0.067 


0.032 


0.030 


0.14 








0.30 


Bronze 


0.10 



In each case the power to drive the machine without load should be 
added. G. M. Campbell (Proc. Engr. Soc. W., Pa., 1906) gives, exclu- 
sive of friction losses, H.F. = Kw, K being a constant and w the pounds 
of metal removed per minute. For hard steel K = 2.5; for soft steel 
K = 1.8; for wrought iron, K = 2.0; for cast iron, if = 1.4. This formula 
gives results about 50 % lower than Prof. Benjamin's. 

The Westinghouse Elec. and Mfg. Co. (1906) gives a set of formulae 
based on the dimensions of the machine. 

For Engine Lathes using one cutting tool of water-hardened steel, cutting 
20 ft. per minute, H.P. = 0.15 S — l?for heavy engine lathes, as forge 
lathes, H.P. = 0.234 S - 2, S being the swing of the lathe, inches. 

For Boring Mills using one cutting tool of water-hardened steel, cutting 
20 ft. per min., H.P. = 0.25 S — 4. S = swing of mill, inches. 

For Milling Machines using water-hardened steel cutters at 20 ft. per 
minute, H.P. =0.3 W. W= distance between housings, inches. 

For Drill Presses using water-hardened steel drills, running at a periph- 
eral cutting speed of 20 feet per minute, H.P. = 0.06 8. 

For Heavy Radial Drill Presses, H.P. = 0.1 S. 

S = swing of drill, inches, in both cases. 

In general, in all the above Westinghouse formulae, if high-speed steel 
tools are used, running at higher cutting speeds than above, the increase 
in horse-power is proportional to the increase in speed. 

Planers. For planers, in which the length of bed in feet is approximately 
two-tenths of the width between housings in inches, using- water-hardened 
steel tools, cutting at 15 to 20 ft. per minute, H.P. = 3 W. 

For Heavy Forge Planers, H.P. = 4.92 W. 
W = width between housings, feet. 

These formulae are for planers having a ratio of return to cutting speeds 
of about 3:1, and are for planers with two tools in operation. If more 
than two tools are operated, or if the ratio of cutting and return speeds 
is increased, or if the length of bed is greater than given above, the horse- 
power given by the above formulae should be increased. The horse- 
power required by motor-driven planers is principally determined by the 
current inrush at the instant of quick reverse, rather than by that actually 
required to cut the metal. Motors for operating planers should have 
greater overload capacity than for any other tool. 



POWER REQUIRED FOR MACHINE TOOLS. 1259 





Horse 


-power 


to Drive Machine Tools. 








Cut, 


Inches. 


C 




H.P.Re 
quired. 












fg 










Is 








1* 




J 


£ 




■j 


-6 


ji 


ts& 


£ a 


] 


- 





1 










-J^ 








o 
H 


eS 
8 


4) 

fa 


Q 


Qfa 
CQ 


£" 


< 




fa 


1 


72-in. wheel 


Hard steel 


Vl2 


3/16 & 1/4 


13.7 


1.69 


4.5 


4.2 


25 H.P. shunt 


lathe 




1/8 


3/16&V4 


11.6 


2.15 


6.4 


5.4 


wound vari- 






3/16 


/l6& 3 /8 


13.2 


5.55 


8.4 


13.9 


able speed. 






3/16 


3/8 &3/ 8 


13.2 


6.3 


12.0 


15.7 




90-in. whee] 


Hard steel 


3/16 


3/l6& 3 /l6 


13.0 


3.1 


12.0 


7.7 


25 H.P. shunt 


lathe 




3/16 


5 /l6& 5 /l6 


8.8 


3.5 


8.1 


8.7 


wound vari- 






1/5 


1/4 &V4 


15.5 


5.3 
2.33 


9.0 


13.2 


able speed. 


42-in. lathe 


Soft steel 


Vl6 


1/4 


44 


3.8 


4.2 


15 H.P. shunt 






Vl6 


1/8 


44 


1.17 


1.7 


1.9 


wound vari- 




" " 


Vl6 


1/8 


44 


1.17 


2.6 


1.9 


able speed. 




Cast iron 


1/16 


1/8 


108 


2.63 


5.8 


3.7 






" " 


Vl6 


3/16 


46 


1.74 


2.9 


2.5 








1/16 


3/16 


58 


2.12 


2.2 


3.0 




30-in. lathe 


Wro't iron 


1/8 


3/16 


54. 


4.2 


6.6 


8.4 


10 H.P. shunt 






1/8 


3/16 


42 


3.2 


4.0 


6.4 


wound vari- 




Cast iron 


3/32 


5 /32 


42 


1.92 


3.0 


2.7 


able speed. 






3/32 


Vl6 


61 


1.12 


1.5 


1.6 








1/64 


1/4 


47 


2.30 


2.0 


3.2 




Axle lathe 


Soft steel 


3 /l6 


1/4 


27 


4.3 


5.9 


7.7 


35 H.P. sh. w'd 






1/16 


1/4 


51 


2.7 


5.0 


4.9 


var. speed. 


72-in. boring 


Soft steel 


1/8 


1/16&V32 


44 


1.76 


2.9 


3.2 


25 H.P. shunt 


mill . . 




3/16 


I/32&V16 


40 


2.38 


2.6 


4.3 


wound vari- 




" " 


1/8 


1/8 &V8 


51 


5.41 


9.6 


9.7 


able speed. 




" " 


1/8 


3/16 


47 


3.75 


7.2 


6.8 






Cast iron 


Vl6 


3/8 


28 


2.05 


2.6 


2.9 








1/16 


1/4 


39 


1.90 


2.7 


2.7 




24-in. drill 


Wro't iron 


1/64 


1 l/ 4 to3* 


25.1 


0.81 


2.3 


1.6 




press 


" " 


1/64 


1 l/ 4 to 3* 


29.7 


0.96 


2.7 


1.9 






" " 


1/64 


U/4to3* 


25.9 


0.83 


1.3 


1.7 






•+ << 


1/64 


11/ 4 drill 


74.5 


0.52 


3.5 


1.0 






" " 


1/64 


11/4 drill 


20.9 


0.54 


1.2 


1.1 




60-in. planer 


Soft steel 


1/6 


1/4 


25.5 


3.62 


5.9 


6.5 


20 H.P. com- 




" " 


1/6 


1/4 


25.7 


3.65 


6.5 


6.6 


pound 




Wro't iron 


3 /l6 


5/l6& 5 /l6 


23 


8.95 


21.0 


17.9 


wound vari- 






1/2 


1/32 & 1/32 


17.5 


1.82 


2.7 


3.6 


able speed. 




Cast iron 


1/8 


1/8 &Vl6 


22.2 


1.72 


6.5 


3.4 








i/s & Vie 


1/4 &5/16 


30 


4.74 


9.3 


6.6 








1/7 


1/4 &V4 


22.6 


5.03 


7.6 


7.1 








1/4 


7/l6&3/ 8 


28.9 


18.3 


23.2 


25.6 




42-in. planer 


Soft steel 


5 /32 


Vs 


24.3 


4.73 


12.1 


9.5 


15 H.P. com- 






1/8 


Vs 


36 


3.7 


7.8 


11.4 


pound 




Cast iron 


3/l6 


3/16 


37 


4.06 


4.7 


5.7 


wound vari- 






3/16 


L /8 


37 


2.71 


4.1 


3.8 


able speed. 


19-in. slotter 


Hard steel 


V32 


L/4 


30.0 


0.8 


2.0 


2.0 


13 H.P. comp. 




Soft steel 


1/32 


V8 


23.3 


0.93 


1.3 1.7 


w'd var. speed. 



* Enlarging hole from smaller dimensions to larger. 



1260 



THE MACHINE-SHOP. 



Actual tests (1906) of a number of machine tools in the shops of the 
Pittsburg and Lake Erie R. R. showed the horse-power absorbed in driv- 
ing under the conditions given in the table on page 1259. The results 
obtained are compared with those computed by Campbell's formula 
above. 

L. L. Pomeroy {Gen. Elec. Rev., 1908) gives: H.P. required to drive = 
12 FDSNC, in which F = feed and D = depth of cut, in inches, S = 
speed in ft. per min., N = number of tools cutting, C = a constant, 
whose values with ordinary carbon steel tools are: for cast iron, 0.35 to 
0.5; soft steel or wrought iron, 0.45 to 0.7; locomotive driving-wheel 
tires, 0.7 to 1.0; very hard steel, 1.0 to 1.1. This formula is based on 
Prof. Flather's dynamometer tests. An analysis of experiments by Dr. 
Nicholson of Manchester, which confirm the formula, showed the average 
H.P. required at the motor per pound of metal removed per minute to 
be as follows: Medium or soft steel, or wrought iron, 2.4 H.P.; hard steel, 
2.65 H.P.; cast-iron, soft or medium, 1.00 H.P.; cast iron, hard, 1.36 H.P. 

Size of Motors for Machine Tools. (Elec. World, May 27, 1905.) — 
The average size of motor usually fitted to machine tools is shown by the 
table below, being compiled by the Electro- Dynamic Co. from published 
data. In special cases the power required may be several times the 
value here given. v 

Boring Mills. 



34 and 36 in. . . 
42, 48 and 50 in. 


H.P. 
. 5 

. 71/2 


H.P. 
60 in.. ..... 10 

6 ft. and 7 ft. . . 15 


8 ft 

10 ft 


H.P. 
. . 20 
. . 25 


Engine Lathes. 


12 and 14 in. . . 

16 in 

20 to 25 in. . . . 


H.P. 
. 1 

. H/2 
. 2 


H.P. 
20 and 30 in. ... 3 
36 in 4 

42 and 48 in. ... 5 


54 in 

60 in 

72 in 


H.P. 
. . 6 

• • 71/2 
. . 10 


Drill Presses. 


21 to 32 in. . . 


H.P 
. 2 


1 H.P. 
1 36 to 48 in. . . . 3 


50 to 60 in. . 


H.P. 
. . 5 


Planers. 







H.P. 






H.P. 


17 X 17in. 


X 3 to 6 ft. . 


. 4 


42 X 42 in. 


X 10 to 12 ft. . 


10 


22 X 24 in. 


X 4 to 10 ft. . 


. 5 


48 X 48 in 


X 12 to 14ft. . 


15 


26 X 26 in 


X 6 to 12 ft. . 


6 


50 X 60 in. 


X 14 to 18 ft. . 


20 


30 X 30 in. 


X 6 to 1 4 ft. . 


. 7i/ 3 


60 X 60 in. 


X 20 to 22 ft. . 


25 


36 X 36 in. 


X 8 to 16 ft. . 


. 71/2 


72 X 72 in. 


X 20 to 24 ft. . 


30 



H.P. I 
. 5 I 16 and 18 in. 



H.P. I 
71/21 26 to 36 in. 



H.P. 
10 







Shapers. 








12 to 16 in. . 
18 to 20 in. . 


H.P. 
. . 2 
. . 3 


24 to 26 in. . . 
28 to 30 in. . . 


H.P. 
. 5 
. 6 


36 in. . . . 


H.P 
... 8 



The values given above for engine lathes are less than those used by 
the R. K. LeBlond Mach. Tool Co., which recommends (1907) the fol- 
lowing size motors for use with its lathes. 



Swing of lathe. 


Horse-power of Motor. 


Speed 
ratio. 


Maximum speed 


in. 


Medium duty. 


Heavy duty. 


range R.P.M. 


12 and 14 

16 

18, 20, 22 

24, 27, 30 

32, 36 

24* 


"l 

3 

5 

71/2 
15 


2 
3 

5 

71/2 
10 
25 


3 to 1 
3 to 1 
3 to 1 
3 to 1 
3 to 1 
2 to 1 


1500 
1500 
1500 
1500 
1500 
750-1500 



High Speed Roughing Lathe. 



POWER REQUIRED FOR MACHINE TOOLS. 1261 



Horse-power Required to Drive Shafting. — Samuel Webber in 
his "Manual of Power" gives, among numerous tables of power required 
to drive textile machinery, a table of results of tests of shafting. A line 
of 2 i/8-in. shafting, 342 ft. long, weighing 4098 lb., with pulleys weigh- 
ing 5331 lb., or a total of 9429 lb., supported on 47 bearings, 216 rev- 
olutions per minute, required 1.858 H.P. to drive it. This gives a 
coefficient of friction of 5.52%. In seventeen tests the coefficient ranged 
from 3.34% to 11.4%, averaging 5.73%. 

Horse-power consumed in Machine-shops. — How much power 
is required to drive ordinary machine tools? and how many men 
can be employed per horse-power? are questions which it is impos- 
sible to answer by any fixed rule. The power varies greatly according 
to the conditions in each shop. The following table given by J. J. Flather 
in his work on Dynamometers gives an idea of the variation in several 
large works. The percentage of the total power required to drive the 
shafting varies from 15 to 80, and the number of men employed per total 
H.P. varies from 0.62 to 6.04. 



Horse- 


power; Friction 


; Men Employed. 










Horse-power. 




"3 
o 










CD 
> 


> 


> 






Name of Firm. 


Kind 

of 
Work. 




■a 
Q 

2bi 


•a 

§6 


■a 

Q 


3 


a 



4> 

a 






1 

o 




'3 § 


a 

<hcX! 


a 

3 




0+ 3 






H 


ti 


« 


PM 


fc 


& 


fc 


Lane & Bodley . . 


E. & W. W. 


58 








132 


2.27 




J. A. Fay & Co. . . 


W. W. 


100 


15 


85 


15 


300 


3.00 


3.53 


Union Iron Works . 


E..M.M. 


400 


95 


305 


23 


1600 


4.00 


5.24 


Frontier Iron & Brass 


















Works 


M. E., etc. 


25 


8 


17 


32 


150 


6.00 


8.82 


Taylor Mfg. Co. . . 
Baldwin Loco. Works 


E. 


95 








230 


2.42 




L. 


2500 


2000 


500 


80 


4100 


1.64 


8.20 


W. Sellers & Co. (one 


















department) . . . 
Pond Mach. Tool Co. 


H.M. 


102 


41 


61 


40 


300 


2.93 


4.87 


M.T. 


180 


75 


105 


41 


432 


2.40 


4.11 


Pratt & Whitney Co. 




120 








725 


6.04 




Brown & Sharpe Co. 




230 








900 


3.91 




Yale & Towne Co. . 


C. &L. 


135 


67 


68 


49 


700 


5.11 


10.25 


Ferracute Mach. Co. 


P. &D. 


35 


11 


24 


31 


90 


2.57 


3.75 


T. B. Wood's Sons . 


P. &S. 


12 








30 


2.50 




Bridgeport Forge Co. 


H. F. 


150 


75 


75 


50 


130 


0.86 


1.73 


Singer Mfg. Co. . . 


S.M. 


1300 








3500 


2.69 




Howe Mfg. Co. . . . 




350 








1500 


4.28 




Worcester Machine 


















Screw Co 


M.S. 


40 








80 


2.00 




Hartford Mach. Screw 


















Company .... 


M.S. 


400 


100 


300 


25 


250 


0.62 


0.83 


Nicholson File Co. . 


F. 


350 








400 


1.14 




Averages . . . 


346.4 






38.6 


818.3 


2.96 


5.13 









Abbreviations: E., engine; W. W., wood-working machinery; M. M., 
mining machinery; M. E., marine engines: L., locomotives; H. M., heavy 
machinery; M. T., machine tools; C. & L., cranes and locks; P. & D., 
presses and dies; P. & S., pulleys and shafting; H. F., heavy forgings; 
S. M., sewing-machines; M. S., machine-screws: F., files. 

J. T. Henthorn states (Trans. A. S. M. E., vi. 462) that in print-mills 
which he examined the friction of the shafting and engine was in 7 cases 



1262 THE MACHINE-SHOP. 



below 20% and in 35 cases between 20% and 30%, in 11 cases from 30% 
to 35% and in 2 cases above 35%, the average being 25.9%. Mr. 
Barrus in eight cotton-mills found the range to be between 18% and 
25.7%, the average being 22%. Mr. Flather believes that for shops 
using heavy machinery the percentage of power required to drive the 
shafting will average from 40% to 50% of the total power expended. 
This presupposes that under the head of shafting are included elevators, 
fans and blowers. 

Power Required to Drive Machines in Groups. — L. P. Alford 
(Am. Mach., Oct. 31, 1907) gives the results of an investigation to 
determine the power required to drive machinery in groups. The method 
employed comprised disconnecting parts of the shafting in a belt-driven 
plant, and driving the disconnected portion with its machines by an 
electric motor, readings of the power required being taken every 5 min- 
utes. The average power required for the entire factory was consider- 
ably less than the sum of the power required for the individual machines, 
due to tools being stopped at some portion of the day for adjustment, 
replacement of work, etc. The conditions of group driving are such that 
fixed rules cannot be laid down, but a study must be made of each individ- 
ual case. 

ABRASIVE PROCESSES. 

Abrasive cutting is performed by means of stones, sand, emery, glass, 
corundum, carborundum, crocus, rouge, chilled globules of iron, and in 
some cases by soft, friable iron alone. (See paper by John Richards, 
read before the Technical Society of the Pacific Coast, Am. Mach., Aug. 
20, 1891, and Eng. & M. Jour., July 25 and Aug. 15, 1891.) 

The " Cold Saw." — For sawing any section of iron while cold 
the cold saw is sometimes used. This consists simply of a plain soft 
steel or iron disk without teeth, about 42 inches diameter and 3/ 16 inch 
thick. The velocity of the circumference is about 15,000 feet per minute. 
One of these saws will saw through an ordinary steel rail cold in about 
one minute. In this saw the steel or iron is ground off by the friction 
of the disk, and is not cut as with the teeth of an ordinary saw. It has 
generally been found more profitable, however, to saw iron with disks or 
band-saws fitted with cutting-teeth, which run at moderate speeds and 
cut the metal as do the teeth of a milling-cutter. 

Rfese's Fusing-disk. — Reese's fusing-disk is an application of the 
cold saw to cutting iron or steel in the form of bars, tubes, cylinders, 
etc., in which the piece to be cut is made to revolve at a slower rate of 
speed than the saw. By this means only a small surface of the bar to 
be cut is presented at a time to the circumference of the saw. The 
saw is about the same size as the cold saw above described, and is rotated 
at a velocity of about 25,000 feet per minute. The heat generated by 
the friction of this saw against the small surface of the bar rotated against 
it is so great that the particles of iron or steel in the bar are actually fused, 
and the "sawdust" welds as it falls into a solid mass. This aisk will cut 
either cast iron, wrought iron, or steel. It will cut a bar of steel 13/s 
inch diameter in one minute, including the time of setting it in the machine, 
the bar being rotated about 200 turns per minute. 

Cutting Stone with Wire. — A plan of cutting stone by means 
of a wire cord has been tried in Europe. While retaining sand as the 
cutting agent, M. Paulin Gay, of Marseilles, has succeeded in applying 
it by mechanical means, and as continuously as formerly the sand-blast 
and band-saw, with both of which appliances his system — that of the 
"helicoidal wire cord" — has considerable analogy. An engine puts in 
motion a continuous wire cord (varying from five to seven thirty-seconds 
of an inch in diameter, according to the work), composed of three mild- 
steel wires twisted at a certain pitch, that is found to give the best results 
in practice, at a speed of from 15 to 17 feet per second. 

The Sand-blast. — In the sand-blast, invented by B. F. Tilghman, 
of Philadelphia, and first exhibited at the American Institute Fair, 
New York, in 1871, common sand, powdered quartz, emery, or any sharp 
cutting material is blown by a jet of air or steam on glass, metal, or other 
comparatively brittle substance, by which means the iatter is cut, drilled, 
or engraved. To protect those portions of the surface which it is desired 
shall not be abraded it is only necessary to cover them with a soft or 
tough material, such as lead, rubber, leather, paper, wax, or rubber- 



EMERY WHEELS AND GRINDSTONES 1263 

paint, (See description in App. Cyc. Mech.; also U. S. report of Vienna 
Exhibition, 1873, vol. iii. 316.) 

A "jet of sand" impelled by steam of moderate pressure, or even by 
the blast of an ordinary fan, depolishes glass in a few seconds; wood is 
cut quite rapidly; and metals are given the so-called "frosted" surface 
with great rapidity. With a jet issuing from under 300 pounds pressure, 
a hole was cut through a piece of corundum 1 1/2 inches thick in 25 minutes. 

The sand-blast has been applied to the cleaning of metal castings and 
sheet metal, the graining of zinc plates for lithographic purposes, the 
frosting of silverware, the cutting of figures on stone and glass, and the 
cutting of devices on monuments or tombstones, the recutting of files, 
etc. The time required to sharpen a worn-out 14-inch bastard file is 
about four minutes. About one pint of sand, passed through a No. 
120 sieve, and 4 H.P. of 60-lb. steam are required for the operation. 
For cleaning castings, compressed air at from 8 to 10 pounds pressure 
per square inch is employed. Chilled-iron globules instead of quartz 
or flint-sand are used with good results, both as to speed of working and 
cost of material, when the operation can be carried on under proper 
conditions. With the expenditure of 2 H.P. in compressing air, 2 square 
feet of ordinary scale on the surface of steel and iron plates can be 
removed per minute. The surface thus prepared is ready for tinning, 
galvanizing, plating, bronzing, painting, etc. By continuing the opera- 
tion the hard skin on the surface of castings, which is so destructive to 
the cutting edges of milling and other tools, can be removed. Small 
castings are placed in a sort of slowly rotating barrel, open at one or 
both ends, through which the blast is directed downward against them 
as they tumble over and over. No portion of the surface escapes the 
action of the sand. Plain cored work, such as valve-bodies, can be 
cleaned perfectly both inside and out. One hundred lbs. of castings 
can be cleaned in from 10 to 15 minutes with a blast created by 2 H.P. 
The same weight of small forgings can be scaled in from 20 to 30 minutes. 
— Iron Age, March 8, 1894. 

EMERY WHEELS AND GRINDSTONES. 

References: " Precision Grinding," by Darbyshire; " Emery Wheels, 
their Selection and Use," published by Brown & Sharpe Mfg. Co.; " Points 
on Grinding," C. H. Norton; " Versuche ueber die Leistung von Schmirgel 
und Karborundum Scheiben bei Wasserzufuehrung," G. Schlesinger; 
" Die Festigkeit der kuenstlichen Schmirgel und Karborundum Scheiben, 
ihre Arbeitsleistung und ihre Wirthshaftlichkeit im Werkstattbetriebe," 
G. Schlesinger. 

Selection of Grinding Wheels. (Contributed by Norton Co., 1908.) — 
The essential features of a modern grinding wheel which should be thor- 
oughly understood by the user are: the definition of grain and grade, and 
the particular conditions of grinding which cause them to vary. 

Grain. — Abrasive grains are numbered according to the meshes per 
lineal inch of the screen through which they have been graded. The 
numbers used in wheels are 8, 10, 12, 14, 16, 20, 24, 30, 36, 46, 54, 60, 70, 
80, 90, 120, 150, 180, and 200; when finer than 200, the grits are termed 
flours, being designated as F, FF, FFF and SF; F being the coarsest and 
SF the finest. Grits from 12 to 30 are generally used on all heavy work, 
such as snagging; 36 to 80 cover nearly all tool-grinding, saw-gumming, 
and nearly all operations where precision in measurement is sought; 90 
and finer are used for special work, such as grinding steel balls and fine 
edge work; over 200 is used mostly for oil and hand rubbing stones. 

Grade. — When the retentive properties of the bond are great, the 
wheel is called hard; when the grains are easily broken out, it is called 
soft. A wheel is of the proper grade when its cutting grains are auto- 
matically replaced when dulled. Wheels that are too hard glaze. Dress- 
ing re-sharpens them, the points of the dresser breaking out and breaking 
off the cutting grains by percussion. 

Soft wheels are used on hard materials, like hardened steel. Here the 
cutting particles are quickly dulled and must be renewed. On softer 
materials, like mild steel and wrought iron, harder grades can be used, 
the grains not dulling so quickly. 

The area of surface to be ground in contact with the wheel is of the 
utmost importance in determining the grade. If it is a point contact 
like grinding a ball or if an extremely narrow fin is to be removed, we 



1264 THE MACHINE-SHOP. 

must use a very strongly bonded wheel, on account of the leverage exerted 
on its grain, which tends to tear out the cutting particles before they have 
done their work. If the contact is a broad one, as in like grinding a hole, 
or where the work brings a large part of the surface of the wheel into 
operation, softer grades must be used, because the depth of cut is so 
infinitely small that the cutting points in work become dulled quickly and 
must be renewed, or the wheel glazes and loses its efficiency. 

Vibrations in grinding machines cause percussion on the cutting grains, 
necessitating harder wheels. Wheels mounted on rigid machines can be 
softer in grade and are much more efficient. 

Speeds of Grinding Wheels. — The factor of safety in vitrified wheels 
is proportional to the grade of hardness. Bursting limits are from 12,000 
to 25,000 feet per minute, surface speed. Wheels are tested by standard 
makers at 10,000 feet , corresponding to a stress of 250 lbs. per square inch. 
Running speeds in practice are from 4000 to 6000 feet, depending on 
work, condition of machine, and mounting. 

Generally speaking, grinding of tools, reamers, cutters, and surface 
grinding is done at about 4000 feet, snagging and rough forms of hand 
grinding at 5000 to 5500 feet, cylindrical grinding, or where the work is 
rigidly held and where the wheel feed is under control, from 5500 to 6500 
feet, and in some instances as high as 7500 feet. 

These speeds are all for vitrified wheels. The same speeds will apply 
to wheels made by the elastic and silicate processes. 

Grades of Emery. — The numbers representing the grades of emery 
run from 8 to 120, and the degree of smoothness of surface they leave may 
be compared to that left by files as follows: 

8 and 10 represent the cut of a wood rasp. 

" a coarse-rough file. 
" " an ordinary rough file. 
" " a bastard file. 
" " a second-cut file. 
" " a smooth 
" " a superfine " 
" " a dead-smooth file. 

Speed of Polishing-wheels. 

Wood covered with leather, about 7000 ft. per minute. 

Wood covered with a hair brush, about 2500 revs, for largest. 

Wood covered IV2" to 8" diam., hair 1" to 11/4" long, 

ab 4500 revs, for smallest. 

Walrus-hide wheels, about 8000 ft. per minute. 

Rag-wheels, 4 to 8 in. diameter about , .7000 ft. per minute. 

Safe Speeds for Grindstones and Emery-wheels. — G. D. Hiscox 
(Iron Age, April 7, 1892), by an application of the formula for centrifugal 
force in fly-wheels (see Fly-wheels), obtains the figures for strains in 
grindstones and emery-wheels which are given in the tables below. His 
formulas are: 

Stress per sq. in. of section of a grindstone = (0.7071D X A) 2 X 0.0000795 
Stress per sq. in. of section of an emery-wheel= (0.7071D X A) 2 X 0.00010226 

D = diameter in feet, A = revolutions per minute. 

He takes the weight of sandstone at 0.078 lb. per cubic inch, and that 
of an emery-wheel at 0.1 lb. per cubic inch; Ohio stone weighs about 0.081 
lb. and Huron stone about 0.089 lb. per cubic inch. The Ohio stone will 
bear a speed at the periphery of 2500 to 3000 ft. per min., which latter 
should never be exceeded. The Huron stone can be trusted up to 4000 
ft., when properly clamped between flanges and not excessively wedged 
in setting. Apart from the speed of grindstones as a cause of bursting, 
probably the majority of accidents have really been caused by wedging 
them on the shaft and over-wedging to true them. The holes being 
square, the excessive driving of wedges to true the stones starts cracks in 
the corners that eventually run out until the centrifugal strain becomes 
greater than the tenacity of the remaining solid stone. Hence the 
necessity of great caution in the use of wedges, as well as the holding of 
large quick-running stones between large flanges and leather washers. 

The Iron Age says the strength of grindstones when wet is reduced 40 
to 50%. A section of a stone soaked all night in water broke at a stress 



16 


20 


24 


30 


36 


40 


46 


60 


70 


80 


90 


" 100 


L20 


F and FF 



EMERY WHEELS AND GRINDSTONES. 



12G5 



Revolutions per 31inute Required for Specified Rates of 

Periphery Speed. Also Stress per Square Inch on 

Norton Wheels at the Specified Rates. 











Surface Speeds 


, Feet per Minute. 






a 


1000 


1 2000 


3000 


1 4000 1 5000 1 6000 1 7000 1 8000 


9000 


10000 


1 


Stress per Square Inch, Pounds. 


3 


12 1 27 


48 | 75 1 108 1 147 1 192 


243 


300 


5 


Revolutions per Minute. 


1 


3820 


7639 


11459 


15279 


19099 


22918 


26738 


30558 


34377 


38197 


7 


1910 


3820 


5730 


7639 


9549 


11459 


13369 


15279 


17189 


19098 


3 


1273 


2546 


3820 


5093 


6366 


7639 


8913 


10186 


11459 


12732 


4 


955 


1910 


2865 


3820 


4775 


5729 


6684 


7639 


8594 


9549 


5 


764 


1528 


2292 


3056 


3820 


4584 


5347 


6111 


6875 


7639 


6 


637 


1273 


1910 


2546 


3183 


3820 


4456 


5093 


5729 


6366 


7 


546 


1091 


1637 


2183 


2728 


3274 


3820 


4365 


4911 


5457 


8 


477 


955 


1432 


1910 


2387 


2865 


3342 


3820 


4297 


4775 


10 


382 


764 


1146 


1528 


1910 


2292 


2674 


3056 


3438 


3820 


12 


318 


637 


955 


1273 


1591 


1910 


2228 


2546 


2865 


3183 


14 


273 


546 


818 


1091 


1364 


1637 


1910 


2183 


2455 


2728 


16 


239 


477 


716 


955 


1194 


1432 


1671 


1910 


2148 


2387 


18 


212 


424 


637 


849 


1061 


1273 


1485 


1698 


1910 


2122 


20 


191 


382 


573 


764 


955 


1146 


1337 


1528 


1719 


1910 


?.?. 


174 


347 


521 


694 


868 


1042 


1215 


1389 


1563 


1736 


24 


159 


318 


477 


637 


796 


955 


1114 


1273 


1432 


1591 


30 


127 


255 


382 


509 


637 


764 


891 


1018 


1146 


1273 


36 


106 


212 


318 


424 


530 


637 


743 


849 


955 


1061 









Table to Figure Surface Speeds of Wb 


eels. 










(Circumferences in Feet, Diameters in Inches.) 






^ 




_^ 




+3 




^ 




^ 








fa 




fa 




fa 




fa 




fa ■ 




fa 


a 




fl 




a 




a 




a 




a 




M 


«H 




•H 


1-1 


y 


1-1 


1 


M 


•a 


M 


1 

3 


1 


1 


i 


| 




i 


I 


1 


1 


1 


fa 


o 


3 

13 


o 


25 


o 


(A 
37 


O 


fa 
49 


o 


fa 


Q 


1 


.262 


3.403 


6.546 


9.687 


12.828 


61 


15.970 


2 


.524 


14 


3.665 


26 


6.807 


38 


9.948 


50 


13.090 


62 


16.232 


3 


.785 


15 


3.927 


27 


7.069 


39 


10.210 


51 


13.352 


63 


16.493 


4 


1.047 


16 


4.189 


28 


7.330 


40 


10.472 


52 


13.613 


64 


16.755 


5 


1.309 


17 


4.451 


29 


7.592 


41 


10.734 


53 


13.875 


65 


17.017 


6 


1.571 


18 


4.712 


30 


7.854 


42 


10.996 


54 


14.137 


66 


17.279 


7 


1.833 


19 


4.974 


31 


8.116 


43 


11.257 


55 


14.499 


67 


17.541 


8 


2.094 


20 


5.236 


32 


8.377 


44 


11.519 


56 


14.661 


68 


17.802 


9 


2.356 


21 


5.498 


33 


8.639 


45 


11.781 


57 


14.923 


69 


18.064 


10 


2.618 


72 


5.760 


34 


8.901 


46 


12.043 


58 


15.184 


70 


18.326 


11 


2.880 


7.3 


6.021 


35 


9.163 


47 


12.305 


59 


15.446 


71 


18.588 


12 


3.142 


24 


6.283 


36 


9.425 


48 


12.566 


60 


15.708 


72 


18.850 



To find surface speed, in feet, per minute, of a wheel. 

Rule. — Multiply the circumference (see above table) by its revolu- 
tions per minute. 

Surface speed and diam. of wheel being given, to find number of revo- 
lutions of wheel spindle. 

Rule. — Multiply surface speed, in feet, per min., by 12 and divide the 
product by 3.14 times the diam. of the wheel in inches. 



1266 



THE MACHINE-SHOP. 



of 80 lb. per sq. in. A section of the same stone dry, broke at 146 lb. per 
sq. in. A better quality stone broke at stresses of 186 and 116 lb. per sq. 
in. when dry and wet respectively. 

Selection of Emery Wheels. — The Norton Co. (1907) publishes the 
following table showing the proper grain and grade of wheel for different 
services. The column headed grain indicates the coarseness of the 
material composing the wheel, being designated by the number of meshes 
per inch of a sieve through which the grains pass. A No. 20 grain will 
pass through a 20-mesh sieve, but not through a 30-mesh, etc. 

Table for Selection of Grades. 



Class of Work. 



Large cast iron and steel castings . 

Small cast iron and steel castings . 

Large malleable iron castings . . . 

Small malleable iron castings . . . 

Chilled iron castings 

Wrought iron 

Brass castings 

Bronze castings 

Rough work in general 

General machine-shop use .... 

Lathe and planer tools 

Small tools 

Wood-working tools 

Twist drills (hand grinding) . . . 

Twist drills (special machines) . . 

Reamers, taps, milling cutters, etc 
(hand grinding) 

Reamers, taps, milling cutters, etc 
(special machines) 

Edging and joining agricultural im- 
plements . . 

Grinding plow points 

Surfacing plow bodies 

Stove mounting 

Finishing edges of stoves 

Drop forgings 

Gumming and sharpening saws . . 

Planing-mill and paper-cutting knives 

Car- wheel grinding 



No. of 
Grain or 
Degree of 
Coarse- 
ness usu- 
ally Fur- 
nished. 



12 to 20 
20 " 30 
20 

30 
20 
30 
30 
30 
30 



46 
100 
60 
60 
60 

100 

60 



Grade 
Letters 
or De- 
grees of 
Hardness 
usually 

Fur- 
nished. 



Q to R 
P " Q 
Q " R 
P " Q 
Q " R 
' Q 
P 

P 

O 
P 

1 N 
N 
M 



Grade Letters or 
Degrees of Hard- 
ness. Furnished 
in Exceptional 



Some- 


Some- 


times 


times 


Soft as 


Hard as 


P 


U 





R 


P 


W 





U 


p 


u 





R 


N 


Q 




R 





R 


M 


P 


L 




H 


O 




* w 




u 


M 


Q 


L 


o 


I 


M 


N 


R 



EXPLANATION OF GRADE LETTERS. 



Extremely 


Soft. 


Soft 




A 


E 


B 


F 


C 


G 


D 


. H 



Medium 


Medium. 


Medium 


Hard. 


Extremely 


Soft. 




Hard. 




Hard. 


I 


M 


Q 


U 


Y 


J 


N 


R 


V 


Z 


K 


O 


S 


w 




L 


P 


T 


X 





The intermediate letters between those designated as soft, medium 
soft, etc., indicate so many degrees harder or softer; e.g., L is one grade 
or degree softer than medium; O, 2 degrees harder than medium but not 
quite medium hard. 



EMERY WHEELS AND GRINDSTONES. 



1267 



For Grinding High-speed Tool Steel, The American Emery Wheel Co. 
recommends a wheel one number coarser and one grade softer than a wheel 
for grinding carbon steel for the same service. 

Special Wheels. — Rim wheels and iron-center wheels are specialties 
that require the maker's guarantee and assignment of speed. 

Strains in Grindstones. 

Limit of Velocity and Approximate Actual Strain per Square 

Inch of Sectional Area for Grindstones of 

Medium Tensile Strength. 



Diam- 


Revolutions per Minute. 


eter. 


100 


150 


200 


250 


300 


350 


400 


feet. 


lbs. 


lbs. 
3.57 
5.57 
8.04 
10.93 
14.30 
18.08 
22.34 
32.17 


lbs. 
6.35 
9.88 
14.28 
19.44 
27.37 
32.16 


lbs. 

9.93 
15.49 
22.34 
30.38 


lbs. 
14.30 
22.29 
32.16 


lbs. 
18.36 
28.64 


lbs. 


21/2 
3 


2.47 
3.57 
4.86 
6.35 
8.04 
9.93 
14.30 
19.44 


39.75 


3V2 












ft 

6 

7 






Approximate breaking strain ten 
times the strain for size opposite the 













The figures at the bottom of columns designate the limit of velocity 
(in revolutions per minute at the head of the columns) for stones of the 
diameter in the first column opposite the designating figure. 

A general ruie of safety for any size grindstone that has a compact and 
strong grain is to limit the peripheral velocity to 47 feet per second. 

Joshua Rose (Modern Machine-shop Practice) says: The average cir- 
cumferential speed of grindstones in workshops may be given as follows: 

For grinding machinists' tools, about 900 feet per minute. 

" carpenters' " " 600 " 

The speeds of stones for file-grinding and other similar rapid grinding 
is thus given in the " Grinders' List." 

Diamft 8 71/ 2 7 6l/ 2 * 6 51/ 2 5 41/ 2 4 31/ 2 3 

Revs, per min. 135 144 154 166 180 196 216 240 270 308 360 

The following table, from the Mechanical World, is for the diameter of 
stones and the number of revolutions they should run per minute (not to 
be exceeded), with the diameter of change of shift-pulleys required, vary- 
ing each shift or change 2i/ 2 inches, 21/4 inches, or 2 inches in diameter 
for each reduction of 6 inches in the diameter of the stone. 



Diameter of 


Revolutions 
per Minute. 


Shift of Pulleys, in inches. 


Stone. 


21/ 2 


21/4 


2 


ft. in. 










8 


135 


40 


36 


32 


7 6 


144 


37i/ 2 


333/4 


30 


7 


154 


35 


311/2 


28 


6 6 


166 


32l/ 2 


291/ 4 


26 


6 


180 


30 


27 


24 


5 6 


196 


271/2 


24i3/ 4 


22 


5 


216 


25 


221/2 


20 


4 6 


240 


221/2 


2OI/4 


18 


4 


270 


20 


18 


16 


3 6 


308 


171/2 


153/4 


14 


3 


360 


15 


131/2 


12 


1 


2 


3 


4 


5 



1268 



THE MACHINE-SHOP. 



Columns 3, 4, and 5 are given to show that if we start an 8-foot stone 
with, say, a countershaft pulley driving a 40-inch pulley on the grind- 
stone spindle, and the stone makes the right number (135) of revolutions 
per minute, the reduction in the diameter of the pulley on the grinding- 
stone spindle, when the stone has been reduced 6 inches in diameter, will 
require to be also reduced 21/2 inches in diameter, or to shift from 40 
inches to 371/2 inches, and so on similarly for columns 4 and 5. Any 
other suitable dimensions of pulley may be used for the stone when eight 
feet in diameter, but the number of inches in each shift named, in order 
to be correct, will have to be proportional to the numbers of revolutions 
the stone should run, as given in column 2 of the table. 



Varieties of Grindstones. 

(Joshua Rose.) 

For Grinding Machinists' Tools. 



Name of Stone. 



Nova Scotia, ] 

Bay Chaleur (New ) 

Brunswick), J 

Liverpool or Melling 



Kind of Grit. 



All kinds, from 
finest to coarsest 
Medium to finest 
Medium to fine 



Texture of Stone. Color of Stone. 



All kinds, from 
hardest to softes 
Soft and sharp 

Soft, with sharp 
grit 



Blue or yellowish 

gray. 
Uniformly light 

blue 
Reddish 



For Woodworking Tools. 



Wickersley . . . 

Liverpool or Melling 

Bay Chaleur (New ) 

Brunswick), J 

Huron, Michigan . 



Medium to fine 
Medium to fine j 

Medium to finest 
Fine 



Very soft 

Soft, with sharp 

grit 
Soft and sharp 
Soft and sharp 



Grayish yellow 
Reddish 

Uniform light blue 
Uniform light blue 



For Grinding Broad Surfaces, as Saws or Iron Plates. 



Newcastle . . 
Independence 
Massillon . . . 



Coarse to med'm 

Coarse 

Coarse 



The hard ones 
Hard to medium 
Hard to medium 



Yellow 

Gravish white 
Yellowish white 



SCREWS, SCREW-THREADS, ETC. 

Efficiency of a Screw. — Let a = angle of the thread, that is, the 
angle whose tangent is the pitch of the screw divided by the circum- 
ference of a circle whose diameter is the mean of the diameters at the top 
and bottom of the thread. Then for a square thread 



Efficiency = 



1 — / tan a 
1 + / cotan a' 



in which f is the coefficient of friction. (For demonstration, see Cotterill 
and Slade, Applied Mechanics.) Since cotan = 1 -*- tan, we may sub- 
stitute for cotan a the reciprocal of the tangent, or if p = pitch, and 
c = mean circumference of the screw, 



Efficiency = 



- fp/c , 



1 + fc/p 







si 



SCREWS, SCREW-THREADS, ETC. 



1269 






SSgS ; 












oo S3 S 8 „ 8 si? oo^ S-§? c § S-S? *>!><-?? «.!?<-§? «-§ *-§? 

: a • • • s 

:.o •& . : :«g :. :^ :::::::.:::... . 

j ; g oo*'"S"""S""* 

• • • • *CQ ■ • •§§" • • • • -^ • ■ -$T • • '^~ ■ • • 

* * " ' SO tH ' ° CD CO ' ' CO SO ' ' ' 

^ : :^ : :s^ : :p- : :$-§- ::::::::: . 

jojo co_S.?i 2? Jo .»£?■ CO^^.N CYJ,CO.CO 00 CO [ ".-4? -5?! '.'.'.'.'.'• 



OO ■ -coco • -f* • -<NcN • -<n<vj 

(SCS • •— — • • — — ■ . — — . • — — 

oo oo ao oo vo o ^o \C m ^ -<i- tJ- — — oq«N — — • •©© • • 

vO^O'0*1 , ^ , ^ , tMNNNOO--OOOOo > >»0>0»(l 



4S 

Q 






^2 to 

3^ 



°& 



f3 ° 
•3 2 



o o> 

«3 OJO 



o 
O . 

CD 1> 
CO 






. 






,fi CI 


'>, 


C 


cm 


H 


s 


- 


r w 


-d 


T>' 








§ 


£ : 




^ 


■" 


£ 


H 


i 


^ 




jj 


O 




53 H3 



1270 THE MACHINE-SHOP. 

Example. — Efficiency of square-threaded screws of 1/2 inch pitch. 
Diameter at bottom of thread, in. . . 1 2 3 4 

Diameter at top of thread, in H/ 2 21/2 31/2 41/2 

Mean circumference of thread, in.. , . 3.927 7.069 10.21 13.35 

Cotangent a = c + p =7.854 14.14 20.42 26.70 

Tangent a = p -i- c =0.1273 .0707 .0490 .0375 

Efficiency if/ = 0.10 =55.3% 41.2% 32.7% 27.2% 

Efficiency if f= 0.15 =45% 31.7% 24.4% 19.9% 

The efficiency thus increases with the steepness of the pitch. 

The above formulae and examples are for square-threaded screws, and 
consider the friction of the screw-thread only, and not the friction of the 
collar or step by which end thrust is resisted, and which further reduces 
the efficiency. The efficiency is also further reduced by giving an inclina- 
tion to the side of the thread, as in the V-threaded screw. For discussion 
of this subject, see paper by Wilfred Lewis, Jour. Frank. Inst. 1880; also 
Trans. A. S. M. E., vol. xii, 784. 

Efficiency of Screw-bolts. — Mr. Lewis gives the following approxi- 
mate formula for ordinary screw-bolts (V-threads, with collars): p= pitch 
of screw, d = outside diameter of screw, F = force applied at circum- 
ference to lift a unit of weight, E = efficiency of screw. For an average 
case, in which the coefficient of friction may be assumed at .15, 
p== P + d F y 

3d ' v + d 

For bolts of the dimensions given above, 1/2-inch pitch, and outside 
diameters H/2, 21/2, 31/2, and 41/2 inches, the efficiencies according to this 
formula, would be, respectively, 0.25, 0.167, 0.125, and 0.10. 

James McBride (Trans. A. S. M. E., xii, 781) describes an experiment 
with an ordinary 2-inch screw-bolt, with a V-thread, 41/2 threads per inch, 
raising a weight of 7500 pounds, the force being applied by turning the 
nut. Of the power applied 89.8 per cent was absorbed by friction of the 
nut on its supporting washer and of the threads of the bolt in the nut. 
The nut was not faced, and had the flat side to the washer. 

Professor Ball in his "Experimental Mechanics" says: "Experiments 
showed in two cases respectively about 2/3 and 3/ 4 of the power was lost. " 

Trautwine says: "In practice the friction of the screw (which under 
heavy loads becomes very great) make the theoretical calculations of 
but little value." 

Weisbach says: "The efficiency is from 19 per cent to 30 per cent." 

Efficiency of a Differential Screw. — A correspondent of the 
American Machinist describes an experiment with a differential screw- 
punch, consisting of an outer screw 2 inch diameter, 3 threads per 
inch, and an inner screw 13/ 8 inch diameter, 3 1/2 threads per inch. The 
pitch of the outer screw being 1/3 inch and that of the inner screw 2/ 7 inch 
the punch would advance in one revolution 1/3 — 2 / 7 ^ V21 inch. 
Experiments were made to determine the force required to punch an 
11/16-inch hole in iron 1/4 inch thick, the force being applied at the end 
of a lever-arm of 473/4 inch. The leverage would be 473/ 4 x 2tt x 21 = 
6300. The mean force applied at the end of the lever was 95 pounds, 
and the force at the punch, if there was no friction, would be 6300 X 
95 = 598,500 pounds. The force required to punch the iron, assuming 
a shearing resistance of 50,000 pounds per square inch, would be 50,000 X 
n /i6 X t X V4 = 27,000 pounds, and the efficiency of the punch would 
be 27,000 -4- 598,500 = only 4.5 per cent. With the larger screw only 
used as a punch the mean force at the end of the lever was only 82 pounds. 
The leverage in this case was 473/4 X 2ir X 3 = 900, the total force 
referred to the punch, including friction, 900 X 82 = 73,800, and the 
efficiency 27,000 -e- 73,800 = 36.7 per cent. The screws were of tool- 
steel, well fitted, and lubricated with lard-oil and plumbago. 

TAPER BOLTS, PINS, REAMERS, ETC. 

Taper Bolts for Locomotives. — Bolt-threads, U. S. Standard, ex- 
cept stay-bolts and boiler-studs, V-threads, 12 per inch; valves, cocks, 
and plugs, V-threads, 14 per inch, and Vs-inch taper per 1 inch. Standard 
bolt taper V16 inch per foot. 

Taper Reamers. — The Pratt & Whitney Co. makes standard taper 
reamers for locomotive work taper 1/16 inch per foot from 1/4 inch diameter; 



TAPER BOLTS, PINS, REAMERS, ETC.. 



1271 



4 inch length of flute to 2 inch diameter; IS inch length of flute, diameters 
advancing by 16ths and 32ds. P. & W. Co.'s standard taper pin reamers 
taper 1/4 inch per foot, are made in 15 sizes of diameters, 0.135 to 1.250 
inches; length of flute 17/ 16 inches to 14 inches. 











31orse Tapers. 


















bf2 
G'fi 




faO 

9 


0>GG 


w 

a 
Q 


CO £, 

m 


■£$ 

M 

a 

0) 


fa 

& . 


' 5 
^§ 

3 

-; 


O . 
35 3 

3 c 
So 

s 


"o . 

s s 

H 


0) 

— 9 

~ 


Ha « 

w W 

9 1= 


0. 
Oi 

Q 
a 

Si 

.9 

m 






4) 

a 
H 


e 


D 

252 


A 
356 


P 

2 


B 


H 


K 


L 


IF 


T 


d 


« 


72 


a 


S 






211/32 


21/32 


U5/16 


9/16 


.160 


1/4 


.24 


5/32 


5/32 


.04 


27/32 


.625 





.369 


.475 


21/8 


29/16 


23/16 


21/16 


3/4 


.213 


1/5 


.35 


13/64 


3/16 


.05 


23/8 


.600 


1 


, .572 


.700 


29/16 


31/16 


25/s 


21/2 


7/8 


26 


3/8 


17/32 


1/4 


1/4 


.06 


27/s 


.602 


2 


.778 


.938 


33/16 


33/ 4 


31/4 


31/16 


H/16 


.322 


7/16 


3/ 4 


5/16 


9/32 


.08 


39/16 


.602 


3 


1.020 


1.231 


41/16 


43/ 4 


41/8 


3 7 8 


11/4 


.478 


1/2 


31/32 


15/32 


5/16 


.10 


41/2 


.623 


4 


1.475 


1.748 


53/16 


6 


51/4 


415/i 6 


11/2 


.635 


•V8 


113/32 


5/8 


3/8 


.12 


53/ 4 


.630 


5 


2.116 


2.494 


71/4 


85/i 6 


7 3/8 


7 


13/4 


.76 


7/8 


2 


3/4 


1/2 


.15 


8 


.626 


6 


2.75 


3.27 


10 


115/ 8 


101/8 


91/2 


25/s 


1.135 


13/8 


2H/16 


11/8 


3/4 


.18 


111/4 


.625 


7 



Brown & Sharpe Mfg. Co. publishes (Machy's Data Sheets) a list of 
18 sizes of tapers ranging from 0.20 in. to 3 in.-diam. at the small end; 
taper 0.5 in. to 1 ft., except No. 10, which is 0.5161 in. per ft. 



^f^fa ^ 




Fig. 192. — Morse Tapers. See table above. 

The Jarno Taper is 0.05 inch per inch = 0.6 inch per foot. The 
number of the taper is its diameter in tenths of an inch at the small end, 
in eighths of an inch at the large end, and the length in halves of an inch. 



1272 THE MACHINE-SHOP. 

Thus, No. 3 Jarno taper is 1 1/2 inches long, 0.3 inch diameter at the small 
end and 3/ 8 inch diameter at the large end. 

Standard Steel Taper-pins. — The following sizes are made by The 
Pratt & Whitney Co.: Taper 1/4 inch to the foot. 
Number: 

123 456789 10 

Diameter large end: 

0.156 0.172 0.193 0.219 0.250 0.289 0.341 0.409 0.492 0.591 0.706 
Approximate fractional sizes: 

5/32 H/64 3 /l6 7/32 Vi 19 /64 U/32 l 3 /32 V2 19 /32 23/32 

Lengths from 

3/4 3/ 4 3/ 4 3/4 3/ 4 3/ 4 3/ 4 1 H/ 4 H/ 2 U/ 2 

To* 

1 H/4 H/2 l 3 /4 2 21/4 31/4 33/4 41/2 51/4 6 

Diameter small end of standard taper-pin reamer :f 
0.135 0.146 0.162 0.183 0.208 0.240 0.279 0.331 0.398 0.482 0.581 
Standard Steel Mandrels. (The Pratt & Whitney Co.) — These 
mandrels are made of tool-steel, hardened, and ground true on their 
centers. Centers are also ground to true 60 degree cones. The ends are 
of a form best adapted to resist injury likely to be caused by driving. 
They are slightly taper. Sizes, 1/4 inch diameter by 33/ 4 inches long to 
4 inches diameter by 17 inches long, diameters advancing by 16ths. 

PUNCHES AND DIES, PRESSES, ETC. 

Clearance between Punch and Die. — For computing the amount 
of clearance that a die should have, or, in other words, the difference 
in size between die and punch, the general rule is to make the diam- 
eter of die-hole equal to the diameter of the punch, plus 2/ 10 the thickness 
of the plate. Or, D = d + 0.2t, in which D = diameter of die-hole, 
d = diameter of punch, and t = thickness of plate. For very thick 
plates some mechanics prefer to make the die-hole a little smaller than 
called for by the above rule. For ordinary boiler-work the die is made 
from 1/10 to 3/ 10 of the thickness of the plate larger than the diameter 
of the punch; and some boiler-makers advocate making the punch fit 
the die accurately. For punching nuts, the punch fits in the die. (Am. 
Mach.) 

Kennedy's Spiral Punch. (The Pratt & Whitney Co.) — B. Mar- 
tell, Chief Surveyor of Lloyd's Register, reported tests of Kennedy's 
spiral punches in which a 7/ 8 -inch spiral punch penetrated a 5/ 8 -inch 
plate at a pressure of 22 to 25 tons, while a flat punch required 33 to 35 
tons. Steel boiler-plates punched with a flat punch gave an average 
tensile strength of 58,579 pounds per square inch, and an elongation in 
two inches across the hole of 5.2 per cent, while plates punched with a 
spiral punch gave 63,929 pounds, and 10.6 per cent elongation. 

The spiral shear form is not recommended for punches for use in metal 
of a thickness greater than the diameter of the punch. This form is of 
greatest benefit when the thickness of metal worked is less than two 
thirds the diameter of punch. 

Size of Blanks used in the Drawing-press. — Oberlin Smith 
{Jour. Frank. Inst, Nov. 1886) gives three methods of finding the 
size of blanks. The first is a tentative method, and consists simply in a 
series of experiments with various blanks, until the proper one is found. 
This is for use mainly in complicated cases, and when the cutting por- 
tions of the die and punch can be finally sized after the other work is 
done. The second method is by weighing the sample piece, and then, 
knowing the weight of the sheet metal per square inch, computing the 
diameter of a piece having the required area to equal the sample in 
w eight. Th e third method is by computation, and the formula is x=> 
v d 2 + 4dh for a sharp-cornered cup, where x = diameter of blank, 
d = diameter of cup, h = height of cup. For a round-cornered cup 

* Lengths vary by 1/4 inch each size. 

t Taken 1/2 inch from extreme end. Each size overlaps smaller one 
about 1/2 inch. 



FORCE AND SHRINK FITS. 1273 

where the corner is sm all, say radi us of corner less than 1/4 height of cup, 
the formula is x = (V(d 2 + 4 dh) — r, about; r being the radius of the 
corner. This is based upon the assumption that the thickness of the 
metal is not to be altered by the drawing operation. 

Pressure attainable by the Use of the Drop-press. (R. H. 
Thurston, Trans. A. S. M. E., v, 53.) — A set of copper cylinders 
was prepared, of pure Lake Superior copper; they were subjected to the 
action of presses of different weights and of different heights of fall. 
Companion specimens of copper were compressed to exactly the same 
amount, and measures were obtained of the loads producing compression, 
and of the amount of work done in producing the compression by the 
drop. Comparing one with the other it was found that the work done 
with the hammer was 90 per cent of the work which should have been 
done with perfect efficiency. That is to say, the work done in the test- 
ing-machine was equal to 90 per cent of that due the weight of the drop 
falling the given distance. 

_, , , , , Weight of drop X fall X efficiency 

Formula: Mean pressure in pounds = : -• 

compression 

For pressures per square inch, divide by the mean area opposed to 
crushing action during the operation. 

Similar experiments on Bessemer steel plugs by A. W. Moseley and 
J. L. Bacon (Trans. A. S. M. E., xxvii, 605) indicated an efficiency for the 
drop hammer of about 70 per cent. 

Flow of Metals. (David Townsend, Jour. Frank. Inst., March, 
1878.) — In punching holes 7/ 16 -inch diameter through iron blocks 13/4 
inches thick, it was found that the core punched out was only li/ie 
inches thick, and its volume was only about 32 per cent of the volume 
of the hole. Therefore, 68 per cent of the metal displaced by punching 
the hole flowed into the block itself, increasing its dimensions. 

F.ORCING, SHRINKING AND RUNNING FITS. 

Forcing Fits of Pins and Axles by Hydraulic Pressure. — A 

4-inch axle is turned 0.015 inch diameter larger than the hole into which 
it is to be fitted. They are pressed on by a pressure of 30 to 35 tons. 
(Lecture by Coleman Sellers, 1872.) 

For forcing the crank-pin into a locomotive driving-wheel, when the 
pinhole is perfectly true and smooth, the pin should be pressed in with a 
pressure of 6 tons for every inch of diameter of the wheel fit. Wheji the 
hole is not perfectly true, which may be the result of shrinking the tire on 
the wheel center after the hole for the crank-pin has been bored, or if the 
hole is not perfectly smooth, the pressure may have to be increased to 9 
tons for every inch of diameter of the wheel-fit. (Am. Machinist.) 

Shrinkage Fits. — In 1886 the American Railway Master Mechanics' 
Association recommended the following shrinkage allowances for tires of 
standard locomotives. The tires are uniformly heated by gas-flames, 
slipped over the cast-iron centers, and allowed to cool. The centers are 
turned to the standard sizes given below, and the tires are bored smaller 
by the amount of the shrinkage designated for each: 

Diameter of center, in 38 44 50 56 62 66 

Shrinkage allowance, in 040 .047 .053 .060 .066 .070 

This shrinkage allowance is approximately Vso inch per foot, or 1/960- 
A common allowance is V1000. Taking the modulus of elasticity of steel at 
30,000,000, the strain caused by shrinkage would be 30,000 lb. per sq. in., 
less an uncertain amount due to compression of the center. 

Amer. Machinist published at a later date a table of " M. M. allowances 
for shrink fits" which correspond to the following: Allowance = 0.001 
(d+ 1) .for d = 20 to 40 in.: 0.001 (d + 2) for d = 41 to 60 in.; 0.001 
(d+ 3) for d =61 to 83 in.; 0.088 for d = 84 in. d = diam. of wheel center. 
For running force fits, Am. Mach. gives the following allowances: d=diam. 
of bearing or hole, a = allowance. 



d = 


1 » 


* 


3 


4 


5 1 6 


7 


8 1 9 1 10 


Running, a =... 


... —0.001 
.1+0.001 


.002 
.003 


.003 
.005 


.0035 
006 


.0037 .004 
.007 (.008 


.0042 
0085 


.0042 .0043 .0044 
.009 |.01 |.0105 













1274 



THE MACHINE-SHOP. 



d = 


11 


12 


13 


14 


15 


16 


17 | 18 


19 


20 


Running, a= 


-0.0045 
+ 011 


.0046 
.0115 


.0047 
.012 


.0048 
.013 


.0049 
014 


.005 
.0145 


.0051 .0052 
.015 I .0155 


.0053 
.016 


.0055 
.017 







Allowances for drive fits are one-half those for force fits. 

Limits of Diameters for Fits. C. W. Hunt Co. (Am. Mach., July 16, 
1903.) — For parallel shafts and bushings (shafts changing): d = diam. 
in ins. 
Shafts: Press fit, + 0.001 d + (0 to 0.001 in.). Drive fit, + 0.0005 d + 

(0. to 0.001 in.). 
Shafts: Hand fit, + 0.001 to 0.002 in. for shafts 1 to 3 in.; 0.002 to 0.003 

in. for 4 to 6 in.; 0.003 to 0.004 in. for 7 to 10 in. 
Holes: all fits to - 0.002 in. for 1 to 3 in.; to - 0.003 in. for 4 to 6 in.; 
to — 0.004 in. for 7 to 10 in. 

Parallel journals and bearings (journals changing): 

Close fit - 0.001 d + (0.002 to 0.004 in.); Free fit - 0.001 d +(0.007 
to 0.01 in.); Loose fit, - 0.003 d+ (0.02 to 0.025). Limits of diameters 
for taper shaft and bushings (holes changing). Shaft turned to standard 
taper 3/ 16 in. per ft., large end to nominal size ± 0.001 in. Holes are 
reamed until the large end is small by from 0.001 d + 0.004 to 0.005 in. 
for press fit, from 0.0005 d+ 0.001 in. for drive fit, and from to 0.001 in. 
for hand fit. In press fits the shaft is pressed into the hole until the 
true sizes match, or 1/16 in. for each Viooo in. that the hole is small. 
The above formulae apply to steel shafts and cast-iron wheels or other 
members. 

Shaft Allowances for Electrical Machinery. — In use by General 
Electric Co. (John Riddell, Trans. A.S.M. E., xxiv, 1174). 



l.s 
S 


2 


4 


8 


12 


16 


20 


24 


28 


32 


36 


40 


44 


48 


A, B 


0.0005 


.00075 


.001 


.001 


.0012 


.0012 


.0015 


.0015 


.0017 


.0017 


.002 


.0o2 


0023 


C 


0.0005 


.00075 


.0015 


.0017 


.0020 


.0023 


.0025 


.0028 


.003 


.0033 


.0035 


.0038 


004 


D 


0.0005 


.00075 


.0017 


.0025 


.0033 


.004 


.0045 


.005 


.0058 


.0063 


.0068 


.0073 


.008 


E 


0.0015 


.0027 


.0045 


.0057 


.007 


.008 


.0093 


.0115 


.0125 


.0128 


.0138 


.015 


.016 



A, minus allowance for sliding fit. B, plus allowance for commuta- 
tors and split hubs. C, press fit for armature spiders, so^'d steel. D, 
do., solid cast iron. E, press fit for couplings, and shrink fit. 

Running Fits. — Wm. Sangster (Am. Mach., July 8, 1909) gives the 
practice of different manufacturers as follows: 

An electric manufacturing Co. allows a clearance of 0.003 to 0.004 in. for 
shafts 11/2 to 21/4 in. diam.; 0.003 to 0.006 for 2i/ 2 ins.; 0.004 to 0.006 for 
23/4 to 31/2 ins.; 0.005 to 0.007 in. for 4 and 41/2 ins.; 0.006 to 0.008 in. 
for 5 ins.; 0.009 to 0.011 in. for 6 ins. Dodge Mfg. Co. allows from 1/64 
for 1-in. ordinary bearings to a little over 1/32 in. for 6-in. Clutch sleeves, 
0.008 to 0.015 in.; loose pulleys as close as 0.003 in. in the smaller sizes, 
and about 1/54 in. on a 21/2-in. hole. 

Watt Mining Car Wheel Co. allows Vie in. for all sizes of wheels, and 
i/ie in. end play. A large fan-blower concern allows 0.005 to 0.01 in. 
on fan journals from 9/i6 to 27/ie ins. 

Pressure Required for Press Fits. (Am. Mach., March 7, 1907.) — 
The following approximate formulae give the pressures required for press 
fits of cranks and crank-pins, as used by an engine-building firm. jP = total 
pressure on ram, tons; D = diameter inches. 



Crank fits up to D =10. 
Crank fits D = 12 to 24. 
Straight crank-pins. 
Taper crank-pins. 



p = 


9.9 D 


- 14. 


p = 


5 D + 40. 


p = 


13 D. 




p = 


14 D ■ 


- 7. 






FORCE AND SHRINK FITS. 



1275 



The allowance for cranks and straight pins is 0.0025 inch per inch of 
diameter. Taper cranks, taper Vi6 inch per inch, are fitted on the 
lathe to within l/s inch of shoulder and then forced home. 

Stresses due to Force and Shrink Fits. — S. H. Moore, Trans. 
A. S. M. E., vol. xxiv, gives the following allowances for different fits 

For shrinkage fits, d =(i7/ie D + 0.5) h- 1000. For forced fits d = 
(2 D + 0.5) -*- 1000. For driven fits, d = (i/ 2 D + 0.5) -r- 1000. d = 
allowance or the amount the diameter of the shaft exceeds the diameter 
of the hole in the ring and D = nominal diameter of the shaft. A. L. 
Jenkins, Eng. News, Mar. 17, 1910, says the values obtained from the 
formula for forced fits are about twice as large as those frequently used 
in practice, and in many cases they lead to excessive stresses in the ring. 
He calculates from Lamg's formula for hoop stress in a ring subjected to 
internal pressure the relation between the stress and the allowance for 
fit, and deduces the following formulae. 

S hl = 15,000,000 d + (fc + 0.6); S hi = i 5 ,000,000 d * (1 + 0.6//;); for a 

cast-iron ring on a steel shaft. 
S hl = 30,000,000 d -*- (1 + fc); S h2 = 30,000,000 d -*- (1 + 1/K); for a 

steel ring on a steel shaft. 
5^= radial unit pressure between the surfaces; S^ 2 = unit tensile or 

hoop stress in the ring; 
d = allowance per inch of diameter, K a constant whose value depends 
on t, the thickness, and r, the radius of the ring, as follows. 
Values of t -f- r, 

0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.25 1.5 1.75 2.0 3.0 
Values of K, 
3.083 2.600 2.282 2.058 1.892 1.766 1.666 1.492 1.380 1.300 1.250 1.133. 

The allowances for forced and shrinkage fits should be based on the 
stresses they produce, as determined by the above formula, and not on 
the diameter of the shaft. 

Force Required to Start Force and Shrink Fits. (Am. Mach., 
Mar. 7, 1907.) — A series of experiments was made at the Alabama Poly- 
technic Institute on spindles 1 in. diam. pressed or shrunk into cast-iron 
disks 6 in. diam., 1 1/4 in. thick. The disks were bored and finished with 
a reamer to 1 in. diam. with an error believed not to exceed 0.00025 in. 
The shafts were ground to sizes 0.001 to 0.003 in. over 1 in. Some of the 
spindles were forced into the disks by a testing machine, the others had 
the disks shrunk on. Some of each sort were tested by pulling the 
spindle from the disk in the testing machine, others by twisting the disk 
on the spindle,. The force required to start the spindle in the twisting 
tests was reduced to equivalent force at the circumference of the spindle, 
for comparison with the tension tests. The results were as follows: 
D = diam. of spindle; F = force in lbs.: 



Force Fits, 
Tension. 


Force Fits, 
Torsion. 


Shrink Fits, 
Tension. 


Shrink Fits, 
Torsion. 


D 


F.lbs. 


Per 

sq.in. 


D 


F.lbs. 


Per 

sq. in. 


D 


F.lbs. 


Per 

sq. in. 


D 


F,lbs. 


Per 
sq. in. 


1.001 
1.0015 
1.002 
1.0025 


1000 
2150 
2570 
4000 


318 
685 
818 
1272 


1.0015 
1.0015 
1.002 
1 .0025 


2200 
2800 
4200 
4600 


700 

892 
1335 
1465 


1.001 

1.001 

1.002 

1.002 

1.0025 

1.0025 


5320 
5820 
7500 
8100 
9340 
9710 


1695 

1853 
2385 
2580 
2974 
3090 


1.001 

1.0015 

1.0015 

1.0025 

1.003 


2200 
7200 
9800 
13800 
17000 


700 
2290 
3118 
4395 
5410 































1276 THE MACHINE-SHOP. 



PROPORTIONING PARTS OP MACHINES IN A SERIES 
OF SIZES. 

The following method was used by Coleman Sellers (Stevens Indicator, 
April, 1892) to get the proportions of the parts of machines, based upon 
the size obtained in building a large machine and a small one to any series 
of machines. This formula is used in getting up the proportion-book and 
arranging the set of proportions from which any machine can be con- 
structed of intermediate size between the largest and smallest of the series. 

Rule to Establish Construction Formulae." — Take difference be- 
tween-the nominal sizes of the largest and the smallest machines that have 
been designed of the same construction. Take also the difference between 
the sizes of similar parts on the largest and, small est machines selected. 
Divide the latter by the former, and the result obtained will be a 
" factor, " which, multiplied by the nominal "capacity of the intermediate 
machine, and increased or diminished by a constant "increment," will 
give the size of the part required. To find the "increment:" Multiply 
the nominal capacity of some known size by the factor obtained, and sub- 
tract the result from the size of the part belonging to the machine of 
nominal capacity selected. 

Example. — Suppose the size of a part of a 72-inch machine is 3 inches, 
and the corresponding part of a 42-inch machine is l'7/ 8 , or 1.875 inches: 
then 72 - 42 = 30, and 3 inches - 17/ 8 inches = Us inches = 1.125. 
1.125-H30 = 0.0375 = the " factor, " and .0375X42 = 1.575. Then 1.875- 
1.575 = .3 = the "increment" to be added. Let D = nominal capacity; 
then the formula will read: x = D X .0375 + .3. 

Proof: 42 X .0375 + .3 = 1.875, or 17/ 8 , the size of one of the selected 
parts. 

Some prefer the formula: aD + c = x, in which D = nominal capacity 
in inches or in pounds, c is a constant increment, a is the factor, and 
x = the part to be found. 

KEYS. 

Sises of Keys for Mill-gearing. (Trans. A. S. M. E., xiii, 229.)— 
E. G. Parkhurst's rule: Width of key= Vs diameter of shaft, depth = 
1/9 diameter of shaft; taper Vs inch to the foot. 

Custom in Michigan saw-mills: Keys of square section, side = 1/4 
diameter of shaft, or as nearly as may be in even sixteenths of an inch. 

J. T. Hawkins's rule: Width = 1/3 diameter of hole; depth of side abut- 
ment in shaft = 1/8 diameter of hole. 

W. S. Huson's rule: 1/4-inch key for 1 to 11/4-in. shafts, 5/i6-in. key for 
11/4 to 11/2-inch shafts, 3/ 8 -inch key for 1 1/2 to 13/ 4 -inch shafts and so on. 
Taper i/s inch to the foot. Total thickness at large end of splrce, 4/5 
width of key. 

Unwin (Elements of Machine Design) gives: Width = 1/4 d + 1/ 8 inch. 
Thickness = Vs d 4- i/s inch, in which d = diameter of shaft in inches. 
When wheels or pulleys transmitting only a small amount of power are 
keyed oh large shafts, he says, these dimensions are -excessive. In that 
case, if H.P. = horse-power transmitted by the wheel or pulley, N = 
r.p.m., P = force acting at the circumference, in pounds, and R = radius 
of pulley in inches, take 



r= J/ 100 H.P MM 

V jV or T 630 



Prof. Coleman Sellers (Stevens Indicator, April, 1892) gives the follow- 
ing- The size of keys, both for shafting and for machine tools, are the 
proportions adopted bv William Sellers & Co., and rigidly adhered to 
during a period of nearly forty years. Their practice in making keys and 
fitting them is, that the keys shall always bind tight sidewise, but not top 
and bottom ; that is, not necessarily touch either at the bottom of the key- 
seat in the shaft or touch the top of the slot cut in the gear-wheel that is 



1277 



fastened to the shaft; but in practice keys used in this manner depend 
upon the fit of the wheel upon the shaft being a forcing fit, or a fit that is 
so tight as to require screw-pressure to put the wheel in place upon the 
shaft. 

Size of Keys for Shafting. 

Diameter of Shaft, in. Size of Key, in. 

H/4 17/16 HI/16 5/l6X3/ 8 

H5/16 23/i6 7/16XV2 

27/16 9/ie X 5/ 8 

211/16 215/i6 33/i6 3.7/i 6 U/ 16 X 3/ 4 

315/16 47/ie 415/ie 13/ 16 X 7/ 8 

57/i6 515/i 6 67/ie 15/ 16 X 1 

615/ie 77/i6 715/ie 87/is 815/i 6 H/ttXU/s 

Length of key-seat for coupling == U/2X nominal diameter of shaft. 



Size of Keys for Machine Tools. 



Diam. of Shaft, in. 

i5/i6 and under . 

1 to 13/ie . . 

H/4 to 17/ie . . 

1 1/ 2 to 1 U/16 . . 
13/4 to 23/ie . . 
21/4 to 2U/16 



Size of Key, 
in. sq. 

... 1/8 

. • • 3/16 
... 1/4 
• • . 5/16 
. . . 7/ 16 
9/16 



23/4 tO 315/16 U/16 



Diam. of Shaft, in, 
4 to 57/ie 
51/2 to 615/ie 
7 to 815/ie 
9 tO 1015/16 
11 to 1215/ie 
13 to 1415/16 



Size of Key, 
in. sq. 
. . 13/ie 

• • 15/16 

• • H/16 
. . 13/16 

• • 15/16 

• • 17/ie 



John Richards, in an article in Cassier's Magazine, writes as follows: 
There are two kinds or systems of keys, both proper and necessary, but 
widely different in nature. 1. The common fastening key, usually made 
in width one fourth of the shaft's diameter, and the depth five eighths to 
one third the width. These keys are tapered and fit on all sides, or, as 
it is commonly described, "bear all over." They perform the double 
function in most cases of driving or transmitting and fastening the keyed- 
on member against movement endwise on the shaft. Such keys, when 
properly made, drive as a strut, diagonally from corner to corner. 

2. The other kind or class of keys are not tapered and fit on their sides 
only, a slight clearance being left on the back to insure against wedge 
action or radial strain. These keys drive by shearing strain. 

For fixed work where there is no sliding movement such keys are com- 
monly made of square section, the sides only being planed, so the depth 
is more than the width by so much as is cut away in finishing or fitting. 

For sliding bearings, as in the case of drilling-machine spindles, the 
depth should be increased, and in cases where there is heavy strain there 
should be two keys or feathers instead of one. 

The following tables are taken from proportions adopted in practical 
use. 

Flat keys, as in the first table, are employed for fixed work when the 
parts are to be held not only against torsional strain, but also against 
movement endwise; and in case of heavy strain the strut principle being 
the strongest and most secure against movement when there is strain each 
way, as in the case of engine cranks and first movers generally. The 
objections to the system for general use are, straining the work out of 
truth, the care and ^expense required in fitting, and destroying the evi- 
dence of good or bad fitting of the keyed joint. When a wheel or other 
part is fastened with a tapering key of this kind there is no means of 
knowing whether the work is well fitted or not. For this reason such 
keys are not employed by machine-tool-makers, and in the case of accu- 
rate work of any kind, indeed, cannot be, because of the wedging strain, 
and also the difficulty of inspecting completed work. 



1278 THE MACHINE-SHOP. 

I. Dimensions of Flat Keys, in Inches. 



Diam. of shaft . . 


1 


11/4 


U/, 


I3/ 4 


2 


2 V, 


3 


31/ ? 


4 


5 


6 


7 


8 


Breadth of keys 


1/4 


5/16 


3/8 


7/1 fi 


V?, 


5/8 


3/4 


7/8 


1 


H/8 


13/8 


H/2 


13/4 


Depth of keys . . 


5 /32 


3/l6 


1/4 


^32 


5/16 


3/8 


V/16 


1/2 


•V8 


H/16 


13/16 


'/8 


1 



II. Dimensions of Square Keys, in Inches. 



Diameter of shaft . . 

Breadth of keys 

Depth of keys . 



13/4 
H/32 
3/8 



2 
13/32 
7/16 



21/2 
15/32 

1/2 



3 
17/32 
9/16 



31/2 

9/16 
5/8 



4 
11/16 
3/4 



III. Dimensions of Sliding Feather-keys, in Inches. 



Diameter of shaft . 
Breadth of keys . . . 
Depth of keys 



11/4 


U/» 


13/4 


2 


21/4 


21/?, 


3 


31/2 


4 


1/4 


1/4 


V16 


5/16 


3/8 


3/8 


1/2 


9/16 


9/16 


3/8 


3/8 


7/16 


7/16 


1/2 


1/2 


5/8 


3/4 


»/4 



41/2 

5/8 
7/8 



P. Pryibil furnishes the following table of dimensions to the Am. 
Machinist. He says: "On special heavy work and very short hubs we 
put in two keys in one shaft 90 degrees apart. With special long hubs, 
where we cannot use keys with noses, the keys should be thicker than 
the standard. 



Diameter of 
Shafts, Inches. 


Width, 
Inches. 


Thick- 
ness, In. 


Diameter of 
Shafts, Inches. 


Width, 
Inches. 


Thick- 
ness, In. 


3/4 to 1 Vie 

1 1/8 to 1 5/ 16 
1 7/ie to 1 H/16 
115/ 16 to23/ 16 
27/ 16 to 211/ie 
215/ 16 to33/ 16 


3/16 
5/16 

3/8 

1/2 
5/8 
3/4 


3/16 
1/4 
5/16 
3/8 
1/2 
9/16 


37/i 6 to 311/i 6 
315/ 16 to43/ 16 
47/ 16 to 4H/ 16 
47/ 8 to 53/ 8 
57/ 8 to 63/ 8 
67/s to 73/ 8 


:$ 

11/2 
13/ 4 


5/8 
11/16 

3/4 
15/16 
1 
U/8 



Keys longer than 10 inches, say 14 to 16 inches, l/i6inch thicker; keys 
longer than 10 indie's, say 18 to 20 inches, l/s inch thicker; and so on. 
Special short hubs to have two keys. 

For description of the Woodruff system of keying, see circular of the 
Pratt & Whitney Co.; also Modern Mechanism, page 455. 

For keyways in milling cutters see page 1248. 



HOLDING-POWER OF KEYS AND SET-SCREWS. 

Tests of the Holding-power of Set-screws in Pulleys. (G. Lanza, 

Trans. A. S. M. E., x, 230.) — These tests were made by using a pulley 
fastened to the shaft by two set-screws with the shaft keyed to the 
holders: then the load required at the rim of the pulley to cause it to 
slip was determined, and this being multiplied by the number 6.037 
(obtained by adding to the radius of the pulley one-half the diameter 
of the wire rope, and dividing the sum by twice the radius of the shaft, 
since there were two set-screws in action at a time) gives the holding- 
power of the set-screws. The set-screws used were of wrought iron, 
5/8 of an inch in diameter, and ten threads to the inch ; the shaft used was 



HOLDING-POWER OF KEYS AND SET-SCREWS. 1279 



of steel and rather hard, the set-screws making but little impression upon 
it. They were set up with a force of 75 pounds at the end of a ten-inch 
monkey-wrench. The set-screws used were of four kinds, marked 
respectively A, B, C, and D. The results were as follows: 

A, ends perfectly flat, 9/i6-in. diam. 1412 to 2294 lbs.; average 2064. 

B, radius of rounded ends about 1/2-in. 2747 to 3079 lbs.; average 2912. 

C, radius of rounded ends about 1/4-in. 1902 to 3079 lbs.; average 2573. 

D, ends cup-shaped and case-hardened 1962 to 2958 lbs.; average 2470. 

Remarks. — A. The set-screws were not entirely normal to the shaft; 
hence they bore less in the earlier trials, before they had become flattened 
by wear. 

B. The ends of these set-screws, after the first two trials, were found 
to be flattened, the flattened area having a diameter of about 1/4 inch. 

C. The ends were found, after the first two trials, to be flattened, as 
in B. 

D. The first test held well because the edges were sharp, then the 
holding-power fell off till they had become flattened in a manner similar 
to B, when the holding-power increased again. 

Tests of the Holding-power of Keys. (Lanza.) — The load was 
applied as in the tests of set-screws, the shaft being firmly keyed to the 
holders. The load required at the rim of the pulley to shear the keys 
was determined, and this, multiplied by a suitable constant, determined 
in a similar way to that used in the case of set-screws, gives us the shear- 
ing strength per square inch of the keys. 

The keys tested were of eight kinds, denoted, respectively, by the 
letters A, B, C, D, E, F, G and H, and the results were as follows: A, B, D, 
and F, each 4 tests ;.E, 3 tests; C, G, and H, each 2 tests. 

A, Norway iron, 2" X 1/4" X 15/32*, 40,184 to 47,760 lbs. ; average, 42,726 

B, refined iron, 2" X 1/4" X 15/32", 36,482 to 39,254 lbs. ; average, 38,059 

C, tool steel, 1" X V4" X 15/32", 91,344 & 100,056 lbs. ; 

D, mach'y steel, 2" X 1/4" X 15/32" 64,630 to 70,186 lbs. ; average, 66,875 

E, Norway iron, 1 1/3" X W X 7/ie" 36,850 to 37,222 lbs. ; average, 37,036 

F, cast-iron, 2" X 1/4" X 15/32", 30,278 to 36,944 lbs. ; average, 33,034 

G, cast-iron, 1 1/3" X W X 7/l6", 37,222 & 38,700. 
H, cast-iron, 1" X V2" X 7/i 6 ", 29,814 & 38,978. 

In A and B some crushing took place before shearing. In E, the 
keys, being only 7/ 16 inch deep, tipped slightly in the key-way. In H, in 
the first test, there was a defect in the key-way of the pulley. 



M 



1280 THE MACHINE-SHOP. 



DYNAMOMETERS. 

Dynamometers are instruments used for measuring power. They are 
of several classes, as: 1. Traction dynamometers, used for determining 
the power required to pull a car or other vehicle, or a plow or harrow. 
2. Brake or absorption dynamometers, in which the power of a rotating 
shaft or wheel is absorbed or converted into heat by the friction of a 
brake; and 3. Transmission dynamometers, in which the power in a 
rotating shaft is measured during its transmission through a belt or other 
connection to another shaft, without being absorbed. 

Traction Dynamometers generally contain two principal parts: (1) A 
spring or series of springs, through which the pull is exerted, the extension 

of the spring measuring the 
amount of the pulling force; and 
(2) a paper-covered drum, rotated 
either at a uniform speed by clock- 
work, or at a speed proportional 
to the speed of the traction, 
through gearing, on which the 
extension of the spring is regis- 
tered by a pencil. From the 
average height of the diagram 
drawn by the pencil above the 
Fig. 193. zero-line the average pulling force 

in pounds is obtained, and this 
multiplied by the distance traversed, in feet, gives- the work done, in 
foot-pounds. The product divided by the time in minutes and by 33,000 
gives the horse-power. 

The Prony brake is the typical form of absorption dynamometer. 
(See Fig. 193, from Flather on Dynamometers.) 

Primarily this consists of a lever connected to a revolving shaft or pulley 
in such a manner that the friction induced between the surfaces in contact 
will tend to rotate the arm in the direction in which, the shaft revolves. 
This rotation is counterbalanced by weights P, hung in the scale-pan at 
the end of the lever. In order to measure the power for a given number 
of revolutions of pulley, we add weights to the scale-pan and screw up 
on bolts b,b, until the friction induced balances the weights and the lever 
is maintained in its horizontal position while the revolutions of the shaft 
per minute remain constant. 

For small powers the beam is generally omitted — the friction being 
measured by weighting a band or strap thrown over the pulley. Ropes 
or cords are often used for the same purpose. 

Instead of hanging weights in a scale-pan, as in Fig. 107 : the friction 
may be weighed on a platform-scale; in this case, the direction of rotation 
being the same, the lever-arm will be on the opposite side of the shaft. 

In a modification of this brake, the brake-wheel is keyed to the shaft, 
and its rim is provided with inner flanges which form an annular trough 
for the retention of water to keep the pulley from heating. A small 
stream of water constantly discharges into the trough and revolves with 
the pulley — the centrifugal force of the particles of water overcoming the 
action of gravity; a waste-pipe with its end flattened is so placed in the 
trough that it acts as a scoop, and removes all surplus water. The brake 
consists of a flexible strap to which are fitted blocks of wood forming the 
rubbing-surface; the ends of the strap are connected by an adjustable 
bolt-clamp, by means of which any desired tension may be obtained. 
The horse-power or work of the shaft is determined from the following: 
Let W = work of shaft, equals power absorbed, per minute; 

P = unbalanced pressure or weight in pounds, acting on lever- 
arm at distance L; 
L = length of lever-arm in feet from center of shaft ; 
V = velocity of a point in feet per minute at distance L, if arm 

were allowed to rotate at the speed of the shaft ; 
N = number of revolutions per minute; 
H.P. = horse-power. 



DYNAMOMETERS. 



1281 



Then will W = PV =2 nLNP. 

Since H.P. = PV -5- 33,000, we have H.P. = 2 nLNP -*- 33,000. 

If L = 33 + 2 ?r, we obtain H.P. = NP -5- 1000. 33-^-2 « is practically 
5 ft. 3 in., a value often used in practice for the length of arm. 

If the rubbing-surface be too small, the resulting friction will show 
great irregularity — probably on account of insufficient lubrication ■ — 
the jaws being allowed to seize the pulley, thus producing shocks and 
sudden vibrations of the lever-arm. 

Soft woods, such as bass, plane-tree, beech, poplar, or maple, are all 
to be preferred to the harder woods for brake-blocks. The rubbing-sur- 
face should be well lubricated with a heavy grease. 

The Alden Absorption-dynamometer. (G. I. Alden, Trans. A. S. 
M. E., vol. xi, 958; also xii, 700 and xiii, 429.) — This dynamometer is a 
friction-brake, which is capable in quite moderate sizes of absorbing 
large powers with unusual steadiness and complete regulation. A 
smooth cast-iron disk is keyed on the rotating shaft. This is inclosed 
in a cast-iron shell, formed of two disks and a ring at their circumference, 
which is free to revolve on the shaft. To the interior of each of the sides 
of the shell is fitted a copper plate, inclosing between itself and the side a 
water-tight space. Water under pressure from the city pipes is admitted 
into each of these spaces, forcing the copper plate against the central disk. 
The chamber inclosing the disk is filled with oil. To the outer shell is 
fixed a weighted arm, which resists the tendency of the shell to rotate 
with the shaft, caused by the friction of the plates against the central 
disk. Four brakes of this type, 56 in. diam., were used in testing the 
experimental locomotive at Purdue University {Trans. A. S. M. E., 
xiii, 429). Each was designed for a maximum moment of 10,500 foot- 
pounds with a water-pressure of 40 lbs. per sq. in. The area in effective 
contact with the copper plates on either side is represented by an annular 
surface having its outer radius equal to 28 ins. and its inner radius equal 
to 10 ins. The apparent coefficient of friction between the plates and the 
disk was 31/2%. : 

Capacity of Friction-brakes. — W. W. Beaumont (Proc. Inst. C. E.. 
1889) has deduced a formula by means of which the relative capacity of 
brakes can be compared, judging from the amount of horse-power ascer- 
tained by their use. 

If W = width of rubbing-surface on brake-wheel in inches; V = vel. 
of point on circum. of wheel in feet per minute; K = coefficient; then 
K= WV + H.P. 

Prof. Flather obtains the values of K given in the last column of the 
subjoined table: ? 






Brake- 
pulley. 



Design of Brake. 



150 
148.5 
146 
180 
150 
150 
142 
100 
76.2 
290\ 
250 f 
3221 
290/ 



33 

33.38 
32.19 
32 

32 



38.31 
126.1 
191 



273/4 



Royal Ag. Soc, compensating. . . . 

McLaren, compensating. 

McLaren, water-cooled arid comp 
Garrett, water-cooled and comp . 
Garrett, water-cooled and comp . 

Schoenheyder, water-cooled 

Balk 

Gately & Kletsch, water-cooled . . 
Webber, water-cooled 

Westinghouse, water-cooled 

Westinghouse, water-cooled . 



802 
741 
749 
282 

1385 
209 

84.7 
465 



The above calculations for eleven brakes give values of K varying from 
84.7 to 1385 for actual horse-powers tested, the average being K = 655. 



1282 ICE-MAKING OR REFRIGERATING MACHINES. 

Instead of assuming an average coefficient, Prof. Flather proposes the 
following: 

Water-cooled brake, non-compensating, K = 400; W= 400 H.P. -*■ V. 

Water-cooled brake, compensating, If = 750; W = 75Q H.P. -r- V. 

Non-cooling brake, with or without compensating device, K = 900; W — 
900 H.P. + V. 

A brake described in Am. Mach., July 27, 1905, had an iron water- 
cooled drum, 30 in. diam., 20 in. face, with brake blocks of maple attached 
to an iron strap nearly surrounding the drum. At 250 r.p.m., or a cir- 
cumferental speed of 1963 ft. per min., the limit of its capacity was about 
140 H.P.; above that power the blocks took fire. At 140 H.P. the total 
surface passing under the brake blocks per minute was 3272 sq. ft., or 
23.37 per H.P. This corresponds to a value of K = 285. 

Several forms of Prony brake, including rope and strap brakes, are 
described by G. E. Quick in Am. Mach., Nov. 17, 1908. Some other 
forms are shown in Am. Electrician, Feb., 1903. 

A6000H.P. Hydraulic Absorption Dynamometer, built by the West- 
inghouse Machine Co., is described by E. H. Longwell in Eng. News, 
Dec. 30, 1909. It was designed for testing the efficiency of the Melville 
and McAlpine turbine reduction gear (seepage 1071). This dynamometer 
consists of a rotor mounted on a shaft coupled to the reduction gear and 
rotating within a closed casing which is prevented from turning by a 
6i ft. lever arm, the end of which transmits pressure through an I-beam 
lever to a platform scale. The rotor carries several rows of steam turbine 
vanes and the casing carries corresponding rows of stationary vanes, so 
arranged as to baffle and agitate the water passing through the brake, 
which is heated to boiling temperature by the friction. The dynamom- 
eter was run for 40 hours continuously, and proved to be a highly 
accurate instrument. 

Transmission Dynamometers are of various forms, as the Batchelder 
^dynamometer, in which the power is transmitted through a "train-arm" 
of bevel gearing, with its modifications, as the one described by the author 
in Trans. A. I. M. E., viii, 177, and the one described by Samuel Webber 
in Trans. A, S. M. E., x, 514; belt dynamometers, as the Tatham; the 
Van Winkle dynamometer, in which the power is transmitted from a 
revolving shaft to another in line with it, the two almost touching, 
through the medium of ceiled springs fastened to arms or disk keyed to 
the shafts; the Brackett and the Webb cradle dynamometers, used for 
measuring the power required to run dynamo-electric machines. De- 
scriptions of the four last named are given in Flather on Dynamometers. 

The Kenerson transmission dynamometer is described in Trans. A. S< 
M. E., 1909. It has the form of a shaft coupling, one part of which con- 
tains a cavity filled with oil and covered by a flexible copper diaphragm. 
The other part, by means of bent levers and a thrust ball-bearing, brings 
an axial pressure on the diaphragm and on the oil, and the pressure of the 
oil is measured by a gauge. 

Much information on various forms of dynamometers will be found in 
Trans. A. S. M. E., vols, vii to xv, inclusive, indexed under Dynamometers. 

ICE-MAKING OR REFRIGERATING 
MACHINES. 

References. — An elaborate discussion of the thermodynamic theory 
of the action of the various fluids used in the production of cold was 
published by M. Ledoux in the Annates des Mines, and translated in Van 
Nostrand's Magazine in 1879. This work, revised and additions made in 
the light of recent experience by Professors Denton, Jacobus, and Riesen- 
berger, was reprinted in 1892. (Van Nostrand's Science Series, No. 46.) 
The work is largely mathematical, but it also contains much information 
of immediate practical value, from which some of the matter given below 
is taken. Other references are Wood's Thermodynamics, Chap. V, and 
numerous papers bv Professors Wood, Denton, jacobus, and Linde in 
Trans. A. S. M. E., vols, x to xiv Johnson's Cyclopaedia, article on 
Refrigeratins'-machines : and the following books: Siebel's Compend of 
Mechanical Refrigeration; Modern Refrigerating: Machinery, by Lorenz, 
translated by Pope; Refrigerating Machines, by Gardner T. Voorhees; Re- 



ICE-MAKING OR REFRIGERATING MACHINES. 1283 

frigeration, by J. Wemyss Anderson, and Refrigeration, Cold Storage and 
Ice-making, by A. J. Wallis-Taylor. For properties of Ammonia and Sul- 
phur Dioxide, see papers by Professors Wood and Jacobus, Trans. A. S. 
M. E., vols, x and xii. 

For illustrated descriptions of refrigerating-machines, see catalogues of 
builders, as Frick & Co., Waynesboro, Pa.; De La Vergne Refrigerating- 
machine Co., New York; Vilter Mfg. Co., Milwaukee; York Mfg., York, Co., 
Pa.; Henry Vogt Machine Co., Louisville, Ky.; Carbondale Machine Co., 
Carbondale, Pa. ; and others. See also articles in Tee and Refrigeration. 

Operations of a Refrigerating-machine. — Apparatus designed for 
refrigerating is based upon the following series of operations: 

Compress a gas or vapor by means of some external force, then relieve 
it of its heat so as to diminish its volume; next, cause this compressed gas 
or vapor to expand so as to produce mechanical work, and thus lower 
its temperature. The absorption of heat at this stage by the gas, in 
resuming its original condition, constitutes the refrigerating effect of the 
apparatus. 

A refrigerating-machine is a heat-engine reversed. 

From this similarity between heat-motors and freezing-machines it 
results that all the equations deduced from the mechanical theory of heat 
to determine the performance of the first, apply equally to the second. 

The efficiency depends upon the difference between the extremes of 
temperature. 

The useful effect of a refrigerating-machine depends upon the ratio 
between the heat-units eliminated and the work expended in compressing 
and expanding. 

This result is independent of the nature of the body employed. 

Unlike the heat-motors, the freezing-machine possesses the greatest 
efficiency when the range of temperature is small, and when the final 
temperature is elevated. 

If the temperatures are the same, there is no theoretical advantage in 
employing a gas rather than a vapor in order to produce cold. 

The choice of the intermediate body would be determined by practical 
considerations based on the physical characteristics of the body, such as 
the greater or less facility for manipulating it, the extreme pressures 
required for the best effects, etc. 

Air offers the double advantage that it is everywhere obtainable, and 
that we can vary at will the higher pressures, independent of the tempera- 
ture of the refrigerant. But to produce a given useful effect the apparatus 
must be of larger dimensions than that required by liquefiable vapors. 

The maximum pressure is determined by the temperature of the con- 
denser and the nature of the volatile liquid; this pressure is often very 
high. 

When a change of volume of a saturated vapor is made under constant 
pressure, the temperature remains constant. The addition or subtraction 
of heat, which produces the change of volume, is represented by an 
increase or a diminution of the quantity of liquid mixed with the vapor. 

On the other hand, when vapors, even if saturated, are no longer in 
contact with their liquids, and receive an addition of heat either through 
compression by a mechanical force, or from some external source of heat, 
they comport themselves nearly in the same way as permanent gases, 
and become superheated. 

It results from this property, that refrigerating-machines using a 
liquefiable gas will afford results differing according to the method of 
working, and depending upon the state of the gas, whether it remains 
constantly saturated, or is superheated during a part of the cycle of 
working. 

The temperature of the condenser is determined by local conditions. 
The interior will exceed by 9° to 18° the temperature of the water fur- 
nished to the exterior, this latter will vary from about 52° F., the 
temperature of water from considerable depth below the surface, to 
about -95° F., the temperature of surface-water in hot climates. The 
volatile liquid emploved in the machine ought not at this temperature to 
have a tension above that which can be readily managed by the apparatus. 

On the other hand, if the tension of the gas at the minimum temperature 
is too low, it becomes necessary to give to the compression-cylinder 
large dimensions, in order that the weight of vapor compressed by a 



1284 ICE-MAKING OR REFRIGERATING MACHINES. 



single stroke of the piston shall be sufficient to produce a notably useful 
effect. 

These two conditions, to which may be added others, such as those 
depending upon the greater or less facility of obtaining the liquid, upon 
the dangers incurred in its use, either from its inflammability or unhealth- 
fulness, and finally upon its action upon the metals, limit the choice to a 
small number of substances. 

The gases or vapors generally available are: sulphuric ether, sulphurous 
oxide, ammonia, methylic ether, and carbonic acid. 

The following table, derived from Regnault, shows the tensions of the 
vapors of these substances at different temperatures between — 22° and 
+ 104°. 



Pressures 


and Boiling-points of Liquids available for Use 






in Refrigerating-machines. 






Temp. 
















of 
Ebulli- 




Tension of Vapor, in lbs. per s 


q. in., above Zero. 




tion. 
















Deg. 


Sul- 
phuric 
Ether. 


Sulphur 


Ammonia. 


Methylic 


Carbonic 


Pictet 


Ethyl 
Chloride. 


Fahr. 


Dioxide. 


Ether. 


Acid. 


Fluid. 


— 40 






10.22 
13.23 
16.95 
21.51 
27.04 










31 














— 22 


"YM" 


5.56 
7.23 
9.27 


11.15 

13.85 
17.06 






2. 13 


-13 


251.6 
292.9 




2.80 


- 4 


13.5 


3.63 


5 


1.70 


11.76 


33.67 


20.84 


340.1 


16.2 


4.63 


14 


2.19 


14.75 


41.58 


25.27 


393.4 


19.3 


5.84 


23 


2.79 


18.31 


50.91 


30.41 


453.4 


22.9 


7.28 


32 


3.55 


22.53 


61.85 


36.34 


520.4 


26.9 


9.00 


41 


4.45 


27.48 


74.55 


43.13 


594.8 


31.2 


11.01 


50 


5.54 


33.26 


89.21 


50.84 


676.9 


36.2 


13.36 


59 


6.84 


39.93 


105.99 


59.56 


766.9 


41.7 


16.10 


68 


8.38 


47.62 


125.08 


69.35 


864.9 


48.1 


19.26 


77 


10.19 


56.39 


146.64 


80.28 


971.1 


55,6 


22.90 


86 


12.31 


66.37 


170.83 


92.41 


1085.6 


64.1 


27.05 


95 


14.76 
17.59 


77.64 
90.32 


197.83 
227.76 




1207.9 
1338.2 


73.2 
82.9 


31.78 


104 




37.12 









The table shows that the use of ether does not readily lead to the pro- 
duction of low temperatures, because its pressure becomes then very 
feeble. 

Ammonia, on the contrary, is well adapted to the production of low 
temperatures. 

Methylic ether yields low temperatures without attaining too great 
pressures at the temperature of the condenser. Sulphur dioxide readily 
affords temperatures of - 14 to - 5, while its pressure is only 3 to 4 
atmospheres at the ordinary temperature of the condenser. These latter 
substances then lend themselves conveniently for the production of cold 
by means of mechanical force. 

The " Pictet fluid " is a mixture of 97 % sulphur dioxide and 3 % carbonic 
acid. At atmospheric pressure it affords a temperature 14° lower than 
sulphur dioxide. (It is not now used — 1910.) 

Carbonic acid is in use to a limited extent, but the relatively greater 
compactness of compressor that it requires, and its inoffensive character, 
are leading to its recommendation for service on shipboard. 

Certain ammonia plants are operated with a surplus of liquid present 
during compression, so that superheating is prevented. This practice is 
known as the "cold " or " wet " system of compression. 

Ethyl chloride, C>H 5 C1. is a colorless gas which at atmospheric pressure 
condenses to a liquid at 54.5° F. The latent heat at 23° F. is given at 174 
B.T.U. Density of the gas (air = l) = 2.227. Specific heat at constant 
pressure, 0.274; at constant volume, 0.243. 



SULPHUR DIOXIDE AND AMMONIA GAS. 



1285 



Nothing definite is known regarding the application of methylic ether or 
of the petroleum product chymogene in practical refrigerating service. 
The inflammability of the latter and the cumbrousness of the compressor 
required are objections to its use. 



PROPERTIES OF SULPHUR DIOXIDE AND 
AMMONIA GAS. 

Ledoux's Table for Saturated Sulphur-dioxide Gas. 

Heat-units expressed in B.T.U. per pound of sulphur dioxide. 





1 u 


s 


is 


*s 


a 






^ 


11^ 




o 

03-3 


1-2 


3 fe s 


J- 


Increase of 
Volume dur- 
ing Evapo- 
ration. 
u 


Density of Va- 
por or Weigh 
of 1 cu.ft. 
1 + V 




Absolut* 
sure in 
sq. in. 

P -s- 


Total H 
reckom 
32° F. 
A 




+3 O *» 

5« 


HeatEq 
of Ext< 
Work. 
AP 


15* 

c -2 


Deg. F. 


Lbs. 


B.T.U. 


B.T.U. 


B.T.U. 


B.T.U. 


B.T.U. 


Cu.ft. 


Lbs. 


-22 


5.56 


157.43 


-19.56 


176.99 


13.59 


163.39 


13.17 


0.076 


-13 


7.23 


158.64 


- 16.30 


174.95 


13.83 


161.12 


10.27 


.097 


- 4 


9.27 


159.84 


- 13.05 


172.89 


14.05 


158.84 


8.12 


.123 


5 


11.76 


161.03 


- 9.79 


170.82 


14.26 


156.56 


6.50 


.153 


14 


14.74 


162.20 


- 6.53 


168.73 


14.46 


154.27 


5.25 


.190 


23 


18.31 


163.36 


- 3.27 


166.63 


14.66 


151.97 


4.29 


.232 


32 


22.53 


164.51 


0.00 


164.51 


14.84 


149.68 


3.54 


.282 


41 


27.48 


165.65 


3.27 


162.38 


15.01 


147.37 


2.93 


.340 


50 


33.25 


166.78 


6.55 


160.23 


15.17 


145.06 


2.45 


.407 


59 


39.93 


167.90 


9.83 


158.07 


15.32 


142.75 


2.07 


.483 


68 


47.61 


168.99 


13.11 


155.89 


15.46 


140.43 


1.75 


.570 


77 


56.39 


170.09 


16.39 


153.70 


15.59 


138.11 


1.49 


.669 


86 


66.36 


171.17 


19.69 


151.49 


15.71 


135.78 


1.27 


.780 


95 


77.64 


172.24 


22.98 


149.26 


15.82 


133.45 


1.09 


.906 


104 


90.31 


173.30 


26.28 


147.02 


15.91 


131.11 


0.91 


1.046 



E. F. Miller (Trans. A. S. M. E., 1903) reports a series of tests on the 
pressure of SO2 at various temperatures, the results agreeing closely with 
those of Regnault up to the highest figure of the latter, 149° F., 178 lbs. 
absolute. He gives a table of pressures and temperatures for every 
degree between — 40° and 217°. The results obtained at temperatures 
between 113° and 212° are as below: 
Temp. °F. 

113 122 131 140 149 158 167 176 194 203 212 
Pres. lbs. per sq. in. 

104.4 120.1 137.5 156.7 179.5 203.8 230.7 260.5 331.1 371.8 418. 

Density of Liquid Ammonia. (D'Andreff, Trans. A.S.M. E., x, 641. 

At temperature C -10 -5 5 10 15 20 

At temperature F .... +14 23 32 41 50 59 68 

Density .6492 .6429 .6364 .6298 .6230 .6160 .6086 

These may be expressed very nearly by 

8 = 0.6364 - 0.0014£° Centigrade; 
8 = 0.6502 - 0.0007777 10 Fahr. 

Latent Heat of Evaporation of Ammonia. (Wood, Trans. A. S. 
M. E„ x, 641.) 

h e = 555.5 - 0.613 T - 0.000219T 2 (in B.T.U. ,° F); 

Ledoux found h e = 583.33 - 0.5499 T - 0.0001 173 T 72 . 

For experimental values at different temperatures determined by Prof. 
Denton, see Trans. A. S. M, E„ xii, 356. For calculated values, see 
vol. x, 646, 



ICE-MAKING OR REFRIGERATING MACHINES. 



Properties of the Saturated Vapor of Ammonia. 

(Wood's Thermodynamics.) 



Temperature. 


Pressure, 
Absolute. 


Heat of 
Vapori- 
zation, 
thermal 


Volume 
of Vapor 


Volume 
of Liquid 

per lb., 

cu.ft. 


Weight 

of a cu. 

ft. of 

Vapor. 


Degs. 


Abso- 


Lbs. per 


Lbs. per 


per lb., 
cu. ft. 


F. 


lute, F. 


sq.ft. 


sq. in. 


units. 


lbs. 


- 40 


420.66 


1540.7 


10.69 


579.67 


24.372 


0.0234 


0.0410 


- 35 


425.66 


1773.6 


12.31 


576.69 


21.319 


.0236 


.0468 


- 30 


430.66 


2035.8 


14.13 


573.69 


18.697 


.0237 


.0535 


- 25 


435.66 


2329.5 


16.17 


570.68 


16.445 


.0238 


.0608 


- 20 


440.66 


2657.5 


18.45 


567.67 


14.507 


.0240 


.0689 


- 15 


445.66 


3022.5 


20.99 


564.64 


12.834 


.0242 


.0779 


-, 10 


450.66 


3428.0 


23.80 


561.61 


11.384 


.0243 


.0878 


- 5 


455.66 


3877.2 


26.93 


558.56 


10.125 


.0244 


0988 





460.66 


4373.5 


30.37 


555.50 


9.027 


.0246 


.1108 


5 


465.66 


4920.5 


34.17 


552.43 


8.069 


.0247 


1239 


10 


470.66 


5522.2 


38.34 


549.35 


7.229 


.0249 


1383 


15 


475.66 


6182.4 


42.93 


546.26 


6.492 


.0250 


'1544 


20 


480.66 


6905.3 


47.95 


543.15 


5.842 


.0252 


1712 


25 


485.66 


7695.2 


53.43 


540.03 


5.269 


.0253 


1898 


30 


490.66 


8556.6 


59.41 


536.92 


4.763 


.0254 


.2100 


35 


495.66 


9493.9 


65.93 


533.78 


4.313 


.0256 


2319 


40 


5o0.66 


10512 


73.00 


530.63 


3.914 


.0257 


2555 


45 


505.66 


11616 


80.66 


527.47 


3.559 


.0259 


'2809 


50 


510.66 


12811 


88.96 


524. 30 


3.242 


.0261 


..3085 


55 


515.66 


14102 


97.93 


521.12 


2.958 


.0263 


3381 


60 


520.66 


15494 


107.60 


517.93 


2.704 


.0265 


.3698 


65 


525.66 


16993 


118.03 


514.73 


2.476 


.0266 


.4039 


70 


530.66 


18605 


129.21 


511.52 


2.271 


.0268 


.4403 


75 


535.66 


20336 


141.25 


508.29 


2.087 


.0270 


.4793 


80 


540.66 


22192 


154.11 


505.05 


I 920 


.0272 


.5208 


85 


545.66 


24178 


167.86 


501.81 


1.770 


.0273 


.5650 


90 


550.66 


26300 


182.8 


498.11 


1.632 


.0274 


6128 


95 


555.66 


28565 


198.37 


495.29 


1.510 


.0277 


.6623 


100 


560.66 


30980 


215.14 


492.01 


1.398 


.0279 


.7153 


105 


565.66 


33550 


232.98 


488.72 


1.296 


.0281 


.7716 


110 


570.66 


36284 


251.97 


485.42 


1.203 


.0283 


.8312 


115 


575.66 


39188 


272.14 


482.41 


1.119 


.0285 


8937 


120 


580.66 


42267 


293.49 


478.79 


1.045 


.0287 


9569 


125 


585.66 


45528 


.316.16 


475.45 


0.970 


.0289 


1 0309 


130 


590.66 


48978 


340.42 


472.11 


0.905 


.0291 


1 1049 


135 


595.66 


52626 


365.16 


468.75 


0.845 


.0293 


1.1834 


140 


600.66 


56483 


392.22 


465.39 


0.791 


.0295 


1.2642 


145 


605.66 


60550 


420.49 


462.01 


0.741 


.0297 


1.3495 


150 


610.66 


64833 


450.20 


458.62 


0.695 


.0299 


1 4388 


155 


615.66 


69341 


481.54 


455.22 


0.652 


.0302 


1.5337 


160 


620.66 


74086 


514.40 


451.81 


0.613 


.0304 


1.6343 


165 


625.66 


79071 


549.04 


448.39 


0.577 


.0306 


1.7333 



Density of Ammonia Gas. — Theoretical, 0.5894; experimental, 
0.596. Regnault (Trans. A. S. M. E., x, 633). 

Specific Heat of Liquid Ammonia. (Wood, Trans. A. S. M. E., 
x, 645.) — The specific heat is nearly constant at different temperatures, 
and about equal to that of water, or unity. From 0° to 100° F., it is 
c = 1.096 - 0.00127 1 , nearly. 

In a later paper by Prof. Wood (Trans. A. S. M. E., xii, 136) he gives 
a higher value, viz., c= 1.12136 + 0.000438 T. 

L. A. Elleau and Wm. D. Ennis (Jour. Franklin Inst., April, 1898) 
give the results of nine determinations, made between 0° and 20° C, 
which range from 0.983 to 1.056, averaging 1.0206. Von Strombeck 



PROPERTIES OF AMMONIA. 



1287 



{Jour. Franklin Inst., Dec, 1890) found the specific heat between 62° and 
31° C. to be 1.22876. Ludeking and Starr {Am. Jour. Science, iii, 45, 200) 
obtained 0.886. Prof. Wood deduced from thermodynamic equations 
c = 1.093 at —34° F. or —38° C., and Ledoux in like manner finds 
c = 1.0058+ 0.003658 t° C. Elleau and Ennis give Ledoux's equation 
with a new constant derived from their experiments, thus c = 0.9834 + 
0.003658 £° C. 

50° F. 
8 10 12 14 16 18 

.966 .960 .953 .945 .938 .931 
26 28 30 32 34 36 
.907 .902 .897 .892 .888 .884 
Specific Heat of Ammonia Vapor at the Saturation Point. (Wood, 
Trans. A. S. M. E., x, 644.) — For the range of temperatures ordinarily 
used in engineering practice, the specific heat of saturated ammonia is 
negative, and the saturated vapor will condense with adiabatic expansion. 
The liquid will evaporate with the compression of the vapor, and when all 
is vaporized will superheat. 

Regnault (Rel. des. Exp., ii, 162) gives for specific heat of ammonia-gas 
0.50836. (Wood, Trans. A. S. M. E., xii, 133.) 

Weight of Superheated Ammonia Vapor at 15.67 lbs. Gauge Pressure 
( = 30.67 lbs. abs.) (C. E. Lucke, Ice and Refrigeration, Mar., 1908.) 
Weight at 0° F. 0.1107 lbs. 



Strength of Aqua Ammonia at ( 

% NH 3 by wt. 2 4 6 

Sp.gr. 0.986 .979 .972 

% NH 3 20 22 24 

Sp.gr. 0.925 .919 .913 



Temp. 


Lb. per 


Temp. 


Lb. per 


Temp. 


Lb. per 


Temp. 


Lb. per 


°F. 


cu. ft. 


°F. 


cu.ft. 


°F. 


cu. ft. 


°F. 


cu. ft. 


5 


0.1095 


25 


0.1050 


125 


0.08706 


225 


0.07438 


10 


0.1085 


50 


0.09986 


150 


0.08351 


250 


0.07176 


15 


0.1072 


75 


0.0952 


175 


0.08033 


275 


0.06932 


20 


0.1061 


100 


0.09096 


200 


0.07713 


300 


0.06703 


Specif 


ic Heat 


and Available Lat 


jnt Hea 


t of Hot 


Liquid Ammonia 


at 15.67 


bs. gauge 


; pressure. (Lucke 


) Latent 


heat at 1 


5.67 lbs. 


and 0° F. 


= 550.5 


B.T.U. 


Specific heat = 1.0 


96 - 0.0 


012 T°. 






Temp. 

of 
Liquid 
Supply. 


Specific 
Heat. 


Correc- 
tion for 
Cooling. 


Available 

Latent 

Heat for 

Saturated 

Vapor. 


Temp. 

of 
Liquid 
Supply. 


Specific 
Heat. 


Correc- 
tion for 
Cooling. 


Available 
Latent 
Heat for 
Satu- 
rated 
Vapor. 


5 


1.090 


5.45 


550.05 


55 


1.030 


56.65 


498.85 


10 


1.084 


10.84 


544.66 


60 


1.024 


61.44 


494.06 


15 


1.078 


16.17 


539.33 


65 


1.018 


66.17 


489.33 


20 


1.072 


21.44 


534.06 


70 


1.012 


70.84 


484.66 


25 


1.066 


26.65 


528.85 


75 


1.006 


-75.45 


480.05 


30 


1.060 


31.80 


523.70 


80 


1.000 


80.00 


475.50 


35 


1.054 


36.89 


518.61 


85 


0.994 


84.49 


471.01 


40 


1.048 


41.92 


513.68 


90 


0.988 


88.92 


466.58 


45 


1.042 


46.89 


508.61 


95 


0.982 


93.29 


462.21 


50 


1.036 


51.80 


503.70 


100 


0.976 


97.60 


457.90 



The latent heat for saturated vapor is subject to three corrections in 
determining the available latent heat. First, for the temperature of the 
liquid which must be cooled from its supply temperature to the tem- 
perature corresponding to the back pressure, as in the table above; 
second, for wetness of vapor, a deduction of 5.555 B.T.U. for each 1% of 
moisture; third, for superheat of vapor in case it leaves the expansion 
coils or cooler hotter than the temperature corresponding to the pressure, 
an addition of the number of degrees superheat multiplied by the specific 
heat, taken as 0.508. 



1288 ICE-MAKING OR REFRIGERATING MACHINES. 



"Solubility of Ammonia. (Siebel.) — One pound of water will dis- 
solve the following weights of ammonia at the pressures and temperatures 
F° stated. 



Abs. 








Abs. 








Abs. 








Press. 


32° 


68° 


104° 


Press. 


32° 


68° 


104° 


Press. 


32° 


68° 


104° 


per 








per 








per 








sq.in. 








sq.m. 






Tb~ 


sq. m. 


~Tb7 






lb. 


lb. 


lb. 


lb. 


lb. 


lb. 


lb. 


lb. 


lb. 


lb. 


14.67 


0.899 


0.518 


0.338 


21.23 


1.236 


0.651 


0.425 


27.99 


1.603 


0.780 


0.486 


15.44 


0.937 


0.635 


0.349 


22.19 


1.283 


0.669 


0.434 


28.95 


1.656 


0.801 


0.493 


16.41 


0.980 


0.556 


0.363 


23.16 


1.330 


0.685 


0.445 


30.88 


1.758 


0.842 


0.511 


17.37 


1.029 


4). 574 


0.378 


24.13 


1.388 


0.704 


0.454 


32.81 


1.861 


0.881 


0.530 


18.34 


1.077 


0.594 


0.391 


25.09 


1.442 


0.722 


0.463 


34.74 


1.966 


0.919 


0.547 


19.30 


1.126 


0.613 


0.404 


26.06 


1.496 


0.741 


0.472 


36.67 


2.070 


0.955 


0.565 


20.27 


1.177 


0.632 


0.414 


27.02 


1.549 


0.761 


0.479 


38.60 




0.992 


0.579 



Properties of Saturated Vapors . — The figures in the following table 
are given by Lorenz, on the authority of Mollier and of Zeuner. 





Heat of 
Vaporization, 


Heat of Liquid, 
B.T.U. per lb. 


Absolute 
Pressure, 


Volume of 
lib., 


c F 


B.T.U. per lb. 


lbs. per sq. in. 


cubic feet. 




NH 3 


C0 2 


S0 2 


NH 3 


C0 2 


S0 2 


NH 3 
27.1 


C0 2 


S0 2 


NH 3 
10 33 


C0 2 
312 


S0 2 


- 4° 


589 


117 6 


171 


-31.21 


-17.19 


-11.16 


288.7 


9 27 


8 06 


+ 14° 


580 


110 7 


168 2 


-15.89 


- 9.00 


- 5.69 


41.5 


385.4 


14 75 


6 92 


729 


5 27 


32° 


569 


99 8 


164 2 











61.9 


503.5 


22 53 


4 77 


167 


3 59 


50° 


555 5 


86 


158 9 


16.51 


10.28 


5.90 


89.1 


650.1 


33.26 


3 38 


170 


2 44 


68° 


539 9 


66 5 


152 5 


33.58 


23.08 


12.03 


125.0 


826.4 


47.61 


2,47 


083 


1 71 


86° 


521 4 


27.1 


144 8 


51.28 


45.45 


18.34 


170.8 


1040. 


66.36 


1.83 


048 


1 ?.?, 


104° 


500.4 




135.9 


69.58 




24.88 


227.7 




90.30 


1.39 




0.88 



The figures for CO2 in the above table differ widely from those of 
Regnault, and are no doubt more reliable. 

Heat Generated by Absorption of Ammonia. (Bert helot, from 
Siebel.) — Heat developed when a solution of 1 lb. NH 3 in n lbs. water 
is diluted with a great amount of water = Q = 142/w B.T.U. Assuming 
925 B.T.U. to be developed when 1 lb. NH 3 is absorbed by a great deal 
(say 200 lbs.) of water, the heat developed in making solutions of different 
strengths (1 lb. NH 3 to n lbs. water) = Q t = 925 - 142/rc, B.T.U. Heat 
developed when b lbs. NH 3 is added to a solution of 1 lb. NH 3 + n lbs. 
water = Q 3 = 925 - 142 (2 b + W)/n B.T.U. 

Let the weak liquor enter the absorber with a strength of 10%,= 1 lb. 
NH 3 + 9 lbs. water, and the strong liquor leave the absorber with a 
strength of 25%, = 3 lbs. NH 3 + 9 lbs. water, b = 2, n = 9; Q 3 = 925 X 
2 — 142 (4+ 4)/9 = 1724 B.T.U. Hence by dissolving 2 lbs. of ammonia 
gas or vapor in a solution of 1 lb. ammonia in 9 lbs. water we obtain 
12 lbs. of a 25% solution, and the heat generated is 1724 B.T.U. 

Cooling Effect, Compressor Volume, and Power Required. — The 
following table gives the theoretical results computed on the basis of 
a temperature in the evaporator of 14° F. and in the condenser of 68° F.; 
in the first three columns of figures the cooling agent is supposed to flow 
through the regulating valve with this latter temperature; in the last 
three it is previously cooled to 50° F. 

From the stroke-volume per 100,000 B.T.U. the minimum theoretical 
horse-power is obtained as follows: Adiabatic compression is assumed 
for the ratio of the absolute condenser pressure to that of the vaporizer, 
and the mean pressure through the stroke thus found, in lbs. per sq ft.; 
multiplying this by the stroke volume per hour and dividing by 1,980,000 
gives the net horse-power. The ratio of the mean effective pressure, 
M.P., to the vaporizer pressure, V.P., for different ratios of condenser 
pressure, C.P., to vaporizer pressure is given on the next page, , 



COMPARISON OF DIFFERENT COOLING AGENTS. 1289 



Cooling Effect, Compressor Volume, and Power Required, with 
Different Cooling Agents. (Lorenz.) 



Cooling Agent. 



1 . Temp, in front of regulating 

valve 

2. Vaporizer pressure, lbs. per 

sq. in 

3. Condenser pressure, lbs. per 

sq. in 

4. Heat of evaporation, B.T.U. 

per lb 

5. Heat imparted to the liquid 

6. Cold produced per lb. B.T.U 

7. Cooling agent circulated for 

yield of 100,000 B.T.U. per 
hour, lbs 

8. Stroke volume for 100,000 

B.T.U. per hour, cu. ft 

9. Minimum H.P. per 100,000 

B.T.U. per hour 

10. Ratio Heat of evap. -f- cold 

produced 

11. Ratio total work to minimum 

12. Total I.H.P. per 100,000 

B.T.U. per hour 

13. Cooling effect per I.H.P. hr.. 



NH 3 



68 

41.5 

125.0 

580.2 
49.47 
530.73 

188.4 

1,300 

4.98 

1.093 
1.175 

5.85 
17,100 



C0 2 



68 

385.4 

826.4 

110.7 
32.08 
78.62 

1272. 

292 

4.98 

1.40J 
1.513 

7.53 
13,300 



so 2 



68 

14.75 

47.61 

168.2 
17.72 
150.48 

664.3 

3,507 

4.98 

1.118 
1.202 

5.99 
16,700 



NH 3 



50 

41.5 

125.0 

580.2 
32.4 
547.8 

182.5 
1,264 

4.98 

1.059 
1.138 

5.67 
17,600 



( r> 2 



50 

385.4 

826.4 

110.7 
19.28 
91.42 

1094. 

242 

4.98 

1.211 
1.302 

6.48 
15,400 



S0 2 

50 

14.75 

47.61 

168.2 
11.59 
156.61 

638.5 

3,365 

4.98 

1.074 
1.155 

5.75 
17,400 



Ratios of Condenser Pressure, C. P., and Mean Effective Pres- 







SURE, M. P., TO 


Vaporizer Pressure, 


V. P. 






Ph 
> 


~Ph 

> 


Ph 

> 


Ph 
> 
•1- 


Ph 
> 


Ph 
> 


Ph 
> 


Ph 
> 


Ph 
> 


Ph 
> 


Ph 
> 


Ph 
> 


Ph 


Ph 


Pi 


Ph 


Ph 


Ph 


Ph 


Ph 


Ph 


Ph 


Ph 


Ph 


o 


£ 


o 


S 


O 


S 


O 


£ 


O 


§ 


O 


S 


1.0 


0. 


2.0 


0.752 


3.0 


1.249 


4.0 


1.684 


5.0 


1.947 


6.0 


2.216 


1.2 


0.186 


2,2 


0.865 


3 2 


1.344 


4 2 


1.711 


5.2 


2.006 


7 


2.454 


1.4 


0.350 


2.4 


0.970 


3 4 


1.414 


4.4 


1.766 


5.4 


2.062 


8,0 


2.666 


1.6 


0.487 


2 6 


1.070 


3 6 


1.491 


4 6 


1.829 


5 6 


2.116 


9 


2.858 


1.8 


0.630 


2.8 


1.163 


3.8 


1.564 


4.8 


1.891 


5.8 


2.168 


10.0 


3.036 



The minimum theoretical horse-power thus obtained is increased by 
the ratio of the heat of evaporation to the available cooling action (line 
4 -5- line 6, = line 10 of the table) and by an allowance for the resistance 
of the valves taken at 7.5% to obtain the total H.P. given in the table. 

To the theoretical horse-power given in line 12 Lorenz makes numerous 
additions, viz.: friction of the compression and driving machine 0.90, 
1.10, 0.90, 0.85, 0.95, 0.85 respectively for the six columns in the table; 
also H.P. for stirring 0.3; for cooling-water pumps, 0.45; for brine pumps, 
2.2; for transmission of power, 0.6, making the total H.P. for the six cases 
10.30, 12.18, 10.44, 10.07,10.98, \0.15. He also makes deductions from 
the theoretical generation of cold of 100,000 B.T.U. per hour, for a brewery 
cooling installation, for irregularities of valves, etc., for NH3 and SO2 
machines 10% and for CO2 machines 5%; for cooling loss through stirring 
765 B.T.U., through brine pumps 5610 B.T.U., and through radiation 
4500 B.T.U., making the net cooling for NH 3 and SO2 machines 79,125 
B.T.U. and for CO2 machines 84,125 B.T.U., and the cold generated per 
effective H.P. in the six cases, 7682, 6908, 7578, 7848, 7662, and 7796 
B.T.U. 

The figures given in the tables are not to be considered as holding 
generally or extended to other condenser and evaporator temperatures. 
Each change of condition requires a separate calculation. The final 



1290 ICE-MAKING OR REFRIGERATING MACHINES. 



results indicate that for the various cooling systems no appreciable 
difference exists in the work required for the same amount of cold delivered 
at the place where it is to be applied. 

Properties of Brine Used to Absorb Refrigerating Effect of 
Ammonia. (J. E. Denton, Trans. A.S. M. E., x, 799.) — A solution of 
Liverpool salt in well-water having a specific gravity of 1.17, or a weight 
per cubic foot of 73 lbs., will not sensibly thicken or congeal at 0° F. 

The mean specific heat between 39° and 16° Fahr. was found by Denton 
to be 0.805. Brine of the same specific gravity has a specific heat of 0.805 
at 65° Fahr., according to Naumann. 

Naumann's values are as follows (Lehr- und Handbuch der Thermochemie, 
1882): 

Specific heat 0.791 0.805* 0.863 0.895 0.931 0.962 0.978 

Specific gravity.. .1.187 1.170 1.103 1.072 1.044 1.023 1.012 
Properties of Salt Brine (Carbondale Calcium Co.) 

Deg. Baume 60° F 1 5 10 15 19 23 

Deg. Salinometer 60° F 4 20 40 60 80 100 

Sp. gravity 60° F 1.007 1.037 1.073 1.115 1.150 1.191 

Per cent of salt, by wt 1 5 10 15 20 25 

Wt. of 1.. gallon, lbs 8.40 8.65 8.95 9.30 9.60 9 94 

Wt. of 1 cu. ft., lbs 62.8 64.7 66.95 69.57 71.76 74.26 

Freezing point ° F 31.8 25.4 18. 6 12.2 6.86 1.00 

Specific heat 0.992 0.960 0.892 0.855 0.829 0.783 

Chloride of Calcium solution is commonly used instead of brine. 
According to Naumann, a solution of 1.0255 sp. gr. has a specific heat of 
0.957. A solution of 1.163 sp. gr. in the test reported in Eng'g, July 22, 
1887, gave a specific heat of 0.827. 

H. C. Dickinson (Science, April 23, 1909) gives the following values of the 
specific heat of solutions of chemically pure calcium chloride. 

Density Specific Heat Temperature, C. 

1.07 0.869+0.00057 4 (- 5° to + 15°) 

1.14 0.773 + 0.00064 4 (- 10° to + 20°) 

1.20 0.710 + 0.00064 t (- 20° to + 20°) 

1.26. 0.662 + 0.00064 t (- 25° to + 20°) 

The advantages of chloride of calcium solution are its lower freezing point 
and that it has little or no corrosive action on iron and brass. Calcium 
chloride is sold in the fused or granulated state, in steel drums, contain- 
ing about 75% anhydrous chloride and 25% water, or in solution contain- 
ing 40 to 50% anhydrous chloride, in tank cars. The following data 
are taken from the catalogue of the Carbondale Calcium Co. 

Properties of " Solvay " Calcium Chloride Solution. 



N£ 


, 






<£ 


. 






vj 


. 






a 


> 






a 


> 








> 






3 






o5 • 
mfa 
a> . 


3 

Wfa 


Ofe 




*fa 

05 . 


fQfa 


Ofe 


id 
s-.a 


e5 • 

o?fa 


% D S 


Z* 


'~C 


£Q 


<N& 


a^ 


fc<3 


£Q 


aw 


^ 


£Q 


Q 


m 


fa 


fa 


Q 


02 


fa 


fa 


Q 


Xfl 


Ph 


fa 


1. 


1.007 


1 


+31.10 


21 


1.169 


19 


+ 1.76 


32 


1.283 


30 


-54.40 


5.5 


1.041 


5 


27.68 


22 


1.179 


20 


- 1.48 


35 


1.316 


33 


-25.24 


11 


1.085 


10 


22.38 


23 


1.189 


21 


- 4.90 


35.5 


1.327 


34 


- 9.76 


17 


1.131 


15 


12.20 


26 


1.219 


24 


-17.14 


36.5 


1.338 


35 


+ 2.84 


20 


1.159 


18 


4.64 


29 


1.250 


27 


-32.62 


37.5 


1.349 


36 


14.36 



Quantity of 75% calcium chloride required to make solutions of different 

specific gravities and freezing points. 

Sp. gravity! ....1.250 1.225 1.200 1.175 1.150 1.125 1.100 

Lbs. per cu ft. solu- 
tion 28.06 25.06 22.05 19.15 16.26 13.47 10.70 

Lbs. per gallon 3.76 3.36 2.95 2.56 2.18 1.80 1.43 

Freezing point ° F. .-32.6 -19.5 -8.7 Zero +7.5 +13.3 +18 5 

* Interpolated. 



MACHINES USING DIFFERENT COOLING AGENTS. 1291 

Boiling points of calcium chloride solutions: 

Sp. Gr. at 59° F 1.104 1.185 1.268 1.341 1.383 solid at 59° 

Boiling point ° F . 215.6 221.0 230.0 240.8 248.0 266.0 282.2 306.5 

Sp. gr. at boiling point 1.085 1.119 1.209 1.308 1.365 1.452 1.526 1.619 

"Ice-melting Effect." — It is agreed that the term "ice-melting 
effect" means the cold produced in an insulated bath of brine, on the 
assumption that each 1-14 B.T.U. represents one pound of ice, this being, 
the latent heat of fusion of ice, or the heat required to melt a pound of ice 
at 32° to water at the same temperature. 

The performance of a machine, expressed in pounds or tons of "ice- 
melting capacity," does not mean that the refrigerating-machine would 
make the same amount of actual ice, but that the cold produced is equiva- 
lent to the effect of the melting of ice at 32° to water of the same tempera- 
ture. 

In making artificial ice the water frozen is generally about 70° F. when 
submitted to the refrigerating effect of a machine; second, the ice is 
chilled from 12° to 20° below its freezing-point; third, there is a dissipa- 
tion of cold, from the exposure of the brine tank and the manipulation of 
the ice-cans: therefore the weight of actual ice made, multiplied by its 
latent heat of fusion, 144 thermal units, represents only about three- 
fourths of the cold produced in the brine by the refrigerating fluid per 
I.H.P. of the engine driving the compressing-pumps. Again, there is 
considerable fuel consumed to operate the brine-circulating pump, the 
condensing-water and feed-pumps, and to reboil, or purify, the condensed 
steam from which the ice is frozen. This fuel, together with that wasted 
in leakage and drip water, amounts to about one-half that required to 
drive the main steam-engine. Hence the pounds of actual ice manu- 
factured from distilled water is just about half the equivalent of the 
refrigerating effect produced in the brine per indicated horse-power of the 
steam-cylinders. 

When ice is made directly from natural water by means of the "plate 
system," about half of the fuel, used with distilled water, is saved by 
avoiding the reboiling, and using steam expansively in a compound 
engine. 

Ether-machines, used in India, are said to have produced about 6 lbs. 
of actual ice per pound of fuel consumed. 

The ether machine is obsolete, because the density of the vapor of ether, 
at the necessary working-pressure, requires that the compressing-cylinder 
shall be about 6 times larger than for sulphur dioxide, and 17 times 
larger than for ammonia. 

Air-machines require about 1.2 times greater capacity of compressing 
cylinder, and are, as a whole, more cumbersome than ether machines, 
but they remain in use on shipboard. In using air the expansion must 
take place in a cylinder doing work, instead of through a simple expansion- 
cock which is used with vapor machines. The work done in the expansion- 
cylinder is utilized in assisting the compressor. 

The Allen Dense Air Machine takes for compression air of considerable 
pressure which is contained in the machine and in a system of pipes. The 
air at 60 or 70 lbs. pressure is compressed to 210 or 240 lbs. It is then 
passed through a coil immersed in circulating water and cooled to nearly 
the temperature of the water. It then passes into an expander, which is, 
in construction, a common form of steam-engine with a cut-off valve. 
This engine takes out of the air a quantity of heat equivalent to the 
work done by the air while expanding, to the original pressure of 60 or 
70 lbs., and reduces its temperature to about 90° to 120° F. below the 
temperature of the cooling water supply. The return stroke of the piston 
pushes the air out through insulated pipes to the places that are to be 
refrigerated, from which it is returned to the compressor. 

The air pushed out by the expander is commonly about 35 to 55 below 
zero F. In arrangements where not all the cold is taken out of the air 
by the refrigerating apparatus, the highly compressed air after cooling 
in the coil is further cooled by being brought in surface contact with the 
returning and still cold air, before entering the expander. By this means 
temperatures of 70 to 90 below zero may be obtained. 

The refrigerating effect in B.T.U. per minute is: Lbs. of air handled per 



1292 ICE-MAKING OR REFRIGERATING! MACHINES. 

min. X 0.2375 X difference of temperature of air passing out of ex- 
pander and of that returning to the machine. 

Carbon-dioxide Machines are in extensive use on shipboard. S. H. 
Bunnell (Eng. News, April 9, 1903) says there are over 1500 CO2 plants on 
shipboard. He describes a large duplex C0 2 compressor built by the 
Brown-Cochrane Co., Lorain, O. Tests of C0 2 machines by a committee of 
the Danish Agricultural Society were reported in 1899, in "Ice and Gold 
Storage," of London. Carbon-diosride machines are built also by Kroeschel 
Bros., Chicago. . 

Methyl-Chloride machines are made by Railway and Stationary Refrig- 
erating Co., New York City. The compressor is a rotary pump. When 
driven by an electric motor the complete apparatus is very compact, and 
is therefore suitable for refrigerator cars or other places where space is 
restricted. 

Sulphur-Dioxide Machines. — Results of theoretical calculations 
are given in a table by Ledoux showing an ice-melting capacity per hour 
per horse-power ranging from 134 to 63 lbs., and per pound of coal ranging 
from 44.7 to 21.1 lbs., as the temperature corresponding to the pressure of 
the vapor in the condenser rises from 59° to 104° F. The theoretical 
results do not represent the actual. 

Prof. Denton says concerning Ledoux's theoretical results: The 
figures given are higher than those obtained in practice, because .'the 
effect of superheating of the gas during admission to the cylinder is not 
considered. This superheating may cause an increase of work of about 
25%. There are other losses due to superheating the gas at the brine- 
tank, and in the pipe leading from the brine-tank to the compressor,, so 
that in actual practice a sulphur-dioxide machine, working under the 
conditions of an absolute pressure in the condenser of 56 lbs. per sq.in. 
and the corresponding temperature of 77° F., will give about 22 lbs. of iQe- 
melting capacity per pound of coal, which is about 60% of the theoretical 
amount neglecting friction, or 70% including friction. 

Sulphur-dioxide machines are not now used in the United States (1910). 

Refrigerating-Machines using Vapor of Water. (Ledoux.) — In 
these, machines, sometimes called vacuum machines, water, at ordinary 
temperatures, is injected into, or placed in connection with, a chamber 
in which a strong vacuum is maintained. A portion of the water vapor- 
izes, the heat to cause the vaporization being supplied from the water not 
vaporized, so that the latter is chilled or frozen to ice. If brine is used 
instead of pure water, its temperature may be reduced below the freezing- 
point of water. The water vapor is compressed from, say, a pressure of 
0.1 lb. per sq. in. to IV2 lbs. and discharged into a condenser. It is then 
condensed and removed by means of an ordinary air-pump. The prin- 
ciple of action of such a machine is the same as that of volatile-vapor 
machines. 

A theoretical calculation for ice-making, assuming a lower temperature 
of 32° F., a pressure in the condenser of 11/2 lbs. per sq. in., and a coal 
consumption of 3 lbs. per I.H.P. per hour, gives an ice-melting effect of 
34.5 lbs. per pound of coal, neglecting friction. Ammonia for ice-making 
conditions gives 40.9 lbs. The volume of the compressing cylinder is 
about 150 times the theoretical volume for an ammonia machine for these 
conditions. 

[The Patten Vacuum Ice Co., of Baltimore, has a large plant on this 
system in operation (1910).] 

Ammonia Compression-machines. — "Cold" vs. "Dry" Systems of 
Compression. — In the "cold" system or "humid" system some of the 
ammonia entering the compression cylinder is liquid, so that the heat 
developed in the cylinder is absorbed by the liquid and the temperature 
of the ammonia thereby confined to the boiling-point due to the condenser- 
pressure. No jacket is therefore required about the cylinder. 

In the "dry" or "hot" system all ammonia entering the compressor is 
gaseous, and the temperature becomes by compression several hundred 
degrees greater than the boiling-point due to the condenser-pressure. A 
water-jacket is therefore necessary to permit the cylinder to be properly 
lubricated. 

Dry, "Wet and Flooded Systems. (York Mfg. Co.) — An expansion 
system, or one where the ammonia leaves the coil slightly superheated, 
requires about 33§% more pipe surface than a wet compression system, 



AMMONIA MACHINES. 1293 

in which the ammonia leaves the coils containing sufficient entrained 
liquid to maintain a wet compression condition in the compressor. 

The flooded system is one where the ammonia is allowed to flow through 
the coils and into a trap, where the gas is separated from the liquid, the 
gas passing on to the compressor, while the liquid goes around through 
the coils again, together with the fresh liquid, which is fed into the trap. 
Such a system requires only about one-half the evaporating surface that 
an expansion system does to do the same work. The relative proportions 
of the three systems may be expressed as follows: 

A Dry Compression plant will need, with an Expansion Evaporating 
System, a medium size compressor, a large size evaporating system, a small 
amount of ammonia. 

A Dry Compression plant will need, with a Flooded Evaporating System, 
a small size compressor, a small size evaporating system, a large amount 
of ammonia. 

A Wet Compression plant will need, with a Wet Compression Evapo- 
rating System, a large size compressor, a medium size evaporating system, 
a medium amount of ammonia. 

The Ammonia Absorption-machine comprises a generator which 
contains a concentrated solution of ammonia in water; this generator 
is heated either directly by a fire, or indirectly by pipes leading from a 
steam-boiler. The vapor passes first into an "analyzer," a chamber con- 
nected with the upper part of the generator which separates some of the 
water from the vapor, then into a rectifier, where the vapor is partly 
cooled, precipitating more water, which returns to the generator, and then 
to the condenser. The upper part of the cooler or brine-tank is in com- 
munication with the lower part of the condenser. 

An absorption-chamber is filled with a weak solution of ammonia; a 
tube puts this chamber in communication with the cooling-tank. 

The absorption-chamber communicates with the boiler by two tubes: 
one leads from the bottom of the generator to the top of the chamber, the 
other leads from the bottom of the chamber to the top of the generator. 
Upon the latter is mounted a pump, to force the liquid from the absorp- 
tion-chamber, where the pressure is maintained at about one atmosphere, 
into the generator, where the pressure is from 8 to 12 atmospheres. 

To work the apparatus the ammonia solution in the generator is first 
heated. This releases the gas from the solution, and the pressure rises. 
When it reaches the tension of the saturated gas at the temperature of the 
condenser there is a liquefaction of the gas, and also of a small amount of 
steam. By means of a cock the flow of the liquefied gas into the refriger- 
ating coils contained in the cooler is regulated. It is here vaporized by 
absorbing the heat from the substance placed there to be cooled. As 
fast as it is vaporized it is absorbed by the weak solution in the absorbing- 
chamber. 

Under the influence of the heat in the boiler the solution is unequally 
saturated, the stronger solution being uppermost. The weaker portion is 
conveyed by the pipe entering the top of the absorbing-chamber, the 
flow being regulated by a cock, while the pump sends an equal quantity 
of strong solution from the chamber back to the boiler. 

The working of the apparatus depends upon the adjustment and regu- 
lation of the flow of the gas and liquid; by these means the pressure is 
varied, and consequently the temperature in the cooler may be controlled. 
The working is similar to that of compression-machines. The absorp- 
tion-chamber, fills the office of aspirator, and the generator plays the part 
of compressor. The mechanical force producing exhaustion is here re- 
placed by the affinity of water for ammonia gas, and the mechanical force 
required for compression is replaced by the heat which severs this affinity 
and sets the gas at liberty. 

Reece's absorption apparatus (1870) is thus described by Wallis-Taylor. 
The charge of liquid ammonia (26° Baume) is vaporized bv the application 
of heat, and the mixed vapor passed to the analyzer and rectifier, wherein 
the bulk of the water is condensed at a comparatively elevated temperature 
and returned to the generator. The ammoniacal vapor or gas is then 
passed to the condenser, where it is liquefied under the combined action 
of the cooling-water and of the pressure maintained in the generator. The 
liquid ammonia, practically anhydrous, is then used in the refrigerator 
and the vapor therefrom, still under considerable pressure, is admitted to 



1294 ICE-MAKING OR REFRIGERATING MACHINES. 



the cylinder of an engine used to drive a pump for returning the strong 
solution to the generator, after which it is passed to the absorber, where 
it meets and is absorbed by the weak liquor from the generator, and the 
strong liquor so formed is forced back into the generator by means of the 
pump. The temperature exchanger, introduced in 1875, provides for 
the hot liquor on its way from the generator to the absorber giving up its 
heat to the cooler liquid from the absorber on its way to the generator. 

Wallis-Taylor describes also marine refrigerating, ice-making, cold 
storage, the application of refrigeration in breweries, dairies, etc.; and the 
management and testing of apparatus. 

For the best results the following conditions are necessary (Voorhees): 
1. The generator should have ample liquid evaporating surface to make 
dry gas. 2. The temperature of the gas to the rectifier should be as low 
as possible. 3. The drip liquor returned to the generator from the recti- 
fier should be as hot as possible. 4. The gas from the rectifier to the 
condenser should not be over 10° to 50° hotter than the condensing tem- 
perature of the gas. 5. The exchanger should exchange upwards of 
90% of the heat of the hot weak liquor to the cold strong liquor. The 
weight of strong liquor pumped should be from 7 to 8 times that of the 
anhydrous ammonia circulated in the refrigerator. 

To produce one ton of refrigeration at 8.5 lbs. suction and 170 lbs. gauge 
condenser pressure, about 3.5 times as many heat units are actually used 
by an absorption machine as by a compression machine (compound con- 
densing engine driven), but, owing to the low efficiency of the steam 
engine, due to the heat wasted in the exhaust and in cylinder condensation, 
the actual weight of steam used per hour per ton of refrigeration is the 
same for both the absorption machine and the compressor. 

Belative Performance of Ammonia Compression- and Absorp- 
tion- machines, assuming no Water to be Entrained with the 
Ammonia-gas in the Condenser. (Denton and Jacobus, Trans. A. S. 
M. E., xiii.) — It is assumed in the calculation for both machines that 
1 lb. of coal imparts 10,000 B.T.TJ. to the boiler. The condensed steam 
from the generator of the absorption-machine is assumed to be returned 



Condenser. 


Refrigerat- 
ing Coils. 


fe 


Pounds of Ice-melting Effect 
per lb. of Coal. 


%&i 




u 




u 


Compress. 


Absorption- 


2^1 




ft 

g 

3 




ft 
3 


0> 
0> 


Machine. 


Machine.* 


1 


ft 

8Ph 


"3 . 

8^ 


achine in 
ammonia 

ump ex- 
the gen- 


le amm. 

exhausts 

mosphere 

heater, 

temp, to 
;r. 


ill 


b£ 
V 

a 

d 

a 


ft 
0> 

3, a 

3* 


T3 
ft 

a 

0) 

H 


O) 

ft 


< 
ft 

a 

01 


■eg 

■as 


~ o 


Absorption-m 
which the 
circulating-p 
hausts into 
erator. 


In which t 
circ. pump 
into the at 
through a 
yielding 212° 
the f eed-wat« 


iil 

G &«* 
a ti o 

^5^2 — 

e« 8 ** 
go ft 


61.2 


110.6 


5 


33.7 


61.2 


38.1 


71.4 


38.1 


33.5 


969 


59.0 


106.0 


5 


33.7 


59.0 


39.8 


74.6 


38.3 


33.9 


967 


59.0 


106.0 


5 


33.7 


130.0 


39.8 


74.6 


39.8 


35.1 


931 


59.0 


106.0 


-22 


16.9 


59.0 


23.4 


43.9 


36.3 


31.5 


1000 


86.0 


170.8 


5 


33.7 


86.0 


25.0 


46.9 


35.4 


28.6 


988 


86.0 


170.8 


5 


33.7 


130.0 


25.0 


46.9 


36.2 


29.2 


966 


86.0 


170.8 


-22 


16.9 


86.0 


16.5 


30.8 


33.3 


26.5 


1025 


86.0 


170.8 


-22 


16.9 


130.0 


16.5 


30.8 


34.1 


27.0 


1002 


104.0 


227.7 


5 


33.7 


104.0 


19.6 


36.8 


33.4 


25.1 


1002 


104.0 


227.7 


-22 


16.9 


104.0 


13.5 


25.3 


31.4 


23.4 


1041 



* 5% of water entrained in the ammonia will lower the economy of 
the absorption-machine about 15% to 20 % below the figures given in 
the table. 



EFFICIENCY OF REFRIGERATING MACHINES. 1295 

to the boiler at the temperature of the steam entering the generator. 
The engine of the compression-machine is assumed to exhaust through a 
feed-water heater that heats the feed-water to 212° F. The engine is 
assumed to consume 26 1/4 lbs. of water per hour per horse-power. The 
figures for the compression-machine include the effect of friction, which 
is taken at 15% of the net work of compression. 

(For discussion of the efficiency of the absorption system, see Ledoux's 
work; paper by Prof. Linde, and discussion on the same by Prof. Jacobus, 
Trans. A. S. M. E., xiv, 1416, 1436; and papers by Denton and Jacobus, 
Trans. A. S. M. E., x, 792, xiii, 507. 

Relative Efficiency of a Refrigerating-Machine. — The efficiency 
of a refrigerating-machine is sometimes expressed as the quotient of 
the quantity of heat received by the ammonia from the brine, that is, the 
quantity of useful work done, divided by the heat equivalent of the 
mechanical work done in the compressor. Thus in column 1 of the table 
of performance of the 75-ton machine (page 1311) the heat given by the 
brine to the ammonia per minute is 14,776 B.T.U. The horse-power of 
the ammonia cylinder is 65.7, and its heat equivalent = 65.7 x 33,000 -h 
778 = 2786 B.T.U. Then 14,776 h- 2786 = 5.304, efficiency. The ap- 
parent paradox that the efficiency is greater than unity, which is im- 
possible in any machine, is thus explained. The working fluid, as 
ammonia, receives heat from the brine and rejects heat into the condenser. 
(If the compressor is jacketed, a portion is rejected into the jacket-water.) 
The heat rejected into the condenser is greater than that received from the 
brine; the difference (plus or minus a small difference radiated to or from 
the atmosphere) is heat received by the ammonia from the compressor. 
The work to be done by the compressor is not the mechanical equivalent 
of the refrigeration of the brine, but only that necessary to supply the dif- 
ference between the heat rejected by the ammonia into the condenser and 
that received from the brine. If cooling water colder than the brine were 
available, the brine might transfer its heat directly into the cooling water, 
and there would be no need of ammonia or of a compressor; but since such 
cold water is not available, the brine rejects its heat into the colder 
ammonia, and then the compressor is required to heat the ammonia to 
such a temperature that it may reject heat into the cooling water. 

The maximum theoretical efficiency of a refrigerating machine is ex- 
pressed by the quotient T -s- (T t - T ), in which Tt is the highest and T 
the lowest temperature of the ammonia or other refrigerating agent. 

The efficiency of a refrigerating plant referred to the amount of fuel 
consumed is 

/ PO TsDed r fich'^x e ra 1 Se r l- ° f brine or other 
ice-melting capacity) _ 1 p X f gera'Ture "" ge J circulating fluid 
per pound of fuel J 144 x pounds of fuel used per hour 

The Ice-melting capacity is expressed as follows: 

/ 24 v SSHflS hP«t 1 of brine circulated per 
Tons (of 2000 lbs.) •> 1 v r?n« ?«f % 1 hour 

ice-melting ca- 1 = ± x ran g e of tem P- } 

pacity per 24 hours J 144 x 2000 

The analogy between a heat-engine and a refrigerating-machine is as 
follows: A steam-engine receives heat from the boiler, converts a part of 
it into mechanical work in the cylinder, and throws away the difference 
into the condenser. The ammonia in a compression refrigerating- 
machine receives heat from the brine-tank or cold-room, receives an 
additional amount of heat from the mechanical work done in the com- 
pression-cylinder, and throws away the sum into the condenser. The 
efficiency of the - steam-engine = work done -f- heat received from boiler. 
The efficiency of the refrigerating-machine = heat received from the brine- 
tank or cold-room •*- heat required to produce the work in the compression- 
cylinder. In the ammonia absorption-apparatus, the ammonia receives 
heat from the brine-tank and additional heat from the boiler or generator, 
and rejects the sum into the condenser and into the cooling water supplied 
to the absorber. The efficiency = heat received from the brine •*- heat re- 
ceived from the boiler. 



1296 ICE-M4KING OR REFRIGERATING MACHINES. 



The Efficiency of Refrigerating Systems depends on the tempera- 
ture of the condenser water, whether there is sufficient condenser surface 
for the compressor and whether or not the condenser pipes are free from 
uncondensable foreign gases. With these things right, condenser pressure 
for different temperatures of cooling water should be approximately as 
follows: 

1 gallon per minute per ton per 24 

hours— Cooling water, ° F 60 65 70 75 80 85 90 

Condenser pressure, gage, lb 183 200 220 235 255 280 300 

Condensed liquid ammonia ° F 95 100 105 110 115 120 125 

2 gallons per minute per ton per 24 

hours— Condenser pressure, gage, lb., 130 153 168 183 200 220 235 
Condensed liquid ammonia, ° F. . . . 77 85 90 93 100 105 110 

3 gallons per minute per ton per 24 

hours — Condenser pressure, gage, lb. . 125 140 155 170 185 200 215 

Condensed liquid ammonia, ° F 75 85 90 93 95 100 105 

The evaporating or back pressure within the expansion coils of a. re- 
frigerating system depends upon the temperatures on the outside of such 
coils, i.e., the air or brine to be cooled. For average practice back pres- 
sures for the production of required temperatures should be approxi- 
mately as follows: 

Temperature of room, ° F 10 15 20 28 32 36 40 50 60 

Back pressure, gage, lb 10 12 15 22 25 27 30 35 40 

Temperature of ammonia, ° F... -10-5 8 12 14 17 2226 

The condenser pressure should be kept as low as possible and the back 
pressure as high as possible, narrow limits between such pressures being 
as important to the efficiency of a refrigerating system as wide ones are 
to that of a steam engine in which the economy increases with the range 
between boiler pressure and condenser pressure. (F. E. Matthews, 
Power, Jan. 26, 1909.) 

Cylinder-heating. — In compression-machines employing volatile 
vapors the principal cause of the difference between the theoretical and 
the practical result is the heating of the ammonia, by the warm cylinder 
walls, during its entrance into the compressor, thereby expanding it, so 
that to compress a pound of ammonia a greater number of revolutions 
must be made by the compressing-pumps than corresponds to the density 
of the ammonia-gas as it issues from the brine-tank. 

Volumetric Efficiency. — The volumetric efficiency of a compressor 
is the ratio of the actual weight of ammonia pumped to the amount 
calculated from the piston displacement. Mr. Voorhees deduces from 
Denton's experiments the formula: Volumetric efficiency = E = 1 — 
(t t — £o)/1330, in which ti = the theoretical temperature of gas after 
compression and £ = temperature of gas delivered to the compressor. The 
temperature ti, = T\ — 460, is calculated from the formula for adiabatic 
compression, T x = T (Pi/P ) ' 24 , in which T t and T are absolute tem- 
peratures and Pi and P absolute pressures. In eight tests by Prof. 
Denton the volumetric efficiency ranged from 73.5% to 84%, and they 
vary less than 1% from the efficiencies calculated by the formula. The 
temperature of the gas discharged from the compressor averaged 57° less 
than the theoretical. 

The volumetric efficiency of a dry compressor is greatest when the vapor 
comes to the compressor with little or no superheat; 30° superheat of the 
suction gas reduces the capacity of the compressor 4%, and 100° 9%. 

The following table (from Voorhees) gives the theoretical discharge 
temperatures (h) and volumetric efficiencies (E) by the formula, and the 
actual cubic feet of displacement of compressor (F) per ton of refrigera- 
tion per minute for the given gauge pressures of suction and condenser. 



Suction pressures 



Cond. press. 140 

Cond. press. 170 — 
Cond. press. 200 



tt E F 

323° 0.76 10.35 

221° 0.83 4.57 

167° 0.87 2.96 



15 

Ti E F 

358° 0.73 11.02 
254° 0.81 4.78 
192° 0.86 3.07 



30 

~t E \ F 

388° 0.71 11.57 

280° 0.79 5.03 

216° 0.84 3.21 



AMMONIA MACHINES. 



1297 



Pounds of Ammonia per Minute to Produce 1 Ton of Refrigeration, 
and Percentage of Liquid Evaporated at the Expansion Valve. 



Condenser, Pressure and 
Temperature. 



Refrigerator, pressure and 
temperature lbs.,— 29°. . 

Refrigerator pressure and 

, temperature 15 lbs., — 0°... 

Refrigerator pressure and 
temperature, 30 lbs., -17°. 



140 lbs., 80°. 



170 lbs., 90°. 



200 lbs., 100°. 



0.431 lb., 19% 
0:4201b., 14.4% 
0.415 1b., 11.6% 



0.441 lb., 20.8% 
0.4301b., 16.2% 
0.4251b., 13.4% 



0.451 lb., 22.5% 
0.4401b., 18.0% 
0.434 lb., 15.2% 



Mean Effective Pressure, and Horse-power. — Voorhees deduces 
the following (Ice and Refrig., 1902): M.E.P. = 4.333 p [(Pi/Po) - 231 ~U, 
Po = suction and p t condenser pressure, abs. lbs. per sq. in. The maxi- 
mum M.E.P. occurs when p = p x -r- 3.113. The percentage of stroke 
during which the gas is discharged from the compressor is Vi = (Po/Pi) ' 769 - 
. .The compressor horse-power, C.H.P., is 0.00437 F X M.E.P. 

The friction of the compressor and its engine combined is given by 
Voorhees as 331/3% of the compressor H.P. or 25% of the engine H.P. 
Values of the mean effective pressure per ton of refrigeration (M), the 
compressor Tiorse-power (C) and the engine horse-power (E) are given 
below for the conditions named . 



Suction 
pressure. 



Cond. press., 140. 
Cond. press., 170. 
Cond. press., 200. 



(M) 
46.5 
50.5 
55.0 



(C) 
2.10 

2.42 
2.78 



(E) 
2.80 
3.23 
3.71 



67.0 
74.5 



(C) 
1.19 
1.40 
1.64 



(E) 
1.59 
1.87 
2.19 



as 

75.0 
85.0 



(C 
0.83 
1.00 
1.19 



(E) 
1.11 
1.33 
1.59 



By cooling the liquid between the condenser and the expansion valve 
the capacity will be increased and the horse-power per ton reduced. With 
compression from 15 to 170 lbs., if the liquid at the expansion valve is 
cooled to 76° instead of 90° the H.P. per ton will be reduced 3%. 

Prof. Lucke deduces a formula for the I.H.P. per ton of refrigerating 
capacity, as follows: 

p = mean effective pressure, lbs. per sq. in: L = length of stroke in 
ft.; a = area of piston in sq. ins.; n= no. of compressions per minute: 
E c = apparent volumetric efficiency, the ratio of the volume of ammonia 
apparently taken in per stroke to the full displacement of the piston; 
w c = weight of 1 cu. ft. of ammonia vapor at the back pressure, as it exists 
in the cylinder when compression begins; L c = latent heat of vaporization 
available for refrigeration; 288,000 = B.T.U. equivalent to 1 ton of 
refrigeration; T = tons refrigeration per 24 hours. 

I.H.P. _ pLan •* • 33,000 _ 0.87 

T 



LaE c nw c X L c X 60 X 24 
144 X 288,000 



W C L C * E c 



The Voorhees Multiple Effect Compressor is based upon the fact 
that both the economy and the capacity of a compression machine vary 
with the back pressure. In the past it has always been necessary to run a 
compressor at a gas suction pressure corresponding to the lowest required 
temperature. The multiple effect compressor takes in gas from two or 
more refrigerators at two or more different suction pressures and tem- 
peratures on the same suction stroke of the compressor. The suction gas 
of the higher pressure helps to compress the lower suction pressure gas. 
There are two sets of suction valves in the compressor cylinder; the low 
temperature and corresponding low back pressure being connected to 
one suction port, usually in the cylinder head, and the high back pres- 
sure connected to the other. At the beginning of the stroke the cylinder 
is filled with the low pressure gas and as the piston reaches the end of its 



1298 ICE-MAKING OK REFRIGERATING MACHINES. 



suction stroke, the second or high back pressure port is uncovered, the 
low pressure suction valve closing automatically, and the cylinder is 
completely filled with gas at the high pressure. By this means the 
compressor operates with an economy and capacity corresponding to the 
higher back pressure, making a gain in capacity of often 50% or more. 
{Trans. Am. Soc. Refrig. Engrs., 1906.) 

Quantity of Ammonia Required per Ton of Refrigeration. — 
The following table is condensed from one given by F. E. Matthews in 
Trans. A. S. M. E ., 1905. The weight in lbs. per minute is calculated 
from the formula P = (144 X 2000) -5- [1440 1 - (fit - ho)] in which 
I is the latent heat of evaporation at the back pressure in the cooler, and 
hi and h the heat of the liquid at the temperatures of the condenser and 
the cooler respectively. The specific heat of the liquid has been taken 
at unity. The ton of refrigeration is 2000 lbs. in 24 hours = 288,000 
B.T.U. 



B = 
C = 


Pounds of ammonia evaporated per minute. 

Cubic feet of gas to be handled per minute by the compressor. 


I. 




Head or Condenser Gauge Pressure and Corresponding 
Temperature. 


w. 
B.P. 


100 

lb. 
63.5° 


110 

lb. 
68° 


120 

lb. 
72.6° 


130 

lb. 
77.4° 


140 

lb. 
80.3° 


150 

lb.. 

83.8° 


160 

lb. 
87.4° 


170 

lb. 
90.8° 


180 

lb. 
93.8° 


190 

lb. 
96.9° 


200 

lb. 
100° 


572.78 ) 
.0556 \ 
) 


B 

C 


.4159 
7.482 


.4199 
7.551 


.4240 
7.626 


.4284 
7.703 


.4310 
7.761 


.4343 
7.812 


.4376 
7.870 


.4408 
7.929 


.4440 
7.986 


.4470 
8.041 


.4501 
8.095 


566.14 ) 
.0,33 j 


B 

C 


.4122 
5.636 


.4160 
5.675 


.4202 
5.732 


.4243 
5.790 


.4271 
5.826 


.4308 
5.878 


.4335 
5.914 


.4366 
5.970 


.4397 
5.999 


.4437 
6.039 


.4458 
6.081 


560.69 ) 
.0910} 
10 ) 


B 
C 


.4093 
4.502 


.4130 
4.543 


.4171 
4.587 


.4204 
4.625 


.4237 
4.662 


.4271 
4.698 


.4302 
4.733 


.4332 
4.766 


.4363 
4.799 


.4392 
4.833 


.4423 
4.865 


556.11 ) 
.1083 | 
15 ) 


B 
C 


.4068 
3.756 


.4106 
3.791 


.4145 
3.827 


.4186 
3.866 


.4211 

3.889 


.4244 
3.918 


.4276 
3.948 


.4288 
3.975 


.4336 
4.003 


.4365 
4.030 


.4394 
4.058 


552,83 ) 
.1258 \ 
20 ) 


B 
C 


.4040 
3.211 


.4077 
3.241 


.4116 

3.272 


.4158 
3.305 


.4182 
3,324 


.4214 
3.350 


.4245 
3.375 


.4275 
3.398 


.4304 
3.422 


.4333 
3.444 


.4362 
3.467 


548.40 ) 
.1429 ) 
25 ) 


B 
C 


.4025 
2.819 


.4062 
2.843 


.4102 
2.870 


.4140 
2.898 


.4167 
2.916 


.4198 
2.938 


.4229 
2.959 


.4258 
2.980 


.4287 
3.000 


.4316 
3.020 


.4345 
3.040 


545.13) 
.1600 [ 
30 ) 


B 
C 


.4013 
2.507 


.4049 
2.530 


.4088 
2.555 


.4128 
2.580 


.4152 
2.600 


.4184 
2.615 


.4213 
2.633 


.4243 
2.653 


.4273 
2.671 


.4300 
2.687 


.4329 
2.706 


542.80 ) 
.1766 £ 
35 ) 


B 

C 


.3991 
2.260 


.4028 
2.280 


.4066 
2.302 


.4105 
2.925 


.4130 

2.338 


.4161 
2.356 


.4188 
2.373 


.4220 
2.390 


.4249 
2.406 


.4277 
2.422 


.4305 
2.443 


539.35 ) 
.1941 \ 
40 ) 


B 
C 


.3984 
2.052 


.4020 
2.071 


.4058 
2.090 


.4098 
2.111 


.4122 
2.123 


.4153 
2.139 


.4183 
2.155 


.4211 
2.175 


.4240 
2.185 


.4269 
2.200 


.4296 
2.214 



I, Latent heat of volatilization, w, weight of vapor per cubic foot, 
back pressure or suction gauge pressure. 



10 



8.5° 



15 



-1° 5.66 c 



25 

11.5* 



35 

21.7° 



40 

26.1 



Back Pressures 5 

Temperatures —28.5° —17.5° 

Mr. Matthews defines a standard ton of refrigeration as the equivalent 
of 27 lbs. of anhydrous ammonia evaporated per hour from liquid at 
90° F. into saturated vapor at 15.67 lbs. gauge pressure (0° F.), which 
requires 12,000 B.T.U. ; or 20,950 units of evaporation, each of which is 
equal to 572.78 B.T.U., the heat required to evaporate 1 lb. of ammonia 
from a temperature of — 28.5° F. into saturated vapor at atmospheric 
pressure. 



CAPACITY OF MACHINES. 



1299 



Size and Capacities of Ammonia Refrigerating Machines. — ■ 

York Mfg. Co. Based on 15.67 lbs. back-pressure, 185 lbs. condensing 
pressure, and condensing water at 60° F. 



Si* 

Comp 


gle-Acting Compressors. 


Double-Acting Compressors. 


™essors. 


Engine. 


Capacity 

Tons 
Refrig- 
eration . 


Compressors. 


Engine. 


Capacity 
Tons 


Bore. 


Stroke. 


Bore. 


Stroke. 


Bore. 


Stroke. 


Bore. 


Stroke. 


Refrig- 
eration. 


71/2 


10 


111/9 


10 


10 


9 


15 


131/9 


12 


20 


9 


12 


131/9 


12 


20 


11 


18 


16 


15 


30 


11 


15' 


16 


15 


30 


121/2 


21 


18 


18 


40 


121/2 


18 


18 


18 


40 


14 


24 


20 


21 


65 


14 


21 


20 


21 


65 


16 


28 


24 


24 


90 


16 


24 


24 


24 


90 


18 


32 


26 


28 


125 


18 


28 


26 


28 


125 


21 


36 


281/9 


32 


175 


21 


32 


281/9 


32 


175 


24 


40 


34 


36 


250 


24 


36 


34 


36 


250 


26 


60 


38 


54 


350 


27 


42 


36 


42 


350 












30 


48 


44 


48 


500 













For larger capacities the machines are built with duplex compressors, 
driven by simple, tandem or cross compound engines. 



Displacement and Horse-Power per Ton of Refrigeration. 
Dry Compression. S. A., Single-acting; D. A., double-acting. 





Suction Gauge Pressure and Corresponding Temp. 




51b.= 


101b. = 


15.671b. 


20 lb. = 


25 1b.= 




- 17.5° F. 


-8.5°F. 


= 0°F. 


5.7° F. 


11.5° F. 


Condenser Gauge 
Pressure and Corresp. 














c 




a 














Temp, of Liquid at 


* 


o 
H 




o 




o 




o 




o 


Expansion valve. 


ft 


ft 




ft 




a 


EH 


a 




























fi 


a 


Q 


ft 


H 


ft 


W 


ft 


O 


ft 




c 


fk 


a 


ru 


z 


K 


a 


fk 


g 


Ph 




j3 


K 


3 


w 


6 


W 


6 


m 


D 


W 




o 


1-1 


o 


1-1 


u 


1-1 


u 


'- , 


y 


*-! 


145 lb. 82° F., S.A 


12,608 


1,654 


9,811 


1.4 


7829 


1.195 


6765 


1.065 


5836 


0.943 


145 1b. 82° F.,D.A 


14,645 


1.921 


11,300 


1.612 


8901 


1.358 


7625 


1.2 


6522 


1.054 


165 1b.89°F.,SA 


13,045 


1 834 


10,148 


1 56 


8092 


1.341 


6990 


1.201 6027 


1.071 


165ib.89°F.,D.A 


15,203 


2 137 


11,720 


1.802 


9224 


1.529 


7898 


1.357 6751 


1.2 


185 lb. 95.5° F., S.A. ... 


13,491 


?. on 


10,487 


1 72 


8362 


1.4865 


7219 


1 .336 6223 


1.197 


185 lb. 95. 5° F., DA.... 


15,774 


2 354 


12,150 


1.993 


9555 


1.7 


8176 


1.513 


6985 


1.344 


2051b. 101.4° F., S.A... . 


13,947 


2 192 


10,834 


1.879 


8630 


1.631 


7450 


1.47 


6420 


1,323 


205 1b.101.4°F.,D.A.... 


16,362 


2.571 


12,590 


2.184 


9890 


1.87 


8459 


1.67 


7222 


1.488 



* Cu. in. Displacement per Min. per Ton of Refrigeration. 

The volumetric efficiency ranges from 63.5 to 76.5% for double-acting, 
and from 74.5 to 85.5% for single-acting compressors, increasing with the 
decrease of condenser pressure and with the increase of suction pressure. 

Where the liquid is cooled lower than the temperature corresponding 
to the condensing pressure, there will be a reduction in horse-power and 
displacement proportional to the increase of work done by each pound 
of liquid handled. The I.H.P. is that of the compressor. For Engine 
Horse-Power add 17% up to 20 tons capacity and 15% for larger machines. 



1300 ICE-MAKING OR REFRIGERATING MACHINES. 



Small Sizes of Refrigerating Machines. 



Capacity, tons , 

Compressor, diam., in. 
Compressor, stroke, in 

Engine, diam., in 

Engine, stroke, in 



Single-acting, 
Vertical. 



1 1/4 



41/2 
5 
5 



2-6 
6 
8 
6 



Double-acting, 
Horizontal. 



21/2 



51/2 



10 



Rated Capacity of Refrigerating Machines. — It is customary to 
rate refrigerating machines in tons of refrigerating capacity in 24 hours, 
on the basis of a suction pressure of 15.67 lbs. gauge, corresponding to 
0° F. temperature of saturated ammonia vapor, and a condensing pressure 
of 185 lbs. gauge, corresponding to 95.5° F. The actual capacity increases 
with the increase of the suction pressure, and decreases with the increase 
of the condensing pressure. The following table shows the calculated 
capacities and horse-power of a machine rated at 40 H.P., when run at 
different pressures. (York Mfg. Co.) The horse-power required increases 
with the increase of both the suction and the condensing pressure. 





Suction Gauge Pressure and Corresponding Temp. 




51b = 

-17.5°. 


10 lb = 

-8.5°F. 


15.671b. 
= 0°F. 


20 lb. = 
5.7° F. 


25 lb. = 
11.5° F. 


30 lb. = 
16.8° F. 


Temp. 


o 


P-l 

w 


c 




Ph 

X 


a 

O 

H 




o 


Ph 
W 


a 

o 
H 


P^ 

w 


a 

o 


P4 


145 1b. = 82° F 


26.6 
25.7 
24.8 
24 


50.6 

54.2 
57.4 
60.5 


34.2 
33.1 
32 
31 


55.1 

59.4 
63.3 
67 


42.8 
41.4 
40 
38.9 


58.8 
63.8 
68.6 
72.9 


49.6 
48 
46.5 
45 


60.7 
66.3 
71.4 
76.1 


57.5 
55.7 
53.9 
52.3 


62.3 
68.6 
74.2 
79.6 


65.3 
63.2 
61.3 
59.4 


63 4 


165 1b. = 89° F 

185 1b. = 95.5° F 

205 1b. = 101.4° F 


70.1 
76.5 
86.2 



Piston Speeds and Revolutions per Minute. — There is a great diver- 
sity in the practice of different builders as to the size of compressor, the 
piston speed and the number of revolutions per minute for a given 
rated capacity. F. E. Matthews, Trans. A. S. M. E., 1905, has plotted 
a diagram of the various speeds and revolutions adopted by four promi- 
nent builders, and from average curves the following figures are obtained: 



Tons 

R.P.M 

Piston speeds. . 



20 


30 


40 


50 60 


80 


100 


120 


140 


160 


180 


200 


240 


300 


400 


90 


78 


73 


68 64 


60 


581/-, 


57 


56 


55 


54 


53 


52 


51 


481/9 


200 


215 


228 


240 250 


270 


280 


286 


290 


293 


296 


300 


315 


340 


378 



500 



Mr. Matthews recommends a standard rating of machines based on 
these revolutions and speeds and on an apparent compressor displace- 
ment of 4.4 cu. ft. per minute per ton rating. 

Condensers for Refrigerating Machines are of two kinds: sub- 
merged, and open-air evaporative. The submerged condenser requires 
a large volume of cooling water for maximum efficiency. According 
to Siebel the amount of condensing surface, the water entering at 70° 
and leaving at 80°, is 40 sq ft., for each ton of refrigerating capacity, or 
64 lineal feet of 2-in. pipe. Frequently only 20 sq. ft., or 90 ft. of 11/4-in. 
pipe, is used, but this necessitates higher condenser pressures. If F = 
sq. ft. of cooling surface, h = heat of evaporation of 1 lb. ammonia at 
the condenser temperature, K = lbs. of ammonia circulated per minute, 
m ~ B.T.U. transferred per minute per sq. ft. of condenser surface, 
t = temperature of the ammonia in the coils and t\ the temperature of 
the water outside, F = hK -?• m{t - U), For t = 80 and ti == 70, ni 



CONDENSERS AND COOLING TOWERS. 



1301 



may be taken at 0.5. Practically the amount of water required will 
vary from 3 to 7 gallons per minute per ton of refrigeration. When 
cooling water is scarce, cooling towers are commonly used. 

E. T. Shinkle gives the average surface of several submerged con- 
densers as equal to 167 lineal feet of 1-in. pipe per ton of refrigeration. 

Open air or evaporation surface condensers are usually made of a stack 
of parallel tubes with return bends, and means for distributing the water 
so that it will flow uniformly over the pipe surface. Shinkle gives as the 
average surface of open-air coolers 142 ft. of 1-in. pipe, or 99 ft. of 1 1/4 in. 
pipe per ton of refrigerating capacity. 

Capacity of Condensers. (York Mfg. Co.) — The following table 
shows the capacities and horse-power per ton refrigeration of one section 
counter-current double-pipe condenser, 1 i/4-in. and 2-in. pipe, 12 pipes 
high, 19 feet in length outside of water bends, for water velocities 100 ft. 
to 400 ft. per minute: initial temperature of condensing water 70°. 



High Pressure Constant. 



Condensing Water. 


Cap'y 
Tons 
Refrig. 
per 24 
hours. 


Con- 
densing 
Pressure 
Lbs. per 
sq. in. 


Horse-power per Ton 
Refrigeration. 


Veloc- 
ity 
thr'gh 
1 l/ 4 -in. 
pipe. 
Ft. per 
min. 


Total 

gallons 

used 

per 

min. 


Gallons 
per min 
per ton 
Refrig. 


Fric- 
tion 

thr'gh 
Coil. 
Lbs. 
per 

sq. in. 


Engine 
driving 
Com- 
pressor 


Circu- 
lating 
Water 
thr'gh 
Con- 
denser. 


Total 
Engine 

and 
Water 
Circu- 
lation. 


100 
150 
200 
250 
300 
400 


7.77 
11.65 
15.54 
19.42 
23.31 
31.08 


1.16 

1.165 
1.165 
1.18 
1.24 
1.30 


2.28 
5.75 
9.98 
15. 
21.6 
37.8 


6.7 
10. 
13.4 
16.4 
18.8 
24. 


185 
185 
185 
185 
185 
185 


1.71 
1.71 
1.71 
1.71 
1.71 
1.71 


0.0016 

0.004 

0.007 

0.011 

0.016 

0.030 


1.7116 

1.714 

1.717 

1.721 

1.726 

1.74 



Capacity Constant. 



100 


7.77 


0.777 


2.28 


10. 


225 


2.04 


0.001 


2.041 


150 


11.65 


1.165 


5.75 


10. 


185 


1.71 


0.004 


1.714 


200 


15.54 


1.554 


9.98 


10. 


165 


1.54 


0.009 


1.549 


250 


19.42 


1.942 


15. 


10. 


155 


1.46 


0.018 


1.478 


300 


23.31 


2.331 


21.6 


10. 


148 


1.40 


0.030 


1.43 


400 


31.08 


3.108 


37.8 


10. 


140 


1.33 


0.071 


1.401 



The horse-power per ton is for single-acting compressor with 15.67 lbs. 
suction pressure. 

The friction in water pump and connections should be added to water 
horse-power and to total horse-power. 

Cooling-Tower Practice in Refrigerating Plants. (B. F. Hart, 
Jr., Southern Engr., Mar., 1909.) — The efficiency of a cooling tower de- 
pends on exposing the greatest quantity of water surface to the cooling 
air-currents. In a tower designed to handle 100 gallons per minute the 
ranges of temperature found when handling different quantities of water 
were as follows: 

Gallons of water per minute 148 109 58 

Temperature of the atmosphere 78° 78.5° 78° 

Relative humidity, % 47 49 97 

Initial temperature 85.5° 85° 86° 

Final temperature 78° 76° 75° 

Range 7.5° 9° 11° 



1302 ICE-MAKING OR REFRIGERATING MACHINES. 



The final temperatures which may be obtained when the initial tem- 
perature does not exceed 100° are as follows: 



Atmosphere temp. 


95° I 90° 1 85° 80° 1 75° 1 70° 




Final temperature of water leaving tower. 


(90 


100 


95 


90 


85 


80 


75 


80 


98 


92 


88 


83 


78 


73 


Humidity, % J J} 


95 
92 


90 

88 


86 
83 


80 
78 


76 

74 


71 
69 


50 


89 


84 


79 


75 


70 


66 


140 


85 


80 


76 


71 


67 


63 



For ammonia condensers we figure on supplying 3 gallons per minute of 
circulating water per ton of refrigeration, or 6 gallons per minute per ton of 
ice made per 24 hours, and guarantee a reduction range from 150° to 160° 
down to about 100° when the temperature of the atmosphere does not 
exceed 80° nor the relative humidity 60%. When the temperature of the 
atmosphere and the humidity are both above 90° the speed of the pumps 
and the ammonia pressure must be increased. 

The Refrigerating-Coils of a Pictet ice-machine described by Ledoux 
had 79 sq. ft. of surface for each 100,000 theoretic negative heat-units 
produced per hour. The temperature corresponding to the pressure of 
the dioxide in the coils is 10.4° F., and that of the bath (calcium chloride 
solution) in which they were immersed is 19.4°. 

Comparison of Actual and Theoretical Ice-melting Capacity. — 
The following is a comparison of the theoretical ice-melting capacity of 
an ammonia compression machine with that obtained in some of Prof. 
Schroter's tests on a Linde machine having a compression-cylinder 9.9-in. 
bore and 16.5-in. stroke, and also in tests by Prof. Denton on a machine 
having two single-acting compression-cylinders 12 in. x 30 in.: 



No. of 


Temp, in Degrees F. 
Corresponding to 
Pressure of Vapor. 


Ice-melting Capacity per lb. of Coal, 

assuming 3 lbs. per hour per 

Horse-power. 


Test. 


Condenser. 


Suction. 


Theoretical 
Friction* 
included. 


Actual. 


Per cent of 

Loss Due to 

Cylinder 

Superheating. 


1(24 

fl^26 
£i25 


72.3 
70.5 
69.2 
68.5 

84.2 
82.7 
84.6 


26.6 

14.3 

0.5 

-11.8 

15.0 
- 3.2 
-10.8 


50.4 
37.6 
29.4 
22.8 

27.4 
21.6 
18.8 


40.6 
30.0 
22.0 
16.1 

24.2 
17.5 
14.5 


19.4 
20.2 
25.2 
29.4 

11.7 
19.0 

22.9 



* Friction taken at figures observed in the tesjs, which range from 
14% to 20% of the work of the steam-cylinder. 

TEST-TRIALS OF REFRIGERATING MACHINES. 

(G. Linde, Trans. A.S.M.E., xiv, 1414.) 
The purpose of the test is to determine the ratio of consumption and 
production, so that there will have to be measured both the refrigerative 
effect and the heat (or mechanical work) consumed, also the cooling 
water. The refrigerative effect is the product of the number of heat- 
units (Q) abstracted from the body to be cooled, and the quotient (T c — T) 
•*- T: in which T e = absolute temperature at which heat is transmitted to 
the cooling water, and T = absolute temperature at which heat is taken 
from the body to be cooled. (Continued on page 1305.) 



TEST-TRIALS OP REFRIGERATING MACHINES. 1303 



£ a 



.s- ^ 



3 £3 



2 3 w a. 





•am^'Bjad 
-ui9£ jo aStnjy; -j O of 3urams 
-s-b '^;iobcJb3 Supjaui-ao'i jo 
uo X Ja, d •aa^'BAi' -SuisuapuoQ 


"3 


|22 




•uorjoijjj miM. "Japuipto 
-un3a;g jo '• j-jj J9d anotj iad 
{T30Q jo -sqj f SuiuinssB 'JBOQ JO 
qi aad /C-;iO'Bd'BQ Suppui-aoj 




e> >r\ — 




•^uauiao'B|d 
-siq uo^sij jo (jooj oiqnQ 
jad XjpudTJQ 2upiaui-aoj_ 




ill 

ooo 
ooo 




03^3-2 

S H- S 


•jaAvod 
-asjojj jad jnoq aaj 




ooo 




•uoi;ouj q^JA\. 
•uoissajduioQ jo O 1 
spo^' jo -qi-^JJaj 


1-1 




ooi? t 
o o o 




a 
s 

• 
03 

"3. 

3 

a 
o 

& 

'o 
o 



ft 

q 
ft 




•jaAvod ^ 
-urea^g pa^oipuj io 
jo *uoi-jou j %L\Y ^ 


ft 


ooo 




•uoj^ouj ^noq^t^ ^ 


ft 


OOO 

o-o 




•padojaA 
-9q s^iuq psuuaqx ^ 
aAi^'BSa^ jo jaqranfj 


H 


on <n pq 




•jasuapuog „ 
^-b pa^OBJ^sqy ^ajj O 1 




E"S 




•passaad g 
-uioq BT3Q jo ;qSta^ 5 




ONvOOv 

o' o o 




•uoissaiduioo jo ^ 

pug ^13 SBQ JO 8Jn^BJ3dUI9 J^ "" 


ft 

bi 

Q 


CO o — ' 

— — ^j 




•snoo-3ui}^ja3uj <-i 
-ay; ui ajrissajjj' a^rqosqy + 


3 . 
na 


Isl 




JOCl 

~pu 


•SJI03 

3 A> 
odsaj 


-Sup-BjaSujay; ut 
ajtissajj o^ Sui ,2 
ioq ajn^ujadmaj, 




ft 


ooo 

OO =5. 

7 



3 v G+* g 



1304 ICE-MAKING OE REFRIGERATING MACHINES. 



I g| 

-as 






o 5 

^9 



CO s 



n» a 

a s« . 

« o » w 

* H O h 
c8 S 55 S 

* m -H Q 



S .BO 
A ° H 

3 2-5 
S.-o2 

|Bg 
S oS 

o g w 

05 



sjnoq ^s at X^io-bcJ 
-■bq Sui^aui-aoj jo 
uoj, .lad a;nmj\[ aaj 



• A^iO'Bd'BQ Sulcata 
-ao'j jo uoj, jaj 



•duia^jo 
aSu'B'jjQOf SuiuinssB 
'^uauiaoBidsiQ uo^ 

-91 J JO ■%} ho J8J 



•^uaux 
-ao-BjdstQ uo? 
-sij joHj'no jaj 



uorjou^uii^ 



•uoic> 



•uopouj q^JAi 



•uor> 
-vug %r\omis& 



•uopoijj 
aad ' jnojj aaj 



•uot^oij^j Sui 
-pnpui 'papuadxg; 
5 T J °iWJ°'qi-^ J9 d 



•uopoij^ ^no 
-tjiim 'papuadxg 



nOOOOOOO 

-8§§§gS 



00 fNOO« 



■noo "T o r> ««ii 1 no 
- m 00 cry 00 in eg 

-"* r^ fi Cn] (N CnI 



jaMod-uiBa^g pa^-eo 

-ipuj JO 'UOI^OUJ U^IM. 

iioissaadiuoQ 10 >[-io^y 



•uopouj ^noq^iAi 
uoissajdraoQ 10 i[j6^ 



•papuad 
-xg ^an 01 loajjg; 



ui ^oajjg; Sui^BJQSup'a; 



•jasuapuoQ 
moij An/we pauj'BO ^ajj 



•uoissajdraog 
jo pug %v ajh^'BJadraaj, 



•jasuapuoQ 
ui amssajj a^njosqv 



,Q 01—. 



jasuapuoQ ui jod'B^ I 
jo -ssajjj o? ariQ -draax I 



3-No"' T r'rNfo'"oN"oo" 



sooooo 



"f hN — On -O nO 
_W fNq__rrOO 

£^0 00000 
© 00000 



= S|? 



000000 

^i£irnOOOin (N 
^'N0'fs'~00'"ON"o'"'- " 



-OOnOO(NnO 



^-<r f^ — on r>. -<r 

^fn pnj — on 00 r>' 



^00 o <n T no r>s 



n p> o m in oc 






m I 

< W 

5 S 3 fe 
2 S 

SO « 

fe IS s§ 



00 h 



O p 



On ON On O OO O 


^O OOOOO 

— tn ^ ^ in in in 


(17) 
0.1611 
.1620 
.1628 
.1636 
.1643 
.1649 


(16) 
.000116 
.000114 
.000111 
.000109 
.000107 
.000105 


(15) 
23.4 
20.6 
18.4 
16.5 
14.9 
13.5 


(14) 
26.9 
23.7 
21.1 
18.9 
17.1 
15.5 


(13) 
70.2 
61.8 
55.1 
49.4 
44.7 
40.6 


i~Ntv. m eo -«r no 


(11) 

9,980 

8,790 

7,840 

7,030 

6,360 

5,780 


(10) 
.00504 
.00444 
.00396 
.00355 
.00321 
.00292 


(9) 
.00580 
.00510 
.00455 
.00408 
.00369 
.00335 


(8) 
6,530 
7,280 
8,000 
8,750 
9,480 
10,200 


(7) 

5,680 

6,330 

6,960 

7,610 

8,240 

8,870 


(6) 
4.48 
3.95 
3.52 
3.15 
2.85 
2.59 


(5) 
32.93 
32.31 
31.69 
31.05 
30.41 
29.75 


(4) 
40.28 
40.50 
40.70 
40.90 
41.07 
41.23 


(3) 
224.1 
252.2 
280.2 
308.3 
336.2 
364.0 


O — NO 00 00 

£Tg £j ~4- S on 1 


^0- 00 p> no in t 



TEST-TRIALS OF REFRIGERATING MACHINES. 1305 

The determination of the quantity of cold will be possible with the 
proper exactness only when the machine is employed during the test to 
refrigerate a liquid; and if the cold be found from the quantity of liquid 
circulated per unit of time, from its range of refrigeration, and from its 
specific heat. Sufficient exactness cannot be obtained by the refrigera- 
tion of a current of circulating air, nor from the manufacture of a certain 
quantity of ice, nor from a calculation of the fluid circulating within the 
machine (for instance, the quantity of ammonia circulated by the com- 
pressor). Thus the refrigeration of brine will generally form the basis 
for tests making any pretension to accuracy. The degree of refrigeration 
should not be greater than necessary for allowing the range of temperature 
to be measured with the necessary exactness; a range of temperature of 
from 5° to 6° Fahr. will suffice. 

The condenser measurements for cooling water and its temperatures 
will be possible with sufficient accuracy only with submerged condensers. 

The measurement of the quantity of brine circulated, and of the cooling 
water, is usually effected by water-meters inserted into the conduits. If 
the necessary precautions are observed, this method is admissible. For 
quite precise tests, however, the use of two accurately gauged tanks 
which are alternately filled and emptied must be advised. 

To measure the temperatures of brine and cooling water at the entrance 
and exit of refrigerator and condenser respectively, the employment of 
specially constructed and frequently standardized thermometers is indis- 
pensable; no less important is the precaution of using at each spot simul- 
taneously two thermometers, and of changing the position of one such 
thermometer series from inlet to outlet (and vice versa) after the expiration 
of one-half of the test, in order that possible errors may be compensated. 

It is important to determine the specific heat of the brine used in 
each instance for its corresponding temperature range, as small differ- 
ences in the composition and the concentration may cause considerable 
variations. 

As regards the measurement of consumption, the programme will not 
have any special rules in cases where only the measurement of steam and 
cooling water is undertaken, as will be mainly the case for trials of absorp- 
tion-machines. For compression-machines the steam consumption 
depends both on the quality of the steam-engine and on that of the 
refrigerating-machine, while it is evidently desirable to know the con- 
sumption of the former separately from that of the latter. As a rule • 
steam-engine and compressor are coupled directly together, thus render- 
ing a direct measurement of the power absorbed by the refrigerating- 
machine impossible, and it will have to suffice to ascertain the indicated 
work both of steam-engine and compressor. By further measuring 
the work for the engine running empty, and by comparing the differences 
in power between steam-engine and compressor resulting for wide varia- 
tions of condenser-pressures, the effective consumption of work L e for 
the refrigerating-machine can be found very closely. In general, it will 
suffice to use the indicated work found in the steam-cylinder, especially 
as from this observation the expenditure of heat can be directly deter- 
mined. Ordinarily the use of the indicated work in the compressor- 
cylinder, for purposes of comparison, should be avoided; firstly, because 
there are usually certain accessory apparatus to be driven (agitators, etc.), 
belonging to the refrigerating-machine proper; and secondly, because 
the external friction would be excluded. 

Heat Balance. — We possess an important aid for checking the cor- 
rectness of the results found in each trial by forming the balance in each 
case for the heat received and rejected. Only those tests should be re- 
garded as correct beyond doubt which show a sufficient conformity in 
the heat balance. It is true that in certain instances it may not be easy 
to account fully for the transmission of heat between the several parts of 
the machine and its environment by radiation and convection, but gener- 
ally (particularlv for compression-machines) it will be possible to obtain 
for the heat received and rejected a balance exhibiting small discrepancies 
only. 



1306 ICE-MAKING OR REFRIGERATING MACHINES. 



Report of Test. — Reports intended to be used for comparison with 
the figures found for other machines will therefore have to embrace at 
least the following observations: 
Refrigerator: 

Quantity of brine circulated per hour 

Brine temperature at inlet to refrigerator 

Brine temperature at outlet of refrigerator T 

Specific gravity of brine (at 64° Fahr.) 

Specific heat of brine 

Heat abstracted (cold produced) Q e 

Absolute pressure in the refrigerator 

Condenser: 

Quantity of cooling water per hour 

Temperature at inlet to condenser , 

Temperature" at outlet of condenser T c 

Heat abstracted Qi 

Absolute pressure in the condenser 

Temperature of gases entering the condenser 



Compression-machine. 
Compressor: 

Indicated work L t 

Temperature of gases at inlet 
Temperature of gases at exit 
Steam-engine: 

Feed-water per hour 

Temperature of feed-water . . 
Absolute steam-pressure be- 
fore steam-engine 

Indicated work of steam-en- 
gine L e 

Condensing water per hour.. . 

Temperature of do 

Total sum of losses by radia- 
tion and convection. . ± Q» 
Heat Balance: 

Q e + AL C = Qi ± Qz. 



Absorption-machine. 

Still: 

Steam consumed per hour 

Abs. pressure of heating steam 

Temperature of condensed steam at 

outlet 

Heat imparted to still Q' e 

Absorber: 

Quantity of cooling water per hour. . 

Temperature at inlet 

Temperature at outlet 

Heat removed Q2 

Pump for Ammonia Liquor: 

Indicated work of steam-engine .... 

Steam-consumption for pump 

Thermal equivalent for work of 

pump ALp 

Total sum of losses by radiation and 

convection ± Qs 

Heat Balance: 

Qe + Q'e = <?i + Q* ± Os. 
For the calculation of efficiency and for comparison of various tests, 
the actual efficiencies must be compared with the theoretical maximum 
of efficiency Q -i- (AL) max. ^ T + (T e - T) corresponding to»the tem- 
perature range. 

Temperature Range. — For the temperatures (T and T c ) at which the 
heat is abstracted in the refrigerator and imparted to the condenser, it is 
correct to select the temperature of the brine leaving the refrigerator and 
that of the cooling water leaving the condenser, because it is in principle 
impossible to keep the refrigerator pressure higher than would correspond 
to the lowest brine temperature, or to reduce the condenser pressure 
below that corresponding to the outlet temperature of the cooling water. 
Prof. Linde shows that the maximum theoretical efficiency of a com- 
pression-machine may be expressed by the formula 
Q - (AL) = T +(T C - T), 
in which Q = quantity of heat abstracted (cold produced) ; 

AL --= thermal equivalent of the mechanical work expended; 
L = the mechanical work, and A = 1 ~ 778; 
T = absolute temperature of heat abstraction (refrigerator); 
T c = absolute temperature of heat rejection (condenser). 
If u = ratio between the heat equivalent of the mechanical work AL 
and the quantity of heat Q' which must be imparted to the motor to 
produce the work L, then 

AL -^ Q' = u, and Q' IQ = (T c - T) * (uT), 



PERFORMANCES OF ICE-MAKING MACHINES, 1307 



It follows that the expenditure of heat Q' necessary for the production 
of the quantity of cold Q in a compression-machine will be the smaller, 
the smaller the difference of temperature T c — T. 

Metering the Ammonia. — For a complete test of an ammonia 
refrigerating-machine it is advisable to measure the quantity of ammonia 
circulated, as was done in the test of the 75-ton machine described by 
Prof. Denton. (Trans. A. S. M. E., xii, 326.) 

ACTUAL PERFORMANCES OF ICE-MAKING MACHINES. 

The table given on page 1308 is abridged from Denton, Jacobus, and 
Riesenberger's translation of Ledoux on Ice-making Machines. The 
following shows the class and size of the machines tested, referred to by 
letters in the table, with the names of the authorities: 



Class of Machines. 


Authority. 


Dimensions of Com- 
pression-cylinder in 
inches. 




Bore. 


Stroke. 


A. Ammonia cold-compression 

B. Pictet fluid dry-compression 


Schroter. 

( Renwick & 
\ Jacobus. 
Denton. 


9.9 
11.3 
28.0 

10.0 
12.0 


16.5 
24.4 
23.8 




18.0 


E. Ammonia dry-compression 


30.0 













In class A, a German double-acting machine with compression cylinder 
9.9 in. bore, 16 in. stroke, tested by Prof. Schroter, the ice-melting capac- 
ity ranges from 46.29 to 16.14 lbs. of ice per pound of coal, according as 
the suction pressure varies from about 45 to 8 lbs. above the atmosphere, 
this pressure being the condition which mainly controls the economy of 
compression machines. These results are equivalent to realizing from 
72% to 57% of theoretically perfect performances. The higher per cents 
appear to occur with the higher suction-pressures, indicating a greater 
loss from cylinder-heating (a phenomenon the reverse of cylinder conden- 
sation in steam-engines), as the range of the temperature of the gas in 
the compression-cylinder is greater. 

In E, an American single-acting compression-machine, two compression 
cylinders each 12 X 30 in., operating on the "dry system," tested by 
Prof. Denton, the percentage of theoretical effect realized ranges from 
69.5% to 62.6%. The friction losses are higher for the American machine. 
The latter's higher efficiency may be attributed, therefore, to more perfect 
displacement. 

The largest "ice-melting capacity " in the American machine is 24.16 lbs. 
This corresponds to the highest suction-pressures used in American 
practice for such refrigeration as is required in beer-storage cellars using 
the direct-expansion system. The conditions most nearly corresponding 
to American brewery practice in the German tests are those in line 5, 
which give an "ice-melting capacity" of 19.07 lbs. 

For the manufacture of artificial ice, the conditions of practice are those 
of lines 3 and 4, and lines 25 and 26. In the former the condensing pres- 
sure used requires more expense for cooling water than is common in 
American practice. The ice-melting capacity is therefore greater in the 
German machine, being 22.03 and 16.14 lbs. against 17.55 and 14.52 for 
the American apparatus. 

Class B. Sulphur Dioxide or Pictet Machines. — No records are 
available for determination of the "ice-melting capacity" of machines 
using pure sulphur dioxide. In the " Pictet fluid, " a mixture of about 97 % 
of sulphur dioxide and 3% of carbonic acid, the presence of the carbonic 
acid affords a temperature about 14 Fahr. degrees lower than is obtained 
with pure sulphur dioxide at atmospheric pressure. The latent heat of 
this mixture has never been determined, but is assumed to be equal to 
that of pure sulphur dioxide. 



1308 ICE-MAKING OR REFRIGERATING MACHINES. 



For brewery refrigerating conditions, line 17, we have 26.24 lbs. "ice- 
melting capacity," and for ice-making conditions, line 13, the "ice- 
melting capacity " is 17.47 lbs. These figures are practically as econom- 
ical as those for ammonia, the per cent of theoretical effect realized 
ranging from 65.4 to 57.8. At extremely low temperatures, —15° Fahr., 
lines 14 and 18, the per cent realized is as low as 42.5. 

— Actual Performance of Ice-making Machines. 





02 ^ 




£a . 




Ph «2 -3 




u a * 












3— S 




1 £ § 




^so 1 




<3^ M 






H 














a> 




<S 


c 


a 


a 


T3 




3 






fc 


CJ 


w 


1 


135 


55 


2 


131 


42 


3 


128 


30 


4 


126 


22 


5 


20U 


42 


6 


136 


60 


7 


131 


45 


8 


126 


24 


9 


117 


41 


10 


130 


60 


11 


57 


21 


12 


56 


15 


13 


55 


10 


14 


60 


7 


15 


91 


15 


16 


61 


22 


17 


59 


16 


18 


59 


7 


19 


54 


22 


20 


89 


16 


21 


62 


6 


22 


59 


15 


23 


175 


54 


24 


166 


43 


25 


167 


23 


26 


162 


28 


27 


176 


42 


28 


152 


40 



3 


3 
C 




i 






a 




r , 


y 


a 


s 


w 


% 


3 


£ 






pq 


05 



95 
72 
71 
68 
64 
70 
77 
76 
75 
8) 

104 
81 
80 
79 
75 

103 
82 
65* 
81* 
84 
85 
83 
88 
79 



30 
18 

- 9 
13 
31 
28 
14 

- 2 
-16 

14 

31 

16 

-16 

31 

16 

-17 

-53* 

-40* 

15 



13 



16 



44.9 
45.1 

45.1 

44.8 

45.0 

45.2 

45.1 

44.7 

45.0 

31.7 

57.0 

56.8 

57.1 

57.6 

59.3 

57.3 

57.5 

57. 

35.3 

42.9 

34. 

63.2 

93.4 

58.1 

57.7 

57.9 

58.9 



14.4 
16.7 

16.0 

19.5 

10.5 

10.7 

12.1 

18.0 

13.5 

14.8 

22.9 

22.9 

24.0 

25.7 

16.9 

14.0 

12.8 

21 

22.3 

14.7 

24.3 

21.9 

32.1 

22.7 

18.6 

19.3 

19.7 







M 


, 




p 




-i.S 


"+3 








"S "J^ 






a 

a 

o 


I! 

>> 






03 

21 


£2 

i 




■5 "3 


£0 ^ 


cfe 


®= 




gofl 


t- J3 




a 

O 




Sec 

>> - 

* ° 2 


•y' = 


"43 05 


.E '■'- 

CL z 
7~ 


;£ 

03 a 








l^> 


£ a 


«H.g 


is 


03 03 






Q 


w 


S 


26.2 


40.63 


30.8 


19.1 


54.8 


19.5 


30.01 


33.5 


20.2 


53.4 


13.3 


22.03 


37.1 


25.2 


50.3 


9.0 


16.14 


42.9 


29.1 


44.7 


16.5 


19.07 


36.0 


28.5 


77.0 


29.8 


46.29 


28.5 


19.9 


56.8 


21.6 


33.23 


31.3 


21.9 


56.4 


9.9 


17.55 


41.1 


28.3 


46.1 


20.0 


33.77 


33.1 


22.9 


50.6 


19.5 


45.01 


35.2 


23.8 


52.0 


25.6 


33.07 


39.9 


22.2 


24.1 


17.9 


24.11 


41.3 


24.0 


23.1 


11.6 


17.47 


42.2 


25.2 


20.4 


5.7 


10.14 


54.5 


38.5 


16.8 


15.7 


16.05 


36.2 


23.1 


31.5 


28.1 


36.19 


33.4 


22.5 


26.8 


19.3 


26.24 


34.6 


25.0 


25.6 


6.8 


11.93 


47.5 


33.4 


18.0 


17.0 


38.04 


39.5 


22.6 


22.6 


11.9 


16.68 


37.7 


27.0 


32.7 


3.5 


9.86 


54.2 


39.5 


17.7 


10.3 


3.42 


71.7 


56.9 


26.6 


4.9 


3.0 


80.0 


63.0 


89.2 


73.9 


24.16 


32.8 


11.7 


65 9 


37.9 


14.52 


37.4 


22.7 


57.6 


46.5 


17.55 


34.9 


18.6 


59.9 


74.4 


23.31 


30.5 


13.5 


70.5 


42.2 


20.1 


47.8 











* Temperature of air at entrance and exit of expansion-cylinder. 

t On a basis of 3 lbs. of coal per hour per H.P. of steam-cylinder of 
compression-machine and an evaporation of 11.1 lbs. of water per pound 
of combustible from and at 212° F. in the absorption-machine. 

% Per cent of theoretical with no friction. 

§ Loss due to heating during aspiration of gas in the compression- 
cylinder and to radiation and superheating at brine-tank. 

|| Actual, including resistance due to inlet and exit valves. 



PERFORMANCES OP ICE-MAKING MACHINES. 



1309 



Performance of a 75-ton Ammonia Compression-machine. (J. E. 

Denton, Trans. A. S. M. E., xii, 326.) — The machine had two single- 
acting compression cylinders 12 X 30 in., and one Corliss steam-cylinder, 
double-acting, 18 X 36 in. It was rated by the manufacturers as a 
50-ton machine, but it showed 75 tons of ice-refrigerating effect per 
24 hours during the test. 

The most probable figures of performance in eight trials are as follows: 



H 


Ammonia 
Pressures, 
lbs. above 
Atmosphere. 


Brine 
Tempera- 
tures, 
Degrees F. 


Capacity Tons 
Refrigerating 
. Effect per 24 
hours. 


Efficiency ibs. of 
Ice per lb. of 
Coal at 3 lbs. 
Coal per hour 
perH.P. 


Water-consump- 
tion, gals, of 
Water per min. 
per ton of Ca- 
pacity. 


Ratio of Actual 
Weights of Am- 
monia circu- 
lated. 


o8 

a 

d 




d 


Con- 
densing 


Suc- 
tion. 


Inlet. 


Outlet. 


I 1 


I 

8 
7 
4 
6 
2 


151 
161 
147 
152 
. !05 
135 


28 

27.5 

13.0 
8.2 
7.6 

15.7 


36.76 
36.36 
14.29 
6.27 
6.40 
4.62 


28.86 

28.45 
2.29 
2.03 

-2.22 
3.22 


70.3 

70.1 

42.0 

36.43 

37.20 

27.2 


22.60 

22.27 
16.27 
14.10 
17.00 
13.20 


0.80 

1.09 

0.83 

1.1 

2.00 

1.25 


1.0 
1.0 
1.70 
1.93 
1.91 
2.59 


1.0 
1.0 
1.60 
1.92 
1.88 
2.57 



The principal results in four tests are given in the table on page 1311. 
The fuel economy under different conditions of operation is shown in 
the following table: 





3 
03 

a <» 
_o 

QD 


Pounds of Ice-melting Effect with 
Engines — 


B.T.U.per lb.of Steam 
with Engines — 


Ah 

wija 


Non-con- 
densing. 


Non-com- 
pound Con- 
densing. 


Compound 
Con- 
densing. 


a 

5 M 

8.S 

o 
Sz; 


M 

a 
a 

C 

o 
O 


■si 


•S3 

a 

o 

p 


03 O 

ho 


2B 

u & 


J2 . 
03 O 


a£ 

u <3 


£ . 
03 O 


ai 

03 03 


u 

B a 
o o 


150 
150 
105 
105 


28 
7 

28 
7 


24 
14 

34.5 
22 


2.90 
1.69 
4.16 
2.65 


30 
17.5 
43 
27.5 


3.61 
2.11 
5.18 
3.31 


37.5 
21.5 
54 
34.5 


4.51 
2.58 
6.50 
4.16 


393 
240 
591 
376 


513 
300 

725 
470 


640 
366 
923 
591 



The non-condensing engine is assumed to require 25 lbs. of steam per 
I.H.P. per hour, the non-compound condensing 20 lbs., and the compound 
condensing 16 lbs., and the boiler efficiency is assumed at 8.3 lbs. of water 
per lb. coal under working conditions. The following conclusions were 
derived from the investigation: 

1. The capacity of the machine is proportional, almost entirely, to the 
weight of ammonia circulated. This weight depends on the suction- 
pressure and the displacement of the compressor-pumps. The practical 
suction-pressures range from 7 lbs. above the atmosphere, with which a 
temperature of 0° F. can be produced, to 28 lbs. above the atmosphere, 
with which the temperatures of refrigeration are confined to about 28° F. 
At the lower pressure only abant one-half as much weight of ammonia 
can be circulated as at the upper pressure, the proportion being about in 
accordance with the ratios of the absolute pressures, 22 and 42 lbs. 



1310 ICE-MAKING OR REFRIGERATING MACHINES. 

respectively. For each cubic foot of piston-displacement per minute a 
capacity of about one-sixth of a ton of refrigerating effect per 24 hours 
can be produced at the lower pressure, and of about one-third of a ton at 
the upper pressure. No other elements practically affect the capacity 
of a machine, provided the cooling-surface in the brine-tank or other space 
to be cooled is equal to about 36 sq. ft. per ton of capacity at 28 lbs. back 

Eressure. For example, a difference of 100% in the rate of circulation of 
rine, while producing a proportional difference in the range of tempera- 
ture of the latter, made no practical difference in capacity. 

The brine-tank was 10 1/2 X 13 X 102/3 ft., and contained 8000 lineal 
feet of 1-in. pipe as cooling-surface. The condensing-tank was 12 X 10 X 
10 ft., and contained 5000 lineal feet of 1-in pipe as cooling-surface. 

2. The economy in coal-consumption depends mainly upon both the 
suction-pressures and condensing-pressures. Maximum economy with a 
given type of engine, where water must be bought at average city prices, 
is obtained at 28 lbs. suction-pressure and about 150 lbs. condensing- 
pressure.' Under these conditions, for a non-condensing steam-engine 
consuming coal at the rate of 3 lbs. per hour per I.H.P. of steam-cylinders, 
24 lbs. of ice-refrigerating effect are obtained per lb. of coal consumed. 
For the same condensing-pressure, and with 7 lbs. suction-pressure, which 
affords temperatures of 0° F., the possible economy falls to about 14 lbs. of 
refrigerating effect per lb. of coal consumed. The condensing-pressure is 
determined by the amount of condensing-water supplied to liquefy the 
ammonia in the condenser. If the latter is about 1 gallon per minute 
per ton of refrigerating effect per 24 hours, a condensing-pressure of 
150 lbs. results, if the initial temperature of the water is about 56° F. 
Twenty-five per cent less water causes the condensing-pressure to in- 
crease to 190 lbs. The work of compression is thereby increased about 
20%, and the resulting "economy" is reduced to about 18 lbs. of "ice 
effect" per lb. of coal at 28 lbs. suction-pressure and 11.5 at 7 lbs. If, on 
the other hand, the supply of water is made 3 gallons per minute, the 
condensing-pressure may be confined to about 105 lbs. The work of 
compression is thereby reduced about 25%, and a proportional increase 
of economy results. Minor alterations of economy depend on the initial 
temperature of the condensing-water and variations of latent heat, but 
these are confined within about 5% of the gross result, the main element 
of control being the work of compression, as affected by the back pressure 
and condensing-pressure, or both. If the steam-engine supplying the 
motive power may use a condenser to secure a vacuum, an increase of 
economy of 25% is available over the above figures, making the lbs. of 
"ice effect" per lb. of coal for 150 lbs. condensing-pressure and 28 lbs. 
suction-pressure 30.0, and for 7 lbs. suction-pressure, 17.5. It is, however, 
impracticable to use a condenser in cities where water is bought. The 
latter must be practically free of cost to be available for this purpose. 
In this case it may be assumed that water will also be available for con- 
densing the ammonia to obtain as low a condensing-pressure as about 
100 lbs., and the economy of the refrigerating-machine becomes, for 
28 lbs. back pressure, 43.0 lbs. of " ice-effect " per lb. of coal, or for 7 lbs. 
back pressure 27.5 lbs. of ice effect per lb. of coal. If a compound con- 
densing-engine can be used with a steam-consumption per hour per 
horse-power of 16 lbs. of water, the economy of the refrigerating-machine 
may be 25% higher than the figures last named, making for 28 lbs. back 
pressure a refrigerating-effect of 54.0 lbs. per lb. of coal, and for 7 lbs. 
back pressure a refrigerating effect of 34.0 lbs. per lb. of coal. 



PERFORMANCES OF ICE-MAKING MACHINES. 1311 



Performance of a 75-ton Refrigerating-machine. 


(Denton.) 




T3 <a 


T3 o^ 


TJ $24 


"O 09 






o £ ° 


a 2 « 


Sa 




>>~ 


>>NPQ 


>>in 














w 




83 a s 




U I 


O ^ 


° <* 


O S 




3§Ph 

.5 «rifl 


S3 >> H 6 
a S3 W S 

SSf-i 


S § 2 1 


S3 CM 






Maxi 
Eco 
Brir 
Pre! 


* 8"c£ 


S«eJ 


Av. high ammonia press, above atmos 


151 lbs. 


152 lbs. 


147 lbs. 


161 lba. 


Av. back ammonia press, above atmos 


28 " 


8.2 " 


13 " 


27.5 " 


Av. temperature brine inlet 


36.76° 


6.27° 


14.29° 




Av. temperature brine outlet 


28.86° 


2.03° 


2.29° 


28 45° 


A v. range of temperature 


7.9° 


4.24° 


12 00° 


7.91° 


Lbs. of brine circulated per minute 


2281 


2173 


943 


2374 


Av. temp, condensing-water at inlet 


44.65° 


56.65° 


46.9° 


54.00° 


Av. temp, condensing-water at outlet 


83.66° 


85.4° 


85.46° 


82.86° 


Av. range of temperature 


39 01° 


28 75° 


38 56° 


28 80° 


Lbs. water circulated p. min. thro' cond'ser 


442 


315' 


257 


60K5 


Lbs. water per min. through jackets 


25 


44 


40 


14 


Range of temperature in jackets 


24 0° 


16 2° 


16 4° 


29 1° 


Lbs. ammonia circulated per min 


*28.17 


14^68 


16.67 


28 J2 


Probable temperature of liquid ammonia, 










entrance to brine-tank 


*71.3° 

+ 14° 


*68° 

-8° 


*63.7° 

-5° 


76 7° 


Temp, of amm. corresp. to av. back press. 


14° 


Av. temperature of gas leaving brine-tanks 


34.2° 


14.7° 


3.0° 


29.2° 


Temperature of gas entering compressor — 


*39o 


25° 


10.13° 


34° 


Av. temperature of gas leaving compressor 

Av. temp, of gas entering condenser 

Temperature due to condensing pressure. . . 


213° 


263° 


239° 


221° 


200° 


218° 


209° 


168° 


84.5° 


84.0° 


82.5° 


88.0° 


Heat given ammonia: 










By brine, B.T.U. per minute 


14776 


7186 


8824 


14647 


By compressor, B.T.U. per minute 


2786 


2320 


2518 


3020 


By atmosphere, B.T.U. per minute 


140 


147 


167 


141 


Total heat rec. by amm., B.T.U. per min.. . . 


17702 


9653 


11409 


17708 


Heat taken from ammonia: 










By condenser, B.T.U. per min 


17242 


9056 


9910 


17359 


By jackets, B.T.U. per min 


608 


712 


656 


406 


By atmosphere, B.T.U. per min 


182 


338 


250 


252 


Total heat rej. by amm., B.T.U. per min — 


18032 


10106 


10816 


18017 


Dif. of heat rec'd and rej., B.T.U. per min... 


330 


453 


407 


309 


% work of compression removed by jackets 


22% 


31% 


26% 


13% 


Av. revolutions per min 


58.09 
32.5 


57.7 
27.17 


57.88 
27.83 


58 89 


Mean eff. press, steam-cyl., lbs. per sq. in.. . 


32.97 


Mean eff. press, amm.-cyl., lbs. per sq. in. . . 


65.9 


53.3 


59.86 


70.54 


Av. H.P. steam-cylinder 


85.0 
65.7 
23.0 


71.7 
54.7 
24.0 


73.6 
59.37 
20.0 


88.63 


Av. H.P. ammonia-cylinder 


71.20 


Friction in per Cent of steam H.P 


19.67 


Total cooling water, gallons per min. per 




ton per 24 hours 


0.75 
74.8 


1.185 
36.43 


0.797 

44 64 


0.990 


Tons ice-melting capacity per 24 hours 


74.56 


Lbs. ice-refrigerating eff. per lb. coal at 3 










lbs. per H.P. per hour 


24.1 


14.1 


17.27 


23.37 


Cost coal per ton of ice-refrigerating effect 




at $4 per ton 


$0,166 


$0,283 


$0,231 


$0,170 


Cost water per ton of ice-refrigerating effect 




at$1 per 1000 cu. ft 


$0,128 
$0,294 


$0,200 
$0,483 


$0,136 
$0,467 


$0,169 


Total cost of 1 ton of ice-refrigerating eff. . . 


$0,339 



Figures marked thus (*) are obtained by calculation; all other figures 
Obtained from experimental data; temperatures in Fahrenheit are degrees. 



1312 ICE-MAKING OR REFRIGERATING MACHINES. 

Ammonia Compression-machine. 

Actual Results obtained at the Munich Tests. 
(Prof. Linde, Trans. A. S. M. E., xiv, 1419.) 



No. of Test 


1 


2 


3 


4 


5 






Temp, of refrig- ) Inlet, deg. F 

erated brine ) Outlet, deg. F... 


43.194 


28.344 


13.952 


-0.279 


28.251 


37.054 


22.885 


8.771 


-5.879 


23.072 




0.861 
1,039.38 


0.851 
908.84 


0.843 
633.89 


0.837 
414.98 


0.851 


Brine circ. per hour, cu. ft 


800.93 


Cold produced, B.T.U. per hour. . . 


342,909 


263,950 


172,776 


121,474 


220,284 


Cooling water per hour, cu. ft 


338.76 


260.83 


187.506 


139.99 


97.76 


I.H.P. in steam-engine cylinder. . . 


15.80 


16.47 


15.28 


14.24 


21.61 


Cold pro- ) Per I.H.P. in comp.-cyl 


24,813 


18,471 


12,770 


10,140 


11,151 




21,703 


16,026 


11,307 


8,530 


10,194 


h., B.T.U. ) Per lb. of steam 


1,100.8 


785.6 


564.9 


435.82 


512.12 



A test of a 35-ton absorption-machine in New Haven, Conn., by Prof. 
Denton (Trans. A. S. M. E., x, 792), gave an ice-melting effect of 20.1 lbs. 
per lb. of coal on a basis of boiler economy equivalent to 3 lbs. of steam 
per I.H.P. in a good non-condensing steam-engine. The ammonia was 
worked between 138 and 23 lbs. pressure above the atmosphere. 

Performance of a Single-acting Ammonia Compressor. — Tests 
were made at the works of the Eastman Kodak Co., Rochester, N.Y., of a 
machine fitted with two York Mfg. Co.'s single-acting compressors, 
15 in. diam., 22 in. stroke, to determine the horse-power per ton of refrig- 
eration". Following are the principal average results (Bulletin of York 
Mfg. Co.): 



Date of test, 1908 Mar. 6. Mar. 7 Mar. 



Mar. 
10. 



Mar. 
11. 



Mar. 
14. 



Temp, dischg. gas, av 

Temp, suction gas, av . . . . 
Temp, suction at cooler. . 
Temp, liquid at exp. valve 

Temp, brine, inlet 

Temp, brine, outlet 

Revs, per min 

Lbs. liquid NH3 per min. . 
Sue. press, at mach. lb. . . 

Condenser pressure 

Indicated H.P 

Tons Refrig. Capy, 24 hrs. 
I.H.P. per ton capacity . . 



216.2 
15.2 
9.33 
74.85 
22.89 
13.58 
45.1 
20.76 
20.11 

183.96 
69.35 
49.08 
1.418 



217.8 
14.3 
9.36 
74.16 
23.19 
13.96 
45.0 
20.43 
19.90 

184.41 
69.80 
48.79 
1.427 



250.6 
16.8 
10.37 
71.98 
25.26 
14.44 
45.1 
21.04 
19.97 

186.99 
70.05 
50.38 
1.389 



245.8 
14.8 
9.29 
77.91 
22.73 
13.02 
34.3 
15.59 
20.04 

187.27 
52.57 
37.01 
1.422 



253.0 
13.5 
9.90 
76.61 
27.35 
15.53 
56.0 
25.99 
20.18 

187.90 
89.48 
61.39 
1.425 



242.9 
18.2 
13.20 
82.88 
28.41 
16.06 
67.8 



18.13 
186.8 
105.11 

66.65 
1.439 



255.5 
17.9 
9.13 
76.98 
23.43 
12.87 
44.8 
20.40 
20.38 

183.81 
68.61 
49.31 
1.375 



Full details of these tests were reported to the Am. Socy; of Refrig. 
Engrs. and published in Ice and Refrigeration, 1908. 

Performance of Absorption Machines. — From an elaborate review 
by Mr. Voorhees of the action of an absorption machine under certain 
stated conditions, showing the quantity of ammonia circulated per hour 
per ton of refrigeration, its temperature, etc., at the several stages of 
the operation, and its course through the several parts of the apparatus, 
the following condensed statement is obtained: 

Generator. — 30.9 lbs. dry steam, 38 lbs. gauge pressure condensed, 
evaporates 32.2% strong liquor to 22.3% weak liquor. 

Exchanger. — 3.01 lbs. weak liquor at 264° cools to 111°. 

Absorber. — Adds 0.43 lbs. vapor from the brine cooler, making 3.44 
lbs, strong liquor at 111° to go to the pump. 



PERFORMANCES OF ICE-MAKING MACHINES. 1313 



Exchanger. — 3.44 lbs. heated to 224°, some of it is now gas, and the 
rest liquor of a little less than 32% NH 3 . 

Analyzer. — (A series of shelves in a tank above the generator) delivers 
strong liquor to the generator, while the vapor, 91% NH 3 , 0.4982 lb., goes 
to the rectifier. 

Rectifier. — Cools the gas to 110° separating water vapor as 0.0682 lb. 
drip liquor which returns through a trap to the generator. 

Condenser. — 0.43 lb. NH3 gas at 110° cooled and condensed to liquid 
at 90° by 2 gals, of water per rain, heated from 73° to 86°. 

Expansion Valve and Cooler. — Reduces liquid to 0° and boils it at 0°, 
cooling 3 gals, of brine per min. from 12° to 3°. Gas passes to absorber 
and the cycle is repeated. 

Of the 2 gals, per min. of cooling water flowing from the condenser, 
0.2 gal. goes to the rectifier, where it is heated to 142°, and 1.8 gal. through 
the absorber, where it is heated to 110°. ' 

Heat Balance. — Absorbed in the generator 496; in the brine cooler, 
200, Total 696 B.T.U. Rejected; condenser, 220; absorber, 383; rectifier, 
93; Total 696 B.T.U. 

The following table shows the strength of the liquors and the quantity 
of steam required per hour per ton of refrigeration under the conditions 
stated: 

Condenser Pressures. 





140 170 




200 






Suction Pressures. 







15 


30 





15 


30 





15 


30 




24 

13.13 
30.1 

1.7 


35 

25.75 
27.9 

1.6 


42 
33.70 
22.9 

1.4 


22 

10.85 
41.3 

2.1 


32 
22.3 
30.9 

1.9 


38 
29.15 
26.2 

1.8 


18 

6.28 
48.7 
2.4 


28 
17.7 
34.1 

2.3 


36 


Wl per cent 

SG, pounds.. 

SL, pounds 


26.9 
27.9 
2.2 



SI, strong liquor; Wl, weak liquor; SG, lbs. of .steam per hour per ton 
of refrigeration for the generator, SL, do. for the liquor pump. Pressures 
are in lbs. per sq. in., gauge. 

The following table gives the steam consumption in lbs. per hour per 
ton of refrigeration, for engine-driven compressors and for absorption 
machines with liquor pump not exhausting into the generator at the suc- 
tion and condenser pressures (gauge) given : SC, simple non-condensing 
engine, CC. compound condensing engine, A, absorption machine. 

Condenser Pressures. 





140 170 


200 






Suction Pressures. 







15 


30 





15 


30 





15 


30 


SC 


78.3 
42.0 
31.8 


44.5 
23.8 
29.5 


31.1 
16.6 

24.3 


90.5 

48.4 
43.4 


52.5 
28.0 
32.8 


37.2 
19.0 
28.0 


104.0 
55.6 
51.1 


61.4 
32.7 
36.4 


44.5 


CC 


23.9 


A 


30.1 







The economy of the absorption machine is much better for all conditions 
than that of a simple non-condensing engine-driven compressor. At 
suction gauge pressures above 8 to 10 lbs. the economy of the compound 
condensing engine-driven compressor exceeds that of the absorption 
machine, the absorption machine giving the superior economy at suction 
pressures below 8 to 10 lbs. 



1314 ICE-MAKING OR REFRIGERATING MACHINES. 

Means for Applying the Cold. (M. C. Bannister, Liverpool Eng'g 
Soc'y, 1890.) — The most useful means for applying the cold to various 
uses is a saturated solution of brine or chloride of magnesium, which 
remains liquid at 5° Fahr. The brine is first cooled by being circulated 
in contact with the refrigerator-tubes, and then distributed through 
coils of pipes, arranged either in the substances requiring a reduction of 
temperature, or in the cold stores or rooms prepared for them; the air 
coming- in contact with the cold tubes is immediately chilled, and the 
moisture in the air deposited on the pipes. It then falls, making room 
for warmer air, and so circulates until the whole room is at the tempera- 
ture of the brine in the pipes. 

The Direct Expansion Method consists in conveying the compressed 
cooled ammonia (or other refrigerating agent) directly to the room to be 
cooled, and then expanding it through an expansion cock into pipes in the 
room. Advantages of this system are its simplicity and its rapidity of 
action in cooling a room; disadvantages are the danger of leakage of the 
gas and the fact that the machine cannot be stopped without a rapid rise 
in the temperature of the room. With the brine system, with a large 
amount of cold brine in the tank, the machine may be stopped for a con- 
siderable time without serious cooling of the room, 

Air has also been used as the circulating medium. The ammonia-pipes 
refrigerate the air in a cooling-chamber^ and large conduits are used to 
convey it to and return it from the rooms to be cooled. An advantage of 
this system is that by it a room may be refrigerated more quickly than by 
brine-coils. The returning air deposits its moisture on the ammonia- 
pipes, in the form of snow, which is removed by mechanical brushes. 

ARTIFICIAL-ICE MANUFACTURE. 

Under summer conditions, with condensing water at 70°, artificial-ice 
machines use ammonia at a condenser pressure, about 190 lbs. above the 
atmosphere and 15 lbs. suction-pressure. 

In a compression type of machine the useful circulation of ammonia, 
allowing for the effect of cylinder-heating, is about 13 lbs. per hour per 
indicated horse-power of the steam-cylinder. This weight. of ammonia 
produces about 32 lbs. of ice at 15° from water at 70°. If the ice is made 
from distilled water, as in the "can system," the amount of the latter 
supplied by the boilers is about 33% greater than the weight of ice 
obtained. This excess represents steam escaping to the atmosphere 
from the re-boiler and steam-condenser, to purify the distilled water, or 
free it from air; also, the loss through leaks and drips, and loss by melting 
of the ice in extracting it from the cans. The total steam consumed per 
horse-power is, therefore, about 32 x 1.33 = 43.0 lbs. About 7.0 lbs. 
of this covers the steam-consumption of the steam-engines driving the 
brine circulating-pumps, the several cold-water pumps, and leakage, 
drips, etc. Consequently, the main steam-engine must consume 36 lbs. of 
steam per hour per I.H.P., or else live steam must .be condensed to supply 
the- required amount of distilled water. There is, therefore, nothing to be 
gained by using steam at high rates of expansion in the steam-engines, in 
making artificial ice from distilled water. If the cooling water for the 
ammonia-coils and steam-condenser is not too hard for use in the boilers, 
it may enter the latter at about 175° F., by restricting the quantity to 
11/2 gallons per minute per ton of ice. With good coal 8V2 lbs. of feed- 
water may then be evaporated, on the average, per lb. of coal. 

The ice made per pound of coal will then be 32 ■* (43.0 -h 8.5) = 6.0 
lbs. This corresponds with the results of average practice. 

If ice is manufactured by the "plate system," no distilled water is 
used for freezing. Hence the water evaporated by the boiler may be 
reduced to the amount which will drive the steam-motors, and the latter 
may use steam expansively to any extent consistent with the power 
required to compress the ammonia, operate the feed and filter pumps, 
and the hoisting machinery. The latter may require about 15% of the 
power needed for compressing the ammonia. 

If a compound condensing steam-engine is used for driving the com- 
pressors, the steam per indicated steam horse-power, or per 32 lbs. of 
net ice, may be 14 lbs. per hour. The other motors at 50 lbs. of steam 
per horse-power will use 7.5 lbs. per hour, making the total consumption 
per steam horse-power of the compressor 21.5 lbs. Taking the evapora- 



ARTIFICIAL ICE-MANUFACTURE. 1315 

tion at 8 lbs., the feed-water temperature being limited to about 110°, the 
coal per horse-power is 2.7 lbs. per hour. The net ice per lb. of coal is 
then about 32 h- 2.7 =11.8 lbs. The best results with "plate-system" 
plants, using a compound steam-engine, have thus far afforded about 10V2 
lbs. of ice per lb. of coal. 

In the "plate system" the ice gradually forms, in from 8 to 10 days, to 
a thickness of about 14 inches, on the hollow plates, 10 x 14 feet in area, in 
which the cooling fluid circulates. 

In the "can system" the water is frozen in blocks weighing about 
300 lbs. each, and the freezing is completed in from 40 to 48 hours. The 
freezing-tank area occupied by the "plate system" is, therefore, about 
twelve times, and the cubic contents about four times, as much as required 
in the "can system." 

The investment for the "plate" is about one-third greater than for the 
"can" system. In the latter system ice is being drawn throughout the 
24 hours, and the hoisting is done by hand tackle. Some "can" plants 
are equipped with pneumatic hoists and on large hoists electric cranes are 
used to advantage. In the "plate system" the entire daily product is 
drawn, cut, and stored in a few hours, the hoisting being performed 
by power. The distribution of cost is as follows for the two systems, tak- 
ing the cost for. the "can" or distilled-water system as 100, which repre- 
sents an actual cost of about $1.25 per net ton: 

Can System. Plate System- 
Hoisting and storing ice 14.2 2.8 

Engineers, firemen, and coal-passer 15 .0 13 .9 

Coal at $3.50 per gross ton 42 .2 20 .0 

Water pumped directlv from a natural source 

at 5 cts. per 1000 cubic feet 1.3 2.6 

Interest and depreciation at 10% 24 .6 32 .7 

Repairs 2.7 3.4 

100.00 75.4 

A compound condensing engine is assumed to be used by the "plate 
system." 

Test of the New York Hygeia lee-making Plant. — (By Messrs. 
Hupfel, Griswold, and Mackenzie; Stevens Indicator, Jan., 1894.) 

The final results of the tests were as follows: 

Net ice made per pound of coal, in pounds 7 .12 

Pounds of net ice per hour per horse-power 37 .8 

Net ice manufactured per day (12 hours) in tons 97 

Av. pressure of ammonia-gas at condenser, lbs. per sq. in. above 

atmos. . . 135 .2 

Average back pressure of amm.-gas, lbs. per sq. in. aboveatmos. 15.8 

Average temperature of brine in freezing-tanks, degrees F 19 .7 

Total number of cans filled per week 4389 

Ratio of cooling-surface of coils in brine-tank to can-surface 7 to 10 

An Absorption Evaporator lee-making System, built by the Carbon- 
dale Machine Co. is in operation at the ice plant of the Richmond Ice Co., 
Clifton, Staten Island, N. Y., which produces the extra distilled water by 
an evaporator at practically no fuel cost, and thus about 10 tons of dis- 
tilled water ice per ton of coal is obtained. Steam from the boiler at 
100 lbs. pressure enters an evaporator, distilling off steam at 70 !bs., 
which operates the pumps and auxiliary machinery. These exhaust 
into the ice machine generator under 10 lbs. pressure, where the exhaust 
is condensed. In a 100-ton plant the evaporator will condense 43 tons 
of live steam, distilling off 40 tons of steam to operate the auxiliaries, 
which exhaust into the generator: 20 tons of live steam has to be added 
to this exhaust, making 60 tons in all. which is the amount required to 
operate the generator. The 60 tons of condensation from the generator 
and 43 tons from the evaporator go to the re-boiler, making 103 tons of 
distilled water to be frozen into ice. The total steam consumption is the 
60 tons condensed in the generator plus 3 tons for radiation, or 63 tons 
in all. Hence if the boiler evaporates 6.6 lbs. water per pound of coal 
the economy of the plant will be 10 1/2 lbs. ice per pound of coal, a result 
which cannot be obtained even with compound condensing engines and 
compression machines. 



1316 



MARINE ENGINEERING. 



Heat-exchanging coils, on the order of a closed feed-water heater, are 
used to heat the feed-water going to the boiler. The condensation leav- 
ing the generator and evaporator at a high temperature is utilized for 
this purpose; by this means securing a feed-water temperature con- 
siderably in excess of 212°. 

. Ice-Making with Exhaust Steam. — The exhaust steam from electric 
light plants is being utilized to manufacture ice on the absorption system. 
A 10-ton plant at the Holdredge Lighting Co., Holdredge, Neb., built by 
the Carbondale Machine Co., is described in Elec. World, April 7, 1910. 
Here 11 tons of ice were made per day with exhaust steam from the 
electric engines at 21/2 lbs. pressur3, using 6V3 K.W., or 8 1/2 H.P., for 
driving the circulating pumps. 

Tons of Ice per Ton of Coal. — From a long table by Mr. Voorhees, 
showing the net tons of plate ice that may be made in well-designed 
plants under a variety of conditions as to type of engine, the following 
figures are taken: 

Compression, Simple Corliss engine, non-condensing 6.1 tons 

Absorption liquor pump and auxiliaries not exhausting into 

generator, simple, non-condensing engine , 10.0 

Compression, compound condensing engine , . 11.2 

Compression triple-expansion condensing engine. . . . 12.8 

Absorption, pump and auxiliaries exhausting into generator, 

Corliss non-condensing engine 13.3 

Compression and absorption, compound engine, non-condensing 16.0 
Compression, triple-expansion condensing engine, multiple effect 16.5 
Compression and absorption, triple-expansion non-condensing 

engine, multiple effect 19.5 

Standard Ice Cans or Moulds. 

(Buffalo Refrigerating Machine Co.) 



Weight of 
Block. 


Size of Can. 


Time of 
Freezing. 


Weight of 
Block. 


Size of Can. 


Time of 
Freezing. 


pounds 
25 
50 
100 
150 
150 
200 


4x10x24 
6x12x26 
8x15x32 
8x15x44 
10x15x36 
10x20x36 


hours 
12 
20 
36 
36 
48 
48 


pounds 
100 
200 
300 
400 
200 


11x11x32 
11X22X32 
11x22x44 
11x22x56 
14x14x40 


hours 
48 
54 
54 
54 
66 



The above given time of freezing is with a brine temperature of 15° F. 



MARINE ENGINEERING. 

Rules for Measuring Dimensions and Obtaining Tonnage of 
"Vessels. (Record of American and Foreign Shipping. American Bureau 
of Shipping, N. Y., 1890.) — The dimensions to be measured as follows; 

I. Length, L. — From the fore-side of stem to the after-side of stern- 
post measured at middle line on the upper deck of all vessels, except 
those having a continuous hurricane-deck extending right fore and aft, 
in which the length is to be measured on the range of deck immediately 
below the hurricane-deck. 

Vessels having clipper heads, raking forward, or receding stems, or 
raking stern-posts, the length to be the distance of the fore-side of stem 
from aft-side of stern-post at the deep-load water-line measured at middle 
line. (The inner or propeller-post to be taken as stern-post in screw- 
steamers.) 

II. Breadth, B. — To be measured over the widest frame at its widest 
part: in other words, the molded breadth. 

III. Depth, D. — To be measured at the dead-flat frame and at middle 
line of vessel. It shall be the distance from the top of floor-plate to the 
upper side of upper deck-beam in all vessels except those having a con- 
tinuous hurricane-deck, extending right fore and aft, and not intended 
for the American coasting trade, in which the depth is to be the distance 



MARINE ENGINEERING. 1317 

from top of floor-plate to midway between top of hurricane deck-beam 
and the top of deck-beam of the deck immediately below hurricane-deck. 

In vessels fitted with a continuous hurricane-deck, extending right 
fore and aft, and intended for the American coasting trade, the depth is 
to be the distance from top of floor-plate to top of deck-beam of deck 
immediately below hurricane-deck. 

Rule for Obtaining Tonnage. — Multiply together the length, breadth, 
and depth, and their product by 0.75; divide the last product by 100; 
the quotient will be the tonnage. LX B X D X 0.75^ 100 = tonnage. 

The U. S. Custom-house Tonnage Law, May 6, 1864, provides that 
"the register tonnage of a vessel shall be her entire internal cubic capacity 
in tons of 100 cubic feet each." This measurement includes all the space 
between upper decks, however many there may be. Explicit directions 
for making the measurements are given in the law. 

The Displacement of a Vessel (measured in tons of 2240 lbs.) is 
the weight of the volume of water which it displaces. For sea-water it is 
equal to the volume of the vessel beneath the water-line, in cubic feet, 
divided by 35, which figure is the number of cubic feet of sea-water at 
60° F. in a ton of 2240 lbs. For fresh water the divisor is 35.93. The 
U. S. register tonnage will equal the displacement when the entire internal 
cubic capacity bears to the displacement the ratio of 100 to 35. 

The displacement or gross tonnage is sometimes approximately esti- 
mated as follows: Let L denote the length in feet of the boat, B its extreme 
breadth in feet, and D the mean draught in feet; the product of these 
three dimensions will give the volume of a parallelopipedon in cubic feet. 
Putting V for tins volume, we have V = LX BX D. 

The volume of displacement may then be expressed as a percentage 
of the volume V, known as the " block coefficient. " This percentage varies 
for different classes of ships. In racing yachts with very deep keels it 
varies from 22 to 33 : in modern merchantmen from 55 to 90 ; for ordinary 
small boats probably 50 will give a fair estimate. The volume of dis- 
placement in cubic feet divided by 35 gives the displacement in tons. 

Coefficient of Fineness. — A term used to express the relation between 
the displacement of a ship and the volume of a rectangular prism or box 
whose lineal dimensions are the length, breadth, and draught. 

Coefficient of fineness = D X 35 -^ (L X B X W); D being the displace- 
ment in tons of 35 cubic feet of sea-water to the ton, L the length between 
perpendiculars, B the extreme breadth and W the mean draught, all in feet. 

Coefficient of Water-lines. — An expression of the relation of the dis- 
placement to the volume of the prism whose section equals the midship 
section of the ship, and length equal to the length of the ship. 

Coefficient of water-lines = DX 35-*- (area of immersed water sectionXL). 
Seaton gives the following values: 

Coefficient Coefficient of 
of Fineness. Water-lines 

Finely-shaped ships .55 .63 

Fairly-shaped ships .61 .67 

Ordinary merchant steamers 10 to 11 knots. . . .65 .72 

Cargo steamers, 9 to 10 knots .70 .76 

Modern cargo steamers of large size .78 .83 

Resistance of Ships. — The resistance of a ship passing through water 
mav vary from a number of causes, as speed, form of body, displacement, 
midship 'dimensions, character of wetted surface, fineness of lines, etc. 
The resistance of the water is twofold; 1st. That due to the displacement 
of the water at the bow and its replacement at the stern, with the con- 
sequent formation of waves. 2d. The friction between the wetted sur- 
face of the ship and the water, known as skin resistance. A common 
approximate formula for resistance of v essels is 
Resistance = speed 2 X -^/displacement 2 X a constant, or R = £ 2 D* X C. 

If D = displacement in pounds, S = speed in feet per minute, R 
resistance in foot-pounds per minute, R = CS 2 D%. The work done in 
overcoming the resistance through a distance equal to Sis RX S = CS S D*; 
and if E is the efficiency of the propeller and machinery combined, the 
indicated horse-power I. H.P.= CS 3 D%-i- (EX 33,000). 

If S = speed in knots, D — displacement in tons, and C a constant 



1318 



MARINE ENGINEERING. 



which includes all the constants for form of vessel, efficiency of mechanism, 
etc., I.H.P. - SW^-i-C. 

The wetted surface varies as the cube root of the square of the displace- 
ment; thus, let L be the length of edge of a cube just immersed, whose 
displacement is D and wetted surface W. Then D = L 8 or L =^D, 
and W = 5X L 2 = 5 X ( V- ) 2 - Tnat is > w varie s as D$. 

Another approximate formula is 

I.H.P. = area of immersed midship section X S* ■+■ K. 

The usefulness of these two formulae depends upon the accuracy of the 
so-called "constants" C and K, which vary with the size and form of the 
ship, and probably also with the speed. Seaton gives the following, 
which may be taken roughly as the values of C and K under the condi- 
tions expressed: 



General Description of Ship. 



Speed, 


Value 


Value 


knots. 


of C. 


of K. 


15 to 17 


240 


620 


15 " 17 


190 


500 


13 " 15 


240 


650 


11 " 13 


260 


700 


11 " 13 


240 


650 


9 " 11 


260 


700 


13 " 15 


200 


580 


11 " 13 


240 


660 


9 " 11 


260 


700 


11 " 13 


220 


620 


9 " 11 


250 


680 


11 " 12 


220 


600 


9 " 11 


240 


640 


9 " 11 


220 


620 


11 " 12 


200 


550 


10 " 11 


210 


580 


9 " 10 


230 


620 


9 " 10 


200 


600 



Ships over 400 feet long, finely shaped,. 
.. 300 

Ships over 300 feet long, fairly shaped . 
Ships over 250 feet long, finely shaped . 

Ships over 250 feet long, fairly shaped . 

Ships over 200 feet long, finely shaped . . 

Ships over 200 feet long, fairly shaped . 
Ships under 200 feet long, finely shaped 

Ships under 200 feet long, fairly shaped 



Coe fficient of Perfo rmance of Vessels. — The quotient 

^1 (displacement) 2 X (speed in knots) 3 -4- tons of coal in 24 hours 

gives a coefficient of performance which represents the comparative cost 
of propulsion in coal expended. Sixteen vessels with three-stage expan- 
sion-engines in 1890 gave an average coefficient of 14,810, the range being 
from 12,150 to 16,700. 

In 1881 seventeen vessels with two-stage expansion-engines gave an 
average coefficient of 11,710. In 1881 the length of the vessels tested 
ranged from 260 to 320, and in 1890 from 295 to 400. The speed in knots 
divided by the square root of the length in feet in 1881 averaged 0.539; 
and in 1890, 0.579; ranging from 0.520 to 0.641. (Proc. Inst. M. E., 
July, 1891, p. 329.) 

Defects of the Common Formula for Resistance. — Modern 
experiments throw doubt upon the truth of the statement that the resist- 
ance varies as the square of the speed. (See Robt. Mansel's letters in 
Engineering, 1891; also his paper on The Mechanical Theory of Steam- 
ship Propulsion, read before Section G of the Engineering Congress, 
Chicago, 1893.) 

Seaton says: In small steamers the chief resistance is the skin resistance. 
In very fine steamers at high speeds the amount of power required seems 
excessive when compared with that of ordinary steamers at ordinary 



In torpedo-launches at certain high speeds the resistance increases at a 
lower rate than the square of the speed. 

In ordinary sea-going and river steamers the reverse seems to be the 
case. 



MARINE ENGINEERING. 1319 

Rank'ine's Formula for total resistance of vessels of the "wave-line" 
type is: 

R =ALBV* (1 + 4 sin* 6 + sin 4 6), 

in which equation 6 is the mean angle of greatest obliquity of the stream- 
lines, A is a constant multiplier, B the mean wetted girth of the surface 
exposed to friction, L the length in feet, and V the speed in knots. The 
power demanded to impel a ship is thus the product of a constant to be 
determined by experiment, the area of the wetted surface, the cube oi 
the speed, and the quantity in the parenthesis, which is known as the 
" coefficient of augmentation. " In calculating the resistance of ships the 
last term of the coefficient may be neglected as too small to be practically 
important. In applying the formula, the mean of the squares of the 
sines of the angles of maximum obliquity of the water-lines is to be taken 
for sin 2 6, and the rule will then read thus: 

To obtain the resistance of a ship of good form, in pounds, multiply the 
length in feet by the mean immersed girth and by the coefficient of aug- 
mentation, and then take the product of this "augmented surface," as 
Rankine termed it, by the square of the speed in knots, and by the proDer 
constant coefficient selected from the following: 

For clean painted vessels, iron hulls A = .01 

For clean coppered vessels A =0 .009 to .008 

For moderately rough iron vessels A = .011 + 

The net, or effective, horse-power demanded will be quite closely 
obtained by multiplying the resistance calculated, as above, by the speed 
in knots and dividing by 326. The gross, or indicated, power is obtained 
by multiplying the last quantity by the reciprocal of the efficiency of the 
machinery and propeller, which usually should be about 0.6. Rankine 
uses as a divisor in this ease 200 to 260. 

The form of the vessel, even when designed by skillful and experienced 
naval architects, will often vary to such an extent as to cause the above 
constant coefficients to vary somewhat: and the range of variation with 
good forms is found to be from 0.8 to 1.5 the figures given. 

For well-shaped iron vessels, an approximate formula for the horse- 
power required is H. P. = SV Z + 20,000, in which S is the "augmented 
surface." The expression SV S -5- H.P. has been called by Rankine the 
coefficient of propulsion. In the Hudson River steamer "Mary Powell," 
according to Thurston, this coefficient was as high as 23,500. 

The expression D%V 3 •*• H.P. has been called the locomotive performance. 
(See Rankine's Treatise on Shipbuilding, 1864; Thurston's Manual of the 
Steam-engine, part ii, p. 16; also paper by F. T. Bowles, U. S. N., Proc. 
U. S. Naval Institute, 1883.) 

Rankine's method for calculating the resistance is said by Seaton to 
give more accurate and reliable results than those obtained by the older 
rules, but it is criticised as being difficult and inconvenient of application. 

E. R. Mumford's Method of Calculating Wetted Surfaces is given 
in a paper by Archibald Denny, Eng'g, Sept. 21, 1894. The following 
is his formula, which gives closely accurate results for medium draughts, 
beams, and finenesses; 

S = (L X D X 1.7) + (L X B X C), 

In which S = wetted surface in square feet; L = length between perpen- 
diculars in feet; D = middle draught in feet; B = beam in feet; C = 
block coefficient. 

The formula may also be expressed in the form S = L(1.7 D + BC). 

In the case of twin-screw ships having projecting shaft-casings, or in 
the case of a ship having a deep keel or bilge keels, an addition must be 
made for such projections. The formula gives results which are in 
general much more accurate than those obtained by Kirk's method. It 
underestimates the surface when the beam, draught, or block coefficients 
are excessive; but the error is small except in the case of abnormal forms, 
such as stern-wheel steamers having very excessive beams (nearly one- 
fourth the length), and also very full block coefficients. The formula 
gives a surface about 6% too small for such forms. 



1320 



MARINE ENGINEERING. 



The wetted surface of the block is nearly equal to that of the ship of 
the same length, beam and draught; usually 2% to 5% greater. In 
exceedingly tine hollow-line ships it may be 8% greater. 

Area of bottom of block = (F + M) X B; 

Area of sides = 2 M X H. 



Area of sides of ends = 4 X 



&+® 



XH; 



Tangent of half angle of entrance = y 2 B/F = 5/(2 F). 
From this, by a table of natural tangents, the angle of entrance may be 
obtained: 

Angle of Entrance Fore-body in 
of the Block Model, parts of length. 
Ocean-going steamers, 14 knots and upw'd 18° to 15° 0.3 to .36 

12 to 14 knots 21° to 18° 0.26 to 0.3 

cargo steamers, 10 to 12 knots.. 30° to 22° .22 to .26 

Dr. Kirk's Method. — This method is generally used on the Clyde. 

The general idea proposed by Dr. Kirk is to reduce all ships to so 

definite and simple a form that they may be easily compared; and the 

magnitude of certain features of this form shall determine the suitability 

of the ship for speed, etc. 

The form consists of a middle body, which is a rectangular parallelo- 
piped, and fore-body and after-body, prisms having isosceles triangles for 
bases, as shown in Fig. 194. 





D 


E 


t 


5: 


G 


K 




L 




Fig. 194. 

This is called a block model, and is such that its length is equal to that 
of the ship, the depth is equal to the mean draught, the capacity equal 
to the displacement volume, and its area of section equal to the area of 
immersed midship section. The dimensions of the block model may be 
obtained as follows: Let AG = HB = length of fore- or after-body = F; 
GH = length of middle body = M ; KL = mean draught = H; EK = 
area of immersed midship section -4- KL=B. Volume of block = {F+M) X 
BX H; midship section = BX H; displacement in tons = volume in 
cubic ft. ■*- 35. 

AH = AG+ GH = F+ M = displacement X 35 + (B X H). 

To find the Indicated Horse-power from the Wetted Surface. 
(Seaton.) — In ordinary cases the horse-power per 100 feet of wetted 
surface may be found by assuming that the rate for a speed of 10 knots 
is 5, and that the quantity varies as the cube of the speed. For example: 
To find the number of I.H.P. necessary to drive a ship at a speed of 15 
knots, having a wetted skin of block model of 16,200 square feet: 

The rate per 100 feet = (15/10)3 X 5 = 16.875. 
Then I.H.P. required = 16.875 X 162 = 2734. 

When the shin is exceptionally well-proportioned, the bottom quite 
clean, and the efficiency or the machinery high, as low a rate as 4 I.H.P. 
per 100 feet of wetted skin of block model mov be allowed. 

The gross indicated horse-power includes the power necessary to over- 
come the friction and other resistance of the engine itself and the shafting, 
and also the power lost in the propeller. In other words, I.H.P. is no 
measure of the resistance of the ship, and can only be relied on as a means 
of deciding the size of engines for speed, so long as the efficiency of the 
engine and propeller is known definitely, or so long as similar engines and 



MARINE ENGINEERING. 



1321 



propellers are employed in ships to be compared. The former is difficult 
to obtain, and it is nearly impossible in practice to know how much of 
the power shown in the cylinders is employed usefully in overcoming the 
resistance of the ship. The following example is given to show the vari- 
ation in the efficiency of propellers: 

Knots. I.H.P. 

H.M.S. "Amazon," with a 4-bladed screw, gave 12.064 with 1940 

H.M.S. "Amazon," with a 2-bladed screw, increased 

pitch, and fewer revolutions per minute 12.396 " 1663 

H.M.S. " Iris, " with a 4-bladed screw 16.577 " 7503 

H.M.S. "Iris," with 2-bladed screw, increased pitch, 

fewer revolutions per knot 18.587 " 7556 

Relative Horse-power Required for Different Speeds of Vessels. 

(Horse-power for 10 knots = 1.) — The horse-power is taken usually to 
vary as the cube of the speed, but in different vessels and at different 
speeds it may vary from the 2.8 power to the 3.5 power, depending upon 
the lines of the vessel and upon the efficiency of the engines, the pro- 
peller, etc. (The power may vary at a much higher rate than the 3.5 
power of the speed when the speed is much less than normal, and the 
machinery is therefore working at less than its normal efficiency.) 





4 


6 


8 


10 


12 


14 


16 


18 


20 


22 


24 


26 


28 


30 


FfPoc 






























S 2 ' 8 


0/69 


239 


535 


1. 


1.666 


2,565 


3 729 


5 185 


6.964 


9.095 


11.60 


14.52 


17,87 


21 67 


S 2,9 


0701 


227 


524 


1 


1 697 


2.653 


3.908 


5 499 


7 464 


9,841 


12.67 


15.97 


19 80 


24 19 


S3 


0640 


216 


512 


1. 


1.728 


2 744 


4.096 


5 832 


8. 


10,65 


13 82 


17,58 


21 95 


77 


,S3.1 


0584 


205 


501 


1. 


1 760 


2.838 


4 293 


6 185 


8 574 


11.52 


15 09 


19.34 


24 33 


30 14 


S3* 2 


0533 


195 


490 


1. 


1.792 


2.935 


4.500 


6,559 


9.189 


12.47 


16.47 


21.28 


26.97 


33.63 


S3-3 


0486 


185 


479 


1. 


1.825 


3.036 


4.716 


6 957 


9.849 


13 49 


17,98 


23.41 


29 90 


37,54 


S3'4 


0444 


176 


468 


1. 


1 859 


3.139 


4.943 


7,378 


10,56 


14 60 


19.62 


25 76 


33 14 


41 90 


S3-5 


.0405 


.167 


.458 


1. 


1.893 


3.247 


5.181 


7.824 


11.31 


15.79 


21.42 


28.34 


36.73 


46.77 



Example in Use of the Table. ■ — A certain vessel makes 14 knots 
speed with 587 I.H.P. and 16 knots with 900 I.H.P. What I.H.P. will 
be required at 18 knots, the rate of increase of horse-power with increase of 
speed remaining constant? The first step is to find the rate of increase, 
thus: 14^ : 16# :: 587 : 900. 

x log 16 - x log 14 = log 900 - log 587; 
x (0.204120 - 0.146128) = 2.954243 - 2.768638, 
whence x (the exponent of £ in formula H.P. =c S x ) = 3.2. 

From the table, for S^ 2 and 16 knots, the I.H.P. is 4.5 times the I.H.P. 
at 10 knots; .'. H.P. at 10 knots = 900 -s- 4.5 = 200. 

From the table for S 3 ' 2 and 18 knots, the I.H.P. is 6.559 times the I.H.P. 
at 10 knots; .'. H.P. at 18 knots = 200 X 6.559 = 1312 H.P. 

Resistance per Horse-power for Different Speeds. (One horse- 
power = 33,000 lbs. resistance overcome through 1 ft. in 1 min.) — The 
resistances per horse-power for various speeds are as follows: For a speed 
of 1 knot, or 6080 feet per hour = 101 1/3 ft. per min., 33,000 -4- 101 1/3 = 
325.658 lbs. per horse-power; and for any other speed 325.658 lbs. divided 
by the speed in knots; or for 

1 knot 325.66 lbs. 8 knots 40.71 lbs. 

2 knots 162.83 " 9 " 36.18 " 

3 " 108.55 " 10 " 32.57 " 

4 *' 81.41 " 11 " 29.61 " 

5 " 65.13 " 12 " 27.14 .*' 

6 " 54.28 " 13 " 25.05 " 

7 " 48.52 " 14 " 23.26 " 

More accurate methods than those above given for estimating the horse- 
power required for anv proposed ship are: 1. Estimations calculated 
rom the results of trials of "similar" vessels driven at "corresponding' 



15 knots 21.71 lbs. 



16 ' 


' 20.35 


17 ' 


' 19.16 


18 ' 


' 18.09 


19 * 


' 17.14 


20 ' 


' 16.28 



1322 



MARINE ENGINEERING. 



_., "similar" vessels being those that have the same ratio of length 
to breadth and to draught, and the same coefficient of fineness, and 
"corresponding" speeds those which are proportional to the square roots 
of the lengths of the respective vessels. Froude found that the resistances 
of such vessels varied almost exactly as wetted surface X (speed) 2 . 

2. The method employed by the British Admiralty and by some Clyde 
shipbuilders, viz., ascertaining the resistance of a model of the vessel, 
12 to 20 ft. long, in a tank, and calculating the power from the results 
obtained. 

Estimated Displacement, Horse-power, etc. — The table on the 
next page, calculated by the author, will be found convenient for making 
approximate estimates. 

The figures in 7th column are calculated by the formula H.P. =£ 3 Z)3 -*■ c 
in which c = 200 for vessels under 200 ft. long when C = 0.65, and 210 
when C = 0.55; c = 200 for vessels 200 to 400 ft. long when C =0.75, 
220 when C = 0.65, 240 when C = 0.55; c = 230 for vessels over 400 ft. 
long when C = 0.75, 250 when C = 0.65, 260 when C = 0.55. 

The figures in the 8th column are based on 5 H.P. per 100 sq. ft. of 
wetted surface. 

The di ameters of screw in the 9th column are from formu la D = 3.31 
^J/l.H.P., and in the 10th column from formula D = 2.71 ^I.H.P. 

To find the diameter of screw for any other speed than 10 knots, revolu- 
tions being 100 per minute, multiply the diameter given in the table by 
the 5th root of the cube of the given speed -4- 10. For any other revolu- 
tions per minute than 100, divide by the revolutions and multiply by 100. 

To find the approximate horse-power for any other speed than 10 knots, 
multiply the horse-power given in the table by the cube of the ratio of the 
given speed to 10, or by the relative figure from table on p. 1321. 

F. E. Cardullo, Mach'y, April, 1907.. gives the following formula as 
closely approximating the speed of modern types of hulls: S = 6.35 
3 / IH p 
1/ ' 2/ ,* ' m wn i c h & = speed in knots, D = displacement in tons. If 

we take S = 10 knots, then I.H.P. -j- D 2 /3 = 3.906. Let D = 10,000, and 
S = 10, then H.P. = 1813. The table on page 1323 gives for a displace- 
ment of 10,400 tons and a coefficient of fineness 0.65, 1966 and 1760 H.P., 
averaging 1863 H.P. 

Internal Combustion Marine Engines. — Linton Hope (Eng'g., ! 
April 8, 1910), in a paper on the application of internal combustion engines j 
to fishing boats and fine-lined commercial vessels, gives a table showing 
the brake H.P. required to propel such vessels at various speeds. The 
following table is an abridgment. L=load water line; D = displacement j 
in tons. 



Block Coefficient. 


0.25 


0.3 


0.35 


0.4 


L 


D 


L 


D 


L 


D 


L 


D 


78 


105 


75 


100 


72 


95 


69 


90 


71 


81 


69 


77 


66 


73 


63 


70 


65 


62 


63 


60 


60 


58 


57 


55 


59 


47 


57 


45 


54 


44 


5?. 


42 


54 


36 


52 


35 


50 


34 


48 


32 


50 


28 


48 


27 


46 


26 


44 


25 


46 


22 


44 


21 


42 


20 


40 


19 


41 


17 


40 


16 


38 


15 


37 


14 


J« 


13 


37 


12 


35 


1U/9 


34 


1.1 


35 


9 


34 


81/D! 


32 


8 


31 


71/9, 


32 


6 V? 


31 


6 


30 


5V-> 


29 


5 


30 


4 V? 


29 


41/ 4 


28 


33/4 


21 


31/9, 


28 


3V4 


27 


3 


26 


23/4 


25 


21/2 





Speed 


in Knots 






4 


5 


6 


7 


8 


9 


10 


Brake Horse-power. 



20 
17 

15 



21/2 



30 
25 

22 
19 
16 
13 
12 
11 

9 

7 

51/2 

5 

41/2 



43 
37 
32 
27 
24 
20 
17 
15 
13 
11 

9 

7 

61/2 



MARINE ENGINEERING. 



1323 



Estin: 


late 


I Displacement, Horse-power, etc., 


of Steam-vessels of 








Various Sizes. 








M - 




Si 
A 3 


J* I 


Displacement. 

LBDX C 

35 


Wetted Surface 

LQ..1D+BQ 

sq. ft. 


Estimated Horse- 
power at 10 knots. 


Diam. of S 
revs, pe 


crew for 10, 
(1 and 100 


||. 


Calc. 
from Dis- 


Calc. from 
Wetted 




If Pitch = 


If Pitch = 










tons. 




placem't. 


Surface. 


Diam. 


1.4 Diam. 


12 


3 


1.5 


0.55 


0.85 


48 


4.3 


2.4 


4.4 


3.6 


<«{ 


3 


1.5 


.55 


1.13 


64 


5.2 


3.2 


4.6 


3.8 


4 


2 


.65 


2.38 


96 


8.9 


4.8 


5.1 


4.2 


20 | 


3 


1.5 


.55 


1.41 


80 


6.0 


4.0 


4.7 


3.9 


4 


2 


.65 


2.97 


120 


10.3 


6.0 


5.3 


4.3 


24 { 


3.5 


1.5 


.55 


1.98 


104 


7.5 


5.2 


5 


4.1 


4.5 


2 


.65 


4.01 


152 


12.6 


7.6 


5.5 


4.5 


30 { 


4 


2 


.55 


3.77 


168 


11.5 


8.4 


5.4 


4.4 


5 


2.5 


.65 


6.96 


224 


18.2 


11.2 


5.9 


4.8 


40{ 


4.5 


2 


.55 


5.66 


235 


15.1 


11.8 


5.7 


4.7 


6 


2.5 


.65 


11.1 


326 


24.9 


16.3 


6.3 


5.2 


50 { 


6 


3 


.55 


14.1 


420 


27.8 


21.0 


6.4 


5.4 


8 


3.5 


.65 


26 


558 


43.9 


27.9 


7.1 


1 5.8 


60 { 


8 


3.5 


.55 


26.4 


621 


42.2 


31.1 


7.0 


5.7 


10 


4 


.65 


44.6 


798 


62.9 


39.9 


7.6 


6.2 


70 { 


10 


4 


.55 


44 


861 


59.4 


43.1 


7.5 


6.1 


12 


4.5 


.65 


70.2 


1082 


85.1 


54.1 


8.1 


6.6 


80 { 


12 


4.5 


.55 


67.9 


1140 


79.2 


57.0 


7.9 


6.5 


14 


5 


.65 


104.0 


1408 


111 


70.4 


8.5 


7.0 


90 •{. 


13 


5 


.55 


91.9 


1408 


97 


70.4 


8.3 


6.8 


16 


6 


.65 


160 


1854 


147 


92.7 


9 


7.3 


f 


13 


5 


.55 


102 


1565 


104 


78.3 


8.4 


6.9 


100 | 


15 


5.5 


.65 


153 


1910 


143 


95.5 


8.9 


7.3 


( 


17 


6 


.75 


219 


2295 


202 


115 


9.6 


7.8 


( 


14 


5.5 


.55 


145 


2046 


131 


102 


8.8 


7.2 


120 \ 


16 


6 


.65 


214 


2472 


179 


124 


9.4 


7.6 


i 


18 


6.5 


.75 


30? 


2946 


250 


147 


10 


8.2 


l 


16 


6 


.55 


211 


2660 


169 


133 


9.2 


7.4 


140 { 


18 


6.5 


.65 


306 


3185 


227 


159 


9.8 


8.0 


( 


20 


7 


.75 


420 


3766 


312 


188 


10.5 


8.5 




17 


6.5 


.55 


278 


3264 


203 


163 


9.6 


7.8 


160 ] 


19 


7 


.65 


395 


3880 


269 


194 


10.1 


8.3 


( 


21 


7.5 


.75 


540 


4560 


368 


228 


10.8 


8.8 


( 


20 


7 


.55 


396 


4122 


257 


206 


10.1 


8.2 


180 


22 


7.5 


.65 


552 


4869 


337 


243 


10.6 


8.7 


( 


24 


8 


.75 


74\ 


5688 


455 


284 


11.3 


9.2 


( 


22 


7 


.55 


484 


4800 


257 


240 


10.1 


8.2 


200 


25 


8 


.65 


743 


5970 


373 


299 


10.8 


8.8 


I 


28 


9 


.75 


1080 


7260 


526 


363 


11.6 


9.5 


{ 


28 


8 


.55 


880 


7250 


383 


363 


10.9 


8.9 


250 


32 


10 


.65 


1486 


9450 


592 


473 


11.9 


9.7 


( 


36 


12 


.75 


2314 


11850 


875 


593 


12.8 


10.5 


( 


32 


10 


.55 


1509 


10380 


548 


519 


11.7 


9.6 


300 ! 


36 


12 


.65 


2407 


13140 


806 


657 


12.6 


10.4 


( 


40 


14 


.75 


3600 


17140 


1175 


857 


13.6 


11.1 


( 


38 


12 


.55 


2508 


14455 


769 


723 


12.5 


10.2 


350 ] 


42 


14 


.65 


3822 


17885 


1111 


894 


13.5 


11.0 


( 


46 


16 


.75 


5520 


21595 


1562 


1080 


14.4 


11.8 


( 


44 


14 


.55 


3872 


19200 


1028 


960 


13.3 


10.8 


400 ] 


48 


16 


.65 


5705 


23360 


1451 


1168 


14.2 


11.6 


( 


52 


18 


.75 


8023 


27840 


2006 


1392 


15.2 


12.4 


I 


50 


16 


.55- 


5657 


24515 


1221 


1226 


13.7 


11.2 


450 


54 


18 


.65, 


. 8123 


29565 


1616 


1478 


14.5 


11.9 


( 


58 


20 


jm 


11157 


34875 


2171 


1744 


15.4 


12.6 


500 j 


52 


18 


.55 


7354 


29600 


1454 


1480 


14.2 


11.6 


56 


20 


.65 


10400 


35200 


1966 


1760 


15.1 


12.4 


( 


60 


22 


.75 


14143 


41200 


2543 


2060 


15.9 


13.0 


( 


56 


20 


.55 


9680 


36245 


1747 


' 1812 


14.7 


12.0 


550 \ 


60 


22 


.65 


13483 


42735 


2266 


2137 


15.5 


12.7 


I 


64 


24 


.75 


18103 


49665 


2998 


2483 


16.4 


13.4 


( 


60 


22 


.55 


12446 


42900 


2065 


2145 


15.2 


12.5 


600 \ 


64 


24 


.65 


17115 


50220 


2656 


2511 


15.4 


13.1 




68 


26 


.75 


22731 


58020 


3489 


2901 


16.9 


13.8 



1324 MARINE ENGINEERING. 

THE SCREW-PROPELLER. 

The "pitch" of a propeller is the distance which any point in a blade 
describing a helix will travel in the direction of the axis during one revolu- 
tion, the point being assumed to move around the axis. The pitch of a 
propeller with a uniform pitch is equal to the distance a propeller will 
advance during one revolution, provided there is no slip. In a case of 
this kind, the term " pitch " is analogous to the term "pitch of the thread" 
of an ordinary single-threaded screw. 

Let P = pitch of screw in feet, R = number of revolutions per second, 
V = velocity of stream from the propeller = P X R, v = velocity of the 
ship in feet per second, V — v = slip, A = area in square feet of section 
of stream from the screw, approximately the area of a circle of the same 
diameter, A X V = volume of water projected astern from the ship in 
cubic feet per second. Taking the weight of a cubic foot of sea-water 
at 64 lbs., and the force of gravity at 32, we have from the common for- 

Vi IV Vi *W 

mula for force of acceleration, viz.: F= M-r = — -r- , or i* 1 =* — vi, when 

i second. 

64 A V 
Thrust of screw in pounds = — ^r— (V — v) — 2 AV (V — v). 

Rankine (Rules, Tables, and Data, p. 275) gives the following: To 
calculate the thrust of a propelling instrument (jet, paddle, or screw) in 
pounds, multiply together the transverse sectional area, in square feet, 
of the stream driven astern by the propeller; the speed of the stream 
relatively to the ship in knots; the real slip, or part of that speed which is 
impressed on the stream by the propeller, also in knots; and the constant 
5.66 for sea-water, or 5.5 for fresh water. If S = speed of the screw in 
knots, s = speed of ship in knots, A = area of the stream in square feet 
(of sea-water), 

Thrust in pounds = A X S (S - s) X 5.66. 

The real slip is the velocity (relative to water at rest) of the water pro- 
jected sternward ; the apparent slip is the difference between the speed of 
the ship and the speed of the screw; i.e., the product of the pitch of the 
screw by the number of revolutions. 

This apparent slip is sometimes negative, due to the working of the 
screw in disturbed water which has a forward velocity, following the ship. 
Negative apparent slip is an indication that the propeller is not suited 
to the ship. The apparent slip should generally be about 8% to 10% at 
full speed in well-formed vessels with moderately fine lines; in bluff cargo 
boats it rarely exceeds 5%. 

The effective area of a screw is the sectional area of the stream of water 
laid hold of by the propeller, and is generally, if not always, greater than 
the actual area, in a ratio which in good ordinary examples is 1.2 or there- 
abouts, and is sometimes as high as 1.4; a fact probably due to the stiffness 
of the water, which communicates motion laterally amongst its particles. 
(Rankine's Shipbuilding, p. 89.) --•'"., 

Prof D. S. Jacobus, Trans. A.S.M. E., xi, 1028, found the ratio of the 
effective to the actual disk area of the screws of different vessels to be as 
follows: 

Tug-boat, with ordinary true-pitch screw 1 .42 

Tug-boat, with screw having blades projecting backward .57 

Ferryboat " Bergen, " with or- ( at speed of 12.09 stat. miles per hr. . 1 .53 

dinary true-pitch screw t at speed of 13.4 stat.. miles per hr. . 1 .48 

Steamer "Homer Ramsdell," with ordinary true-pitch screw 1 .20 

Size of Screw. — Seaton savs: The size of a screw depends on so 

many things that it is very difficult to lay down any rule for guidance, 
and much must always be left to the experience of the designer, to allow 
for all the circumstances of each particular case. The following rules are 
given for ordinary cases (Seaton and RoUnthwaite's Pocket-book): 

P = pitch of propeller in feet = ^qqq 3 ,!^ - in which- S = speed in 



THE SCREW-PROPELLER. 



1325 



knots, R = revolutions per minute, and x = percentage of apparent slip. 
For a slip of 10%, pitch = 112.6 S -s- R. 



D = diameter of propeller = K 



I I-H.P. K 



being a coefficient given 



= 20,0 00^ I .H.P. -i-(PXR) 3 . 

t C Vl.H.P. +■ R, in which C is a coeffi- 



in the table below. If K = 20, D = 

Total developed area of blades = 
cient to be taken from the table. 

Anoth er form ula for pitch, given in Seaton's Marine Engineering, is 

C v 3 / 1 H P 
P— p 4/ * ' ' , in which C= 737 for ordinary vessels, and 660 for slow- 
speed cargo vessels with full lines. 



Thickness of blade at root 



V nb 



X k, in which d = diameter of tail 



shaft in inches, n = number of blades, b = breadth of blade in inches 
where it joins the boss, measured parallel to the shaft axis; k = 4 for cast 
iron, 1.5 for cast steel, 2 for gun-metal, 1.5 for high-class bronze. 

Thickness of blade at tip: Cast iron 0.04 D -V 0.4 in.; cast steel 0.03 D + 
0.4 in.; gun-metal 0.03 D + 0.2 in.; high-class bronze 0.02 D +0.3 in., 
where D = diameter of propeller in feet. 

Propeller Coefficients. 



Descriptiou of Vessel. 



gig 



J 

hi 



Bluff cargo boats 

Cargo, moderate lines 

Pass, and mail, fine lines. . 



" very fine.. 
Naval vessels, " " . 
Torpedo-boats, •.' ..." . 



8-10 
10-13 
13-17 
13-17 
17-22 
17-22 
16-22 
16-22 
20-26 



Twin 
One 

Twin 



17 -17.5 

18 -19 
19.5-20.5 
20.5-21.5 

21 -22 

22 -23 

21 -22.5 

22 -23.5 
25 



19 -17.5 
17 -15.5 
15 -13 
14.5-12.5 
12.5-11 
10.5- 9 
11.5-10.5 
8.5-7 
7-6 



Cast iron 
C.LorS. 
G.M.orB 



C. I., cast iron; G. M., gun-metal; B., bronze; S. 



From the formulae D = 20,000 



Vcpx 



x rv 



and P 



steel; F.S., forged steel. 
7371. H. P. 



v/- 



R D 2 



if 



P = D and R = 100, we obtain D = -^ 400 X I.H.P. = 3.31 ^/i.H.P. 

If P = 1.4 D and R = 100, then D = -^145.8 X I.H.P. = 2.71 ^I.H.P. 

From these two formulae the figures for diameter of screw in the table 
on page 1323 have been calculated. They may be used as rough approx- 
imations to the correct diameter of screw for any given horse-power, for 
a speed of 10 knots and 100 revolutions per minute. 

For any other number of revolutions per minute multiply the figures 
in the table by 100 and divide by the given number of revolutions. For 
any other speed than 10 knots, since the I.H.P. varies approximately as 
the cube of the speed, and the diameter of the screw as the 5th root of the 
I.H.P., multiply the diameter given for 10 knots by the 5th root of the 
cube of one-tenth of the given speed. Or, multiply by the following 
factors: 

For speed of knots: 

_4 5_ 6 7 8 9 11 12 13 14 15 16 

$(S - 10)3 

= 0.577 0.660 0.736 0.807 0.875 0.939 1.059 1.116 1.170 1.224 1.275 1.327 



1326 



MARINE ENGINEERING. 



Speed: 
17 18 



19 



20 



21 22 23 24 25 26 27 



yos-s- 10) 3 

= 1.375 1.423 1.470 1.515 1.561 1.605 1.648 1.691 1.733 1.774 1.815 1.855 

For more accurate determinations of diameter and pitch of screw, the 
formulae and coefficients given by Seaton, quoted above, should be used. 

Efficiency of the Propeller. — According to Rankine, if the slip of 
the water be s, its weight W, the resistance R, and the speed of the ship v, 
R — Ws -s- g; Rv = Wsv 4- g. 

This impelling action must, to secure maximum efficiency of propeller, 
be effected by an instrument which takes hold of the fluid without shock 
or disturbance of the surrounding mass, and, by a steady acceleration, 
gives it the required final velocity of discharge. The velocity of the 
propeller overcoming the resistance R would then be 

[v+ (v+6)] + 2 = v+ 8/2; 
and the work performed would be 

R (v+ 8/2) = Wvs ■*■ g+ Ws 2 -J- 2 fit, 
the first of the last two terms being useful, the second the minimum lost 
work; the latter being the wasted energy of the water thrown backward. 
The efficiency is E = v -^ (v + s/2) ; and this is the limit attainable with 
a perfect propelling instrument, which limit is approached the more nearly 
as the conditions above prescribed are the more nearly fulfilled. The 
efficiency of the propelling instrument is probably rarely much above 
0.60, and never above 0.80. 

In designing the screw-propeller, as was shown by Dr. Froude, the 
best angle for the surface is that of 45° with the plane of the disk; but as 
all parts of the blade cannot be given the same angle, it should, where 
practicable, be so proportioned that the "pitch-angle at the center of 
effort" should be made 45°. The maximum possible efficiency is then, 
according to Froude, 77%. 

In order that the water should be taken on without shock and dis- 
charged with maximum backward velocity, the screw must have an 
axially increasing pitch. 

The true screw is by far the more usual form of propeller, in all steamers, 
both merchant and naval. (Thurston, Manual of the Steam-engine, 
part ii, p. 176.) 

The combined efficiency of screw, shaft, engine, etc., is generally taken 
at 50%. In some cases it may reach 60% or 65%. Rankine takes the 
effective H.P. to equal the I.H.P. h- 1.63. 

Results of Researches on the efficiency of screw-propellers are sum- 
marized by S. W. Barnaby, in a paper read before section G of the Engi- 
neering Congress, Chicago, 1893. He states that the following general 
principles have been established: 

(a) There is a definite amount of real slip at which, and at which only, 
maximum efficiency can be obtained with a screw of any given type, 
and this amount varies with the pitch-ratio. The slip-ratio proper to a 
given ratio of pitch to diameter has been discovered and tabulated for a 
screw of a standard type, as below : 

Pitch-ratio and Slip for Screws of Standard Form. 



Pitch-ratio . 


Real Slip of 
Screw. 


Pitch-ratio. 


Real Slip of 
Screw. 


Pitch-ratio. 


Real Slip of 
Screw. 


0.8 


15.55 


1.4 


19.5 


2.0 


22.9 


0.9 


16.22 


1.5 


20.1 


2.1 


23.5 


1.0 


16.88 


1.6 


20.7 


2.2 


24 


1.1 


17.55 


1.7 


21.3 


2.3 


24.5 


1.2 


18.2 


1.8 


21.8 


2.4 


25.0 


1.3 


18.8 


1.9 


22.4 


2.5 


25.4 



(&) Screws of large pitch-ratio, besides being less efficient in them- 
selves, add to the resistance of the hull by an amount bearing some pro- 
portion to their distance from it, and to the amount of rotation left in 
the race. 

(c) The best pitch-ratio lies probably between 1.1 and 1.5. 

(d) The fuller the lines of the vessel, the less the pitch-ratio should be. 



THE SCREW-PROPELLER. 



1327 



(e) Coarse-pitched screws should be placed further from the stern 
than fine-pitched ones. 

(/) Apparent negative slip is a natural result of abnormal proportions 
of propellers. 

(g) Three blades are to be preferred for high-speed vessels, but when 
the diameter is unduly restricted, four or even more may be advantageously 
employed. 

(k) An efficient form of blade is an ellipse having a minor axis equal 
to four-tenths the major axis. 

(t) The pitch of wide-bladed screws should increase from forward to 
aft, but a uniform pitch gives satisfactory results when the blades are 
narrow, and the amount of the pitch variation should be a function of the 
width of the blade. 

0') A considerable inclination of screw-shaft produces vibiation, and 
with right-handed twin-screws turning outwards, if the shafts are inclined 
at all, it should be upwards and outwards from the propellers. 

For results of experiments with screw-propellers, see F. C. Marshall, 
Proc. Inst. M. E., 1881; R. E. Froude, Trans. Inst. Nav. Archs., 1886; 
G. A. Calvert, Trans. Inst. Nav. Archs., 18S7: S. W. Barnaby, Proc. Inst. 
C. E„ 1890, vol. cii, and D. W. Taylor's " Resistance of Ships and Screw 
Propulsion." Also Mr. Taylor's paper in Proc. Soc. Nav. Arch. & Marine 
Engrs., 1904. Mr. Taylor found the highest efficiencies, exceeding 70%, 
in propellers with pitch ratios from 1.0 to 1.5 ratio of width of blade to 
diameter of 1/8 to 1/5, and ratio of developed area of blade to disk area of 
0.201 to 0.322. 

One of the most important results deduced from experiments on model 
screws is that they appear to have practically equal efficiencies through- 
out a wide range both in pitch-ratio and in surface-ratio; so that great 
latitude is left to the designer in regard to the form of the propeller. 
Another important feature is that, although these experiments are not 
a direct guide to the selection of the most efficient propeller for a particu- 
lar ship, they supply the means of analyzing the performances of screws 
fitted to vessels, and of thus indirectly determining what are likely to be 
the best dimensions of screw for a vessel of a class whose results are 
known. Thus a great advance has been made on the old method of trial 
upon the ship itself, which was the origin of almost every conceivable 
erroneous view respecting the screw-propeller. {Proc. Inst. M. E., July, 
1891.) 

Mr. Barnaby in Proc. Inst. C. E., 1890, gives a table to be used in cal- 
culations for determining the best dimensions of screws for any given 
speed and H.P. from which the following table is abridged. It is deduced 
from Froude's experiments at Torquay. (Trans. Inst. Nav. Archs., 1886.) 

Ca = disk area in sq. ft. X 7 3 /H.P. Cr = revs, per min. X D/V. 
V = speed in knots, D = diam. of screw in ft. H.P. = effective H.P. 
on the screw shaft. Disk area = 0.7854 D 2 = Cj X I.H.P./P*. Revs, 
per min. = Cr X V/D. The constants Ca and Cr assume a standard 
value of the speed of the wake, equal to 10% of the speed of the ship. 
In a very full shi£ it may amount to 30%, therefore V should be reduced 
when using the constants by amounts varying from 20% to as the 
form varies from "very full" to "fairly fine." 



Effy. of 

Screw, %. 


63 


67 


68 


69 


68 


66 


63 


Pitch ratio. 


Ca 


Cr 


C A 


CR 


C A 


Cr 


C A 


CR 


C A 


Cr 


C A 


Cr 


C A 


Cr 


0.80 


468 


122 


304 


128 


215 


134 


157 


142 


115 


150 


86 


160 


65 


171 


1.00 


546 


99 


355 


104 


251 


109 


184 


115 


135 


123 


100 


131 


76 


140 


1.20 


625 


83 


405 


87 


288 


92 


210 


97 


154 


104 


115 


111 


87 


119 


1.40 


704 


72 


456 


76 


325 


80 


236 


85 


173 


90 


129 


97 


98 


104 


1.60 


780 


63 


507 


67 


360 


71 


263 


75 


193 


80 


144 


87 


109 


93 


1.80 






558 


60 


396 


64 


290 


68 


212 


73 


159 


78 


17.0 


84 


2.QQ 
2.20 
2.40 






609 
660 
710 


55 
50 
47 


432 
469 
505 


58 
54 
50 


315 
342 
369 


62 
57 
53 


231 
250 
270 


67 
62 
57 


173 

187 
202 


72 
67 
62 


131 
142 
153 


77 






7? 






67 









1328 



MARINE ENGINEERING. 



vjj-bs 



lj-bs 'aoBjiug 

SUL}139JJ 



•SJOtTSJ 'IT3UX 

uo paadg 



<IH pa^oipui 









4.'^u9tuaot|dsiQ 



*»J 'n^ia 



•%j 'q+ddQ 



•^j 'q^pTOjy 



*■%} *q;Su8T[ 



•a^d 



^■«■^ON-^0'CO^--- 



OO -"I" — ^tNOOOOOvOTiO 

a^ oo" ao" ©" o" c^f t" "^■"•cTe;* °o" 



)*OONNNNOO»q;Nr«- ■ 
)>Ot>tslNtsI>>OvOvO»CNtsl>, • 



8n 



^-O^T 

- . . • . -sO 04 

rq m •* ■* os • • 



O sO © — if\CM>NN\ON £ 



t»OM>0000»0 — — NNOtf 



OOOOOOOOOOQOOOOO 
U-\000000(NOOOOOOOO 

-o iT> co mmoMfiifio in o o o o o o 
r-drrso*©*©"— "r<"\"T"©"o»"©"©"r>."so" 00*00" 



OOOOOOOOOOmcJCC^Oini^ 



• O* • Cvl its its Os irt s© 

•Os ■ — O © c^ M oo O COtrwt 



l~>.fArsJfr>itsqf<|rOfMrA<S«>00tNO'Osr^! 

irsrsirs)c-q{virsirsirsirgrsi(NrsicorsiNfo 



© m^r 

(AvCNOo'cOpQ-N.-tjaSf 



"V sQ ITS sQ sQ sQ s£ 



• a • '■ 

: o : : 

:« : j 
So g-c 






CfO^^^aop^HoMcQWJ 



I Jjj! »o m 2 •» r 

Ilf|2|fgs 

*— <- -•- • Con 



^^_- - bet-" _=,-, 

.ceo c •- c° ^S 












• rap-si h§i 

(- . .oS ^ sU >-i c M cd 

lis "ilii jl 

I 1*1 of If || 

■^N.iUCB 












MARINE PRACTICE 



1329 



Marine Practice, 1901. — The following tables and "summary of 
results" are taken from a paper on "Review of Marine Engineering in 
the Last Ten Years," by Jas. McKechnie, Proc. Inst. M. E., 1901: Eng. 
News, Aug. 29, 1901. 

Particulars of Cargo Steamers for North Atlantic Trade, to illustrate 
Fuel Economy of Large-Capacity Ships. (All are three-decked vessels, 
with shelter deck, to Class 100 Al at Lloyd's. Speed of all at sea, 13 
knots.) 





Draft, 
ft. ins. 


Dis- 
place- 
ment, 




Dead- 
w'ght, 
tons. 






Immersed . 


C to 


Dimensions. 


Area, 


Girth 


S*- 
— ^ 














fT ° 


sq.ft. 


ft. 


£ 















Q ° 






" 


390'x45'9"x29'6". .. 


24 6l/ 2 


8,640 


0.69 


5,000 


3.475 


266 


1,092 


87.8 


8.0 


415'x4&'9"x31'0". .. 


25 6 


10,240 


0.696 


6,000 


3,725 


277 


1,209 


92.46 


7.1 


438'x51'5"x32'8". .. 


26 31/2 


11,870 


0.702 


7,000 


3,970 


287 


1,314 


96.46 


6.5 


458'x53'9"x34'0". .. 


27 OI/2 


13,500 


0.71 


8,000 


4,225 


295 


1,412 


100.0 


6.05 


475'x55'9"x35'5". .. 


27 11 


15,100 


0.715 


9,000 


4,475 


300 


1,513 


103.64 


5.7 


493'x58'0"x36 / 7". .. 


28 7 


16,750 


72 


10,000 


4,725 


305 


1,610 


107.0 


5 42 


521' X6I' 2"x38' 9". .. 


30 


19,850 


0.728 


12,000 


5,200 


311 


1,780 


112.8 


4.97 


535' x 62' 9"x39'9". .. 


30 7 


21,47(1 


O.Jil 


13,000 


5,430 


313 


1,862 


115.4 


4.8 


548' x 64' 1"X4C9". .. 


31 3 


23,070 


0.736 


14,000 


5,675 


314 


1,946 


118.0 


4 66 


570' X 66' 9" X 42' 4". .. 


32 41/2 


26,150 


0.742 


16,000 


6,130 


316 


2,097 


122.5 


4.4 



* The rate of coal consumption is assumed in all cases at 1.5 lbs. per 
I.H.P. per hour. 

Comparison of Marine Engines for the Years 1872, 1881, 1891, 1901. 



Boilers, Engines and Coal. 



Boiler press., lbs. per sq. in 

Heating surface, per sq. ft. grate 

Heat'g surf., per I.H.P., sq. ft 

Coal, per sq. ft. of grate, lbs. per hr.. 

Revolutions per minute 

Piston speed, ft. per min 

Coal per I.H.P. per hr., lbs 

Av. consumption, long voyage 



Average Results. 



52.4 
"aA\ 



55.67 
376 
2.11 



77.4 
30.4 

3.917 
13.8 
59.76 

467 

1.83 

2.0 



158.5 
31.0 
3.275 
15.0 
63.75 
529 
1.52 
1.75 



197 
38 & 43* 

3.0 
18&28* 
87 
654 
1.48 
1.55 



* Natural and forced draft respectively. 

Summary of Results. — Steam pressures have been increased in the 
merchant marine from 158 lbs. to 197 lbs. per sq. in., the maximum 
attained being 267 lbs. per sq. in., and 300 lbs. in the naval service. 
The piston speed of mercantile machinery has gone up from 529 to 654 ft. 
per minute, the maximum in merchant practice being about 900 ft., 
and in naval practice 960 ft. for large engines, and 1300 ft. in torpedo- 
boat destroyers. Boilers also yield a greater power for a given surface, 
and thus the average power per ton of machinery has gone up from an 
average of 6 to about 7 I.H.P. per ton of machinery. The net result 
in respect of speed is that while ten years ago the highest sustained 
ocean speed was 20.7 knots, it is now 23.38 knots; the highest speed for 
large warships was 22 knots and is now 23 knots on a trial of double 
the duration of those of ten years ago; the maximum speed attained by 
any craft was 25 knots, as compared with 36.581 knots now. while the 
number of ships of over 20 knots was 8 in 1891, and is 58 now [1901]. 



1330 



MARINE ENGINEERING. 



Turbines and Boilers of the "Lusitania." (Thomas Bell, Proc. 
Inst. Nav. Archts., 1908.) — Some of the principal dimensions of the 
turbines and boilers of the "Lusitania" are as follows: 





Diameter 

of Rotor, 

ins. 


Length of Blades, ins. 


Turbines. 


In First 
Expansion. 


In Last 
Expansion. 


H.P 


96 
140 
104 


23/ 4 
21/ 4 


123/ 8 
22 


L.P 




8 







Total cooling surface, main condensers, 82,800 sq. ft; area of exhaust 
inlet, 158 sq. ft; bore of circulating discharge pipes, 32 ins. 

Boilers. — Working pressure, 195 lbs. per sq. in.; 23 double-ended 
boilers, 17 ft. 6 in. mean diameter by 22 ft. long; 2 single-ended boilers, 
17 ft. 6 in. mean diameter by 11 ft. 4 in. long; total number of furnaces, 
192; total grate surface, 4048 sq. ft.; total heating surface, 158,352 sq. ft.; 
total length of boiler-rooms, 336 ft.; total length of main and auxiliary 
engine rooms, 149 ft. 8 in. 

The following are the weights of the various revolving parts, together 
witli the size of bearings and the pressure: 

Weight of one H.P. turbine rotor complete, 86 tons; one L.P. rotor, 
120 tons; one astern rotor, 62 tons. 





Main B 
Jour 

Diameter. 


earing 
rials. 

Effective 
Length. 


Pressure 
Per Sq. In. 
of Bearing 
Surface. 


At 190 Revs. 

Surface Speed 

of Journal . 


H.P. rotor 


27 1/ 8 in. 
331/s in. 
24 1/ 8 in. 


443/4 in. 
561/2 in. 
343/ 4 in 


80 lbs. 
72 lbs. 
83 lbs. 










1200 ft. per min. 







Performance of the " Lusitania." (Thos. Bell, Proc. Inst. Nav. 

Archts., 1908; Power, May 12, 1908.) — The following records were ob- 
tained in the official trials: 

Speed in knots 15 . 77 18 21 23 25.4 

Shaft horse-power 13,400 20,500 33,000 48,000 68,850 

Steam cons, per shaft, H.P. hr. 

of turbines, lbs 21.23 17.24 14.91 13.92 12.77 

of auxiliaries, lbs 5.3 3.72 2.6 2.01 1.69 

totallbs 26.53 20.96 17.51 15.93 14.46 

Temperature of feed water, 

°F 200 200 199 179 165 

Coal cons. lbs. per shaft . . 

H.P. hr 2.52 2.01 1.68 1.56 1.43 

Estimated steam and coal consumption under service conditions, at 

same speeds: 
Steam cons, of auxiliaries, 

per shaft H.P. hr., lbs.. 6.97 4.92 3.41 2.65 2.17 
Steam cons, of total per 

shaft H.P. hr., lbs 28.20 22.16 18.32 16.57 14.94 

Coal cons., lbs. per shaft 

H.P. hr., lbs 2.76 2.17 1.8 1.62 1.46 

Est. coal cons., on a voyage 

of 3100 nautical miles, 

gross tons 3,270 3,440 3,930 4,700 5,490 

The following figures are taken from the records of a voyage from 
Queenstown to Sandy Hook, 2781 nautical miles, Nov. 3-8, 1908, 4 days, 
18 hrs. 40 m.: Averages: Steam pressure at boilers, 168 lbs.; temperature 
hot-well, 74.5°; feed water, 197°; vacuum, 28.1 in.; speed, 24.25 knots; 



THE PADDLE-WHEEL. 1331 

speed, best day, 24.8 knots; revolutions, 181.1; slip, 15.9%. Total coal, 
4976 tons. Steam consumption: main turbines, 851,500 lbs., = 13.1 lbs. 
per shaft H.P. hr. (on a basis of 65,000 shaft H.P.); auxiliary machinery, 
114,000 lbs., = 1.75 per H.P. hr.; evaporating plant and healing, 32,500 Lbs., 
= 0.5 lb. per H.P. hr. Total, 998,000 lbs., = 15.35 lbs. per shaft H.P. 
hour. Average coal burned, 43 1/2 tons per hour. Water evaporated 
per lb., coal 10.2 lbs. from feed at 196°, = 10.9 lbs. from and at 212°. 
Coal for all purposes per shaft H.P. hour, 1.5 lbs. Coal per sq. ft. of 
grate per hour, 24.1 lbs. The coal was half Yorkshire and half South 
Wales. 

In September, 1909, the " Lusitania " made the westward passage, 2784 
miles from Daunt's Rock near Queenstown to Ambrose Channel Lightship, 
off Sandy Hook, in 4 days 11 h. 42 m., averaging 25.85 knots for the entire 
passage. Four successive days' runs, from noon to noon, were 650, 652, 
651 and 674 miles. 

Relation of Horse-Power to Speed. — If &i and S2 are two successive 
speeds and P1P2 the corresponding horse-powers, then to find the value 
of the exponent x in the equation H.P. a> S x , we have 

x = (log Pi - log PO h- (log S 2 - log £,). 
Applying this formula to the horse-powers and speeds of the " Lusitania" 
we find that between 15.77 and 18 knots x = 3.21; between 18 and 21 
knots x = 3.09; between 21 and 23 knots x = 4.12; between 23 and 
25.4 knots x = 3.63. 

Reciprocating Engines with a Low-Pressure Turbine. — The 
"Laurentic, " built for the Canadian trade of the White Star Line, 
14,000 tons gross register, is a triple-screw steamer, with the two outer 
screws driven by four-cylinder triple-expansion engines, and the central 
screw by a Parsons turbine. The steam, of 200 ibs. boiler pressure, first 
passes to the reciprocating engines, where it expands to from 14 to 17 lbs. 
absolute, and then passes to the turbine. For manoeuvering the ship 
into and out of port the turbine is not used, and the steam passes directly 
from the engines to the condensers. During the trial trip the combined 
engine-turbine outfit developed 12,000 H.P., with a speed of 171/2 knots, 
and showed a coal consumption of 1.1 lbs. and a water consumption of 
11 lbs. per indicated horse-power hour. {Power, May 18, 1909.) 

The " Kronprinzessin Cecilie" of the North German Lloyd Co., is 
probably the last high-speed transatlantic steamer of very great power 
that will be built with reciprocating engines. Its dimensions are: length, 
706 ft.; beam, 72 ft.; depth, 44 ft. 2 in.; displacement, 26,000 tons. Four 
12,000 H.P. engines, two on each shaft, in tandem. Cylinders, 373/s, 
49V4, 747/8 and 1121/4 ins., by 6 ft. stroke. Steam, 230 lbs., delivered 
from 19 cylindrical boilers, through four 17-in. steampipes. Coal used 
I in 24 hours, 764 tons, in 124 furnaces; 1.4 lbs. per H.P. hour, including 
! auxiliaries. Speed on trial trip on a 60-mile course, 24.02 knots. (Set. 
\Am., Aug. 24, 1907.) 

THE PADDLE-WHEEL. 

Paddle-wheels with Radial Floats. (Seaton's Marine Engineering.) — 
The effective diameter of a radial wheel is usually taken from the centers 
of opposite floats; but it is difficult to say what is absolutely that diameter, 
as much depends on the form of float, the amount of dip, and the waves 
set in motion by the wheel. The slip of a radial wheel is from 15 to 30 
per cent, depending on the size of float. 

Area of one float =CX I.H.P. -h D. 
D is the effective diameter in feet, and C is a multiplier, varying from 0.25 
in tugs to 0.175 in fast-running light steamers. 

The breadth of the float is usually about 1/4 its length, and its thickness 
about 1/8 its breadth. The number of floats varies directly with the diam- 
eter, and there should be one float for every foot of diameter. 

(For a discussion of the action of the radial wheel, see Thurston, 
Manual of the Steam-engine, part ii, p. 182.) 

Feathering Paddle-wheels. (Seaton.) — The diameter of a feather- 
ing-wheel is found as follows: The amount of slip varies from 12 to 20 
per cent, although when the floats are small or the resistance great it 
is as high as 25 per cent; a well-designed wheel on a well-formed ship 
Should not exceed 15 per cent under ordinary circumstances. 



1332 MARINE ENGINEERING. 



If K is the speed of the ship in knots, S the percentage of slip, and R the 
revolutions per minute, 

Diameter of wheel at centers = K (100 + S) -s- (3.14 X R). 
The diameter, however, must be such as will suit the structure of the 
ship, so that a modification may be necessary on this account, and the 
revolutions altered to suit it. 

The diameter will also depend on the amount of "dip" or immersion of 
float. 

When a ship is working always in smooth water the immersion of the 
top edge should not exceed i/s the breadth of the float; and for general 
service at sea an immersion of 1/2 the breadth of the float is sufficient. 
If the ship is intended to carry cargo, the immersion when light need not 
be more than 2 or 3 inches, and should not be more than the breadth of 
float when at the deepest draught; indeed, the efficiency of the wheel falls 
off rapidly with the immersion of the wheel. 

Area of one float = C X I.H.P. -*■ D. 
C is a multiplier, varying from 0.3 to 0.35; D is the diameter of the 
wheel to the float centers, in feet. 

The number of floats = 1/2 (D +2). 
The breadth of the float = 0.35 X the length. 
The thickness of floats = V12 the breadth. 
Diameter of gudgeons = thickness of float. 
Seaton and Rounthwaite's Pocket-book gives: _ 
Number of floats =60-5- Vi?, 
where R is number of revolutions per minute. 

. fl ■■. r , +N I.H.P. X 33,000 X K 
Area of one float (in square feet) = — at y (n Y R^ ' 

where 2V = number of floats in one wheel. 

For vessels plying always in smooth water K = 1200. For sea-going 
steamers K = 1400. For tugs and such craft as require to stop and 
start frequently in a tide-way K = 1600. 

It will be quite accurate enough if the last four figures of the cube 
(D X R) 3 be taken as ciphers. 

For illustrated description of the feathering paddle-wheel see Seaton's 
Marine Engineering, or Seaton and Rounthwaite's Pocket-book. The 
diameter of a feathering- wheel is about one-half that of a radial wheel 
for equal efHciencv. (Thurston.) 

Efficiency of Paddle-wheels. — Computations by Prof. Thurston of 
the efficiency of propulsion by paddle-wheels give for light river steamers 
with ratio of velocity of the vessel, v, to velocity of the paddle-float at 
center of pressure, V, or v/V, = 3/4, with a dip = 3/ 2 o radius of the wheel 
and a slip of 25 per cent, an efficiency of 0.714; and for ocean steamers 
with the same slip and ratio of v/V, and a dip = 1/3 radius, an efficiency of 
0.685. 

JET-PROPULSION. 

Numerous experiments have been made in driving a vessel by the 
reaction of a jet of water pumped through an orifice in the stern, but 
they have all resulted in commercial failure. Two-jet propulsion steamers, 
the " Waterwitch," 1100 tons, and the "Squirt," a small torpedo-boat, 
were built by the British Government. The former was tried in 1867, 
and gave an efficiency of apparatus of only 18 per cent. The latter gave 
a speed of 12 knots, as against 17 knots attained by a sister-ship having a 
screw and equal steam-power. The mathematical theory of the efficiency 
of the jet was discussed by Rankine in The Engineer, Jan. 11, 1867, and 
he showed that the greater the quantity of water operated on by a jet- 
propeller, the greater is the efficiency. * In defiance both of the theory 
and of the results of earlier experiments, and also of the opinions of many 
naval engineers, more than $200,000 were spent in 1888-90 in New York 
upon two experimental boats, the "Prima Vista" and the "Evolution," 
in which the jet was made of very small size, in the latter case only 5/s-mch 
diameter, and with a pressure of 2500 lbs. per square inch. As had been 
predicted, the vessel was a total failure. (See article by the author in 
Mechanics, March, 1891.) 

The theory of the jet-propeller is similar to that of the screw-propeller. 
If A = the area of the jet in square feet, V its velocity with reference to 
the orifice, in feet per second, v = the velocity of the ship in reference to 



FOUNDATIONS. 1333 

the earth, then the thrust of the jet (see Screw-propeller, ante) is 2 A V 
(V — v). The work done on the vessel is 2 AV(V — v)v, and the work 
wasted on the rearward projection of the jet is 1/2 X 2 AV(V — v) 2 . 
„, ffi . . 2AV(V-v)v 2v 

The efficiency is . „ . T . r^ — ; — . „ , T . rr = ■=-— ■ This expression 

2 AV (V - v) v + AV (V -v) 2 V+v 
equals unity when V = v, that, is, when the velocity of the jet with refer- 
ence to the earth, or V — v, = ; but then the thrust of the propeller is 
also 0. The greater the value of V as compared with v, the less the 
efficiency. For V = 20 v, as was proposed in the "Evolution," the 
efficiency of the jet would be less than 10 per cent, and this would be 
further reduced by the friction of the pumping mechanism and of the 
water in pipes. 

The whole theory of propulsion may be summed up in Rankine's 
words: "That propeller is the best, other tilings being equal, which drives 
astern the largest body of water at the lowest velocity." 

It is practically impossible to devise any system of hydraulic or jet 
propulsion which can compare favorably, under these conditions, with 
the screw or the paddle-wheel. 

Reaction of a Jet. — If a jet of water issues horizontally from a vessel, 
the reaction on the side of the vessel opposite the orifice is equal to the 
weight of a column of water the section of which is the area of the orifice, 
and the height is twice the head. 

The propelling force in jet-propulsion is the reaction of the stream 
issuing from the orifice, and it is the same whether the jet is discharged 
under water, in the open air, or against a solid wall. For oroof , see 
account of trials by C. J. Everett, Jr., given by Prof. J. Burkitt Webb, 
Trans. A. S. M. E., xii, 904. 



CONSTRUCTION OP BUILDINGS.* 

FOUNDATIONS. 

Bearing Power of Soils. — Ira O. Baker, "Treatise on Masonry 
Construction." 



Kind of Material. 



Rock — the hardest — in thick layers, in native bed. 

Rock equal to best ashlar masonry 

Rock equal to best brick masonry 

Rock equal to poor brick masonry 

Clay on thick beds, always dry 

Clay on thick beds, moderately dry 

Clay, soft 

Gravel and coarse sand, well cemented 

Sand, compact, and well cemented 

Sand, clean, dry 

Quicksand, alluvial soils, etc 



Bearing Power in 
Tons per Square Foot. 



Minimum. 


Maximum. 


200 

25 




30 


15 


20 


5 


10 


4 


6 


2 


4 


1 


2 


8 


10 


4 


6 


2 


4 


0.5 


1 



* The limitations of space forbid any extended treatment of this subject. 
Much valuable information upon it will be found in Traut wine's 'Civil 
Engineers' Pocket-book," and in Kidder's " Architects and Builders 
Pocket-book." The latter in its preface mentions the following works of 
reference: "Notes on Building Construction," 3 vols., Rivingtons, pub- 
lishers, London; "Building Superintendence," by TM Clark (J. R. 
Oseood & Co.. Boston); " The American House Carpenter, and The Theory 
of Transverse Strains," both bv R. G. Hatfield; "Graphical Analysis of 
Roof-trusses," by Prof. C. E. Greene: "The Fire Protection of Mills, by 
C. J. H. Woodbury; "House Drainage and Water Service," by James C. 
Bayles; "The Builder's Guide and Estimator's Price-book," and "Plaster- 
ing Mortars and Cements," by Fred.T. Hodgson; "Foundations and Con- 
crete Works," and "Art of Building," by E. Dobson, Weale s Series, 
London. 



1334 



CONSTRUCTION OF BUILDINGS. 



The building code of Greater New York specifies the following as the 
maximum permissible loads for different soils: 

" Soft clay, one ton per square foot; 

" Ordinary clay and sand together, in layers, wet and springy, two 
tons per square foot; 

" Loam, clay or fine sand, firm and dry, three tons per square foot; 

" Very firm coarse sand, stiff gravel or hard clay, four tons per square 
foot, or as otherwise determined by the Commissioner of Build- 
ings having jurisdiction." 

Bearing Power of Piles. — Engineering News Formula: Safe load in 
tons = 2 Wh -*- (S + 1). W = weight of hammer in tons, h = height of fall 
of hammer in feet, 8 = penetration under last blow, or the average under 
last five blows. 

Safe Strength of Brick Piers, exceeding six diameters in height. 
(Kidder.) 

Piers laid with rich lime mortar, tons per sq. in., 110 — 5 H/D. 
Piers laid with 1 to 2 natural cement mortar, 140 — 51/2 H/D. 
Piers laid with 1 to 3 Portland cement mortar, 200 - 6 H/D. 
H = height; D = least horizontal dimension, in feet. 

Thickness of Foundation Walls. (Kidder.) 



Height of Building. 


Dwellings, 
Hotels, etc. 


Warehouses. 


Brick. 


Stone. 


Brick. 


Stone. 




Inches. 
12 or 16 

16 

20 

24 

28 


Inches. 
20 
20 
24 
28 
32 


Inches. 
16 
20 
24 
24 
28 


Inches. 
20 




24 




28 




28 




32 







MASONRY. 

Allowable Pressures on Masonry in Tons per Square Foot. 



(Kidder.) 



Different Cities.* 


(l) 


(2) 


(3) 


(4) 


(5) 


(6) 


(7) 




60 
40 
30 




72-172 

50-165 

28-115 

18 

15 

n Vs 

8 








40 


















12 




121/2 
9 

'61/2 


15 

i i 1/2 
u 




Hard-burned brick in natural cement 

Hard-burned brick in cement and lime . . . 
Hard-burned brick in lime mortar 


15 
12 
8 


9 

"6' 

12 
9 
5 

6 

4 


15 
12 
8 


9 
*8' 














12 
12 

30 
10 
4 






8 

is"" 

8 


5-7 

"a 




10 


In foundations: 










15 


















* From building laws, (1) Boston, 1 
York, 1899; (4) Chicago, 1S93; (5) St 
1899; (7) Denver, 1898. 

Crushing Strength of 12-in. Cu 

Pounds per square foot. The concret 
cement, 2 parts sand, with average cone 


S97; 
. Lc 

l>es 

3 W3 

rete 


(2) 
uis, 

of 

s in 
ston 


Buffa 
1897; 

Concr 

ade o 
e and 


lo, 1 

(6) 

ete. 

f 1 I 
grav< 


S97; 
Phila 

(Kic 
)art ] 
jI, as 


delp 

der 
Port 
belo 


Vew 
hia, 

and 

W. 



BEAMS AND GIRDERS. 



1335 





10 days. 


45 days. 


3 mos. 


6 mos. 


1 year. 




130,750 
136,750 


172,325 
266,962 


324,875 


361,600 
298,037 


440,040 




396,200 






408,300 


6 parts (3/4 stone, V4 grano- 
lithic) 










388,700 




99,900 


234,475 


385,612 
234,475 


265,550 
220,350 


406,700 




266,300 











Reinforced Concrete. —The building laws of New York, St. Louis, 
Cleveland and Buffalo, and the National Board of Fire Underwriters agree 
in prescribing the following as the maximum allowable working stresses: 
Extreme fiber stress in compression in con- 
crete 500 lbs. per sq. in. 

Shearing stress in concrete 50 " " 

Direct compression in concrete 350 " 

Adhesion of steel to concrete 50 

Tensile stress in steel 16,000 

Shearing stress in steel 10,000 

BEAMS AND GIRDERS. 

Safe Loads on Beams. — Uniformly distributed load: 
Safe load in lbs. 



Breadth in inches = 



2 X breadth X square of depth X A 
span in feet 
span in feet X load 
2 X square of depth X A 



The depth is taken in inches. The coefficient A, is Vi8 the maximum 
fiber stress for safe loads, and is the safe load for a beam 1 in. square, 1 ft. 
span. The following values of A are given by Kidder as one-third of 
the breaking weight of timber of the quality used in first-class buildings. 
The values for stones are based on a factor of safety of six. 

Values for A. — Coefficient for Beams. 



Cast iron 308 

Wrought iron 666 

Steel 888 

American Woods: 

Chestnut 60 

Hemlock 55 

Oak, white 75 

Pine, Georgia yellow 100 

Pine, Oregon 90 

Pine, red or Norway 70 

Pine, white, Eastern 60 

Pine, white, Western 65 



Pine, Texas yellow 90 

Spruce 70 

Whitewood (poplar) 65 

Redwood (California) 60 

Bluestone flagging (Hudson 

River) 25 

Granite, average 17 

Limestone 14 

Marble 17 

Sandstone 8 to 11 

Slate 50 



Maximum Permissible Stresses in Structural Materials used in 
Buildings. (Building Ordinances of the City of Chicago, 1893.) — Cast 
iron, crushing stress: For plates, 15,000 lbs. per square inch; for lintels, 
brackets, or corbels, compression 13,500 lbs. per square inch, and tension 
3000 lbs. per square inch. For girders, beams, corbels, brackets, and 
trusses, 16,000 lbs. per square inch for steel and 12,000 lbs. for iron. 

For plate girders: 

Flange area = maximum bending moment in ft .-lbs. -i-(CD). 

D = distance between center of gravity of flanges in feet. 

C = 13,500 for steel, 10,000 for iron. 

Web area = maximum shear -+--C. 

C = 10,000 for steel; 6,000 for iron. 



1336 



CONSTRUCTION OF BUILDINGS. 



For rivets in single shear per square inch of rivet area: 

If shop-driven, steel, 9000 lbs., iron, 7500 lbs.; if field-driven, steel, 

7500 lbs., iron, 6000 lbs. 

For timber girders: S = cbd 2 -s- I. 

b = breadth of beam in inches, d = depth of beam in inches, I = length 

of beam in feet, c = 160 for long-leaf yellow pine, 120 for oak, 100 for 

white or Norway pine. 

Safe Loads in Tons, Uniformly Distributed, for White-oak Beams. 

(In accordance with the Building Laws of Boston.) 

W = safe load in pounds; P, extreme fiber- 
tp i TT7 _ 4 PBD 2 stress = 1000 lbs. per square inch, for white 

oak; B, breadth in inches; D, depth in inches; 
L, distance between supports in inches. 



3L 



• SI 



Distance between Supports in Feet. 



10 11 12 14 I 15 16 17 18 i 19 21 I 23 i 25 i 26 



Safe Load in Tons of 2000 Pounds. 



2x6 
2x8 
2x10 
2x12 
3X6 
3x8 
3x10 
3x12 
3x14 
3x16 
4x10 
4x12 
4x14 
4x16 
4x18 



0.67 
1.19 
1.85 
2.67 
1.00 
1.78 
2.78 
4.00 
5.45 
7.11 
3.70 
5.33 
7.26 
9.48 
12.00 



0.50 

0.89 

1.39 

2.00 

0.75 

1.33 

2 

3.00 

4.08 

5.33 

2.78 

4.00 

5.44 

7 

9.00 



0.29 
0.51 
0.79 
1.14 
0.43 
0.76 
1.19 
1.71 
2.37 
3.05 
1.59 
2.2.9 
3.11 
4.06 
5.14 



0.22 
0.40 
0.62 
0.39 
0.33 
0.59 
0.93 
I .33 
1.82 
2.37 
1 .23 
1.78 
2.42 



4.00 



26 
72 
25 
17 
68 
29 
3.1613.00 
79 



0.34 
0.53 
0.76 
0.29 
0.51 
0.79 
1.14 
1.56 
2.03 
1.06 
1.52 
2.07 
2.71 
3.43 



0.28 
0.43 
0.64 



0.43 
0.62 



0.41 
0.64 
0.92 
1.25 
1.64 
0.85 
1.23 
1.68 
2.19 
2.77 



For other kinds of wood than white oak multiply the figures in the 
table by a figure selected from those given below (which represent the 
safe stress per square inch on beams of different kinds of wood according 
to the building laws of the cities named) and divide by 1000. 





Hem- 
lock. 


S P™- Ptae' 6 


Oak. 


Yellow 
Pine. 




800 


900 900 

750 750 

900 


1100 
TOOOf 

1080 


1100* 
1250 
1440 















* Georgia pine. t White oak. 

WALLS. 

Thickness of Walls of Buildings. — Kidder gives the following gen- 
eral rule for mercantile buildings over four stories in height: 

For brick equal to those used in Boston or Chicago, make the thickness 
of the three upper stories 16 ins., of the next three below 20 ins., the next 
three 24 ins., and the next three 28 ins. For a poorer quality of materia 
make only the two upper stories 16 ins. thick, the next three 20 ins., anc 
so on down. 

In buildings less than five stories in height the top story may be IS 
ins. in thickness. 



WALLS. 



1337 



Thickness of Walls in Inches, for Mercantile Buildings and for 
all Buildings over Five Stories in Height . (The figures show the 
range of the thicknesses required by the ordinances of eight different 
cities. — Condensed from Kidder.). 



Stories 
High. 



Stories. 



1st. 2d. 3d. 4th. 5th. 6th. 7th. 8th. 9th- 10th 11th 12th 



12-18 
13-20 
16-22 
18-22 
20-26 
20-28 
22-32 
24-32 
24-36 
28-36 
28-40 



12-13 

12-1 

16-18 

16-22 

18-22 

20-26 

20-28 

24-32 

24-32 

28-36 

28-36 



12-16 
12-18 
16-20 
16-22 
18-24 
20-26 
20-28 
24-32 
24-32 
28-36 



12-16 
12-20 
16-20 
16-22 
18-24 
20-26 
20-28 
24-30 
24-32 



12-16 
13-20 
16-20 
16-22 
20-24 
20-26 
24-28 
24-32 



12-16 
13-20 
16-20 
16-22 
20-24 
20-26 
24-28 



12-17 
13-20 
10-20 
16-22 
20-24 
20-26 



12-17 
16-20 
16-20 
20-22 
20-24 



12-17 
16-20 
16-20 
20-22 



13-17 
16-20 



(Extract from the Building Laws of the City of New York, 1893.) 

Walls of Warehouses, Stores, Factories, and Stables. — 25 feet 

or less in width between walls, not less than 12 in. to height of 40 ft.; 

If 40 to 60 ft. in height, not less than 16 in. to 40 ft., and 12 in. thence to 

top; 

60 to 80 ft. in height, not less than 20 in. to 25 ft., and 16 in. thence to 

top; 
75 to 85 ft. in height, not less than 24 in. to 20 ft.; 20 in. to 60 ft., and 

16 in. to top; 
85 to 100 ft. in height, not less than 28 in. to 25 ft.; 24 in. to 50 ft.; 
20 in. to 75 ft., and 16 in. to top; 
Over 100 ft. in height, each additional 25 ft. in height, or part thereof, 
next above the curb, shall be increased 4 inches in thickness, the 
upper 100 feet remaining the same as specified for a wall of that 
height. 
If walls are over 25 feet apart, the bearing-walls shall be 4 inches 
thicker than above specified for every 12 1/2 feet or fraction thereof that 
said walls are more than 25 feet apart. 

Strength of Floors, Roofs, and Supports. 

Floors calculated to 
bear safely per sq. ft., in 
addition to their own wt. 
Floors of dwelling, tenement, apartment-house or hotel, not 

less than 70 lbs. 

Floors of office-building, not less than 100 " 

Floors of public-assembly building, not less than 120 " 

Floors of store, factory, warehouse, etc., not less than 150 " 

Roofs of all buildings, not less than 50 " 

Every floor shall be of sufficient strength to bear safely the. weight to be 
imposed thereon, in addition to the weight of the materials of which the 
floor is composed. 

Columns and Posts. — The strength of all columns and posts shall 
be computed according to Gordon's formula, and the crushing weights in 
pounds, to the square inch of section, for the following-named materials, 
shall be taken as the coefficients in said formula?, namely: Cast iron, 80,000; 
wrought or rolled iron, 40,000: rolled steel. 4S,000: white pine and spruce, 
3500: pitch or Georgia pine, 5000: American oak, 6000. T^e breaking 
strength of wooden beams and girders shall be computed according to 
the formulae in which the constants for transverse strains for central load 
shall be as follows, namely: Hemlock, 400; white pine, 450; spruce, 450; 
pitch or Georgia pine, 550; American oak, 550; and for wooden beams and 
girders carrying a uniformly distributed load the constants will be doubled. 



1338 CONSTRUCTION OF BUILDINGS. 

The factors of safety shall be as one to four for all beams, girders, and 
other pieces subject to a transverse strain; as one to four for all posts, 
columns, and other vertical supports when of wrought iron or rolled steel; 
as one to five for other materials, subject to a compressive strain; as one 
to six for tie-rods, tie-beams, and other pieces subject to a tensile strain. 
Good, solid, natural earth shall be deemed to sustain safely a load of four 
tons to the superficial foot, or as otherwise determined by the super- 
intendent of buildings, and the width of footing-courses shall be at least 
sufficient to meet this requirement. In computing the width of walls, 
a cubic foot of brickwork shall be deemed to weigh 115 lbs. Sandstone, 
white marble, granite, and other kinds of building-stone shall be deemed 
to weigh 160 lbs. per cubic foot. The safe-bearing load to apply to 
good brickwork shall be taken at 8 tons per superficial foot when good 
lime mortar is used, 11V2 tons per superficial foot when good lime and 
cement mortar mixed is used, and 15 tons per superficial foot when good 
cement mortar is used. 

Fire-proof Buildings — Iron and Steel Columns. — All cast-iron, 
wrought-iron, or rolled-steel columns shall be made true and smooth at 
both ends, and shall rest on iron or steel bed-plates, and have iron or 
steel cap-plates, which shall also be made true. All iron or steel trimmer- 
beams, headers, and tail-beams shall be suitably framed and connected 
together, and the iron girders, columns, beams, trusses, and all other iron- 
work of all floors and roofs shall be strapped, bolted, anchored, and con- 
nected together, and to the walls, in a strong and substantial manner. 
Where beams are framed into headers, the angle-irons, which are bolted 
to the tail-beams, shall have at least two bolts for all beams over 7 inches 
in depth, and three bolts for all beams 12 inches and over in depth, and 
these bolts shall not be less than 3/ 4 inch in diameter. Each one of such 
angles or knees, when bolted to girders, shall have the same number of 
bolts as stated for the other leg. The angle-iron in no case shall be less 
in thickness than the header or trimmer to which it is bolted, and the 
width of angle in no case shall be less than one third the depth of beam, 
excepting that no angle-knee shall be less than 21/2 inches wide, nor 
required to be more than 6 inches wide. All wrought-iron or rolled-steel 
beams 8 inches deep and under shall have bearings equal to their depth, 
if resting on a wall; 9 to 12 inch beams shall have a bearing of 10 inches, 
and all beams more than 12 inches in depth shall have bearings of not 
less than 12 inches if resting on a wall. Where beams rest on iron sup- 
ports, and are properly tied to the same, no greater bearings shall be 
required than one third of the depth of the beams. Iron or steel floor- 
beams shall be so arranged as to spacing and length of beams that the 
load to be supported by them, together with the weights of the materials 
used in the construction of the said floors, shall not cause a deflection of 
the said beams of more than 1/30 of an inch per linear foot of span; and 
they shall be tied together at intervals of not more than eight times the 
depth of the beam. 

Under the ends of all iron or steel beams, where they rest on the walls, a 
stone or cast-iron template shall be built into the walls. Said template 
shall be 8 inches wide in 12-inch walls, and in all walls of greater thickness 
said template shall be 12 inches wide; and such templates, if of stone, 
shall not be in any case less than 21/2 inches -in thickness, and no template 
shall be less than 12 inches long. 

No cast-iron post or columns shall be used in any building of a less 
average thickness of shaft than three quarters of an inch, nor shall it 
have an unsupported length of more than twenty times its least lateral 
dimensions or diameter. No wrought-iron or rolled-steel column shall 
have an unsupported length of more than thirty times its least lateral 
dimensions or diameter, nor shall its metal be less than one fourth of an 
inch in thickness. 

Lintels, Bearings and Supports. — All iron or steel lintels shall 
have bearings proportionate to the weight to be imposed thereon, but no 
lintel used to span any opening more than 10 feet in width shall have a 
bearing less than 12 inches at each end, if resting on a wall; but if resting 
on an iron post, such lintel shall have a bearing of at least 6 inches at each 
end, by the thickness of the wall to be supported. 

Strains on Girders and Rivets. — Rolled iron or steel beam girders, 
or riveted iron or steel plate girders used as lintels or as girders, carrying 



FLOORS. 1339 

a wall or floor or both, shall be so proportioned that the loads which may 
come upon them shall not produce strains in tension or compression upon 
the flanges of more than 12,000 lbs. for iron, nor more than 15,000 lbs. 
for steel per square inch of the gross section of each of such flanges, nor 
a shearing strain upon the web-plate of more than 6000 lbs. per square 
inch of section of such web-plate, if of iron, nor more than 7000 pounds 
if of steel; but no web-plate shall be less than 1/4 inch in thickness. Rivets 
in plate girders shall not be less than 5/g inch in diameter, and shall not be 
spaced more than 6 inches apart in any case. They shall be so spaced 
that their shearing strains shall not exceed 9000 lbs. per square inch, on 
their diameter, multiplied by the thickness of the plates through which 
they pass. The riveted plate girders shall be proportioned upon the 
supposition that the bending or chord strains are resisted entirely by the 
upper and lower flanges, and that the shearing strains are resisted en- 
tirely by the web-plate. No part of the web shall be estimated as flange 
area, nor more than one half of that portion of the angle-iron which lies 
against the web. The distance between the centers of gravity of the 
flange areas will be considered as the effective depth of the girder. 

The building laws of the city of New York contain a great amount of 
detail in addition to the extracts above, and penalties are provided for 
violation. See An Act creating a Department of Buildings, etc., Chapter 
275, Laws of 1892. Pamphlet copy published by Baker, Voorhies & Co., 
New York. 

FLOORS. 
Maximum Load on Floors. (Etig'g, Nov. 18, 1892, p. 644.) — Maxi- 
mum load per square foot of floor surface due to the weight of. a dense 
crowd. Considerable variation is apparent in the figures given by many 
authorities, as the following table shows: 

Authorities. Weight of Crowd, 

lbs. per sq. ft. 

French practice, quoted by Trautwine and Stoney 41 

Hatfield (" Transverse Strains, " p. 80) 70 

Mr. Page, London, quoted by Trautwine 84 

Maximum load on American highway bridges according to 

Waddell's general specifications 100 

Mr. Nash, architect of Buckingham Palace 120 

Experiments by Prof. W. N. Kernot, at Melbourne j ^43 1 

Experiments by Mr. B. B. Stoney ("On Stresses," p. 617) 147.4 

Experiments by Prof. L. J. Johnson, Eng. News, April 14, ( 134.2 

1904 Uo 156.9 

The highest results were obtained by crowding a number of persons 
previously weighed into a small room, the men being tightly packed so as 
to resemble such a crowd as frequently occurs' on the stairways and plat- 
forms of a theatre or other public building. 

Safe Allowances for Floor Loads. (Kidder.) Pounds per square 
foot. 

For dwellings, sleeping and lodging rooms 40 lbs. 

For schoolrooms 50 " 

For offices, upper stories 60 " 

For offices, first story 80 " 

For stables and carriage houses 65 " 

For banking rooms, churches and theaters 80 " 

For assembly halls, dancing halls, and the corridors of all 

public buildings, including hotels 120 " 

For drill rooms 150 " 

For ordinary stores, light storage, and light manufactur- 
ing 120* *« 

* Also to sustain a concentrated load at any point of 4000 lbs. 

STRENGTH OF FLOORS. 

(From circular of the Boston Manufacturers' Mutual Insurance Co.) 
The following tables were prepared by C. J. H. Woodbury, for determin- 
ing safe loads on floors. Care should be observed to select the figure 
giving the greatest possible amount and concentration of load as the one 



1340 CONSTRUCTION OF BUILDINGS. 

which may be put upon any beam or set of floor-beams; and in no case 
should beams be subjected to greater loads than those specified, unless a 
lower factor of safety is warranted under the advice of a competent 
engineer. 

Beams or heavy timbers used in the construction of a factory or ware- 
house should not be painted, varnished or oiled, filled or encased in 
impervious concrete, air-proof plastering, or metal for at least three years, 
lest fermentation should destroy them by what is called "dry rot." 

It is, on the whole, safer to make floor-beams in two parts with a small 
open space between, so that proper ventilation may be secured. 

These tables apply to distributed loads, but the first can be used in 
respect to floors which may carry concentrated loads by using half the 
figure given in the table, since a beam will bear twice as much load when 
evenly distributed over its length as it would if the load was concentrated 
in the center of the span. 

The weight of the floor should be deducted from the figure given in the 
table, in order to ascertain the net load which may be placed upon any 
floor. The weight of spruce may be taken at 36 lbs. per cubic foot, and 
that of Southern pine at 48 lbs. per cubic foot. 

Table I was computed upon a working modulus of rupture of Southern 
pine of 2160 lbs., using a factor of safety of six. It can also be applied 
to ascertaining the strength of spruce beams if the figures given in the 
table are multiplied by 0.78; or in designing a floor to be sustained by 
spruce beams, multiply the required load by 1.28, and use the dimensions 
as given by the table. 

These tables are computed for beams one inch in width, because the 
strength of beams increase directly as the width when the beams are 
broad enough not to cripple. 

Example. — Required the safe load per square foot of floor, which 
may be safely sustained by a floor on Southern pine 10 X 14 in. beams, 
8 ft. on centers, and 20 ft. span. In Table I a 1 X 14 in. beam, 20 ft. 
span, will sustain 118 lbs. per foot of span; and for a beam 10 ins. wide 
the load would be 1180 lbs. per foot of span, or 1471/2 lbs. per sq. ft. of 
floor for Southern-pine beams. From this should be deducted the weight 
of the floor, 17 1/2 lbs. per sq. ft., leaving 130 lbs. per sq. ft. as a safe load. 
If the beams are of spruce, multiply 1471/2 by 0.78, reducing the load to 
115 lbs. Deducting the weight of the floor, 16 lbs., leaves the safe net 
load as 90 lbs. per sq. ft. for spruce beams. 

Table II applies to floors whose' strength must be in excess of that 
necessary to sustain the weight, in order to meet the conditions of deli- 
cate or rapidly moving machinery, to the end that the vibration or dis- 
tortion of the floor may be reduced to the least practicable limit. 

In the table the limit is that of a load which would cause a bending of 
the beams to a curve of which the average radius would be 1250 ft. 

This table is based upon a modulus of elasticity obtained from obser- 
vations upon the deflection of loaded storehouse floors, and is taken at 
2,000,000 lbs. for Southern pine; the same table can be applied to spruce, 
whose modulus of elasticity is taken as 1,200,000 lbs., if six tenths of 
the load for Southern pine is taken as the proper load for spruce; or, in 
the matter of designing, the load should be increased one and two thirds 
times, and the dimension of timbers for this increased load as found in 
the table should be used for spruce. 

It can also be applied to beams and floor-timbers supported at each 
end and in the middle, remembering that the deflection of a beam sup- 
ported in that manner is only 0.4 that of a beam of equal span which 
rests at each end; that is to say, the floor-planks are 21/2 times as stiff, 
cut two bays in length, as they would be if cut only one bay in length. 
When a floor-plank two bays in length is evenly loaded, 3/ 16 f the load 
on the plank is sustained by the beam at each end of the plank, and 10/15 
by the beam under the middle of the plank; so that for a completed floor 
3/g of the load would be sustained by the beams under the joints of the 
plank, and 5/g of the load by the beams under the middle of the plank: 
this is the reason of the importance of breaking joints in a floor-plank 
every 3 ft. in order that each beam shall receive an identical load. If 



STRENGTH OF FLOORS. 



1341 



it were not so, 3/ 8 of the whole load upon the floor would be sustained by 
every other beam, and 5/ 8 of the load by the corresponding alternate 
beams. 

Repeating the former example for the load on a mill floor on Southern 
pine-beams 10 X 14 ins., and 20 ft. span, 8 ft. centers: In Table II a 
1 X 14 in. beam should receive 61 lbs. per foot of span, or 75 lbs. 
per sq. ft. of floor, for Southern-pine beams. Deducting the weight of 
the floor, 17 1/2 lbs. per sq. ft., leaves 57 lbs. per sq. ft. as the advisable 
load. 

If the beams are of spruce, the result of 75 lbs. should be multiplied 
by 0.6, reducing the load to 45 lbs. The weight of the floor, in this 
instance amounting to 16 lbs., would leave the net load as 29 lbs. for 
spruce beams. 

If the beams were two spans in length, they could, under these con- 
ditions, support two and a half times as much load with an equal amount 
of deflection, unless such load should exceed the limit of safe load as found 
by Table I, as would be the case under the conditions of this problem. 

Mill Columns. ■ — Timber posts offer more resistance to fire than iron 
pillars, and have generally displaced them in millwork. Experiments 
at the U. S. Arsenal at Watertown, Mass., show that sound timber posts 
of the proportions customarily used in millwork yield by direct crushing, 
the strength being directly as the area at the smallest part. The columns 
yielded at about 4500 lbs. per sq. in., confirming the general practice of 
allowing 600 lbs. per sq. in. as a safe load. Square columns are one 
fourth stronger than round ones of the same diameter. 



I. Safe Distributed Loads upon Southern-pine Beams One Inch 
in Width. 

(C. J. H. Woodbury.) 

(If the load is concentrated at the center of the span, the beams will 
sustain half the amount given in the table.) 



flj 


Depth of Beam in inches. 


a 


2 


* 


* 


5 


*6 | 7 | 8 | 9 | 10 1 11 1 12 | 13 


14 


u 


16 




Load in pounds per foot of Span. 



38 
27 
20 
15 


86 
60 

44 
34 
27 
22 


154 

107 

78 
60 
47 
38 
32 
27 


240 
167 
122 
94 
74 
60 
50 
42 
36 
31 
27 


346 
240 
176 
135 
107 
86 
71 
60 
51 
44 
38 
34 
30 


470 
327 
240 
184 
145 
118 
97 
82 
70 
60 
52 
46 
41 
36 


614 
427 
314 
240 
190 
154 
127 
107 
90 
78 
68 
60 
53 
47 
43 
38 


m 

540 
397 
304 
240 
194 
161 
135 
115 
99 
86 
76 
67 
60 
54 
49 
44 


960 
667 
490 
375 
296 
240 
198 
167 
142 
123 
107 
94 
83 
74 
66 
60 
54 
50 
45 


807 
593 
454 
359 
290 
240 
202 
172 
148 
129 
113 
101 
90 
80 
73 
66 
60 
55 
50 
46 


705 
540 
427 
346 
286 
240 
205 
176 
154 
135 
120 
107 
96 
86 
78 
71 
65 
60 
55 


828 
634 
501 
406 
335 
282 
240 
207 
180 
158 
140 
125 
112 
101 
92 
84 
77 
70 
65 


735 

581 
470 
389 
327 
278 
240 
209 
184 
163 
145 
130 
118 
107 
97 
89 
82 
75 


667 

540 

446 

375 

320 

276 

240 » 

211 

187 

167 

150 

135 

122 

112 

102 

94 

86 















































































































































759 
614 
508 
474 
364 
314 
273 
240 
217 
190 
170 
154 
139 
127 
116 
107 
98 



1342 



CONSTRUCTION OP BUILDINGS. 



II. Distributed Loads upon Southern-pine Beams Sufficient to 
Produce Standard Limit of Deflection. 



"5 
«£ 

a 
a 


Depth of Beam, in inches. 


a" 


■I»l« 


.|« 


7 | 8 


9 


10|ll 


- 


M 


14 


|W 


| 16 






Loac 


in pounds per foot of Span 










5 
6 
7 
8 
9 


3 

2 


10 
7 
5 
4 


23 
16 
12 
9 
7 
6 


44 
31 
23 
17 
14 
11 
9 


77 
53 
39 
30 
24 
19 
16 
13 
11 


122 

85 
62 
48 
38 
30 
25 
21 
18 
16 
14 


182 
126 
93 
71 
56 
46 
38 
32 
27 
23 
20 
18 
16 


259 
180 
132 
101 
80 
65 
54 
45 
38 
33 
29 
25 
22 
20 
18 


247 
181 
139 
110 
89 
73 
62 
53 
45 
40 
35 
31 
27 
25 
22 
20 


241 
185 
146 
118 
98 
82 
70 
60 
53 
46 
41 
37 
33 
30 
27 
24 
22 


240 
190 
154 
127 
107 
91 
78 
68 
60 
53 
47 
43 
38 
35 
32 
29 
27 
25 


305 
241 
195 
16! 
136 
116 
100 
87 
76 
68 
60 
54 
49 
44 
40 
37 
34 
31 


301 

244 
202 
169 
144 
124 
108 
95 
84 
75 
68 
61 
55 
50 
46 
42 
39 


300 
248 
208 
178 
153 
133 
117 
104 
93 
83 
75 
68 
62 
57 
52 
48 


301 
253 
215 
186 
162 
147 
126 
112 
101 
91 
83 
75 
69 
63 
58 


.0300 
.0432 
.0588 
.0768 
.0972 


in 






.1200 


ii 






.1452 


i?, 








.1728 


H 










.2028 


14 










.2352 


15 












.2700 


16 












.3072 


17 














.3468 


18 














3888 


19 
















.4332 


?n 
















.4800 


71 


















.5292 


?? 


















.5808 


?3 




















.6348 


74 




















.6912 


75 






















.7500 





















Maximum Spans for 1, 2 and 3 Inch Plank. (Am. Mach., Feb. 11, 
1904.) — Let w = load per sq. ft.; I = length in ins.; W = wl/12; S =• 
safe fiber stress, using a factor of safety of 10; b = width of plank; d = 
thickness: p = deflection, E = coefficient of elasticity, / = moment of 
inertia = V12 bd 3 . 

Then Wl/S = Sbd 2 /6; s = 5 Wl 3 h- 384 EI. Taking S at 1200 lbs., E 
at 850,000 and s = I -*■ 360 for long-leaf yellow pine, the following figures 
for maximum span, in inches, are obtained: 

Uniform load, lbs. per sq. ft. . 40 

1 in nlank i For strength . . 75 
1-m. plank | For deflection . 37 

9 in n i an vf For strength.. 151 
2-111 • plank \ For deflection . 75 

q in nla nk I For Strength . . 227 
d-in. piank j For deflection . 113 

For white oak S mav be taken at 1000 and E at 550,000; for Canadian 
spruce, S = 800, E = 600,000; for hemlock, S = 600, E = 450,000. 



60 


80 


100 


150 


200 


250 


300 


61 
33 


53 
30 


48 

28 


39 

24 


33 
22 






123 
66 


107 
60 


96 
55 


78 
48 


67 

44 


60 
41 


55 
38 


185 
99 


161 
90 


144 
83 


117 
73 


101 
66 


91 
61 


83 

58 



COST OF BUILDINGS. 

Approximate Cost of Mill Buildings. — Chas. T. Main (Eng. News, 
Jan. 27, 1910) gives a series of diagrams of the cost in New England 
Jan., 1910. per sq. ft. of floor space of different sizes of brick mill build- 
ings, one to six stories high, of the type known as "slow-burning," cal- 
culated for total floor loads of about 75 lbs. per sq. ft. Figures taken 
from the diagrams are given in the table below. The costs include 
ordinary foundations and plumbing, but no heating, sprinklers or lighting. 



MILL BUILDINGS. 



1343 



Cost of Brick Mill Buildings per sq. ft. of Floor Area. 



Length, feet. 



50 



100 150 200 250 300 350 400 500 



One Story. 



Width 25 ft. 


$1.90 


$1.66 


$1.58 


$1.54 


$1.51 


$1.49 


$1.48 


$1.47 


$1.46 


50 


1.52 


1.29 


1.21 


1.18 


1.16 


1.15 


1.14 


1.13 


1.13 


75 


1.41 


1.21 


1.12 


1.08 


1.06 


1.04 


1.03 


1.02 


1.02 


125 


1.32 


1.09 


1.02 


0.98 


0.96 


0.94 


0.94 


0.93 


0.92 



25 


2.00 


1.62 


1.52 


1.47 


1.44 


1.41 


1.39 


1.38 


1.36 


50 


1.50 


1.21 


1.13 


1.09 


1.06 


1.05 


1.04 


1.03 


1.02 


75 


1.34 


1.08 


1.01 


0.97 


0.94 


0.92 


0.92 


0.91 


0.90 


125 


1.22 


0.97 


0.90 


0.86 


0.84 


0.82 


0.81 


0.80 


0.86 



Three Stories. 



25 


1.98 


1.57 


1 47 


1.42 


1.39 


1.38 


1.36 


1.35 


1.34 


50 


1.47 


1.17 


1.07 


1.03 


1.01 


1.00 


0.98 


0.98 


0.98 


75 


1.30 


1.05 


0.98 


0.94 


0.91 


0.89 


0.88 


0.87 


0.86 


125 


1.18 


0.93 


0.86 


0.82 


0.80 


0.78 


0.77 


0.76 


0.76 



Four Stories. 



25 


2.00 


1.61 


1.50 


1.45 


1.42 


1.40 


1.38 


1.37 


1.36 


50 


1.38 


1.17 


1.10 


1.05 


1.02 


1.00 


LOO 


0.99 


0.98 


75 


1.32 


1.08 


97 


0.93 


0.90 


0.88 


0.88 


0.87 


0.87 


125 


1.20 


0.93 


0.85 


0.81 


0.78 


0.77 


0.76 


0.75 


0.74 



25 


2.10 


1 7?. 


1.57 


1.51 


1.48 


1.46 


1.44 


1.43 


1.42 


50 


1.53 


1.21 


1.12 


1.08 


1.05 


1.04 


1.03 


1.02 


1.02 


75 


1.35 


1.08 


0.98 


0.94 


0.92 


0.90 


0.89 


0.88 


0.86 


125 


1.22 


0.96 


0.86 


0.82 


0.79 


0.78 


0.77 


0.76 


0.76 



The cost per sq. ft. of a building 100 ft. wide will be about midway 
between that of one 75 ft. wide and one 125 ft. wide, and the cost of a five- 
story building about midway between the costs of a four- and a six-story. 

The data for estimating the above costs are as follows: 





Stories High. 




1 


2 


3 


4 


5 


6 


Foundations, includ- ) o, lt< ,: j_ wa u„ 

Brick walls, cost per ) Outside walls. . 
sq. ft. of surface. . . J Inside walls 


$2.00 
1.75 

0.40 
0.40 


$2.90 
2.25 

0.44 
0.40 


$3.80 
2.80 

0.47 
0.40 


$4.70 
3.40 

0.50 
0.43 


$5.60 
3.90 

0.53 
0.45 


$6.50 
4.50 

0.57 
0.47 



Columns, including piers and castings, cost each $15. 

Assumed Height of Stories. — From ground to first floor, 3 ft. Buildings 
25 ft. wide, stories 13 ft. high; 50 ft. wide, 14 ft. high; 75 ft. wide, 15 ft. 
high; 100 ft. and 125 ft. wide, 16 ft. high. 

Floors, 32 cts. per sq. ft. of gross floor space not including columns. 
Columns included, 38 cts. 

Roof, 25 cts. per sq. ft., not including columns. Columns included, 
30 cts. Roof to project 18 ins. all around buildings. 

Stairways, including partitions*, $100 each flight. Two stairways and 
one elevator tower for buildings up to 150 ft. long; two stairways and two 
elevator towers for buildings up to 300 ft. long. In buildings over two 
stories, three stairways and three elevator towers for buildings over 300 ft. 
long. 



1344 ELECTRICAL ENGINEERING. 

In buildings over two stories, plumbing $75 for each fixture including 
piping and partitions. Two fixtures on each floor up to 5000 sq. ft. of 
floor space and one fixture for each additional 5000 sq. ft. of floor or 
fraction thereof. 
Modifications of the above Costs: 

1. If the soil is poor or the conditions of the site are such as to require 
more than ordinary foundations, the cost will be increased. 

2. If the building is to be used for ordinary storage purposes with low 
stories and no top floors, the cost will be decreased from about 10% for 
large low buildings to 25% for small high ones, about 20% usually being 
a fair allowance. 

3. If the building is to be used for manufacturing and is substantially 
built of wood, the cost will be decreased from about 6% for large one- 
story buildings to 33% for high small buildings; 15% would usually be a 
fair allowance. 

4. If the building is to be used for storage with low stories and built 
substantially of wood, the cost will be decreased from 13% for large 
one-story buildings to 50% for small high buildings; 30% would usually 
be a fair allowance. 

5. If the total floor loads are more than 75 lbs. per sq. ft. the cost is 
increased. 

6. For office buildings, the cost must be increased to cover architectural 
features on the outside and interior finish. 

Reinforced-concrete buildings designed to carry floor loads of 100 lbs. 
per sq. ft. or less will cost about 25% more than the slow-burning type 
of mill construction. 



ELECTRICAL ENGINEERING. 

STANDARDS OF MEASUREMENT. 

C.G.S. (Centimeter, Gramme, Second) or " Absolute " System 
of Physical Measurements: 

Unit of space or distance = 1 centimeter, cm. ; 

Unit of mass = 1 gramme, gm.; 

Unit of time = 1 second, s.; 

Unit of velocity = space -f- time = 1 centimeter in 1 second; 

Unit of acceleration = change of 1 unit of velocity in 1 second ; 

Acceleration due to gravity, at Paris, = 9S1 centimeters in 1 second; 

Unit of force = 1 dyne = ^- gramme = -°Qg046 lb. = 0.000002247 lb. 

A dyne is that force which, acting on a mass of one gramme during one 
second, will give it a velocity of one centimeter per second. The weight 
of one gramme in latitude 40° to 45° is about 980 dynes, at the equator 
973 dynes, and at the poles nearly 984 dynes. Taking the value of g, 
the acceleration due to gravity, in British measures at 32.185 feet per 
second at Paris, and the meter = 39.37 inches, we have 

1 gramme = 32.185 X 12 ~ 0.3937 = 981.00 dynes. 
Unit of work = 1 erg =1 dyne-centimeter = 0.00000007373 ft.-lb.; 
Unit of power = 1 watt = 10 million ergs per second, 

= 0.7373 foot-pound per second, 

= 0^73 = _L of 1 horse-power =0.00134 H.P. 
550 746 * 

C.G.S. unit magnetic pole is one which reacts on an equal pole at a 
centimeter's distance with the force of 1 dyne. 

C.G.S. unit of magnetic field strength, the gauss, is the intensity of 
field which surrounding unit pole acts on it with a force of 1 dyne. 

C.G.S. unit of electro-motive force = the force produced by the cutting 
of a field of 1 gauss intensity at a velocity of 1 centimeter per second (in 
a direction normal to the field and to the conductor) by 1 centimeter of 
conductor. The volt is 100,000,000 times this unit. 

C.G.S. unit of electrical current = the current in a conductor (located 
in a plane normal to the field) when each centimeter is urged across a 
magnetic field of 1 gauss intensity with a force of 1 dyne. One-tenth of 
this is the ampere. 



STANDARDS OF MEASUREMENT. 1345 

The C.G.S. unit of quantity of electricity is that represented by the 
flow of 1 C.G.S. unit of current for 1 second. One-tenth of this is the 
coulomb. 

The Practical Units used in Electrical Calculations are: 

Ampere, the unit of current strength, or rate of how, represented by /. 

Volt, the unit of electro-motive force, electrical pressure, or difference 
of potential, represented by E. 

Ohm, the unit of resistance, represented by R. 

Coulomb (or ampere-second), the unit of quantity, Q. 

Ampere-hour = 3600 coulombs, Q'. 

Watt (ampere- volt, or volt-ampere), the unit of power, P. 

Joule (volt-coulomb), the unit of energy or work, W. 

Farad, the unit of capacity, represented by C. 

Henry, the unit of inductance, represented by L. 

Using letters to represent the units, the relations between them may 
be expressed by the following formulae, in which t represents one second 
and T one hour: 

/=|. Q = It, Q'=IT, C=§. W=QE, P=IE. 

As these relations contain no coefficient other than unity, the letters 
may represent any quantities given in terms of those units. For exam- 
ple, if E represents the number of volts electro-motive force, and R the 
number of ohms resistance in a circuit, then their ratio E -r- R will give 
the number of amperes current strength in that circuit. 

The above six formulae can be combined by substitution or elimination, 
so as to give the relations between any of the quantities. The most 
important of these are the following: 

EI E 2 

<?=§*, C = j;t, W=IEt=^t=PRt=Pt, 

H-IB. V-f. P=f=/ 2 tf=f=<f. 

The definitions of these units as adopted at the International Electrical 
Congress at Chicago in 1893, and as established by Act of Congress of 
the United States, July 12, 1894, are as follows: 

The ohm is substantially equal to 10 9 for 1,000,000,000) units of resist- 
ance of the C.G.S. system, and is represented by the resistance offered 
to an unvarying electric current by a column of mercury at 32° F., 14.4521 
grammes in mass, of a constant cross-sectional area, and of the length of 
106.3 centimeters. 

The ampere is'Vio of the unit of current of the C.G.S. system, and is 
the practical equivalent of the unvarying current which when passed 
through a solution of nitrate of silver in water in accordance with standard 
specifications deposits silver at the rate of 0.001118 gramme per second. 

The volt is the electro-motive force that, steadily applied to a con- 
ductor whose resistance is one ohm, will produce a current of one ampere, 
and is practically equivalent to 1000/1434 (or 0.6974) of the electro- 
motive force between the poles or electrodes of a Clark's cell at a tem- 
perature of 15° C, and prepared in the manner described in the standard 
specifications. 

The coulomb is the quantity of electricity transferred by a current of one 
ampere in one second. 

The farad is the capacity of a condenser charged to a potential of one 
volt by one coulomb of electricity. 

The joule is equal to 10,000,000 units of work in the C.G.S. system, and 
is practically equivalent to the energy expended in one second by an 
ampere in an ohm. 

The watt is equal to 10,000,000 units of power in the C.G.S. system, and 
is practically equivalent to the work done at the rate of one joule per 
second. 

The henry is the induction in a circuit when the electro-motive force 
induced in this circuit is one volt, while the inducing current varies at the 
rate of one ampere per second. 

The ohm, volt, etc,, as above defined, are called the "international" 
ohm, volt, etc.. to distinguish them from the "legal" ohm, B.A. unit, etc. 

The value of the ohm, determined by a committee of the British Asso- 
ciation in 1863, called the B.A. unit, was the resistance of a certain piece 



1346 ELECTRICAL ENGINEERING. 

of copper wire. The so-called "legal" ohm, as adopted at the Inter- 
national Congress of Electricians in Paris in 1884, was a correction of the 
B.A. unit, and was defined as the resistance of a column of mercury 
1 square millimeter in section and 106 centimeters long, at a temperature 
of 32° F. 

1 legal ohm = 1.0112 B.A. units, 1 B.A. unit = 0.9889 legal ohm; 

1 international ohm = 1.0136 B.A. units, IB. A. unit = 0.9866 int. ohm; 
1 international ohm = 1.0023 legal ohm, 1 legal ohm = 0.9977 int. ohm. 

Derived Units. 

1 megohm = 1 million ohms; 
1 microhm = 1 millionth of an ohm; 
1 milliampere = tyiooo of an ampere; 
1 micro-farad = 1 millionth of a farad. 

Relations of Various Units. 

1 ampere =1 coulomb per second ; 

1 volt-ampere =1 watt = 1 volt-coulomb per sec. ; 

r = 0.7373 foot-pound per second, 
1 watt \ = 0.0009477 heat-unit per sec. (Fahr.), 

I = V746 of one horse-power; 

r = 0.7373 foot-pound, 
1 joule < = work done by one watt in one sec, 

1 = 0.0009477 heat-unit; 

1 British thermal unit = 1055.2 joules; 

1 kilowatt, or 1000 watts = 1000/746 or 1.3405 horse-powers; 

1 kilowatt-hour, r = 1.3405 horse-power hours, 

1000 volt-ampere hours, \ = 2,654,200 foot-pounds, 

1 British Board of Trade unit, (. = 3412 heat-units; 

1 hm-^P nowpr J = 746 watts = 746 volt-amperes, 

1 horse-power { = 33000 foot-pounds per minute. 

The ohm, ampere, and volt are defined in terms of one another as 
follows: Ohm, the resistance of a conductor through which a current of 
one ampere will pass when the electro-motive force is one volt. Ampere, 
the quantity of current which will flow through a resistance of one ohm 
when the electro-motive force is one volt. Volt, the electro-motive force 
required to cause a current of one ampere to flow through a resistance of 
one ohm. 

For Methods of making Electrical Measurements, Testing, etc., 
see Munroe & Jamieson's Pocket-Book of Electrical Rules, Tables, and 
Data; S. P. Thompson's Dynamo-Electric Machinery; Carhart & Patter-: 
son's Electrical Measurements; and works on Electrical Engineering. 

Equivalent Electrical and 3fechanical Units. — H. Ward Leonard 
published in The Electrical Engineer, Feb. 25, 1895, a table of useful 
equivalents of electrical and mechanical units, from which the table on 
page 1347 is taken, with some modifications. 

Units of the Magnetic Circuit. 

Unit magnetic pple is a pole of such strength that when placed at a dis- 
tance of one centimeter from a similar pole of equal strength it repels it 
with a force of one dyne. 

Magnetic Moment "is the product of the strength of either pole into the 
distance between the two poles. . . 

Intensity of Magnetization is the magnetic moment of a magnet divided . 
by its volume. 

Intensity of Magnetic Field is the force exerted by the field upon a unit 
magnetic pole. The unit is the gauss. 

Gauss = unit of field strength, or density, symbol H, is that intensity of 
field which acts on a unit pole with a force of one dyne, =one line of force 
per square centimeter. One gauss produces 1 dyne of force per centi- 
meter length of conductor upon a current of 10 amperes, or an electro- 
motive force of 1/100,000,000 volt in a centimeter length of conductor 
when its velocity across the field is 1 centimeter per second. A field of 



EQUIVALENT ELECTRICAL AND MECHANICAL UNITS. 1347 






5"3o ! 



0<~ w 
2 u £ 

oS»a 

— o© 






v O.S 3 K s. 
_c< — m §(Nr^£;£ 















«8' 
2" 



5 a a 'S 






, N © O 









— ©©©©> 



^s 



atl! g -ij: 



2 .£&' 
a S 3..J 

a£ cw 



£'*a a 



•a S g+? P ! o p 
• ag . S o5 d • < 
o -i w£ "a £ is -a „ 

5 d^,r, j a — £ 



-^5 



a a '3 »-^> Sjn 

f? a o o . o3 

o'oijgd «N t-.' 



as iS 

o e t* X 

3 93 Q,° 

5 a +> O 






1348 ELECTRICAL ENGINEERING. 

H units is one which acts with H dynes on unit pole, or H lines per 
square centimeter. A unit magnetic pole has 4?r lines of force proceeding 
from it. 

Maxwell = unit of magnetic flux, is the amount of magnetism passing 
through a square centimeter of a field of unit density. Symbol, <f>. 

In non-magnetic materials a unit of intensity of flux is the same as 
unit intensity of field. The name maxwell is given to a unit quantity 
of flux, and one maxwell per square centimeter in non-magnetic materials 
is the same as the gauss. In magnetic materials the flux produced by 
the molecular magnets is added to the field (Norris). 

Magnetic Flux, <£, is equal to the average field intensity multiplied by 
the cross-sectional area. The unit is the maxwell. Maxwells per square 
inch = gausses X 6.45. 

Magnetic Induction, symbol B, is the flux or the number of magnetic 
lines per unit of area of cross-section of magnetized material, the area 
being at every point perpendicular to the direction of the flux. It is 
equal to the product of the field intensity, H, and the permeability, n. 

Gilbert = unit of magnetomotive force, is the amount of M.M.F. that 
would be produced by a coil of 10 -h 4?r or 0.7958 ampere-turns. Symbol F. 

The M.M.F. of a coil is equal to 1.2566 times the ampere-turns. 

If a solenoid is wound with 100 turns of insulated wire carrying a current 
of 5 amperes, the M.M.F. exerted will be 500 ampere-turns X 1.2566 == 
628.3 gilberts. 

Oersted = unit of magnetic reluctance; it is the reluctance of a cubic centi- 
meter of an air-pump vacumm. Symbol, R. 

Reluctance is that quantity in a magnetic circuit which limits the flux 
under a given M.M.F. It corresponds to the resistance in the electric cir- 
cuit. 

Permeance is the reciprocal of reluctance. 

The reluctivity of any medium is its specific reluctance, and in the C.G.S. 
system is the reluctance offered by a cubic centimeter of the body between 
opposed parallel faces. The reluctivity of nearly all substances, other 
than the magnetic metals, is sensibly that of vacuum, is equal to unity, 
and is independent of the flux density. 

Permeability is the reciprocal of magnetic reluctivity. It is a number 
and the symbol is n. 

Materials differ in regard to the resistance they offer to the passage 
of lines of force; thus iron is more permeable than air. The permeability 
of a substance is expressed bv a coefficient, n., which denotes its relation 
to the permeability of air, which is taken as 1. If H = number of mag- 
netic lines per square centimeter which will pass through an air-space 
between the poles of a magnet, and B the number of lines which will 
pass through a certain piece of iron in that space, then n = B -v- H. The 
permeability varies with the quality of the iron, and the degree of satura- 
tion, reaching a practical limit for soft wrought iron when B= about 
18,000 and for cast iron when B = about 10,000 C.G.S. lines per square 

The permeability of a number of materials may be determined by means 
of the table on page 1384. 

ANALOGIES BETWEEN THE FLOW OF WATER AND 
ELECTRICITY. 

Water. Electricity. 

Head, difference of level, in feet. \ Volts; electro-motive force; differ- 

Difference of pressure, lbs. per sq. in. J ence of potential ; E. or E.M.F. 

Resistance of pines, apertures, etc., 1 Ohms, resistance, R. Increases di- 
increases with length of pipe, with rectly as the length of the conduc- 
contractions, roughness, etc.: de- \ tor or wire and inversely as its sec- 
creases with increase of sectional tional area, R <» I -f- ,s. It varies 
area. I with the nature of the conductor. 

Rate of flow, as cubic ft. per second, 1 Amperes: current; current strength; 
gallons per min., etc., or volume intensity of current; rate of flow; 
divided by the time. In the min- [ 1 ampere = 1 coulomb per second, 
ing regions sometimes expressed Amr>pr^— volts • r— — • Tf — TJ? 
in " miners' inches. " J Am P eres ~ ohms - l ~ R • *-■"*• 



ELECTRICAL RESISTANCE. 



1349 



ANALOGIES BETWEEN THE FLOW OF WATER AND 
ELECTRICITY — Continued. 



Water. 
Quantity, usually measured in cubic 
ft. or gallons, but is also equiva- 
lent to rate of flow X time, as cu. 
ft. per second for so many hours. 

Work, or energy, measured in foot- 
pounds; product of weight of fall- 
ing water into height of fall; in 
pumping, product of quantity in 
cubic feet into the pressure in lbs. 
per square foot against which the 
water is pumped. 

Power, rate of work. Horse-power = 
ft.-lbs. of work in 1 min. ~ 33,000. 
In water flowing in pipes, rate of 
flow in cu. ft. per second X resist- 
ance to the flow in lbs. per sq. ft. 
-r- 550. 



Electricity? 

Coulomb, unit of quantity, Q, — 
rate of flow X time, as ampere- 
seconds. 1 ampere-hour = 3600 
coulombs. 
,Joule, volt-coulomb, W, the unit of 
work, = product of quantity by 
the electro-motive force = volt- 
ampere-second. 1 joule = 0.7373 
foot-pound. 

If C (amperes) = rate of flow, and 
E (volts) = difference of pressure 
between two points in a circuit, 
energy expended = IEt, = PRt. 

Watt, unit of power, P, = volts X 
amperes, = current or rate of 
flow X difference of potential. 

1 watt = 0.7373 foot-pound per sec. 
= 1746 of a horse-power. 



ELECTRICAL RESISTANCE. 

Laws of Electrical Resistance. — The resistance, R, of any con- 
ductor varies directly as its length, I, and inversely as its sectional area, s, 
or R oo l h- s. 

If r = the resistance of a conductor 1 unit in length and 1 square unit 
in sectional area, R = rl -=- s. The common unit of length for electrical 
calculations in English measure is the foot, and the unit of area of wires 
is the circular mil = the area of a circle 0.001 in. diameter. 1 mil-foot = 
1 foot long 1 circ.-mil area. 

Resistance of 1 mil-foot of soft copper wire at 51° F. = 10 international 
ohms. 

Example. — What is the resistance of a wire 1000 ft. long, 0.1 in. diam.? 
0.1 in. diam. = 10,000 circ. mils. 

R = rl -r- 8 = 10 X 1000 -4- 10,000 = 1 ohm. 

Specific resistance, also called resistivity, is the resistance of a material 
of unit length and section as compared with the resistance of soft copper. 

Conductivity is the reciprocal of specific resistance, or the relative 
conducting power compared with copper taken at 100. 

Relative Conductivities of Different Metals at 0° and 100° C. 

(Matthiessen.) 





Conductivities. 


Metals. 


Conductivities. 


Metals. 


At 0°C. 
At32°F. 


At 100° C. 
At 212° F. 


At 0°C. 
At 32° F. 


At 100° C. 
At 212° F. 




100 
99.95 
77.96 
29.02 
23.72 
18.00 
16.80 


71.56 
70.27 
55.90 
20.67 
16.77 


Tin 


12.36 
8.32 
4.76 
4.62 
1.60 
1.245 


8 67 


Copper, hard .... 

Gold, hard. 

Zinc, pressed .... 




5 86 


Arsenic 

Antimony 

Mercury, pure. . 
Bismuth 


3.33 
3.26 




0.878 















Resistance of Various Metals and Alloys. — Condensed from a 
table compiled by H. F. Parshall and H. M. Hobart from different authori- 
ties. R = resistance in ohms per mil foot = resistance per centimeter 
cube x 6.015. C=«= percent increase of resistance per degree C. 



1350 



ELECTRICAL ENGINEERING. 



Aluminum, 99% pure 

Aluminum, 94; copper, 6.. 
Al. bronze, Al 10; Cu, 90.. 
Antimony, compressed. . . 

Bismuth, compressed 

Cadmium, pure 

Copper, annealed, (D) 

Copper, annealed, (M) . . . 

Copper, 88; silicon, 12 

Copper, 65.8; zinc, 34.2. . . . 

Copper, 90; lead, 10 

Copper, 97; aluminum, 3. . 

Cu, 87; Ni ,6.5;A1, 6.5 

Copper, 65; nickel, 25 

Cu, 70; manganese, 30 

German silver 

Cu, 60; Zn, 25; Ni, 15.... 

Gold, 99.9% pure 

Gold, 67; silver, 33 

Iron, very pure. 



R 


C 


15.4 


0.423 


17.4 


.381 


75.5 


.105 


211 


.389 


780 


.354 


60 


.419 


9.35 


.428 


9.54 


.388 


17.7 




37.8 


.158 


31.7 




53.0 


.090 


89.5 


.065 


205 


.019 


605 


.004 


180 


.036 


13.2 


.377 


61.8 


.065 


54.5 


.625 



White cast iron 

Gray cast iron 

Wrought iron , 

Soft steel, C, 0.045 

Manganese steel, Mn, 12. 

Nickel steel, Ni, 4.35 

Lead, pure 

Manganin, 

Cu, 84; Mn, 12;Ni, 4 

Cu, 80.5;Mn,3;Ni, 16.5 
Cu, 79.5 ;Mn, 19.7; Fe,0.{ 

Mercury , 

Nickel 

Palladium, pure 

Platinum, annealed 

Platinum, 67; silver, 33 . . . 

Phosphor bronze 

Silver, pure , 

Tin, pure , 

Zinc, pure 



340 
684 

82.8 

63 
401 
177 
123 

287 

294 

393 

566 
73.7 
61.1 

539 

145 
33.6 
8.82 
78.5 
34.5 



.127 
.201 
.411 

.000 
.000 
.000 
.072 
.62 
.354 
.247 
.133 
.394 
.400 
.440 
.406 



(D) Dewarand Fleming; (M) Matthiessen. 

Conductivity of Aluminum. — J. W. Richards (Jour. Frank.. Inst, 
Mar., 1897) gives for hard-drawn aluminum of purity 98.5, 99.0, 99.5, 
and 99.75% respectively a conductivity of 55, 59, 61, and 63 to 64%, 
copper being 100%. The Pittsburg Reduction Co. claims that its purest 
aluminum has a conductivity of over 64.5%. (Eng'g News, Dec. 17, 
1896.) 

German Silver. — The resistance of German silver depends on its 
composition. Matthiessen gives it as nearly 13 times that of copper, 
with a temperature coefficient of 0.0004433 per degree C. Weston, how- 
ever (Proc. Electrical Congress, 1893, p. 179), has found copper-nickel- 
zinc alloys (German silver) which had a resistance of nearly 28 times 
that of copper, and a temperature coefficient of about one-half that given 
by Matthiessen. 

Conductors and Insulators in Order of their Value. 

(non-conductors). 
Ebonite 
Gutta-percha 
India-rubber 
Silk 

Dry paper 
Parchment 
Dry leather 
Porcelain 
Oils 

According to Culley, the resistance of distilled water is 6754 million 
times as great as that of copper. Impurities in water decrease its resist- 
ance. 

Resistance Varies with Temperature. — For every degree Centi- 
grade the resistance of copper increases about 0.4%, or for every degree F. 
0.2222%. Thus a piece of copper wire having a resistance of 10 ohms 
at 32° would have a resistance of 11.11 ohms at 82° F. 

The following table shows the amount of resistance of a few substances 
used for various electrical purposes by which 1 ohm is increased by a 
rise of temperature of 1° C. 

I Gold, silver 0.00065 

Cast iron , 0.00080 

I Copper 0.00400 



CONDUCTORS. 


INSULATORS 


All metals 


Dry air 


Well-burned charcoal 


Shellac 


Plumbago 


Paraffin 


Acid solutions 


Amber 


Saline solutions 


Resins 


Metallic ores 


Sulphur 


Animal fluids 


Wax 


Living vegetable substances 


Jet 


Moist earth 


Glass 


Water 


Mica 



Platinoid 0.00021 

Platinum silver 0.00031 

German silver (see above).. 0.00044 I 



DIRECT ELECTRIC CURRENTS. 1351 

Annealing. — Resistance is lessened by annealing. Matthiessen gives 
the following relative conductivities for copper and silver, the comparison 
being made with pure silver at 100° C: 

Metal. Temo. C. Hard. Annealed. R,atio. 

Copper 11° 95.31 97.83 1 to 1 .027 

Silver 14.6° 95.36 103.33 1 to 1 .084 

Dr. Siemens compared the conductivities of copper, silver, and brass 
with the following results. .Ratio of hard to annealed: 

Copper.... 1 to 1 .058 Silver. .. .1 to 1 .145 Brass. .. .1 to 1 .180 

Standard of Resistance of Copper Wire. (Trans. A. I. E. E., 
Sept. and Nov., 1890.) — Matthiessen's standard is: A hard-drawn copper 
wire 1 meter long,, weighing 1 gramme, has a resistance of 0.1469 B.A. 
unit at 0° C. Relative conducting power (Matthiessen): silver, 100; 
hard or unannealed copper, 99.95; soft or annealed copper, 102.21. Con- 
ductivity of copper at other temperatures than 0° C, C t =C (1 — 0.00387 t 
+ 0.000009009 t 2 ). 

The resistance is the reciprocal of the conductivity, and is 
R t = R d (1 + 0.00387 t + 0.00000597 t 2 ). 

The shorter formula R t = R Q (1 + 0.00406 is commonly used. , 

A committee of the Am. Inst. Electrical Engineers recommend the 

following as the most correct form of the Matthiessen standard, taking 

8.89 as the sp. gr. of pure cooper: 

A soft copper wire 1 meter long and 1 mm. diam. has an electrical 

resistance of 0.02057 B.A. unit at 0° C. From this the resistance of a soft 

copper wire 1 foot long and 0.001 in. diam. (mil-foot) is 9.720 B.A. units 

at 0.° C. \ 

Standard Resistance at 0° C. B.A. Units. Legal Ohms. Internat. 

Ohms. 
Meter-millimeter, soft copper 0.02057 0.02034 0.02029 

Cubic centimeter " 0.000001616 0.000001598 0.000001593 

Mil-foot " 9.720 9.612 9.590 

1 mil -ft. of soft copper at 10°. 22 Cor 50°. 4 F. 10. 9.977 

" " " " r ' " 15°.5 " 59°. 9 F. 10.20 10.175 

" " " " " " 23°.9 " 75° F. 10.53 10.505 

Hard-drawing and annealing are found to produce proportional changes 
in the conductivity and the temperature coefficient. The range of con- 
ductivity of numerous samples representative of the copper now in com- 
mon use for electrical purposes is from 94.5% to 101.8% (on the basis of 
100% corresponding to 1.7213 micro-ohms per centimeter-cube, at 20°C. 

Using this result, a measurement of the conductivity of a sample gives 
also its temperature coefficient. Thus. 020 (in the formula, R^ — R20 [1 + 
a w (t - 20)] for a sample of copper is given by multiplying 0.00393 by the 
percentage conductivitv. The value assumed by the Am. Inst. El. En., 
Oq = 0.0042, or ao = 0.00387, is the true temperature coefficient for 
copper of 98.6% conductivity. (J. H. Dellinger, Elec. Rev., May 7, 1910.) 

For tables of the resistance of copper wire, see pages 1357 and 1358, 
also page 240. 

Taking Matthiessen's standard of pure copper as 100%, some refined 
metal has exhibited an electrical conductivity equivalent to 103%. 
Matthiessen found that impurities in copper sufficient to decrease its 
density from 8.94 to 8.90 produced a marked increase of electrical resist- 
ance. 

DIRECT ELECTRIC CURRENTS. 

Ohm's Law. — This law expresses the relation between the three 
fundamental units of resistance, electrical pressure, and current. It is: 
_, L electrical pressure , E , „ ,„ A E 

Current ^ resistance ; 7= R : whence * = /«. and B - r 



1352 ELECTRICAL ENGINEERING. 

In terms of the units of the three quantities, 

. volts .■ ; volts 

Amperes = —r ; volts = amperes X ohms; ohms = — • 

ohms amperes 

Examples: Simple Circuits. — 1. If the source has an effective electrical 
pressure of 100 volts, and the resistance is two ohms, what is the current? 

E 
= R ~~ 

2. What pressure will give a current of 50 amperes through a resistance 
of 2 ohms? E = IR = 50 X 2 = 100 volts. 

3. What resistance is required to obtain a current of 50 amperes when 
the pressure is 100 volts? R = E + I = 100 -s- 50 = 2 ohms. 

Ohm's law applies equally to a complete electrical circuit and to any 
part thereof. 

Series Circuits. — If conductors are arranged one after the other they 
are said to be in series, and the total resistance of the circuit is the sum of 
the resistances of its several parts. Let A, Fig. 195, be a source of current, 
such as a battery or generator, producing a difference of potential or 
E.M.F. of 120 volts, measured across ab, and let the circuit contain four 
conductors whose resistances, n, ri, r%, r 4 , are 1 ohm each, and three 

a ri /-\ r» s-\ other resistances, Ri, R2, R3, each 2 ohms. The 

1 -* — ( ) — — ( h total resistance is 10 ohms, and by Ohm's law 

S: R Ro tne current I = E + R = 120 + 10 = 12 ana- 

's- A - 1 2 r 3 p ereS- This current is constant throughout the 

I ^- ^ circuit, and a series circuit is therefore one of 

i: if. \_) constant current. The drop of potential in the 

* R whole circuit from a around to b is 120 volts, 

F IG 195 or E = RI. The drop in any portion depends 

on the resistance of that portion; thus from a to 

Ri the resistance is 1 ohm, the constant current 12 amperes, and the drop 

1 X 12 = 12 volts. The drop in passing through each of the resistance 

Ri, R2, #3 is 2 X 12 = 24 volts. 

Parallel, Divided, or Multiple Circuits. — Let B, Fig. 196, be a 
generator producing an E.M.F. of 220 volts across the terminals ab. 
The current is divided, so that part 
flows through the main wires ac and 
part through the "shunt" s, having a 
resistance of 0.5 ohm. Also the current 
has three paths between c and d, viz., 
through the three resistances in parallel Sg 
Ri, R2, R3, of 2 ohms each. Consider 
that the resistance of the wires is so small 
that it may be neglected. Let the con- 
ductances of the four paths be repre- 
sented by C s . Ci, C 2> Cs. The total Fig. 196. 
conductance is C s + C t + Ci + Cs = C and the total resistance R =• 
1 -*■ C. The conductance of each path is the reciprocal of its resistance, 
the total conductance is the sum of the separate conductances, and the 
resistance of the combined or "parallel" paths is the reciprocal of the 
total conductance. 

*=H6VH4)= i+3 - 5=0 - 286ohm - 

The current I = E -*■ R = 770 amperes. 

Conductors in Series and Parallel. — Let the resistances in parallel 
be the same as in Fig. 196, with the additional resistance of 0.1 ohm 
in each of the six sections of the main wires, ac, bd, etc., in series. The 
voltage across ab being 220 volts, determine the drop in voltage at the 
several points, the total current, and the current through each path. 
The problem is somewhat complicated. It may be solved as follows: 
Consider first the points eg; here there are two paths for the current, 
efgh and eg. Find the resistance and the conductance of each and the 
total resistance (the reciprocal of the joint conductance) of the parallel 




DIRECT ELECTRIC CURRENTS. 1353 



paths. Next consider the points cd; here there are two paths — one 
through e and the other through cd. Find the total resistance as before. 
Finally consider the points ab\ here there are two paths — one through 
c, the other through s. Find the conductances of each and their sum. 
The product of this sum and the voltage at ab will be the total amperes 
of current, and the current through any path will be proportional to the 
conductance of that path. The resistances, R, and conductances, C, 
of the several paths are as follows: 

R C 

R a of efRzhg = 0.1 + 2 + 0.1 = 2.2 0.4545 

R b of eR 2 g = 2 0.5 



Joint R c = 1.048 0.9545 



R d oice+ dg+ R c =1.248 0.8013 

R e of cRid «= 2 0.5 



Joint R/ = 0.7687 1.3013 

R g of ac+bd+ Rf = 0.9687 1.0332 

Rh of s = 0.5 2 

Joint R a + R h = 0.330 3.0332 

Total current = 220 X 3.0332 = 667.3 amperes. 
Current through s = 220 X 2 = 440 amp.; through c = 227.3 amp. 
"c.Rid = 227.3 X 0.5 -f- 1.3013 = 87.34 amp. 

e = 227.3 X 0.8013 -f- 1.3013 = 139.96 " 
" eR?g = 139.96 X 0.5 h- 0.9545 = 73.31 " 
" fRz = 139.96 X 0.4545 -H 0.9545 = 66.65 " 

The drop in voltage in any section of the line is found by the formula 
E — RI, R being the resistance of that section and / the current in it. 
As the R of each section is 0.1 ohm we find E for ac and bd each = 22.7 
volts, for ce and dg each 14.0 volts, and for ef and gh each 6.67 volts. 
The voltage across cd is 220 - 2X 22.7 = 174.6 volts; across eg, 174.6- 2 
X 14.0 = 146.6, and across fh 146.6 - 2 X 667 = 133.3 volts. Taking 
these voltages and the resistances R\, R2, R3, each 2 ohms, we find from 
J - E -*- R the current through each of these resistances 87.3, 73.3, and 
66.65 amperes as before. 

Internal Resistance. — In a simple circuit we have two resistances, 
that of the circuit R and that of the internal parts of the source of electro- 
motive force, called internal resistance, r. The formula of Ohm's law 
when the internal resistance is considered is / = E ■*■ (R + r). 

Power of the Circuit. — The power, or rate of work, in watts = ' 
current in amperes X electro-motive force in volts = / X E. Since 
/ = E -i- R, watts = E 2 -r- R = electro-motive force 2 4- resistance. 

Example. — What H.P. is required to supply 100 lamps of 40 ohms 
resistance each, requiring an electro-motive force of 60 volts? 

E 2 60 2 
The number of volt-amperes for each lamp is -=- = — , 1 volt-ampere 

60 2 
-0.00134 H.P.; therefore — X 100 X 0.00134 = 12 H.P. (electrical) 

very nearly. 

Electrical, Brake, and Indicated Horse-power. — The power given 
by a dynamo = volts X amperes -f- 1000 = kilowatts, kw. Volts X out 
amperes -=- 746 = electrical horse-power, E.H.P. The power put into a 
dynamo shaft by a direct-connected engine or other prime mover is 
called the shaft or brake horse-power, B.H.P. If ei is the efficiency of the 
dynamo, B.H.P. = E.H.P. -f- e\. If e<> is the mechanical efficiency of the 
engine, the indicated horse-power, I. H.P. = brake H.P. ~ ei = E.H.P. -~- 

(61 X 62). 



1354 ELECTRICAL ENGINEERING. 

If ex and e% each = 91.5%, I.H.P. = E.H.P. X 1.194 = kw. X 1.60. In 
direct-connected units of 250 kw. or less the rated H.P. of the engine is 
commonly taken as 1.6 X the rated kw. of the generator. 

Electric motors are rated at the H.P. given out at the pulley or belt. 
H.P. of motor = E.H.P. supplied X efficiency of motor. 

Heat Generated by a Current. — Joule's law shows that the heat 
developed in a conductor is directly proportional, 1st, to its resistance; 
2d, to the square of the current strength; and 3d, to the time during 
which the current flows, or H = PRt. Since I = E + R, 

PRt = ^IRt = EIt = E^t = ~- 

Or, heat = current 2 X resistance X time 

— electro-motive force X current X time. 
■= electro-motive force 2 X time -*- resistance. 
Q = quantity of electricity flowing = It = (Et ~ R). 
H = EQ; or heat = electro-motive force X quantity. 

The electro-motive force here is that causing the flow, or the difference 
in potential between the ends of the conductor. 

The electrical unit of heat, or "joule" = 10 7 ergs = heat generated in 
one second by a current of 1 ampere flowing through a resistance of one 
ohm = 0.239 gramme of water raised 1° C. H = PRt X 0.239 gramme 
calories = PRt X 0.0009478 British thermal units. 

In electric lighting the energy of the current is converted into heat in 
the lamps. The resistance of the lamp is made great so that the required 
quantity of heat may be developed, while in the wire leading to and from 
the lamp the resistance is made as small as is commercially practicable, 
so that as little energy as possible may be wasted in heating the wire. 

Heating of Conductors. (From Kapp's Electrical Transmission of 
Energy.) — It becomes a matter of great importance to determine before- 
hand what rise in temperature! is to be expected in each given case, and 
if that rise should be found -o be greater than appears safe, provision must 
be made to increase the rate at which heat is carried off. This can gen- 
erally be done by increasing the superficial area of the conductor. Say 
we have one circular conductor of 1 square inch area, and find that with 
1000 amperes flowing it would become too hot. Now by splitting up this 
conductor into 10 separate wires each one-tenth of a square inch cross- 
sectional area, we have not altered the total amount of energy trans- 
formed into heat, but we have increased the surface exposed to the cooling 
action of the surrounding air in the ratio of 1 : Vio, and therefore the ten 
thin wires can dissipate more than t-hree times the heat, as compared with 
the single thick wire. 

Prof. Forbes states that an insulated wire carries a greater current with- 
out overheating than a bare wire if the diameter be not too great. Assum- 
ing the diameter of the cable to be twice the diam. of the conductor, a 
greater current can be carried in insulated wires than in bare wires up to 
1.9 inch diam. of conductor. If diam. of cable = 4 times diam. of con- 
ductor, this is the case up to 1.1 inch diam. of conductor. 

Heating of Bare Wires. — The following formula are given by 
Kennelly: 

T= ■*, X 90,000 +t; 

T = temperature of the wire and t that of the air, in Fahrenheit degrees; 
/ — current in amperes, d = diameter of the wire in mils. 



If we take T - t = 90° F., ^90 - 4.48, then 



d = 10 ^JP and I = ^d 3 + 1000. 

This latter formula gives for the carrying capacity in amperes of bare 
wires almost exactly the figures given for weather-proof wires in the 
Fire Underwriters' table, except in the case of Nos. 18 and 16, B. & S. 
gauge, for which the formula gives 8 and 11 amperes, respectively, instead 
of 5 and 8 amperes, given in the table. 



DIRECT ELECTRIC CURRENTS. 



1355 



Heating of Coils. — The rise of temperature in magnet coils due to 
the passage of current through the wire is approximately proportional to 
the watts lost in the coil per unit of effective radiating surface, thus: 
. PR I PR 

t being the temperature rise in degrees Fahr.; S, the effective radiating 
surface; and k a coefficient which varies widely, according to condition. 
In electromagnet coils of small size and power, k may be as large as 0.015. 
Ordinarily it ranges from 0.012 down to 0.005; a fair average is 0.007. 
The more exposed the coil is to air circulation, the larger is the value of k\ 
the larger the proportion of iron to copper, by weight, in the core and 
winding, the thinner the winding with relation to its dimension parallel 
with the magnet core, and the larger the "space factor" of the winding, 
the larger will be the value of k. The space factor is the ratio of the 
actual copper cross-section of the whole coil to the gross cross-section of 
copper, insulation, and interstices. 

Fusion of Wires. — W. H. Preece gives a formula for the current 
required to fuse wires of different metals, viz., I = aS, in which d is the 
diameter in inches and a a coefficient whose value for different metals 
is as follows: Copper, 10,244; aluminum, 7585; platinum, 5172; German 
silver, 5230; platinoid, 4750; iron, 3148; tin, 1462; lead, 1379; alloy of 2 
lead and 1 tin, 1318. 

Allowable Carrying Capacity of Copper "Wires. 

(For inside wiring, National Board of Fire Underwriters' Rules.) 



B.&S. 


Circular 


Amperes. 


Circular 


Amperes. 










Gauge. 


Mils. 


Rubber 


Other In- 


Mils. 


Rubber 


Other In- 






Covered . 


sulation. 




Covered. 


sulation. 


18 


1,624 


3 


5 


200,000 


200 


300 


16 


2,583 


6 


8 


300,000 


270 


400 


14 


4,107 


12 


16 


400,000 


330 


500 


12 


6,530 


17 


23 


500,000 


390 


590 


10 


10,380 


24 


32 


600,000 


450 


680 


8 


16,510 


33 


46 


700,000 


500 


760 


6 


26,250 


46 


65 


800,000 


550 


840 


5 


33,100 


54 


77 


900,000 


600 


920 


4 


41,740 


65 


92 


1,000,000 


650 


1,000 


3 


52,630 


76 


110 


1,100,000 


690 


1,080 


2 


66,370 


90 


131 


1,200,000 


730 


1,150 


1 


83,690 


107 


156 


1,300,000 


770 


1,220 





105,500 


127 


185 


1,400,000 


810 


1,290 


00 


133,100 


150 


220 


1 ,600,000 


890 


1,430 


000 


167,800 


177 


262 


1,800,000 


970 


1,550 


0000 


211,600 . 


210 


312 


2,000,000 


1,050 


1,670 



Wires smaller than No. 14 B. & S. gauge must not be used except in fix- 
tures and pendant cords. 

The lower limit is specified for rubber-covered wires to prevent deteriora- 
tion of the insulation by the heat of the wires. 

For insulated aluminum wire the safe-carrying capacity is 84 per cent of 
that of copper wire with the same insulation. 

See pamphlets published by the National Board of Fire Underwriters, 
New York, for complete specifications and rules for wiring. 

Underwriters' Insulation. — The thickness of insulation required 
by the rules of the National Board of Fire Underwriters varies with the size 
of the wire, the character of the insulation, and the voltage. The thick- 
ness of insulation on rubber-covered wires carrying voltages up to 600 
varies from 1/32 inch for a No. 18 B. & S. gauge wire to 1/8 inch for a wire of 
1,000,000 circular mils. Weather-proof insulation is required to be slightly 
thicker. For voltages of over 600 the insidation is required to be at least 
V32 inch thick for all sizes from No. 14 B. & S. gauge to 500,000 mils and 
L/8 inch thick for larger sizes. 



1356 



ELECTRICAL ENGINEERING. 



Drop of Voltage of Wires with Currents Allowed by Underwriters* 
Rules, as in the above Table. 





Volts 


Volts drop per 




Volts 


Volts d 


rop per 


B.&S. 


drop per 
1000 


1000 ft. 


Circular 
Mils. 


drop per 
1000 


1000 ft. 


Gauge. 


Rubber 


Weather 


Rubber 


Weather 




feet. 


Covered . 


proof. 




feet. 


Covered. 


proof. 


14 


2.56 


30.0 


39.7 


200,000 


0.052 


10.5 


15.7 


12 


1.6 


26.5 


35.7 


300,000 


.035 


9.5 


14. 


10 


1.05 


23.5 


31.4 


400,000 


.026 


8.7 


13.8 


8 


.685 


20.6 


28.6 


500,000 


.021 


8.2 


12.4 


6 


.400 


17.6 


25.0 


600,000 


.018 


7.9 


11.7 


5 , 


.316 


16.6 


23.6 


700,000 


.015 


7.5 


11.4 


4 


.252 


15.8 


22.5 


800,000 


.013 


7.2 


11.0 


3 


.200 


14.8 


21.4 


900,000 


.0118 


7.0 


13.8 


2 


.158 


13.7 


20. 


1,000,000 


.0105 


6.8 


10.5 


1 


.126 


13.0 


18.9 


1,100,000 


.0095 


6.6 


10.3 





.100 


12.7 


17.7 


1,200,000 


.00875 


6.3 


9.9 


00 


.079 


11.4 


16.7 


1,300,000 


.00808 


6.2 


9.8 


000 


.063 


10.8 


16. 


1,400,000 


.0075 


6.1 


9.7 


0000 


.049 


10.1 


15. 


1,600,000 


.00655 


5.84 


9.4 










1,800,000 


.00582 


5.65 


9.1 










2,000,000 


.00524 


5.5 


8.8 



Copper- wire Table. — The table on pages 1357 and 1358 is abridged from 
one computed by the Committee on Units and Standards of the Ameri- 
can Institute of Electrical Engineers {Trans., Oct., 1893). 

Wiring Table for Motor Service. 

Carrying Capacity in Amperes is Figured at 25% increased Capacity, as 
Required by the Underwriters. 



Safe Carrying Capacity in 
Amperes 


9.6|13.6 


20. 


26. 


36. 


42.4 


50.4 


60. 
3 


70.4 
2 


80. 
1 


100 



120 


Wire Gauge No. B. 


and S . . . 


14 


12 


10 


8 


6 


5 


4 


00 


Horse-power. 


Distance in Feet that the Differe 
Horse-powers 
can be Transmitted with a Loss of Oi 




At Volts. 


At 
amperes 


e Volt. 


115 


230 


500 






1/2 
1 

"l" 
■-•■ 

4 

"71/2 
10 

...... 

26" 

25 " 


1.0 
2.0 
2.3 
4.0 
4.5 
6.0 
7.5 
9.0 
12.5 
16.5 
18.0 
21.1 
25.0 
28.2 
33.1 
37.6 
42.0 
56.5 
75.3 
113.0 


192 
96 
83 
48 
43 
32 
25 
21 
15 


308 
154 
135 

77 
68 
51 
40 
34 
24 
18 


490 
245 
213 
122 
108 
81 
65 
54 
40 
29 
27 
23 
20 


778 
389 
348 
194 
173 
127 
104 
86 
61 
47 
43 
37 
30 
27 
23 


1232 
616 
535 
308 
273 
205 
164 
137 
100 
76 
68 
58 
50 
43 
37 
32 
29 




















780 
680 
390 
346 
260 
208 
173 
125 
96 
86 
77 
62 
55 
47 
41 
38 


960 
834 
480 
426 
320 
258 
213 
153 
118 
106 
91 
76 
68 
58 
51 
45 
34 














1/2 














608 
540 
405 
328 
270 
194 
147 
135 
115 
97 
86 
76 
64 
58 
43 
32 


780 
700 
520 
416 
347 
250 
189 
173 
146 
125 
110 
94 
83 
73 
55 
41 


985 
875 
656 
525 
438 
315 
239 
219 
186 
157 
140 
119 
104 
93 
70 
52 


1232 
1095 
821 
657 
547 
394 
298 
273 
233 
197 
174 
148 
131 
116 
87 
65 
43 




V2 


1 


1395 
1045 






836 


1 


2 
3 


697 
501 

380 


2 


4 
5 


348 
297 
750 




71/2 

io" 
...... 

20 
30 


?,?,?, 


4 








189 










164 


5 










143 


71/2 










111 


10 














82 


15 
















55 



























DIRECT ELECTRIC CURRENTS. 1357 



^rsle^^r^.^^^.l^^'^f^^<> — P>if«MAOi 



^ISS??^2^£ 



OOOOSOOOOQOOOOOOOOOOOOOSOOOO 2^i^S!r^^^,^-,o 

o § § § 8 o o S o o o o S o o S.o © S © © © o © o o o o o o © o o § © o o S o o o S 



IslS 



=i o cd o o o cr . :.■ o S o o o o e 
ooooooooooooooSoooooc 



-orsv^poOfNO'Q^covO'A^iN^vo-oa: 



■OQ? — ^^NOrsNOOirvQvO>piAO'^ , TNaO^«Ac>N 

IN«ONOC>iAONOONOrs3r^OO-N«r.-ONC>-«f>Oin^^C>'^rsN 

OQOOoSoOOOQOQOOOOOOOOOO ■ N^TinrNSNNO-OON- 

OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO---- — r^i^r^in 

ooooooooooooooooooooooooooooooobooooooooo 



OOOOOOOON^OC>'0-n , iA-QN^»tA«-t»A-»r>N^-tfMAOOOtCNOt^^- 



-•^O'lJ'OOMooo- r** >o »r» r-» cvj o ^o 









OOC0N>ONIS , Oc0a0N'O00C0O*tC>->0OO>0-pv0^C>OO--^a^NN 



"Bf*X&S!£i3§ 









>o oo o>o<«go-ogT o^oo-oooo»5ou;o 3 oo- o £. o«oc~ ©©.©©£© 

O^lft0-O , TO , TO^^O'S«»O7^-O<A(sS'r'T00O^(y-»nO^ON-iATC0rNO^ 

S?,iCj9S-5^<<i5Sa3S^^SSoocc2££2_!mj2z2£ ' ' 00 ° or ^'^" 00 ' r " rs oo 



p t 






I I § 



1358 



ELECTRICAL ENGINEERING. 



* 2; 



i 

6 

d 

§ 

1 

1 


rfc. 

a" 


006259 
007267 
007892 
009952 
01047 
01252 
01255 
01583 
01635 
0.01996 
02051 
0.02516 
02649 
0317,3 
03205 
03957 
0.04001 
05008 
05045 
06362 
0.06541 
07586 
08022 
08903 
0.1012 
1276 
0^1282 
1583 
0.1608 
0.2003 
0.2028 
0.2558 
0.2616 
0.3225 
0.4067 
0.5129 
0.6466 
0.8011 

8154 
1.028 

1 296 


o- 


0-005648 
006558 
007122 
008980 
009443 
01130 
01132 
01428 
01475 
0.01801 
01851 
02271 
02390 
02863 
02892 
03570 
03610 
04519 
04552 
05740 
05902 
0.06845 
0.07239 
08033 
0.09128 
0.1151 
0.1157 
0.1428 
1451 
0.1807 
0.1830 

2308 i 
0.2361 
0.2910 
3669 
4627 
5835 
7230 
7357 
9277 
1.170 


II 


005055 
•0 005870 
006374 
008038 
008452 
01011 
01014 
01278 
01321 
01612 
01657 
02032 
02139 
02563 
02588 
03196 
03231 
04045 
04075 
05138 
0.05283 
06127 
06479 
07190 
0.08170 
1030 
0.1035 
1278 
1299 
1618 
1638 
2066 
0.2113 

0.2605 1 
0.3284 
0.4142 
0.5222 
0.6471 
0.6585 
8304 
1.047 


■ft 

Is 


8153 
J 099 

1 296 

2 061 

2 279 
3.262 

3 278 
5 212 
5 565 
8 287 
8 756 

13 18 

14 60 

20 95 

21 38 

32 58 

33 32 
52 19 
52 97 
84 23 
89 04 

119 8 
133 9 
165 
213 
338 6 
342 
521 3 
538 4 
835 1 
856 2 
1,361 } 
1.425 

2,165 ! 
3,441 
5,473 
8.702 

13,360 i 
13,870 ' 
22,000 
34,980 


j 




197 8 
170.4 
156 9 
124 4 
118 3 
98 90 
98 66 
78 24 
75 72 
62 05 
60 36 
49 21 
46 75 
. 39 02 
38 63 
31 29 
30 95 
24 73 
24 54 
19 46 
18 93 
16 32 
15 43 
13 91 
12 24 
9 707 
9 658 
7 823 
7 698 
6 181 
6 105 
4 841 
4 733 
3.839 
3 045 
2 414 
1.915 
1 545 
1.519 
1.204 
0.9550 


1 


161 3 

187 3 
203 4 
256 5 
269 7 

322 6 

323 4 
407 8 
421 4 
514 2 
528.6 
648.4 
682 6 
817 6 
825 9 

1,020 

1.031 

1.290 

1.300 

1.639 

1,685 

1,955 

2.067 

2,294 

2,607 

3,287 

3.304 

4.078 

4.145 

5,162 

5.227 

6,591 

6,742 

8,311 
10,480 
13.210 
16,660 
20;650 
21.010 
26,500 
33.410 


i 
1 




1 226 
9097 
7713 
4851 
4387 
3066 
3051 
1919 
1797 
1207 
1142 
07589 
06849 
04773 
04678 
03069 
03002 
01916 
01888 
001187 
01123 
008350 
007466 
006062 
004696 
002953 
082924 
0001918 
001857 
0001197 
001168 
0007346 
0007019 
0004620 
0002905 
0001827 
0001149 
000007484 
00007210 
00004545 
00002858 


oi 

■fiU, 


006200 
005340 
004917 
003899 
003708 
003100 
003092 
002452 
002373 
001945 
001892 
001 542 
001465 
001223 
001211 
0009808 
0009699 
0007749 
0007692 
0.0006100 
0005933 
0005116 
0004837 
0.0004359 
0.0003836 
0003042 
0003027 
0002452 
0002413 
0.0001937 
0.0001913 
000(517 
0.0001483 
0,0001203 
00009543 
00007568 
00006001 
00004843 
00004759- 
00003774 
00002993 




Il3§a§§53§§§iif5§a5^ 




04526 
04200 
04030 
03589 
03500 
03200 
03196 
02846 
02800 
02535 
0250 
02257 
0.0220 
0.02010 
0200 
0180 
01790 
0.0160 
01594 
0142 
0.0140 
0.0130 
0.01264 
0120 
0.01126 
01003 
0.0100 
0090 
0.008928 
0.0080 
0.007950 
007080 
0.0070 
006305 
0056 15 
0.0050 
004453 
0.0040 
0.003965 
003531 
0.003145 


i 

6 


CQtJQ 


— ^fS N N N <M<S <s| J^P* «"* «**\ «* *\ *\ €** 


CJai 


°" *->*'«- "« ««?««•«• 



ELECTRIC TRANSMISSION, DIRECT CURRENTS 1359 



ELECTRIC TRANSMISSION, DIRECT CURRENTS. 

Cross-section of Wire Required for a Given Current. — 

Let R = resistance of a given line of copper wire, in ohms; 
r = " "1 mil-foot of copper; 

L = length of wire, in feet ; 
e = drop in voltage between the two ends; 
/ = current, in amperes; 
A = sectional area of wire, in circular mils; 

then /= ^ ; R = 7 ; R = r ~r ; whence A = 

R I A e 

The value of r for soft copper wire at 75° F. is 10.505 international ohms. 
For ordinary drawn copper wire the value of 10.8 is commonly taken, cor- 
responding to a conductivity of 97.2 per cent. 

For a circuit, going and return, the total length is 2L, and the formula 
becomes A = 21.6 IL -5- e, L here being the distance from the point of 
supply to the point of delivery. 

If E is the voltage at the generator and a the per cent of drop in the line, 

then e = Ea + 100, and A = 2160IL . 
aE 

P 91 fiO PT 

If P = the power in watts, = EI, then / = ~, and A = " • 

tL aE 1 

If P k = the power in kilowatts, A = 2,160,000 P^L -*- aE 2 . 
If L m = the distance in miles and A c the area in circular inches, then 
A c = 6405 Pj c L m -*- aE 2 . If A s = area in square inches, A s = 5030 Pj c L m 
h- aE 2 . When the area in circular mils has been determined by either 
of these formulae reference should be made to the table of Allowable Capac- 
ity of Wires, to see if the calculated size is sufficient to avoid overheating. 
For all interior wiring the rules of the National Board of Fire Underwriters 
should be followed. See Appendix to Vol. II of " Crocker's Electric 
Lighting." 

Weight of Copper for a Given Power. — Taking the weight of 
a mil-foot of copper at 0.0000030271b., the weight of copper in a circuit of 
length 2 Land cross-section A, in circ. mils, is 0.000006054 LA lbs., = W. 
Substituting for A its value 2 160 PL -4- aE 2 we have 
W = 0.0130766 PL 2 -f- aE 2 ; P in watts, L in ft. 

W = 13.0766 P k L 2 -4- aE 2 ; P k in kilowatts, L in ft. 

17 = 364,556,000 P k L 2 m + aE 2 ; P k in kilowatts, L m in miles. 

The weight of copper required varies directly as the power transmitted ; 
inversely as the percentage of drop or loss; directly as the square of the 
distance; and inversely as the square of the voltage. 

From the last formula the following table has been calculated: 

Weight of Copper Wire to Carry 1000 Kilowatts with 10% Loss. 



Distance 
in miles. 


1 


5 


10 


20 


50 


100 


Volts. 


Weight in lbs. 


500 


145,822 

36,456 

9,114 

1,458 

365 

91 


3,645,560 

911,390 

227,848 

36,456 

9,114 

2,278 

570 










1,000 
2,000 
5,000 
10,000 
20,000 
40,000 
60,000 


3,645,560 
911,390 
145,822 
36,456 
9,114 
2,278 
1,013 








3,645,560 

593,290 

145,822 

36,456 

9,114 

4,051 






3,645,560 
911,390 
227,848 
56,962 
25,316 




3,645,560 
911,390 

227,848 




101,266 









In calculating the distance, an addition of about 5 per cent should be 
made for sag of the wires. 



1360 



ELECTRICAL ENGINEERING. 



Short-circuiting. — From the law 7 = E/R it is seen that with any pres- 
sure E, the current 7 will become very great if R is made very small. In 
short-circuiting the resistance becomes small and the current therefore 
great. Hence the dangers of short-circuiting a current. 

Economy of Electric Transmission. — Lord Kelvin's rule for the 
most economical section of conductor for a given voltage is that for which 
the annual interest on capital outlay is equal to the annual cost of energy 
wasted. 

Tables have been compiled by Professor Forbes and others in accordance 
with modifications of this rule. For a given entering horse-power the ques- 
tion is merely one as to what current density, or how many amperes per 
square inch of conductor, should be employed. Kelvin's rule gives about 
393 amperes per square inch, and Professor Forbes's tables give a current 
density of about 380 amperes per square inch as most economical 

Bell (" Electric Transmission of Power") shows that while Kelvin's rule 
correctly indicates the condition of minimum cost in transmission for a 
given current and line, it omits many practical considerations and is inappli- 
cable to most power transmission work. Each plant has to be considered 
on its merits and very various conditions are likely to determine the line 
loss in different cases. Several cases are cited by Bell to show that neither 
Kelvin's law nor any modification of it is a safe guide in determining the 
proper allowance for loss of energy in the line. 

Wire Tables. — The tables on this and the following page show the 
relation between load, distance, and " drop " or loss by voltage in a two- 
wire direct-current circuit of any standard size of wire The tables are 
based on the formula 

(21.6 IL) -*- A ■= Drop in volts. 
7 = current in amperes, L = distance in feet from point of supply to point 
of delivery, A = sectional area of wire in circular mils. The factors 7 and 
L are combined in the table, in the compound factor " ampere feet." 

Wire Table — Relation between Load, Distance, Loss, and Size 
of Conductor. 
Note. — The numbers in the body of the tables are Ampere-Feet, i.e., 
Amperes X Distance (length of one wire). See examples on next page. 

Table I. — 110-volt and 220-volt Two-wire Circuits. 



Wire 


Sizes; 


Line Loss in Percentage of the Rated Voltage; and Power 


B. & S. Gauge. 


Loss in Percentage of the Delivered Power. 


110 V. 


220 V. 


1 


U/2 


2 


3 


4 


5 


6 1 8 


10 




0000 


21,550 


32,325 


43,100 


64,650 


86,200 


107,750 


129,300 


172,400 


215,500 




000 


17,080 


25,620 


34,160 


51,240 


68,320 


85,400 


102,480 


136,640 


170,800 




00 


13,550 


20,325 


27,100 


40,650 


54,200 


67,750 


81,300 


108,400 


135,500 


0000 





10,750 


16,125 


21,500 


32,250 


43,000 


53,750 


64,500 


86,000 


107,500 


000 


1 


8,520 


12,780 


17,040 


25,560 


34,080 


42,600 


51,120 


68,160 


85,200 


00 


2 


6,750 


10,140 


13,520 


20,280 


27,040 


33,800 


40,560 


54,080 


67,600 





3 


5,360 


8,040 


10,720 


16,080 


21,440 


26,800 


32,160 


42,880 


53,600 


1 


4 


4,250 


6,375 


8,500 


12,750 


17,000 


21,250 


25,500 


34,000 


42,500 


2 


5 


3,370 


5,055 


6,740 


10,110 


13,480 


16,850 


20,220 


26,960 


33,700 


3 


6 


2,670 


4,005 


5,340 


8,010 


10,680 


13,350 


16,020 


21,360 


26,700 


4 


7 


2,120 


3,180 


4,240 


6,360 


8,480 


10,600 


12,720 


16,960 


21,200 


5 


8 


1,680 


2,520 


3,360 


5,040 


6,720 


8,400 


10,800 


13,440 


16,800 


6 


9 


1,330 


1,995 


2,660 


3,990 


5,320 


6,650 


7,980 


10,640 


13,300 


7 


10 


1,055 


1,582 


2,110 


3,165 


4,220 


5,275 


6,330 


8,440 


10,550 


8 


11 


838 


1,257 


1,675 


2,514 


3,350 


4,190 


5,028 


6,700 


8,380 


9 


12 


665 


997 


1,330 


1,995 


2,660 


3,320 


3,990 


5,320 


6,650 


10 


13 


527 


790 


1,054 


1,580 


2,108 


2,635 


3,160 


4,215 


5,270 


11 


.14 


418 


627 


836 


1,254 


1,672 


2,090 


2,508 


3,344 


4,180 


12 




332 


498 


665 


997 


1,330 


1,660 


1,995 


2,660 


3,325 


14 




209 


313 


418 


627 


836 


1,045 


1,354 


1,672 


2,090 



ELECTRIC TRANSMISSION, DIRECT CURRENTS. 1361 





Table II. — 500, 1000, and 2000 Volt Circui 


ts. 




Wire Sizes; 
B. & S. Gauge. 


Line Loss in Percentage of the Rated Voltage; and 
Power Loss in Percentage of the Delivered Power. 


500 V. 


1000 V. 


2000 V. 


1 


M/2 


2 


2V2 


3 


4 


5 


0000 
000 

00 

1 
2 
3 

4 
5 
6 

7 
8 

9 
10 
11 
12 


0000 

000 

00 



1 

2 
3 
4 
5 
6 

7 
8 
9 
10 
11 

12 
13 
14 



1 
2 
3 
4 

5 
6 

7 
8 
9 

10 
11 
12 
13 
14 


97,960 
77,690 
61,620 

48,880 
38,750 

30,760 
24,370 
19,320 
15,320 
12,150 

9,640 
7,640 
6,060 
4,805 
3,810 

3,020 
2,395 
1,900 
1,510 
950 


146,940 
116,535 
92,430 
73,320 
58,125 

46,140 
36,555 
28,980 
22,980 
18,225 

14,460 
11,460 
9,090 
7,207 
5,715 

4,530 
3,592 
2,850 
2,265 
1,425 


195,920 
155,380 
123,240 
97,760 
77,500 

61,520 
48,740 
38,640 
30,640 
24,300 

19,280 
15,280 
12,120 
9,610 
7,620 

6,040 
4,790 
3,800 
3,020 
1,900 


244,900 
194,225 
154,050 
122,200 
96,875 

76,900 
60,925 
48,300 
38,300 
30,375 

24,100 
19,100 
15,150 
12,010 
9,525 

7,550 

5,985 
4,750 
3,775 
2,375 


293,880 
233,970 
184,860 
146,640 
116,250 

92,280 
73,110 
57,960 
45,960 
36,450 

28,920 
22,920 
18,180 
14,415 
11,430 

9,060 
7,185 
5,700 
4,530 
2,850 


391,840 
310,760 
246,480 
195,420 
155,000 

123,040 
97,480 
77,280 
61,280 
48,300 

38,560 
30,560 
24,240 
19,220 
15,220 

12,080 
9,580 
7,600 
6,040 
3,800 


489,800 
388,450 
308,100 
244,400 
193,750 

153,800 
121,850 
96,600 
76,600 
60,750 

48,200 
38,200 
30,300 
24,025 
19,050 

15,100 
11,975 
9,500 
7 550 


14 






4 750 











Examples in the Use of the Wire Tables. — 1. Required the maxi- 
mum load in amperes at 220 volts that can be carried 95 feet by No. 6 
wire without exceeding \\% drop. 

Find No. 6 in the 220-volt column of Table I; opposite this in the \\% 
column is the number 4005, which is the ampere-feet. Dividing this by 
the required distance (95 feet) gives the load, 42.15 amperes. 

Example 2. A 500-volt line is to carry 100 amperes 600 feet with a drop 
not exceeding 5%; what size of wire will be required? 

The ampere-feet will be 100 X 600 = 60,000. Referring to the 5% column 
of Table II, the nearest number of ampere-feet is 60,750, which is opposite 
No. 3 wire in the 500-volt column. 

These tables also show the percentage of the power delivered to a line 
that is lost in non-inductive alternating-current circuits. Such circuits are 
obtained when the load consists of incandescent lamps and the circuit wires 
lie only an inch or two apart, as in conduit wiring. 

Efficiency of Electric Systems. — The efficiency of a system is the ratio 
of the power delivered by the electric motors at the distant end of the 
line to the power delivered to the dynamo-electric machines at the other 
end. The efficiency of a dynamo or motor varies with its load and with 
the size of machine, ranging about as follows for dynamos at full load: 

Kilowatts 30 50 100 200 500 1000 

Efficiency % 90 91 92 93 94 95 

For motors at full load the efficiences run about as follows: 

H.P. 1 2 5 10 20 50 75 100 

Effy. % 75 80 85 88.5 90 91 91.5 91.6 

The efficiency of both generators and motors decreases, at first very 
slowly and then more rapidly, as the load decreases. Each machine 
has its " characteristic " curve of efficiency, showing the ratio of output 
to input at different loads. The following is a rough approximation for 
direct-current machines: Decrease of efficiency at half-load, 3%; 1/4 load, 
10% ; Vs load, 20 % ; Vi6 load, 50%. The loss in transmission, due to fall in 



1362 



ELECTRICAL ENGINEERING. 



Resistances of Pure Aluminum Wire.* 

Conductivity 62 in the Matthiesen Standard Scale. Pure aluminum weighs 
167.111 pounds per cubic foot. 



of o 


Resistances at 70° F. 


« 6 


Resistances at 7C 


°F. 


gfc 








'i z 
























^ 
!« 


Ohms 
per 1000 
Feet. 


Ohms 
.per 
Mile. 


Feet 
per 
Ohm. 


Ohms per 
Pound. 




Ohms 
per 1000 
Feet. 


Ohms 
per 
Mile. 


Feet 
per 
Ohm. 


Ohms per 
Pound. 


0000 


0.07904 


0.41730 


12652. 


0.00040985 


19 


12.985 


68.564 


77.05 


11.070 


000 


.09966 


.52623 


10034. 


.00065102 


20 


16.381 


86.500 


61.06 


17.595 


00 


.12569 


.66362 


7956. 


.0010364 


21 


20.649 


109.02 


48.43 


27.971 





.15849 


.83684 


6310. 


.0016479 


22 


26.025 


137.42 


38.44 


44.450 


1 


.19982 


1 .0552 


5005. 


.0026194 


23 


32.830 


173.35 


30.45 


70.700 


2 


.25200 


1 .3305 


3968. 


.0041656 


24 


41.400 


218.60 


24.16 


112.43 


3 


.31778 


1.6779 


3147. 


. 0066250 


25 


52.200 


275.61 


19.16 


178.78 


4 


.40067 


2.1156 


2496. 


.010531 


26 


65.856 


347.70 


15.19 


284.36 


5 


.50526 


2.6679 


1975. 


.016749 


27 


83.010 


438.32 


12.05 


452.62 


6 


.63720 


3.3687 


1569. 


.026628 


28 


104.67 


552.64 


9.55 


718.95 


7 


.80350 


4.2425 


1245. 


.042335 


29 


132.00 


697.01 


7.58 


1142.9 


8 


1.0131 


5.3498 


987.0 


.067318 


30 


166.43 


878.80 


6.01 


1817.2 


9 


1.2773 


6.7442 


783.0 


.10710 


31 


209.85 


1108.0 


4.77 


2888.0 


10 


1.6111 


8.5065 


620.8 


.17028 


32 


264.68 


1397.6 


3.78 


4595.5 


11 


2.0312 


10.723 


492.4 


.27061 


33 


333.68 


1760.2 


3.00 


7302.0 


12 


2.5615 


13.525 


390.5 


.43040 


34 


420.87 


2222.2 


2.38 


11627. 


13 


3.2300 


17.055 


309.6 


.68437 


35 


530.60 


2801.8 


1.88 


18440. 


14 


4.0724 


21.502 


245.6 


1.0877 


36 


669.00 


3532.5 


1.50 


29352. 


15 


5.1354 


27.114 


194.8 


1.7308 


37 


843.46 


4453.0 


1.19 


46600. 


16 


6.4755 


34.190 


154.4 


2.7505 


38 


1064.0 


5618.0 


0.95 


74240. 


17 


8.1670 


43.124 


122.5 


4.3746 


39 


1341.2 


7082.0 


0.75 


118070. 


18 


10.300 


54.388 


97.10 


6.9590 


40 


1691.1 


8930.0 


0.59 


187700. 



* Calculated on the basis of Dr. Matthiessen's standard, viz.: The re- 
sistance of a pure soft copper wire 1 meter long, having a weight of 1 
gram = 0. 141729 International Ohm at 0° C. 

(From Aluminum for Electrical Conductors; Pittsburgh Reduction Co.) 



electrical pressure or " drop " in the line, is governed by the size of the 
wires, the other conditions remaining the same. For a long-distance 
transmission plant this will vary from 5% upwards. 

With generator efficiency and motor efficiency each 90%, and trans- 
mission loss 5%, the combined efficiency is 0.90 X 0.90 X 0.95 = 76.95%. 

The methods for long-distance transmission may be divided into three 
general classes: (1) continuous current; (2) alternating current; and (3) 
rotary-conventer or " motor-dynamo " systems. There are many factors 
which govern the selection of a system. For each problem considered 
there will be found certain fixed and certain unfixed conditions. In 
general the fixed factors are: (1) capacity of source of power; (2) cost of 
power at source; (3) cost of power by other means at point of delivery; 
(4) danger considerations at motors; (5) operating conditions; (6) con- 
struction conditions (length of line, character of country, etc.). The 
partly fixed conditions are: (7) power which must be delivered, i.e., the 
efficiency of the system; (8) size and number of delivery units. The 
variable conditions are: (9) initial voltage; (10) pounds of copper on line; 
(11) original cost of all apparatus and construction; (12) expenses, operat- 
ing (fixed charges, interest, depreciation, taxes, insurance, etc.); (13) 
liability of trouble and stoppages; (14) danger at station and on line; (15) 
convenience in operating, making changes, extensions, etc. 



ELECTRIC TRANSMISSION. DIRECT CURRENTS. 1363 



Systems of Electrical Distribution in Common Use. 

I. Direct Current. 

A. Constant Potential. 

110 to 125 and 220 to 250 Volts.— Distances less than, say, 
1500 feet. 

For incandescent lamps. 

For arc-lamps, usually 2 in series. 

For motors of moderate sizes. 
200 to 250 and 440 Volts, 3-wire. — Distances less than, sav 
5000 feet. 

For incandescent lamps. 

For arc-lamps, usually 2 in series on each branch. 

For motors 110 or 220 volts, usually 220 volts. 
500 Volts. — Distances less than, say, 20,000 feet. 

Incidentally for arc-lamps, usually 10 in series. 

For motors, stationary and street-car. 

B. Constant Current. 

Usually 5, 6V2, or 9V2 amperes, the volts increasing to several 
thousand, as demanded, for series arc-lamps. 

II. Alternating Current. 

A. Constant Potential. 

For incandescent lamps, arc-lamps, and motors. 
Polyphase Systems. 

For arc and incandescent lamps, motors, and rotary con- 
verters for giving direct current. 
Polyphase — 2- and 3-phase — high tension (25,000 volts and 

over), for long-distance transmission; transformed by 

step-up and step-down transformers. 

B. Constant Current. 

Usually 5 to 6.6 amperes. For arc-lamps. 
The Relative Advantages of Different Systems vary with each par- 
ticular transmission problem, but in a general way may be tabulated as 
below: 





System. 


Advantages. 


Disadvantages. 




( Low voltage. 


Safety, simplicity. 


Expense for copper. 


3 



( High voltage. 


Economy, simplicity. 


Danger; difficulty of 
building machines. 


.5 



8 


3-wire. 


Low voltage on machines 
and saving in copper. 


Not saving enough in 
copper for long dis- 
tances. Necessity for 
" balanced " system. 


Multiple-wire. 


Low voltage at machines 
and saving in copper. 




Single phase. 


Economy of copper. 


Cannot start under load. 
Low efficiency. 


a 


Multiphase. 


Economy of copper, syn- 
chronous speed unnec- 
essary; applicable to 
very long distances. 


Requires more than two 
wires. 


< 


Motor-dynamo. 


High- voltage A.C. trans- 
mission. Low- voltage 
D.C. delivery. 


Expensive. 
Low efficiency. 



1364 



ELECTRICAL ENGINEERING 



TABLE OF ELECTRICAL HORSE-POWERS. 



Volts X Amperes _ 



H.P., or 1 volt ampere = .00 13405 H.P. 







Read amperes at top and volts at side 


or vice versa. 














Volts or Amperes. 


Is 










1 


10 


20 


30 


40 


50 


60 


70 


80 


90 


100 


110 


120 


1 


.00134 


.0134 


.0268 


.0402 


.0536 


.0670 


.0804 


.0938 


.1072 


.1206 


.1341 


.1475 


.1609 


2 


.00268 


.0268 


.0536 


.0804 


.1072 


.1341 


.1609 


.1877 


.2145 


.2413 


.2681 


.2949 


.3217 


3 


.00402 


.0402 


.0804 


.1206 


.1609 


.2011 


.2413 


.2815 


.3217 


.3619 


.4022 


.4424 


.4826 


4 


.00536 


.0536 


.1072 


.1609 


.2145 


.2681 


.3217 


3753 


.4290 


4826 


.5362 


.5898 


.6434 


5 


.00670 


.0670 


.1341 


.2011 


.2681 


.3351 


.4022 


.4692 


.5362 


.6032 


.6703 


.7373 


•8043 


6 


.00804 


.0804 


.1609 


.2413 


.3217 


.4022 


.4826 


.5630 


.6434 


.7239 


.8043 


.8847 


.9652 


7 


.00938 


.0938 


.1877 


.2815 


.3753 


.4692 


.5630 


.6568 


.7507 


.8445 


.9384 


1.032 


1.126 


8 


.01072 


.1072 


.2145 


.3217 


.4290 


.5362 


.6434 


.7507 


.8579 


.9652 


1.072 


1.180 


1 287 


9 


.01206 


.1206 


.2413 


.3619 


.4826 


.6032 


.7239 


.8445 


.9652 


1.086 


1.206 


1.327 


1.448 


10 


.01341 


.1341 


.2681 


.4022 


.5362 


.6703 


.8043 


.9383 


1.072 


1.206 


1.341 


1.475 


1.609 


11 


.01475 


.1475 


.2949 


.4424 


.5898 


.7373 


.8847 


1.032 


1.180 


1.327 


1.475 


1.622 


1.769 


12 


.01609 


.1609 


.3217 


.4826 


.6434 


.8043 


.9652 


1.126 


1.287 


1.448 


1.609 


1.769 


1.930 


13 


.01743 


.1743 


.3485 


.5228 


.6970 


.8713 


1.046 


1.220 


1.394 


1.568 


1.743 


1.917 


2.091 


14 


.01877 


.1877 


.3753 


.5630 


.7507 


.9384 


1.126 


1.314 


1.501 


1.689 


1.877 


2.064 


2.252 


15 


.02011 


.2011 


.4022 


.6032 


.8043 


1.005 


1.206 


1.408 


1.609 


1.810 


2.011 


2.212 


2.413 


16 


.02145 


.2145 


.4290 


.6434 


.8579 


1.072 


1.287 


1.501 


1.716 


1.930 


2.145 


2.359 


2.574 


17 


.02279 


.2279 


.4558 


.6837 


.9115 


1.139 


1.367 


1.595 


1.823 


2.051 


2.279 


2.507 


2.735 


18 


.02413 


.2413 


.4826 


.7239 


.9652 


1.206 


1.448 


1.689 


1.930 


2.172 


2.413 


2.654 


2.895 


19 


.02547 


.2547 


.5094 


.7641 


1.019 


1.273 


1.528 


1.783 


2.037 


::".■: 


2.547 


2.801 


3.056 


20 


.02681 


.2681 


.5362 


.8043 


1.072 


1.340 


1.609 


1.877 


2.145 


2.413 


2.681 


2.949 


3.217 


21 


.02815 


.2815 


.5630 


.8445 


1.126 


1.408 


1.689 


1.971 


2.252 


2.533 


2.815 


3.097 


3.378 


22 


.02949 


.2949 


.5898 


.8847 


1.180 


1.475 


1.769 


2.064 


2.359 


2.654 


2.949 


3.244 


3.539 


23 


.03083 


.3083 


.6166 


.9249 


1.233 


1.542 


1.850 


2.158 


2.467 


2.775 


3.083 


3.391 


3.700 


24 


.03217 


.3217 


.6434 


.9652 


1.287 


1.609 


1.930 


: !.)■■ 


2.574 


2.895 


3.217 


3.539 


3.861 


25 


.03351 


.3351 


.6703 


1.005 


1.341 


1.676 


2.011 


2.346 


2.681 


3.016 


3.351 


3.686 


4.022 


26 


.03485 


.3485 


.6971 


1.046 


1.394 


1.743 


2.091 


2.440 


2.788 


3.137 


3.485 


3.834 


4.182 


27 


.03619 


.3619 


.7239 


1.086 


1.448 


1.810 


2.172 


2.534 


2.895 


3.257 


3.619 


3.981 


4.343 


28 


.03753 


.3753 


.7507 


1.126 


1.501 


1.877 


2.252 


2.627 


3.003 


3.378 


3.753 


4.129 


4.504 


29 


.03887 


.3887 


.7775 


1.166 


1.555 


1.944 


2.332 


2.721 


3.110 


3.499 


3.887 


4.276 


4.665 


30 


.04022 


.4022 


.8043 


1.206 


1.609 


2.011 


2.413 


2.815 


3.217 


3.619 


4.022 


4.424 


4.826 


31 


.04156 


.4156 


.8311 


1.247 


1.662 


2.078 


2.493 


2.909 


3.324 


3.740 


4.156 


4.571 


4.987 


32 


.04290 


.4290 


.8579 


1.287 


1.716 


2.145 


2.574 


3.003 


3.432 


3.861 


4.290 


4.719 


5.148 


33 


.04424 


.4424 


.8847 


1.327 


1.769 


2.212 


2.654 


3.097 


3.539 


3.986 


4.424 


4.866 


5.308 


34 


.04558 


.4558 


.9115 


1.367 


1.823 


2.279 


2.735 


3.190 


3.646 


4.102 


4.558 


5.013 


5.469 


35 


.04692 


.4692 


.9384 


1.408 


1.877 


2.346 


2.815 


3.284 


3.753 


: ■; 


4.692 


5.161 


5.630 


40 


.05362 


.5362 


1.072 


1.609 


2.145 


2.681 


3.217 


3.753 


4 290 


4.826 




5.898 


6.434 


45 


.06032 


.6032 


1.206 


1.810 


2.413 


3.016 


3.619 


4.223 


4.826 


5.439 


6.032 


6.635 


7.239 


50 


.06703 


.6703 


1.341 


2.011 


2.681 


3.351 


4.022 




5.362 


6.032 


6.703 


7.373 


8.043 


55 


.07373 


.7373 


1.475 


2.212 


2.949 


3.686 


4.424 


5.161 




6.635 


7.373 


8.110 


8.847 


60 


.08043 


.8043 


1.609 


2.413 


3.217 


4.022 


4.826 


5.630 


6^434 


7.239 


8.043 


8.047 


9.652 


65 


.08713 


.8713 


1.743 


2.614 


3.485 


4.357 


5.228 


6.099 


6.970 


7.842 


8.713 


9.584 


10.46 


70 


.09384 


.9384 


1.877 


2.815 


3.753 


4.692 


5.630 


6.568 


7.507 


8.445 


9.384 


10.32 


11.26 


75 


.10054 


1.005 


2.011 


3.016 


4.021 


5.027 


6.032 


7.037 


8.043 


9.048 


10.05 


11.06 


12.06 


80 


.10724 


1.072 


2.145 


3.217 


4.290 


5.362 


6.434 


7.507 


8- 579 


9.652 


10.72 


11.80 


12.87 


85 


.11394 


1.139 


2.279 


3.418 


4.558 


5.697 


6.836 


7.976 


9.115 


10.26 


11.39 


12.53 


13.67 


90 


.12065 


1.206 


2.413 


3.619 


4.826 


6.032 


7.239 


8.445 


9.652 


10.86 


12.06 


13.27 


14.48 


95 


.12735 


1.273 


2.547 


3.820 


5.094 


6.367 


7.641 


8.914 


10.18 


11.46 


12.73 


14.01 


15.28 


100 


.13405 


1.341 


2.681 


4.022 


5.362 


6.703 


8.043 


9.384 


10.72 


12.06 


13.41 


14.75 


16.09 


200 


.26810 


2.681 


5.362 


8.043 


10.72 


13.41 


16.09 


18.77 


21.45 


24.13 


26.81 


29.49 


32.17 


300 


.40215 


4.022 


8.043 


12.06 


16.09 


20.11 


21.13 


28.15 


32.17 


36.19 


40.22 


44.24 


48.26 


400 


.53620 


5.362 


10.72 


16.09 


21.45 


26.81 


32.17 


37.53 


42.90 


48.26 


53.62 


58.98 


64.34 


500 


.67025 


6.703 


13.41 


20.11 


26.81 


33.51 


40.22 


46.92 


53.62 


60.32 


67.03 


73.73 


80.43 


600 


.80430 


8.043 


16.09 


24.13 


32.17 


40.22 


48.26 


56.30 


64.34 


72.39 


80.43 


88.47 


96.52 


700 


.93835 


9.384 


18.77 


28.15 


37.53 


46.92 


56.30 


65.68 


75.07 


84.45 


93.84 


103.2 


112.6 


800 


1.0724 


10.72 


21.45 


32.17 


42.90 


53.62 


64.34 


75.07 


85.79 


96.52 


107.2 


118.0 


128.7 


900 


1.2065 


12.06 


24.13 


36.19 


48.26 


60.32 


72.39 


84.45 


96.52 


108.6 


120.6 


132.7 


144.8 


1.000 


1.3405 


13.41 


26.81 


40.22 


53.62 


67.03 


80.43 


93.84 


107.2 


120.6 


134.1 


147.5 


160.9 


2,000 


2.6810 


26.81 


53.62 


80.43 


107.2 


134.1 


160.9 


187.7 


214.5 


241.3 


268.1 


294.9 


321.7 


3,000 


4.0215 


40.22 


80.43 


120.6 


160.9 


201.1 


241.3 


281.5 


321.7 


361.-9- 


402.2 


442.4 


482.6 


4,000 


5.3620 


53.62 


107.2 


160.9 


214.5 


268.1 


321.7 


375.3 


429.0 


482.6, 


536.2 


589.8 


643.4 


5,000 


6.7025 


67.03 


134.1 


201.1 


268 1 


335 1 


402.2 


469.2 


536.2 


603.2 


670.3 


737.3 


804.2 


6,000 


8.0430 


80.43 


160.9 


241.3 


321.7 


402.2 


482.6 


563.0 


643.4 


723.9 


804.3 


884.7 


965.2 


7,000 


9.3835 


93.84 


187.7 


281.5 


375.3 


469.2 


5(i3.0 


656.8 


750.7 


844.5 


938.4 


1032 


1126 


8.000 10.724 


107.2 


214.5 


321.7 


429.0 


536.2 


613.4 


750.7 


857.9 


1IH5.2 


1072 


1180 


1287 


9,000 12.065 


120.6 


241.3 


361.9 


482.6 


603.2 


723.9 


844.5 


965.2 


1086 


1206 


1327 


1448 


10,000 13.405 


134.1 


268.1 


402.2 


536.2 


670.3 


804.3 


938.3 


1072 


1206 


1341 


1475 


1609 



ELECTRIC TRANSMISSION, DIRECT CURRENTS. 1365 



Cost of Copper for Long-distance Transmission. 

(Westinghouse El. and Mfg. Co.) 

Cost of Copper Required for the Delivery of One Mechanical 
horse-power at motor shaft with various voltages at motor 
Terminals, or at Terminals of Lowering Transformers. 
Loss of energy in conductors (drop) equals 20%. Motor efficiency, 90%. 
Length of conductor per mile of single distance, 11,000 ft., to allow for 
sag. Cost of copper taken at 16 cents per pound. 



Miles. 


1000 v. 


2000 v. 


3000 v. 


4000 v. 


5000 v. 


10,000 v. 


1 


$2.08 


$0.52 


$ 0.23 


$0.13 


$0.08 


$0.<52 


2 


8.33 


2.08 


0.93 


0.52 


0.33 


0.08 


3 


18.70 


4.68 


2.08 


1.17 


0.75 


0.19 


4 


33.30 


8.32 


3.70 


2.08 


1.33 


0.33 


5 


52.05 


13.00 


5.78 


3.25 


2.08 


52 


6 


74.90 


18.70 


8.32 


4.68 


3.00 


0.75 


7 


102.00 


25.50 


11.30 


6.37 


4.08 


1 02 


8 


133.25 


33.30 


14.80 


8.32 


5.33 


1.33 


9 


168.60 


42.20 


18.75 


10.50 


6.74 


1.69 


10 


208.19 


52.05 


23.14 


13.01 


8.33 


2.08 


11 


251 .90 


63.00 


28.00 


15.75 


10.08 


2.52 


12 


299.80 


75.00 


33.30 


18.70 


12.00 


3.00 


13 


352.00 


88.00 


39.00 


22.00 


14.08 


3.52 


14 


408.00 


102.00 


45.30 


25.50 


16.32 


4.08 


15 


468.00 


117.00 


52.00 


29.25 


18.72 


4.68 


16 


533.00 


133.00 


59.00 


33.30 


21.32 


5.33 


17 


600.00 


150.00 


67.00 


37.60 


24.00 


6.00 


18 


675.00 


169.00 


75.00 


42.20 


27.00 


6.75 


19 


750.00 


188.00 


83.50 


47.00 


30.00 


7.50 


20 


833.00 


208.00 


92.60 


52.00 


33.32 


8.33 



Cost of Copper required to deliver One Mechanical Horse-power 
at Motor-shaft with varying Percentages of Loss in Conductors, 
upon the assumption that the potential at motor terminals is 
in Each Case 3000 Volts. 

Motor efficiency, 90%. Cost of copper equals 16 cents per pound. 
Length of conductor per mile of single distance, 11,000 ft. 



Miles. 


10% 


15% 


20% 


25% 


30% 


1 


$0.52 


$0.33 


$0.23 


$0.17 


$0.13 


2 


2.08 


1.31 


0.93 


0.69 


0.54 


3 


4.68 


2.95 


2.08 


1.55 


1.21 


4 


8.32 


5.25 


3.70 


2.77 


2.15 


5 


13.00 


8.20 


5.78 


4.33 


3.37 


6 


18.70 


11.75 


8.32 


6.23 


4.85 


7 


25.50 


16.00 


11.30 


8.45 


6.60 


8 


33.30 


21.00 


14.80 


11.00 


8.60 


9 


42.20 


26.60 


18.75 


14.00 


10.90 


10 


52.05 


32.78 


23.14 


17.31 


13.50 


11 


63.00 


39.75 


28.00 


21.00 


16.30 


12 


75.00 


47.20 


33.30 


24.90 


19.40 


13 


88.00 


55.30 


39.00 


29.20 


22.80 


14 


102.00 


64.20 


45.30 


33.90 


26.40 


15 


117.00 


73.75 


52.00 


38.90 


30.30 


16 


133.00 


83.80 


59.00 


44.30 


34.50 


17 


150.00 


94.75 


67.00 


50.00 


39.00 


18 


169.00 


106.00 


75.00 


56.20 


43.80 


19 


188.00 


118.00 


83.50 


62.50 


48.70 


20 


208.00 


131.00 


92.60 


69.25 


54.00 



1366 ELECTRICAL ENGINEERING. 



ELECTRIC RAILWAYS. 

Space will not admit of a proper treatment of this subject in this work. 
Consult Crosby and Bell, The Electric Railway in Theory and Practice; 
Fairchild, Street Railways; Merrill, Reference Book of Tables and Formulae 
for Street Railway Engineers; Bell, Electric Transmission of Power; 
Dawson, Engineering and Electric Traction Pocket-book; The Standard 
Handbook for Electrical Engineers; and Foster's Electrical Engineers' 
Pocket-book. The last named devotes 240 pages to the subject of electric 
railways. 

Electric Railway Cars and Motors. (Foster.) — Small cars weighing 
10 to 12 tons may be fitted with two 35-H.P. motors and be geared for a 
maximum speed of 25 to 30 miles per hour. Larger cars of the single- 
truck variety weighing close to 15 tons may be equipped with 40-H.P. 
motors. Suburban cars weighing 18 to 25 tons and measuring 45 ft. over 
all may be equipped with four 50-H.P. motors and be geared for a maxi- 
mum speed of 40 m.p.h. Larger types of suburban cars, 50 ft. over all, 
seating 52 passengers, weigh 28 to 30 tons and are equipped with four 
75-H.P. motors geared for a maximum speed of 45 m.p.h. The largest 
type of suburban car is equipped with four 125-H.P. motors, and is geared 
for a maximum speed of 60 m.p.h. 

Grades upon city lines may run as high as 13 per cent, and to surmount 
these it is necessary to have every axle on the car equipped with motors; 
thus single-truck cars require two, and double-truck cars four motors; 
and even then the cars will be unable to surmount these grades with very 
bad conditions of track. The motor capacity per car should be liberal, 
not so much from the danger of overheating the motors as to prevent 
undue sparking when surmounting the heavy grades. 

A 4000-H.P. Electric Locomotive, built by the Westinghouse El. 
& Mfg. Co., for the New York terminal and tunnel of the Penna. R.R., is 
described in Eng'g News, Nov. 11, 1909. 

In wheel arrangement, weight distribution, and general character of 
the running gear it is the practical equivalent of two American-type steam 
locomotives coupled back to back. The motors are mounted upon the 
frame and are side-connected through jack shafts to driving wheels by a 
system of cranks and parallel connecting rods. The connecting rods are 
all rotating links between rotating elements, and thus can be perfectly 
counterbalanced for all speeds. The center of gravity is approximately 
72 ins. above the rails. 

In these electric locomotives the variable pressure of the unbalanced 
piston of the steam locomotive is replaced by the more constant torque 
and more constant rotating effort of the drive wheels, so that the pull 
upon the drawbar is thereby constant and uniform. The engine will 
start a train of 550 tons trailing load upon grades of approximately 2%. 
A tractive effort of 60,000 lbs., and a normal speed of 60 miles per hour, 
with full train load on a level track, are guaranteed. 

The total weight of the locomotive is 332,100 lbs., of which 208,000 lbs. 
is on the eight drivers. The locomotive is claimed to develop 4000 H.P. 
for short times, say 20 minutes, without abnormal temperature rise. Each 
half of the locomotive carries a single motor, four 68-in. drive wheels and 
one four-wheel, swing-bolster, swivel truck, with 36-in. wheels. Each 
section has its own steel cab, the two cabs being connected by a vestibule. 

The rigid wheel-bases are 7 ft. 2 in. and the total wheel-base of each 
half is 23 ft. The motive power consists of two motors of a 600-volt, 
2000-H.P., commutating-pole type. Each motor weighs complete with- 
out its crank, 42,000 lbs. The main-field winding is in two sections, both 
of which are used together at low-speed operation. At high speeds only 
one-half is needed, and at intermediate control points one is shunted with 
resistance. These field positions are available for all series and parallel 
groupings of the motors, so that eight running positions (or speeds) are 
possible. Bridging connections are used in passing from series to parallel 
groupings of the motors, so that the main circuits are not opened in the 
process. 



ELECTRIC LIGHTING — ILLUMINATION. 1367 



ELECTRIC LIGHTING. — ILLUMINATION. 

Illumination. — Some writers distinguish "lighting" and "illumina- 
tion." Lighting refers to the character of the lights themselves, as 
dazzling, brilliant, or soft and pleasing, and illumination to the quantity 
of light reflected from objects, by which they are rendered visible. If 
the objects in a room are clearly seen, then the room is well illuminated. 

The quantity of light is estimated in candle-power per square foot of 
area or per cubic foot of space. The amount of illumination given by 
one candle at a distance of 1 ft. is known as a candle-foot. Since the 
illumination varies inversely as the square of the distance, one candle- 
foot is given by a 16-candle-power lamp at a distance of 4 ft., or by a 
25-c-p. lamp at a distance of 5 ft. 

Terms, Units, Definitions. — Quantity of light proceeding from a source 
of light, measured in units of luminous flux, cr lumens. 

Intensity with which the flux is emitted from a radiant in a single 
direction, called candle-power. 

Illumination, density of the light flux incident upon an area. 

Luminosity, brightness of surface; flux emitted per unit area of surface. 

Candle-power, the unit of luminous intensity. A spermaceti candle 
burning at the rate of 120 grains per hour is the old standard used in the 
gas industry. It is very unsatisfactory as a standard and is being dis- 
placed by others. 

The hefner lamp, burning amyl acetate, is the legal standard in Ger- 
many. The unit of luminous intensity produced by this lamp when con- 
structed and operated as prescribed is called a hefner. The standard 
laboratories of Great Britain, France and America have agreed upon 
the following relative values of the units used in the several countries: 
1 International Candle = 1 Pentane Candle =1 Bougie Decimale=l Ameri- 
can Candle = 1.11 Hefners = 0.1 04 Carcel unit. 1 Hefner = 0.90 Inter- 
national Candle. 

Intrinsic Brilliancy of a source of light = candle-power per square inch 
of surface exposed in a given direction. 

Lumen, the unit of luminous flux, is the quantity of light included in 
a unit solid angle and radiated from a source of unit intensity. A unit 
solid angle is the angular space subtended at the surface of a sphere by 
an area equal to the square of the radius, or by 1 -4-4*, or 1/12.5664 of the 
surface of the sphere. The light of a source whose average intensity in 
all directions is 1 candle-power, or one mean spherical candle-power, has 
a total flux of 12.5664 lumens. 

Foot-candle, the unit of illumination, = 1 lumen per square foot; the 
illumination received by a surface every point of which is distant one 
foot from a source of one candle-power. 

Lux, or meter-candle, 1 lumen per square meter; 1 foot-candle = 10.76 
meter-candles. 

Law of Inverse Squares. — The illumination of any surface is inversely 
proportional to the square of its distance from the source of light. This 
is strictly true when the source of light is a point, and is very nearly true 
in all cases when the distance is more than ten times the greatest dimen- 
sion of the light-giving surface. 

Law of Cosines. When a surface is illuminated by a beam of light 
striking it at an angle other than a right angle, the illumination is pro- 
portional to the cosine of the angle the beam makes with a normal to 

If E = the illumination at any point in a surface, / the intensity of light 
coming from a source, 9 the angle of deviation of the direction of the 
beam from a normal to the surface, and I the distance from the source, 
then E = I cos h- V*. 

Relative Color Values of Various Illuminants. — The light pro- 
ceeding from any source may be analyzed in terms of the elementary 
color elements, red, green and blue, by means of the spectroscope or by 
a colorimeter. The following relative values have been obtained by the 
Ives colorimeter {Trans. III., Eng. Soc. iii, 631). In all cases the red 
rays in the light are taken as 100, and the two figures given are respec- 
tively the proportions of green and blue relative to 100 red. 

Average daylight, 100,100. Blue sky, 106,120. Overcast sky, 92,85. 
Afternoon sunlight, 91, 56. Direct-current carbon arc, 64, 39. Mercury 



1368 



ELECTRICAL ENGINEERING. 



arc (red 100), 130, 190. Moore carbon dioxide tube, 120, 520. Wels- 
bach mantle, 3/ 4 % cerium, 81, 28. Do., 1 1/4% cerium, 69, 14.5. Do., 1 3/ 4 % 
cerium, 63, 12.3. Tungsten lamp, 1.25 watts per mean horizontal candle- 
power, 55, 12.1. Nernst glower, bare, 51.5, 11.3. Tantalum lamp, 2 
watts per m. h. c.-p., 49, 8.3. Gem lamp, 2.5 watts per m. h. c.-p., 48, 8.3. 
Carbon incandescent lamp, 3.1 watts per m.h.c.-p., 45, 7.4. Flaming 
arc, 36.5, 9. Gas flame, open fish-tail burner, 40, 5.8. Moore nitrogen 
tube, 28, 6.6. Hefner lamp, 35, 3.8. 

Relation of Illumination to Vision. — Wickenden gives the follow- 
ing summary of the principles of effective vision: 

1. The eye works with approximately normal efficiency upon surfaces 
possessing an effective luminosity of one lumen per square foot or more. 

2. Excessive illumination and inadequate illumination strain and 
fatigue the eye in an effort to secure sharp perception. 

3. Intrinsic brilliancy of more than 5 c.-p. per sq. in. should be reduced 
by a diffusing medium when the rays enter the eye at an angle below 60° 
with the horizontal. 

4. Flickering, unsteady, and streaky illumination strains the retina 
in the effort to maintain uniform vision. 

5. True color values are obtained only from light possessing all the 
elements of diffused daylight in approximately equivalent proportions. 

6. An excess of ultra-violet rays is to be avoided for hygienic reasons. 

7. ^Esthetic considerations commend light of a faint reddish tint as 
warm and cheerful in comparison with the cold effects of the green tints, 
although the latter are more effective in revealing fine detail. 

Arc Lamps are divided into three classes: 1. Those which produce 
light by the incandescence of intensely hot refractory electrodes. 2. 
Those which produce light mainly from the luminescence in the arc of 
mineral salts vaporized from carbon electrodes. 3. Those which produce 
light by the luminescence of metallic vapor derived solely from the cathode, 
the anode being unconsumed. 

The Carbon Arc. — In direct-current open arcs the anodes are consumed 
at the rate of 1 to 2 inches per hour, and the cathodes, or negatives, at 
half this rate. In alternating-current open arcs the consumption is equal 
in both carbons, 1 to 1.5 inches per hour. Enclosed arcs have longer life 
owing to the restricted oxidation of the carbons, but they are of reduced 
brilliancy and lower efficiency. Carbons of the ordinary sizes burn Vie 
to 1/8 in. per hour, giving a life of 100 to 150 hours for direct-current and 
80 to 100 hours for alternating-current lamps. The enclosing globes 
absorb from 8 to 40% of the light. 

The Flaming Arc. — The carbons are impregnated with calcium fluoride 
or other luminescent salts. The current is usually 8 to 12 amperes and 
the voltage per lamp 35 to 60. The regenerative flame arc is a highly 
efficient variety of the flame arc. 

The Magnetite Arc has for a cathode a thin iron tube packed with a 
mixture of magnetite, Fe 3 4 , and titanium and chromium oxides. The 
anode consists of copper or brass. It is well adapted to series operation 
with low currents. The 4-ampere lamp, using 80 volts per lamp, is highly 
successful for street illumination. 

Illumination by Arc Lamps at Different Distances. — Several 
diagrams and curves showing the light distribution in a vertical plane 
and the illumination at different distances of different types of lamps are 
given by Wickenden. From the latter are taken the approximate figures 
in the table below. The carbon and the magnetite lamps were 25 ft. high, 
the flame arcs 21 ft. 



Horizontal Distance from Lamp, Feet. 


20 1 30 1 40 I 50 | 100 1 150 1 200 1 250 


Kind of Lamp. 


Foot-candles, normal illumi- 
nation. 


A. Open carbon arc, D.C., 6.6 amps. 

B. Enclosed carbon arc, A.C. 6.6 " 


0J0 


0.40 
.19 


0.29 
.135 


0.20 
.10 

1. 10 
.65 
.51 
.21 


.032 

.027 

.31 

.15 

.15 

.07 


.014 
.013 
.14 
.055 
.075 
.035 


.006 
.006 
.08 
.03 
.045 
.022 


.002 
.002 
05 








.85 
.69 
.30 


n? 


E. Magnetite arc, 6.6 " 

F. Magnetite arc, 4. " 


".Al 


1.00 
.40 


.025 
.018 



ELECTRIC LIGHTING — ILLUMINATION. 



13G9 



A. 6.6 amp., D. C, open arc, clear globe. 

B. 6.6 amp., A. C, enclosed arc, opal inner and clear outer globe, 
small reflector. 

C. 10 amp., flame arc, vertical electrodes ; 50 volts, 1520M.H.C.-P.;* 0.33 
watt per M.L.H.C.-P.;* 10 hours per trim. 

D. 7 amp regenerative flame arc, 70 volts, 2440 M.L.H.C.-P., 0.2 watt 
per M.L.H.C.-P., 70 hours per trim. 

E.G. 6 amp., D.C.series magnetite arc, 79 volts, 510 watts, 1450 M.L.H.C.-P. 
75 to 100 hours per trim. 

F. 4 amp., D.C. series magnetite arc, 80 volts, 320 watts, 575 M.L.H.C.-P., 
150 to 200 hours per trim. 

Data of Some Arc Lamps. 



Type of Lamp. 



D.C. series carbon, open 

D.C. series carbon, enclosed. 

A.C. series carbon, enclosed. 

D.C. multiple carbon, en- 
closed 

A.C. multiple carbon, en- 
closed 

D.C. flame arcs, open 

Regenerative, semi-enclosed 

A.C. flame arcs, open 

Magnetite, open 



Hours 

per 
Trim. 


Am- 
peres. 


Ter- 
minal 
Volts. 


Ter- 
minal 
Watts. 


9 to 12 
100 to 150 
70 to 100 


9.6 
6.6 
7.5 


50 
72 
75 


480 
475 
480 


100 to 150 


5.0 


110 


550 


70 to 100 
10 to 16 

70 
10 to 16 
70 to 100 


6.0 
10 

5 
10 

6.6 


110 
55 
70 
55 
80 


430 
440 
350 

467 
528 



2.25 

2.40 
0.45 
0.26 
0.55 
0.45 



Values of watts per m.l.h. c.-p. approximate for open carbon arcs and 
magnetite arcs with clear globes, enclosed arcs with opalescent inner and 
clear outer globes, and for flame and regenerative arcs with opal globes. 

Watts per Square Foot Required for Arc Lighting. — W. D'A. 

Ryan {Am. Elect' n, Feb., 1903) gives the following table, deduced from 
experience, showing the amount of energy required for good illumination 
by means of enclosed arcs, based on watts at lamp terminals. 



Building. 



Machine-shops; high roofs, electrically driven machinery, no 

belts 

Machine-shops; low roofs, belts and other obstructions 

Hardware and shoe stores 

Department stores; light material, bric-a-brac, etc 

Department stores ; colored material 

Mill lighting; plain white goods 

Mill lighting; colored goods, high looms 

General office; no incandescents 

Drafting rooms 



Watts per 
sq. ft. 



0.5 to 1 
0.75 to 1.25 
0.5 to 1 
0.75 to 1.25 
1 to 1.5 
0.9 to 1.3 
1.1 to 1.5 
1.25 to 1.75 
1.5 to 2 



The space in sq. yds. properly illuminated by 450-watt enclosed arc 
lamps is given as follows in the Int. Library of Technology, vol. 13: Out- 
door areas, 2000-2500 sq. yds.; trainsheds, 1400-1600; foundries (general 
illumination), 600-800; machine-shops, 200-250; thread and cloth mills, 
200-230. 

The Mercury Vapor Lamp, invented by Peter Cooper Hewitt, is an 
arc of luminous mercury vapor contained in a glass tube from which the 
air has been exhausted. A small quantity of mercury is contained in the 
tube, and platinum wires are inserted in each end. When the tube is 
placed in a horizontal position, so that a thin thread of mercury lies along 
it, making electric connection with the wires, and a current is passed 
through it, part of the mercury is vaporized, and on the tube being in- 
clined so that the liquid mercury remains at one end, an electric arc is 

* M. H. C.-P. = mean horizontal candle-power; M.L.H.C.-P. =mean lower 
hemispherical candle-power, 



1370 



ELECTRICAL ENGINEERING. 



formed in the vapor throughout the tube. The tubes are made about 
1 in. in diameter and of different lengths, as below. The mercury vapor 
lamp is very efficient, but the color of the light is unsatisfactory, being 
deficient in red rays. The spectrum consists of three bands, of yellow, 
green and violet, respectively. The intrinsic brilliancy of the lamp is 
very moderate, about 17 candle-power per square inch. Commercial 
lamps are made of the sizes given below. The lamp is essentially a direct- 
current lamp, but it may be adapted to alternating-current by use of the 
principle of the mercury arc rectifier. The tubes have a life ordinarily 
of about 1000 hours. 

Mercury Arc Lamps. 



Type. 


Kind of 
Circuit. 


Length, 
inches. 


Volts. 


Am- 
peres. 


Watts. 


Hemi- 
spher. 
Candle- 
power. 


Watts 

per 
Candle 


H 
K 
U 
P 
F 


d.c. 
d.c. 
d.c. 
d.c. 
a.c. 


203/4 

45 

78 

50 

50 


52-55 
100-120 
206-240 
100-120 
100-120 


3.5 
3.5 
2.0 
3.5 


177-193 
350-420 
412-480 
350-420 
400-520 


300 
700 
900 
800 
750-900 


0.64 
0.55 
0.48 
0.48 
0.53-0.58 









Incandescent Lamps. — Candle-power of nominal 16-c.p. 110-volt 
carbon lamp: 

Mean horizontal 15.7 to 16.6, mean spherical 12.7 to 13.8, mean hemi- 
spherical 14.0 to 14.6, mean within 30° from tip 7.9 to 10.9. 

Ordinary carbon lamps take from 3 to 4 watts per candle-power. A 16- 
candle-power lamp using 3.5 watts per candle-power or 56 watts at 110 
volts takes a current of 56-^110 = 0.51 ampere. For a given efficiency 
or watts per candle-power the current and the power increase directly as 
the candle-power. An ordinary lamp taking 56 watts, 13 lamps take 1 
H.P. of electrical energy, or 18 lamps 1.008 kilowatts. 

Rating of Incandescent Lamps. — Lamps are commonly rated in 
terms of their mean horizontal candle-power, and their energy consump- 
tion in terms of watts per mean horizontal candle-power. The mean 
spherical intensity differs from the horizontal intensity by a factor which 
varies with different kinds and styles of lamp. In carbon lamps it is 
usually about 82%, and in tantalum and tungsten lamps about 76 to 78% 
of the mean horizontal candle-power. 

The new lamp ratings (May, 1910) of the National Electric Lamp 
Association^ designate all lamps by wattage instead of by candle-power 
as formerly. 

Lamps are labeled with a three-voltage label and the regular type of 
16 c.-p. carbon lamp, in general use, will be made on the basis of 3.1 watts 
per c.-p. at top voltage. 

Carbon Lamps. 



Nom- 
inal 
Watts. 


Actual 

Watts. 


Actual 
Watts 

per 
Candle. 


Actual 
Candle- 
power. 


3<2 

a3 


Nom- 
inal 
Watts 


Actual 
Watts. 


Actual 
Watts 

per 
Candle. 


Actual 
Candle- 
power. 


3 '* 


10 




10 


5.00 


2.0 


2000 


( 


T. 60.0 


2.97 


20.2 


700 


20 




20 


4.15 


4.8 


2000 


60 1 


M. 57.9 


3.18 


18.3 


1000 


( 


T 


25 


3.10 


8.1 


500 


1 


B. 55.7 


3.39 


16.4 


1500 


25 


M. 


24.1 


3.31 


7.3 


725 


( 


T. 100.0 


2.97 


33.6 


600 


( 


R 


?3 2 


3.52 


6.6 


1050 


100 \ 


M. 96.4 


3.18 


30.5 


850 


( 


T 


30 


3.23 


9.3 


1050 


1 


B. 92.9 


3.39 


27.4 


1350 


30 




28 9 


3.46 


8.4 


1500 


( 


T. 120.0 


2.97 


40.4 


600 


( 


R 


7.7 8 


3.69 


7.5 


2100 


120 \ 


M. 115.8 


3.18 


36.6 


850 


( 


T 


50 


2.97 


16.8 


700 


) 


B. 111.4 


3.39 


32.8 


1350 


5 o{ 


M. 
B. 


48.2 
46.4 


3.18 
3.39 


15.2 
13.7 


1000 
1500 













T, top; M, middle; B, bottom voltage. 



ELECTRIC LIGHTING — ILLUMINATION. 



13T1 



The 50- and 60-watt sizes correspond respectively to the old 16-c -p., 3.1- 
watt lamp (at top voltage) and the old 16-c-p., 3.5-watt lamp (at bottom 
voltage). 

The hours life of all of the listed carbon lamps shows the total life and 
not the useful life or that formerly given as to 80% of initial c.-p. 

The Gem Lamp is an improved type of the carbon lamp, having a carbon 
filament heated to such a degree in an electric oven that it takes on the 
properties of metal and hence the name, Gem " Metalized Filament." 

Variation in Candle-Power, Efficiency, and Life. — The follow- 
ing table shows the variation in candle-power, etc., of standard 100 to 
125 volt, 3.1 and 3.5 watt carbon lamps, due to variation in voltage sup- 
plied to them. It will be seen that if a 3.1-watt lamp is run at 10% 
below its normal voltage, it may have over 9 times as long a life, but it 
will give only 53% of its normal lighting power, and the light will cost 
50% more in energy per candle-power. If it is run at 6% above its normal 
voltage, it will give 37% more light, will take nearly 20% less energy for 
equal light power, but it will have less than one-third of its normal life. 



Per cent 


Per cent of 
Normal 
Candle- 
power. 


Watts per 


Relative 


Watts per 


Relative 


Normal 


Candle, 3.1 


Life, 3.1 


Candle, 


Life, 


Voltage. 


watt Lamp. 


watt 


3.5 watts. 


3.5 watts. 


90 


53 
61 
69.5 


4.65 
4.24 
3.90 


9.41 

5.55 
3.45 


5.36 
4.85 
4.44 




92 




94 


'"im" 


96 


79 


3.60 


2.20 


4.09 


2.47 


98 


89 


3.34 


1.46 


3.78 


1.53 


99 


94.5 


3.22 


1.21 


3.64 


1.26 


100 


100 


3.10 


1.00 


3.50 


1.00 


101 


106 


2.99 


.818 


3.38 


.84 


102 


112 


2.90 


.681 


3.27 


.68 


104 


124 


2.70 


.452 


3.05 


.47 


106 


137 


2.54 


.310 


2.85 


.31 



The candle-power of a lamp falls off with its length of life, so that during 
the latter half of its life it has only 60 per cent or 70 per cent of its rate 
candle-power, and the watts per candle-power are increased 60 per cent or 
70 per cent. After a lamp has burned for 500 or 600 hours it is more eco- 
nomical to break it and supply a new one if the price of electrical energy 
is that usually charged by central stations. 

Incandescent Lamp Characteristics. — From a series of curves given 
in Wickenden's " Illumination and Photometry " the following approxi- 
mate figures have been derived : 



LIFE, CANDLE-POWER AND WATTS PER CANDLE-POWER. 



Hours 





50 


100 


Lamps 
Carbon 
Tantalum 
Tungsten 


100 
100 
100 


102 
144 
104 


96 
119 
110 


Carbon 

Tantalum 

Tungsten 


100 
100 
100 


99 
80 
97 


98 
90 
96 



200 300 400 500 600 
Per cent of candle-power. 

95 91 88 86 83 81 

100 97 95 93 90 88 
112 110 104 100 98 95 

Per cent Watts per candle. 

103 107 109 111 112 115 

101 104 106 107 109 109 
97 100 102 103 107 108 



700 800 900 



84 80 

92 90 

119 

110 112 

11Q 111 



RELATION OP CANDLE-POWER TO TERMINAL VOLTS. 

Per cent normal volts 84 88 92 ' 96 100 104 108 112 

Per cent normal candle-power. 
Carbon .. 46 60 78 100 123 154 

Tantalum 46 56 68 82 100 118 139 161 

Tungsten 54 63 73 86 100 115 134 158 

The above figures show the necessity of close regulation of voltage of 
lighting circuits. Slight reductions of voltage cause the light to fall far 
below normal, while excess voltage greatly diminishes the life of the lamps. 



1372 



ELECTRICAL ENGINEERING 



RELATION OF ENERGY CONSUMPTION TO TERMINAL VOLTS. 



Per cent normal volts 92 94 96 98 100 102 


104 


106 


108 


Per cent normal watts per candle-power. 








Carbon 124 116 108 100 94 
Tantalum 126 118 112 106 100 95. 
Tungsten 120 115 110 105 100 96 


88 
90 
92 


82 
87 
88 


83 
85 



Average Performance of Tantalum and Tungsten Lamps. - 

(Winchenden.) 100 to 125 volts. 





Tantalum. 


Tungsten. 


Rated horizontal c-p 

Mean spherical c-p 

Rated watts per c-p 

Watts per m. spher. c-p.. . 


12.5 
8.9 
2.5 
2.53 

25. 

900* 


20 
15.8 
2.0 

2.53 
40. 
900* 


40 
31.6 

2.0 

2.53 

80 
800f 


20 
15.6 
1.25 
1.60 

25 

800 


32 

24.0 

1.25 

1.62 

35-45 

800 


48 
37.6 
1.25 
1.59 
50-70 
800 


80 

62.9 
1.25 
1.58 

85-115 
800 


200 
152 
1.25 
1.64 
230-270 




800 







*For direct current; 500 hrs. for 60 cycle alt. current. f500 to 700 hrs. 
for alt. current. 

Specifications for Lamps. (Crocker.) — The initial candle-power of 
any lamp at the rated voltage should not be more than 9 per cent above 
or below the value called for. The average candle-power of a lot should 
be within 6 per cent of the rated value. The standard efficiencies (of the 
carbon lamp) are 3.1, 3.5, and 4 watts per candle-power. Each lamp at 
rated voltage should take within 6 per cent of the watts specified, and the 
average for the lot should be within 4 per cent. The useful life of a lamp 
is the time it will burn before falling to a certain candle-power, say 80 
per cent of its initial candle-power. For 3.1 watt lamps the useful life 
is about 400 to 450 hours, for 3.5 watt lamps about 800, and 4 watt lamps 
about 1600 hours. 

Special Lamps. — The ordinary 16 c-p. 110-volt is the old standard 
for interior lighting. Improved forms of incandescent lamp, such as the 
tungsten, are now, 1910, rapidly coming into use, so that no one style of 
lamp can be considered the standard. Thousands of varieties of lamps 
for different voltages and candle-power are made for special purposes, 
from the primary lamp, supplied by primary batteries using three volts 
and about 1 ampere and giving 1/2 c.-p., and the 3/4 c.-p. bicycle lamp, 4 
volts and 0.5 ampere, lamps of 100 c-p. at 220 volts. Series lamps of 
1 c.-p. are used in illuminating signs, 2/3 
ampere and 12.5 to 15 volts, eight lamps 
being used on a 110-volt circuit. Standard 
sizes for different voltages, 50, 110, or 220, 
are 8, 16, 24, 32, 50, and 100 c.-p. 

The Nernst Lamp depends for its oper- 
ation upon the peculiar property of certain 
rare earths, such as yttrium, thorium, zir- 
conium, etc., of becoming electrical con- 
ductors when heated to a certain tem- 
perature; when cold, these oxides are 
non-conductors. The lamp comprises a 
" glower " composed of rare earths mixed 
with a binding material and pressed info a 
small rod; a heater for bringing the glower 
up to the conducting temperature; an auto- 
matic cut-out for disconnecting the heater 
when the glower lights up, and a " ballast " 
consisting of a small resistance coil of wire 
having a positive temperature-resistance co- 
efficient. The ballast is connected in series with the glower; its presence 
is required to compensate the negative temperature-resistance coefficient of 




ELECTRIC LIGHTING — ILLUMINATION. 



the glower; without the ballast, the resistance of the glower would become 
lower and lower as its temperature rose, until the flow of current through 
it would destroy it. Fig. 195 shows the elementary circuits of a simple 
Nernst lamp. The cut-out is an electromagnet connected in series with the 
glower. When current begins to flow through the glower, the magnet 
pulls up the armature lying across the contacts of the cut-out, thereby 
cutting out the heater. Tne heater is a coil of fine wire either located 
very near the glower or encircling it. The glower is from V32 to Vi6 
inch in diameter and about 1 inch long. 

In the original Nernst lamp the glowers were adapted only for alternat- 
ing-current, but direct-current glowers are now made. 

The lamps are made with one glower, or with two, three, or six glowers 
connected in parallel, and for operation on 100 to 120 and 200 to 240 volt 
circuits. A 30-glower lamp for 220 volts, rated at 2000 c.-p., is also made. 

Lamps with one glower are rated at 66 watts (110 volt), 88 (220 v.), 
110 and 132 watts (110 or 220 v.) with a corresponding mean horizontal 
candle-power of 50, 77, 96 and 114, respectively. The 2- 3- and 4-glower 
lamps are multiples of the 132 watt (220 v.) single glower lamps, their 
m.h.c.-p. being respectively 231, 359 and 504. The Nernst lamp is 
commonly used where units of intermediate size between incandescent 
and arc lamps are desired. 

Cost of Electric Lighting. A. A. Wohlauer (El. World, July, 1908.) 
— The following table shows the relative cost of 1000 candle-hours of 
illumination by lamps of different kinds, based on costs of 2, 4 and 10 cents 
per K.W. hour for electric energy. The life, K, is that of the lamp for 
incandescent lamps, of the glower for Nernst lamps, of the electrode for 
arc lamps, and of trie vapor tube for vapor lamps. 

L s = mean spherical candle-power. 
S s = watts per mean spherical candle. 
P = renewal cost per trim or life, cents. 
K = life in hours. 
C r = 1000 P/(KL S ). 

C t = (£ s X R) + C t = cost per 1000 candle hours. 
R = rate in cts. per K.W. hour. 



Amp. Volts. 



Rating. 










Incandescent Lamps. 




R=2 


4 


10 




0.31 
0.45 
2.3 
1.0 
0.36 
0.91 


110 
110 
110 
110 
110 
110 


13.2 
16.5 

82 
42.5 
17 
72 


3.8 
3.05 
3.05 
2.6 
2.3 
1.4 


8 
10 
35 

32.5 
25 
100 


450 
450 
450 
500 
700 
800 


1.35 
1.35 
0.95 
1.5 
2.25 
1.8 


16 c.p. 
20 c.p. 
100 c.p. 
110 Watt 
20 c.p. 
80 c.p. 


10.3 

8.8 

8 

8.2 

9.1 

6.4 


17.9 
14.8 
14.1 
13.4 
13.7 
9.2 


40.7 




33.2 




37, 4 




29 




77 5 


Tungsten 


17.6 



Direct-Current Arc Lamps. 



Open arc 

Enclosed 

Carbon 

Miniature 

Magnetite 

Flaming 

Blondel 

Inclined flaming. . 

Inclined enclosed 

flaming 



10 


55 


400 


1.3 


4 


10 


1 


10 amp. 


4 6 


7.2 


5.0 


110 


760 


2 1 


4 5 


150 


0.1 


5 


4 4 


8.6 


10 


110 


550 


2 


4 


16 


0.5 


10 


5 


9 


2.5 


110 


150 


1 8 


3 


20 


1. 


2.5 


5 6 


9 ?. 


3.5 


110 


7.25 


1 7 


5 


150 


0.155 


3.5 


3 71 


7 11 


10 


55 


600 


75 


8 5 


10 


1 2 


10 


3 9 


5 4 


5 


55 


550 


5 


17.5 


18 


1.25 


5 


3 5 


4.5 


10 


55 


1100 


0.5 


9 


10 


0.8 


10 


2.6 


3.6 


5.5 


100 


1500 


0.365 


15 


70 


1.55 


5.5 


1.03 


1.76 



15 

21.2 

21 

20 

17.2 
9.9 
7.5 
6.6 



1374 



ELECTRICAL ENGINEERING. 



Illuminant. 



Amp, Volts. 



P K C r Rating. 



Ct = (S g X R) 

+ C r 



Alternating-Current Arc Lamps. 





15 
7.5 
10 
10 
10 




300 
230 
425 
1000 
715 


1.75 
2.6 
0.8 
0.55 
0.5 


5 

4.5 

8.5 

9 

12.5 


13 

100 
7 
10 
15 


1.1 

0.2 

2.8 

0.65 

1.15 


15 amp. 
7.5 
10 
10 
10 


5.7 
5.6 
7.2 
2.9 
3.3 


9.2 
10.8 
8.8 
4 
4.3 


19.7 




26.4 


Flaming 

Inclined flaming. . 
Blondel 


13.6 
7.3 
37. 



Mercury-Vapor Lamps. 



Cooper Hewitt I 3.5 | 

Quartz 1 4.0 I 



110 I 7701 0.5 I 600 1400010.2 13.5 amp. 1 1.4 I 2.4 I 5.4 
220 I2740| 0.33| 350 |l000|0. 125|4.2 0.85 1.45 3.25 



ELECTRIC WELDING. 

The apparatus most generally used consists of an alternating-current 
dynamo, feeding a comparatively high-potential current to the primary 
coil of an induction-coil or transformer, the secondary of which is made so 
large in section and so short in length as to supply to the work currents 
not exceeding two or three volts, and of very large volume or rate of flow. 
The welding clamps are attached to the secondary terminals. Other 
forms of apparatus, such as dynamos constructed to yield alternating 
currents direct from the armature to the welding-clamps, are used. 

The conductivity for heat of the metal to be welded has a decided influ- 
ence on the heating, and in welding iron its comparatively low heat conduc- 
tion assists the work materially. (See papers by Sir F. Bramwell, Proc. 
Inst. C. E., part iv., vol. cii. p. 1; and Elihu Thomson, Trans. A. I. M. E., 
xix. 877.) 

Fred. P. Royce, Iron Age, Nov. 28, 1892, gives the following figures 
showing the amount of power required to weld axles and tires: 

AXLE- WELDING. 

Seconds 

1-inch round axle requires 25 H.P. for 45 

1-inch square axle requires 30 H.P. for. 48 

1 1/4-inch round axle requires 35 H.P. for ". . . . 60 

ll/4-inch square axle requires 40 H.P. for 70 

2-inch round axle requires 75 H.P. for 95 

2-inch square axle requires 90 H.P. for 100 

The slightly increased time and power required for welding the square 
axle is not only due to the extra metal in it, but in part to the care which 
it is best to use to secure a perfect alignment. 

TIRE- WELDING. 

Seconds. 

1 X 3/i6-inch tire requires 11 H.P. for 15 

1V4 X3/g-inch tire requires 23 H.P. for.. , 25 

IV2 X3/g-inch tire requires 20 H.P. for 30 

IV2 XV2-inch tire requires 23 H.P. for 40 

2 X 1/2-inch tire requires 29 H.P. for 55 

2 X3/4-inch tire requires 42 H.P. for 62 



The time above given for welding is of course that required for the actual 
application of the current only, and does not include that consumed by 
placing the axles or tires in the machine, the removal of the upset and 
other finishing processes. From the data thus submitted, the cost of 
welding can be readily figured for any locality where the price of fuel and 
cost of labor are known. 



ELECTRIC HEATERS. 1375 



In almost all cases the cost of the fuel used under the boilers for produc- 
ing power for electric welding is practically the same as the cost of fuel 
used in forges for the same amount of work, taking into consideration the 
difference in price of fuel used in either case. 

Prof. A. B. Kennedy found that 21/2-inch iron tubes 1/4-inch thick were 
welded in 61 seconds, the net horse-power required at this speed being 23.4 
(say 33 indicated horse-power) per square inch of section. Brass tubing 
required 21.2 net horse-power. About 60 total indicated horse-power 
would be required for the welding of angle-irons 3 X3 XV2-inch in from two 
to three minutes. Copper requires about 80 horse-power per square inch 
of section, and an inch bar can be welded in 25 seconds. It takes about 
90 seconds to weld a steel bar 2 inches in diameter. 



ELECTRIC HEATERS. 

Wherever a comparatively small amount of heat is desired to be auto- 
matically and uniformly maintained, and started or stopped on the instant 
without waste, there is the province of the electric heater. 

The elementary form of heater is some form of resistance, such as coils 
of thin wire introduced into an electric circuit and surrounded with a sub- 
stance which will permit the conduction and radiation of heat, and at the 
same time serve to electrically insulate the resistance. 

This resistance should be proportional to the electro-motive force of the 
current used and to the equation of Joule's law: 

H = PRtX 0.24, 

where I is the current in amperes; R, the resistance in ohms; t, the time in 
seconds; and H, the heat in gram-centigrade units. 

Since the resistance of metals increases as their temperature increases, a 
thin wire heated by current passing through it will resist more, and grow 
hotter and hotter until its rate of loss of heat by conduction and radiation 
equals the rate at which heat is supplied by the current. In a short wire, 
before heat enough can be dispelled for commercial purposes, fusion will 
begin; and in electric heaters it is necessary to use either long lengths of 
thin wire, or carbon, which alone of all conductors resists fusion. In the 
majority of heaters, coils of thin wire are used, separately embedded in 
some substance of poor electrical but good thermal conductivity. 

The Consolidated Car-heating Co.'s electric heater consists of a galvan- 
ized iron wire wound in a spiral groove upon a porcelain insulator. Each 
heater is 305/g in. long, 87/g in. high, and 65/s in. wide. Upon it is wound 
392 ft. of wire. The weight of the whole is 231/2 lbs. 

Each heater is designed to absorb 1000 watts of a 500-volt current. Six 
heaters are the complement for an ordinary electric car. For ordinary 
weather the heaters may be combined by the switch in different ways, so' 
that five different intensities of heating-surface are possible, besides the 
position in which no heat is generated, the current being turned off. 

For heating an ordinary electric car the Consolidated Co. states that 
from 2 to 12 amperes on a 500-volt circuit is sufficient. With the outside 
temperature at 20° to 30°, about 6 amperes will suffice. With zero or 
lower temperature, the full 12 amperes is required to heat a car effectively. 

Compare these figures with the experience in steam-heating of railway- 
cars, as follows: 

1 B. T. U. = 0.29084 watt-hours. 

6 amperes on a 500-volt circuit = 3000 watts. 

A current consumption of 6 amperes will generate 3000 *■ 0.29084 = 
10,315 B.T.U. per hour. 

In steam-car heating, a passenger coach usually requires from 60 lbs. of 
steam in freezing weather to 100 lbs. in zero weather per hour. Supposing 
the steam to enter the pipes at 20 lbs. pressure, and to be discharged at 
200° F., each pound of steam will give up 983 B.T.U. to the car, Then 



1376 ELECTRICAL ENGINEERING. 

the equivalent of the thermal units delivered by the electrical-heating 
system in pounds of steam, is 10,315 -*■ 983 = 10'V2, nearly. 

Thus the Consolidated Co.'s estimates for electric-heating provide the 
equivalent of IOV2 lbs. of steam per car per hour in freezing weather and 
21 lbs. in zero weather. 

Suppose that by the use of good coal, careful firing, well-designed boilers 
and triple-expansion engines we are able in daily practice to generate 
1 H.P. delivered at the fly-wheel with an expenditure of 21/2 lbs. of coal per 
hour. 

We have then to convert this energy into electricity, transmit it by wire 
to the heater, and convert it into heat by passing it through a resistance- 
coil. We may set the combined efficiency of the dynamo and line circuit 
at 85%, and will suppose that all the electricity is converted into heat in 
the resistance-coils of the radiator. Then 1 brake H.P. at the engine = 
0.85 electrical H.P. at the resistance coil = 1,683,000 ft.-lbs. energy per 
hour =2180 heat-units. But since it required 2V2 lbs. of coal to develop 
1 brake H.P., it follows that the heat given out at the radiator per pound 
of coal burned in the boiler furnace will be 2 180 -e- 2 1/2 = 872 H.U. An 
ordinary steam-heating system utilizes 9652 H.U. per lb. of coal for heat- 
ing; hence the efficiency of the electric system is to the efficiency of the 
steam-heating system as 872 to 9652, o>r about 1 to 11. (Eng'g News, 
Aug. 9, '90; Mar. 30, '92; May 15, '93.) 

Electric Furnaces. (Condensed from an article by J. Wright in 
Elec. Age, May, 1904. The original contains illustrations of many styles 
of furnace.) — Electric furnaces may be divided into two main classes, 
(1) those in which the heating effect is produced by the electric arc estab- 
lished between two carbon or other electrodes connected with the source 
of current, commonly known as arc furnaces; and (2) those in which the 
heating effect is produced by the passage of the current through a resist- 
ance, which either forms part of the furnace proper, or is constituted, 
by a suitable conducting train, of the material to be treated in the furnace. 
Such furnaces are known as resistance furnaces. 

The Moissan arc furnace consists of two chalk blocks, bored out to 
receive a carbon crucible which encloses the center or hearth of the furnace 
proper. Into this cavity pass two massive carbon electrodes, through 
openings provided for them in the walls of the structure, which is held 
together by clamps. The arc established between the ends of the carbons 
when the current is turned on plays over the center of the crucible, heat- 
ing its contents. 

In the Siemens arc furnace a refractory crucible of plumbago, magnesia, 
lime, or other suitable material is supported at the center of a cylinder 
or jacket, and packed around with broken charcoal, or other poor con- 
ductor of heat. The negative electrode consists of a massive carbon rod 
passing vertically through the lid of the crucible, and free to move 
vertically therein. The positive electrode, which may be of iron, plati- 
num or carbon, consists of a rod passing up through the base of the crucible. 
The furnace was originally designed for the fusion of refractory metals 
and their ores. Electrical contact is established between the lower 
electrode and the semi-metallic mass in the crucible, and the arc continues 
to play between the surface of the mass and the movable carbon rod. 
As the current through the furnace increases, that through the shunt 
winding of a solenoid which controls the position of the movable rod 
diminishes, thereby raising the negative electrode and restoring equilib- 
rium. 

The Willson furnace is a modification of the Siemens, the solenoid 
regulation of the upper movable carbon being replaced by a worm and 
hand wheel, while the furnace is made continuous in operation by the 
provision of a tapping hole for drawing off the molten products. This 
type of furnace was employed by Willson in the manufacture of calcium 
carbide; many other types of arc furnaces have been developed from 
these earlier forms. (See El. Age, May, 1904, for illustrations.) 

The Borchers furnace is typical of that class in which a core, forming 
part of the furnace itself, is heated by the passage of the current through 
it, and imparts its heat to the surrounding mass of material contained in 
the furnace. It consists of a block of refractory material, im the center of 
which is an opening forming the crueible, into which is fed the material to 



PRIMARY BATTERIES. 



1377 



be treated. This space is bridged by a thin carbon rod which is attached, 
at its extremities, to two carbon electrodes, passing through the walls of 
the furnace. The current heats the smaller rod to a very high tempera- 
ture, and the rod diffuses its heat throughout the mass, from its center 
outwards. 

H. I. Irvine has brought out a resistance furnace in which the heated 
column consists of a fused electrolyte, maintained in a state of fusion by 
the passage of the current, and communicating its heat by radiation and 
diffusion, to the encircling charge, which is packed around it. 

A novel type of resistance furnace, patented independently, with some 
slight variation of detail, by Colby, Ferranti, and Kjellin, is worked on 
the inductive principle, and consists of an annular, or helical, channel in 
a refractory base, filled with a conducting, or semi-conducting, medium, 
which constitutes the furnace charge, and has a heavy current induced 
in it by a surrounding coil of many turns, carrying an alternating current. 
The device, in fact, acts as the closed-circuit secondary of a step-down 
transformer. 

The Acheson furnace for the manufacture of carborundum is a rough 
firebrick structure, through the end walls of which project the electrodes 
consisting of composite bundles of carbon rods set in metal clamps. The 
space between the two electrodes is bridged by a conducting path of coke, 
which constitutes the core of the furnace. This core is packed round 
with the raw material, consisting of coke, sand, sawdust and common salt. 

A 2 1/2 ton H6roult electric steel furnace has been installed by the Firth- 
Sterling Steel Co. at Demmler, Pa. In this furnace an arc is formed 
between the bath of metal and two graphite electrodes which are sus- 
pended over it. Single-phase, sixty-cycle alternating current is used 
and is stepped down to 110 volts by transformers from the 11, 000- volt 
mains. The furnace consumes about 250 kilowatts. It produces steel 
equal in quality to crucible steel, at a cost little greater than open-hearth 
steel. (El. Review, May 14, 1910.) 

The Iron Trade Review, 1906, contains a series of illustrated articles 
on electric furnaces, by J. B. C. Kershaw. See also paper by C. F. Bur- 
gess, in Trans. Western Socy. of Engrs., 1905, and papers in Trans. Am. 
Electro Chemical Society, 1902 and later dates. 

Silundum, or silicified carbon, is a product obtained when carbon is 
heated in the vapor of silicon in an electric furnace. It is a form of car- 
borundum, and has similar properties; it is very hard, resists high tem- 
peratures and is acid-proof. It is a conductor of electricity, its resistance 
being about three times that of carbon. It can be heated in the air up 
to 1600° C. without showing any sign of oxidation. At about 1,700°, 
however, the silicon leaves the carbon and combines with the oxygen of 
the air. Silundum cannot be melted. The first use to which the material 
was applied was for electric cooking and heating. For heating purposes 
the silundum rods can be used single, in lengths up to 32 ins., depending 
on the diameter, as solid, round, flat or square rods or tubes, or in the 
form of a grid mounted in a frame and provided with contact wires. 
(El. Review, London. Eng. Digest, Feb., 1909.) 

PRIMARY BATTERIES. 

Following is a partial list of some of the best known primary cells or 



batteries. 












Name. 


Elements. 
+ 


Electrolyte. 


Depolarizer. 


E.M.F. 
volts. 




Cu 

Cu 

Pt 

C 

Cu 

C 

Pt 

Pt 

C 


Zn 
Zn 
Zn 
Zn 
Zn 
Zn 
Zn 
Cd 
Zn 


Dilute H2SO4 

ZnSC-4 
Dilute H2SO4 
Dilute H2SO4 
Cone. NaOH 

NH4CI 

ZnSC-4 

CdSC-4 
Various electro 


Concent. CuS0 4 
Concent. CuSCh 
HNO3 
K 2 Cr 2 7 
CuO 
Mn0 2 
Hg 2 S0 4 
Hg 2 S0 4 
yte pastes. 


1.07 




1. 




1.9 


Fuller 


2.1 


Edison- Lalande 


0.7-0.9 
1.4 


Clark 

Weston 

Dry battery 


1.44 
1.02 

l-rl.,8 



1378 ELECTRICAL ENGINEERING. 



The gravity cell is used for telegraph work. It is suitable for closed 
circuits, and should not be used where it is to stand for a long time on 
open circuit. 

The Fuller cell is adapted to telephones or any intermittent work. It 
can stand on open circuit for months without deterioration. 

The Edison-Lalande cell is suitable for either closed or open circuits. 

The Leclanche" cell is adapted for open circuit intermittent work, such 
as bells, telephones, etc. 

The Clark and Weston cells are used for electrical standards. The 
Weston cell has largely superseded the Clark. 

Dry cells are in common use for house service, igniters for gas engines, 
etc. 

Batteries are coupled in series of two or more to obtain an e.m.f. greater 
than that of one cell, and in multiple to obtain more amperes without 
change of e.m.f. 

Spark coils, or induction coils with interrupters, are used to obtain 
ignition sparks for gas engines, etc. 



ELECTRICAL ACCUMULATORS OR STORAGE-BATTERIES. 

The original, or Plants, storage battery consistedof two plates of metallic 
lead immersed in a vessel containing sulphuric acid. An electric current 
being sent through the cell the surface of the positive plate was converted 
into peroxide of lead, Pb02. This was called charging the cell. After 
being thus charged the cell could be used as a source of electric current, 
or discharged. Plante and other authorities consider that in charging, 
Pb02 is formed on the positive plate and spongy metallic lead on the 
negative, both being converted into lead oxide, PbO, by the discharge, 
but others hold that sulphate of lead is made on both plates by discharg- 
ing, and that during the charging Pb0 2 is formed on the positive plate and 
metallic Pb on the other, sulphuric acid being set free. 

The acid being continually abstracted from the electrolyte as the dis- 
charge proceeds, the density of the solution becomes less. In the charging 
operation this action is reversed, the acid being reinstated in the liquid 
and therefore causing an increase in its density. 

The difference of potential developed by lead and lead peroxide im- 
mersed in dilute H 2 S0 4 is about two volts. A lead-peroxide plate gradu- 
ally loses its electrical energy by local action, the rate of such loss varying 
according to the circumstances of its preparation and the condition of the 
cell. 

In the Faure or pasted cells lead plates are coated with minium or lith- 
arge made into a paste with acidulated water. When dry these plates 
are placed in a bath of dilute H 2 S0 4 and subjected to the action of the 
current, by which the oxide on the positive plate is converted into peroxide 
and that on the negative plate reduced to finely divided or porous lead. 

The " Chloride Accumulator " made by The Electric Storage Battery 
Co., of Philadelphia, consists of modified Plante positives and modified 
Faure negatives. The positive plate, called the Manchester type, con- 
sists of a hard lead grid into which are pressed " buttons " of corrugated 
pure lead tape, rolled into spirals. When electrolytically " formed," 
these buttons become coated with lead peroxide. The negative is the 
so-called " Box " type, in which the grid is made in two halves which are 
riveted together after " pasting " with lead oxide, the latter upon charg- 
ing being reduced to spongy lead. The outside faces are covered with 
perforated lead sheet, which serves to retain the spongy lead or active 
material. 

The following tables give the elements of several sizes of " chloride " 
accumulators. Type G is furnished in cells containing 11-75 plates, and 
type H from 21 plates to any greater number desired. The voltage of cells 
of all sizes is slightly above two volts on open circuit, and during discharge 



ELECTRICAL ACCUMULATORS. 



1379 



varies from that point at the begining to 1.75 at the end when working 
at the normal (eight-hour) rate. At higher rates the final voltage is lower. 

Accumulators are largely used in central lighting and power stations, in 
office buildings and other large isolated plants, for the purpose of absorbing 
the energy of the generating plant during times of light load, and for giving 
it out during times of heavy load or when the generating plant is idle. The 
advantages of their use for such purposes are thus enumerated : 

1. Reduction in coal consumption and general operating expenses, due 
to the generating machinery being run at the point of greatest economy 
while in service, and being shut down entirely during hours of light load 
the battery supplying the whole of the current. 



TYPE. 

Size of Plates. 



"C M 
43/ 8 x4 in. 



"D" 

6x6m. 



Number of plates 

r>. . • i For'8 hours . . 

Dl lt* T SJ For 5 hours „. 

amperes. .^ For 3 hours , 

Normal charge rate 

Outside dimensions of \ \Vlcif h 
rubber jar, inches: (Height 

Outside dimensions of \ \yjjf n 
glass jar, inches: ( Height 

Weight of electrolyte. [ fjgg/*™ 

lbs - : { jar: 

Weight of cell com- { *ggj 
plete,withacid,lbs.: irl 

^Height of cell over 
all, inches: 



. jars 
glass jars 
rubber 
jars. 



8V2 



'43/ 4 



71/4 
64/ 2 

83/ 4 
8I/4 
91/2 



63 
471/4 

v 2 



* 41/2, 51/2, and 6I/2 ins. 1 8/4, I, and I V4. lbs. X 7l/ 2 , 9l/ 2 and 1 1 1/2 lbs 
"D "Yacht type, rubber jars, 5, 7, and 9 plates, 2V2 in. higher than standard. 



TYPE'E.'" 
Size of Plates, 73/ 4 x73/ 4 in. 


TYPE " F.'' 
Size of Plates, 
11x101/2 in. 


Number of plates. . . . 


5 


7 


9 


11 


13 


15 


9 


II 


13 


15 


1; 


D* 


10 


15 


20 


25 


30 


35 


40 


50 


60 


70 


80 


5 




i1 


21 


28 


35 


42 


49 


56 


JO 


84 


98 


112 


7 


peres: |Fbr3hrs. 


30 


40 


W , 


60 ' 


70 


80 


100 


120 


140 


160 


10 


iFor 1 hr. 


40 


60 


HO • 


100 


120 


140 


160 


200 


240 


280 


320 


20 




10 


15, 
37/ 8 


20 


25 


30 


35 


40 


M) 


60 


70 


80 


5 


V5 Length, in. 1 rub- 


27/8 


5 


61/8 


8V« 


8V2 


11. 


U> 


163/4 


1*3/8 


20 


Vh 


4» £ Width, in. >ber 


8 l/o 


8'/? 


8V ? 


81/? 


»!/■> 


81/2 


i*Vs 


15 


15 


15 






11 


1! 


II 


d-Vs 


II 


II 




201/4 
103/g 


201/4 


201/4 


201/4 






51/, 


63/ 4 


8 


II 


113/s 


9 


l06/ 8 


12 






O £ Width, in.} S oi 


91/8 


91/8 


91/8 


?V8 


91/8 


91/8 


121/2 


12 V? 


123/4 


123/4 






*3 Height, in.)^""' 


11 3/ 8 


H3/8 


1 r*/» 


it 3/8 


M3/ 8 


II 1/8 


I'l 


M 


1/ 


17 


































Weight of 


jars. 


I8I/2 


20 


241/2 


26 


35 


34 


63 


09 


67 


79 . 






electrolyte: 


ber 




























jars. 


51/2 


8 


101/2 


12 


17 


I8V 2 




99 


111 


123 


133 


6 


Weight of 
tell com- 
plete, with 


glass 
jar. 
rub-. 


49 


60 


74 


86 1/2 


104 


112 














acid: 


jar. 

glass 
jar. 

rub- 
jar. 


29V2 


40»/2 


52 


63 


77 


87 


tank 




332 


372 


411 


20 


Height of cell 
over all, in 
inches: 


20 

121/2 


20 
121/2 


20 

mf 2 


20 
12 1/2 


20 

121/2 


20 

nu 2 


273/4 
£ank 


273/4 

331/4 


273/4 

331/4 


273/4 

331/4 


273/4 
331/4 





*D — addition per plate from 25 to 75 plates 
sions and weights. 



approximate as to dimen- 



1380 



ELECTRICAL ENGINEERING. 



type'"g." 

Size of Plates, I55/ I6 x 1 5 5/ 16 i n . 


TYPE " H." 
Size of Plates. 
15 5/16X30 "/to in. 


Number of platea 


II 


13 


15 


17 


25 


75 


D* 


21 


23 


25 


75 


D* 


Discharge |f- f hrs. 


100 


120 


140 


160 


240 


740 


10 


400 


440 


480 


480 


20 


140 


168 


196 


224 


336 


1036 


14 


560 


616 


672 


2072 


28 


nlrpV" |For3hrs. 


200 


240 


280 


320 


480 


1480 


20 


800 


880 


960 


2960 


40 


Peres. ( For , hr 


400 


480 


560 


640 


960 


2960 


40 


1600 


1760 


1920 


5920 


20 


Nornjal charge rate . 


100 


120 


140 


160 


240 


740 


10 


400 


440 


480 


480 


20 


Outside fr,eneth 
dimensions ) w: .f. 
of tank. Sc- 
inches: [Height. 


151/2 


I6I/4 


I8V2 


20 


275/ 8 


697/ 8 


7/8 


25 V 


26 3/4 


283/ 8 


697/ 


Va 


l93/ 4 


193/ 4 


193/4 


193/4 


203/4 


21V, 




2U/2 


21 1/ 2 


2ll/ 2 


211/2 

497/2 




26 


26 


26 


26 


261/2) 


277/- 




487/8 


487/ 8 


487/ 




Weight of electrolyte 


























in pounds 


188 


210 


231 


253 


338 


876 


10.5 


583 


625 


668 


1741 


21 5 


Weight of cell, com- 


























plete, with electro- 
lyte in lead-lined 


















































tank, pounds 


568 


645 


719 


798 


1165 


3300*" 40 


1967 


2121 


2278 


6215 


78 


Height of cell over 


























all, inches 


39 


39 


39 


39 


40, 


4U/2 


■:•' 


62V4 


62.1/4 


621/4 


631/4 



_ *D = addition per plate from 25 to 75 plates; approximate as to dimen- 
sions and weights. 



2. The possibility of obtaining good regulation in pressure during fluc- 
tuations in load, especially when the day load consists largely of elevators 
and similar disturbing elements. 

3. To meet sudden demands which arise unexpectedly, as in the case of 
darkness caused by storm or thunder-showers; also in case of emergency 
due to accident or stoppage of generating-plant. 

4. Smaller generating-plant required where the battery takes the peak 
of the load, which usually only lasts for a few hours, and yet where no 
battery is used necessitates sufficient generators, etc., being installed to 
provide for the maximum output, which in many cases is about double 
the normal output. 

The Working Current, or Energy Efficiency, of a storage-cell 
is the ratio between the value of the current or energy expended in the 
charging operation, and that obtained when the cell is discharged at any 
specified rate. 

In a lead storage-cell, if the surface and quantity of active material be 
accurately proportioned, and if the discharge be commenced immediately 
after the termination of the charge, then a current efficiency of as much as 
98% may be obtained, provided the rate of discharge is low and well regu- 
lated. Since the current efficiency decreases as the discharge rate in- 
creases, and since very low discharge rates are seldom used in practice, 
efficiencies as high as this are never obtained practically, the average 
being about 90%. 

As the normal average discharging electro-motive force of a lead 
secondary cell never exceeds 2 volts, and as an average electro-motive 
force during normal charge of about 2.35 volts is required at its poles 
to overcome both its opposing electro-motive force and its internal 
resistance, there is an initial loss of at least 15% between the voltage 
required to charge it and that at which it discharges. Thus with a cur- 
rent efficiency of 90% and a volt efficiency of 85% the energy efficiency 
under the best conditions cannot be much over 75%, while in practice 
it is nearer 70%. 

Important General Rules. — Storage cells should not be excessively 
charged, undercharged or allowed to stand when completely discharged. 

In setting up new cells the manufacturer should always be consulted 
as to the proper purity and specific gravity of the electrolyte (solution) 
to be used in the cells and also as to the duration of the initial charge. 



ELECTROLYSIS. 1381 



Charging should be done at the normal rate (as given by the manu- 
facturer) or as near to it as possible. At regular periods once each week 
or two weeks, depending on whether the cells have to be charged daily 
or not, an overcharge should be given, lasting until the specific gravity 
of the electrolyte and the cell voltage have risen to a maximum and 
remained constant for about one hour. The end of charge voltage may 
vary from 2.40 to 2.70 volts per cell. All other charges termed " regular 
charges " should cease shortly before the maximum values obtained on 
the preceding overcharge are reached. If cells are standing idle they 
should receive an overcharge once every two weeks. 

Discharges should be stopped when the cell voltage has fallen to 1.80 
volts with current flowing at or about the normal rate. The fall in 
specific gravity of the electrolyte is also useful as a guide on the discharge 
and the manufacturer should be consulted as to the proper limits. 

The level of the electrolyte should be kept above the top of the plates 
by adding pure fresh water. Addition of new electrolyte is seldom 
necessary and should be done only on advice from the manufacturer. 

The sediment which collects in the bottom of the cells should always 
be removed before it touches the plates. 

The battery room should be well ventilated, especially when charging, 
and great care taken not to bring an exposed flame near the cells when 
charging or shortly after. 

Metals or impurities of any kind must not be allowed to get into the 
cells. If such should happen, the impurity should be removed at once, 
and if badly contaminated, the electrolyte replaced with new. If in 
doubt as to the purity of electrolyte or water, the manufacturers should 
be consulted. 

To take cells out of commission, the electrolyte should be drawn off; 
the cells filled with water and allowed to stand for 12 or 15 hours. The 
water can then be drawn off and the plates allowed to dry. When 
putting into service again, the same procedure should be followed as with 
the initial charge. 

ELECTROLYSIS, 

The separation of a chemical compound into its constituents by means 
of an electric current. Faraday gave the nomenclature relating to elec- 
trolysis. The compound to be decomposed is the Electrolyte, and the 
process Electrolysis. The plates or poles of the battery are Electrodes. 
The plate where the greatest pressure exists is the Anode, and the other 
pole is the Cathode. The products of decomposition are Ions. 

Lord Rayleigh found that a current of one ampere will deposit 0.017253 
grain, or 0.001118 gram, of silver per second on one of the plates of a 
silver voltameter, the liquid employed being a solution of silver nitrate 
containing from 15% to 20% of the salt. The weight of hydrogen similarly 
set free by a current of one ampere is 0.00001038 gram per second. 

Knowing the amount of hydrogen thus set free, and the chemical equiva- 
lents of the constituents of other substances, we can calculate what weight 
of their elements will be set free or deposited in a given time by a given 
current. Thus, the current that liberates 1 gram of hydrogen will liberate 
8 grams of oxygen, or 107.7 grams of silver, the numbers 8 and 107.7 
being the chemical equivalents for oxygen and silver respectively. 

To find the weight of metal deposited by a given current in a given time, 
find the weight of hydrogen liberated by the given current in the given 
time, and multiply by the chemical equivalent of the metal. 

The table on page 1382 (from " Practical Electrical Engineering ") is 
calculated upon Lord Rayleigh's determination of the electro-chemical 
equivalents and Roscoe's atomic weights. 



1382 



ELECTRICAL ENGINEERING. 



ELECTRO-CHEMICAL EQUIVALENTS. 











H? 


> 






c 




0) 


W 


* 

>> 


£ 


1 , 








a 


a 


s| 






o> o> 


oj 




^13 


> 


<3 


O ro 


Hi 


1.00 


1.00 


Ki 


39.04 


39.04 


Nai 


22.99 


22.99 


Al 3 


27.3 


9.1 


Ma-., 


23.94 


11.97 


AU3 


196.2 


65.4 


Agi 


107.66 


107.66 


Cu 2 


63.00 


31.5 


C Ul 


63.00 


63.00 


H>, 


199.8 


99.9 


H gl 


199.8 


199.8 


Sm 


117.8 


29.45 


Sn 2 


117.8 


58.9 


Fa, 


55.9 


18.64$ 


Fe 2 


55.9 


27.95 


Ni 2 


58.6 


29.3 


Zn 2 


64.9 


32.45 


Pb 2 


206.4 


103.2 


Oo 


15.96 


7.98 


CMi 


35.37 


35.37 


Ii 


126.53 


126.53 


Br, 


79.75 


79.75 


^3 


14.01 


4.67 



lil^ 

si 11 
lit! 




o 03 



Electro-positive. 

Hydrogen 

Potassium 

Sodium 

Aluminum 

Magnesium 

Gold 

Silver 

Copper (cupric) 

(cuprous) 

Mercury (mercuric)., 
(mercurous) 

Tin (stannic) 

" (stannous) 

Iron (ferric) 

" (ferrous) 

Nickel 

Zinc 

Lead 

Electro-negative. 

Oxygen 

Chlorine 

Iodine 

Bromine 

Nitrogen 



0.010384 

0.40539 

0.23873 

0.09449 

0.12430 

0.67911 

1.11800 

0.32709 

0.65419 

1.03740 

2.07470 

0.30581 

0.61162 

0.19356 

0.29035 

0.30425 

0.33696 

1.07160 



0.08286 
0.36728 
1.31300 
0.82812 
0.04849 



96293.00 
2467.50 
4188.90 
1058.30 

804.03 
1473.50 

894.41 
3058.60 
1525.30 

963.99 

481.99 
3270.00 
1635.00 
5166.4 
3445.50 
3286.80 
2967.10 

933.26 



0.0373 8 
1.4595° 
0.8594^ 
0.34018 
0.44747 
2.4448° 
4.0250° 
1.1770° 
2.35500 
3.73450 
7.46900 
1.10090 
2.20180 
0.69681 
1 .04480 
1 .09530 
1 .21330 
3.85780 



*Valency is the atom-fixing or atom-replacing power of an element com- 
pared with hydrogen, whose valency is unity. 

fAtomic weight is the weight of one atom of each element compared 
with hydrogen, whose atomic weight is unity. 

JBecquerel's extension of Faraday's law showed that the electro-chemical 
equivalent of an element is proportional to its chemical equivalent. The 
latter is equal to its combining weight, and not to atomic weight -5- valency, 
as defined by Thompson, Hospitalier, and others who have copied their 
tables. For example, the ferric salt is an exception to Thompson's rule, 
as are sesqui-salts in general. 

Thus: Weight of silver deposited in 10 seconds by a current of 10 amperes 
= weight of hydrogen liberated per second X number of seconds X current 
strength X 107.7 = 0.00001038 X 10 X 10 X 107.7 = 0.11178 gram. 

Weight of copper deposited in 1 hour by a current of 10 amperes = 

0.00001038X 3600X10X 31.5 = 11.77 grams. 

Since 1 ampere per second liberates 0.00001038 gram of hydrogen, 
strength of current in amperes 

= weight in grams of H liberated per second -s- 0.00001038 
weight of element liberated per second 
— 0.00001038 Xchemical equivalent of element 



THE MAGNETIC CIRCUIT. 1383 

THE MAGNETIC CIRCUIT. 

For units of the magnetic circuit, see page 1346. 

Lines and Loops of Force. — It is conventionally assumed that the 
attractions and repulsions shown by the action of a magnet or a con- 
ductor upon iron filings are due to " lines of force " surrounding the 
magnet or conductor. The " number of lines " indicates the magnitude 
of the forces acting. As the iron filings arrange themselves in concentric 
circles, we may assume that the forces may be represented by closed 
curves or "loops of force." The following assumptions are made con- 
cerning the loops of force in a conductive circuit: 

1. That the lines or loops of force in the conductor are parallel to the 
axis of the conductor. 

2. That the loops of force external to the conductor are proportonal in 
number to the current in the conductor, that is, a definite current gener- 
ates a definite number of loops of force. These may be stated as the 
strength of field in proportion to the current. 

3. That the radii of the loops of force are at right angles to the axis oi 
the conductor. 

The magnetic force proceeding from a point is equal at all points on the 
surface of an imaginary sphere described by a given radius about that 
point. A sphere of radius 1 cm. has a surface of 4rc square centimeters 
If <j> = total flux, expressed as the number of lines of force emanating from 
a magnetic pole having a strength M , 

Magnetic moment of a magnet = product of strength of pole M and its 
length, or distance between its poles L. Magnetic moment =(f>L-t- 4x. 

If B = number of lines flowing through each square centimeter of cross- 
section of a bar-magnet, or the " specific induction," and A = cross-section 
Magnetic Moment = LAB + <lx. 

If the bar-magnet be suspended in a magnetic field of density H and so 
placed that the lines of the field are all horizontal and at right angles to the 
axis of the bar, the north pole will be pulled forward, that is, in the direc- 
tion in which the lines flow, and the south pole will be pulled in the 
opposite direction, the two forces producing a torsional moment or torque, 
Torque = ML H =LABH -f- 4tt, in dyne-centimeters. 

Magnetic attraction or repulsion emanating from a point varies inversely 
as the square of the distance from that point. The law of inverse squares, 
however, is not true when the magnetism proceeds from a surface of appre- 
ciable extent, and the distances are small, as in dynamo-electric machines 
and ordinary electromagnets. 

The Magnetic Circuit. — In the electric circuit 

Current = ^ — ' ' , or 7=-^; Amperes = — r — • 
Resistance R ohms 

Similarly, in the magnetic circuit 

_,. Magnetomotive Force . F _, _, Gilberts 

Flux= ■ — p , — - , or <£= „ • Maxwells = — 



Reluctance ' R Oersteds 

Reluctance is the reciprocal of permeance, and permeance is equal to 
permeability X path area -f- path length (metric measure); hence 
<f>= Fjua-r- I. 
One ampere-turn produces 1.257 gilberts of magnetomotive force and 
one inch equals 2.54 centimeters; hence, in inch measure, 

<£= (1.257 A t )n6A5a+ 2.54?= 3.192/xaA^H- I. 
The ampere-turns required to produce a given magnetic flux in a given 
path will be 

A t *= 4>l+ 3.192 /ia = 0.3133 <j>l+na. 
Since magnetic flux -f- area of path = magnetic density, the ampere-turn 
required to produce a density B, in lines of force per square inch of area 
of path, will be 

A t = 0.3133 Bl + p. 
This formula is used in practical work, as the magnetic density must 
be predetermined in order to ascertain the permeability of the material 
under its working conditions. When a magnetic circuit includes several 
qualities of material, such as wrought iron, cast iron, and air, it is most 
direct to work in terms of ampere-turns per unit length of path. The 



ia84 



ELECTKICAL ENGINEERING. 



ampere-turns for each material are determined separately, and the wind- 
ing is designed to produce the sum of all the ampere-turns. The following 
table gives the average results from a number of tests made by Dr. Samuel 
Sheldon: 

Values of B and H 





a 


g 

3 

5*8 


Cast Iron. 


Cast Steel. 


Wrought Iron. 


Sheet Metal. 


H 


<g 


o3 & • 


<D 


e3 a • 


a> 


1 V 

x a . 


$ 


1 O) 

« a . 




3*8 


B0 4 | 




m i| 


SJ2.S 
O-r, . 


m il 


||.S 


m ,1 


a — -5 








g& 




g=l 




O o3 
72 OJO 




10 


7.95 


20.2 


4.3 


27.7 


11.5 


74.2 


13.0 


83.8 


14.3 


92.2 


20 


15.90 


40.4 


5.7 


36.8 


13.8 


89.0 


14.7 


94.8 


15.6 


100.7 


30 


23.85 


60.6 


6.5 


41.9 


14.9 


96.1 


15.3 


98.6 


16.2 


104.5 


40 


31.80 


80.8 


7.1 


45.8 


15.5 


100.0 


15.7 


101.2 


16.6 


107.1 


50 


39.75 


101.0 


7.6 


49.0 


16.0 


103.2 


16.0 


103.2 


16.9 


109.0 


60 


47.70 


121.2 


8.0 


51.6 


16.5 


106.5 


16.3 


105.2 


17.3 


111.6 


70 


55.65 


141.4 


8.4 


59.2 


16.9 


109.0 


16.5 


106.5 


17.5 


112.9 


80 


63.65 


161.6 


8.7 


56.1 


17.2 


111.0 


16.7 


107.8 


17.7 


114.1 


90 


71.60 


181.8 


9.0 


58.0 


17.4 


112.2 


16.9 


109.0 


18.0 


116.1 


100 


79.50 


202.0 


9.4 


60.6 


17.7 


114.1 


17.2 


110.9 


18.2 


117.3 


150 


119.25 


303.0 


10.6 


68.3 


18.5 


119.2 


18.0 


116.1 


19.0 


122.7 


200 


159.0 


404.0 


11.7 


75.5 


19.2 


123.9 


18.7 


120.8 


1.96 


126.5 


250 


198.8 


505.0 


12.4 


80.0 


19.7 


127.1 


19.2 


123.9 


20.2 


13C.2 


300 


238.5 


606.0 


13.2 


85.1 


20.1 


129.6 


19.7 


127.1 


20.7 


133.5 



H = 1.257 ampere-turns per cm. = 0.495 ampere-turns per inch. 

Example. — A magnetic circuit consists of 12 ins. of cast steel of 8sq. 
ins. cross-section; 4 ins. of cast iron of 22 sq. ins. cross-section; 3 ins. of 
sheet iron of 8 sq. ins. cross-section; and two air-gaps each Vi6in. long and 
of 12 sq. ins. area. Required, the ampere-turns to produce a flux of 
768,000 maxwells, which is to be uniform throughout the magnetic circuit. 

The flux density in the steel is 768,000-^-8 = 96,000 maxwells; the am- 
pere-turns per inch of length, according to Sheldon's table, are 60.6, so 
that the 12 in. of steel will require 727.2 ampere-turns. 

The density in the cast iron is 768,000-^22 = 34,900; the ampere-turns 
= 4X40=160. 

The density in the sheet iron = 768,000 -5- 8 = 96,000; ampere-turns per 
inch = 30; total ampere-turns for sheet iron = 90. 

The air-gap density is 768,000 -=- 12 = 64,000; ampere-turns per in. = 
0.3133B; ampere-turns required for air-gap = 0.3133 X 64,000 ■*- 8=2506.4. 

The entire circuit will require 727.2+ 160+ 90 + 2506.4 = 3483.6 am- 
pere-turns, assuming uniform flux throughout. 

In practice there is considerable "leakage" of magnetic lines of force; 
that is, many of the lines stray away from the useful path, there being no 
material opaque to magnetism and therefore no means of restricting it to 
a given path. The amount of leakage is proportional to the permeance 
of the leakage paths available between two points in a magnetic circuit 
which are at different magnetic potentials, such as opposite ends of a 
magnet coil. It is seldom practicable to predetermine with any approach 
to accuracy the magnetic leakage that will occur under given conditions 
unless one has profuse data obtained experimentally under similar con- 
ditions. In dynamo-electric machines the leakage coefficient varies from 
1.3 to 2. 

Tractive or Lifting Force of a Magnet. — The lifting power or 
" pull " exerted by an electro-magnet upon an armature in actual contact 
with its pole-faces is given by the formula 

Lbs.= B*a + 72, 134,000, 
a being the area of contact in square inches and B the magnetic density 
over this area. If the armature is very close to the pole-faces this for- 
mula also applies with sufficient accuracy for all practical puposes, but 
a considerable air-gap renders it inapplicable. 

The design of solenoids for the coil-and-plunger type of electro-magnets 



DYNAMO-ELECTRIC MACHINES. 1385 

is discussed in a series of articles by C. R. Underbill, in Elec. World, 
April 29, May 13, and Oct. 7, 1905. 

Various forms of magnetic chucks are illustrated and described by O. S. 
Walker, in Am. Mach., Feb. 11, 1909. 

For magnets used in hoisting, see page 1169. 

Determining the Polarity of Electro-magnets. — If a wire is 
wound around a magnet in a right-handed helix, the end at which the 
current flows into the helix is the south pole. If a wire is wound around 
an ordinary wood-screw, and the current flows around the helix in the 
direction from the head of the screw to the point, the head of the screw is 
the south pole. If a magnet is held so that the south pole is opposite the 
eye of the observer, the wire being wound as a right-handed helix around 
it, the current flows in a right-handed direction, with the hands of a clock. 

Determining the Direction of a Current. — Place a wire carrying 
a current above and parallel to a pivoted magnetic needle. If the cur- 
rent be flowing along the wire from N. to S., it will cause the N.-seeking 
pole to turn to the eastward; if it be flowing from S. to N., the pole will 
turn to the westward. If the wire be below the needle, these motions 
will be reversed. 

Maxwell's rule. The direction of the current and that of the resisting 
magnetic force are related to each other as are the rotation and the for- 
ward travel of an ordinary (right-handed) corkscrew. 

DYNAMO-ELECTRIC MACHINES. 

There are three classes of dynamo-electric machines, viz.: 

1. Generators, for the conversion of mechanical into electrical energy. 

2. Motors, for the conversion of electrical into mechanical energy. 
Generators and motors are both subdivided into direct-current and 

alternating-current machines. 

3. Transformers, for the conversion of one character or voltage of cur- 
rent into another, as direct into alternating or alternating into direct, or 
from one voltage into a higher or lower voltage. 

Kinds of Dynamo-electric Machines as regards Manner of 
Winding. 

1. Separately-excited Dynamo. — The field magnet coils have no connec- 
tion with the armature-coils, but receive their current from a separate 
machine or source. 

2. Series-wound Dynamo. — The field winding and the external circuit 
are connected in series with the armature winding, so that the entire arma- 
ture current must pass through the field-coils. 

Since in a series-wound dynamo the armature-coils, the field, and the ex- 
ternal circuit are in series, any increase in the resistance of the external 
circuit will decrease the electromotive force from the decrease in the mag- 
netizing currents. A decrease in the resistance of the external circuit will, 
in a like manner, increase the electromotive force from the increase in the 
magnetizing current. The use of a regulator avoids these changes in the 
electromotive force. 

3. Shunt-wound Dynamo. — The field magnet coils are placed in a shunt 
to the armature circuit, so that only a portion of the current generated 
passes through the field magnet coils, but all the difference of potential of 
the armature acts at the terminals of the field-circuit. 

In a shunt-wound dynamo an increase in the resistance of the external 
circuit increases the electromotive force, and a decrease in the resistance 
of the external circuit decreases the electromotive force. This is just the 
reverse of the series-wound dynamo. 

In a shunt-wound dynamo a continuous balancing of the current occurs, 
the current dividing at the brushes between the field and the external cir- 
cuit in the inverse proportion to the resistance of these circuits. If the 
resistance of the external circuit becomes greater, a proportionately greater 
current passes through the field magnets, and so causes the electromotive 
force to become greater. If, on the contrary, the resistance of the external 
circuit decreases, less current passes through the field, and the electro- 
motive force is proportionately decreased. 

4. Compound-wound Dynamo. — The field magnets are wound with two 
separate sets of coils, one of which is in series with the armature and the 
external circuit, and the other in shunt with the armature or the external 
circuit. 



1386 



ELECTRICAL ENGINEERING. 



Motors. — The above classification in regard to winding applies also to 
motors. 

Moving Force of a Dynamo-electric Machine. — A wire through 
which a current passes has, when placed in a magnetic field, a tendency 
to move perpendicular to itself and at right angles to the lines of the 
field. The force producing this tendency is P=IBI dynes, in which 
Z=length of the wire, 7 = the current in C.G.S. units, and B=the induc- 
tion, or flux density, in the field in gausses or lines per square centimeter. 

If the current / is taken in amperes, P = lBI-i- 10 = IBIX 10 -1 . 

If Pjff. is taken in kilograms, 

P k = IBI + 9,810,000 = 10.1937 IBIX 10~ 8 kilograms. 

Example. — The mean strength of field, B, of a dynamo is 5000 C.G.S. 
lines; a current of 100 amperes flows through a wire; the force acts upon 
10 centimeters of the wire = 10.1937 X 10 X 100X5000 X 10" 8 =0.5097 kilo- 
grams. 

Torque of an Armature. — The torque of an armature is the moment 
tending to turn it. In a generator it is the moment which must be 
applied to the armature to turn it in order to produce current. In a motor 
it is the turning moment which the armature gives to the pulley. 

Let / = current in the armature in amperes, £' = the electromotive force 
in volts, T = the torque in pound-feet, <£= the flux through the armature 
in maxwells, N = the number of conductors around the armature, and n = 
the number of revolutions per second. Then 

Watts = IE = 2nnTX 1.356.* 

In any machine if the flux be constant, E is directly proportional to the 
speed and = 4>Nn -J- 10 8 ; whence 

<j>NI-r- 10 8 = 2xTX1.356; 
<j>NI <j>NI 

10 8 X 2tt X 1.356 8.52 X 10 8 P ouna - Ieet - 

Let I = length of armature in inches, d = diameter of armature in inches, 
B = flux density in maxwells per square inch, and let m = the ratio of the 
conductors under the influence of the pole-pieces to the whole number of 
conductors on the armature. Then 

4> = %ndXlX BXm. 

These formulae apply to both generators and motors. They show that 
torque is independent of the speed and varies directly with the current and 
the flux. The total peripheral force is obtained by dividing the torque by 
the radius (in feet) of the armature, and the drag on each conductor is 
obtained by dividing the total peripheral force by the number of conductors 
under the influence of the pole-pieces at one time. 

Example. — Given an armature of length I = 20 inches, diameter d = 12 
inches, number of conductors N = 120, of which 80 are under the influence 
of the pole-pieces at one time; let the flux density B = 30,000 maxwells 
per sq. in. and the current / = 400 amperes. 

4> = ~- X 20 X 30,000 X y^j = 7,540,000. 
„ 7,540,000X120X400 , OJ _ , . . 

T = 8.52 X 100,000,000 = 424 " 8 P ound " feet - 
Total peripheral force = 424.8 -e- 0.5 = 849.6 lbs. 
Drag per conductor = 849.6 -s- 120 = 7.08 lbs. 

The work done in one revolution = torque X circumference of a circle 
of 1 foot radius = 424.8 X 6.28 = 2670 foot-pounds. 

Let the revolutions per minute equal 500, then the horse-power 
^2670X500 
33000 
Torque, Horse-power and Revolutions. — T= torque in pound-feet, 
H.P. = T X Rpm. X 6.2832 -r- 33,000 = IE -J- 746. Whence Torque 
= 7.0403 EI h- Rpm. or 7 times the watts -*- the revs, per min. nearly. 
Electromotive Force of the Armature Circuit. — From the horse- 
power, calculated as above, together with the amperes, we can obtain 
the E.M.F., for IE = H.P. X 746, whence E.M.F. or E = H.P. X 746-=-/. 
* 1 ft.-lb. per second = 1.356 watts. 



DYNAMO-ELECTRIC MACHINES. 1387 

If H.P., as above, = 40.5, and /= „ 

400 

The E.M.F. may also be calculated by the following formulae: 
I = Total current through armature; 
e a = E.M.F. in armature in volts; 

N = Number of active conductors counted all around armature; 
V = Number of pairs of poles (p = 1 in a two-pole machine); 
n= Speed in revolutions per minute; 
$ = Total flux in maxwells. 

_,, , . I e n =4>N — 10 -8 for two-pole machines. 

Electromotive J a 60 

force: j = p<f>N j% for multipolar machines with series- 

{. a 10 8 60 wound armature 

Strength of the Magnetic Field. — Let / = current in amperes, N = 
number of turns in the coil, A = area of the cross-section of the core in 
square centimeters, 1= length of core in centimeters, n the permeability of 
the core, and <£= flux in maxwells. Then 

_ Magnetomotive Force _ 1.257 NI 



r Reluctance (£-e-A/i) 

In a dynamo-electric machine the reluctance will be made up of three 
separate quantities, viz.: that of the field magnet cores, that of the air 
spaces between the field magnet pole-pieces and the armature, and that 
of the armature. The total reluctance is the sum of the three. Let L it 
L 2 , L 2 be the length of the path of magnetic lines in the field magnet 
cores,* in the air-gaps, and in the armature respectively; and let A t , 
A 2 , A3 be the areas of the cross-sections perpendicular to the path of the 
magnetic lines in the field magnet cores, the air-gaps, and the armature 
respectively. Let the permeability of the field magnet cores be m, and of 
the armature nz. The permeability of the air-gaps is taken as unity. Then 
the total reluctance of the machine will be 

Li L2 , L3 > 
Aifii A 2 A S fi s 

™_ « . 1.257 NI 

The flUX, <£ = 77 — — : . , fT — . . , IT -. : . 

(Lj -i- Aifj-i) + (L 2 ■*■ A 2 ) + {Lz -5- A 3^3) 

The ampere-turns necessary to create a given flux in a machine may be 

found by the formula, 

Arr , [(Lt -5- AtMi) + (L 2 -4-A 2 ) + (L 8 -?• Az^s)] 
NI = * L257 ' 

But the total flux generated by the field coils is not available to produce 
current in the armature. There is a leakage between the field magnets, 
and this must be allowed for in calculations. The leakage coefficient 
varies from 1.3 to 2 in different machines. The meaning of the coefficient 
is that if a flux of say 100 maxwells per square cm. are desired in the field 
coils, it will be necessary to provide ampere turns for 1.3 X 100 = 130 
maxwells, if the leakage coefficient be 1.3. 

Another method of calculating the ampere-turns necessary to produce a 
given flux is to calculate the magnetomotive force required in each portion 
of the machine, separately, introducing the leakage coefficient in the calcu- 
lation for the field magnets, and dividing the sum of the magnetomotive 
forces by 1.257. 

In the ordinary type of multipolar machine there are as many magnetic 
circuits as there are poles. Each winding energizes part of two circuits. 
The calculation is made in the same manner as for a single magnetic circuit. 

*The length of the path in the field magnet cores L t includes that portion 
of the path which lies in the piece joining the cores of the various field 
magnets. 



1388 ELECTRICAL ENGINEERING. 



ALTERNATING CURRENTS.* 

The advantages of alternating over direct currents are: 1. Greater 
simplicity of dynamos and motors, no commutators being required; 2. 
The feasibility of obtaining high voltages, by means of static transformers, 
for cheapening the cost of transmission; 3. The facility of transforming 
from one voltage to another, either higher or lower, for different purposes. 

A direct current is uniform in strength and direction, while an alternat- 
ing current rapidly rises from zero to a maximum, falls to zero, reverses 
its direction, attains a maximum in the new direction, and again returns to 
zero. This series of changes can best be represented by a curve the abscis- 
sas of which represent time and the ordinates either current or electro- 
motive force (e.m.f.). The curve usually chosen for this purpose is the 
sine curve, Fig. 172; the best forms of alternators give a curve that is a 
very close approximation to the sine curve, and all calculations and de- 
ductions of formulae are based on it. The equation of the sine curve is 
y = sin x, in which y is any ordinate, and x is the angle passed over by 
a moving radius vector. 

After the flow of a direct current has been once established, the only 
opposition to the flow is the resistance offered by the conductor to the 
passage of current through it. This resistance of the conductor, in treat- 
ing of alternating currents, is sometimes spoken of as ohmic resistance. 
The word resistance, used alone, always means the ohmic resistance. In 
alternating currents, in addition to the resistance, several other quantities, 
which affect the flow of current, must be taken into consideration. These 
quantities are inductance, capacity, and skin effect. They are discussed 
under separate headings. 

The current and the e.m.f. may be in phase with each other, that is, 
they may attain their maximum strength at the same instant, or they 
may not, depending on the character of the circuit. In a circuit containing 
only resistance, the current and e.m.f. are in phase; in a current contain- 
ing inductance the e.m.f. attains its maximum value before the current, 
or leads the current. In a circuit containing capacity the current leads 
the e.m.f. If both capacity and inductance are present in a circuit, they 
will tend to neutralize each other. 

Maximum, Average, and Effective Values. — The strength and the 
e.m.f. of an alternating current being constantly varied, the maximum 
value of either is attained only for an instant in each period. The maxi- 
mum values are little used in calculations, except in deducing formulae 
and for proportioning insulation, which must stand the maximum pressure. 

The average value is obtained by averaging the ordinates of the sine 
curve representing the current, and is 2 -f- t or 0.637 of the maximum 
value. 

The value of greatest importance is the effective, or " square root of the 
mean square," value. It is obtained by taking the square root of the 
mean of the squares of the ordinates of the sine curve. The effective value 
is the value shown on alternating-current measuring instruments. The 
product of the square of the effective value of the current and the resist- 
ance of the circuit is the heat lost in the circuit. 

The comparison of the maximum, average, and effective values is as 
follows: 
#Effec. =#Max. X 0.707; #Aver. =#Max.X 0.637; #Max. = 1.41 X #Effec. 

Frequency. — The time required for an alternating current to pass 
through one complete cycle, as from one maximum point to the next (a 
and b, Fig. 172), is termed the period. The number of periods in a second 
is termed the frequency of the current. Since the current changes its 
direction twice in each period, the number of reversals or alternations is 

*Only a very brief treatment of the subject of alternating currents can 
be given in this book. The following works are recommended as valuable 
for reference: Alternating Currents and Alternating Current Machinery, 
by D. C. and J. P. Jackson; Standard Polyphase Apparatus and Systems, 
by M. A. Oudin; Polyphase Electric Currents, by S. P. Thompson; Electric 
Lighting, by F. B. Crocker, 2 vols.; Electric Power Transmission, by Louis 
Bell; Alternating Currents, by Bedell and Crehore; Alternating-current 
Phenomena, by Chas. P. Steinmetz. The two last named are highly 
mathematical. 




ALTERNATING CURRENTS 1389 

double the frequency. A current of 120 alternations per second has a 
period of i/eo and a frequency of 60. The frequency of a current is equal 
to one-half the number of poles on the generator, multiplied by the number 
of revolutions per second. Frequency is denoted by the letter/. 

The frequencies most generally used in the United States are 25, 40, 60, 
125, and 133 cycles per second. The Standardization Report of the 
A I.E.E. recommends the adoption of three frequencies, viz. 25, 60 and 120. 

With the higher frequencies both transformers and conductors will be 
less costly in a circuit of a given resistance but the capacity and inductance 
effects in each will be increased, and these tend to increase* the cost. With 
high frequencies it also becomes difficult to operate alternators in parallel. 

A low frequency current cannot be used on lighting circuits, as the lights 
will flicker when the frequency drops below a certain figure. For arc lights 
the frequency should not be less than 40. For incandescent lamps it should 
not be less than 25. If the circuit is to supply both power and light a 
frequency of 60 is usually desirable. For power transmission to long dis- 
tances a low frequency, say 25, is considered desirable, in order to lessen 
the capacity effects. If the alternating current is to be converted into 
direct current for lighting purposes a low frequency may be used, as the 
frequency will then have no effect on the lights. 

Inductance. — Inductance is that property of an electrical circuit by 
which it resists a change in the current. A current flowing through a 
conductor produces a magnetic flux 
around the conductor. If the current 
be changed in strength or direction, 
the flux is also changed, producing 
in the conductor an e.m.f. whose direc- 
tion is opposed to that of the current 
in the conductor. This counter e.m.f. 
is the counter e.m.f. of inductance. 
It is proportional to the rate of change 
of current, provided that the perme- 
ability of the medium around the con- Fig. 198. 
ductor remains constant. The unit of 

inductance is the henry, symbol L. A circuit has an inductance of one 
henry if a uniform variation of current at the rate of one ampere per 
second produces a counter e.m.f. of one volt. 

The effect of inductance on the circuit is to cause the current to lag 
behind the e.m.f. as shown in Fig. 198, in which abscissas represents time, 
and ordinates represent e.m.f. and current strengths respectively. 

Capacity. — Any insulated conductor has the power of holding a quan- 
tity of static electricity. This power is termed the capacity of the body. 
The capacity of a circuit is measured by the quantity of electricity in it 
when at unit potential. It may be increased by means of a condenser. 
A condenser consists of two parallel conductors, insulated from each other 
by a non-conductor. The conductors are usually in sheet form. 

The unit of capacity is a farad, symbol C. A condenser has a capacity 
of one farad when one coulomb of electricity contained in it produces a dif- 
ference of potential of one volt, or when a rate of change of pressure of 
one volt per second produces a current of one ampere. The farad is too 
large a unit to be conveniently used in practice, and the micro-farad or 
one-millionth of a farad is used instead. 

The effect of capacity on a circuit is to cause the e.m.f. to lag behind the 
current. Both inductance and capacity may be measured with a Wheat- 
stone bridge by substituting for a standard resistance a standard of induc- 
tance or a standard of capacity. 

Power Factor. — In direct-current work the power, measured in watts, 
is the product of the volts and amperes in the circuit. In alternating-cur- 
rent work this is only true when the current and e.m.f. are in phase. If 
the current either lags or leads, the valuee shown on the volt and ammeters 
will not be true simultaneous values. Referring to Fig. 172, it will be 
seen that the product of the ordinates of current and e.m.f. at any partic- 
ular instant will not be equal to the product of the effective values which 
are shown on the instruments. The power in the circuit at any instant is 
the product of the simultaneous values of current and e.m.f., and the volts 
and amperes shown on the recording instruments must be multiplied 
together and their product multiplied by a power factor before the true 



1390 



ELECTRICAL ENGINEERING. 



watts are obtained. This power factor, which is the ratio of the volt- 
amperes to the watts, is also the cosine of the angle of lag or lead of the 
current. Thus 

P= IX EX power factor= I XEXcos9, 
where 6 is the angle of lag or lead of the current. 

A watt-meter, however, gives the true power in a circuit directly. The 
method of obtaining the angle of lag is shown below, in the section on Im- 
pedance Polygons. 

Reactance, Impedance, Admittance. — In addition to the ohmic 
resistance of a circuit there are also resistances due to inductive, capacity, 
and skin effect. The virtual resistance due to inductance and capacity 
is termed the reactance of the circuit. If inductance only be present in 
circuit, the reactance will vary directly as the inductance. If capacity 
only be present, the reactance will vary inversely as the capacity. 
Inductive reactance = 2 nfL. 

Condensive reactance = ■ . 

The total apparent resistance of the circuit, due to both the ohmic resist- 
ance and the total reactance, is termed the impedance, and is equal to the 
square root of the s um of the sq uares of the resistance and the reactance. 
Impedance = Z = v / R 2 + (2tt/L) 2 w hen inductance is present in the circuit. 

Impedance = Z = ^R i + ( - — ^ J when capacity is present in the circuit. 

Admittance is the reciprocal of impedance, = 1 -s- Z. 

If both inductance and capacity are present in the circuit, the reactance 
of one tends to balance that of the other; the total reactance is the alge- 
braic sum of the two reactances; thus, 

Total reactance = X = 2 tt/L - -^-^ ; Z = \j R* + ( 2 n/L - tt^tptY- 

2 irjC M \ 2 irJC / 

In all cases the tangent of the angle of lag or lead is the reactance divided 
by the resistance. In the last case 

2nfL--^ 
tan0 = ^- C . 

Skin Effect. — Alternating currents tend to have a greater density at 
the surface than at the axis of a conductor. The effect of this is to make 
the virtual resistance of a wire greater than its true omhic resistance. 
With low frequencies and small wires the skin effect is small, but it becomes 
quite important with high frequencies and large wires. 

The skin effect factor, by which the ohmic resistance is to be multiplied 
to obtain the virtual resistance, for different sizes of wire and frequencies 
is as follows: 



Wire No. 





00 


000 


0000 


1/2 in- 


3/ 4 in. 


1 in. 










1.001 
1.006 
1.027 


1.002 
1.008 
1.039 


1 .UO/ 
1.040 
1.156 


1.020 




i .66i 

1.008 


1.002 
1.010 


1.005 
1.017 


1.111 


130 cycles, factor 


1.397 



Ohm's Law applied to Alternating-Current Circuits. — To apply 
Ohm's law to alternating-current circuits a slight change is necessary 
in the expression of the law. Impedance is substituted for resistance. 
The law should read 

E E m 

Impedance Polygons. — 1. Series Circuits. — The impedance of a circuit 
can be determined graphically as follows. Suppose a circuit to con- 
tain a resistance R and an inductance L, and to carry a current / of fre- 
quency/. In Fig. 199 draw the line ab proportional to R, and representing 
the direction of current. At b erect be perpendicular to ab and propor- 
tional to 2 tt/L. Join a and c. The line ac represents the impedance of 
the circuit. The angle d between ab and ac is the angle of lag of the cur- 



ALTERNATING CURRENTS. 



1391 



rent behind the e.m.f., and the power factor of the circuit is cosine 6 
e.m.f. of the circuit is E = IZ. 





Fig. 199. 



Fig. 200. 



If the above circuit contained, instead of the inductance L, a capacity C, 
then would the polygon be drawn as in Fig. 200. The line be woula be pro- 
portional to - and would be drawn in a direction opposite to that of 

be in Fig. 199. The impedance would again ba Z, the e.m.f. would be 
Z XI, but the current would lead the e.m.f. by the angle 0. 

Suppose the circuit to contain resistance, inductance, and capacity. 
The lines of the impedance polygon would then be laid off as in Fig. 201. 
The impedance of the circuit would be represented by ad, and the angle of 
lag by 6. If the capacity of the circuit had been such that cd was less than 
be, then would the e.m.f. have led the current. 



1 

27T/JC.. 





Fig. 201. 



Fig. 202. 



If between the inductance and capacity in the circuit in the previous ex- 
amples there be interposed another resistance, the impedance polygon will 
take the form of Fig. 202. The lines representing either resistances, in- 
ductances, or capacities in the circuit follow each other in all cases as do 
the resistances, inductances, and capacities in the circuit, each line having 
its appropriate direction and magnitude. 

Example. — A circuit (Fig. 203) contains a resistance, R lt of 15 ohms, a 
capacity, C it of 100 microfarads (0.000100 farad), a resistance, R 2 , of 12 



R.r=15 Kj =.0001 0Q R 2 =12 




Fig. 203. 

ohms, and inductance of L u of 0.05 henry, and a resistance R3, of 20 ohms. 
Find the impedance and electromotive force when a current of 2 amperes 
is sent through the circuit, and the current when e.m.f. of 120 volts is 
impressed on the circuit, frequency being taken as 60. Also find the angle 
of lag, the power factor, and the power in the circuit when 120 volts are 
iin Dressed 
The resistance is represented in Fig. 204 by the horizontal line ab, 15 



1392 



ELECTRICAL ENGINEERING. 



Ri— 15 




Fig. 204. 



units long. The capacity is represented by the line be, drawn downwards 
from b and whose length is 

2j7/Ci = 2X3.1416X60X0.0001 = 26>55 - 
From the point c a horizontal line cd, 12 units long, is drawn to represent 
R 2 . From the point d the line de is drawn vertically upwards to represent 
the inductance L x . Its length is 

2nfLi=2 X3.1416 X60 X 0-05= 18.85. 
From the point e a horizontal line ef, 20 
units long, is drawn to represent Rz. The 
)\fi r=20 / nne adjoining a and / will represent the 
impedance of the circuit in ohms. The 
angle 0, between ab and af, is the angle of 
lag of the e.m.f. behind the current. The 
impedance in this case is 47.5 ohms, and 
the angle of lag is 9° 15'. 

The e.m.f. when a current of 2 amperes 
is sent through is 

IZ = E = 2 X 47.5 = 95 volts. 
If an e.m.f. of 120 volts be impressed on the circuit, the current flowing 
through will be 

, 120 120 n co 

/= -7T = -T~-g = 2.53 amperes. 

The power factor = cos = cos 9° 15' = 0.987, 

The power in the circuit at 120 volts is 

/ X E X cos d = 2.53 X 120 X 0.987 = 299.6 watts. 

2. Parallel Circuits. — If two circuits be arranged in parallel, the current 
flowing in each circuit will be inversely proportional to the impedance of 
that circuit. The e.m.f. of each circuit is the e.m.f. across the terminals 
at either end of the main circuit, where the various branches separate. 
Consider a circuit, Fig. 205, consisting of two 
branches. The first branch contains a resist- 
ance Rt and an inductance Li in series with 
it. The second branch contains a resistance 
R 2 in series with an inductance L 2 . The im- 
pedance of the circuit may be determined by 
treating each of the two branches as a sepa- 
rate series circuit, and drawing the impedance 
polygon for each branch on that assumption. 
Having found the impedance the current flow- 
ing in either branch will be the reciprocal of the impedance multiplied 
by the e.m.f. across the terminals. The current in the entire circuit is the 
geometrical sum of the current in the two branches. 

The admittance of the equivalent simple circuit may be obtained by 
drawing a parallelogram, two of whose adjoining sides are made parallel to 
the impedance lines of each branch and equal to the two admittances 
respectively. 

The diagonal of the parallelogram will represent the admittance of the 
equivalent simple circuit. The admittance multiplied by the e.m.f. gives 
the total current in the circuit. 

Example.— Given the circuit in Fig. 206, consisting of two branches. 
Branch 1 consists of a resistance R t = 12 ohms, an inductance L x = 0.05 
henry, a resistance R 2 = 4 ohms, and a capacity Ci = 120 microfarads 
(0.00012 farad). Branch 2 consists of an inductance L 2 = 0.015 henry, a 
resistance R 3 = 10 ohms, and an inductance L 3 = 0.03 henry. An e.m.f. 
of 100 volts is impressed on the circuit at a frequency of 60. Find the ad- 
mittance of the entire circuit, the current, the power factor, and the power 
in the circuit. Construct the impedance polygons for the two branches 
separately as shown in Fig. 207, a and b. The impedance in branch 1 is 
16.4 ohms, and the current is (1/16.4) X 100 = 6.19 amperes. The angle 
of lead of the current is 1° 45'. The impedance in branch 2 is 19.5 ohms 
and the current is (1/19.5) X 100 = 5. 13 amperes. The angle of lag of the 
current is 61°. 

The current in the entire circuit is found by taking the admittances of 



Ri L a 

r-VVWWfifH 

Fig. 205. 



ALTERNATING CURRENTS. 



1393 



the two branches, and drawing them from the point o, in Fig 207 c parallel 
to the impedance lines in their respective polygons. The diagonal from o 
is the admittance of the entire circuit, and in this case is equal to 0.092. 

R! = 12 U=.05 R 2 =4 Ki^.00012 

-A/WWoWtfMA/V— [=> 



£-g 



O- 



E.M.F.=100 

L 2 =.015 R 3 =10 L 3 =.03 

Fig. 206. 
R 2 -=4 




Ri<=42 





■^=.0619 

Fig. 207. 

The current in the circuit is 0.092 X 100 = 9.2 amperes. The power factor 
is 0.944 and the power in the circuit is 100 X 0.944 X 9.2 = 868.48 watts. 

Self-Inductance of Lines and Circuits. — The following formulae 
and table, taken from Crocker's " Electric Lighting," give a method of cal- 
culating the self-inductance of two parallel aerial wires forming part of the 
same circuit and composed of copper, or other non-magnetic material: 

L per foot = (l5.24 + 140.3 log ^~\ 10~ 9 . 

L per mile = (80.5 + 740 log ~\ 10 -6 . 

in which L is the inductance in henrys of each wire, A is the interatrial dis- 
tance between the two wires, and d is the diameter of each, both in inches. 
If the circuit is of iron wire, the formulas become 

L per foot = (2286 + 140.3 log ~\ 10 -9 . 
h per mile = (l2070 + 740 log 2A} lO" 8 , 



1394 



ELECTRICAL ENGINEERING. 



Inductance, in Millihenrys per Mile, for Each of Two Parallel 
Copper Wires. 



Interaxial 








American Wire Gauge Number. 








Distance, 


























Ins. 


0000 


000 


00 





1 


2 


3 


4 


6 


8 


10 


12 


6 


1 130 


1,168 


1 205 


1,242 


1,280 


1,317 


1.354 


1 392 


1,466 


1.540 


1,615 


1 690 


12 


1 353 


1 391 


1 428 


1,465 


1.502 


1.540 


1.577 


1 614 


1.689 


1,764 


1,838 


1 913 


24 


1.576 


1.614 


1.651 


1.688 


1.725 


1.764 


1.800 


1.838 


1.912 


1.986 


2.061 


2,135 


36 


1 707 


1 745 


1 784 


1 818 


1 856 


1.893 1.931 


1 968 


2 043 


2.117 


2 192 


2 7,66 


60 


1 871 


1,909 


1 946 


1 982 


2.023 


2.058 2.095 


2 132 


2 208 


2 282 


2 356 


2.432 


96 


2.023 


2.059 


2.097 


2.134 


2.172 


2.2102.246 


2.283 


2.358 


2.433 


2.507 


2.582 



Capacity of Conductors. — All conductors are included in three 
classes, viz.: 1. Insulated conductors with metallic protection; 2. Single 
aerial conductor with earth return; 3. Metallic circuit consisting of two 
parallel aerial wires. The capacity of the lines may be calculated by 
means of the following formula taken from Crocker's " Electric Lighting." 



-, „ * l 7361 k 10 -15 _ 

Class 1. C per foot = , — (D ^ ,y , C per mile== 

™ ' ~ , . 7361 X 10 -15 _ ., , 

Class 2. C per foot = log(4ft + d) , C per mile = ^ft 



38. 83 k 10~ 9 
,-„ (D * d) * 
38.83 X 10~ 9 



Class 3 



,.t 



per foot of each wire : 



3681 X IO-1 5 



log (2A+d) 
w ., , . . 19.42 X 10-° 

C per mile of each wire = log ( 2 A+d) ' 



In which C is the capacity in farads, D the internal diameter of the metallic 
covering, d the diameter of the conductor, h the height of the conductor 
above the ground, and A the interaxial distance between two parallel wires 
all in inches; A; is a dielectric constant which for air is equal to 1 and for 
pure rubber is equal to 2.5. The formulae in classes 2 and 3 assume the wires 
to be bare. If they are insulated, k must be introduced in the numerator 
and given a value slightly greater than 1. 

Single-phase and Polyphase Currents. — A single-phase current 
is a simple alternating current carried on a single pair of wires, and is 
generated on a machine having a single armature winding. It is repre- 
sented by a single sine curve. 

Polyphase currents are known as two-phase, three-phase, six-phase, or 
any other number, and are represented by a corresponding number of sine 
curves. The most commonly used systems are the two-phase and three- 
phase. 

1. Two-phase Currents. — In a two-phase system there are two single- 
phase alternating currents bearing a definite time relation to each other 
and represented by two sine curves (Fig. 208). 
The two separate currents may be generated by 
the same or by separate machines. If by sepa- 
rate machines, the armatures of the two should 
be positively coupled together. Two-phase cur- 
rents are usually generated by a machine with 
two armature windings, each winding termi- 
nating in two collector rings. The two windings 
are so related that the two currents will be 90° 
apart. For this reason two phase-currents are also called " quarter- 
phase " currents. 

Two-phase currents may be distributed on either three or four wires. 
The three- wire system of distribution is shown in Fig. 209. One of the 
return wires is dispensed with, connection being made across to the other 
as shown. The common return wire should be made 1.41 times the area 
of either of the other two wires, these two being equal in size. 




Fig. 208. 



ALTERNATING CURRENTS. 



1395 



The four-wire system of distribution is shown in Fig. 210. The two 
phases are entirely independent, and for lighting purposes may be operated 
as two single-phase circuits. 




g ^txro ; (S^^QQQQa 



Fig. 209. 



Fig. 210. 



2. Three-phase Currents. — Three-phase currents consist of three alter- 
nating currents, differing in phase by 120°, and represented by three sine 
curves, as in Fig. 211. They may be distributed by three or six wires. If 
distributed by the six-wire system, it is analogous to the four-wire, two- 
phase system, and is equivalent to three single-phase circuits. In the 
three-wire system of distribution the circuits may be connected in two 
different ways, known respectively as the Y or star connection, and the A 
(delta) or mesh connection. 



^ffiffiffi. 




Fig. 211. 



Fig. 212. 



The Y connection is shown in Fig. 212. The three circuits are joined 
at the point o, known as the neutral point, and the three wires carrying the 
current are connected at the points a, b, and c, respectively. If the three 
circuits ao, bo, and co are composed of lights, they must be equally loaded 
or the lights will fluctuate. If the three circuits are perfectly balanced, 
the lights will remain steady. In this form of connection each wire may 
be considered as the return wire for the other 
two. If the three circuits are unbalanced, a 
return wire may be run from the neutral point 
o to the neutral point of the armature wind- 
ing on the generator. The system will then 
be four-wire, and will work properly with un- 
balanced circuits. 

The A connection is shown in Fig. 213. 
Each of the three circuits ab, ac, be, receives 
the current due to a separate coil in the arma- 
ture winding. This form of connection will , 
work properly even if the circuits are unbal- 
anced; and if the circuit contains lamps, they 
will not fluctuate when the circuit changes 
from a balanced to an unbalanced condition, 
or vice versa. 

Measurement of Power in Polyphase Circuits. — 1. Two-phase 
Circuits. — The power of two-phase currents distributed by four wires 
may be measured by two wattmeters introduced into the circuit as shown 
in Fig. 210. The sum of the readings of the two instruments is the total 
power. If but one wattmeter is available, it should be introduced first in 
one circuit, and then in the other. If the current or e.m.f. does not vary 
during the operation, the result will be correct. If the circuits are per- 
fectly balanced, twice the reading of one wattmeter will be the total power. 




Fig. 213. 



1396 



ELECTRICAL ENGINEERING. 



The power of two-phase currents distributed by three wires may oe 
measured by two wattmeters as shown in Fig. 209. The sum of the two 
readings is the total power. If but one wattmeter is available, the coarse- 
wire coil should be connected in series with the wire e/and one extremity 
of the pressure-coil should be connected to some point on ef. The other 
end should be connected first to the wire a and then to the wire d, a read- 
ing being taken in each position of the wire. The sum of the readings 
gives the power in the circuits. 

2. Three-phase Circuits. — The power in a three-phase circuit may be 
measured by three wattmeters, connected as in Fig. 214 if the system is 
Y-connected, and as in Fig. 215 if the system is A-connected. The sum of 





Fig. 214. 



Fig. 215. 



the wattmeter readings gives the power in the system. If the circuits are 
perfectly balanced, three times the reading of one wattmeter is the total 
power. 

The power in a A-connected system may be measured by two watt- 
meters, as shown in Fig. 216. If the power factor of the system is greater 
than 0.50, the arithmetical sum of the readings is the power in the circuit. 
If the power factor is less than 0.50, the arithmetical difference of the 
readings is the power. Whether the power factor is greater or less than 
0.50 may be discovered by interchanging the wattmeters without dis- 
turbing the relative connection of their coarse- and fine-wire coils. If the 
deflections of the needles are reversed, 
the difference of the readings is the 
power. If the needles are deflected in 
the same direction as at first, the sum of 
the readings is the power. 

Alternating-current Generators. — 
These differ little from direct current 
generators in many respects. Any direct- 
current generator, if provided with col- 
lector rings instead of a commutator, 
could be used as a single-phase alternator. 
The frequency would in most cases, how- 
ever, be too low for any practical use. 
The fields of alternators are always 
separately excited; the machines are 
sometimes compounded by shunting some of their own current around the 
fields through a rectifying device which changes the current to pulsating 
direct current. In all large machines the armature is stationary and the 
field magnets Tevolve. 




Fig. 216. 



ALTERNATING-CURRENT CIRCUITS. 

Calculation of Alternating-current Circuits. — The following 
formulae and tables are issued by the General Electric Co. They afford a 
convenient method of calculating the sizes of conductors for, and determin- 
ing the losses in, alternating-current circuits. They apply only to circuits 
in which the conductors are spaced 18 inches apart, but a slight increase 
or decrease in this distance does not alter the figures appreciably. If 
the conductors are less than 18 inches apart, the loss of voltage is de- 
creased, and vice versa. 






ALTERNATING-CURRENT CIRCUITS. 



1397 



Let W = total power delivered In watts: 

D = distance of transmission (one way) In feet; 

p* = per cent loss of delivered power ( W) ; 

E' = voltage between main conductors at consumer's end of circuit; 

K = a constant; for continuous current = 2160; 

T = a variable depending on the system and nature of the load; for 

continuous current = 1; 
M = a variable, depending on the size of wire and frequency; for con- 
tinuous current =1; 
A = a factor; for continuous current = 6.04. 



Area of conductor, circular mils = 



DX WXK. 



PXE* 

Current in main conductors = W X T -s- E 
Volts lost in lines = PXEXM -f- 100; 
D*X WX KX A 



Pounds copper = 



P X E* X 1,000,000 



The following tables give values for the various constants: 







Values 'or M — Wires 18 In. Apart.* 










,-—25 Cycles - 




, 40 Cycles * 


, 60 Cycles - 






125 Cycles — » 


Factors— 


.95 .90 .85 


.80 


95 .90 .85 80 


95 .90 .85 


80 


.95 


.90 .85 80 
















0000 


1.17 1 16 1.12 


1 (M. 


1.32 1.36 1.36 1 32 


1.53 1/64 1.67 




2 21 


2 54 .2.72 2.76 
2 22.2 34 2:37 


000 


1 12 1.09 1 05 


99 


1.24 1.26- 1.24 1.19 


1 41 1 49 1 ,50 


1 47 


1.97 


00 


108 1.0,4 99 


97 


1 18 1 18 1.14 1.09 


1.32 1 36; 1.35 


1 11 


1 77 


1 96 2.04 2.04 





1.05 1.00 94 


a? 


1 13 1 II 1.06 1.01 


1.24 1.26 1.24 


1 19 


1.61 


1.74 -180 1.79 


1 


1 .02 .96 .90 


81 


1.09 1 05 1 00 .94 


1.18 1 17 1.14 


1 ,)H 


1 47 


1.57 1 59 1.56 


2 


1.00 .93 .86 


79 


1 .05 1 01 .,95 ,88 


1.12 1.10 1 06 


1 (HI 


1.37 


1 42 1 42 1 39 


3 


98 .91 .84 


M 


1.02 .97 .90 83 


1.08 1.05 .99 


91 


1 27 


1 30 1 28 t 24 




.96 ,89 .81 


74 


100 .94 .86 .80 


1.05 1.00- .94 


.87 


1 20 


1 21 1 18 1 13 


5 


.95 .88 .80 


77, 


.98 ;92 .84 .77 


1 .02 .97 .90 


Hi 


1.15 


1.13 1 09 1 03 


* 


,94 .86 .78 


7(1 


97 .90 .82 .74 


1 00 94 .87 


79 


1.10 


1.07 1.02 .96 


7 


.94 .85 .77 


69 


.95 .88 .80 .72 


98 ..91 .84 


76 


1 06 


1.02 .96 „90 


8 


.93 .85 .76 


AH 


94 .87 .79 ,71 


.97 .89 .82 


74 


1 03 


.98 .92' 85 


<> 


.92 .84 .76 


6/ 


94 .86 .77 .69 


.95 ,88 .801 


7? 


1 01 


.95 .88 81 


10 


.92 .83. .75 


.67 


,93 .85 .76 .68- 


.94- .86. .79 


.71 


.99 


.92 .85 .78 




Wires 36 in. Apart, t 


'■ JT-(.+i*a.«)«*r«. 






0000 


1.22 1.23 1.20 


\ 15 






000 
00 



1.16 1.15 111 
III 1.08 I-.04 
1.07 1.03 .98 


1.05 
.97 
91 


X ■= Reactance. 

ft, = Resistance, ohms per 1 000 ft. at 60° F. (Wire 100% 

Matthiessen's standard.) 


1 

2 


104 .99 .93 

1 02 .95 89 


86 
.82 


X = 0.000882 [logio 0) + 0.109 J 








t For higher volt- 
ages. 10.000-200,000. 


/ 


= inches between wire 
= radius of wire.rtnche 
= cycles per sec. 


Sj 





Per cent of 


Value of K. 


Value of T. 


<0 ' 

3-3 


Power Factor. 


100 


95 1 85 


80 


100 


95 


85 


80 




System: 


2160 
1080 
1080 


2400 
1200 
1200 


3000 
1500 
1500 


3380 
1690 
1690 


1.00 
0.50 
0.58 


1.05 
0.53 
61 


1.17 
0.59 
68 


1.25 
0.62 
7? 


6 04 




12.08 


Three-phase, 3-wire 


9 06 













*P should be expressed as a whole number, not as a decimal; thus a 5 
per cent loss should be written 5 and not .05. 



1398 



ELECTRICAL ENGINEERING 



Relative Weight of Copper Required ill Different Systems for 
Equal Effective Voltages, 

Direct current, ordinary two-wire system 1.000 

** three-wire system, all wires same size 0.375 

. ' . " ". " " neutral one-half size 0.313 

Alternating current, single-phase two-wire, and two-phase four-wire. 1 . 000 
Two-phase three-wire, voltage between outer and middle 'wire same 

as in single-phase two-wire . 729 

._, voltage between two outer wires same 1 .457 

Three-phase three-wire 0.750 

" " m four-wire 0.333 

The weight of copper is inversely proportional to the squares of the 
voltages, other things being equal. The maximum value of an alternating 
e.m.f. is 1.41 times its effective rating. For derivation of the above figures 
see Crocker's Electric Lighting, vol. ii. 

Approximate Rule for Size of Wires for Three-Phase Transmission 
Lines. (General Electric Co.) 

The table given below is for use in making rough estimates for the sizes 
of wires for three-phase transmission, as in the following example. 

Required. — The size of wires to deliver 500 Kw. at 6000 volts, at the 
end of a three-phase line 12 miles long, allowing an energy loss of 10% 
and a power factor of 85%. If the example called for the transmission o£ 
100 Kw. (on which the table is based), we should look in the 6000- volt 
column for the nearest figure to the given distance, and take the size of wire 
corresponding. But the example calls for the transmission of five times 
this amount of power, and the size of wire varies directly as the distance, 
which in this case is 12 miles. Therefore we look for the product 5 X 12 = 
60 in the 6000-volt column of the table. The nearest value is 60.44 and 
the size of wire corresponding is No. 00. which is, therefore, the size capable 
of transmitting 100 Kw. over a line 60.44 miles long, or 500 Kw. over a 
lln ® \ 2 miles long, as required by the example. 

, *! *£ ls desired to ascertain the size of wire which will give an energy loss 
of 5%, or one-half the loss for which the table is computed, it is only 
necessary to multiply the value obtained by 2, since the area varies in- 
versely as the per cent energy loss 

di3tance9 to which 100 kw. three-phas3 current can be transmitted over dlffer- 
ent'Sizes of Wires at Deferent Potentiaxs, Assummimg an Enefgt Loss Of 10% 
and A Power Factor of 85% 



Num- 
1 ber 
B.&S. 


Circular 
Mils. 


Distance of Transmission for Various Potentials 


at Receiving End, in feet 


2.000 


3,000 


4.000 


5.000 


6.000 


8,000 


10.Q00 | 12,000 


15.000 


20,000 


25,000 


30,000 


6 
9 
4 


26,250 
33JOO 
41.740 


1 32 

1 66 
2.10 


2.98 
3.75 
4.74 


5.28 
8.40 


8 27 
10.40 
13 15 


11 92 
15.00 
18.96 


21.12 
26.56 
33.60 


33 1 

41.6 
52.6 


47 68 
60 00 
75 84 


74 50 
93 75 
118.50 


132 4 
166.4 
210.4 


206 75 
260 00 
328 75 


298 
375 
474 


3 

2 
1 


52,630 
66,370 
83,690 


2.54 
3 33 
4.21 


5.96 
7.51 
9 48 


10.16 
13.32 
16,84 


16.55 
20.85 
26 32 


23.84 
30 04 
37.92 


40.64 
53 28 
67.36 


66.2 
83.4 
HJ5.3 


95 36 
120.16 
151.6* 


149 00 
187.75 
212.00 


254.8 
333 6 
421.2 


413 75 

521.25 
658.00 


596 
751 
948 




00 
( 000 


105,500 
133,100 
.167,800 


5.29 
6 71 
8.45 


11 92 
15.11 
19 04, 


21.16 
26 84 
33 80 


33 10 
41 97 
52 85 


47 68 
60.44 
76.16 


84.64 

107 36 
135.20 


132 4 
167 9 
211.4 


191 72 
241 76 
304.64 


298 00 
377 75 
476.00 


529 6 
671 6 
845.6 


827 50 
1049.25 
1321 25 


1192 
1511 
1904 


,0000 


211.600 
250.000 
500,000 


10 62 23 92 
12.58 28.33 
25.17 56 66 


42 48 
50 32 
100 68 


66 42 
78.67 
157 35 


95.68 
113 32 
226 64 


169.92 

201 28 
402 72 


265 7 
314 7 
629 4 


382 72 
453 28 
906 56 


598.00 
708,25 
I4I6 1 50 


1062 8 
1258 8 
2517 6 


1660.50 
1966 75 
3933 75 


2392 
2833 
5666 



Notes on High-tension Transmission. (General Electric Co., 1909.)- 
The cross-sectional area and, consequently, weight of conductors varies 
inversely as the square of the voltage for a given power transmission. 
The cost of conductors is therefore reduced 75% every time the voltage 
is doubled. The cost of other apparatus and appliances increases with, 
increasing voltage. In the longest lines, from about 190 miles up, the 
saving in copper with the highest practicable voltages is so great that the 



ALTERNATING-CURRENT CIRCUITS. 



1399 



other expenses are rendered practically negligible. In the shorter lines, 
however, from about one mile to 60 or 75 miles, the most suitable voltage 
must be determined in each individual case. The voltages in the follow- 
ing table will serve as a guide. 

Voltages Advisable for Various Line Lengths. 



Miles. 


Volts. 


Miles. 


Volts. 


Miles. 


Volts. 


1 

1-2 
2-3 


500-1000 
1000-2300 
2300-6600 


3-10 
10-15 
15-20 


6,600-13,200 
13,200-22,000 
22,000-44,000 


20-40 
40-60 
60-100 


44,000- 66,000 
66,000- 88,000 
88,000-110,000 



Standard machinery is made for 2300, 6600, 13,200, 22,000, 33,000, 
44,000, 66,000, 88,000 and 110,000 volts, and standard generators are 
made for the above voltages up to and including 13,200 volts. When 
the line voltage is higher than 13,200, step-up transformers must be 
employed. In a given case the saving in cost of conductor by using the 
higher voltage may be more than offset by the cost of transformers, and 
the question of voltage must be determined for each case. 

Line Spacing. — Line conductors should be so spaced as to lessen the 
tendency to leakage and to prevent the wires from swinging together 
or against the towers. With suspended disk insulators the radius of free 
movement is increased, and special account should be taken of spacing 
when these insulators are used. The spacing should be only sufficient 
for safety, since increased spacing increases the self-induction of the line, 
and while it lessens the capacity, it does so only in a slight degree. The 
following spacing is in accordance with average practice. 

Conductor Spacing Advisable for Various Voltages. 



Volts. 


Inches. 


Volts. 


Inches. 


Volts. 


Inches. 


5,000 
15,000 
30,000 


28 
40 
48 


45,000 
60,000 
75,000 


60 

72 
84 


90,000 
105,000 
120,000 


96 
108 
120 



Skin Effects. — For the frequencies and sizes of cables used In trans- 
mission lines, skin effect does not appreciably alter the resistance; for 
example, the resistance of a solid copper wire 3/ 4 in. diameter at 60 cycles 
is increased only 21/2%, the resistance of a stranded cable of the same 
external diameter being increased a still smaller amount. This refers 
only to non-magnetic materials; with steel cable skin effect cannot be 
neglected, and a calculation must be made for it. 

Frequency. — So far as the transmission line alone is concerned, the 
lower frequencies are the more desirable, because they reduce the in- 
ductance drop and charging current. Oscillations of dangerous magni- 
tude are less likely with the lower frequencies than with the higher. The 
A.I.E.E. recognizes two frequencies, viz: 25 and 60, as standard, but 
frequencies of 15 and in some cases 12.5 are being advocated. 

Aluminum Conductors. — The conductivity of aluminum is generally 
taken at 63.3% that of hard-drawn copper of the same cross-sectional 
area. The weight of Al is 30.2% that of copper, and therefore an Al 
conductor of the same length and conductivity as a given copper con- 
ductor weighs 47.7% as much. The cost of Al must therefore be 2.097 
times that of hard-drawn copper to give equal cost for the same length 
and conductivity. Owing to the mechanical unreliability of solid Al 
conductors, stranded conductors are used in all sizes, including even the 
smallest. 



1400 



ELECTRICAL ENGINEERING. 



«100 VoltT*] k-100 Voft 



100 Turns 



100 Turns 

MJULX 



innywoinri 

86 Turns 



(70 o qOooo" 

100 Tunu 



^60 Volts- 



U 



-50 Vr- 



-60 Volts- 



Fig. 217. 



TRANSFORMERS, CONVERTERS, ETC. 

Transformers. — A transformer consists essentially of two coils of wire, 
one coarse and one fine, wound upon an iron core. The function of a trans- 
former is to convert electrical energy from one potential to another. If 
the transformer causes a change from high to low voltage, it is known as a 
" step-down " transformer; if from low to high 
voltage, it is known as a " step-up " trans- 
former. 

The relation of the primary and secondary vol- 
tages depends on the number of turns in the two 
coils. Transformers may also be used to change 
current of one phase to current of another phase. 
The windings and the arrangement of the trans- 
formers must be*adapted to each particular case. 
In Fig. 217 an arrangement is shown whereby 
two-phase currents may be converted into three- 
phase. Two transformers are required, one 
having its primary and secondary coils in the 
relation of 100 to 100, and the other having its 
primary and secondary in the relation of 100 
to 86. The secondary of the 100-to-100 trans- 
former is tapped at its middle point and joined to one terminal of the 
other secondary. Between any pair of the three remaining terminals of 
the secondaries there will exist a difference of potential of 50. 

There are two sources of loss in the transformer, viz., the copper loss and 
the iron loss. The copper loss is proportional to the square of the current, 
being the PR loss due to heat. If It, Ri, be the current and resistance 
respectively of the primary, and I 2 , R2, the current and resistance respec- 
tively of the secondary, then the total copper loss is W c =It 2 Rt +/ 2 2 ^2 and 

the percentage of copper loss is — — ^sr~^ — " » wnere W p is the energy 

delivered to the primary. The iron loss is constant at all loads, and is 
due to hysteresis and eddy currents. 

Transformers are sometimes cooled by means of forced air or water cur- 
rents or by immersing them in oil, which tends to equalize the temperature 
in all parts of the transformer. 

Efficiency of Transformers. — The efficiency of a transformer is the ratio 
of the output in watts at the secondary terminals to the input at the 
primary terminals. At full load the output is equal to the input less the 
iron and copper losses. The full-load efficiency of a transformer is usually 
very high, being from 92 per cent to 98 per cent. As the copper loss varies 
as the square of the load, the efficiency of a transformer varies consider- 
ably at different loads. Transformers on lighting circuits usually operate 
at full load but a very small part of the day, though they use some current 
all the time to supply the iron losses. For transformers operated only a 
part of the time the " all-day " efficiency is more important than the full- 
load efficiency. It is computed by comparing the watt-hours output to 
the watt-hours input. 

The all-day efficiency of a 10-K.W. transformer, whose copper and iron 
losses at full load are each 1.5 per cent, and which operates 3 hours at full 
load, 2 hours at half load, and 19 hours at no load, is computed as follows: 

Iron loss, all loads = 10 X 0.015 = 0.15 K.W. 

Copper loss, full load = 10 X 0.015 = 0.15K.W. 

Copper loss, 1/2 load = 0. 15 X (V2) 2 = 0.0375 K.W. 

Iron loss K. W. hours = 0. 15 X24 = 3.6. 

Copper loss, full load, K. W. hours = 0. 15 X3 = 0.45. 

Copper loss, 1/2 load, K.W. hours = 0.0375 X2= 0.075. 

Output, K.W. hours =H (10 X3) +(5 X2) }-=40. 

Input, K.W. hours = 40+3.6+0.45+0.075 = 44.125. 

All-day efficiency = 40 -5- 44. 125 = 0.907. 
The transformers heretofore discussed are constant-potential trans- 
formers and operate at a constant voltage with a variable current. For 
the operation of lamps in series a constant-current transformer is required. 
There are a number of types of this transformer. That manufactured by 
the General Electric Co. operates by causing the primary and secondary 
coils to approach or to separate on any change in the current. 



ELECTRIC MOTORS. 1401 

Converters, etc. — In addition to static transformers, various ma- 
chines arc used for the purpose of changing the voltage of direct currents 
or the voltage phase or frequency of alternating currents, and also for 
changing alternating currents to direct or vice versa. These machines are 
all rotary and are known as rotary converters, motor-dynamos, and 
dynamotors. 

A rotary converter consists of a field excited by the machine itself, and 
an armature which is provided with both collector rings and a commuta- 
tor. It receives direct current and changes it to alternating, working as a 
direct-current motor, or it changes alternating to direct current working 
as a synchronous motor. 

A motor-dynamo consists of a motor and a dynamo mounted on the 
same base and coupled together by a shaft. 

A dynamotor has one field and two armature windings on the same core. 
One winding performs the functions of a motor armature, and the other 
those of a dynamo armature. 

A booster is a machine inserted in series in a direct-current circuit to 
change its voltage. It may be driven either by an electric motor or other- 
wise. 

The Mercury Arc Rectifier consists of a mercury vapor arc enclosed 
in an exhausted glass vessel into which are sealed two terminal anodes 
connected to the two wires of an alternating-current circuit. A third 
terminal, at the bottom of the vessel, is a mercury cathode. When an 
arc is operating, it is a good conductor from either anode to the cathode, 
but practically an insulator in the other direction. The two anodes 
connected across the terminals of the alternating-current line become 
alternately positive and negative. While either anode is positive, there 
is an arc carrying the current between it and the cathode. When the 
polarity of the alternating-current reverses, the arc passes from the other 
anode to the mercury cathode, which is always negative. The current 
leading out from the mercury cathode is uni-directional. By means of 
reactances, the pulsations are smoothed out and the current at the cathode 
becomes a true direct current with pulsations of small amplitude. 

ELECTRIC MOTORS. 

Classification of Motors. — (From the Standardization Rules of 
the A. I, E. E.) 

a. Constant-speed Motors, in which the speed is either constant or does 
not materially vary; such as synchronous motors, induction motors with 
small slip, and ordinary direct-current shunt motors. 

b. Multi-speed Motors (two-speed, three-speed, etc.), which can be op- 
erated at any one of several distinct speeds, these speeds being practically 
independent of the load, such as motors with two armature windings. 

c. Adjustable-speed Motors, in which the speed can be varied gradually 
over a considerable range; but when once adjusted remains practically 
unaffected by the load, such as shunt motors designed for a considerable 
range of field variation. 

d. Varying-speed Motors, or motors in which the speed varies with the 
load, decreasing when the load increases; such as series motors. 

The selection of a motor for a specified service involves, 

a. Mechanical ability to develop the requisite torque and speeds, as 
given by its speed-torque curve. 

6. Ability to commutate successfully the current demanded. 

c. Ability to operate in service without occasioning a temperature rise 
in any part which will endanger the life of the insulation. 

The nominal rating, or the horse-power output which a motor can give 
with a rise of temperature not exceeding 90 degrees at the commutator 
and 75 degrees at any other part after an hour's run on a test stand is a 
method of designating motors which is in common usage, though it is 
not a proper measure of service capacity. 

Motor Classification of the Am. Assn. of Electric Motor Manu- 
facturers. (Elec. Jour., Aug. 1909.) — Alternating-current motors and 
direct-current motors can easily be classified under the same speed head- 
ings, and this has been done as below. 

A. — Constant Speed Motors — in which the speed is either constant 
or does not vary materially, such as synchronous motors, induction motors 
with small slip, ordinary direct-current shunt motors, and direct current 



1402 



ELECTRICAL ENGINEERING. 



compound-wound motors, the no-load speed of which is not more than 
20 per cent higher than the full-load speed. 

B. — Multi-Speed Motors — (two-speed, three-speed, etc.) — which can 
be operated at any one of several distinct speeds, these speeds being 
practically independent of the load, such as direct-current motors with 
two armature windings and induction motors with primary windings 
capable of being grouped so as to form different numbers of poles. 

C. — Adjustable Speed Motors. — - (1) Shunt-wound motors in which 
the speed can be varied gradually over a considerable range, but when 
once adjusted remains practically unaffected by the load, such as motors 
designed for a considerable range of speed by field variation. 

(2) Compound-wound motors in which the speed can be varied 
gradually over a considerable range, as in (1), and, when once adjusted, 
varies with the load, similar to compound-wound constant-speed motors 
or varying-speed motors, depending upon the percentage of compounding. 

D. — ■ Varying Speed Motors, or motors in which the speed varies with 
the load, decreasing when the load increases, such as series motors and 
heavily compounded motors. Examples of heavily compounded motors 
are those designed for bending roll service and mill service, in which 
shunt-winding is provided only to limit the light-load operating speed. 

Many motor applications can be made more intelligently if, in addition 
to using the classification given above, the service is described in terms of 
continuous or intermittent duty, and load constant or varying. In order 
to make this point clear, the following table has been prepared, giving 
one example of each of the different classes of service. Practically every 
motor application can be listed under one or the other of these headings. 



Classification of Motors. 



Constant. 
Adjustable. 
Varying. 
Multi-speed. 



Duty. 

Continuous. 

Intermittent. 

Continuous. 

Intermittent. 

Continuous. 

Intermittent. 

Continuous. 

Intermittent. 



Load. 

{Constant. 
Varying. 
{Constant. 
Varying. 
( Constant. 
\ Varying. 
| Constant. 
( Varying. 
| Constant. 
( Varying. 
( Constant. 
1 Varying. 
| Constant. 
I Varying. 

{Constant. 
Varying. 



Example. 

Fan. 

Line-shaft. 
Vacuum pump. 
Paper-cutter. 
Paper calender. 
Printing press. 
Vacuum pump. 
Lathe. 
Small fan. 
Bending press. 
House pump. 
Crane. 
Fan. 
* 

Fire pump. 



The Auxiliary-pole Type of Motor. (J. M. Hippie, El. Jour., May, 
1906.) — 

Among the methods of controlling the motor speed, the most satis- 
factory is the single voltage direct-current system in which the variation 
of speed is obtained by. shunt-field control. The insertion of resistance 
in the shunt-field circuit varies the strength of the magnetic field, and as 
the strength of field is decreased the speed of the motor is increased in 
direct proportion. 

An ordinary shunt- wound motor operating under the above conditions 
over a speed range of four to one will spark excessively at the brushes 
unless the motor is rated considerably under its normal capacity. This 
sparking is due principally to the weakened magnetic field and to the 
distortion or shifting of this field due to reaction on it by the field produced 
by the ampere turns in the armature. 

The use of an auxiliary field by correcting this condition produces 



*Multi-speed motors are at present almost exclusively alternating- 
current motors. The classes of service in which these motors are used are 
limited, but a considerable field may develop later. 



ELECTRIC MOTORS. 1403 



sparkless commutation and a condition of practical stability of field and 
consequently of speed in the motor. This auxiliary field is produced by 
a winding in series with the armature and placed on pole-pieces midway 
between the main pole-pieces. The distortion at the point of commuta- 
tion which would occur if there was no auxiliary winding is prevented by 
the field produced by the auxiliary winding. This field being always 
proportional to the load the commutation is accomplished sparkle, sly at 
all loads up to heavy overloads. 

Motors of this type are reversible with no change in setting of brushes 
or other adjustment. The brushes being fixed in the neutral position it 
is only necessary to reverse the current in both auxiliary field and arma- 
ture to secure exactly similar operating conditions in the reverse as in the 
forward direction. 

Speed of Electric Motors. — Any direct-current motor, no matter 
what its type of field winding, if supplied with current of constant potential 
at its terminals, will run at constant speed if its field strength and the load 
do not change. The speed of a given motor is directly proportional 
to the net impressed e.m.f. divided by the effective field strength. The 
net impressed e.m.f. is that part of the supply e.m.f. which must be 
exactly opposed by the counter e.m.f. of the armature. Thus, if the 
supply voltage is 250 volts, the lead 50 amperes and the armature circuit 
resistance 0.2 ohm, the net impressed e.m.f. will be 240 volts, because the 
armature drop is 0.2 x50= 10 volts. The " effective " field strength Is 
the actual field flux set up by the fieid winding after overcoming the arma- 
ture reaction, which always weakens the field slightly. 

In the case of a shunt-wound motor operated on a constant-potential 
circuit with an adjustable external resistance in series with the armature, 
no matter at what point the external resistance may be set, so long as it 
remains at that point, giving unchanging voltage at the motor terminals, 
the speed will be constant unless the field strength or load be altered, 
The speed of a series-wound motor increases very rapidly with decreasing 
load when operated on a constant-potential circuit, becoming so high at 
no load as to be destructive to the armature. The reason for this is that 
the armature current passes also through the field winding, so that any 
decrease in armature current weakens the field and causes the speed to 
increase far beyond the rate it would attain with a constant field. (C.P. 
Poole, Power, July, 1907.) 

The speed of a shunt motor is dependent upon the details of its entire 
design. The following equation shows the relation of the speed to the 
main elements of the machine: 

(E-I a R a )c 10 8 

W= MpN ' 

where E is the impressed electromotive force, R a the resistance of the 
armature, I a the current through it, c the number of parallel circuits for 
the current through the armature, M the magnetic flux (number of lines 
of force) per pole, p the number of poles, N the number of armature con- 
ductors, and n the speed in revolutions per second. (El. Review, July 17, 
1909.) 

The simplest form cf an electric motor is the shunt-wound machine. 
When connected with an ordinary electric lighting circuit, it. runs at a 
steady speed, drawing hardly any current until it is required to furnish 
power, and at that moment it consumes power only in proportion to the 
work done. If connected to a circuit of lower pressure, it will run equally 
well, but at lower speed. If required to make extra effort, as in starting 
machinery, it will furnish up to five times its full power without trouble. 

When running free, if its speed is increased by the application of exter- 
nal power, as by a belt, it becomes a dynamo and pumps current into the 
line; this, in turn, throws work upon the machine and tends to slow it 
down. The machine is, therefore, in itself a factor tending to the pres- 
ervation of constancy of speed and to the preservation of constancy in 
the pressure on the circuit, and it is ideal in its simplicity, having abso- 
lutely no governing or accessory parts. 

The shunt-wound motor runs at practically constant speed under all 
loads, and if closer uniformity of speed is desired, it can be arranged to 
run within any desired limits of variation by setting the brushes in a 
position shifted slightly from their usual place, or by adding to the field 



1404 ELECTRICAL ENGINEERING. 

winding a few turns, connected in series with the armature, and reversed 
in comparison with the main winding. Either of these arrangements 
causes the motor to speed up under load, and the extent of this action 
may be adjusted to equal precisely the tendency ordinarily met of slowing 
down under load. (S. S. Wheeler, Elec. Age, Dec, 1904.) 

Speed Control of Electric Motors. Rheostats. (The Electric Con- 
troller and Mfg. Co.) — A motor of any size, when its armature is at rest, 
offers a very low resistance to the flow of current and an excessive and 
perhaps destructive current would flow through it if it were connected 
across the supply mains while at rest. Take the case of a motor adapted 
to a normal full-load current of 100 amperes and having a resistance of 
0.25 ohm; if this motor were connected across a 250- volt circuit a current 
of 1,000 amperes would flow through its armature — in other words, it 
would be overloaded 900% with consequent danger to ils windings and 
also to the driven machine. In the case of the same motor, with a rheostat 
having a resistance of 2.25 ohms inserted in the motor circuit, at the time 
of starting the total resistance to the flow of current would be the resist- 
ance of the motor (0.25 ohm) plus the resistance of the rheostat (2.25 
ohms), or a total of 2.5 ohms. Under these conditions exactly full-load 
current, or 100 amperes, would flow through the motor, and neither the 
motor nor the driven machine would be overstrained in starting. This 
shows the necessity of a rheostat for limiting the flow of current in starting 
the motor from rest. 

An electric motor is simply an inverted generator or dynamo — con- 
sequently when its armature begins to revolve a voltage is generated within 
its windings just as a voltage is generated in the windings of a generator 
when driven by a prime-mover. This voltage generated within the moving 
armature of a motor opposes the voltage of the circuit from which the 
motor is supplied, and hence is known as a " counter-electromotive force." 
The net voltage tending to force current through the armature of a motor 
when the motor is running is, therefore, the line voltage minus the counter- 
electromotive force. 

In the case of the motor above cited, when the armature reaches such 
a speed that a voltage of 125 is generated within its windings, the effective 
voltage will be 250 minus 125, or 125 volts, and, therefore, the resistance 
of the rheostat may be reduced to one ohm without exceeding the full- 
load current of the motor. As the armature further increases its speed 
the resistance of the rheostat may be further reduced until when the motor 
has almost reached full speed all of the rheostat may be cut out, and the 
counter-electromotive force generated by the motor will almost equal 
the voltage supplied by the line so that an excessive current cannot flow 
through the armature. 

In practice, a rheostat is provided for starting an electric motor, the 
resistance conductor being divided into sections, such that the entire 
length or maximum resistance of the rheostat is in circuit with the motor 
at the instant of starting and the effective length of the conductor, and 
hence its resistance may be reduced as the motor comes up to speed. 

In cutting out the resistance of a starting rheostat care must be used 
not to cut it out too rapidly. If the resistance is cut out more rapidly 
than the armature can speed up-, a sufficient counter-electromotive force 
will not be generated to properly oppose the flow of current, and the 
motor will be overloaded. 

If all the resistance of the starting rheostat is not cut out the motor will 
operate at reduced voltage, and hence at less than normal speed. A 
rheostat so arranged that all or a portion of its resistance may be left in 
a motor circuit to secure reduced speeds is called a " rheostatic controller." 
Such rheostatic controllers are used for controlling series and compound- 
wound motors driving cranes, and similar machinery requiring variable 
speed under the control of an operator. 

In a series- wound motor the speed varies inversely as the load — the 
lighter the load the higher the speed. A series-wound motor of any size 
when supplied with full voltage under no load, or a very light load, will 
" run, away " just as will a steam-engine without a governor when given 
an open throttle. 

For a given load a series-wound motor draws the same current irrespec- 
tive of the speed and for a given load the speed varies directly as the volt- 
age. The speed at a given load may be varied by varying the resistance 



ELECTRIC MOTORS. 1405 



in the motor circuit — in the meantime if the load on the motor be con- 
stant the current drawn from the line will be constant regardless of the 



The above statements relate to the use of a rheostat in series with a 
series-wound motor. If a resistance or rheostat be placed in parallel 
with the field of a series- wound motor the speed will be increased instead 
of decreased at a given load. This is known as shunting the field of the 
motor. This shunt would never be applied till the motor has been brought 
up to normal full speed by cutting out the starting resistance. With a 
" shunted field " a motor is driving a load at a speed higher than normal 
and therefore requires a correspondingly increased current. 

If a resistance is placed in parallel with the armature of a series motor, 
the motor will operate at less than normal speed when all of the starting 
resistance has been cut out. This connection is known as a " shunted 
armature connection " and is useful where a low speed is desired at light 
loads and is particularly useful in some cases where the load becomes a 
negative one, that is, where the load tends to overhaul the motor, as in 
lowering a heavy weight. 

A shunt-wound motor, unlike a series motor, when supplied with full 
voltage, maintains practically a constant speed regardless of variations in 
load within the limits of its capacity. It automatically acts like a steam- 
engine having a very efficient governor. 

The speed of a shunt-wound motor may be decreased below normal by 
a rheostatic controller in series with its armature and may be increased 
above normal by means of a rheostat in series with its field winding. The 
latter rheostat is known as a " field rheostat," and, to be effective, must 
have a high resistance owing to the small current which flows through the 
shunt-field winding. 

A compound-wound motor is a hybrid between a series and shunt- 
wound motor and its characteristics are likewise of a hybrid nature. 

A compound-wound motor will not " run away " under no load as will 
a series motor, but its speed decreases as the load increases, though not 
so rapidly as is the case with a series-wound motor. 

The characteristics of a compound-wound motor are particularly valu- 
able in cases where the load is subject to wide variation. It will give a 
strong torque in starting and driving heavy loads and at the same time 
will not race dangerously when the load is suddenly relieved. 

The speed of a compound-wound motor may be reduced below normal 
by means of a rheostat in the circuit of its armature. The speed may be 
increased above normal by shunting and even short-circuiting the series 
field winding, and may be still further increased by means of a field rheostat 
in series with the shunt-field winding. 

Rheostatic controllers are also employed for the control of alternating 
current induction motors of the so-called " slip-ring type." Such motors 
have characteristics in many ways similar to those of direct current shunt- 
wound motors, and speeds lower than normal may be obtained by insert- 
ing resistance in series with the windings of the secondary or rotor. 

Selection of Motors for Different Kinds of Service. (F. B. Crocker 
and M. Arendt, El. World, Nov., 1907.)— The types of direct-current 
motor are as follows: 

DIRECT-CURRENT MOTORS. 

Type. Operative Characteristics. 

Shunt-wound motors Starting torque usuallv 50 to 100 per cent 

greater than rated running torque, and 

fairly constant speed over wide load 

ranges. 
Series-wound motors Powerful starting torque, speed varying 

greatly (inversely) with load changes. 
Compound-wound motors.. . .Compromise between shunt and series 

types. 
Differently-wound motors ...Starting torque very small, speed can be 

made almost absolutely constant for load 

changes within rated capacity. 

The conditions under which machinery operates, in regard to varying 
speed and power required of the driving motor, may be divided into four 



1406 ELECTRICAL ENGINEERING. 



classes, and certain types of motors are usually best suited to these divi- 
sions, which are as follows: 

(a) Work which requires the motor to operate automatically at a 
practically constant speed, regardless of load changes or other conditions. 

(6) Work requiring frequent starting and stopping and wide varia- 
tions in speed, including sometimes rapid acceleration. 

(c) An approximately steady load or work that varies as some function 
of the speed should it change. 

(d) Work in which the power varies regardless of the speed, or where 
speed variations with constant torque may be desired. 

The first case (a) applies to line-shaft equipments with many machines 
operated by the same motor and where slight speed variations may be 
allowed; the direct-current shunt or slightly compounded motor or the 
alternating-current induction motor would answer, depending upon the 
character of electric current available. A refinement of this problem is 
encountered in the driving of textile machinery, especially silk looms, with 
which even a slight speed variation might affect the appearance of the 
finished product. In such instances the alternating-current. motors, poly- 
phase induction or polyphase synchronous, are generally employed be- 
cause the speed of direct r current motors varies considerably with voltage 
changes and the variation in temperature which occurs after several hours 
of operation, whereas the speed of the alternating-current motors, unless 
the voltage varies greatly, is primarily dependent upon the frequency 
of the supplied current. 

The second class (b) is divided into two parts, the first being electric 
traction and crane service, in which the motor is frequently started and 
stopped and rapidly accelerated at starting; or where the speed is to be 
adjusted automatically to the load, slowing down when heavily loaded 
or climbing a steep grade. These conditions are well satisfied by the 
series motor of either the direct or alternating-current types, depending 
upon the current supplied. Elevator service is of this character as regards 
frequent starting and stopping, but after rapid acceleration it calls for 
a speed independent of the load. Hence, to fulfill both requirements, 
elevator motors when of direct-current type are heavily over-compounded 
to give the series characteristic at starting; then, when the motor is up 
to speed, the series field winding is short-circuited and it operates as a 
shunt machine. Recently, however, two-speed shunt motors have been 
employed for this service, the field being of maximum strength for start- 
ing and sparking prevented by use of inter-poles. If only alternating 
current is available the polyphase induction motor should be employed, 
but for powerful starting torque either slip-ring or compensator control 
would be necessary. For the second subdivision of this clr.ss the motor 
must be started and stopped frequently and not rapidly accelerated, but 
on the contrary simply " inched " forward at the start, as in the operation 
of printing presses, gun turrets, etc. These conditions of service are 
satisfied by a direct-current compound motor provided with double 
armature and series-parallel control of the machine. 

The third class (c) of work is the operation of pumps, fans or blower 
equipments and its requirements are satisfied by the series motor, whose 
speed adjusts itself to the work, and also because it exerts the maximum 
torque required at starting. It must be, however, either geared or directly 
connected to the apparatus, because the breaking of the belt or the sudden 
removal of the load would cause a series motor to race and become injured. 
The operation of pumps by electric motors is usually effected by gearing, 
since ordinary plunger pumps do not operate efficiently if driven in excess 
of fifty strokes per minute, and to accomplish this by direct connection 
would demand a very low speed and costly motor. Centrifugal pumps 
operating at high speed may be direct driven. 

The fourth class (d) is found in individual machine-tool service, for 
which the maximum allowable cutting or turning speed requires the 
number of revolutions of the work or tool to vary inversely as the diameter 
of the cut. This condition is satisfied best by the direct-current shunt or 
slightly compounded motors, as they are readily controlled in speed by 
variation of the applied voltage, shunt field weakening, etc. 

It is to be noted that (a) and (c) regulate automatically to maintain a 
constant speed while (6) and (d) are controlled by hand to give variable 
speeds. Furthermore, (6) is usually under control of the hand all the time, 



ELECTRIC MOTORS. 1407 

whereas (d) is set to operate at a desired speed for some time and regulates 
automatically when so adjusted. 

The Electric Drive in the Machine-Shop. (A. L. De Leeuw, 
Trans. A.S.M.E., 1909.) — Absence of reliable data is apparent all over 
the field of this subject, and it will therefore be impossible to say before- 
hand with any fair degree of certainty how much, if anything, can be 
gained by the conversion of a shop from a shaft to motor drive. 

Nothing but an exhaustive study of the entire plant in all its aspects 
will clearly show what may be accomplished. The saving of power is 
by no means the only nor the most important economy resulting from a 
conversion to electric drive, and such a conversion may even be highly 
economical, though there be an actual loss in power consumed. 

The question whether alternating or direct current should be used is 
especially difficult of solution, and there is a wide difference of opinion 
among engineers as to which is best. Given a plant covering a large area 
and using large amounts of current, of which only a small portion is used 
for variable-speed machinery, and of sufficient size to permit of the use of 
a separate unit for lighting current, then alternating current would be the 
logical solution. On the other hand, given a compact plant, using a large 
portion of the power for variable-speed machinery, direct-driven by mo- 
tors, and of which the lighting load is small in the daytime, then it would 
be natural to select direct current. As a rule, however, conditions are not 
so simple. Of late the problem has been complicated by the fact that 
many machine tools may be had with single-pulley drive, to which an 
alternating-current or a direct-current motor is equally applicable. 

The points in favor of the alternating-current motor are: 

a High break-down point; that is, the motor goes on with no material 
change of speed under very heavy overload. 

b Freedom from commutator trouble. This is especially valuable 
where fine chips are made, or where compressed air is used in connection 
with the machine. The better makes of direct-current motors are now 
equally free from this kind of trouble. 

c Most cities are now lighted by alternating current, so that city cur- 
rent can be used in smaller plants, provided the machine tools are arranged 
for this kind of motor. 

The points in favor of the direct-current motor are: 

a Wider air-gap, allowing a greater amount of wear in the bearings 
before the motor has to be repaired. 

b The possibility of power and lighting-loads on the same circuits with- 
out the poor regulation due to inductive load. 

c The possibility of using variable-speed motors. This is, perhaps, 
the greatest argument in favor of the direct-current motor. Though it is 
possible to run a great many machine tools by a motor, yet one of the 
greatest advantages of such a drive is not available, unless the motor is of 
the variable-speed variety. 

The combination of alternating and direct current has its advantages, 
especially where it is possible to purchase current from some large power 
company which delivers its product as alternating current. Transformers 
reduce the voltage at the entrance to the shop, and the low-voltage alter- 
nating current can be used for all purposes except for driving variable- 
speed motors, and perhaps some auxiliary apparatus such as magnetic 
clutches, lifting magnets, etc. 

See also papers on this subject by Chas. Robbins and John Riddell, 
Trans. A.S.M.E., 1910. 

Choice of Motors for Machine Tools. (Chas. Fair, Proc. A. I.E. E., 
1910.) — Shunt-wound direct-current, or squirrel-cage rotor, alternating 
current: For bolt cutter; boring machine; boring mill; boring bar; center- 
ing machine; chucking machine; boring, milling and drilling machines; 
drill, radial; drill press; grinder-tool, etc.; keyseater, milling-broach ; lathe; 
milling machine; pipe-cutter; saw, small circular; screw machine; tapper. 

Compound-wound direct-current, or squirrel-cage rotor: For grinder- 
castings; reciprocating keyseater; saw, cold bar and I-beam; saw, hot; 
shaper; slotter; tumbling barrel or mill. 

Compound-wound direct-current or squirrel-cage rotor, or squirrel- 
cage rotor with high starting torque: For bolt and rivet header; bulldozer; 
bending machine; corrugating roll; punch press; shear. 

Other machines may be driven as indicated below, (a) shunt, (&> 



1408 ELECTRICAL ENGINEERING. 

compound, (c) series, direct-current motors, (d) squirrel-cage rotor, 
(e) ditto, high starting torque, (/) slip ring induction motor with external 
rotor resistance. Raising and lowering cross rails oo boring mills and 
planers, (&), (c), (e). Bending rolls, (6), (c), (/). Gear cutters, (a), (b), 
(d). Drop hammers, (6), (e). Tire lathes, (/) may be used, as it allows 
for slowing down when cutting hard spots. Lathe carriages, (c), (e). 
Heavy slab milling, (a), (&), (d). Planers, (6), (d), (e). Planers, rotary, 
(«), (&), (d). Swaging, (b), (d), (e). Shunt motors are used in the follow- 
ing cases: when the work is of a fairly steady nature; when considerable 
range of adjustment of speed is required, as on lathes and boring mills; 
and on group and lineshaft drives, etc. 

Compound-wound motors are used where there are sudden calls for 
excessive power of short duration, as on planers, punch presses, etc. 

Series motors should be used where speed regulation is not essential 
and where excessive starting torque and slow starting speeds are required, 
as for operating cranes. 

When in doubt as to the choice of compound or series motors of small 
horse-power, the choice might be determined by the simplicity of control 
in favor of the series motor. Series motors, however, should never be 
used when the motor can run without load, as the speed would accelerate 
beyond the point of safety. 

The alternating current motor of the squirrel-cage rotor type corresponds | 
to the constant-speed, shunt, direct-current motor, but with a high-resist- 
ance rotor it approaches more closely the characteristics of a compound 
direct-current motor. Variable speed machines, driven by squirrel-cage 
rotors must have the necessary mechanical speed changes. 

The slip-ring induction motor with external rotor resistance would be 
used for variable speed, but this must not be construed to mean that it 
corresponds to a direct-current, adjustable-speed motor, as it has the 
characteristics of a direct-current shunt motor with armature control. 

The self-contained, rotor resistance type would be used for lineshaft 
drives, and for groups when of sufficient size. 

Multi-speed, alternating-current motors are those giving a number of 
definite speeds, usually 600 and .1200 or 600, 900, 1200 and 1800 rev. 
per min., and are made for both constant horse-power and constant 
torque. These motors would be used where alternating current only was 
available, or direct current limited; and the speed range of the motor, 
together with one or two change gears, would give the required speeds. 



ALTERNATING-CURRENT MOTORS. 

Synchronous Motors. — Any alternator may be used as a motor, pro- 
vided it be brought into synchronism with the generator supplying the cur- 
rent to it. The operation of the alternating-current motor and generator 
is similar to the operation of two generators in parallel. It is necessary to 
supply direct current to the field. The field circuit is left open until the ma- 
chine is in phase with the generator. If the motor has the same number of 
poles as the generator, it will run at the same speed; if a different number, 
the speed will be that of the generator multiplied by the ratio of the number 
of poles of the motor to that of the generator. Single-phase, synchronous 
motors are not self-starting. . Polyphase motors may be made self-starting, 
but it is better to bring the machines to speed by independent means before 
supplying the current. The machines may be started by a small induc- 
tion motor, the load on the synchronous motor being thrown off, or the 
field may be excited by a small direct-current generator belted to the 
motor, and this generator may be used as a motor to start the machine, 
current to run it being taken from a storage battery. If the field of a 
synchronous motor be properly regulated to the load, the motor will 
exercise no inductive effect on the line, and the power factor will be 1. If 
the load varies, the current in the motor will either lead or lag behind the 
e.m.f. and will vary the power factor. If the motor be overloaded so that 
there is a diminution of speed, the motor will fall out of step with the 
generator and stop. 




ALTERNATING-CURRENT MOTORS. 1409 

Synchronous motors are often put on the same circuit with induction 
motors. The synchronous motor in this case may, by increasing the field 
excitation, be made to cause the current to lead, while the induction motor 
will cause it to lag. The two effects will thus tend to balance each other 
and cause the power factor of the circuit to approach 1. 

Synchronous motors are best used for large units of power at high volt- 
ages, where the load is constant and the speed invariable. They are un- 
satisfactory where the required speed is variable and the load changes. 
Two great disadvantages of the synchronous motor are its inability to 
start under load and the necessity of direct-current excitation. 

Induction Motors. — The distinguishing feature of an induction motor 
is the rotating magnetic field. It is thus explained: In Fig. 218 let ab, cd 
be two pairs of poles of a motor, a and b being wound from one leg or pair 
of wires of a two-phase alternating circuit, and c and d from the other 
leg, the two-phases being 90° apart. At the instant when a and b are 
receiving maximum current so as to make a a north 
pole and b a south pole, c and d are demagnetized, and 
a needle placed between the poles would stand as 
shown in the cut. During the progress of the cycle of 
the current the magnetic flux at a decreases and that at 
c increases, causing the point of resultant maximum 
intensity to shift, and the needle to move clockwise 
toward c. A complete rotation of the resultant point 
is performed during each cycle of the current. An 
armature placed within the ring is caused to rotate sim- j> IG 218 

ply by the shifting of the magnetic field without the use 
of a collector ring. The words " rotating magnetic field " refer to an 
area of magnetic intensity and must be distinguished from the words 
" revolving field," which refer to the portion of the machine constituting 
the field magnet. 

The field or " primary " of an induction motor is that portion of the 
machine to which current is supplied from the outside circuit. 

The armature or " secondary " is that portion of the machine in which 
currents are induced by the rotating magnetic field. Either the primary 
or the secondary may revolve. In the more modern machines the second- 
ary revolves. The revolving part is called the " rotor," the stationary 
part the " stator." The rotor may be either of the ring or the drum type, 
the drum type being more common. A common type of armature is the 
" squirrel-cage." It consists of a number of copper bars placed on the 
armature-core and insulated from it. A copper ring at each end connects 
the bars. The field windings are always so arranged that more than one 
pair of poles are produced. This is necessary in order to bring the speed 
down to a practical limit. If but one pair of poles were produced, with a 
frequency of 60, the revolutions per minute would be 3600. 

The revolving part of an induction motor does not rotate as fast as the 
field, except at no load. When loaded, a slip is necessary, in order that the 
lines of force may cut the conductors in the rotor and induce currents 
therein. The current required for starting an induction motor of the squir- 
rel-cage type under full load is 7 or 8 times as great as the current for 
runningat full load. A type of induction motor known as " Form L," built 
by the General Electric Co., will start with the full-load current, provided 
the starting torque is not greater than the torque when running at full load. 

Induction motors should be run as near their normal primary e.m.f. as 
possible, as the output and torque are directly proportional to the square 
of the primary pressure. A machine which will carry an overload of 50 
per cent at normal e.m.f. will hardly carry its full load at 80 per cent of the 
normal e.m.f. 

Induction Motor Applications. (A. M. Dudley, Elec. Jour., July, 
1908.) Squirrel-Cage Motors for Constant Speed Service. — 

Motor-Generator Sets. — Small starting torque is required and good 
speed regulation, which characteristics are preeminently met by a squirrel- 
cage motor with very low resistance in the secondary rings. A fair speci- 
fication on a large set is that it shall start on 30 to 40% of full voltage, 
and draw current not in excess of IV4 times full-load current. 

Pumps. — With a centrifugal pump decreasing the head pumped against 
increases the load on the motor. This type of pump will raise considerably 
more than four-thirds the amount of water 30 feet that it will 40 feet, 
with the result that the motor is overloaded if it is designed for 40 ft. 



1410 



ELECTRICAL ENGINEERING. 



head. In this the centrifugal pump is exactly opposite to the plunger 
or reciprocating pump, which, being positive in its action, increases its 
load with increase of head and vice versa. [In some modern types of 
centrifugal pump the load decreases with decrease of head after reaching 
the maximum load corresponding to the head for which the pump is 
designed. See catalogue of the De Laval Steam Turbine Co., 1910. W. K.] 



Induction Motor Applications. 




Squirrel Cage. 


Phase- Wound . 


Constant Speed. 


Variable Speed. 


Constant Speed. 


Variable Speed. 


! —Motor-generator 


1 — Starting mo- 


1 — Flour mills. 


1 — Hoists and 


sets. 


tors. 


2 — Paper ma- 


winches . 


2— Pumps. 


2 — Crane motors 


chinery, pulp 


2 — Cranes. 


3 — Blowers. 


3— Fly-wheel 


grinders, 


3— Elevators. 


4 — Line-shaft drive. 


service. 


beaters. 


4— Fly-wheel mo- 


5 — Cement machin- 


Punches, 


3— Belt convey- 


tor-generator 


ery. 


Shears, etc. 


ors. 


sets. 


6 — Wood-working 


4 — Sugar centri- 


4 — Wood planers. 


5 — Steel mill ma- 


machinery (ex- 


fugals. 


5 — Air compress- 


chinery, charg- 


cept planers). 


5 — Laundry ex- 


ors. 


ing machines, 


7— Cotton-mill ma- 


tractors. 


6 — Line shafting. 
7 — Driving-wheel 


hoists. 


chinery. 


6 — Brake motors 


6 — Coal and ore 


8 — Paper machin- 


7— Cross-head 


lathes. 


unloaders. 


ery, calenders, 


motors. 




7 — Dredging ma- 


Jordan engines. 


8 — Valve motors. 




chinery. 


9 — Concrete mixers. 






8— Shovels. 

9 — Mine haulage. 



Blowers.— Rotary blowers, except positive blowers, have a charac- 
teristic similar to centrifugal pumps, in that the load varies with the 
amount of air delivered and becomes less as the pressure against which 
the blower is working increases. That is to say, the maximum load 
which could be put on a motor driving a blower of this nature would be to 
take away all delivery pipes and let the blower exhaust into the open air. 

Line Shafting. — Squirrel-cage motors are used very successfully 
for driving line-shafting where the idle belts are run on loose pulleys, in 
this way keeping down the starting torque. 

Cement Mills. — The possibility of entirely covering the bearings and 
the absence of all moving contacts make the squirrel-cage motor succe?s- 
• ful where the more complicated construction and moving contact sur- 
faces of the wound secondary motor or the direct-current machine are 
damaged by accumulation of dust. In starting up a tube mill it must 
be rotated through nearly 90% before the charge of pebbles and cement 
begins to roll. This makes the starting condition severe and a motor 
should have a starting torque of not less than twice full-load torque to 
do the work. 

Wood-working Machinery. — On account of high friction and great 
inertia, the starting torque is sometimes so high and of so long duration 
(thirty seconds to one minute) that it is better to apply a wound-secondary 
motor. 

Paper Machinery. — If calenders are driven with a constant speed 
motor it is necessary to make some provision either by mechanical speed- 
changing devices or a small auxiliary motor for securing a slow threading 
speed. 

Squirrel-Cage Variable Speed Motors. — These motors in general have 
high resistance end rings, high slip and high starting torque. The 
torque increases automatically as the speed decreases. In these general 
respects they resemble a direct-current series motor and are in fact fitted 
for the same class of work, with the added advantage that they have a 
limiting speed and cannot run away under light load. 

Fly-Wheel Service. — In driving tools which are used with fly-wheels 
such as punches, shears, straightening rolls and the like, the usefulness 



ALTERNATING-CURRENT MOTORS. 1411 

of high slip comes in, as if the fly-wheel is to give up its energy, it is 
obliged to slow down in speed when the load comes on. A motor with 
good regulation and low slip would try to run at constant speed, carrying 
the fly-wheel and load as well, but the motor in question " lies down " 
and allows the fly-wheel to carry the peak load, speeding up again when 
the peak has passed. 

Centrifugals. — In sugar centrifugals is an application where the sole 
purpose of the motor is to accelerate the load to full speed, in say thirty 
seconds, where it is allowed to run one minute and then shut down to 
repeat the cycle a minute later. The centrifugal consists of a cylindrical 
basket with perforated walls and mounted around a vertical shaft as an 
axis. The same principle is used in laundry extractors where the wet 
linen is placed in a similarly perforated basket and the water whirled out 
by centrifugal force. 

Constant-Speed Motors with Phase-wound Secondaries. — There are 
classes of service which require a heavy starting torque combined with 
close speed regulation after the motor is up to speed. These require- 
ments are exactly met by a motor with a phase-wound secondary. 
The secondary winding itself has a very low resistance, which means a 
small " slip," high running efficiency and power-factor and good regula- 
tion when the secondary is short-circuited. The insertion of external 
resistance enables the motor to develop maximum torque at the start 
with a moderate starting current. 

Flour-Mills. — The number of line shafts, belts and gears in flour 
mills makes a very heavy starting condition and the nature of the product 
and its quality demand absolute speed within a few revolutions per 
minute. The best solution is the phase-wound rotor. 

Other Examples. — There is another class of machinery which is not 
so exacting about regulation but which has the same feature of heavy 
starting and runs continuously after once up to speed. Under this head 
come most of the applications of this type of motor. They are, paper 
pulp grinders, which, on account of the inertia of the grindstones, are 
hard to start; pulp beaters; belt conveyors, which may be required to 
start when full of coal, rock or cement crushers; air compressors, which 
have a high starting friction because of the construction and the number 
of parts; line shafting where the belts run for the most part on the work- 
ing pulleys and are therefore heavy to start. Under the best possible 
conditions, if line shafting is employed, the loss of power from this source 
alone, due to friction, is 25 to 30% and may run up to 40 or 50%. This 
is a strong argument for individual drive of machines wherever practicable. 

Motors with Phase-wound Secondaries for Variable Speed Service. — 
The application, which is typical of this class, is found in hoist and 
crane service. Motors for this work are designed for intermittent oper- 
ation and given a nominal rating based upon the horse-power which 
they will develop for one-half hour with a temperature rise of 
40° C. They never operate for as long a period as thirty minutes 
continuously and they are called upon at times to develop a torque 
greatly in excess of their nominal rating. For these reasons motors of 
this class should never be applied on a horse-power basis, but always on 
a torque basis. Since torque is the main consideration and the service 
is intermittent these motors are usually wound for the maximum torque 
which they will develop and given a nominal rating based upon one-third 
to one-half of this torque. Double drum hoists, hoisting in balance, and 
large mine haulage propositions in general require a motor rated on a 
different basis. For this service the motor should have the necessary 
maximum torque and be able to develop for about two or three hours, 
with a safe rise in temperature, a horse-power equivalent to the square 
root of the mean square requirement of the hoisting cycle. These are 
only general rules and the most careful consideration should be given in 
each individual case to secure a motor which will perform the work 
satisfactorily. 

Coal and Ore Unloading Machinery. — Dredges — Power-Shovels. — 
Owing to the complication of the cycle of operation there is more diffi- 
culty in providing a motor for this apparatus than in the case of a plain 
hoist. Usually the number of cycles per hour given is the maximum 
which the apparatus can develop and in practice it will not be possible 
to operate at so high a speed. This in itself is somewhat of a factor of 



1412 r ELECTRICAL ENGINEERING. 



safety, though not one which can be relied upon, as the test for accept- 
ance is ordinarily made at the contract number of operations per hour. 

The most impressive application of motors of this class and perhaps 
in the operation of any electrical apparatus is the fly-wheel motor-gen- 
erator set for hoisting or heavy reversing roll service in steel mills. Ser- 
vice of this nature is extremely fluctuating in its requirements, having 
very great peaks one instant and almost nothing the next. This is a 
severe strain on the generating plant from which power is being drawn. 

Alternating-Current Motors for Variable Speed. (W. I. Slichter, 
Trans. A.S.M.E., 1903.) — 

The speed of an alternating-current motor may be controlled in a 
number of ways: 

(a) By varying the potential applied to the primary of a motor having 
a suitable resistance in the secondary. 

(b) By varying the resistance in the secondary circuit. 

(c) By changing the connections of the primary in a manner to change 
the number of poles. 

(d) By varying the frequency of the applied voltage. 

The changeable pole and variable frequency methods are the most 
efficient, but do not permit of a variation through a wide range of speed. 
The rheostatic control is the simplest and easiest of control, giving a range 
from standstill to full speed, but is not as efficient as the first two, although 
more efficient than potential control. The last mentioned has the dis- 
advantages of low efficiency and considerably increased heating in the 
motor itself, and is also unstable at low speeds, say below one-third speed. 
That is, a small variation in torque or a smaller variation in voltage will 
cause a considerable variation in speed. 

Mr. Geo. W. Colles, in a discussion of Mr. Schlichter's paper, says that 
the variable-speed induction-motor problem has not yet been solved. 

Of the four possible methods given, the first is the simplest, as here it is 
merely necessary to insert a compensator in circuit with the motor. This, 
however, is decidedly unsatisfactory, as, owing to the necessity of having 
a high-resistance secondary, even the full-speed efficiency of the motor is 
largely reduced, while at quarter-speed it is about 17%, and even at half- 
speed only 37%. 

All the other solutions given are too complicated, and they cannot be 
regarded as other than makeshifts. The resistance-in-secondary method 
is the only one that has been used to any extent. This nullifies the meri- 
torious natural features of the squirrel-cage motor, whose complete freedom 
from exposed contacts, commutator and slip-rings made it much simpler, 
and therefore cheaper, than the direct-current motor; and it now becomes 
more expensive and delicate, and considerably less efficient. The effi- 
ciency is now but 65% at 3/ 4 load, 43% at V2 load, and only 22 % at 1/4 
load. 

SIZES OF ELECTRIC GENERATORS AND MOTORS. 
(Condensed from Bulletins of the General Electric Co., 1910.) 

Direct-connected Engine-driven Railway Generators. Form S. 

6-pole, Kw 100 150 200 200 200 

Speed, r.p.m 275 200 200 150 120 

8-pole, 300 Kw., 120 and 100 r.p.m.; 400 Kw., 150, 120 and 100 r.p.m.; 

500 Kw., 120 r.p.m. 
10-pole, 500 Kw., 100 and 90 r.p.m. 14-pole, 800 Kw., 100 and 80 r.p.m. ; 
14-pole, 1000 Kw., 100 and 80 r.p.m.; 1200-Kw., 80 r.p.m., 16-pole, 1600 

Kw., 100 and 75 r.p.m. 
20-pole, 2000 Kw., 75 r.p.m.; 24-pole, 2500 Kw., 75 r.p.m.; 26-pole, 2700 
Kw., 90 r.p.m. 

Slow and Moderate Speed Belt-driven Generators. Type CL. 
Form B. 

(6 poles, Kw . 
Speed, 125 and 250 volts 
Slow 1 Speed, 500 volts 
Speed j 6-poles, Kw. 

I Speed, 125 and 250 volts 
LSpeed, 500 volts 

Moderate ( 6 poles, Kw 

Speed 1 Speed, 125, 250 and 500 v. 



16 


22 


22 




30 


40 


750 


900 


725 




700 


650 


815 


850 


725 




700 


650 


55 


75 


100 




150 




625 


550 


550 




550 




625 


550 


525 




455 




25 


35 


45 


60 


75 


90 


1100 


1050 


975 925 


850 


750 



ELECTRIC GENERATORS AND MOTORS. 



1413 



40 



25 


25 


35 


50 


785 


675 


650 


600 


730 


635 


610 


560 


800 


675 


650 


600 


90 


125 


185 




500 


470 


440 




470 


440 


410 




500 


500 


430 




55 


70 


85 105 


150 


900 


850 


800 700 




845 


800 


750 655 


490 



Slow and Moderate Speed Belt-driven Motors. Type CL.. Form B. 
'6 poles, Kw 20 

125 and 250 volts, speed. 690 
110 and 220 volts, speed. 650 

Slow j 500 volts, speed 750 

Speed ] 6 poles, Kw. 65 

125 and 250 volts, speed. 575 
110 and 220 volts, speed. 540 

.500 volts, speed .„. 575 

f 6 poles, Kw 30 

Moderate i 125, 250 and 500 volts, 

Speed j speed 1025 975 

(.110 and 220 volts, speed 965 915 

After a continuous run of 10 hours, at full-rated load, the rise in tem- 
perature above that of the surrounding air, as measured by the ther- 
mometer, will not exceed the following: Armature, 35° C. ; Commutator, 
40° C, Field, 45° C. The motors will operate for two hours at 25% 
overload, and withstand a momentary overload of 50% without injurious 
heating. 

Belt-driven Alternators. Form P. Revolving Field. 

Poles 6 

Kw 30 

Speed 1200 

Amperes at ( balanced 3- phase load 7 . 5 

full load j balanced 2-phase load 6.5 

2300 volts (single-phase load 10 

Built with or without direct-connected exciters. Adapted to 2- or 
3-phase windings without change except in the armature coils. Poten- 
tials, 3-phase, 240, 480, 600, 1150, 2300; 2-phase, 240, 480, 1150, 2300. 
When used as synchronous motors these machines have a condenser 
effect, and in consequence can be used to improve the power factor 
when used in combination with induction motors. 

The full-load single-phase rating at 100% power factor is 80% of the 
full-load 3-phase rating at both 100% and 80% power factor. The full- 
load single-phase rating at any power factor from 100 to 80% is the unity 
power factor single-phase rating multiplied by the power factor. For 
instance, for the 8-100-900 machine, which is the full-load 3-phase rating 
unity and 80% power factor, the single-phase rating for 100% at both 
power factors is 80 Kw., and for 80% power factor it is 80 X 0.8= 64 Kw. 

Slow and Moderate Speed Machines with Commutating Poles. 

Generators, Type DLC, Form A. 



6 


8 


8 


12 


12 


50 


75 


100 


150 


200 


1200 


900 


900 


600 


600 


12.5 


18.8 


25 


37.5 


50 


11 


16.5 


22 


33 


44 


16.5 


24.5 


33 


49 


65 



Slow Speed. 


Moderate Speed. 




Poles. 


Kw. 


Speed. 


Kw. 


Speed. 


Frame. 


125 v. 
250 v. 


500 v. 


575 v. 


125 v. 
250 v. 


500 v. 


575 v. 


1 


4 


20 


950 


950 


1050 


30 


1300 


1300 


1425 


2 


4 


25 


900 


900 


1000 


40 


1200 


1200 


1325 


3 


4 


35 


850 


850 


950 


50 


1150 


1150 


1250 


4 


6 


45 


775 


775 


850 


65 


1100 


1100 


1200 


5 


6 


60 


750 


750 


825 


80 


1050 


1050 


1150 


6 


6 


75 


700 


700 


775 


100 


1000 


1000 


1000 


7 


6 


100 


675 


675 


750 


125 


950 


950 


1050 


8 


6 


125 


650 


650 


700 


150 


900 


875 


900 


9 


6 


150 


600 


600 


650 


200 


*850 


775 


850 


10 


6 


200 


*500 


500 


550 


300 


*750 


700 


750 



* Not to be made for 125 volts. 



1414 



ELECTRICAL ENGINEERING. 



Motors, Type DLC. 



Slow Speed. 



Moderate Speed. 



Frame 


Poles 


H.P 




Speed. 




125 v. 
250 v. 


115v. 
230 v. 


550 v. 


1 


4 


20 


825 


800 


925 


2 


4 


25 


775 


750 


875 


3 


4 


35 


725 


700 


825 


4 


6 


50 


675 


650 


750 


5 


6 


65 


650 


625 


700 


6 


6 


80 


625 


600 


675 


7 


6 


100 


600 


575 


650 


8 


6 


125 


575 


550 


625 


9 


6 


175 


525 


500 


575 


10 


6 


250 


*450 


425 


500 



Speed. 



125 v. 115 v. 
250 v. 230 v. 



1150 
1100 
1050 
1000 
950 
900 
825 
775 
*725 
*675 



1100 
1050 
1000 
.950 
900 
850 
800 
750 
700 
650 



1250 
1200 
1150 
1100 
1025 
975 
925 
850 
750 
675 



* Not to be made for 125 or 115 volts. 

The first eight sizes are made with enclosed and partly enclosed as 
well as open casings. For the several types of casings the horse-powers 
are as below: 



H.P., Slow Speed. 


H.P., Moderate Speed. 


Frame 


Open 


Semi- 
En- 
closed. 


En- 
closed 
Venti- 
lated. 


Totally 

En- 
closed. 


Frame 


Open 


Semi- 
En- 
closed. 


En- 
closed 
Venti- 
lated. 


Totally 

En- 
closed. 


1 

2 
3 
4 
5 
6 
7 
8 


20 
25 
35 
50 
65 
80 
100 
125 


20 
25 
35 
50 
65 
80 
100 
125 


20 
25 
35 
50 
65 
80 
100 
125 


10 

12V2 

171/2 

25 

30 

40 

50 

60 


1 

2 
3 
4 
5 
6 
7 
8 


30 
40 
55 
70 
90 
125 
150 
175 


30 
40 
55 
70 
90 
125 
150 
175 


30 
40 
55 
70 
90 
125 
150 
175 


15 
20 
27 



Small Moderate Speed Engine-driven Alternators. 

Poles 24 26 28 32 36 

Kw 50 75 105 150 240 

Speed 300 276 257 225 200 

Amperes at ( balanced 3-phase load. 12.6 17.6 26.5 37.6 60 

full load \ balanced 2-phase load. 10.8 15.2 23 33 52 

2300 volts ( single-phase load 15 21 32 45 73 

Potentials, 3-phase, 240, 480, 600, 1150, 2300; 2-phase, 240, 480, 1150, 
2300. 

Box-Frame Type of Railway Motors. Four Field Coils. 
H.P., 18, 42, 45, 75, 50, 75, 100, 125, 160, 170, 200, 225. 
The first two sizes are for 24-in. gauge, the next two for 36-in., and the 
others for standard gauge. 

Commutating Pole Railway Motors. 

Made in six sizes 50 to 200 H.P. Wound for 600 volts. The two 
smallest have split frames: the others box frames. 

The commutating poles, located between the main exciting pole pieces, 
are connected up with their windings in series with one another and with 
the armature. The magnetic strength of the commutating poles varies 



ELECTRIC GENERATORS AND MOTORS. 



1415 



therefore with the current through the armature, and a magnetic field is 
produced of such intensity as to properly reverse the current in the 
armature coils short-circuited during commutation. The pole pieces are 
so proportioned and wound as to compensate for armature reaction, and 
practically non-flashing and sparkless commutation is insured up to the 
severest overloads. As the magnetizing current around the commutating 
poles is reversed with the armature, the poles perform their functions 
equally well in whichever direction the motors are running. 

Due to the good commutating characteristics of commutating pole 
railway motors, their overload capacities are considerably increased, and 
a more rugged form of motor is obtained which is less 'subject to injury 
through careless handling by motormen than the present standard rail- 
way motor. 

Small Polyphase Motors. 

60-cycle, 4-pole, 1800 r.p.m., H.P., V 6 , V4, V2, 3 /4, 1, 1 V2, 2, 3, 5, 7V.2, 
10, 15. 

60-cycle, 4-pole, 1200 r.p.m., H.P., 1/4, 1/2, 3 /4, 1, IV2, 2, 3, 5, 71/2. 

60-cycle, 8-pole, 900 r.p.m., H.P., 1/4, V2, 3 /4, 1, 2, 3, 5. 12-pole, 600 
r.p.m.,H.P., 1/4, 1/2, 3 /4, 1, 2, 3. 

40-cycle, 4-pole, 1200 r.p.m., H.P., 1/4, 1/2, 1, IV2, 2, 3, 5. 6-pole, 800 
r.p.m., H.P., 1/4, V2, 1, 2, 3,. 

25-cycle, 2-pole, 1500 r.p.m., H.P., 1/4, V2, 1, 2, 3, 5, 71/2. 

25-cycle, 4-pole, 750 r.p.m., H.P., 1/4, V3, V2, 1, 2, 3, 5. 6-pole, 500 
r.p.m., H.P., 1/4, ¥2, 1, 2, 3. 

The speeds given are synchronous speeds. Full-load speeds are from 
93 to 97% of the synchronous. 

Motors below 1 H.P. are adapted for 110 and 220 volts; others for 
110, 220, 440 and 550 volts. 

Single-phase Motors, 110 and 220 volts. 

60-cycle, 4-pole, 1800 r.p.m., H.P., 1/4, ty& 1, 2, 3, 5, 7 1/2, 10, 15. 
60-cycle, 6-pole, 1200 r.p.m., H.P., 1/4, V2, 1, 1 V2, 2, 3, 5, 71/2, 10. 
25-cycle, 2-pole, 1500 r.p.m., H.P., 1/4, ¥2, 3 /4, 2, 3, 5, 71/2, 10. 
25-cycle, 4-pole, 750 r.p.m., H.P., 1/4, 1/2, 1, IV2, 2, 3, 5. 

Type CQ Motors. Continuous Current. 



No. of 
Poles 



3 
3 
5 
5 

71/2 
71/2 
10 

10 



* Speed (Shunt-Wound Motors). 



110 v. 


115v. 


125 v. 


220 v. 


230 v. 


250 v. 


500 v. 


550 v. 


600 v. 


2200 


2300 
1850 


2450 
1950 


2200 
1800 


2300 
1850 


2450 
1950 








1800 


2100 


2250 


2400 


1600 


1650 


1750 


1600 


1650 


1750 


1850 


2000 


2150 


1425 


1475 


1550 


1425 


1475 


1550 


1675 


1800 


1925 


1935 


2000 


2100 


1935 


2000 


2100 


2240 


2400 


2575 


1240 


1275 


1350 


1240 


1275 


1350 


1450 


1575 


1700 


1825 


1900 


2090 


1825 


1900 


2050 


2200 


2350 


2500 


1060 


1100 


1175 


1060 


1100 


1175 


1250 


1350 


1450 


1600 


1650 


1750 


1600 


1650 


1750 


1850 


2000 


2150 


1060 


1100 


1175 


1060 


1100 


1175 


1250 


1350 


1450 


1600 


1650 


1750 


1600 


1650 


1750 


1850 


2000 


2150 


1060 


1100 


1175 


1060 


1100 


1175 


1250 


1350 


1450 


1475 


1525 


1625 


1475 


1525 


1625 


1725 


1850 


1975 


800 


825 


875 


800 


825 


875 


1050 


1125 


1200 


17,7ft 


1250 


1310 


1220 


1250 


1310 


1400 


1500 


1600 


635 


650 


685 


635 


650 


685 


835 


900 


965- 


975 


1000 


1050 


975 


1000 


1050 


1250 


1350 


1450 


610 


625 


660 


610 


625 


660 


775 


835 


890 


900 


925 


975 


900 


925 


975 


1150 


1250 


1350 



* Speed at full load is subject to a maximum variation of 4% above 
or below standard. 



1416 



ELECTRICAL ENGINEERING. 



The standard CQ open motor will deliver its rated horse-power output 
continuously without a temperature rise in any part exceeding 45° C. 
by the thermometer above the surrounding air. An overload of 25% 
may be maintained for one hour continuously without injurious heating 
or sparking, or a 40% over'oad momentarily. 

Motors developed from the CQl frame and smaller will operate semi 
or totally enclosed within the same load limits as when open. Owing to 
the fact that the CQ2 and larger frames have less radiating surface per 
horse-power than the smaller frames, the ratings attainable with them 
when enclosed are necessarily reduced to keep the heating within estab- 
lished limits. 

The voltages for which standard motors are built are 115, 230 and 550. 
When motors are rated at 115 volts, they may be used on circuits ranging 
between 110 and 125 volts, and when rated at 230 volts, they may be 
used on circuits ranging between 220 and 250 volts, and standard heating 
guarantees will be maintained. 

When motors are rated at 550 volts, they may be used on circuits 
ranging between 500 and 600 volts, inclusive, and standard heating 
guarantees will be maintained up to 550 volts, and at 600 volts the heat- 
ing will not be injurious. 

Se wing-Machine Motors. 

Ratings, H.P., Vao, Vis, Vio, Vs, Ve. 

Speed, r.p.m., 1800, 1800, 1500, 1800, 2300, for direct current ; 

alternating current 1800 r.p.m. for all sizes. 

Wound for 115 and 230 volts, D.C., and 110 and 220 volts, A.C., 60 
cycles. 

On special order, machines may be furnished for any commercial volt- 
age between 50 and 250, and for any standard frequency between 25 
and 145 cycles. 

SYMBOLS USED IN ELECTRICAL DIAGRAMS. 



a o-spst 
i cb o-spdt 
a R: dpst 



4l -®- -&- 

_DPDT Galvanometer. Ammeter. Voltmeter. 



"• jvww| — 
Wattmeter. 



Switches; *S, single; 
D, double; P, pole; 
T, throw. 



Non-inductive 
Resistance. 



Inductive 
Resistance. 



Capacity 
or Condenser. 



Lamps. 



i 13 



£= 



Motor Shunt-wound Motor Series-wound 
or Generator. or Generator. Motor or Generator. 




Two-phase Three-phase Battery. Trans- Compound- Separately 
Generator. Generator. former, wound Motor excited Motor 

or Generator, or Generator. 



INDEX. 



Abbreviations, 1 

Abrasion, resistance to, of manga- 
nese steel, 471 
Abrasive processes, 1262-1268 
Abscissas, 71 
Absolute temperature, 540 

zero, 540 
Absorption of gases, 579 

of water by brick, 348 

refrigerating-machines, 1293-1313 
Accelerated motion, 501 
Acceleration, definition of, 497 

force of, 501 

work of, 504 
Accumulators, electric, 1378 
Acetylene and calcium carbide, 825 
Acetylene blowpipe, 827 

-flame welding, 464 

generators and burners, 826 
Acheson's deflocculated graphite, 

1223 
Acme screw thread, 226 
Adiabatic compression of air, 604 

curve, 929 

expansion, 575 

expansion of air, 606 

expansion in compressed air- 
engines, 608 

expansion of steam, 929 
Adiabatically compressed air, mean 

effective pressures, table, 609 
Admiralty metal, composition of, 

366 
Admittance of alternating currents, 

1389 
Air (see also Atmosphere), 580-653 

and vapor mixture, weight of, 584, 
586 

-bound pipes, 722 

carbonic acid allowable in, 653 

cooling of, 568, 681 

compressed, 593, 604-626 (see 
Compressed air) 

compressor, hydraulic, 622 

compressors, centrifugal, 620 

compressors, effect of intake 
temperatures, 619 

compressors, high altitude, table 
of, 611 

compressors, intercoolers for, 620 

compressors, tables, 614, 615 

density and pressure, 581, 586 

flow of, in pipes, 591 

flow of, in long pipes, 595 

flow of, in ventilating ducts, 655 



Air, flow of, through orifices, 588 

friction of, in underground pas- 
sages, 685 

head of, due to temperature 
differences, 687 

heating of, see also Heating 

heating of, by compression, 604 

horse-power required to com- 
press, 606 

lift pump, 776 

liquid, 579 

loss of pressure of, in pipes, tables, 
593-595 

manometer, 581 

properties of, 580 

pump, 1055 

pump for condenser, 1053, 1055 

pump, maximum work of, 1056 

pyrometer, 528 

specific heat of, 537 

thermometer, 530 

velocity of, in pipes, by anemom- 
eter, 596 

volumes, densities, and pressures, 
581, 586, 663 

volume transmitted in pipes, 591 

weight and volume of, 28 

weight of (table), 586 

weight of, 173 
Alcohol as fuel, 813 

denatured, 813 

engines, 1078 

vapor tension of, 814 
Aiden absorption dynamometer, 

1281 
Algebra, 34-38 
Alsrebraic symbols, 1 
Alligation, 9 
Alloys, 360-385 

aluminum, 371, 375, 376 

aluminum-antimony, 375 

aluminum-copper, 371 

aluminum-silicon-iron, 374 

aluminum, tests of, 374 

aluminum-tungsten, 375 

aluminum-zinc, 375 

antimony, 381, 383 

bearing metal, 380 

bismuth, 379 

caution as to strength of, 373 

composition of, "n brass foundries, 
366 

composition by mixture and by 
analysis, 364 

copper-manganese, 376 



1417 



1418 



INDEX. 



Alloys, copper-tin, 360 

copper-tin-lead, 369 

copper-tin-zinc, 363-367 

copper-zinc, 362 

copper-zinc-iron, 369 

ferro-, 1232 

for casting under pressure, 371 

fusible, 380 

Japanese, 368 

liquation of metals in, 364 

magnetic, of non-magnetic met- 
als, 378 

nickel, 378 

the strongest bronze, 365 

vanadium and copper, 371 

white metal, 382 
Alloy steels, 470-480 (see Steel) 
Alternating-current motors, vari- 
able speed, 1412 
Alternating currents, 1387 

admittance, 1389 

average, maximum, and effective 
values, 1388 

calculation of circuits, 1397 

capacity, 1389 

capacity of conductors, 1394 

converters, 1400 

delta connection, 1395 

frequency, 1388 

generators for, 1396 

impedance, 1389 

impedance polygons, 1390 

inductance, 1389 

induction motor, 1409 

measurement of power in poly- 
phase circuits, 1395 

Ohm's law applied to, 1390 

power factor, 1389 

reactance, 1389 

single and polyphase, 1395 

skin effect, 1390 

synchronous motors, 1409 

transformers, 1400 

Y-connection, 1395 
Alternators, sizes of, tables, 1413 
Altitude by barometer, 582 
Aluminum, 174 

alloys (see Alloys) 

alloys used in automobile con- 
struction, 376 

alloys, various, 371, 375, 376 

alloys, tests of, 374 

brass, 373 

bronze, 371 

bronze wire, 243 

coating on iron, 449 

conductors, cost compared with 
copper, 1399 

effect of, on cast iron, 416 

electrical conductivity of, 1350 

properties and uses, 357 

sheets and bars, table, 220 

solder, 359 

steel, 472 

strength of, 358 

thermit process, 372 

wire, 243, 359 



Aluminum wire, electrical resistance 

of, table, 1362 
Ammonia, carbon dioxide and sul- 
phur dioxide, cooling effect, 
and compressor volume, 1289 
gas, properties of, 1287 
heat generated by absorption of, 

1288 
liquid, density of, 1285 
liquid, specific heat of, 1286 
liquid, specific heat and available 

latent heat, 1287 
solubility of, 1288 
vapor, superheated, weight of, 
1287 
Ammonia-absorption refrigerating 
machine, 1293, 1313 
test of, 1315 
Ammonia-compression refrigerating 
machines, 1292, 1303. 
tests of, 1307-1311 
Ampere, definition of, 1345 
Analyses, asbestos, 257 
boiler scale, 693 
boiler water, 693 
cast iron, 416-419 
coals, 789-797 
crucible steel, 466, 469 
fire-clay, 255 
gas, 824 

gases of combustion, 785 
magnesite, 257 
Analysis of rubber goods, 356 
Analytical geometry, 71-74 
Anchor forgings, strength of, 331 
Anemometer, 596 
Angle, economical, of framed struc- 
tures, 522 
of repose of building material, 
1196 
Angles, Carnegie steel, properties of, 
table, 295-298 
plotting without protractor, 54 
problems in, 39, 40 
steel, table of properties of, 295, 

296 
steel, table of safe loads, 297, 298 
steel, tests of, 340 
trigonometrical properties of, 67 
Angular velocity, 498 
Animal power, 507-509 
Annealing, effect on conductivity, 
1351 
effect of, on steel, 454, 455 
influence of, on magnetic capa- 
city of steel, 459 
malleable castings, 431 
of steel, 460, 468 (see Steel) 
of steel forgings, 458 
of structural steel, 460 
Annuities, 15-17 
Annular gearing, 1145 
Anthracite, classification of, 787 
composition of, 787 
gas, 815 
sizes of, 792 
space occupied by, 793 






INDEX. 



1419 



Anti-friction curve, 51, 1209 

metals, 1199 
Anti-logarithm, 135 
Antimony, in alloys, 383, 336 

properties of, 175 
Apothecaries' measure and weight, 

18,20 
Arbitration bar, for cast iron, 418 
Arc, circular, length of, 59 

circular, relations of, 59 

lamps, see Electric lighting 

lighting of areas, watts per 
square foot required for, 1369 

lights, electric, 1368 
Arcs, circular, table, 123, 124 
Arches, corrugated, 186 
Area of circles, table, 111-119 

of circles, square feet, diameters 
feet and inches, 127, 128 

of geometrical plane figures, 
55-62 

of irregular figures, 57, 58 

of sphere, 63 
Arithmetic, 2-33 
Arithmetical progression, 10 
Armature, torque of, 1385 
Armature-circuit, e.m.f. of, 1386 
Armor-plates, heat treatment of, 

458 
Asbestos, 257 

Asphaltum coating for iron, 447 
Asses, work of, 509 
Asymptotes of hyperbola, 74 
Atmosphere, see also Air 

equivalent pressures of, 27 

moisture in, 583 

pressure of, 581 
Atomic weights (table), 170 
Autogenous welding, 464 
Austenite, 456 

Automatic cut-off engines, 937 
Automobile engines, rated capacity 
of, 1077 

gears, efficiency of , 1148 

screws and nuts, table, 222 
Automobiles, steel used in, 486 
Avogadro's law of gases, 578 
Avoirdupois weight, 19 
Axles, forcing fits of, by hydraulic 
pressure, 1273 

railroad, effect of cold on, 441 

steel, specifications for, 483, 485 

steel, strength, of, 332 

Babbitt metal, 383, 384 

Babcock & Wilcox boilers, tests 

with various coals, 799 
Bagasse as fuel, 809 
Balances, to weigh on incorrect, 20 
Ball-bearings, 1210 

saving of power by, 1214 
Balls and rollers, carrying capacity 

of, 317 
Balls for bearings, grades of, 1214 

hollow copper, 322 
Band brakes, design of, 1217 



Bands and belts for carrying coal, 
etc., 1175 
and belts, theory of, 1115 
Bank discount, 13 
Bar iron, see also Wrought iron 
Bars, eye, tests of, 338 

iron and steel, commercial sizes 

of, 179 
Lowmoor iron, strength of, 330 
of various materials, weights of, 

178 
steel, 461, see Steel 
twisted, tensile strength of, 264 
wrought-iron, compression tests 
of, 337 
Barometer, leveling with, 582 

to find altitude by, 582 
Barometric readings for various alti- 
tudes, 582 
Barrels, number of, in tanks, 133 

to find volume of, 66 
Basic Bessemer steel, strength of, 

452 
Batteries, primary electric, 1377 

storage, 1378 
Baume's hydrometer, 172 
Bazin's experiments on weirs, 732 
Beams and girders, safe loads on, 
1335 
formula for flexure of, 282 
formulae for transverse strength 

of, 282-285 
of uniform strength, 286 
special, coefficients for loads on, 

285 
steel, formulae for safe loads on, 

284 
wooden, safe loads, by building 

laws, 1336 
yellow pine, safe loads on, 1336, 
1340 
Beardslee's tests on elevation of 

elastic limit, 261 
Bearing pressure on rivets, 403 
Bearing pressures with intermittent 

loads, 1207 
Bearings, allowable pressure on, 
1203, 1206 
and journals clearance in, 1206 
ball, 1210 

calculating dimensions of, 1025 
cast-iron, 1199 
conical roller, 1211 
engine, temperature of, 1209 
for high rotative speeds, 1208 
for steam turbines, 1208 
knife-edge, 1214 
mercury pivot, 1209 
of Corliss engines, 1208 
of locomotives, 1208 
oil pivot, in Curtis steam turbine, 

1063 
oil pressure in, 1204 
overheating of, 1205 
pivot, 1205, 1209 
roller, 1210 
shaft, length of, 1015 



1420 



bea-bol 



INDEX. 



Bearings, steam-engine, 1165 

thrust, 1208 
Bearing-metal alloys, 380-384 

practice, 382 
Bearing-metals, anti-friction, 1199 

composition of, 367 
Bed-plates of steam-engine, 1025 
Bell-metal, composition of , 366 
Belt conveyors, 1175 
Belt dressings, 1128 

factors, 1119 
Belts, arrangement of, 1126 

care of, 1127 

cement for leather or cloth, 1128 

centrifugal tension of, 1115 

endless, 1127 

evil of tight, 1126 

lacing of, 1124 

length of, 1125 

open and crossed, 1112 

quarter twist, 1124 

sag of, 1126 

steel, 1120 
Belting, 1115-1132 

Barth's studies on, 1123 

formulae, 1116 

friction of, 1115 

horse-power of, 1116-1119 

notes on', 1123 

practice, 1116 

rubber, 1128 

strength of, 335, 1127 

Taylor's rules, 1120-1122 

theory of, 1115 

vs. chain drives, 1132 

width for given horse-power, 
1118 
Bends, effects of, on flow of water 
in pipes, 721 

in pipes, 593 

in pipes, table, 214, 215 

pipe, flexibility of, 215 

valves, etc., resistance to flow in, 
848 
Bending curvature of wire rope, 
1188 

tests of steel, 454 
Bent lever, 511 
Bernouilli's theorem, 734 
Bessemer converter, temperature 
in, 527 

steel, 451 {see Steel, Bessemer) 
Bessemerized cast iron, 429 
Bevel wheels, 1144 
Billets, steel, specifications for, 483 
Binomial, any power of, 34 

theorem, 38 
Bins, coal-storage, 1172 
Birmingham gauge, 29 
Bismuth alloys, 379 
Bismuth, properties of, 175 
Bituminous coal {see Coal) 
Black body radiation, 552 
Blast area of fans, 629 

furnaces, consumption of char- 
coal in, 806 

furnaces, steam-boilers for, 865 



Blast furnaces, temperatures in, 528 

pipes, see Pipes 
Blechynden's tests of heat trans- 
mission, 567 
Blocks or pulleys, 513 

efficiency of, table, 1158 

strength of, 1157 
Blooms, steel, weight of, table, 185 
Blow, force of, 504 
Blowers, see also Fans. 
Blowers and fans, 626-652 

and fans, comparative efficiency, 
631 

blast-pipe diameters for, 643 

capacity of, 632 

experiments with, 629 

for cupolas, 633, 634 

in foundries, 1227 

rotary, 649 

rotary, table of, 650 

steam-jet, 651 

velocity due to pressure, 629 
Blowing-engines, dimensions of, 
652 

machines, centrifugal, 622 
Blue heat, effect on steel, 458 
Board measure, 20 
Boats, see Ships 
Bodies, falling, laws of, 497 
Boiler compounds, 898 

explosions, 902 

feeders, gravity, 908 

feed-pumps, 761 

furnaces, height of, 889 

furnaces, use of steam in, 824 

heads, 885 

heads, strength of, 314, 316 

heating-surface for steam heat- 
ing, 664, 667 

plate, strength of, at high tem- 
peratures, 439 

scale, analyses of, 693 

tubes used as columns, 341 

tubes, expanded, holding power 
of, 342 

tubes, dimensions of, table, 209 

tube joints, rolled, slipping point 
of, 342 
Boilers for house heating, 665 

horse-power of, 854 

incrustation of, 691, 692 

locomotive, 1089 

natural gas as fuel for, 817 

of the "Lusitania" 1330 

for steam-heating, 667 

steam, 854 {see Steam-boilers) 
Boiling, resistance to, 543 
Boiling-point of water, 690 
Boiling-points of substances, 532 
Bolts and nuts, 221-228 

and pins, taper, 1271 

effect of initial strain in, 325 

holding power of in white pine, 
324 

square-head, table of weights of, 
229 



INDEX 



bol-can 



1421 



Bolts, strength of, tables, 325, 326 

track, weight of, 230 

variation in size of iron for, 223 
Boyle's or Mariotte's law, 574, 577 
Braces, diagonal, stresses in, 516 
Brackets, cast-iron, strength of, 277 
Brake horse-power, definition of, 
991 

Prony, 1280 
Brakes, band, design of, 1217 

electric, 1217 

friction, 1216 

magnetic, 1217 
Brass alloys, 366 

and copper tubes, coils and bends, 
214 

influence of lead on, 369 

plates and bars, weight of, 
tables, 219, 220 

rolled, composition of, 367 

sheet and bars, table, 220 

tube, seamless, table, 215, 216 

wire, weight of, table, 219 
Brazing of aluminum bronze, 373 

metal, composition of, 366 

solder, composition of, 366 
Brick, absorption of water by, 348 

kiln, temperature in, 528 

piers, safe strength of, 1334 

sand-lime, tests of, 349 

specific gravity of, 174 

strength of, 336, 347-350 

weight of, 174, 347 
Bricks, fire, number required for 
various circles, table, 254 

fire, sizes and shapes of, 253 
Bricks, magnesia, 257 
Brickwork, allowable pressures on, 
1334 

measure of, 177 

weight of, 177 
Bridge iron, durability of, 442 

links, steel, strength of, 331 

members, strains allowed in, 272 

trusses, 517-521 
Brine, boiling of, 543 

properties of, 543, 544 
Brinell's tests of hardness, 342 
Briquettes, coal, 801 
Britannia metal, composition of, 

383 
British thermal unit (B.T.U.), 

532, 837 
Brittleness of steel, see Steel 
Bronze, aluminum, strength of, 372 

ancient, composition of, 364 

deoxidized, composition of, 371 

Gurley's, composition of, 366 

manganese, 377 

navy-yard, strength of, 374 

phosphor, 370 

strength of, 319, 321, 334 

Tobin, 367, 368 

variation in strength of, 362 
Buildings, construction of, 1333- 
1344 

fire-proof, 1338 



Buildings, heating and ventilation 

of, 656 
mill, approximate cost of, 1342 

transmission of heat through 

walls of, 659 
walls of, 1336 
Building-laws, New York City, 

1337-1340 
on columns, New York, Boston, 

and Chicago, 277 
Building-materials, coefficients of 

friction of, 1196 
sizes and weights, 174, 17S, 1S6, 

190 
Bulkheads, plating and framing for, 

table, 316 
stresses in due to water-pressure, 

315 
Buoyancy, 690 
Burmester's method of calculating 

cone pulleys, 1113 
Burning of steel, 457 
Burr truss, stresses in, 518 
Bush-metal, composition of, 366 
Bushel of coal and of coke, weight 

of, 803 
Butt-joints, riveted, 405 

C. G. S. system of measurements, 

1344 
C0 2 , carbon dioxide, carbonic acid 
C0 2 recorders, autographic, 860 
C0 2 , temperature required for pro- 
duction of, 822 
Cable, formula for deflection of, 
1180 

traction ropes, 247 
Cables, chain, proving tests of, 251 

chain, wrought-iron, 251-252 

flexible steel wire, 249 

galvanized steel, 248 

suspension-bridge, 248 
Cable-ways, suspension, 1181 
Cadmium, properties of, 175 
Calcium carbide and acetylene, 825 

chloride in refrigerating-ma- 
chines, 1290 
Calculus, 74-83 
Caloric engines, 1071 
Calorie, definition of, 532 
Calorimeter for coal, Mahler bomb, 
798 

steam, 912-915 

steam, coil, 913 

steam, separating, 914 

steam, throttling, 913 
Calorimetric tests of coal, 797, 798 
Cam, 512 
Campbell's formula for strength of 

steel, 453 
Canals, irrigation, 704 
Candle-power and life of lamps, 
"1370 

definition of, 1367 

of electric lights, 1368-1373 

of gas lights, 830 
Canvas, strength of, 335 



1422 



INDEX. 



Capacity, electrical, 1389 

electrical, of conductors, 1394 
Cap-screws, table of standard, 225 
Cars, steel plate for, 483 
Car-heating by steam, 673 
Car-journals, friction of, 1204 
Car-wheels, cast iron for, 426, 427 
Carbon, burning out of steel, 461 
dioxide, see C0 2 
effect of on strength of steel, 452 
gas, 814 
Carbonic acid allowable in air, 653 
Carbonizing see Case-hardening, 
Carborundum, made in the electric 

furnace, 1377 
Cargo hoisting by rope, 390 
Carnegie steel sections, properties 

of, 287-306 
Carnot cycle, 572, 574 

cycle, efficiencies of, 967 
cycle, efficiency of steam in, 850 
Carriages, resistance of, on roads, 

509 
Carriers, bucket, 1172 
Case-hardening of iron and steel, 

486, 1246 
Casks, volume of, 66 
Cast copper, strength of, 334, 360 
Cast-iron, 414-429 

addition to, of ferro-silicon, 
titanium, vanadium and man- 
ganese, 426 
analyses of, 416-419 
and aluminum alloys, 375 
bad, 429 

bars, tests of, 419 
beams, strength of, 427 
Bessemerized, 429 
chemistry of, 415-419 
columns, eccentric loading of, 278 
columns, strength of, 274-278 
columns, tests of, 275 
columns, weight of, table, 191 
combined carbon changed to 

graphitic by heating, 424 
compressive strength of, 267 
corrosion of, 441 
cylinders, bursting strength of, 

427 
durability of, 442 
effect of cupola melting, 425 
expansion in cooling, 423 
growth of by heating, 1231 
hard, due to excessive silicon, 

1231 
influence of length of bar on 

strength, 422 
influence of phosphorus, sulphur, 

etc., 415 
journal bearings, 1199 
malleable, 429 
manufacture of, 414 
mixture of, with steel, 429 
mobility of molecules of, 424 
permanent expansion of, by heat- 
ing, 429 



Cast-iron pipe, 191-195 (see Pipe, 
cast-iron) 
pipe-fittings, sizes and weights, 

196, 199 
relation of chemical composition 

to fracture, 421 
shrinkage of, 415, 423, 1231 
specifications for, 418 
specific gravity and strength, 428 
strength of, 421 
strength in relation to silicon and 

cross-section, 422 
strength in relation to size of 
bar and to chemical constitu- 
tion, 421 
tests of, 330, 419, 420 
theory of relation of strength to 

composition, 421 
variation of density and tenacity , 

428 
water pipe, transverse strength 

of, 427 
white, converted into gray by 
heating, 424 
Castings, deformation of, by shrink- 
age, 423 
from blast-furnace metal, 425 
hard, from soft pig, 425 
hard to drill, due to low Mn., 426 
iron, analysis of, 417 
iron, strength of, 330 
made in permanent cast-iron 

molds, 1232 
malleable, rules for use of 433 
shrinkage of, 1231 
specifications for, 418 
steel, 464-466 

steel, specifications for, 464, 486 
steel, strength of, 333 
weakness of large, 1230 
weight of, from pattern, 1233 
Catenary, to plot, 53 
Cement as a preservative coating, 
447 
for leather belts, 1128 
Portland, strength of, 336 
Portland, tests of, 351 
weight and specific gravity of, 
174 
Cements, mortar, strength of, 350 
Cementation or case-hardening, 

486, 1246 
Cementite, 416, 456 
Center of gravity, 492 
of regular figures, 492. 
of gyration, 494 
of oscillation, 494 
of percussion, 494 
Centigrade Fahrenheit conversion 
table, 524, 525 
thermometer scale, 524, 525 
Centrifugal fans (see Fans, cen- 
trifugal) 
fans, high-pressure, 621 
force, 497 
force in fly-wheels, 1029 



INDEX. 



1423 



Centrifugal pumps (see Pumps, 
centrifugal), 764-770 

tension of belts, 1115 
Chains, formulas for safe load on. 
326 

link belting, 1172 

monobar, 1174 

pin, 1174 

.pitch, breaking and working 
strains of, 252 

roller, 1174 

sizes, weights and properties, 
251, 252 

specifications for, 251 

strength of, table, 251, 252 

test of, table, 251, 252 
Chain-blocks, efficiency of , 1158 
Chain-cables, proving tests of, 251 

weight and strength of, 251 
Chain-drives, 1129 

vs. belting, 1132 

silent, 350 H.P., 1132 
Chain-hoists, 1157 
Chalk, strength of, 349 
Change gears for lathes, 1237 
Channels, Carnegie steel, properties 
of, table, 292 

open, velocity of water in, 704 

safe loads, table, 293 

strength of, 330 
Charcoal, 805-807 

absorption of gases and water 
by, 806 

bushel of, 177 

composition of, 806 

pig iron, 417, 428 

results of different methods of 
making, 806 

weights per cubic foot, 177 
Charles's law, 574, 578 
Chatter in tools, 1241 
Chemical elements, table, 170 

symbols, 170 
Chemistry of cast iron, 415 
Chezy's formula for flow of water, 

699 
Chilling cast iron, 418 
Chimneys, 915-928 

draught, power of, 917 

draught, theory, 915 

effect of flues on draught, 918 

for ventilating, 683 

height of, 919 

height of water column due to 
unbalanced pressure in, 917 

largest in the world, 923 

lightning protection of, 920 

radial brick, 923 

rate of combustion due to, 918 

reinforced concrete, 927 

sheet iron, 928 

size of, 919-928 

size of, table, 921 

stabilitv of, 924 

steel, 925 

steel, design of, 925 

steel, foundation for, 926, 928 



Chimneys, tall brick, 922 
velocity of air in, 917 
Chisels, cold, cutting angle of, 1238 
Chord of circle, 59 
Chords of trusses, strains in, 519 
Chrome paints, anti-corrosive, 445 

steel, 471 
Chromium vanadium steels, 476- 

478 
Cippoleti weir, 733 
Circle, 58-61 
area of, 58 
diameter of to enclose a number 

of rings, 52 
equation of, 72 

large, to describe an arc of, 52 
length of arc of, 59 
length of arc of, Huyghen's 

approximation, 59 
length of chord of, 59 
problems, 40-42 
properties of, 58, 59 
relations of arc, chord, etc., of, 59 
relations of, to equal, inscribed 
and circumscribed square, 60 
sectors and segments of, 61 
area in square feet, diameter in 
inches (tables of cylinders), 
127, 128 
circumference and area of, table, 

111-119 
circumferences in feet, diameters 

in inches, table, 1265 
circumferences of, 1 inch to 32 
feet, 120 
Circuits, alternating current, see 
Alternating current 
electric, see Electric circuits 
electric, e.m.f. in, 1352 
electric, polyphase, 1395 (see 

Alternating currents) 
electric, power of, 1353 
magnetic, 1383 
Circular arcs, lengths of, 59 
lengths of, tables, 123, 124 
curve, formulas for, 60 
functions, Calculus, 82 
inch, 18 
measure, 20 
mil, 18, 30, 31 
mil wire gauge, 31 
mil wire gauge, table, 30 
pitch, 1134 
ring, 61 

segments, areas of, 121, 122 
Circumference of circles, 1 inch to 
32 feet, table, 120 
of circles, table, 111-119 
Cisterns and tanks, no. of barrels 
in, 133 
capacity of, 128 
Classification of iron and steel, 413 
Clay, cubic feet per ton, 178 
fire, analysis, 255 
melting point of, 529 
Clearance between journal and 
bearing, 1206 



1424 



cle-com 



INDEX. 



Clearance in steam-engines, 936, 996 
Clutches, friction, 1155, 1216 

friction coil, 1156 
Coal, analysis of, 789-797 

analyses of various, table, 794 

and coke, Connellsville, 793 

approximate heating value of, 
791 

anthracite, sizes of, 792 

bituminous, classification of, 787 

caking and non-caking, 788 

calorimeter, 798 

calorimetric tests of, 797, 798 

cannel, 788 

classification of, 786, 787 

conveyors, 1172 

cost of for steam power, 983 

cubic feet per ton, 177 

Dulong's formula for heating 
value of, 798 

efficiencies of, in gas-engine tests, 
823 

evaporative power of, 799 

foreign, analysis of, 796 

furnaces for different, 798 

heating value of, 789-792, 797 

products of distillation of, 803 

proximate analysis and heating 
value of, table, 790 

purchase of by specification, 799 

Rhode Island graphitic; 788 

sampling of, for analysis, 797 

semi-anthracite, 793 

semi-bituminous, composition of, 
787-792 

space occupied by anthracite, 
793 

steam, relative value of, 797 

storage bins, 1172 

tests of, 791 

vs. oil as fuel, 812 

washing, 802 

weathering of, 800 

Welsh, analysis of, 796 
Coal-gas, composition of, 830 

manufacture, 828 
Coatings, preservative, 447-450 
Coefficient of elasticity, 260, 351 

of fineness, 1317 

of friction, definition, 1194 

of friction of journals, 1197 

of friction, rolling, 1195 

of friction, tables, 1195-1197 

of performance of ships, 1318 

of propellers, 1325 

of transverse strength, 282 

of water lines, 1317 

of expansion, 539 (see Expansion 
by heat) 
Coils and bends of brass tubes, 214 
Coils, electric, heating of, 1355 
Coils, heat radiated from, in 

blower system, 679 
Coiled pipes, 214 
Coke, anaiyses of, 802 

by-products of manufacture of, 
802, 803 



Coke, foundry, quality of, 1232 

weight of, 177 
Coke-ovens, generation of steam 

from waste heat of, 803 
Coking, experiments in, 802 
Cold, effect of, on railroad axles, 
441 
effect of on strength of iron and 
steel 440 
Cold-chisels, form of, 1238 
Cold-drawing, effect of, on steel, 

339 
Cold-drawn steel, tests of, 339 
Cold-rolled steel, tests of, 339 
Cold-rolling, effect of, on steel, 455 
Cold-saw, 1262 

Collapse of corrugated furnaces, 
318 
of tubes, tests of, 320 
resistance of hollow cylinders 
to, 318-322 
Collars for shafting, 1109 
Cologarithm, 136 

Color determination of tempera- 
ture, 531 
scale for steel tempering, 469 
values of various illuminants, 
1367 
Columns, Bethlehem shapes, 309, 
310 
built, 272 
Carnegie channel, dimensions 

and safe loads, 305, 306 
cast-iron, strength of, 274-278 
cast-iron, tests of, 275 
cast-iron, weight of, table, 191 
eccentric, loading of, 278 
Gordon's formula for, 270 
Hodgkinson's formula for, 269 
made of old boiler tubes, tests 

of, 341 
mill, 1341 

permissible stresses in, 277 
strength of, 274 

strength of, by New York build- 
ing laws, 1337 
wrought-iron, tests of, 338 
wrought-iron, ultimate strength 

of, table, 271 
steel, built, 272 

Z-bar, tables of safe loads on, 
300-304 
Combination, 10 
Combined stresses, 312 
Combustion, analyses of gases of 

heat of, 533 

of fuels, 784 

of gases, rise of temperature 
in, 786 
rate of, due to chimneys, 918 

theory of, 784 
Composition of forces, 489 
Compound engines (see Steam- 
engines, compound), 946-953 

interest, 14 

locomotives, 1098, 1101 



1425 



Compound numbers, 5 
proportion, 7 

units of weights and measures, 
27, 28 
Compressed-air, 593, 604-626 
adiabatic and isothermal com- 
pression, 604 
adiabatic expansion and com- 
pression, tables, 609, 610 
compound compression, 609 
cranes, 1168 
diagrams, curve of, 611 
drills driven by, 616 
engines, adiabatic expansion in, 

608 
engines, efficiency, 613 
flow of, in pipes, 594 
for motors, effect of heating, 612 
formulae, 606 
for street railways, 625 
heating of, 604 
hoisting engines, 618 
horse-power required to com- 
press air, 606 
locomotive, 1104 
losses due to heating, 606 
. loss of energy in, 604 

machines, air required to run, 

616, 618 
mean effective pressures, tables, 

609, 610 
mine pumps, 625 
moisture in, 584 
motors, 612 
motors with return-air circuit, 

620 
Popp system, 612 
practical applications of, 619 
pumping with (see also Air- 
lift), 617 
reheating of, 619 
tramways, 624, 625 
transmission, 593 
transmission, efficiencies of, 613 
volumes, mean pressures per 

stroke, etc., table, 605 
work of adiabatic compression, 
607 
Compressed steel, 464 
Compressibility of liquids, 172 

of water, 691 
Compression, adiabatic, formulae 
for, 606 
and flexure combined, 312 
and shear combined, 312. 
and torsion combined, 312 
in steam-engines, 935 
of air, adiabatic, tables, 609, 610 
Compressive strength, 267-269 
strength of iron bars, 337 
strengths of woods, 344, 346 
tests, specimens for, 268 
Compressors, air, effect of intake 
temperature, 619 
air, tables of, 614-615 
Concrete, crushing strength of 12- 
in. cubes, 1334 



Concrete, durability of iron in, 412 
reinforced, allowable working 
stresses, 1335 
Condenser, barometric, 1051 

the Leblanc, 1057 
Condensers, 1050-1061 
air-pump for, 1053, 1055 
calculation of surface of, 910 
choice of, 1059 
circulating pump for, 1057 
cooling towers for, 1060 
cooling water required, 1050 
continuous use of cooling water 

in, 1058 
contraflow, 1053 
ejector, 1051 

evaporative surface, 1057 
for refrigerating machines, 1300 
heat transference in, 1052 
increase of power due to, 1058 
jet, 1050 
surface, 1051 
tubes and tube plates of, 1054, 

1055 
tubes, heat transmission in, 563 
Condensing apparatus, power used 

by, 1053 
Conduction of heat, 553 
of heat external, 554 
of heat internal, 553 
Conductivity, electric (see Elec- 
tric conductivity) 
electrical, of metals, 1349 
Conductors, electrical, heating of, 
1354 
electrical, in series or parallel, 
resistance of, 1352 
Conduit, water, efficiency of, 735 
Cone, measures of, 63 

pulleys, 1112 
Connecting-rods, steam-engine, 
1003, 1004 
tapered, 1005 
Conic sections, 74 
Conoid, parabolic, 66 
Conservation of energy, 506 
Constantan, copper-nickel alloy, 

379 
Constants, steam-engine, 941 
Construction of buildings, 1333- 

1344 
Controllers, for electric motors, 

1404 
Convection, loss of heat due to, 

570 
Convection of heat, 553 

Dulong's law of, table of factors 
for, 571 
Conversion tables, metric, 23-27 
Converter, Bessemer, temperature 

in, 527 
Converters, electric, 1400 
Conveying of coal in mines, 1178 
Conveyors, belt, 1175 
cable-hoist, 1181 
coal, 1172 
horse-power required for, 1173 



1426 



Conveyors, screw, 1175 

Cooling agents in refrigeration, 

1289 
Cooling of air, 568 

for ventilation, 681 
Cooling-tower practice in refrigerat- 
ing plants, 1301 
for condensers, 1060 
Co-ordinate axes, 71 
Copper, 175 

Copper and vanadium alloys, 371 
Copper ball pyrometer, 526 
balls, hollow, 322 
cast, strength of, 334, 360 
drawn, strength of, 334 
effect of on cast iron, 415 
manganese alloys, 376 
nickel alloys, 378 
plates, strength of, 334 
rods, weight of, table, 218 
steels, 475 
strength of at high temperatures, 

344 
tubing, bends and coils, 214 
tubing, weight of, table, 216 
weight required in different 
systems of transmission, 1398 
wire and plates, weight of, table, 

219 
wire, carrying capacity of, Un- 
derwriter's table, 1355 
wire, cost of for long-distance 

transmission, 1363 
wire, cross section required for a 

given current, 1359 
wire, electrical resistance, table, 

1357, 1358 
wire, stranded, 242 
wire, weight of for electric cir- 
cuits, 1359 
tin-aluminum alloys, 375 
tin alloys, 360 

tin alloys, properties and com- 
position of, 360 
tin-zinc alloys, properties and 

composition, 363 
tin-zinc alloys, law of variation 

of strength of, 364 
zinc alloys, strength of, 364 
zinc alloys, table of composition 

and properties, 362 
zinc-iron alloys, 369 
Cord of wood, 805 
Cordage, technical terms relating 
to, 388 
weight of, table, 386-391, 1157 
Cork, properties of, 355 
Corn, weight of, 178 
Corrosion by stray electric currents, 
446 
due to overstrain, 446 
electrolytic theory of, 444 
of iron, 443 

of steam-boilers, 443, 897 
prevention of, 444 



Corrosion, resistance of aluminum 
alloys to, 376 
resistance to of nickel steel, 474 
Corrosive agents in atmosphere, 

442 
Corrugated arches, 186 
furnaces, 319, 881 
iron, sizes and weights, 186 
plates, properties of Carnegie 
steel, table, 289 
Cosecant of an angle, table, 166-169 
Cosine of an angle, 67 

table, 166, 169 
Cost of coal for steam-power, 983 
of steam-power, 981, 982-984 
Cotangent of an angle, 67 
Cotangents of angles, table, 166- 

169 
Cotton ropes, strength of, 335 
Coulomb, definition of, 1345 
Counterbalancing of hoisting-en- 
gines, 1163 
of locomotives, 1102 
of steam-engines, 980 
Counterpoise system of hoisting, 

1164 
Couples, 491 
Couplings, flange, 1109 

hose, standard sizes, 207 
Coverings for steam-pipe, tests of, 

558-561 
Coversine of angles, table, 166-169 
Cox's formula for loss of head, 717 
Crane chains, 251, 252 
installations, notable, 1168 
pillar, 150-ton, 1168 
Cranes, 1165 

and hoists, power required for, 

1169 
classification of, 1165 
compressed-air, 1168 
electric, 1166-1168 
electric, loads and speeds of, 

1167 
guyed, stresses in, 516 
jib, 1165 

power required for, 1166 
quay, 1168 

simple, stresses in, 515 
traveling, 1166-1169 
Crank angles, steam-engine, table, 
1040 
arm, dimensions of, 1009 
pins, steam-engine, 1005-1009 
pins, steel, specifications for, 483 
shaft, steam-engine, torsion and 

flexure of, 1019 
shafts, steam-engine, 1017-1019 
Cranks, steam-engine, 1009 
Critical point in heat treatment of 
steel, 456 
temperature and pressure of 
gases and liquids, 580 
Cross-head guides, 1002 

pin, 1009 
Crucible steel, 451, 457, 466-470 



(see Steel, crucible) 






cru-dri 



1427 



Crushing strength of masonry 

materials, 349 
Crystallization of iron by fatigue, 

441 
Cubature of volumes, 78 
Cube root, 9 

roots, table of, 94-109 
Cubes of decimals, table, 109 
Cubes of numbers, table, 94-109 
Cubic feet and gallons, table, 129 

measure, 18 
Cupola fan, power required for, 
1230 
gases, utilization of, 1230 
practice, 1224-1230 
practice, improvement of, 1226 
results of increased driving, 1229 
Cupolas, blast-pipes for, 643 
blast-pressure in, 1224-1228 
blowers for, 633, 634 
charges for, 1224-1227 
charges in stove foundries, 1227 
dimensions of, 1224 
loss in melting iron in, 1230 
rotary blowers for, 650 
slag in, 1225 
Current motors, 734 
Currents, electric (see Electric cur- 
rents) 
Curve of PV n construction of, 576 
Curves in pipe-lines, resistance of, 

721 
Cutting metal, resistance over- 
come in, 1256 
metals by oxyacetylene flame, 

464 
speeds of machine tools (see also 

Tools, cutting), 1235 
speeds of tools, economical, 1243 
stone with wire, 1262 
Cut-off for various laps and travel 

of slide valves, 1042 
Cycloid, construction of, 51 

differential equations of, 82, 83 
integration of, 82 
measures of, 62 
Cycloidal gear-teeth, 1138 
Cylinder-condensation in steam- 
engines, 936-937 
lubrication, 1222 
measures of, 63 
Cylinders, hollow, resistance of to 
collapse, 318-322 
hollow, under tension, 316 
hooped, 317 
hydraulic press, thickness of, 317, 

780 
locomotive, 1088 
steam-engine (see Steam-en- 
gines) 
steam-engine, ratios of, 950, 952, 

956 
tables of capacities of, 127 
thick hollow, under tension, 316 
thin hollow, under tension, 317 
Cylindrical ring, 65 

tanks, capacities of, table, 128 



Dalton's law of gaseous pressures, 

Dam, stability of, 491 

Darcy's formula, flow of water, 704 

formula, table from, of flow of 
water in pipes, 709-711 
Decimal equivalents of fractions, 3 

equivalents of feet and inches, 5 

gauge, 33 
Decimals, 3 

squares and cubes of, 109 
Delta connection for alternating 
currents, 1395 

metal wire, 243, 369 
Denominate numbers, 5 
Deoxidized bronze, 371 
Derrick, stresses in, 516 
Diagonals, formulae for strains in, 

519 
Diametral pitch, 1134 
Diesel oil engine, 1078 
Differential calculus, 74-83 

coefficient, 76 

coefficient, sign of, 79 

gearing, 1145 

of exponential function, 80, 81 

partial, 76 

pulley, 513 

second, third, etc., 78 

screw, 514 

screw, efficiency of, 1270 

windlass, 514 
Differentials of algebraic functions, 

75 
Differentiation, formulas for, 75 
Discount, 12 

Disk fans (see Fans, disk) 
Displacement of ships, l3l7, 1322 
Distillation of coal, 803 
Distiller for marine work, 1061 
Distilling apparatus, multiple sys- 
tem, 543 
Domed heads of boilers, 316 
Domes on steam boilers, 889 
Draught power of chimneys, 916, 

917 
Draught theory of chimneys, 915 
Drawing-press, blanks for, 1272 
Dressings, belt, 1128 
Driers and drying, 547 

performance of, 549 
Drift bolts, resistance of in timber, 

323 
Drill gauge, table, 30 
Drill pres?, horse-power required by, 

1253, 1256 
Drills, high-speed steel, 1253 

rock, air required for, 616. 

rock, requirements of air-driven, 
616 

tap, sizes of, 225, 1269 

twist, experiments with, 1254 

twist, speed of, 1253 
Drilling, high-speed, data on, 1254 

holes, speed of, 1253 

steel and cast iron, power re- 
quired for, 1254 



1428 



dro-ele 



INDEX. 



Drop in electric circuits, 1352 
in voltage of wires of different 

sizes, 1356 
press, pressures obtainable by, 
1273 
Dry measure, 19 

Drying and evaporation, 542-547 
apparatus, design of, 550 
in a vacuum, 546 
of different materials, 547 
Ductility of metals, table, 177 
Dulong's formula for heating value 
of coal, 798 
law of convection, table of factors 

for, 571 
law of radiation, table of factors 
for, 570 
Durability of cutting tools, 1243 

of iron, 441,442 
Durand's rule for areas, 57 
Dust explosions, 807 

fuel, 807 
Duty, measure of, 28 
of pumping-engine, 771 
trials of pumping-engines, 771- 
775 
Dynamic and static properties of 

steels, 476 
Dynamics, fundamental equations 

of, 502 
Dynamo-electric machines, classi- 
fication of, 1385 
machines, e.m.f. of armature 

circuit, 1386 
machines, moving force of, 1385 
machines, strength of field, 1387 
machines, tables of, 1412 
machines, torque of armature, 
1385 
Dynamometers, 1280 
Alden absorption, 1281 
hydraulic absorption, 6000 H.P., 

1282 
Prony brake, 1280 
traction, 1280 
transmission, 1282 
Dyne, definition of, 488 

Earth, cubic feet per ton, 178 
Eccentric loading of columns, 278 

steam-engine, 1020 
Economical angle of framed struc- 
tures, 522 
Economics of power-plants, 984 
Economizers, fuel, 894 
Edison wire gauge, 31 

wire-gauge table, 30 
Efficiency, definition of, 12 

of a machine, 507 

of compressed-air engines, 613 

of compressed-air transmission, 
613 

of electric transmission, 1361 

of fans, 631 

of fans and chimneys for venti- 
lation, 683 

of injector, 907 



Efficiency of pumps, 759 

of riveted joints, 405, 407 

of screws, 1270 

of steam-boilers, 860 

of steam-engines, 934 
Effort, definition of, 503 
Ejector condensers, 1051 
Elastic limit, 259-262 

apparent, 260 

Bauschinger's definition of, 261 

elevation of, 261 

relation of, to endurance, 261 

resilience, 260 

resistance to torsion, 311 

Wohler's experiments on, 261 
Elasticity, coefficient of, 260 

modules of, 260 

module of, of various materials, 
351 
Electric brakes, 1217 
Electric circuits {see Circuits, elec- 
tric) 

current, cost of fuel for, 764 

current, determining the direc- 
tion of, 1384 

current required to fuse wires, 
1355 

currents, alternating, 1387 (se* 
Alternating currents) 

currents, direct, 1352 

currents, heating due to, 1354 

currents, short-circuiting of, 
1360 

drive in the machine-shop, 1407 

furnaces, 1376 

generators, usual sizes, tables, 
1412 

heaters, 684 

light stations, economy of en- 
gines in, 963 

lighting, 1367 

lighting, cost of, 1373 

lighting, terms used in, 1367 

locomotive, 4000 H.P., 1366 

motors {see also Motors), 1385, 
1402 

motors, alternating current, va- 
riable speed, 1412 

motors, auxiliary pole type, 
1402 

motors, commercial sizes, tables, 
1412 

motors for machine tools, 1407 

motors, selection of, for different 
service, 1405 

motors, speed of, 1403 

motors, speed control of, 1404 

motors, types used for various 
purposes, 1410 

process of treating iron surfaces, 
449 

railway cars, resistance of, 1086 

railway cars and motors, 1366 

railways, 1366 

storage-batteries, 1378 

transmission, 1359-1364 {see 
Transmission, electric) 



INDEX. 



1429 



Electric transmission, high tension, 
notes on, 1399 
transmission lines, spacing for 

high voltages, 1399 
welding, 1374 

wires (see Wires and Copper 
wires) 
Electrical and mechanical units, 
equivalent values of, 1347 
conductivity of steel, 453 
distribution, systems in use, 

1364 
engineering, 1344-1416 
heating, 684 
horse-power, 940, 1353 
horse-power, table, 1364 
machinery, alternating current, 

standard voltages of, 1-699 
machinery, shaft fit, allowances 

for, 1274 
machines, tables of (see Dyna- 
mo-electric machines), 1412 
power, cost of, 985 
resistance, 1349 
resistance of different metals 

and alloys, 1350 
symbols, 1416 
systems, relative advantages of, 

1363 
units, relations of, 1346 
Electricity, analogies to flow of 
water, 1348 
standards of measurements, 1344 
systems of distribution, 1364 
units used in, 1344 
Electro-chemical equivalents, 1381 
Electro-magnets, 1384 
polarity of, 1384 
strength of, 1384 
Electro-magnetic measurements, 

1348 
Electro-motive force of armature 

circuit, 1386 
E.M.F. of electric circuits, 1352 
Electrolysis, 1382 
Electrolytic theory of corrosion, 

444 
Elements, chemical, table, 170 
Elements of machines, 510-515 
Elevators, coal, 1172 
gravity discharge, 1172 
perfect discharge, 1172 
Ellipse, construction of, 46, 47 
equations of, 72 
measures of, 61 
Ellipsoid, 65 

Elongation, measurement of, 265 
Emery, grades of, 1263-1266 
wheels, speed and selection of, 

1263, 1266 
wheels, strains in, 1264 
Endless screw, 514 
Endurance of materials, relation of, 

to elastic limit, 261 
Energy, available, of expanding 
steam, 842 
conservation of, 506 



Energy, definition of, 503 

intrinsic or internal, 574 

measure of, 503 

mechanical, of steam expanded 
to various pressures, 933 

of recoil of guns, 506 

of water in a pipe, 720 

of water flowing in a tube, 734 

sources of, 506 
Engines, alcohol, 1078 

automobile, capacity of, 1077 

blowing, 652 

compressed air, efficiency of, 613 

fire, capacities of, 725 

gas, 1071-1084 (see Gas-engines) 

hoisting, 1163 

hot-air or caloric, 1071 

hydraulic, 783 

internal combustion, 1071-1084 

oil and gasoline, 1077 

marine, steam-pipes for, 848 

naphtha, 1071 

petroleum, 1077 

pumping, 771-775 (seePumping- 
engines) 

solar, 988 

steam, 929 (see Steam-engines) 

winding, 1163 
Entropy, definition of, 573 

of water and steam, 576 

of water and steam, tables, 839- 
843 

temperature diagram, 574 
Epicycloid, 51 

Equalization of pipes, 596, 853 
Equation of payments, 14 

of pipes, 853 
Equations, algebraic, 35-37 

of circle, 72 

of ellipse, 72 

of hyperbola, 73 

of parabola, 73 

quadratic, 36 

referred to co-ordinate axes, 7 
Equilibrium of forces, 492 
Equivalent orifice, mine ventila- 
tion, 686 
Equivalents, electro-chemical, 1381 
Erosion of soils by water, 705 
Euler's formula for long columns, 

269 
Evaporation, 542-547 

by exhaust steam, 545 

by multiple system, 543 

factors of, 874-878 

in a vacuum, 546 

in salt manufacture, 543 

latent heat of, 542 

of sugar solutions, 545 

of water from reservoirs and 
channels, 543 

total heat of, 542 

unit of, 855 « 
Evaporator, for marine work, 1061 
Evolution, 8 
Exhauster, steam-jet, 651 



1430 



INDEX. 



Exhaust-steam, evaporation by, 
545 
for heating, 981 
Expansion, adiabatic, formulae for, 
606 
by heat, 538 
coefficients of, 539 
of air, adiabatic, tables, 609, 610 
of cast iron, permanent by heat- 
ing, 429 
of gases, construction of curve of, 

576 
of gases, curve of, 74 
of iron and steel, 441 
of liquids, 540 
of nickel steel, 474 
of solids by heat, 539 
of steam, 929 

of steam, actual ratios of, 935 
of timber, 345 
of water, 687 
Explosions, dust, 807 
Explosive energy of steam-boilers, 

902 
Exponents, theory of, 37 
Exponential function, differential 

of, 80, 81 
Eye bars, tests of, 338 

Factor of safety, 352-355 
of safety, formulas for, 354 
of safety in steam-boilers, 879 
of evaporation, 874-878 
Factory heating by fan system, 

681 
Fahrenheit -Centigrade conversion 

table, 524, 525 
Failures of stand-pipes, 328 

of steel, 462 
Fairbairn's experiments on riveted 

joints, 401 
Falling bodies, graphic represen- 
tation, 498 
bodies, height and velocity of 

tables, 499, 500 
bodies, laws of, 497 
Fans (see also Blowers) 
and blowers, 626-653 
and blowers, comparative effi- 
ciencies, 631 
best proportions of, 627 
blast-area of, 629 
centrifugal, 621, 626 
centrifugal, high-pressure, 621 
cupola, power required for, 1230 
design of, 627 
disk, 647-649 
effect of resistance on capacity 

of, 636 
efficiency of, 631, 641, 648 
experiments on, 630, 631 
for cupolas, 633 

high-pressure, capacity of, 635 
influence of speed on efficiency, 

647 
influence of spiral casings, 646 
methods of testing, 639 



Fans, pipe lines for, 643 
. pressure due to velocity of, 627 
quantity of air delivered by, 628 
theory of efficiency of, 641 
Farad, definition and value of, 

1345 
Fatigue, effect of, on iron, 441 

resistance of steels, 447 
Feed and depth of cut, effect of, on 

speed of tools, 1241 
Feed-pump (see Pumps) 
Feed water, cold, strains caused 
by, 909 
water heaters, 909-911 
water heaters, transmission of 

heat in, 564 
water heating, saving due to, 

909 
water, purification of, 694, 695 
water to boilers by gravity, 908 
Feet and inches, decimal equiva- 
lents of, table, 5 
Fence wires, corrosion of, 444 
Ferrite, 416, 456 

Ferro-alloys for foundry use, 1232 
silicon, addition of, to cast-iron, 

426 
silicon, dangerous, 1232 
Field, magnetic, 1346 
Fifth roots and powers of numbers, 

110 
Fineness, coefficient of, 1317 
Finishing temperature, effect of. 

in steel rolling, 454 
Fink roof truss, 521 
Fire, temperature of, 785 
Fire-brick arches in locomotives, 

1091 
Fire-brick, number required for 
various circles, table, 254 
refractoriness of, 255 
sizes and shapes of, 253 
weight of, 253 
Fire-clay, analysis of, 255 

pyrometer, 526, 529 
Fire-engines, capacities of, 725 
Fire-proof buildings, 1338 
Fire-streams, 722-725 

discharge from nozzles at dif- 
ferent pressures, 723 
effect of increased hose length, 

723 
friction loss in hose, 725 
pressure required for given 
length of, table, 723 
Fireless locomotive, 1103 
Fits, force and shrink, 1273 

force and shrink, pressure re- 
quired to start, 1275 
limits of diameter for, 1274 
press, pressure required for, 

1274 
running, 1274 
stresses due to, 1275 
Fittings (see Pipe-fittings) 

cast-iron pipe, sizes and weights, 
table, 196-197 



INDEX. 



fla-for 



1431 



Flagging, strength of, 550 

Flanges, cast-iron, forms of, 202 
forged and rolled steel, 200 
forged steel, for riveted pipe, 

214 
for riveted pipe, 201 
pipe, extra heavy, table, 199 
pipe, standard, table, 198 

Flat plates in steam-boilers, 880, 
885, 888 
plates, strength of, 313 
steel ropes, 248 
surfaces in steam-boilers, 888 

Flanged fittings, cast-iron, 203 
fittings, cast-steel, 204 

Flexure of beams, formula for, 282 
and compression combined, 312 
and tension combined, 312 
and torsion combined, 312 

Flight conveyors, 1172 

Flights, sizes and weights of, 1174 

Floors, maximum load on, 1337, 
1340 
strength of, 1337-1340 

Flow of air in long pipes, 595 
of air in pipes, 591 
of air through orifices, 588, 642 
of compressed air, 594 
of gases, 579 
of gas in pipes, 834-836 
of gas in pipes, tables, 835 
of metals, 1273 
of steam at low pressure, 669 
of steam, capacities of pipes, 

847 
of steam in long pipes, 847 
of steam in pipes, 845 
of steam, loss of pressure due to 

friction, 845 
of steam, loss of pressure due to 

radiation, 849 
of steam, Napier's rule, 844 
of steam, resistance of bends, 

valves, etc., 848 
of steam through a nozzle, 844, 

1065 
of steam through safety valves, 

905 
of steam, tables of, 669, 846, 847 
of water, 697 
of water, approximate formulse, 

720 
of water, Chezy's formula, 699 
of water, D'Arcy's formula, 704 
of water, experiments and tables, 

706-713 
of water, exponential formula, 

718 
of water, fall per mile and slope, 

table, 700 
of water, formulse for, 697-706 
of water in cast-iron pipe, 706 
of water in house service pipes, 

table, 712 
of water in pipes, 699 



Flow of water in pipes at uniform 

velocity, table, 710 
of water in pipes, table from 

D'Arcy's formula, 709-711 
of water in pipes, table from 

Kutter's formula, 707, 708 
of water in 20-in. pipe, 706 
of water in riveted steel pipes, 

714 
of water, Kutter's formula, 701 
of water over weirs, 697, 731 
of water through nozzles, table, 

713 
of water through orifices, 697 
of water through rectangular 

orifices, 72_9 
of water, VV for pipes and con- 
duits, table, 701 
of water, values of c, 703 
of water, values of coefficient of 

friction, 715 
Flowing water, horse-power of, 

734 
water, measurement of, 727- 

733 
Flues, collapsing pressure of, 318 
corrugated, British rules, 318, 881 
corrugated, U. S. rules, 886 

{see also Tubes and Boilers) 
Flux, magnetic, 1348 
Fly-wheels, centrifugal force in, 

1029 
diameters for various speeds, 

1030 
steam-engine, 1026-1034 {see 

Steam-engines) 
wire-wound, for extreme speeds, 

1034 
weight of, for alternating current 

units, 1028 
Foaming or priming of steam- 
boilers, 692, 899 
Foot-pound, unit of work, 503 
Force, centrifugal, 497 
definitions of, 488 
graphic representation of, 489 
moment of, 490 
of a blow, 504 
of acceleration, 501 
of wind, 597 
units of, 488 
Forces, composition of, 489 
equilibrium of, 492 
parallel, 491 
parallelogram of, 489 
parallelopipedon of, 490 
polygon of, 489 
resolution of, 489 
work, power, etc., 503 
Forced draught in steam-boilers, 

894 
Forcing and shrinking fits, 1273 

{see Fits) 
Forging and grinding of tools, 1240 
heating of steel for, 468 
hydraulic. 782 
of tool steel, 464, 468, 1240 



1432 



for-gal 



INDEX. 



Forgings, steel, annealing of, 458 

strength of, 331 
Forging-press, hydraulic, 782 
Foundation walls, thickness of, 

1334 
Foundations of buildings, 1333 

masonry, allowable pressures on, 
1334 
Foundry coke, quality of, 1232 

irons (see Pig iron and Cast iron) 

ladles, dimensions of, 1234 

molding-sand, 1233 

practice, 1224-1234 

practice, shrinkage of castings, 
1231 

practice, use of softeners, 1230 

use of ferro alloys in, 1232 
Fractions, 2 

product of, in decimals, 4 
Frames, steam-engine, 1025 
Framed structures, stresses in, 515- 

522 
Framing, for tanks with flat sides, 

316 
Francis's formulae for weirs, 731 
Freezing point of water, 690 
French measures and weights, 22- 
27 

thermal unit, 532 
Frequency of alternating currents, 
1387 

standard, in electric currents, 
1399 
Friction and lubrication, 1194-1223 

brakes and friction clutches, 1216 

brakes, capacity of, 1281 

clutches, 1155 

coefficient of, definition, 1194 

coefficient of, in water-pipes, 715 

coefficient of, tables, 1195-1197 

drives, power transmitted by, 
1154 

fluid, laws of, 1196 

laws of, of lubricated journals, 
1201 

loss of head by, in water-pipes , 
716 

moment of, 1205 

Morin's laws of, 1200 

of car iournals, 1204 

of hydraulic packing, 780, 1217 

of lubricated journals, 1199-1209 

of air in mine passages, 685 

of metals, under steam pressure, 
1200 

of motion, 1194, 1197 

of pivot bearings, 1205, 1209 

of rest, 1195 

of solids, 1195 

of steam-engines, 1215 

of steel tires on rails, 1195 

rollers, 1210 

rolling, 1195 

unlubricated, law of, 1195 

work of, 1205 
Frictional gearing, 1154 

heads, flow of water, 716 



Frustum of cone, 63 

of parabolic conoid, 66 

of pyramid, 63 

of spheroid, 65 

of spindle, 66 
Fuel, 784-827 

bagasse, 809 

charcoal, 805-807 (see Charcoal) 

coke, 801-804 (see Coke) 

combustion of, 784 

dust, 807 

economizers, 894 

for cupolas, 1225, 1232 

gas, 814 (see Gas) 

gas, for small furnaces, 824 

heat of combustion of, 533,784 

liquid, 810-814 

peat, 808 

pressed, 801 

sawdust, 808 

solid, classification of, 786 

straw, 808 

theory of combustion of, 784 

turf, 808 

weight of, 177 

wet tan bark, 808 

wood, 804, 805 
Functions, of sun and difference of 
angles, 69 

of twice an angle, 70 

trigonometric, tables of, 166, 169 

trigonometric, of half an angle, 70 
Furnace flues, steam-boiler, for- 

mulse for, 881 
Furnace for melting iron for mallea- 
ble castings, 430 

heating (see Heating) 
Furnaces, blast, gases of, 825 

blast, temperature in, 528 

corrugated, 319 

down draught, 890 

electric, 1376 

for different coals, 798 

for house heating, 664 

gas, fuel for, 824 

hot-air, heating of, 661 

industrial, temperatures, in, 527 

open hearth, temperature in, 528 

steam-boiler (see Boiler-furnaces) 
Fusibility of metals, 175-177 
Fusible alloys, 380 

plugs in boilers, 379, 889 
Fusing temperatures of substances, 

527, 532 
Fusing-disk, 1262 
Fusion, latent heat of, 541 

of electrical wires, 1355 

g, value of, 498 

Gallon, British and American, 28 

Gallons and cubic feet, table, 129 

per minute, cubic feet per second, 
129 
Galvanic action, corrosion by, 443 
Galvanized wire rope, 247 

wire, test for, 450 



INDEX. 



gal-gen 



1433 



Galvanizing by cementation, 450 

iron surfaces, 449, 450 
Gas (see also Fuel-gas, Water-gas, 
Producer gas, Illuminating gas) 

ammonia, 1285-1289 

analyses by volume and weight, 
824 

and oil engines, rules for testing, 
1081 

and vapor mixtures, laws of, 578 

anthracite, 815 

bituminous, 816 

carbon, 814 

coal, 828 

flow of, in pipes, 834-836 (see 
Flow of gas) 

flow of, in long pipes, 596 

fuel (see also Water-gas) 

fuel, cost of, 833 

fuel for small furnaces, 824 

illuminating, 828-834 (see Illu- 
minating-gas) 

natural, 817, 818 

perfect, equations of a, 574 

producer, 818 

producer, combustion of, 819 

producer, from ton of coal, 818 

sulphur-dioxide, 1285 

water, 817, 829-833 (see Water- 
gas) 
Gases, absorption of, by liquids, 
579 

Avogadro's law of, 578 

combustion of, rise of tempera- 
ture in, 786 

cupola, utilization of, 1230 

densities of, 578 

expansion of, 575, 577 

expansion of by heat, table, 538 

flow of, 579 

heat of combustion of, 533 

law of Charles, 574, 578 

liquefaction of, 579 

Mariotte's law of, 577 

of combustion, analyses of, 785 

physical properties of, 577-580 

specific heats of, 535, 537 

waste, use of, under boilers, 865, 
866 

weight and specific gravity of, 
table, 173 
Gas-engine, economical perform- 
ance of, 1080 

heat losses in, 1080 

tests with different coals, 823 
Gas-engines, 1071-1084 

calculation of the power of, 1073 

conditions of maximum effi- 
ciency, 1079 

efficiency of, 1079 

four-cycle and two-cycle, 1072 

governing, 1079 

horse-power, estimate of, 1077 

ignition, 1078 

mean effective pressure in, 1076 

pressures developed in, 1072 



Gas-engines, sizes of, 1076 

temperatures and pressures in, 

1072, 1074 
tests of, 1081-1084 
Gas-exhausters, rotary, 651 
Gas-producer practice, 821 
Gas-producers and scrubbers, pro- 
portions of, 819 
use of steam in, 824 
Gasoline engines, 1077 

vapor pressures of, 814 
Gauge, decimal, 33 
sheet metal, 29, 31-33 
Stub's wire, 29, 30 
wire, 29-31 
Gauges, limit, for iron for screw 

threads, 223 
Gauss, definition and value of, 

1346, 1348 
Gear, reduction, for steam turbines, 

1071 
reversing, 1020 
wheels, calculation of speed of. 

1137 
wheels, formulae for dimensions, 

1135, 1136 
wheels, milling cutters for, 1138 
wheels, proportions of, 1137 
worm, 514 
Gears, automobile, efficiency of, 

1148 
lathe, for screw cutting, 1236 
of lathes, quick change, 1237 
Gears, spur, machine-cut, 1153 

with short teeth, 1135 
Gearing, annular, 1145 
bevel, 1144 
chordal pitch, 1135 
comparison of formulae, 1150- 

1153 
cycloidal teeth, 1138 
differential, 1145 
efficiency of, 1146-1148 
forms of teeth, 1138-1145 
formulae for dimensions of, 1135, 

1136 
frictional, 1154 
involute teeth, 1140 
pitch, pitch-circle, etc., 1133 
pitch diameters for 1-inch circu- 
lar pitch, 1135 
proportions of teeth, 1135, 1136 
racks, 1141 
raw-hide, 1153 
relation of diametral and circular 

pitch, 1134 
speed of, 1153 
spiral, 1143 
stepped, 1143 
strength of, 1148-1156 
toothed-wheel, 514, 1133-1153 
twisted, 1143 
worm, 1143 

worm, efficiency of, 1147 
Generator sets, standard dimensions 

of, 979 



1434 



gen-hea 



INDEX. 



Generators, alternating current, 
1396 (see Dynamo electric 
machines) 
electric, 1385, 1412 
Geometrical problems, 38-54 
progression, 11 
propositions, 54 
Geometry,, analytical, 71 
German silver, 334, 378 
conductivity of, 1350 
Gesner process, treating iron sur- 
faces, 449 
Gilbert, unit of magneto-motive 

force, 1348 
Girders, allowed stresses in plate 
and lattice, 274 
and beams, safe load on, 1334 
building, New York building 

laws, 1338 
iron-plate, strength of, 331 
steam-boiler, rules for, 882 
Warren, stresses in, 520 
Glass, skylight, sizes and weights, 
190 
strength of, 343 
weight of, 174 
Gordon's formula for columns, 270 
Gold, mating temperature of, 527 

properties of, 175 
Governing of gas-engines, 1079 
Governor, inertia, 1048 
Governors, steam-engine, 1047- 

1050 
Grade line, hydraulic, 721 
Grain, weight of, 178 
Granite, strength of, 335, 348 
Graphite, Acheson's deflocculated, 
1223 
lubricant, 1223 
paint, 447 
Grate surface, for house heating, 
boilers and furnaces, 665 
surface in locomotives, 1091 
surface of a steam-boiler, 857 
Gravel, cubic feet per ton, 178 
Gravity, acceleration due to, 497 
boiler-feeders, 908 
center of, 492 

specific (see Specific gravity), 
170-174 
Grease lubricants, 1221 
Greatest common measure or 

divisor, 2 
Greek letters, 1 

Greenhouses, hot-water, heating 
of, 674 
steam-heating of, 673 
Grinding of tools, 1240, 1241 

wheel for high-speed tools, 1240, 

1267 
wheels (see Grindstones and 

Emery wheels) 
wheels, speeds of, 1264 
Grindstones, speed of, 1267 
strains in, 1267 
varieties of, 1268 



Guest's formula for combined 

stresses, 312 
Gun-bronze, variation in strength 

of, 362 
Gun-iron, variation in strength of, 

428 
Gun-metal (bronze), composition 

of, 366 
Guns, energy of recoil of, 506 
Gurley's bronze, composition of, 366 
Guy ropes, wire, 247 

for stand-pipes, 327 
Guy-wires, table of weights, and 

strength, 249 
Gyration, center of, 494 
radius of, 279 
table of radii of, 495 

H-columns, Bethlehem steel, 309, 

310 
Halpin heat storage system, 897, 

987 
Hammering, effect of, on steel, 464 
Hardening of steel, 455 
Hardness of copper-tin alloys, 361 
of metals, Brinell's tests, 342 
electro-magnetic tests of, 343 
scleroscope tests, 343 
of water, 694 
Harvey process of hardening steel, 

1246 
Haulage, wire-rope, 1177-1181 
wire-rope, endless rope system, 

1178 
wire-rope, engine-plane, 1178 
wire-rope, inclined-plane, 1177 
wire-rope, tail-rope system, 1178 
wire-rope tramway, 1179 
Hauling capacity of locomotives, 

1087 
Hawley down-draught furnace, 890 
Hawsers, flexible steel wire, 249 
steel, table of sizes and strength, 

249 
steel, weight of, 249 
Head, frictional, in cast-iron pipe, 
table, 719 
loss of, 714-722 (see Loss of 

head) 
of air, due to temperature differ- 
ences, 687 
of water, 699 

of water, comparison of, with 
various units, 689 
Heads of boilers, 885 

of boilers, unbraced, wrought - 
iron, strength of, 314 
Heat, 523-577 

conducting power of metals, 553 
conduction by various substances, 

554-561 
conduction of, 553 
convection of, 553 
effect of on grain of steel, 456 
expansion due to, 538 
generated by electric current, 
1354 



INDEX. 



1435 



Heat, latent, 541 (see Latent heat) 

loss by convection, 570 

losses in steam power plants, 985 

mechanical equivalent of, 532, 
837 

of combustion, 533 

of combustion of fuels, 533, 784 

quantitative measurement of, 
532 

radiating power of substances, 
552 

radiation of, 551 (see also Radia- 
tion) 

reflecting power of substances, 
552 

resistance, coefficients of, 556 

resistance, reciprocal of con- 
ductivity, 555 

specific, 534-538 (see Specific 
heat) 

steam, storing of, 897, 987 

storage, Halpin system, 897, 987 

transmission, Blechynden's tests 
of, 567 

transmission from flame to water, 
567 

transmission from gases to water, 
566 

transmission from steam to water, 
561, 652 

transmission, in condenser tubes, 
563 

transmission in feed water heater, 
564 

transmission in radiators, 669 

transmission, resistance of metals, 
553 

transmission through building 
walls, etc., 557, 659 

transmission through plates, 553, 
567 

transmission through plates from 
steam or hot water to air, 569 

treatment of steel (see Steel) 

treatment of high speed tool 
steel, 1242 

unit of, 532, 837 

units per pound of water, 688 
Heaters and condensers, calcula- 
tion of surface of, 910 

cast iron, for hot-blast heating, 
680 

cast iron, tests of, 680 

electric, 1375 

feed-water, 909-911 

feed-water, open type, 911 

feed-water, transmission of heat 
in, 564 
Heating a building to 70°, 683 
Heating and Ventilation, 653-687 

allowance for exposure and leak- 
age, 660 

blower system, 678-681 

boiler heating surface, 667 

computation of radiating surface, 
669 

heating surface, indirect, 669 



Heating and Ventilation, heating 

value of radiators, 656, 668 

hot-water heating, 674-678 (see 

Hot-water heating) 
overhead steam pipes, 673 
steam-heating, 665-674 (see 

Steam-heating) 
transmission of heat through 
building walls, 659 
Heating air, heat absorbed in, 662 
Heating, blower system, capacity 
of fans for, 682 
by electricity, 684 
by exhaust steam, 981 
by hot-air furnaces, 661 
by hot water, 675 (see Hot-water 

heating) 
by steam (see Steam-heating) 
furnace, size of air pipes for, 663 
furnace, with forced air supply, 

664 
guarantees, performance of, 683 
of electrical conductors, 1354 
of factories by blower system, 681 
of greenhouses, 673 
of large buildings, 656 
of steel for forging, 468 
of tool steel, 467 
value of coals, 797, 798 
value of wood, 804 
water by steam coils, 565 
Heating-surface of steam boiler, 

855, 856 
Heat-insulating materials, tests 

of, 555 
Height, table of, corresponding to 

a given velocity, 499 
Helical steel springs, 395 
Helix, 62 

Hemp rope, table of strength and 
weight of, 386, 387 
rope strength of, 335 
Henry, definition and value of, 

1345 
High speed tool steel (see Steel, 

and Tools) 
Hindley worm gear, 1144 
Hobson's hot-blast pyrometer, 528 
Hodgkinson's formula for columns, 

269 
Hoisting by hydraulic pressure, 
781 
counterpoise system, 1164 
cranes, 1165 (see Cranes) 
effect of slack rope, 1162 
endless rope system, 1165 
engines, 1163 

engines, compressed-air, 618 
engines, counterbalancing of, 

1163 
horse-power required for, 1162 
Koepe system, 1165 
limit of depth for, 1162 
loaded wagon system, 1164 
of cargoes, 390 
pneumatic, 1163 



1436 



Hoisting rope, 386 

rope, iron or steel, dimensions, 
strength, and properties, table, 
244 
ropes, sizes and strength of, 390, 

906 
ropes, stresses in, on inclined 

planes, 1179 
rope, tension required to pre- 
vent slipping, 1182 
suspension cable ways, 1181 
tapering ropes, 1164 
Holding power of bolts in white 
pine, 324 
power of expanded boiler tubes, 

342 
power of lag-screws, 324 
power of nails in wood, 324 
power of nails, spikes and screws, 

323 
power of tubes expanded into 

sheets, 342 
power of wood screws, 324 
Hollow cylinders, resistance of to 
coUapse, 318-322 
shafts, torsional strength of, 311 
Homogeneity test for fire-box 

steel, 484 
Hooks and shackles, strength of, 
1161 
heavy crane, 1159 
proportions of, 1159 
Horse-gin, 509 
Horse, work of, 508 
Horse-power, brake, definition of, 
991 
computed from torque, 1386 
constants, of steam-engines, 

941-944 
cost of, 735 
definition of, 28, 503 
electrical, 940, 1353 
electrical, table of, 1364 
hours, definition of, 503 
nominal, definition of, 944 
of fans, 630 
of flowing water, 734 
of marine and locomotive boilers, 

857 
of steam-boilers, 854 
of steam-boilers, builders' rat- 
ing, 857 
of steam-engines, 940-946 
Hose couplings, national stand- 
ard, 207 
fire, friction losses in, 725 
hydrant pressures required with 

different lengths of, 723 
rubber-lined, friction loss in, 725 
Hot-air engines, 1071 
Hot-air heating (see Heating) 
Hot-blast pyrometer, Hobson's, 
528 
system of heating, 680 (see Heat- 
ing) 
Hot boxes, 1205 



Hot-water heating, 674-678 

heating, arrangement of mains, 

674 
heating, computation of radiating 

surface, 675, 677 
heating, indirect, 676 
heating of greenhouses, 674 
heating, rules for, 674 
heating, size of pipes for, 675 
heating, sizes of flow and return 

pipes, 678 
heating, velocity of flow, 674 
heating with forced circulation, 
678 
House-heating (see Heating) 
House-service pipes, flow of water 

in, table, 712 
Howe truss, stresses in, 520 
Humidity, relative, table of, 551, 

583 
Hyatt roller bearings, 1211 
Hydraesfer process, treating iron 

surfaces, 449 
Hydrant pressures required with 

different lengths of hose, 723 
Hydraulic air compressor, 622 
apparatus, efficiency of, 780 
cylinders, thickness of, 780 
engine, 783 
forging, 782 
formulae, 697-706 
formulae, approximate, 720 
grade-line, 721 
packing, friction of, 780 
pipe, table, 212 
power in London, 781 
press, thickness of cylinders for, 

317 
presses in iron works, 781 
pressure, hoisting by, 781 
pressure, transmission, 779-783 
pressure transmission, energy of, 

779, 780 
pressure transmission, speed of 
water through pipes and 
valves, 781 
ram, 778, 779 
riveting machines, 782 
Hydraulics (see Flow of water) 
Hydrometer, 172 

dry and wet bulb, 583 
Hyperbola, asymptotes of, 74 
construction of, 50 
curve on indicator diagrams, 

944 
equations of, 73 
Hyperbolic logarithms, tables of, 

163-165 
Hypocycloid, 51 

I-beams (see also Beams) 

Carnegie, table of, 288 

safe loads on, 290 

spacing of, for uniform load, 291' 
Ice, properties of, 691 

strength of, 344 



INDEX. 



1437 



Ice-making, absorption evaporator 
system, 1316 

making machines, 1282-1316 (see 
Refrigerating machines) 

making plant, test of, 1315 

making, tons of ice per ton of 
coal, 1316 

making with exhaust steam, 1316 

manufacture, 1314 (see Refrige- 
erating machines) 

melting effect, 1291 
Ignition in gas engines, 1078 
Illuminating-gas, 828-834 

calorific equivalents of constitu- 
ents, 830 

coal-gas, 828 

fuel value of, 833 

space required for plants, 832 

water-gas, 829 
Illumination, 1367 

by arc lamps at different dis- 
tances, 1368 

of buildings, watts per square foot 
required for, 1369 

relation of, to vision, 1368 
Illuminants, relative color values 

of, 1367 
Impact, 505 
Impedance, 1389 

polygons, 1390 
Impulse water wheels, 749 (see Wa- 
ter wheel, tangential) 
Impurities of water, 691 
Incandescent lamp, 1370 

lamps (see Lamps) 
Inches and fractions as decimals 

of a foot, table, 5 
Inclined-plane, 512 

motion on, 502 

stresses in hoisting ropes on, 1179 

wire-rope haulage, 1177 
Incrustation and scale, 691, 692 
India rubber, action under tension, 
356 

vulcanized, tests of, 356 
Indicated horse-power, 940-946 
Indicator diagrams, analysis of, 992 

rig, 939 

tests of locomotives, 1098 
Indicators, steam-engine, 938-946 
(see Steam-engines) 

steam-engine, errors- of, 939 
Indirect heating radiators, 669 
Inductance, 1389 

of lines and circuits, 1393 
Induction, magnetic, 1348 

motor applications, 1410 

motors, 1409 
Inertia, definition of, 488 

moment of, 279, 493 
Ingots, steel, segregation in, 462 
Injector, 776 

efficiency of, 907 

equation of, 906 
Inoxidizable surfaces, production 

of, 448 
Inspection of steam-boilers, 901 



Insulation, underwriters', 1355 
Insulators, electrical value of, 1350 

heat, 555 
Intensity of magnetization, 1346 
Integrals, 76 ■ 

table of, 81, 82 
Integration, 77 
Intercoolers for air compressors, 

620 
Interest, 12 

compound, 13 
Interpolation, formula for, 87 
Invar, iron-nickel alloy, 475, 540 
Involute, 53 
gear-teeth, 1140 

gear-teeth, approximation of, 
1142 
Involution, 7 

Iron and steel, 175, 413-484 
and steel, classification of, 413 
and steel, effect of cold on 

strength of, 440 
and steel, inoxidizable surface 

for, 448 
and steel, Pennsylvania Rail- 
road specification for, 438 
and steel, preservative coatings 

for, 447-450 
and steel, relative corrosion of, 

444 
and steel, rustless coatings for, 

447-450 
and steel sheets, weight of, 181 
and steel, specific heat of, 535, 

536 
and steel, tensile strength at 
high temperatures, 439 
Iron bars (see Bars) 

bars, weight of square and round, 

180 
bridges, durability of, 442 
cast, 414-429 (see Cast-iron) 
coefficients of expansion of, 441 
color of, at various temperatures, 

531 
copper-zinc alloys, 369 
corrosion of, 443 
corrugated, sizes and weights, 

186 
durability of, 441-442 
flat-rolled, weight of, 182, 183 
for bolts, variation in size of, 223 
for stay-bolts, 438 
latent heat of fusion of, 541 
malleable, 429 (see Malleable 

iron) 
pig (see Pig-iron and Cast-iron) 
plates, approximating weight of, 

461 
plate, weight of, table, 184 
properties of, 175 
rivets, shearing resistance of, 407 
rope, flat, table of strength of, 

387 
lope, table of strength of, 386 
shearing strength of, 340 
sheets, weights of, 33, 181 



1438 



INDEX. 



Iron tubes, collapsing pressure of, 

silicon-aluminum alloys, 374 

wrought, 435-439 (see Wrought 
iron) 
Iridium, properties of, 175 
Irregular figure, area of, 57, 58 

solid, volume of, 66 
Irrigation canals, 704 
Isothermal compression of air, 604 

expansion, 575 

expansion of steam, 929 

Japanese alloys, composition of, 

368 
Jarno tapers, 1271 
Jet condensers, 1050 

propulsion of ships, 1333 

reaction of a, 1333 
Jets, vertical water, 722 
Joints, riveted, 401-412 (see Riv- 
eted joints) 
Joists, contents of, 21 
Joule, definition and value of, 1345 
Joule's equivalent, 533 
Journals (see also Shafts, and Bear- 
ings) 

coefficients of frictioa of, 1197 
Journal-bearings, cast-iron, 1199 

friction of, 1199-1209 

of engines, 1015 

Kaolin, melting point of, 529 
Kelvin's rule for electric trans- 
mission, 1360 
Kerosene for scale in boilers, 899 
Keys, dimensions of, 1276 
for machine tools, 1277 
for shafting, sizes of, 1277 
holding power of, 1278 
sizes of, for mill-gearing, 1276 
Keyways for milling cutters, 1248 
Kinetic energy, 503 
King-post truss, stresses in, 517 
Kirkaldy's test on strength of 

materials, 330-336 
Knife-edge bearings, 1214 
Knot, or nautical mile, 17 
Knots, 391-392 

Koepe's system of hoisting, 1165 

Krupp steel tires and axles, 332 

Kutter's formula, flow of water, 701 

formula, table from, of flow of 

water in pipes, 707, 708 

Lacing of belts, 1124 

Ladles, foundry, sizes of, 1234 

Lag screws, 234 

holding power of, 324 
Lamp, mercury vapor, 1369 
Lamps, arc, 1368 

arc, data of, 1369 

arc, illumination by, at different 
distances, 1368 

incandescent, characteristics of, 
1371 



Lamps, incandescent electric, 1370 

incandescent, rating of, 1370 

incandescent, variation in can- 
dle-power, efficiency and life, 
1371 

life of, 1370-1376 

Nernst, 1372 

specifications for, 1372 

tantalum and tungsten, 1372 
Land measure, 17 
Lang lay rope, 246 
Lap and lead in slide valves, 1034- 

1036 
Lap-joints, riveted, 406 
Latent heat of ammonia, 1285 

heat of evaporation, 542 

heat of fusion of various sub- 
stances, 541 

heat of fusion of iron, 541 
Lathe, change-gears for, 1237 

cutting speed of, 1235 

horse-power to run, 1257-1260 

rules for screw-cutting gears, 
1236 

setting taper in, 1238 

tools, forms of, 1238 
Lattice girders, allowed stresses in, 

274 
Laws of falling bodies, 497 

of motion, 488 
Lead and tin tubing, 217, 218 

coatings on iron surfaces, 450 

effect of, on copper alloys, 369 

pipe, tin-lined, sizes and weights, 
table, 217 

pipe, weights and sizes of, table, 
217 

properties of, 175 

sheet, weight of, 218 

waste-pipe, weights and sizes of, 
218 
Lead-lined iron pipe, 218 
Leakage of steam in engines, 946 
Least common multiple, 2 
Leather, strength of, 335 
Le Chatelier's pyrometer, 526 
Lentz compound engine, 9"" 
Leveling by barometer, 582 

by boiling water, 582 
Lever, 510 

bent, 511 
Lighting, electric, 1367 

electric, cost of, 1373 
Lightning protection of chimneys, 

920 
Lignites, analysis of, 796 
Lime and cement mortar, strength 
of, 350 

weight of, 178 
Limestone, strength of, 349 
Limit, elastic, 259-262 . 

gages for screw-thread iron, 223 
Lines of force, 1382 
Links, steel bridge, strength of, 331 i 

steam-engine, size of, 1020 
Link-belting, sizes and weights, 
1174 



_. 



INDEX. 



lin-mag 



1439 



Link-motion, locomotive, 1095 

steam-engine, 1044-1046 
Lintels in buildings, 1338 
Liquation of metals in alloys, 364 
Liquefaction of gases, 579 
Liquid air, 579 

measure, 18 
Liquids, absorption of gases by, 579 

compressibility of, 172 

expansion of, 540 

specific gravity of, 172 

specific heats of, 535 
Loading and storing machinery, 

1169 
Locomotive boilers, size of, 1089 

crank-pin, quantity of oil used 
on, 1223 

cylinders, 1088 

electric, 4000 H.P., 1366 

engine performance, 1099 

forgings, strength of, 331 

link-motion, 1095 

testing, 1099 
Locomotives, 1084-1105 

boiler pressure, 1093 

classification of, 1092 

compounding of , 1101 

compressed-air, 1104 

compressed-air, with compound 
cylinders, 1105 

counterbalancing of, 1102 

dimensions of, 1096-1098 

drivers, sizes of, 1094 

economy of high pressures in, 
1092 

effect of speed on cylinder pres- 
sure, 1093 

efficiency of, 1087 

exhaust-nozzles, 1091 

fire-brick arches in, 1091 

fireless, 1103 

fuel efficiency of, 1095 

fuel waste of, 1101 

grate surface of, 1091 

hauling capacity of, 1087 

horse-power of, 1089 

indicator tests of, 1098 

light, 1103 

leading types of, 1092 

Mallet compound, 1096 

narrow gauge, 1103 

performance of high speed, 1094 

petroleum burning, 1103 

smoke-stacks, 1091 

speed of, 1094 

steam distribution of, 1093 

steam-ports, size of, 1094 

superheating in, 1102 

tractive power of, 1088, 1101 

types of, 1092 

valve travel, 1094 

water consumption of, 1098 

weight of, 1100 

Wootten, 1090 
Logarithmic curve, 74 

ruled paper, 85 

sines, etc., table, 169 



Logarithms, 80 

hyperbolic, tables of, 163-165 

tables of, 136-163 

use of, 134-136 
Logs, area of water required to 
store, 254 

weight of, 254 
Loop, steam, 852 
Loops of force, 1382 
Long measure, 17 
Loss and profit, 12 

of head, 714-722 

of head, Cox's formula, 717 

of head in cast-iron pipe, tables, 
719 

of head in riveted steel pipes, 714 
Lowmoor iron bars, strength of, 330 
Lubricant water as a, 1222 
Lubricants, examination of, 1219 

grease, 1221 

measurement of durability, 1218 

oil, specifications for, 1219 

qualifications of good, 1219 

relative value of, 1219 

soda mixture, 1223 

solid, 1223 

specifications for petroleum, 1219 
Lubrication, 1218-1223 

of engines, quantity of oil needed 
for, 1221 

of steam-engine cylinders, 1222 
Lumber, weight of, 254 
Lumen, definition of, 1367 
"Lusitania," turbines and boilers 
of, 1330 

performance of, 1330 
Lux, definition of, 1367 

Machine screws, A.S.M.E. stan- 
dard, table, 226 
screws, taps for, 1269 
shop, 1235-1279 
shop, electric drive in, 1407 
shops, horse-power required in, 
1256-1262 
Machines, dynamo-electric (see 

Dynamo-electric machines) 
Machine tools, electric motors for, 
1260, 1407 
tools, keys for, 1277 
tools, power required for, 1256- 

1260 
tools, proportioning a series of 

sizes of, 1276 
tools, soda mixture for, 1222 
tools, speed of, 1235 
Machines, efficiency of, 507 

elements of, 510-515 
Machinery, coal-handling, 1172- 
1177 
horse-power required to run, 
1256-1262 
Maclaurin's theorem, 79 
Magnalium, magnesium-aluminum 

alloy, 376 
Magnesia bricks, 257 
Magnesium, properties of, 176 



1440 



mag-met 



INDEX. 



Magnet, use of, to determine har- 
dening temperature of steel, 
1246 
agnets, electro-, 1384 
lifting, 1169 
Magnetic alloys of non-magnetic 
metals, 378 
balance, 459 
brakes, 1217 

capacity of iron, effect of anneal- 
ing on, 459 
circuit, 1382 
circuit, units of, 1348 
fie?d, 1346 

field, strength of, 1387 
flux, magnetic induction, 1348 
moment, 1346 

pole, unit of, definition, 1346 
Magnetization, intensity of, 1346 
Magneto-motive force, 1348, 1383 
Magnolia metal, composition of, 

381 
Mahler's calorimeter, 798 
Malleability of metals, table, 177 
Malleable castings, annealing, 431 
castings, design of, 433 
castings, pig iron for, 430 
castings, rules for use of, 433 
castings, tests of, 435 
iron, 429 
iron, composition and strength 

of, 430 
iron, improvement in quality, 

434 
iron, physical characteristics, 

432 
iron, shrinkage of, 431 
iron, specifications, 433 
iron, strength of, 430, 434 
iron test bars, 432 
Mandrels, standard steel, 1272 
Manganese bronze, 377 
-copper alloys, 376 
effect of, on cast-iron, 415, 426 
effect of, on steel, 452 
properties of, 176 
steel, 470 
Manila rope, 386 

rope, weight and strength of, 391 
Manograph, a high-speed engine- 
indicator, 939 
Manometer, air, 581 
Man-wheel, 508 
Man, work of, tables, 507, 508 
Marble, strength of, 335 
Marine engine, internal combus- 
tion, 1322 
engineering. 1316-1333 (see 

Ships and Steam-engines) 
practice, 1329 
Mariotte's law of gases, 577 
Martensite, 416, 456 
Masonry, allowable pressures on, 
1334 
crushing strength of, 349 
materials, weight and specific 
gravity of, 174 



Mass, definition of, 487, 501 

= weight h- g, 503 
Materials, 170-257 
strength of, 258-359 
strength of, Kirkaldy's tests, 

330—336 
various, weights of, table, 178 
Maxima and minima, 79, 80 
Maxwell, definition and value of, 

1348 
Measure and weights, compound 
units, 27, 28 
and weights, metric system, 22-27 
Measures, apothecaries, 18, 20 
board and timber, 20 
circular, 20 
dry, 19 
liquid, 18 
long, 17 
nautical, 17 

of work, power and duty. 28 
old land, 17 
shipping, 19 
solid or cubic, 18 
square, 18 
surface, 18 
time, 20 
Measurement of vessels, 1316 
of air velocity, 596 
of elongation, 265 
of flowing water, 727-733 
Measurements, miner's inch, 730 
Mechanics, 487-522 
Mechanical and electrical units, 
equivalent values of, 1347 
equivalent of heat, 532, 837 
powers, 510 
stokers, 889 
Mekarski compressed-air tram- 
way, 624 
Melting points of substances, 532 

temperatures, 527 
Mensuration, 55-67 
Mercury, properties of, 176 

vapor lamp, 1369 
Mercury-bath pivot, 1209 
Mercurial thermometer, 523 
Mesure and Nouel's pyrometric 

telescope, 529 
Metacenter, definition of, 690 
Metals, anti-friction, 1179 

coefficients of expansion of, 539 
coefficients of friction of; 1196 
electrical conductivity of, 1349 
flow of, 1273 

heat-conducting power of, 553 
life of under shocks, 262 
properties of, 174-177 
resistance overcome in cutting 

of, 1256 
specific gravity of, 171 
specific heats of, 535, 536 
table of ductility, infusibility, 
malleability and tenacity, 177 
tenacity of at various tempera- 
tures, 439 
weight of, i; I 



INDEX. 



1441 



Metaline lubricant, 1223 

Metallography, 456 

Meter, Venturi, 728 

Meters, water delivered through, 

722 
Metric conversion tables, 23-27 

measures and weights, 22-27 

screw-threads, cutting of, 1238 
Microscopic constituents of cast- 
iron and steel, 416, 456 
Mil, circular, 18, 30, 31 
Mill buildings, approximate cost 
of, 1342 

columns, 1341 

power, 735 
Milling cutters, for gear-wheels, 
1138 

cutters, helical, tests with, 1251 

cutters, inserted teeth, 1248 

cutters, key ways in, 1248 

cutters, lubricant for, 1252 

cutters, number of teeth in, 1248 

cutters, pitch of teeth, 1247 

cutters, side, 1248 

cutters, spiral, 1248 

cutters, steel for, 1247 

machines, cutting speed of, 1249 

machines, feed of, 1249 

machines, high results with, 
1250 

machines, typical jobs on, 1251 

machines vs. planer, 1252 

power required for, 1249 

practice, modern, 1252 
Mine fans, experiments on, 645 

ventilation, 685 
Mines, centrifugal fans for, 644 
Mine- ventilating fans, 645 
Miner's inch, 18 

inch measurements, 730 
Modulus of elasticity, 260 

of elasticity of various materials, 
351 

of resistance or section modulus, 
280 

of rupture, 282 
Moisture in atmosphere, 583 

in steam, determination of, 912- 
915 
Molding-sand, 1233 
Molds, cast-iron, for iron castings, 

analysis of, 1233 
Moment of a couple, 491 

of a force, 490 

of friction, 1205 

of inertia, 279, 493 

statical, 490 
Moments, method of, for deter- 
mining stresses, 519 

of inertia of regular solids, 493 

of inertia of structural shapes, 
279 
Momentum, 502 
Mond gas producer, 822 
Monel metal, copper-nickel alloy, 

379 
Monobar, chain conveyor, 1173 



Morin's laws of friction, 1200 
Morse tapers, 1271 
Mortar, strength of, 350 
Motion, accelerated, formulae for, 
501 

friction of, 1194, 1197 

Newton's laws of, 488 

on inclined planes, 502 

perpetual, 507 

retarded, 497 
Motor boats, power of engines for, 

1322 
Motors, alternating-current, 1408 

compressed-air, 612 

electric (see Electric motors) 

electric, classification of, 1401 

for electric railways, 1366 

water current, 734 
Moving strut, 511 
Mule, work of, 509 
Multiphase electric currents, 1395 
Multiple system of evaporation, 

543 
Multivane fans, 636 
Muntz metal, composition of, 366 
Mushet steel, 472 

Nails, cut, table of sizes and 
weights, 234 
cut vs. wire, 324 
holding power of, 323 
wire, table of sizes and weights, 
235, 236 
Nail-holding power of wood, 324 
Naphtha engines, 1071 
Napier's rule for flow of steam, 

844 
Natural gas, 817, 818 
Nautical measure, 17 

mile, 17 
Nernst electric lamps, 1372 
Newton's laws of motion, 488 
Nickel-copper alloys, 378 
Nickel, effect of on properties of 
steel, 473 
properties of, 176, 357 
steel, 472 
steel, tests of, 472 
steel, uses of, 474 
-vanadium steels, 475 
Niter process, treating iron sur- 
faces, 449 
Nordberg feed-water heating sys- 
tem, 974 
Nozzles, flow of steam through, 
844, 1065 
flow of water in, 713 
for measuring discharge of pump- 
ing engines, 728 
water, efficiency of, 753 
Nut and bolt heads, thickness of, 
222 

Oats, weight of, 178 
Ocean waves, power of, 755 
Oersted, unit of magnetic reluo 
tance, 1348 



1442 



ohm-pip 



INDEX. 



Ohm, definition and value of, 1345 
Ohm's law, 1352 
law applied to alternating cur- 
rents, 1390 
law applied to parallel circuits, 

1352 
law applied to series circuits, 
1352 
Oil as fuel, 812 
fire-test of, 1220 
for steam turbines, 1221 
lubricating 1218-1223 (see Lu- 
bricants) 
parafflne, 1220 
pressure in a bearing, 1204 
quantity needed for engines, 

1221 
vs. coal as fuel, 812 
well, 1220 
-engines, 1077 

tempering of steel forgings, 458 
Open-hearth furnace, tempera- 
tures in, 527 
steel (see Steel, open-hearth), 451 
Ordinates and abscissas, 71 
Ores, cubic feet per ton, 178 
Orifice, equivalent, in mine venti- 
lation, 686 
flow of air through, 588 
flow of water through, 697 
rectangular, flow of water 
through, table, 729 
Oscillation, center of, 494 

radius of, 494 
Overhead steam-pipe radiators, 673 
Ox, work of, 509 
Oxy-acetylene welding, 464 
Oxygen, effect of on strength of 
steel, 453 

it, value and relations of, 58 
Packing, hydraulic, friction of, 

1217 
Packing-rings of engines, 1000 
Paddle-wheels, 1331 
Paint, 447 

qualities of, 448 

quantity of, for a given surface, 
448 
Paper, logarithmic, ruled, 85 
Parabola, area of by calculus, 77 

construction of, 49, 50 

equations of, 73 

path of a projectile, 501 
Parabolic conoid, 66 

spindle, 66 
Parallel forces, 491 
Parallelogram area of, 55 

of forces, 489 

of velocities, 499 
Parallelopipedon of forces, 490 
Parentheses in algebra, 35 
Partial payments, 14 
Parting and threading tools, speed 

of, 1243 
Patterns, weight of, for castings, 
1233 



Payments, equation of, 14 
Pearlite, 416, 456 
Peat, 808 

Pelton water-wheel, 748 
Pendulum, 496 
conical, 496 
Percentage, 12 
Percussion, center of, 494 
Perforated plates, strength of, 402 
Permeability, magnetic, 1348, 1383 
Permeance, magnetic, 1348 
Permutation, 10 
Perpetual motion, 507 
Petroleum as a metallurgical fuel, 
813 
cost of as fuel, 812 
engines, 1077 
Lima, 810 

products of distillation of, 810 
products, specifications for, 1219 
value of as fuel, 811 
Petroleum-burning locomotives, 

1103 
Pewter, composition of, 383 
Phosphor-bronze, composition of, 
366 
specifications for, 370 
springs, 401 
strength of, 370 
Phosphorus, influence of, on cast- 
iron, 415 
influence of, on steel, 452 
Piano-wire, strength of, 239 
Pictet fluid, for refrigerating, 1284 
Piezometer, 727 
Pig-iron (see also Cast iron) 
analysis of, 416 
charcoal, strength of, 428 
distribution of silicon in, 424 
for malleable castings, 430 
grading of, 414 

influence of silicon, etc., on, 415 
sampling, 418 
specifications for, 418 
tests of, 419 
Piles, bearing power of, 1334 
Pillars, strength of, 269 
Pine, strength of, 344 
Pins, forcing fits of by hydraulic 
pressure, 1273 
taper, 1272 
Pinions, raw-hide, 1153 
Pipe bends, flexibility of, 215 
branches, compound pipes, for- 
mula for, 720 
cast-iron, friction loss in, table, 

719 
cast-iron, specifications for metal 

for, 419 
coverings, tests of, 559 _, 
dimensions, Briggs standard, 

202, 207 
fittings, flanged, 203-206 
fittings, valves, etc., resistance of, 

672 
flanges, extra heavy, table, 199 
flanges, table of standard, 198 



INDEX. 



pip-pla 



1443 



Pipe, iron and steel, strength of, 

341 
iron, tin-lined and lead-lined, 218 
threading of, force required for, 

341 
wooden stave, 218 
Pipes, air, carrying capacity of, 662 
air, loss of pressure in, tables, 

593-595 
air-bound, 722 
and valves for superheated steam, 

851 
bent and coiled, 214, 215 
block-tin, weights and sizes of, 

218 
cast-iron, 191-195 
cast-iron, formulae for thickness 

of, 193 
cast-iron, safe pressures for, 

tables, 194, 195 
cast-iron, thickness of, for vari- 
ous heads, 192, 193 
cast-iron, transverse strength of, 

427 
cast-iron, weight of, 191-195 
coiled, table of, 214 
effects of bends in, 593, 727 
equalization of, table, 597 
equation of, 853 
flow of air in, 59 1 
flow of gas in, 834-836 
flow of steam in, 845 
flow of water in, 699 
for steam heating, 669 
house-service, flow of water in, 

table, 712 
iron and steel, corrosion of, 443 
lead, safe heads for, 217 
lead, tin-lined, sizes and weights, 

table, 217 
lead, weights and sizes of, table, 

217 
lines for fans and blowers, 643 
lines, long, 721 
loss of head in, 714-722 (see 

Loss of head) 
maximum and mean velocities 

in, 727 
proportioning to radiating sur- 
face, 671 
resistance of the inlet, 715 
rifled, for conveying heavy oils, 

721 
riveted flanges for, table, 213 
riveted hydraulic, weights and 

safe heads, table, 212 
riveted-iron, dimensions of, 

table, 211 
riveted, safe pressure in, 887 
riveted steel, loss of head in, 717 
riveted steel, water, 329 
sizes of threads on, 207 
spiral riveted, table of, 213 
steam (see Steam-pipes) 
steam, sizes of in steam heating, 

672 
table of capacities of, 127 



Pipes, volume of air transmitted in 
table, 591 
welded, standard, table of di- 
mensions, 208 
Pipe-joint, Rockwood, 202 
Piping, power-house, identification 

of by different colors, 854 
Piston rings, steam-engine, 1000 
rods, steam-engine, 1001-1003 
Piston valves, steam-engine, 1043 
Pistons, steam-engine, 999 
Pivot-bearings, 1205, 1209 
Pivot-bearing, mercury bath, 1209 
Pitch, diametral, 1134 
of gearing, 1133 
of rivets, 404 
of screw-propeller, 1325 
Pitot tube gauge, 727 

tube, use in testing fans, 640 
Plane, inclined, 512 (see Inclined 
Plane), 
surfaces, mensuration of, 55 
Planer, heavy work on, 1256 
horse-power required to run, 

1258, 1260 
vs. Milling machine, 1252 
Planers, cutting speed of, 1256 
Planished and Russia iron, 449 
Plank, Wooden, maximum spans 

for, 1332 
Plates (see also Sheets) 

acid-pickled, heat transmission 

through, 565 
areas of, in square feet, table, 

130, 131 
boiler, strength of at high tem- 
peratures, 439 
brass, weight of, tables, 219, 220 
Carnegie trough, properties of, 

table, 289 
circular, strength of, 3J3 
copper, strength of, 334 
copper, weight of, table, 219 
corrugated steel, properties of, 

table, 289 
flat, cast-iron, strength of, 313 
flat, for steam-boilers, rules for, 

880, 885, 888 
flat, unstayed, strength of, 314 
for stand-pipes, 327 
iron and steel, approximating 

weight of, 461 
iron, weight of, table, 184 
of different materials, table for 

calculating weights of, 178 
perforated, strength of, 402 
punched, loss of strength in, 401 
staved, strength of, 315 
steel boiler, specifications for, 

483 
steel, for cars, specifications for, 

483 
steel, specifications for, 481 
steel, tests of, 331, 333 
transmission of heat through, 
561 



1444 



pla-pum 



Plates, transmission of heat through, 
from air to water, 566 

transmission of heat through, 
from steag^to air, 569 
Plate-girder, strength of, 331 
Plate-girders, allowed stresses in, 

274 
Plating for bulkheads, table, 316 

for tanks, table, 316 

steel, stresses in, due to water 
pressure, 315 
Platinite, 475, 540 
Platinum, properties of, 176 

pyrometer, 526 

wire, 243 
Plenum system of heating, 678 
Plough-steel rope, 246 

wire, 239 
Plugs, fusible, in steam boilers, 889 
Plunger packing, hydraulic, friction 

of, 1217 
Pneumatic hoisting, 1163 

postal transmission, 624 
Polarity of electro-magnets, 1384 
Polishing wheels, speed of, 1264 
Polyhedron, 64 
Polygon, area of, 56 

construction of, 43-45 
Polygons, impedance, 1390 

of" forces, 489 

table of, 46, 56 
Polyphase circuits, 1395 
Popp system of compressed-air, 612 
Population of the United States, 11 
Portland cement, strength of, 336 
Port opening in steam-engines, 

1039 
Postal transmission, pneumatic, 

624 
Potential energy, 503 
Pound-calorie, definition of, 532 
Pounds per square inch, equiva- 
lents of, 27 
Power and work, measures of, 28 

animal, 507 

definition of, 503 

electrical cost of, 985 

factor of alternating currents, 
1389 

hydraulic, in London, 781 

of a waterfall, 734 

of electric circuits, 1353 

of ocean waves, 755 

unit of, 503 
Powers of numbers, algebraic, 34 

of numbers, tables, 7, 94-110 
Power-plant economics, 984 
Pratt truss, stresses in, 518 
Preservative coatings, 447-450 
Press fits, pressure required for, 
1274 

high-speed steam-hydraulic, 783 

hydraulic forging, 782 

hydraulic, thickness of cylinders 
for, 317 
Presses, hydraulic, in iron works, 
781 



Presses, punches, etc., 1272 

Pressed fuel, 801 

Pressure, collapsing of flues, 318 

collapsing of hollow cylinders, 
318 
Pressures of adiabatically com- 
pressed air, 609 
Priming, or foaming, of steam 

boilers, 692, 899 
Prism, 63 
Prismoid, 64 

rectangular, 63 
Prismoidal formula, 64 
Problems, geometrical, 38-54 

in circles, 40-42 

in lines and angles, 38-40 

in polygons, 43-46 

in triangles, 42 
Process, the thermit, 372 
Producers, gas {see Gas-producers) 
Producer-gas, 818-825 (see Gas) 
Producers, gas, use of steam in, 824 
Profit and loss, 12 
Progression, arithmetical and geo- 
metrical, 10, 11 
Projectile, parabola path of, 501 
Prony brake, 1280 
Propeller shafts, strength of, 332 

screw, 1324 (see Screw-propeller) 
Proportion, 6 

compound, 7 
Pulleys, 1111-1114 

arms of, 1032 

cone, 1112 

convexity of, 1112 

differential, 513 

for rope-driving, 1192 

or blocks, 513 

proportion of , 1111 

speed of, 1125, 1137 
Pulsometer, tests of, 775 
Pumps, air, for condensers, 1053, 
1055 

air-lift, 776 

and pumping engines, 757-779 

boiler-feed, 761 

boiler-feed, efficiency of, 908 

centrifugal, 764-770 

centrifugal, design of, 765 

centrifugal, multi-stage, 765 

centrifugal, relation of height of 
lift to velocity, 766 

centrifugal, tests of, 768, 770 

circulating, for condensers, 1057 

depth of suction of, 757 

direct-acting, efficiency of, 759 

direct-acting, proportion of steam 
cylinder, 759 

feed, for marine engines, 1057 

high-duty, 762 

horse-power of, 757 
'jet, 776 

leakage, test of, 772 

lift, water raised by, 759 

mine, operated by compressed- 
air, 625 

piston speed of, 760 



INDEX. 



pum-ref 



1445 



Pumps, rotary, 770 

speed of water in passages of, 759 

steam, sizes of, tables, 758, 760 

suction of, with hot water, 757 

theoretical capacity of, 757 

vacuum, 775 

valves, 761, 762 
Pump-inspection table, 725 
Pumping by compressed air, 617, 
777 (see also Air-lift) 

by gas-engines, cost of, 764 

by steam pumps, cost of fuel for, 
764 

cost of electric current for, 763 

engine, screw, 762 

engine, the d* Auria, 762 
Pumping-engines, duty trials of, 
771-775 

economy of, 763 

high-duty records, 774 

table of data for duty trials of, 
773 

use of nozzles to measure dis- 
charge of, 728 
Punches, clearance of, 1272 

spiral, 1272 
Punched plates, strength of, 402 
Punching and drilling of steel, 459, 

460 
Purification of water, 694 
Pyramid, 63 

frustum of, 63 
Pyrometer, air, Wiborgh's, 528 

copper-ball, 526 

fire-clay, Seger's, 528 

Hobson's hot-blast, 52S 

LeChatelier's, 526 

principles of, 523 

thermo-electric, 526 

Uehling-Steinbart, 530 
Pyrometers, graduation of, 527 
Pyrometric telescope, 529 
Pyrometry, 523 

Quadratic equations, 36 
Quadrature of plane figures, 77 

of surfaces of revolution, 78 
Quadrilateral, area of, 44 

area of, inscribed in circle, 55 
Quadruple-expansion engines, 956 
Quantitative measurement of heat, 

532 
Quarter-twist belt, 1124 
Quartz, cubic feet per ton, 178 
Queen-post truss, inverted, stresses 
in, 518 

truss, stresses in, 517 
Quenching test for soft steel, 483 

Rack, gearing, 1141 
Radian, definition of, 499 
Radiating power of substances, 
552 
surface, computation of, for hot- 
water heating, 675 
surface, computation of, for 
steam heating, 669 



Radiating surface, proportioning 

pipes for, 671 
Radiation, black body, 552 
of heat, 551 

of various substances, 552, 569 
Stefan and Boltzman's law, 552 
table of factors for Dulong's 
laws of, 570 
Radiators, experiments with, 668, 
679 
indirect, 669 

overhead steam-pipe, 673 
steam and hot-water, 668 
steam, removal of air from, 673 
transmission of heat in, 668 
Radius of gyration, 279, 494 

of gyration, graphical method 

for finding, 280 
of gyration of structural shapes, 

279, 280 
of oscillation, 494 
Rails, steel, specifications for, 484 

steel, strength of, 331 
Railroad axles, 441 

track, material required for one 

mile of, 232 
trains, resistance of, 1084-1087 
trains, speed of, 1094 
Railway, street, compressed-air, 
624, 625 
track bolts and nuts, 230 
Railways, electric, 1366 

narrow-gauge, 1103 
Ram, hydraulic, 778 
Rankine's formula for columns, 

270 
Ratio, 6 

Raw-hide pinions, 1153 
Reactance of alternating currents, 

1389 
Reamers, taper, 1270 
Reaumur thermometer-scale, 523 
Recalescence of steel, 455 
Receiver-space in engines, 950 
Reciprocals of numbers, tables of, 
88-93 
use of, 93 
Recorder, continuous, of water or 
steam consumption, 940 
carbon dioxide, or C0 2 , 860 
Rectangle, definition of, 55 
value of diagonal of, 55 
Rectangular prismoid, 63 
Rectifier, in absorption refrigera- 
ting machine, 1293 
mercury arc, 1401 
Red lead as a preservative, 447 
Reduction, ascending and de- 
scending, 5 
Reese's fusing disk, 1262 
Reflecting power of substances, 

552 
(Refrigerating (see also Ice-making,) 
1282 
direct-expansion method, 1314 



1446 



INDEX. 



Refrigerating-machines, actual and 
theoretical capacity, 1302 
air-machines, 1291 
ammonia absorption, 1293, 1313 
ammonia compression, 1292, 

1303 
condensers for, 1300 
cylinder-heating, 1296 
dry, wet, and flooded systems, 

1292 
ether-machines, 1291 
heat-balance, 1305 
ice-melting effect, 1291 
liquids for, pressure and boiling- 
points of , 1284 
mean effective pressure and 

horse-power, 1297 
operations of, 1283 
performance of, 1307 
performance of a single acting 

compressor, 1312 
pipe-coils for, 1302 
pounds of ammonia per minute, 

1297 
properties of brine, 1290 
properties of vapor, 1284-1287 
quantity of ammonia required 

for, 1298 
rated capacity of, 1300 
relative efficiency of, 1295 
relative performance of am- 
monia-compression and ab- 
sorption machines, 1294 
sizes and capacities, 1299 
speed of, 1300 

sulphur-dioxide machine, 1292 
test reports of, 1306 
temperature range, 1306 
tests of, 1302 
using water vapor, 1292 
volumetric efficiency, 1296 
Voorhees multiple-effect, 1297 
Refrigerating plants, cooling tower 

practice in, 1301 
Refrigerating systems, efficiency 

of, 1296 
Refrigeration, 1282-1316 
a reversed heat cycle, 574 
means of applying the cold, 1314 
Regenerator, heat, 987 
Regnault's experiments on steam, 

838 
Reinforced concrete, working 

stresses of, 1335 
Reluctance, magnetic, 1348, 1383 
Reluctivity, magnetic, 1348 
Reservoirs, evaporation of water in. 

543 
Resilience, elastic, 260 

of materials, 260 
Resistance, elastic, to torsion, 311 
electrical (see Electrical resist- 
ance), 1349 
electrical, effect of annealing on, 

1351 
electrical, effect of temperature 
on, 1350 



Resistance, electrical, in circuits, 

1352 
electrical, internal, 1353 
electrical, of copper-wire, 1351, 

1357 
electrical, of steel, 453 
electrical, standard of, 1351 
elevation of ultimate, 261 
modulus of, or section modulus, 

280 
of copper wire, rule for, 242 
of metals to repeated shocks, 262 
of ships, 1317 
of trains, 1084 
work of, of a material, 260 
Resolution of forces, 489 
Retarded motion, 497 
Reversing-gear for steam-engines, 

dimensions of, 1020 
Rheostats, 1404 
Rhomboid, definition and area of, 

55 
Rhombus, definition and area of, 55 
Rivets, bearing pressure on, 403 
cone-head, for boilers, 231 
diameters of, for riveted joints, 

table, 406 
in steam-boilers, rules for, 879 
pitch of, 404 

pressure required to drive, 412 
round head, weight of, 228 
steel, chemical and physical tests 

of, 412 
steel, specifications for, 481 
tinners', table, 232 
Riveted iron pipe, dimensions of, 

table, 211 
joints, 333, 401-412 
joints, British rules for, 410 
joints, drilled, vs. punched holes, 

401 
joints, efficiencies of, 405 
joints, notes on, 402 
joints of maximum efficiency, 

408 
joints, proportions of, 405 
joints, single riveted lap, 404 
joints, table of proportions, 411 
joints, tests of double riveted 

lap and butt, 406 
joints, tests of, table, 337 
joints, triple and quadruple, 408 
pipe, flow of water in, 714 
pipe, weight of iron for, 213 
Rivet-iron and steel, shearing re- 
sistance of, 407 
Riveting, cold, pressure required 

for, 412 
efficiency of different methods, 

402 
hand and hydraulic, strength of, 

402 
machines, hydraulic, 782 
of structural steel, 459 
pressure required for, 412 
Roads, resistance of carriages on, 

509 



INDEX. 



1447 



Rock-drills, air required for, 616 

requirements of air-driven, 616 
Rods of different materials, table 
for calculating weights of, 178 
Rollers and balls, steel, carrying 

capacity of, 317 
Roller bearings, 1210 

chain and sprocket drives, 1129 
Rolling of steel, effect of finishing 

temperature, 454 
Roofs, strength of, 1337 
Roof-truss, stresses in, 521 
Roofing materials, 186-190 

materials, weight of various, 190 
Rope for hoisting or transmission, 
386 

hoisting, iron and steel, 244 

manila, data of, 1189-1193 

manila, hoisting and transmis- 
sion, life of, 391 

wire (see Wire-rope) 
Ropes and cables, 386-393 

cable-traction, 247 

cotton and hemp, strength of, 
335 

flat iron and steel, table of 
strength of, 248, 387 

hemp, iron and steel, table of 
strength and weight of, 386 

hoisting (see Hoisting-rope) 

"Lang Lay," 246 

locked-wire, 250 

manila, 386 

manila, weight and strength of, 
390, 391 

splicing of, 389 

steel flat, table of sizes, weight 
and strength, 248, 387 

steel-wire hawsers, 249 

table of strength of iron, steel 
and hemp, 386 

taper, of uniform strength, 1183 

technical terms relating to, 388 

wire (see Wire-rope) 
Rope-driving, 1191-1194 

English practice, 1194 

pulleys for, 1192 

horse-power of, 1191 

sag of rope, 1191 

tension of rope, 1190 

various speeds of, 1191 

weight of rope, 1193 
Rope-transmission, 386 
Rotary blowers, 649 

steam-engines, 1062 
Rotation, accelerated, work of, 504 
Rubber belting, 1128 

goods, analysis of, 356 

vulcanized, tests of, 356 
Rule of three, 6, 7 
Running fits, 1274 
Rupture, modulus of, 282 
Russia and planished iron, 449 

Safety, factor of, 352-355 
Safety valves for steam-boilers, 
902-906 



Safety valves, spring-loaded, 904 
Salt, weight of, 178 

solubility of, 544 
Salt-brine manufacture, evapo- 
ration in, 543 

properties of, 543, 544, 1290 

solution, specific heat of, 537 
Sand, cubic feet per ton, 178 

molding, 1233 
Sand-blast, 1262 
Sand-lime brick, tests of, 349 
Sandstone, strength of, 349 
Saturation point of vapors, 578 
Sawing metal, 1262 
Sawdust as fuel, 808 
Scale, boiler, 692, 897 

boiler, analyses of, 693 

effect of, on boiler efficiency, 898 

removal of, from steam boilers, 
900 
Scales, thermometer, comparison 

of, 524, 525 
Scantling, table of contents of, 21 
Schiele pivot bearing, 1209 
Schiele's anti-friction curve, 51 
Scleroscope, for testing hardness, 

343 
Screw, 62 

bolts, efficiency of, 1270 

conveyors, 1175 

differential, 514 

differential, efficiency of, 1270 

efficiency of, 1270 

(elemtjrit of machine), 512 

heads. A.S.M.E. standard, table, 
223' 

propeller, 1324 

propeller, coefficients of, 1325 

propeller, efficiency of, 1326 

propeller, slip of, 1326 
Screws and nuts for automobiles, 
table, 222 

cap, table of standard, 225 

lag, holding power of, 324 

lag, table of, 234 

machine, A.S.M.E. standard, 
226 

set, table of standard, 225 

wood, dimensions of, 234 

wood, holding power of, 324 
Screw-thread, Acme, 223 
Screw-threads, 220-227 

British Association standard, 222 

English or Whit worth standard, 
table, 220 

International (metric) standard, 
222 

limit gauges for, 223 

metric, cutting of, 1238 

standard sizes for bolts and taps, 
224 

U. S. or Sellers standard table of, 
221 
Scrubbers for gas producers, 819 
Sea-water, freezing-point of, 690 
Secant of an angle, 67 
Secants of angles, table of, 166-169 



1448 



INDEX. 



Section modulus of structural 

shapes, 280, 281 
Sector of circle, 61 
Sediment in steam-boilers, 898 
Seger pyrometer cones, 528 
Segment of circle, 61 
Segments, circular, areas of, 121, 

122 
Segregation in steel ingots, 462 
Self-inductance of lines and cir- 
cuits, 1393 
" Semi-steel," 428 
Separators, steam, 911 
Set-screws, holding power of, 1278 

standard table of, 225 
Sewers, grade of, 706 
Shackles, strength of, 1161 
Shaft-bearings, 1015 

bearings, large, tests of, 1206 
couplings, flange, 1109 
Shaft fit, allowances for electrical 
machinery, 1274 
governors, 1048 
Shafts and bearings of engines, 
1023 
hollow, 1109 
hollow, torsional strength of, 

311 
steam-engine, 1010-1019 
steel propeller, strength of, 
Shafting, 1106-1110 
collars for, 1109 
deflection of, 1107 
formulae for, 1106 
horse-power transmitted by, 

1108 
keys for, 1277 
laying out, 1109, 1110 
power required to drive, 1261 
Shaku-do, Japanese alloy, 368 
Shapers, power required to run, 

1260 
Shapes of test specimens, 266 
structural steel, properties of, 
287-310 
Shear and compression combined, 
312 
and tension combined, 312 
poles, stresses in, 516 
Shearing, effect of on structural 
steel, 459 
resistance of rivets, 407 
strength of iron and steel, 340 
Shearing strength of woods, table, 
347 
strength, relation to tensile 
strength, 340 
Sheaves, diameter of, for given 
tension of wire rope, 1186 
for wire rope transmission, 1184 
size of, for manila rope, 390 
Sheets (see also Plates) 
Sheet aluminum, weight of, 220 
brass, weight of, 220 
copper, weight of, 219 
metal, strength of, 334 



Sheet metal, weight of, by decimal 
gauge, 33 
iron and steel, weight of, 181 
Shelby cold-drawn tubing, 210 
Shells for steam-boilers, material 
for, 880 
spherical, strength of, 316 
Shell-plate formulae for steam- 
boilers, 880 
Sherardizing, 450 
Shibu-ichi, Japanese alloy, 368 
Shingles, weights and areas of, 189 
Ship " Lusitania," performance of, 

1330 
Ships, Atlantic steam, perform- 
ance of, 1328 
coefficient of fineness of, 1317 
coefficient of performance, 1318 
coefficient of water lines, 1317 
displacement of, 1317, 1322 
horse-power of, 1321-1323 
horse-power of, from wetted 

surface, 1323 
horse-power of internal com- 
bustion engines for, 1322 
horse-power for given speeds, 

1321 
jet propulsion of, 1332 
relation of horse-power to speed, 

1331 
resistance of, 1317 
resistance of, per horse-power, 

1321 
resistance of, Rankine's formula, 

1319 
rules for measuring, 1316 
rules for tonnage, 1317 
small sizes, engine power re- 
quired for, 1322 
wetted surface of, 1320 
with reciprocating engine, and 
turbine combined, 1331 
Shipbuilding, steel for, 483 
Shipping measure, 19, 1316 
Shocks, resistance of metals to 
repeated, 262 
stresses produced by, 263 
Short circuits, electric, 1360 
Shrinkage fits (see Fits, 1273) 
of cast-iron, 415, 423 
of alloys, 384 
of castings, 1231 
of malleable iron castings, 431 
strains relieved by uniform cool- 
ing, 423 
Sign of differential coefficients, 79 
of trigonometrical functions, 68 
Signs, arithmetical, 1 
Silicon, distribution of, in pig iron, 
424 
excessive, making cast-iron hard. 

1231 
influence of, on cast-iron, 415, 

422 
influence of, on steel, 452 
relation of, to strength of cast- 
iron, 415, 422 



sil-sph 



1449 



Silicon-aluminum-iron alloys, 374 
Silicon-bronze, 371 
Silicon-bronze^wire, 243, 371 
Silundum, 1377 
Silver, melting temperature, 527 

properties of, 176 
Simpson's rule for areas, 57 
Sine of an angle, 67 
Sines of angles, table, 166-169 
Single-phase circuits, 1395 
Siphon, 726 
Sirocco Fans, 633 
Skin effect in alternating currents, 

1390, 1399 
Skylight glass, sizes and weights, 

190 
Slag bricks and slag blocks, 256 
Slag in cupolas, 1225 

in wrought iron, 436 
Slate roofing, sizes, areas, and 

weights, 189 
Slide Rule, 83 
Slide-valves, steam-engine, (see 

Steam-engines, 1034-1047) 
Slope, table of, and fall in feet per 

mile, 700 
Slotters, power required to run, 

1260 
Smoke-prevention, 890-893 
Smoke-stacks, sheet-iron, 928 

locomotive, 1091 
Snow, weight of, 691 
Soapstone lubricant, 1223 

strength of, 349 
Soda mixture for machine tools, 

1222 
Softeners in foundry practice, 

1230 
Softening of water, 695 
Soils, bearing power of, 1333 

resistance of, to erosion, 705 
Solar engines, 988 
Solder, brazing, composition of, 
366 
for aluminum, 359 
Soldering aluminum bronze, 373 
Solders, composition of various, 

385 
Solid bodies, mensuration of, 62- 
67 
measure, 18 
Solid of revolution, 65 
Solubility of common salt, 544 

of sulphate of lime, 545 
Sorbite, 456 
Sources of energy, 506 
Specific gravity, 170-174 

gravity and Baume's hydrometer 

compared, table, 172 
gravity and strength of cast iron, 

428 
gravity of brine, 544 
gravity of cast-iron, 428 
gravity of copper-tin alloys, 360 
gravity of copper-tin-zinc alloys, 

364 
gravity of gases, 173 



Specific gravity of ice, 691 
gravity of liquids, table, 172 
gravity of metals, table, 171 
gravity of steel, 461 
gravity of stones, brick, etc., 174 
Specific heat, 534-538 

heat, determination of, 534 
heat of ammonia, 1286 
heat of air, 587 
heat of gases, 535, 537 
heat of ice, 691 

heat of iron and steel, 535, 536 
heat of liquids, 535 
heat of metals, 536 
heat of saturated steam, 837 
heat of solids, 535 
heat of superheated steam, 838 
heat of water, 536, 691 
heat of woods, 536 
Specifications for boiler-plate, 483 
for castings, 418 
for cast iron, 418 
for chains, 251 
for elliptical steel springs, 399 
for foundry pig iron, 418 
for galvanized wire, 239 
for helical steel springs, 395 
for incandescent lamps, 1372 
for malleable iron, 433 
for metal for cast-iron pipe, 419 
for oils, 1219 

for petroleum lubricants, 1219 
for phosphor-bronze, 370 
for purchase of coal, 799 
for spring steel, 483 
for steel axles, 483, 485 
for steel billets, 483 
for steel castings, 464, 486 
for steel crank-pins, 483 
for steel for automobiles, 486 
for steel forgings, 482 
for steel rails, 484 
for steel rivets, 481 
for steel splice-bars, 485 
for steel tires, 485 
for structural steel, 480 
for structural steel for ships, 483 
for tin and terne-plate, 188 
for wrought iron, 437-438 
Speed of cutting, effect of feed and 

depth of cut on, 1241 
of cutting tools, 1235 
of vessels, 1321 
Sphere, measures of, 63 
Spheres of different materials, table 

for calculating weight of, 178 
table of volumes and surfaces, 

125, 126 
Spherical polygon, area of, 64 
segment, volume of, 65 
shells and domed boiler heads, 

316 
shells, strength of, 316 
shell, thickness of, to resist a 

given pressure, 316 
triangle, area of, 64 
zone, area and volume of, 65 



1450 



sph-ste 



INDEX. 



Spheroid, 65 

Spikes, holding power of, 323 

wire* 233 

railroad and boat, 233 
Spindle, surface and volume of, 65, 

66 
Spiral, 52, 62 

conical, 62 

construction of, 52 

gears, 1143 

plane, 62 
Spiral-riveted pipe-fittings, table, 
214 

pipe, table of, 213 
Splices, railroad track, tables, 233 
Splice-bars, steel, specifications for, 

485 
Splicing of ropes, 388 

of wire rope, 393 
Springs, 394-401 

elliptical, specifications for, 399 

elliptical, sizes of, 399 

for engine-governors, 1048-1050 

helical, 396 

helical, formulae for deflection 
and strength, 395 

helical, specifications for, 395 

helical, steel, tables of capacity 
and deflection, 395-400 

laminated steel, 394 

phosphor-bronze, 401 

semi-elliptical, 394 

steel, strength of, 333 

steel, chromium-vanadiun, 401 

to resist torsion, 399 
Sprocket wheels, 1130 
Spruce, strength of, 345 
Square, definition of, 55 

measure, 18 

root, 8 

roots, tables of, 94-109 

value of diagonal of, 55 
Squares of decimals, table, 109 

of numbers, table, 94-109 
Stability, 490 . 

of dam, 491 
Stand-pipe at Yonkers, N. Y., 328 
Stand-pipes, 327-329 

failures of, 328 

guy-ropes for, 327 

heights of, for various diameters 
and plates, table, 329 

thickness of plates of table, 329 

thickness of side plates, 327 

wind-strain on, 328 
Statical moment, 490 
Static and dynamic properties of 

steel, 476 
Stays, steam-boiler, loads on, 882 

steam-boiler, material for, 882 
Stay-bolt iron, 438 
Stay-bolts in steam-boilers, 888 
Stayed surfaces, strength of, 315 
Steam, 836-854 

determining moisture in, 912-915 

dry, definition, 836 



Steam, dry, identification of, 915 
energy of, expanded to various 

pressures, 933 
entropy of, tables, 839-843 
expanding, available energy of, 

842 
expansion of, 929 
flow of, 844-851 (see Flow of 

steam) 
gaseous, 838 
generation of, from waste heat 

of coke-ovens, 803 
heat required to generate 1 

pound of, 837 
latent heat of, 836 
loop, 852 

loss of pressure in pipes, 849 
maximum efficiency of, in Carnot 

cycle, 850 
mean pressure of expanded, 930 
metal, 368 

power, cost of, 981-984 
receivers on pipe lines, 853 
Reghault's experiments on, 838 
saturated, definition, 836 
saturated, density, volume and 

latent heat of, 839 
saturated, properties of, table, 

839-842 
saturated, specific heat of, 837 
saturated, temperature and pres- 
sure of, 837 
saturated, total heat of, 836 
separators, 911 
superheated (see also Superheated 

steam) 
superheated, definition, 836 
superheated, economy of steam- 
engines with, 969 
superheated, pipes and valves 

for, 851 
superheated, properties of, 843 
superheated, specific heat of, 838 
temperature of, 836 
vessels (see Ships) 
weight of, per cubic foot, table, 

839 
wet, definition, 836 
Steam-boiler, 854-901 
compounds, 898 
efficiency, computation of, 860 
efficiency, relation of, to rate of 

driving, air-supply, etc., 862 
furnaces, height of, 889 
plates, ductility of, 884 
plates, tensile strength of, 884 
tests, heat-balance in, 872 
tests, rules for, 866-874 
tubes, holding power of, 883 
tubes, iron and steel, 883 
tubes, material for, 883 
Steam-boilers, bumped heads, rules 

for, 885 
conditions to secure economy of, 

859, 862 
construction of, 879-889 



i 



1451 



Steam-boilers, construction of, 
United States merchant-vesssl 
rules, 884 

corrosion of, 443, 897 

curves of performance of, 863 

dangerous, 901 

domes on, 889 

down-draught furnace for, 890 

effect of heating air for furnaces 
of, 865 

evaporative tests of, 864-868 

explosive energy of, 902 

factors of evaporation, 874-878 

factors of safety of, 879 

feed-pumps for, efficiency of, 908 

feed-water heaters for, 909-911- 

feed-water saving due to heat- 
ing of, 909 

flat plates in, rules for, 880, 885, 
888 

flues and gas passages, propor- 
tions of, 858 

foaming or priming of, 692, 899 

for blast-furnaces, 865 

forced combustion in, 894 

fuel economizers, 894 

furnace formulae, 881 

fusible plugs in, 889 

girders, rules for, 882 

grate-surface, 855, 857 

grate-surface, relation to heating- 
surface, 857 

gravity feeders, 908 

heating-surface in, 855, 856 

heating-surface, relation of, to 
grate-surface, 857 

heat losses in, 861 

height of chimney for, 919, 921 

high rates of evaporation, 865 

horse-power of, 854 

hydraulic test of, 879 

incrustation of, 897-902 

injectors on, 906-908 (see In- 
jectors) 

marine, corrosion of, 900 

maximum efficiency with Cum- 
berland coal, 865 

measure of duty of, 855 

mechanical stokers for, 889 

performance of, 858 

pressure allowable in, 884-888 

proportions of, 855-858 

proportions of grate and heat- 
ing-surface for given horse- 
power, 855, 857 

proportions of grate-spacing, 857 

riveting, rules for, 879 

safety-valves, discharge of steam 
through, 905 

safety-valves for, 902-906 

safety-valves, formula? for, 902 

safety-valves, spring-loaded, 904 

safe working-pressure, 887 

scale compounds, 898 

scale in, 897-902 

sediment in, 898 

shells, material for, 880 



Steam-boilers, shell-plate, formula? 
for, 880 

smoke prevention, 890-893 

stay bolts in, 888 

stays, loads on, 882 

stays, material for, 882 

strain caused by cold feed-water, 
909 

strength of, 879-889 

strength of rivets, 879 

tests of, at Centennial Exposi- 
tion, 864 

tube-plates, rules for, 882 

use of kerosene in, 899 

use of zinc in, 901 

using waste gases, 865, 866 
Steam-calorimeters, 912-915 
Steam-consumption in engines, 
Willans law, 962 

continuous recorder of, 940 
Steam-domes on boilers, 889 
Steam-engines, 929 

advantages of compounding, 946 

advantages of high initial and 
low back pressure, 967 

and turbine, in 1904, best econ- 
omy of, 977 

bed-plates, dimensions of, 1025 

bearings, size of, 1015 

clearance in, 936 

compound, 946-953 

compound, best cylinder ratios, 
952 

compound, calculation of cylin- 
ders of, 952 

compound, combined indicator 
diagram, 949 

compound condensing, test of 
with and without jackets, 976 

compound, economy of, 968 

cylinder condensation, experi- 
ments on, 937 

cylinder condensation, loss by ,936 

compound, two vs. three cylin- 
ders, 968 

compound, formulae for expan- 
sion and work in, 951 

compound, high-speed, perform- 
ance of, 960, 961 

compound, high-speed, sizes of, 
960, 961 

compound, non-condensing, effi- 
ciency of, 971 

compound, receiver, ideal dia- 
gram, 947 

compound, receiver space in, 950 

compound, receiver type, 947 

compound, steam-jacketed, per- 
formances of, 960 

compound, steam-jacketed, test 
of, 976 

compound, Sulzer, water con- 
sumption of, 969 

compound, velocity of steam in 
passages of, 956 

compound vs. triple-expansion, 



1452 



INDEX. 



Steam-engines, compound, water 

consumption of, 959 
compound, Wolff, ideal diagram, 

947 
compression, effect of, 935 
condensers, 1050-1061 (see Con- 
densers) 
connecting-rod ends, 1005 
connecting-rods, dimensions of, 

1003-1005 
cost of, 981-984 
counterbalancing of, 980 
crank-pins, dimensions of, 1005- 

1009 
crank-pins, pressure on, 1008 
crank-pins, strength of, 1007 
cranks, dimensions of, 1009 
crank-shafts, dimensions of, 

1017-1019 
crank-shafts for torsion and 

flexure, 1019 
crank-shafts for triple-expansion, 

1019 
crank-shafts, three-throw, 1019 
cross head and crank, relative 

motion of, 1042 
cross head-pin, dimensions of, 

1009 
cut-off, most economical point of, 

981 
cylinders, dimensions of, 996, 997 
cylinder-head bolts, size of, 999 
cvlinder-heads, dimensions of, 

998 
design, current practice, 1022 
dimensions of parts of, 979, 996- 

1026 
eccentric-rods, dimensions of, 

1020 
eccentrics, dimensions of, 1020 
effect of moisture in steam, 972 
economic performance of, 957- 

981 
economy at various loads and 

speeds, 963, 964 
economy, effect on, of wet steam, 

972 
economy of compound vs. triple- 
expansion, 984 
economy of, in central stations, 

963 
economy of, simple and com- 
pound compared, 968 
economy under variable loads, 

963 
economy with superheated steam 

969 
efficiency in thermal units per 

minute, 934 
estimating I.H.P. of single cylin- 
der and compound, 940 
exhaust steam used for heating, 

981 
expansions in, table, 935 
fly-wheels, 1026-1034 
fly-wheels, arms of, 1032 



Steam-engines, fly-wheels, centrifu- 
gal force in, 1029 
fly-wheels, diameters of, 1030 
fly-wheels, formulae for, 1026, 

1027 
fly-wheels, speed, variation in, 

1026, 1027 
fly-wheels, strains in, 1031 
fly-wheels, thickness of rim of, 

1032 
fly-wheels, weight of, 1027, 1028 
fly-wheels, wooden rim, 1033 
foundations embedded in air, 980 
frames, dimensions of, 1025 
friction of, 1215 
governors, fly-ball, 1047 
governors, fly-wheel, 1048 
governors, shaft, 1048 
governors, springs for, 1048-1050 
guides, sizes of, 1002 
highest economy of, 975 
high piston speed in, 966 
high-speed, British, 966 
high-speed Corliss, 966 
high-speed, economy of, 965 
high-speed, performance of, 959- 

962 
high-speed, sizes of, 959-962 
high-speed throttling, 967 
horse-power constants, 941-944 
indicated horse-power of single- 
cylinder, 940-946 
indicator diagrams, 938 
indicator diagram, analysis of, 

992 
indicator diagrams, to draw 

clearance line on, 944 
indicator diagrams, to draw ex- 
pansion curve, 944 
indicator rigs, 939 
indicators, effect of leakage, 946 
indicators, errors of, 939 
influence of vacuum and super- 
heat on economy, 972 
Lentz compound, 968 
limitations of speed of, 966 
link motions, 1044-1046 
links, size of, 1020 
mean and terminal pressures, 930 
mean effective pressure, calcu- 
lations of, 931 
measures of duty of, 933 
non-condensing, 958, 960, 961 
oil required for, 1221 
pipes for, 848 
pistons, clearance of, 996 
pistons, dimensions of, 999 
piston-rings, size of, 1000 
piston-rod guides, size of, 1002 
piston-rods, fit of, 1001 
piston-rods, size of, 1001 
piston-valves, 1043 
prevention of vibration in, 980 
proportions, current practice, 

1021 
proportions of, 996-1026 
quadruple expansion, 956 



INDEX. 



1453 



Steam-engines, quadruple, perform- 
ance of, 974 
ratio of expansion in, 932 
reversing gear, dimensions of, 

1020 
rolling-mill, sizes of, 980 
rotary, 1062 

setting the valves of, 1043 
shafts and bearings, 1010-1023 
shafts, bearings for, 1015 
shafts, bending resistance of, 

1012 
shafts, dimensions of, 1010-1017 
shafts, equivalent twisting mo- 
ment of, 1012 
shafts, fly-wheel, 1013 
shafts, twisting resistance of, 

1010 
single-cylinder, economy of, 957 
single-cylinder, high-speed, sizes 

and performance of, 960 
single-cylinder, water consump- 
tion of, 957-959 
slide-valve, definitions, 1034 
slide-valve diagrams, 1035-1039 
slide-valve, effect of changing 

lap, lead, etc., 1039 
slide-valve, effect of lap and lead, 

1034-1036 
slide-valve, lead, 1039 
slide-valve, port opening, 1039 
slide-valve, ratio of lap to travel, 

1040 
slide-valves, crank-angles, table, 

1040 
slide-valves, cut-off for various 
lap and travel, table, 1042, 
1043 
slide-valve, setting of, 1043 
slide-valves, relative motion of 

crosshead and crank, 1042 
small, coal consumption of, 964 
small, water consumption of, 963 
steam consumption of different 

types, 969 
steam-jackets, influence of, 975 
steam-turbines and gas-engines 

compared, 986 
Sulzer compound and triple-ex- 
pansion, 969 
superheated steam in, 969 
to change speed of, 1048 
to put on center, 1043 
three-cylinder, 1019 
rules for tests of, 988 
triple-expansion, 953-956 
triple-expansion and compound, 

relative economy, 984 
triple-expansion, crank-shafts 

for, 1019 
triple-expansion, cylinder pro- 
portions 953-955 
triple-expansion, cylinder ratios, 

956 
triple-expansion, high-speed, 
sizes and performances of, 961, 
962 



Steam - engines, triple - expansion, 
non-condensing, 961 

triple-expansion, sequence of 
cranks in, 956 

triple-expansion, steam-jacketed, 
performance of, 961, 962 

triple-expansion.theoreticalmean 
effective pressures, 954 

triple-expansion, types of, 956 

triple-expansion, water consump- 
tion of, 959, 969 

use of reheaters in, 975 

using superheated steam, 972- 
974 

valve-rods, dimensions of, 1019 

Walschaert valve-gear, 1046 

water consumption from indi- 
cator-cards, 945 

water consumption of, 937 

with fluctuating loads, wasteful, 
934 

with sulphur-dioxide addendum, 
978 

wrist-pin, dimensions of, 1009 
Steam fire-engines, capacity and 

economy of, 964 
Steam heating, 665-674 

heating, diameter of supply 
mains, 671, 673 

heating, indirect, 669 

heating, indirect, size of regis- 
ters and ducts, 669 

heating of greenhouses, 673 

heating, pipes for, 669 

heating, vacuum systems of, 673 

jackets on engines, 975 

jet blower, 651 

jet exhauster, 651 

jet ventilator, 652 

pipe coverings, tests of, 558-561 

pipes, 851-854 

pipes, copper, tests of, 851 

pipes, copper, strength of, 851 

pipes, failures of, 851 

pipes for engines, 848 

pipes for marine engines, 848 

pipes, proportioning for mini- 
mum loss by radiation and 
friction, 849 

pipes, riveted -st eel, 852 

pipes, uncovered, loss from, 853 

pipes, underground, condensa- 
tion in, 853 

pipes, valves in, 852 

pipes, wire- wound, 851 

turbines, 1062-1071 

turbine, low-pressure, combined 
with high pressure reciprocating 
engine, 1331 

turbines, testing oil for, 1221 

turbines and gas-engine, com- 
bined plant of, 986 

turbine and steam-engine com- 
pared, 978 

turbines, efficiency of, 1067 

turbines, impulse and reaction, 
1062, 1066 



1454 



Steam turbines, low-pressure, 
1069 
turbines, reduction gear for, 1071 
turbines, speed of the blades, 

1066 
turbines, steam consumption of, 

1067 
turbines, theory of, 1063 
turbines using exhaust, from re- 
ciprocating engines, 1069, 1331 
Steamships, Atlantic, performances 

of, 1328 
Steel, 451-487 

alloy, heat treatment of, 479 

aluminum, 472 

analyses and properties of, 452 

and iron, classification of, 413 

annealing of, 459, 460, 468 

axles, specifications for, 483, 485 

axles, strength of, 332 

bars, effect of nicking, 461 

beams, safe load on, 284 

bending tests of, 454 

Bessemer basic, ultimate strength 

of, 452 
Bessemer, range of strength of, 

454 
billets, specifications for, 483 
blooms, weight of, table, 185 
bridge-links, strength of, 331 
brittleness due to heating, 458 
burning carbon out of, 461 
burning, overheating, and re- 
storing, 457 
castings, 464-466 
castings, specifications for, 464, 

486 
castings, strength of, 333 
cementation or case-hardening 

of, 1246 
chrome, 471 

chromium- vanadium, 476-478 
chromium-vanadium spring, 401 
cold-drawn, tests of, 339 
cold-rolled, tests of, 339 
color-scale for tempering, 469 
comparative tests of large and 

small pieces, 455 
copper, 475 
corrosion of, 443, 444 
crank-pins, specifications for, 483 
critical point in heat treatment 

of, 456 
crucible, 466-470 
crucible, analyses of, 466, 469 
crucible, effect of heat treatment, 

457, 466 
crucible, selection of grades of, 

466 
crucible, specific gravities of, 466 
effect of annealing, 455 
effect of annealing on grain of, 454 
effect of annealing on magnetic 

capacity, 459 
effect of cold on strength of, 440 
effect of finishing temperature in 

rolling, 454 



Steel, effect of heating, 457 

effect of heat on grain, 456, 466 
effect of oxygen on strength of, 

453 
electrical conductivity of, 453 
endurance of, under repeated 

stresses, 463. 
expansion of, by heat, 540 
eye-bars, test of, 338 
failures of, 462 
fatigue resistance of, 477 
fire-box, homogeneity test for, 

'484 
fluid-compressed, 464 
for car-axles, specifications, 483, 

485 
for different uses, analyses of, 

481-486 
forgings, annealing of, 458 
forgings, oil-tempering of, 458 
forgings, specifications for, 482 
for rails, specifications, 484 
hardening of, 455 
hardening temperature of, use of 

a magnet to determine, 1246 
harveyizing, 1246 
heating in a lead bath, 467 
heating in melted salts by an 

electric current, 467 
heating of, for forging, 468 
heat treatment of Cr-Va steel, 

478 
high-speed tool, 470 
high-speed tool, emery wheel for 

grinding, 1240, 1267 
high-speed tool new, tests of, 

1246 
igh-speed tool, Taylor's ex- 
periments, 1238 
high-strength, for shipbuilding, 

483 
ingots, segregation in, 462 
life of, under- shock, 263 
low strength of, 453 
low strength due to insufficient 

work, 454 
manganese, 470 

manganese, resistance to abra- 
sion of, 470-471 
manufacture of, 451 
melting, temperature of, 528 
mixture of, with cast iron, 429 
Mushet, 472 
nickel, 472 
nickel, tests of, 472 
nickel- vanadium, 475 
of different carbons, uses of, 469 
open-hearth, range of strength 

of, 454 
open-hearth, structural, strength 

of, 454 
plates (see Plates, steel) 
rails, specifications for, 484 
rails, strength of, 331 
range of strength in, 454 
recaleseence of, 455 



INDEX. 



ste-str 



1455 



Steel, relation between chemical 
composition and physical char- 
acter of, 452 
rivet, shearing resistance of, 407 
rivets, specifications for, 481 
rope, flat, table of strength of, 

387 
rope, table of strength of, 386 
shearing strength of, 340 
sheets, weight of, 181 
soft, quenching test for, 483 
specifications for, 480-487 
specific gravity of, 461 
splice-bars, specifications for, 485 
spring, strength of, 333 
springs (see Springs, steel) 
static and dynamic properties of, 

476 
strength of, Kirkaldy's tests, 331 
strength of, variation in, 454 
structural, annealing of, 460 
structural, drilling of, 460 
structural, effect of punching and 
. shearing, 459 

structural, for bridges, specifica- 
tions of, 480 
structural, for buildings, specifi- 
cations of, 480 
structural, for ships, specifica- 
tions of, 483 
structural, punching of, 460 
structural, riveting of, 459 
structural shapes, properties of, 

287-310 
structural, specifications for, 480 
structural, treatment of, 459-460 
structural, upsetting of, 460 
structural, welding of, 460 
struts, 271 
tempering of, 468 
tensile strength of, at high tem- 
peratures, 439 
tensile strength of, pure, 453 
tires, specifications for, 485 
tires, strength of, 332 
tool, composition and heat treat- 
ment of, 1243 > 
tool, heating of, 467 
tungsten, 472 
used in automobile construction, 

486 
very pure, low strength of, 453 
water-pipe, 329 
welding of, 460, 463 
wire gauge, tables, 30 
working of, at blue heat, 458 
working stresses in bridge mem- 
bers, 272 
Stefan and Boltzman law of radia- 
tion, 552 
Sterro metal, 369 
St. Gothard tunnel, loss of pressure 

in air-pipe mains in, 595 
Stoker, Taylor gravity underfeed, 

890 
Stokers, mechanical, for steam- 
boilers, 889 



Stokers, under-feed, 890 
Stone, strength of, 335, 347 

weight and specific gravity of, 
table, 174 
Stone-cutting with wire, 1262 
Storage of steam heat, 897, 987 
batteries, 1378 
batteries, efficiency of, 1380 
batteries, rules for care of, 1381 
Storms, pressure of wind in, 599 
Stoves, for heating compressed-air, 
efficiency of, 612 
foundries, cupola charges in, 1227 
Straight-line formula for columns, 

271 
Strain and stress, 258 
Strand, steel wire, for guys, 249 
Straw as fuel, 808 
Stream, open, measurement of 

flow, 729 
Streams, fire, 722-725 (see Fire- 
streams) 
running, horse-power of, 734 
Strength and specific gravity of 
cast iron, 428 
compressive, 267-269 
compressive, of woods, 344, 346 
loss of, in punched plates, 401 
of anchor-forgings, 331 
of aluminum, 358 
of aluminum-copper alloys, 371 
of basic Bessemer steel, 452 
of belting, 335 
of blocks for hoisting, 1157 
of boiler-heads, 314, 315 
of boiler-plate at high tempera- 
tures, 439 
of bolts, 325, 326 
of brick, 336 

of brick and stone, 347, 350 
of bridge-links, 331 
of bronze, 334, 360 
of canvas, 335 
of castings, 330 
of cast iron, 421 
of cast-iron beams, 427 
of cast-iron columns, 274 
of cast-iron cylinders, 427 
of cast-iron flanged fittings, 428 
of cast iron, relation to size of 

bar, 421 
of cast-iron water-pipes, 194, 

427 
of chain cables, table, 251, 252 
of chains, table, 251, 252 
of chalk, 349 
of cement mortar, 350 
of columns, 269-278, 1337 
of copper at high temperatures • 

344 
of copper plates, 334 
of copper-tin alloys, 361 
of copper-tin-zinc alloys, graphic 

representation, 364 
of copper-zinc alloys, 364 
of cordage, table, 386-391, 1157 
of crank-pins, 1007 



1456 



INDEX. 



Strength of electro-magnet, 1386 
of nagging, 350 
of flat plates, 313 
of floors, 1337-1340 
of German silver, 334 
of glass, 343 
of granite, 335 
of gun-bronze, 362 
of hand and hydraulic riveted 

joints, 402 
of ice, 344 
of iron and steel, effect of cold 

on, 440 
of iron and steel pipe, 341 
of lime-cement mortar, 350 
of limestone, 349 
of locomotive forgings, 331 
of Lowmoor iron bars, 330 
of malleable iron, 430, 434 
of marble, 335 
of masonry, 349 
of materials, 258-359 
of materials, Kirkaldy's tests 

330-336 
of perforated plates, 402 
of phosphor-bronze, 370 
of Portland cement, 336 
of riveted joints, 337, 401-411 
of roof trusses. 521 
of rope, 335, 386, 1193 
of sandstone, 349 
of sheet metal, 334 
of silicon-bronze wire, 371 
of soapstone, 349 
of spring steel, 333 
of spruce timber, 345 
of stayed surfaces, 315 
of steam-boilers, 879-889 
of steel axles, 332 
of steel castings, 333 
of steel, open-hearth structural 

454 
of steel propeller-shafts, 332 
of steel rails, 331 
of steel tires, 332 
of structural shapes, 287-310 
of timber, 344-347 
of twisted iron, 264 
of unstayed surfaces, 314 
of welds, 251, 333 
of wire, 335, 336 
of wire and hemp rope, 334, 335 
of wrought-iron columns, 271 
of yellow pine, 344 
range of, in steel, 454 
shearing, of iron and steel, 340 
shearing, of woods, table, 347 
tensile, 265 
tensile, of iron and steel at high 

temperatures, 439 
tensile, of pure steel, 453 
torsional, 311 
transverse, 282-286 
Stress and strain, 258 

due to temperature, 312 
Stresses allowed in bridge members, 

272 



Stresses combined, 312 
effect of, 258 

in framed structures, 515-522 
in plating of bulkheads, etc., 

due to water-pressure, 315 
in steel plating due to water 

pressure, 315 
produced by shocks, 263 
Structures, framed, stresses in, 515 
Structural materials, permissible 
stresses in, 1335 
shapes, elements of, 280 
shapes, moment of inertia of, 

279 
steel shapes, properties of, 287- 

310 
shapes, radius of|gyration of, 279 
shapes, steel (see Steel, struc- 
tural, also Beams, angles, 
etc.), 
steel, rolled sections, proper- 
ties of, 287-310 
Strut, moving, 511 
Struts, steel, formulae for, 271 
strength of, 269 

wrought-iron, formulas for, 271 
Suction lift of pumps, 757 
Sugar manufacture, 809 

solutions, concentration of, 545 
Sulphate of lime, solubility of, 545 
Sulphur dioxide addendum to 
steam-engine, 978 
dioxide and ammonia-gas, pro- 
perties of, 1285 
dioxide refrigerating-machine, 

1292 
influence of, on cast iron, 415 
influence of, on steel, 452 
Sum and difference of angles, 

functions of, 69 
Sun, heat of, as a source of power, 

988 
Superheated steam, effect of on 
steam consumption, 972 
steam, economy of steam-en- 
gines with, -969 
steam, practical application of, 
973 
Superheating, economy due to, 
978 
in locomotives, 1102 
Surface condensers, 1051 

of sphere, table, 125, 126 
Surfaces of geometrical solids, 
62-67 
of revolution, quadrature of, 78 
unstayed flat, 314 
Suspension cableways, 1181 
Sweet's slide-valve diagram, 1036 
Symbols, chemical, 170 

electrical, 1416 
Synchronous-motor, 1409 

T-shapes, properties of Carnegie 

steel, table, 294 
Tackle, hoisting, 1158 
Tackles, rope, efficiency of, 391 



1457 



Tail-rope, system of haulage, 1178 
Tanbark as fuel, 808 
Tangent of an angle, 67 
Tangents of angles, table of, 166- 

169 
Tangential or impulse water- 
wheels, tables of, 751 
Tanks andjcisterns, number of bar- 
rels in, 133 
capacities of, tables, 128, 132 
with flat sides, plating and fram- 
ing for, 316 
Tantalum electric lamps, 1371 
Taps, A.S.M.E. standard, 227 
formulae and table for screw- 
threads of, 224 
Tap-drills, tables of, 227, 1269 
Taper, to set in a lathe, 1238 
Tapered wire rope, 1183 
Taper pins, 1272 
Tapers, Jarno, 1271 

Morse, 1271 
Taylor's experiments on cutting 
tools of high-speed steel, 1238 
Taylor's rules for belting, 1120 

theorem, 79 
Teeth of gears, forms of, 1138- 
1145 
of gears, proportions of, 1135, 
1136 
Telegraph-wire, joints in, 239 

tests of, table, 238 
Telpherage, 1171 
Temperature, absolute, 540 

determination of by color, 531 
determinations of melting-points 

effect 'of on strength, 344, 439- 

441 
of fire, 785 
rise of, in combustion of gases, 

786 
stress due to, 312 
Temperature-entropy diagram, 574 
-entropy diagram of water and 
steam, 576 
Temper carbon, in cast-iron, 416 
Tempering, effect of, on steel, 468 
of steel, 468 

oil, of steel forgings, 458 
Tenacity of different metals, 177 
of metals at various tempera- 
tures, 344, 439 
Tensile strength, 265 

strength, increase of, by twist- 
ing, 264 
strength of iron and steel at 

high temperatures, 439 
strength of pure steel, 453 
strength (see Strength) 
tests, precautions in making, 

266 
tests, shapes of specimens for, 
266 
Tension and flexure combined, 312 

and shear, combined, 312 
Terne-plate, 188 
Terra cotta, weight of, 186 



Tests, compressive (see Compres- 
sive strength) 
of steam-boilers, rules for, 866 
of steam-engines, rules for, 988 
of strength of materials (see 

Strength) 
tensile (see Strength and Ten- 
sile strength) 
Test-pieces, comparison of large 

and small, 455 
Thermal capacity, 534 
storage, 897, 987 
units, 532 
Thermit process, the, 372 

welding process, 463 
Thermodynamics, 571-577 

laws of, 572 
Thermometer, air, 530 

centigrade and Fahrenheit com- 
pared, tables, 524 
Threads, pipe, 202, 207 
Threading and parting tools, speed 
of, 1243 
pipe, force required for, 341 
Three-phase transmission, rule for 
sizes of wires, 1398 
circuits, 1395 
Thrust bearings, 1208 
Tides, utilization of power of, 756 
Ties, railroad, required per mile 

of track, 232 
Tiles, weight of, 186 
Timber (see also wood) 

beams, safe loads, 1335, 1341 
beams, strength of, 344 
expansion of, 345 
measure, 20 
preservation of, 347 
strength of, 344-347 
table of contents in feet, 21 
Time, measures of, 20 
Tin, alloys of (see Alloys) 
lined iron pipe, 218 
plates, 187 
properties of, 176 
plates, 187 
Tires, locomotive, shrinkage fits, 
1273 
steel, friction of on rails, 1195 
steel, specifications for, 485 
steel, strength of, 331 
Titanium, additions to cast-iron, 
416, 426 
aluminum alloy, 375 
Tobin bronze, 368 
Toggle-joint, 511 
Tool steel (see also Steel) 

steel high-speed, composition 

and heat-treatment, of, 1242 
steel, best quality, 1242, 
steel, high-speed, new (1909), 
tests of, 1246 

steel, high-speed, Taylor's ex- 
periments, 1238 
steel in small shops, best treat- 
ment of, 1243 
steel of different qualities, 1243 



1458 



INDEX. 



Tools, cutting, durability of, 1243 
economical cutting speed of, 

1243 
cutting, effect of feed and depth 

of cut on speed of, 1241 
cutting, in small shops, best 

method of treatment, 1243 
cutting, interval between grind- 

ings of, 1241 
cutting, pressure on, 1241 
forging and grinding of, 1240 
cutting, use of water on, 1241 
machine (see Machine tools) 
parting and thread, cutting speed 
of, 1243 
Toothed-wheel gearing, 514, 1133 
Tonnage of vessels, 1316 
Tons per mile, equivalent of, in lbs. 

per yard, 28 
Torque computed from watts and 
revolutions, 1386 
horse-power and revolutions, 

1386 
of an armature, 1386 
Torsion and compression com- 
bined, 312 
and flexure combined, 312 
elastic resistance to, 311 
of shafts, 1010,1106 
tests of refined iron, 339' 
Torsional strength, 311 
Track bolts, 232 

spikes, 233 
Tractive force of a locomotive, 

1087 
Tractrix, Schiele's anti-friction 

curve, 51 
Trains, railroad, resistance of, 1084 
railroad, speed of, 1094 
loads, average, 1101 
Trammels, to describe an ellipse 

with, 46 
Tramways, compressed-air 624 

wire-rope, 1180 
Transformers, efficiency of, 1400 

electrical, 1400 
Transmission, compressed-air (see 
compressed-air) 
electric, 1359, 1396 
electric, area of wires, 1359 
electric, cost of copper, 1365 
electric, economy of, 1360 
electric, efficiency of, 1361 
electric, systems of, 1363 
electric, weight of copper for, 1359 
electric, wire table for, 1360 
hydraulic-pressure (see Hy- 
draulic-pressure transmis- 
sion, 
of heat (see Heat) 
of power bv wire-rope (see Wire- 
rope), 1183-1189 
pneumatic postal, 624 
rope, iron and steel, 245 
rope (see Rope-driving) 
wire-rope (see Wire-rope) 
Transporting power of water, 565 



Triple-expansion engine (see 

Steam-engines) 
Transverse strength, 282-286 
Trapezium and Trapezoid, 55 
Triangles, mensuration of, 55 

problems in, 42 

spherical, 64 

solution of, 70 
Trigonometrical computations by 
slide rule, 84 

formulae, 69 

functions, table, 166-169 

functions, logarithmic, 169 
Trigonometry, 67-70 
Triple effect evaporators, 543 
Troostite, 456 

Trough plates, properties of, 289 
Troy weight, 19 
Trusses, bridge, stresses in, 517 

roof, stresses in, 521 
Tubes, boiler, table, 209 

boiler, used as columns, 341 

brass, seamless, 216 

collapse of, formulas for, 320 

collapse of, tests of, 320 

collapsing pressure of, table, 321 

copper, 216 

expanded, holding . power of, 
342, 883 

lead and tin, 217 

of different materials, weight of, 
178 

seamless aluminum bronze, 372 

steel, cold-drawn, Shelby, 210 

surface per foot of length, 211 

welded, extra strong, 209 

Tube-plates, steam-boiler, rules for, 

882 
Tungsten and aluminum alloy, 375 

electric lamps, 1371 

steel, 472 
Turbine wheel, tests of, 742 

wheels, 737-748 

wheels, proportions of , 739 

wheel tables, 751 
Turbines, fall-increaser for, 747 

of 13,500 H.P., 747 

rating and efficiency of, 743 

steam (see Steam-turbines) 
Turf or peat, as fuel, 808 
Turnbuckles, 231 
Tuyeres for cupolas, 1224 
Twist drills (see Drills) 

drills, sizes and speeds, 1254 
Twist-drill gauge, table, 30 
Twisted steel bars, strength of, 264 
Two-phase currents, 1394 
Type-metal, 384 

Uehling and Steinbart pyrometer, 

530 
Underwriters' rules for electrical 

wiring, 1355 
Unequal arms on balances, 20 
Unit o.f evaporation, 855 
of force, 488 
of power, 503 



INDEX. 



1459 



Unit of heat, 532 

of work, 502 
Units, electrical and mechanical, 
equivalent values of, 1347 

electrical, relations of, 1346 

of the magnetic, circuit, 1346 
United States, population of, 11 

standard sheet metal, gauge, 31 
Unstayed surfaces, strength of, 314 
Upsetting of structural steel, 459 



Vacuum at different temperatures, 
757 
drying in, 546 
high advantage of, 1059 
high, influence of on economy, 

972 
inches of mercury and absolute 

pressures, 1053 
pumps, 775 

systems of steam heating, 673 
Valve-gear, Stephenson, 1044 

Walschaert, 1046 
Valves and elbows, friction of air 
in, 593 
and fittings, loss of pressure due 

to, 721 
pump, 762 
in steam pipes, 852 
straight-way gate, 199 
Valve-stem or rod, design of, 1019 

(see Steam-engines) 
Vanadium and copper alloys, 371 
effect of on cast iron, 416, 426 
steel spring, 401 
-chrome steel, 476-478 
-nickel steels, 475 
Vapor pressures of various liquids, 
814 
water, and air mixture, weight 

of, 584, 586 
ammonia, carbon dioxide and 
sulphur dioxide, properties of, 
1288 
and gases, mixtures of, 578 
saturation point of, 578 
Vaporizer pressures in refrigerating, 

1288 
Varnishes, 448 
Velocity, angular, 498 

due to filling a given height, 500 
parallelogram of, 499 
table of height corresponding to 
a given, 499 
Ventilating ducts, quantity of air 
carried by, 655 
fans, 626-648 
Ventilation (see also Heating and 
Ventilation) 
cooling air for, 681 
of mines (see Mine-Ventilation) 
by a steam-jet, 652 
of mines, equivalent orifice, 686 
Ventilators, centrifugal for mines, 

644 
Venturi meter, 728 



Versed line of an arc, 68 

sines, table, 166-169 
Verticals, formulae for strains in, 

519 
Vessels (see also Ships) 
Vessels, framing of, table, 316 
Vibrations in engines, preventing, 

980 
Vis- viva, 502 
Volt, definition of, 1345 
Voltages used in long-distance 

transmission, 1399 
Volumes of revolution, cubature of, 

78 
Vulcanized India rubber, 356 

Walls of buildings, thickness of, 
1336 

of warehouses, factories, etc., 
1337 

windows, etc., heat loss through, 
659 
Walschaert valve-gear, 1046 
Warren girder, stresses in, 520 
Washers, wrought and cast, tables 

of, 230 
Washing of coal 
Water, 687-697 

amount of to develop a given 
horse-power, 753 

abrading power of, 705 

analysis of, 693 

as a lubricant, 1222 

boiling point of, 690 

boiling point at various baro- 
metric pressures, 582 

comparison of head in feet with 
various units, 689 

compressibility of, 691 

conduits, long, efficiency of, 735 

consumption of locomotives, 1098 

consumption of steam-engines 
(see Steam-engines) 

current motors, 734 

erosion and abrading by, 705 

flow of (see Flow of water) 

flowing in a tube, power of, 734 

flowing, measurement of, 727 

freezing-point of, 690 

hammer, 722 

hardness of, 694 

head of, 689 

heating of, by steam coils, 565 

heat-units per pound of, 688 

horse-power required to raise, 757 

impurities of, 691 

in pipes, loss of energy in, 780 

jets, vertical, 722 

meters, capacity of, 722 

pipe, cast-iron, transverse 
strength of, 427 

pipes, compound with branches, 
720 

power, 734 

power plants, high pressure, 754 

power, value of, 735 

pressures and heads, table, 689 



1460 



INDEX. 



Water pressure on vertical surfaces, 
690 
pressure per square inch, equiva- 
lents of, 28, 689 
prices charged for in cities, 722 
pumping by compressed air, 776 
purification of, 694-697 
quantity of discharged from 

pipes, 707-712 
specific heat of, 536, 691 
total heat and entropy of, 839- 

842 
tower (see Stand-pipe) 
tower at Yonkers, N. Y., 328 
transporting power of, 565 
under pressure, energy of, 734 
units of pressure and head, 689 
velocity of, in open channels, 704 
velocity of, in pipes, 707-712 
vapor and air mixture weight of, 

584, 586 
weight at different temperatures, 

687, 688 
weight of one cubic foot, 28 
wheels, 737 

wheels, jet, power, of, 755 
wheels, Pelton, 748 
wheels, tangential, 750 
wheels, tangential choice of, 749 
wheel, tangential table, 751 

Waterfall, power of a, 734 

Water-gas, 829 
analyses of, 830 
manufacture of, 830 
plant, efficiency of, 831 
plant, space required for, 832 

Waber-softening apparatus, 695 

Waves, ocean, power of, 755 

Weathering of coal, 800 

Webster's formula for strength of 
steel, 452 

Wedge, 512 
volume of, 63 

Weighing on an incorrect balance, 20 

Weight, definition of, 487 

and specific gravity of materials 
171-174 (see also Material in 
question) 
measures of, 19 

Weir dam measurement, 731 
flow of water over, 731 
trapezoidal, 733 

Welds, strength of, 333 

Welding by oxy-acetylene flame,464 
electric, 1374 
of steel, 460, 463 
process, the thermit, 463 

Welding by oxy-acetylene flame, 
464 
electric, 1374 
of steel, 460, 463 
process, the thermit, 463 

Wheat, weight of, 178 

Wheel and axle, 514 

Wheels, turbine (see Turbine Wheel) 

Whipple truss, 518 

White-metal alloys, 382, 383 



Whitworth process of compressing 

steel, 464 
Wiborgh air-pyrometer, 528 
Wildwood pumping-engine, high 

economy of, 774 
Willans law of steam consumption, 

962 
Wind, 597-603 
force of, 597 

pressure of, in storms, 598 
strain on stand-pipes, 328 
Winding engines, 1163 
Windlass, 514 

differential, 514 
Windmills, 599-604 

capacity and economy, 601 
Wire, aluminum, properties of, 

243, 1362 
aluminum bronze, 243 
brass, properties of, 243 
brass, weight of, table, 219 
copper, hard-drawn, specification 

for, 243 
copper, stranded, 242 
copper, rule for resistance of, 242 
copper, table of size, weight and 

resistance of Edison gauge, 240 
copper, telegraph and telephone, 

241 
copper, weight of bare and insu- 
lated, 241 
galvanized, for telegraph and 

telephone lines, 238 
galvanized iron, specifications for, 

239 
galvanized steel strand, 249 
gauges, tables, 29 
insulated copper, 241 
iron and steel 237-239 
nails, 235, 236 
phosphor-bronze, 243 
piano, strength of, 239 
platinum, properties of, 243 
plow steel, 239 
of different metals, 243 
silicon-bronze, 243,371 
steel, properties of, 237 
stranded feed, table, 242 
telegraph, joints in, 239 
telegraph, tests of, 238 
weight per mile-ohm 238 
Wires of various metals, strength of 

336 
Wire-rope, 244-250 

rope, bending curvature of, 1188 

rope, bending stress of, 1184 

rope, breaking strength of, 1184 

rope, flat, 248 

rope, galvanized, 247 

rope haulage (see Haulage) 

rope, horse-power transmitted by 

1185 
rope, horse-power transmitted 

1185 
rope, locked, 250 
rope, notes on use of, 250 
rope, plow steel, 246 



1461 



Wire-rope, radius of curvature of, 
1189 

rope, sag or deflection of, 1187 

rope, splicing of, 395 

ropes, strength of, 334 

rope, sheaves for, 1184 

rope, tapered, 1183 

rope tramways, 1179 

rope transmission, deflection of 
rope, 1180, 1187 

rope transmission, inclined, 1188 

rope transmission, limits of span, 
1187 

rope transmission, long distance, 
1188 

rope, transmission of power by, 
1183 

rope transmission, sheaves for 
1186 
Wire-wound fly-wheels, 1034 
Wiring rules, Underwriters' 355, 

table for direct currents, 1360 

table for motor service, 1356 

table for three-phase transmis- 
sion lines, 1398 
Wohler's experiments on strength 

of materials, 261 
Wood (see also Timber) 

as fuel, 804 

composition of, 805 

drying of, 347 

expansion of, by heat, 345 

expansion of, by water, 345 

heating value of, 804 

holding power of bolts in, 323 

nail-holding power of, 323 

screws, dimensions of, 234 

screws, holding power of, 323 

strength of, 344-347 

strength of, Kirkaldy's tests, 336 

weight of, table, 173 

weight and heating values of, 804 

weight per cord, 255 



Woods, American, shearing strength 
of, 347 

tests of, 346 
Wooden fly-wheels, 1033 

stave pipe, 218 
Woolf compound engines, 947 
Wooten locomotive, 1090 
Work, definition of, 28, 502 

energy, power, 502 

of adiabatic compression, 607 

of acceleration, 504 

of accelerated rotation, 504 

of a man, horse, etc., 507-509 

of friction, 1205 
Worm gearing, 514, 1143 
Wrist-pins, dimensions of, 1009 
Wrought iron, chemical composi- 
tion of, 436 

iron, effect of rolling on strength 
of, 437 

iron, manufacture of, 435 

iron, slag in, 436 

iron, specifications, 437, 438 

strength of, 330, 337, 435-439 

iron, strength of, at high tem- 
peratures, 439 

iron, strength of, Kirkaldy's tests, 
331 

Yacht rigging, galvanized steel, 248 
Yield point, 259 

Z-bar columns, dimensions of, 300- 

304 
Z-bars, Carnegie, properties of, 299 
Zero, absolute, 540, 837 
Zeuner's slide-valve diagram, 1036 
Zinc alloys (see Alloys) 

properties of, 177 

use of, in steam boilers, 901 
Zone, spherical, 65 

of spheroid, 65 

of spindle, 65 



ALPHABETICAL INDEX TO ADVERTISEMENTS. 

PAGE 

ALPHONS CUSTODIS CHIMNEY CONSTRUCTION COMPANY. . 4 

AMERICAN ENGINE COMPANY 15 

AMERICAN PIPE MANUFACTURING COMPANY 13 

AMERICAN STEEL & WIRE COMPANY 17 

ANSONIA BRASS AND COPPER COMPANY 14 

ATLAS PORTLAND CEMENT COMPANY 16 

BABCOCK & WILCOX COMPANY, THE 4 

BALDWIN LOCOMOTIVE WORKS 2 

BOSTON BELTING COMPANY 15 

BROWN HOISTING MACHINERY COMPANY, THE 17 

CHAPMAN VALVE MANUFACTURING COMPANY 13 

CRESSON & COMPANY, GEORGE V 11 

HUNT, ROBERT W. & COMPANY 19 

INGERSOLL-RAND COMPANY 7 

KEUFFEL & ESSER COMPANY 20 

LESCHEN & SONS ROPE COMPANY, A 10 

LIDGERWOOD MANUFACTURING COMPANY 6 

LODGE & SHIPLEY MACHINE TOOL COMPANY, THE 12 

LUNKENHEIMER COMPANY, THE 5 

MANNING, MAXWELL & MOORE 2 

MAURER & SON, HENRY 16 

MORSE TWIST DRILL AND MACHINE COMPANY 9 

NATIONAL TUBE COMPANY 3 

NEW YORK BELTING & PACKING COMPANY 8 

NORWALK IRON WORKS COMPANY, THE 9 

PENNSYLVANIA WIRE GLASS COMPANY 19 

PITTSBURGH MANUFACTURING COMPANY 12 

RANDOLPH-CLOWES COMPANY 14 

RIDER-ERICSSON ENGINE COMPANY 12 

ROEBLING'S SONS COMPANY, JOHN A 20 

RUGGLES-COLES ENGINEERING COMPANY 6 

SELLERS & COMPANY, WILLIAM, INCORPORATED 11 

SIMMONS COMPANY, JOHN 14 

STANDARD STEEL WORKS COMPANY 2 

UNDER-FEED STOKER COMPANY OF AMERICA, THE 8 

WILEY & SONS, JOHN 18 

YALE & TOWNE MANUFACTURING COMPANY, THE 1 



CLASSIFIED INDEX TO ADVERTISEMENTS. 

PAGE 

Aerial Wire Rope Tramways. Leschen & Sons Rope Co., A 10 

Belting and Hose. 

Boston Belting Co 15 

New York Belting & Packing Co 8 

Boiler Tubes. National Tube Co 3 

Boiler Tubes (Brass). Randolph-Clowes Co 14 

Boilers, Steam. Babcock & Wilcox Co., The 4 

Brass Rods, Sheets, Tubes, Wire, etc. 

Ansonia Brass and Copper Co 14 

Randolph-Clowes Co 14 

Bureau op Inspection, Tests and Consultation. 

Robert W. Hunt & Co 19 

Cables. Leschen & Sons Rope Co., A 10 

Cableways (Aerial Wire Rope). Leschen & Sons Rope Co., A 10 

Car Wheels — Solid Forged, Rolled and Steel Tired. 

Standard Steel Works Co 2 

Cement, American Portland. Atlas Portland Cement Co 16 

Chain Blocks — Triplex, Duplex and Differential. 

Blocks. The Yale & Towne Manufacturing Co 1 

Chimneys. Alphons Custodis Chimney Construction Co 4 

Chucks, Milling Cutters, Reamers, Spring Cutters, Taps, etc. 

Morse Twist Drill and Machine Co 9 

Compressors — Air, Gas, etc. 

Norwalk Iron Works Co., The 9 

Concrete Construction (Reinforced). 

Brown Hoisting Machinery Co., The 8 

Alphons Custodis Chimney Construction Co 4 

Concrete Reinforcement — Wire. American Steel & Wire Co 17 

Copper Wires, Cables, Bars, Sheets, Tubes, etc. 

Ansonia Brass and Copper Co , 14 

Crushers — Ore, Rock, Stone. 

Geo. V. Cresson Co 11 

Drills — Compressed and Electric Air. 

Ingersoll-Rand Co 7 

Drills, Power and Hand. 

Norwalk Iron Works Co., The 9 

Drills, Twist. Morse Twist Drill and Machine Co 9 

Dyers— Mineral and Grain. 

Ruggles-Coles Engineering Co 6 

Electric Hoists. The Yale & Towne Manufacturing Co 1 

Engineering Requisites. Lunkenheimer Co., The 5 

Engineers and Contractors. 

Brown Hoisting Machinery Co., The 17 

Engineers — Founders — Machinists. 

Pittsburgh Manufacturing Co 12 

Engines. 

American Engine Co 15 

Rider-Ericsson Engine Co 12 

Engines, Blowing. 

Lidgerwood Mfg. Co 6 

Fire Brick, Tiles, Slabs, Cupola Linings, Clay Retorts, etc. 

Maurer & Son, Henry 1«6 



CLASSIFIED INDEX TO ADVERTISEMENTS. 

PAGE 

Fuel-Economizers and Furnaces. 

Under-Feed Stoker Co. of America, The 8 

Hoisting Machinery — Elevators, Conveyors, etc. 

Brown Hoisting Machinery Co., The 17 

Lidgerwood Mfg. Co 6 

Hydrants. 

Chapman Valve Mfg. Co 13 

Pittsburgh Manufacturing Co 12 

Insulated Wires and Cables. 

Ansonia Brass and Copper Co 11 

Locomotives. Baldwin Locomotive Works 2 

Machine Tools. 

Manning, Maxwell & Moore 2 

Mechanical Stokers. Under-Feed Stoker Co. of America, The. ... 8 

Milling Machines, Shapers, Planers, Punches, Rolls, Shears, 
Lathes, Machine Tools, Bolts, etc. 

Lodge & Shipley Machine Tool Co., The 12 

Sellers & Co., William (Incorporated) 13 

Mining and Quarrying Machinery. 

Brown Hoisting Machinery Co., The 17 

Ingersoll-Rand Co 7 

Norwalk Iron Works Co., The <) 

Packing — Piston, Valve, Joint. 

Boston Belting Co 15 

New York Belting & Packing Co 8 

Pipe, Water and Gas. 

American Pipe Mfg. Co 13 

National Tube Co 3 

Simmons Co., John 14 

Pumping Machinery. 

Rider-Ericsson Engine Co 12 

Railway Supplies. Manning, Maxwell & Moore , 2 

Rivets — -Boiler and Structural. 

Pittsburgh Manufacturing Co 12 

Rope (Wire). 

Leschen & Sons Rope Co., A 10 

Roebling's Sons Co., John A 20 

Rope (Wire and Manila). Leschen & Sons Rope Co., A 10 

Rubber Goods. 

Boston Belting Co 15 

New York Belting & Packing Co 8 

Stokers — Automatic. Under-Feed Stoker Co. of America, The 8 

Surveying Instruments. Keuffel & Esser Co 20 

Telegraph. Telephone and Trolley Wire. 

Roebling's Sons Co., John A 20 

Tramways (Aerial Wire Rope). Leschen & Sons Rope Co., A. . . . 10 

Valves — Gas, Water, and Steam. 

Chapman Valve Mfg. Co 33 

Lunkenheimer Co., The. 5 

Water-Supply. Rider-Ericsson Engine Co 12 

Water-Works, Contractors for. American Pipe Mfg. Co 13 

Wire for Concrete Reinforcement. American Steel & Wire Co.. . 17 

Wire Glass. Pennsylvania Wire Glass Co 19 



In 1876 

WE first made the Differential 
Chain Block; we were the 
exclusive manufacturers un- 
der the Weston patents and the exclu- 
sive Weston licensees. 

We can fairly say that the whole 
history of the evolution of chain 
hoists has been written in our shops — 
thirty-four years of unceasing search 
for improvement. 

The Triplex Block of today — (the best hand 
hoist made ; the highest mechanical efficiency) — 
has cut-steel gears ; bronze bushings ; drop-forged 
pinions and shaft; welded hand chains; steel 
gear cover. 

Every part of the Triplex Block is standard- 
ized and interchangeable. The whole dirt-proof, 
durable, efficient. 

4 styles: Differential, Duplex, Triplex, Electric. 
41 sizes: An eighth of a ton to forty tons. 
300 active stocks: ready for instant call all over 
the United States. 

The Yale & Towne Mfg, Co, 

Only Makers of Genuine Yale Locks 
9 Murray Street, - - New York 

Foreign Warehouses : The Fairbanks Co., London and Glasgow. 
Fenwick Freres & Co., Paris, Brussels, Liege and Turin. 
Yale & Towne Co., Ltd., Hamburg. F.W. Home, Yokohama. 

Canadian Warehouses : The Canadian Fairbanks Co., Ltd., Mon- 
treal, Toronto, St. John, N.B., Winnipeg, Calgary, Vancouver. 



Baldwin Locomotive Works 

MANUFACTURERS OF 

locomotives 

OF EVERY DESCRIPTION 

PHILADELPHIA, PA., U. S. A. 
Gable Address : - - - " Baldwin," Philadelphia 



STANDARD STEEL WORKS CO. 

HARRISON BLDG., PHILADELPHIA, PA., U. S. A. 

SOLID FORGED ROLLED AND 
STEEL TIRED WHEELS 

mounted on axles fitted with Motor Gears for 

Electric Railway Service. 

LOCOMOTIVE TIRES RAILWAY SPRINGS 

FORGINGS CASTINGS 



Manning, Maxwell & Moore 

(INCORPORATED) 

Machine Tools and Railway Supplies 

Owning and Operating 

THE SHAW ELECTRIC CRANE CO. 

Shaw Electric Traveling Cranes 
Shaw Wrecking Cranes 

THE ASHCROFT MFG. CO. 

Steam Pressure or Vacuum Gauges 
Tabor Steam Engine Indicators 
Edson Recording Gauges 

THE CONSOLIDATED SAFETY VALVE CO. 

Consolidated Pop Safety Valves 

THE HANCOCK INSPIRATOR CO. 

Hancock Inspirators 
Hancock Ejectors 
Hancock Valves 

THE HAYDEN & DERBY MFG. CO. 

Metropolitan Injectors 
H-D Ejectors 

85-87-89 LIBERTY STREET, NEW YORK 



Thought It Was Steel, but It Wasn't 




7 



9 



The Master Mechanic of a large Eastern Railway System 
recently received as a " sample " from a competitor of ours, 
a small section of Boiler Tube tagged — " Spellerized Steel." 

It was a rather worn-looking specimen, as the illustration par- 
tially indicates. (The holes shown were drilled by the chemist, 
but otherwise it is in the same condition as received.) 

It was shown to one of our representatives, and on examina- 
tion he was a little inclined to doubt whether it was " Spellerized 
i Steel," and sent it to the Mill for examination and analysis. 

A careful analysis indicated that the material was charcoal 
IRON and NOT STEEL. 

While the circumstances in this case are a little unusual, yet 
it is typical of the attitude which prevails in many instances. 
In other words, it is assumed (in many cases) that if a Boiler 
Tube rusts quickly, it is steel, and if it lasts any considerable 
length of time, it is iron. There is no basis of fact for such a 
presumption. 

We formerly manufactured both iron and steel Boiler Tubes ; 
becoming convinced, however, by the experience of ourselves 
and many others, that the steel Boiler Tube was the "MODERN 
BOILER TUBE," and the most economical tube, we abandoned 
the manufacture of iron tubes and are now confining our atten- 
tion in the Boiler Tube line to the steel tube. 

This action was not taken lightly nor without due reference to 
all known circumstances, and our actual knowledge of the goods, 
based on years of manufacturing experience. 

Many of the largest consumers have reduced their Boiler Tube 
expense by the use of the "MODERN BOILER TUBE." 

Do you feel that you can profitably afford to ignore their 
experience? 

NATIONAL TUBE COMPANY 

General Sales Offices, Frick Building, Pittsburgh, Pa. 
DISTRICT SALES OFFICES 

ATLANTA NEW ORLEANS PITTSBURGH ST. LOUIS 

CHICAGO NEW YORK PORTLAND SALT LAKE CITY 

DENVER PHILADELPHIA SAN FRANCISCO SEATTLE 

Export Representatives: U S. Steel Products Export Co., New York City 
3 



The Babcock & Wilcox Co, 

85 Liberty Street, New York. 

flakers of 

BABCOCK & WILCOX 

Stirling, Rust, 

Water Tube Steam Boilers 



Steam Superheaters, 

Mechanical Stokers. 



Works : 
Bayonne, New Jersey. Barberton, Ohio* 

Tj 

CHIMNEY CONSTRUCTION COMPANY ll 

\HEWYOBK^ ] ^ BENNETT BLDG^/ 



CHIMNEYS. 

PERFORATED 
I RADIAL BRICK. 

I REINFORCED j 
I CONCRETE. I 



Main Office: BENNETT BUILDING, NEW YORK. 

BRANCHES: 

CHICAGO, PHILADELPHIA, BOSTON, ATLANTA, CLEVELAND, 

ST. LOUIS, DETROIT, PITTSBURG, KANSAS. 

Catalogue on application. 

4 






1 



■ 






1 



LIDGERWOOD 

HOISTING ENGINES 

STEAM AND ELECTRIC 

MORE THAN 300 STYLES AND SIZES 
TO SUIT ALL CONDITIONS 

ALL BUILT ON THE 
DUPLICATE PART 

SYSTEM 

OVER 

32,000 

STEAM AND ELEC- 
TRIC HOiSTS 
IN USE 

Send for Catalogs 





We Design and Manufacture 

DRYERS 

STANDARD AND SPECIAL 

FOR ALL KINDS OF 

MINERALS, GRAINS, Etc. 

USING 

DIRECT HEAT, INDIRECT HEAT, OR STEAM HEAT 



RUGGLES-COLES ENGINEERING CO. 



NEW YORK— CHICAGO 
6 



AIR POWER 
MACHINERY 



For Forty Years the World's Standard 
of Economy 

AIR AND GAS COMPRESSORS 

ROCK DRILLS 

HAMMER DRILLS 

ELECTRIC-AIR DRILLS 

PLUG DRILLS 

COAL MINING MACHINES 

STONE CHANNELERS 

ELECTRIC-AIR CHANNELERS 

PNEUMATIC PUMPS 

PNEUMATIC TOOLS 

CORE DRILLS 

Descriptive Literature Sent on Request 



INGERSOLL=RAND 
COMPANY 

NEW YORK LONDON 

OFFICES IN ALL PRINCIPAL CITIES OF THE WORLD 



New York Belting and Packing Co. 

LIMITED 

91 AND 93 CHAMBERS STREET, N. Y. 

for more than sixty years manufacturers of high- 
grade mechanical rubber goods, including 

" 1846 " PARA BELTING 

AIR BRAKE, FIRE, GARDEN, STEAM, AND WATER 
HOSE, ETC. 

COBB'S PISTON ROD PACKING 
INDESTRUCTIBLE WHITE SHEET PACKING, ETC. 



ORIGINAL MANUFACTURERS OF 

INTERLOCKING RUBBER TILING 



Moulded Rubber Goods of Every Description 



THE JONES STOKER 

The ONLY system of mechanical stoking 
in which, the fuel supply and the air supply 
are automatically proportioned to each other 
and to varying loads by the steam pressure. 
THE ADVANTAGES OF SUCH AUTOMATIC 
REGULATION ARE OBVIOUS. 



THE 

Under=Feed Stoker Co. of America 

MARQUETTE BUILDING, CHICAGO 



Morse Twist Drill & Machine Co, 

New Bedford, Mass., U. S. A. 

MAKERS OF MORSE 



Arbors 
Center Keys 

Chucks 

Counterbores 

Countersinks 

Cutters 

Dies 

Drills 

Gauges 

Lathe Centers 

Machines 



Mandrels 

Metal Slitting Saws 

Mills 

Reamers 

Screw Plates 

Sleeves 

Sockets 

Taps 

Taper Pins 

Threading Tool 

Wrenches 



THE NORWALK AIR COMPRESSOR 

OF STANDARD PATTERN 

^ is built with Tandem 
Compound Air Cylind- 
ers. Corliss Air valves 

on the intake cylinders 
insure small clearance 
spaces. The Intercooler 
between the cylinders 
saves power by remov- 
ing the heat of compres- 
sion before the work is 
done, not after, and 
the compressing is all 
done by a straight pull 
and push on a continu- 
ous piston rod. The 
Compressor is self-con- 
tained ; the repair bills 

are reduced to a minimum, and the machine is economical and efficient. 

Special machines for high pressures and for liquefying gases. Compound aad 

Triple Steam Ends. 

4 catalog, explaining its many points of superiority, is sent free to 
business men and engineers who apply to 

THE NORWALK IRON WORKS CO., 

SOUTH NORWALK, CONN. 

9 




ESTABLISHED 1857 

L LESGHEN & SONS ROPE GO. 

920-932 NORTH FIRST STREET, ST, LOUIS, MO. 

WIRE ROPE AERIAL WIRE ROPE 

for . TRAMWAYS. 

MIMES, QUARRIES, single and double 

ELEVATORS, ETC. ROPE SYSTEMS. 



BRANCH OFFICES: 

NEW YORK 



10 



WM. SELLERS & CO. 

(INCORPORATED) 

PHILADELPHIA, PA. 



LABOR-SAVING MACHINE TOOLS 

Tool Grinders, Drill Grinders 

TRAVELING CRANES, JIB CRANES, SHAFTS 

PULLEYS, HANGERS, COUPLINGS, Etc. 
For Power Transmission 

HYDRAULIC TESTING MACHINES 

Sellers-Emery System 

IMPROVED INJECTORS FOR BOILERS 
TURNTABLES FOR LOCOMOTIVES AND CARS 

GEO.V.CRESSONCU, 

Moan Office amd Works, 

Allegheny Ave. west of Seventeenth St., Philadelphia, Pa. 

New York Office: 90 West St. 

Engineers, Founders, and MachinlstSc 

Manufacturers of 

POWER TRANSMITTING MACHINERY, 

CRUSHING ROLLS and JAW CRUSHERS, 



Builders of 

SPECIAL MACHINERY TO ORDER. 

11 



Pittsburgh Manufacturing Company 

ENGINEERS— FO UNDERS— MACHINISTS 
PITTSBURGH, PA. 

MANUFACTURERS 

BOILER AND STRUCTURAL RIVETS 

TIE RODS AND FOUNDATION BOLTS 
BRIDGE PINS AND FORGINGS COLUMN BASES 



FIRE HYDRANTS AND GATE VALVES SLUICE GATES 



DOMESTIC WATER-SUPPLY 




" REECO " RIDER HOT-AIR 
PUMPING ENGINES 

" REECO " ERICSSON HOT-AIR 
PUMPING ENGINES 

"REECO" ELECTRIC PUMPS 

New catalogue on application to nearest 
store 



RIDER-ERICSSON ENGINE CO. 

35 Warren St., New York 239 & 241 Franklin St., Boston 
17 W. Kinsie St., Chicago 40 North 7th St., Philadelfhia 

Engine and Turret LATHES 

with 

PATENT OR CONE PULLEY HEADSTOCK 

Sizes 14" to 48" swing 



The Lodge and Shipley Machine Tool Co. 

CINCINNATI, OHIO, U. S. A. 
12 



AMERICAN PIPE AND 
CONSTRUCTION CO. 

ENGINEERS AND CONTRACTORS 

MANUFACTURERS OF 

PHIPP ? S HYDRAULIC PIPE 

112 NORTH BROAD STREET 
PHILADELPHIA 



CHAPMAN VALVE MFG. CO., 

WORKS AND MAIN OFFICE: 

INDIAN ORCHARD, MASS. 

BRANCH OFFICES: 

BOSTON, NEW YORK, PHILADELPHIA, BALTIMORE, 
ALLENTOWN, PA.; CHICAGO, ST. LOUIS, SAN FRAN- 
CISCO, LONDON, ENGLAND; PARIS, FRANCE; AND 
JOHANNESBURG, SOUTH AFRICA. 



VALVES 



MADE IN ALL SIZES AND 
FOR ALL PURPOSES AND 
PRESSURES. 



CORRESPONDENCE SOLICITED* 

13 



TO BIN BRONZE 

Trade Mark, "Registered in U. S. Patent Office " 

MOTOR BOAT SHAFTING ?SS?t. t SSi?te?tSj 

NON-CORROSI VE IN SEA WA TER. Can be forged at Cherry Red Heat. 
Tensile Strength equal to tliat of machinery steel 

Round, Square and Hexagon Rods for Studs, Bolts, Nuts, etc Rolled 
Sheets and Plates for Pump Linings, Condensers, Rudders, Center 
Boards, etc. Hull Plates for Yachts and Launches, Powder Press 
Plates, Boiler and Condenser Tubes. Pump Piston Rods. 

For tensile, torsional and cruising tests see descriptive pamphlet, 
furnished on application. 
THE ANSONIA BRASS AND COPPER CO., 99 John Street, New York, Sole Manufacturers 



Randolph-Clowes Co 

Waterbury, Conn. 
Brass and Copper Rolling Mills 

AND 

Tube Works. 

SEAMLESS BRASS and COPPER 

TUBES and SHELLS 

Up to 36 Inches Diameter. 




BOSTON BELTING- CO. 



MAKERS OF HIGH GRADE 



RUBBER BELTING 

for power transmission and conveying 
materials 

HOSE 

for water, steam, gas, air, suction, fire 
protection, etc. 

PACKINGS 

in great variety for rods, flanges and 
joints 

GASKETS, VALVES, RUBBER-COVERED ROLLERS 
and MECHANICAL RUBBER GOODS 




that are 



Superior in quality 
atisfactory in service 



Boston New York 

256-260 Devonshire St. 100-102 Reade St. 



Buffalo 
90 Pearl St. 



AMERICAN-BALL DUPLEX 
COMPOUND ENGINE 

AND 

DIRECT-CONNECTED 
GENERATOR. 

The latest develop- 
ment in practical 
steam-engineering. 

The highest econ- 
omy of steam with 
the simplest possi- 
ble construction. 

Complete electric and steam equipments fur" 
nished of our own manufacture. 

AMERICAN ENGINE CO., 
^ew York GfSee-95 Liberty St. Bound Brook, H. J. 




PORTLAND 



ILAO CEMENT 




The U. S. government bought 4,500,000 barrels of 
'"Atlas " for use in the construction of the Panama Canal. 

The ATLAS Portland CEMENT Co. 

30 BROAD STREET, NEW YORK 



Daily productive capacity over 50,000 barrels — the largest in the 
world 

ESTABLISHED 1856. 



HENRY MAURER & SON, 

MANUFACTURERS OF 

FIBE BRISK T T1LES. SLABS, GOPOLfl LI9IIH&S, 

Of All Shapes and Sizes. 

Office, 420 East 23d Street, 

Works, Maurer, N. J. NFW YflRl^ 

P. O., Telegraph, and R. R. Statiea.) IN d VV I V-/r\r\. 

16 



fCTIlff 7T 1 



/ V 7" 



i XI- y^ 7 - 



7X7X 




REINFORCED CONCRETE 
CONSTRUCTION 

using a special corrugated iron ; attached to buildings in 

the ordinary way and plastered with Portland cement, 

making a light, strong, fire-proof construction for roofs, 

walls, floors, etc. 

THE BROWN HOISTING MACHINERY CO., 

Engineers, Designers, and Builders of 
Hoisting Machinery of Every Description, 

Main Office and Works, CLEVELAND, OHIO. 

Branch Offices, NEW YORK and PITTSBURG 
17 



BOOKS ON GAS TESTING, GAS ANALYSIS 
AND THE GAS ENGINE 



CLERK. THE GAS, PETROL, AND OIL ENGINE. 

Vol. I. General Principles of the Internal-combustion Engine, 
together with Historical Sketch. New Edition, Revised and 
Enlarged. 8vo, vi + 390 pages, 126 figures. Cloth, $4.00 nee. 

GILL. GAS AND FUEL ANALYSIS FOR ENGINEERS. 

A Compend for Those Interested in the Economical Application 
of Fuel. Fifth Edition, Revised. 12mo, vi+117 pages, 20 
figures. Cloth, $1.25. 

HUTTON. THE GAS-ENGINE. 

Third Edition, Revised. 8vo, xx+562 pages, 241 figures. 
Cloth, $5.00. 

JONES. THE GAS-ENGINE. 

8vo, ix + 447 pages, 142 figures. Cloth, $4.00. 

LEVIN. THE MODERN GAS-ENGINE AND THE GAS 
PRODUCER. 

Svo, xviii + 485 pages, 181 figures. Cloth, $4.00 net. 

MacFARLAND. STANDARD REDUCTION FACTORS 
FOR GASES. 

A Number of Tables Necessary for the Reduction of the 
Volume of Any Gas at Any Temperature, Pressure, and Degree 
of Saturation to its Equivalent Volume under Standard Con- 
ditions. Together with a Table for the Numerical Solution of 
Certain Exponential Equations. Svo, xi + 54 pages. Cloth, 
$1.50. 

MEHRTENS. GAS-ENGINE THEORY AND DESIGN. 

Large 12mo, v + 256 pages, 241 figures. Cloth, $2.50. 

STONE. PRACTICAL TESTING OF GAS AND GAS 

METERS. 
Svo, x + 337 pages, 51 figures. Cloth, $3.50. 



JOHN WILEY & SONS 
43 and 45 East 19th Street, New York City 

London, CHAPMAN & HALL, Ltd. Montreal, Can., RENOUF PUB. CO. 

18 



Robert W. Hunt, Jno. J. Cone, Jas. C. Hallsted, D. W. McNaugher 

ROBERT W. HUNT & CO., ENGINEERS 

Bureau of Inspection, Tests and Consultation 

NEW YORK, CHICAGO, PITTSBURG, ST. LOUIS, 

90 West St. 1121 The Rookery. Monongahela Bank Bldg. Syndicate Trust Bldg. 

LONDON, SAN FRANCISCO, MONTREAL, MEXICO CITY, 

Cannon St., Norfolk House. 425 Washington St. Canadian Ex. Bldg. 20 San Francisco Bldg. 

CONSULTING, DESIGNING AND SUPERVISING 
ENGINEERS ON ALL ENGINEERING MATTERS 

Inspection of All Materials of Construction at Points 
of Manufacture 

RESIDENT INSPECTORS IN ALL INDUSTRIAL CENTERS 

Chemical and Physical Laboratories 

REPORTS ON PROPERTIES AND PROCESSES 

FOR 

TRAIN SHEDS, FERRY HOUSES, PIERS, POWER HOUSES, MOTOR 
FACTORIES, MACHINE SHOPS, GAS PLANTS AND SIMILAR BUILD- 
INGS SUBJECT TO EXCEPTIONAL STRAIN AND EXPOSED TO EX- 
TRAORDINARY STRESSES DUE TO OCCUPANCY AND ENVIRONMENT 
USE 



SOLIDWIREGLASS 



MADE BY THE CONTINUOUS PROCESS, TO IMMEDIATE AND PERMA- 
NENT ADVANTAGE 

IT POSSESSES GREATER STRENGTH THAN ANY OTHER MAKE AND 
WHEN PROPERLY GLAZED, STANDS AGAINST FIRE AND 
WEATHER. 

^M MM Pennsylvania Building 

YI f\/ A MIiA Philadelphia 

qI im vr\ii|ir\ 

I RE ML kSSWQ 100 Broadway, New York 
19 




KEUFFEL & ESSER CO. 

127 FULTON ST., N. Y. General Offices and Factories, HOBOKEN, N. J. 
CHICAGO ST. LOUIS — SAN FRANCISCO — MONTREAL 

DRAWING MATERIALS. MATHEMATICAL AND SURVEYING 
iNSTRUMENTS. MEASURING TAPES 

Our Paragon Drawing Instruments enjoy 
an excellent and wide leputation. They are 
of the most precise workmanship, the finest 
finish, the most practical design, z/nd are made 
in the greatest variety. We also h ave Key , 
Excelsior and other brands of instruments. 

We carry the largest and most complete 
assortment of Drawing Papers, Tracing Cloths 
and Papers, Blueprint, Blackprintand Brown- 
print Papers, Profile Papers. 

K & E Measuring Tapes, Steel, Metallic. Linen. 
Most accurate. Best quality. Largest assortment. 
We make the greatest variety of engine-divided 
Slide Rules, and call especial attention to our Patented 
Adjustment, which insures permanent, smooth work- 
ing of the slide. Some of our other well-known cal- 
culating instruments are the Reckoning Machine, 
Fuller's Slide Rule,Thacher's Calculating Instrument, 
Sperry's Pocket Calculator, etc. 

Our complete 

(550 page) catalogue 

on request 






